Subgroups — C₇₃×#59408 #32968812

Order 18688.

3180 conjugacy classes of subgroups.

The subgroup lattice has 1302 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#553×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₄²×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₃×#2703	C₂	1	2	yes	maximal, complemented
4	C₇₃×#2685	C₂	1	2	yes	maximal, complemented
5	C₇₃×#2559	C₂	1	2	yes	maximal, complemented
6	C₇₃×#2539	C₂	1	2	yes	maximal, complemented
7	C₇₃×#2490	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₃×#2487	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₃×#2454	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₃×#2445	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₃×#2428	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇₃×#2424	C₂	1	2	yes	maximal, complemented
13	C₇₃×#2418	C₂	1	2	yes	maximal, complemented
14	C₇₃×#2414	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₃×#2410	C₂	1	2	yes	maximal, complemented
16	C₇₃×#2408	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇₃×#2408	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇₃×#2363	C₂	1	1	yes	maximal, characteristic, complemented
19	D₄×C₂²⋊C₄×C₇₃	C₂	1	2	yes	maximal, complemented
20	D₄×C₂²⋊C₄×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×#121×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#121×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#390×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂³×D₄×C₇₃	C₂²	1	1	yes	characteristic
25	C₂³×D₄×C₇₃	C₂²	1	1	yes	characteristic
26	C₂³×D₄×C₇₃	C₂²	1	2	yes	—
27	#553×C₇₃	—	2	8	no	—
28	D₄²×C₇₃	—	2	8	no	—
29	C₂×#127×C₇₃	C₂²	1	1	yes	characteristic
30	C₂×#126×C₇₃	C₂²	1	2	yes	complemented
31	C₂×#125×C₇₃	C₂²	1	1	yes	characteristic, complemented
32	C₂×#123×C₇₃	C₂²	1	2	yes	complemented
33	C₂×#123×C₇₃	C₂²	1	2	yes	complemented
34	C₂×#121×C₇₃	C₂²	1	2	yes	—
35	C₂×#121×C₇₃	C₂²	1	1	yes	characteristic
36	C₂×#121×C₇₃	C₂²	1	1	yes	characteristic
37	C₂×#121×C₇₃	C₂²	1	1	yes	characteristic
38	C₂×#121×C₇₃	C₂²	1	1	yes	characteristic
39	C₂×#121×C₇₃	C₂²	1	1	yes	characteristic, complemented
40	C₂×#121×C₇₃	C₂²	1	2	yes	complemented
41	C₂×#121×C₇₃	C₂²	1	2	yes	complemented
42	C₂×#121×C₇₃	C₂²	1	1	yes	characteristic, complemented
43	C₂×#120×C₇₃	C₂²	1	2	yes	—
44	C₂×#120×C₇₃	C₂²	1	2	yes	—
45	C₂×#120×C₇₃	C₂²	1	2	yes	complemented
46	C₂×#120×C₇₃	C₂²	1	2	yes	complemented
47	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
49	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic, complemented
50	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic, complemented
51	C₂×C₄×D₄×C₇₃	C₂²	1	2	yes	complemented
52	C₂×C₄×D₄×C₇₃	C₂²	1	2	yes	complemented
53	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic, complemented
54	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic, complemented
55	C₂×#117×C₇₃	C₂²	1	1	yes	characteristic, complemented
56	C₂²×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic, complemented
57	C₂²×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	complemented
58	C₂²×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	complemented
59	C₂²×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	complemented
60	C₂²×C₄²×C₇₃	C₂²	1	1	yes	characteristic, complemented
61	#400×C₇₃	C₂²	1	2	yes	complemented
62	#399×C₇₃	C₂²	1	2	yes	complemented
63	#399×C₇₃	C₂²	1	2	yes	complemented
64	#397×C₇₃	C₂²	1	2	yes	complemented
65	#396×C₇₃	C₂²	1	2	yes	complemented
66	#394×C₇₃	C₂²	1	2	yes	complemented
67	#394×C₇₃	C₂²	1	2	yes	complemented
68	#394×C₇₃	C₂²	1	2	yes	complemented
69	#394×C₇₃	C₂²	1	2	yes	complemented
70	#394×C₇₃	C₂²	1	2	yes	complemented
71	#394×C₇₃	C₂²	1	2	yes	complemented
72	#394×C₇₃	C₂²	1	2	yes	complemented
73	#392×C₇₃	C₂²	1	2	yes	complemented
74	#392×C₇₃	C₂²	1	2	yes	complemented
75	#392×C₇₃	C₂²	1	2	yes	complemented
76	#392×C₇₃	C₂²	1	2	yes	complemented
77	#390×C₇₃	C₂²	1	1	yes	characteristic
78	#390×C₇₃	C₂²	1	1	yes	characteristic
79	#390×C₇₃	C₂²	1	1	yes	characteristic
80	#390×C₇₃	C₂²	1	1	yes	characteristic, complemented
81	#390×C₇₃	C₂²	1	1	yes	characteristic, complemented
82	#390×C₇₃	C₂²	1	1	yes	characteristic, complemented
83	#390×C₇₃	C₂²	1	2	yes	complemented
84	#390×C₇₃	C₂²	1	2	yes	complemented
85	#390×C₇₃	C₂²	1	1	yes	characteristic, complemented
86	#390×C₇₃	C₂²	1	1	yes	characteristic, complemented
87	#390×C₇₃	C₂²	1	2	yes	complemented
88	#390×C₇₃	C₂²	1	2	yes	complemented
89	#390×C₇₃	C₂²	1	2	yes	complemented
90	#389×C₇₃	C₂²	1	1	yes	characteristic, complemented
91	#389×C₇₃	C₂²	1	1	yes	characteristic, complemented
92	#389×C₇₃	C₂²	1	1	yes	characteristic, complemented
93	#389×C₇₃	C₂²	1	1	yes	characteristic, complemented
94	#388×C₇₃	C₂²	1	1	yes	characteristic, complemented
95	#388×C₇₃	C₂²	1	2	yes	complemented
96	#388×C₇₃	C₂²	1	2	yes	complemented
97	#388×C₇₃	C₂²	1	1	yes	characteristic, complemented
98	#388×C₇₃	C₂²	1	2	yes	complemented
99	#388×C₇₃	C₂²	1	2	yes	complemented
100	#386×C₇₃	C₂²	1	2	yes	—
101	#386×C₇₃	C₂²	1	1	yes	characteristic
102	#386×C₇₃	C₂²	1	2	yes	complemented
103	#386×C₇₃	C₂²	1	2	yes	complemented
104	#386×C₇₃	C₂²	1	2	yes	complemented
105	#386×C₇₃	C₂²	1	2	yes	complemented
106	#386×C₇₃	C₂²	1	1	yes	characteristic, complemented
107	#386×C₇₃	C₂²	1	2	yes	complemented
108	#386×C₇₃	C₂²	1	2	yes	complemented
109	#385×C₇₃	C₂²	1	2	yes	complemented
110	#385×C₇₃	C₂²	1	2	yes	complemented
111	#380×C₇₃	C₂²	1	2	yes	complemented
112	#380×C₇₃	C₂²	1	1	yes	characteristic, complemented
113	#380×C₇₃	C₂²	1	1	yes	characteristic, complemented
114	#380×C₇₃	C₂²	1	1	yes	characteristic, complemented
115	#380×C₇₃	C₂²	1	1	yes	characteristic, complemented
116	#379×C₇₃	C₂²	1	2	yes	complemented
117	#379×C₇₃	C₂²	1	2	yes	complemented
118	#379×C₇₃	C₂²	1	2	yes	complemented
119	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic, complemented
120	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic, complemented
121	C₄×C₂²⋊C₄×C₇₃	C₂²	1	1	yes	characteristic, complemented
122	C₄×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	complemented
123	C₄×C₂²⋊C₄×C₇₃	C₂²	1	1	yes	characteristic, complemented
124	C₄×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	complemented
125	C₂⁵×C₇₃	C₂³	1	2	yes	—
126	C₂⁵×C₇₃	C₂³	1	2	yes	—
127	C₂²×D₄×C₇₃	—	2	8	no	—
128	C₂²×D₄×C₇₃	—	2	4	no	—
129	C₂²×D₄×C₇₃	—	2	4	no	—
130	C₂²×D₄×C₇₃	—	2	8	no	—
131	C₂²×D₄×C₇₃	—	2	4	no	—
132	C₂²×D₄×C₇₃	—	2	4	no	—
133	C₂²×D₄×C₇₃	—	4	2	no	—
134	C₂²×D₄×C₇₃	—	4	2	no	—
135	C₂²×D₄×C₇₃	—	4	4	no	—
136	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
137	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
138	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
139	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
140	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
141	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
142	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
143	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
144	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
145	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
146	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
147	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
148	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
149	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
150	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
151	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
152	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
153	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
154	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
155	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
156	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
157	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
158	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
159	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
160	#127×C₇₃	—	2	4	no	—
161	#126×C₇₃	—	2	8	no	—
162	#125×C₇₃	—	2	4	no	—
163	#123×C₇₃	—	2	8	no	—
164	#123×C₇₃	—	4	4	no	—
165	#121×C₇₃	—	2	4	no	—
166	#121×C₇₃	—	2	8	no	—
167	#121×C₇₃	—	2	4	no	—
168	#121×C₇₃	—	2	4	no	—
169	#121×C₇₃	—	2	4	no	—
170	#121×C₇₃	—	2	8	no	—
171	#121×C₇₃	—	4	4	no	—
172	#121×C₇₃	—	4	2	no	—
173	#121×C₇₃	D₄	1	8	yes	complemented
174	#120×C₇₃	—	2	8	no	—
175	#120×C₇₃	—	2	8	no	—
176	#120×C₇₃	—	4	4	no	—
177	#120×C₇₃	—	4	4	no	—
178	C₄×D₄×C₇₃	—	2	8	no	—
179	C₄×D₄×C₇₃	—	2	4	no	—
180	C₄×D₄×C₇₃	—	2	4	no	—
181	C₄×D₄×C₇₃	—	2	4	no	—
182	C₄×D₄×C₇₃	—	2	4	no	—
183	C₄×D₄×C₇₃	—	4	2	no	—
184	C₄×D₄×C₇₃	—	4	2	no	—
185	C₄×D₄×C₇₃	—	4	4	no	—
186	#117×C₇₃	—	2	4	no	—
187	C₂×C₄⋊C₄×C₇₃	—	2	4	no	—
188	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
189	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
190	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
191	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
192	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
193	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
194	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
195	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
196	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
197	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
198	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
199	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
200	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
201	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
202	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
203	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
204	C₂×C₂²⋊C₄×C₇₃	—	4	4	no	—
205	C₂×C₂²⋊C₄×C₇₃	—	4	4	no	—
206	C₂×C₂²⋊C₄×C₇₃	—	4	4	no	—
207	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
208	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
209	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
210	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
211	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
212	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
213	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
214	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
215	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
216	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
217	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
218	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
219	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
220	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
221	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
222	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
223	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
224	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
225	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
226	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
227	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
228	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
229	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
230	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
231	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
232	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
233	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
234	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
235	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
236	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
237	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
238	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
239	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
240	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
241	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
242	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
243	C₂×C₄²×C₇₃	—	4	2	no	—
244	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
245	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
246	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
247	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
248	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
249	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
250	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
251	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
252	#95×C₇₃	C₂³	1	1	yes	characteristic
253	#95×C₇₃	C₂³	1	1	yes	characteristic
254	#95×C₇₃	C₂³	1	1	yes	characteristic
255	#95×C₇₃	C₂³	1	2	yes	—
256	#95×C₇₃	C₂³	1	2	yes	—
257	#95×C₇₃	C₂³	1	2	yes	—
258	#95×C₇₃	C₂³	1	1	yes	characteristic
259	#95×C₇₃	C₂³	1	1	yes	characteristic
260	#95×C₇₃	C₂³	1	2	yes	—
261	#95×C₇₃	C₂³	1	1	yes	characteristic
262	#95×C₇₃	C₂³	1	2	yes	—
263	#95×C₇₃	C₂³	1	2	yes	—
264	#95×C₇₃	C₂³	1	2	yes	—
265	C₂⁴×C₇₃	—	2	4	no	—
266	C₂⁴×C₇₃	—	2	4	no	—
267	C₂⁴×C₇₃	—	2	4	no	—
268	C₂⁴×C₇₃	—	2	4	no	—
269	C₂⁴×C₇₃	—	2	4	no	—
270	C₂⁴×C₇₃	—	2	4	no	—
271	C₂⁴×C₇₃	—	2	4	no	—
272	C₂⁴×C₇₃	—	4	2	no	—
273	C₂⁴×C₇₃	—	4	2	no	—
274	C₂⁴×C₇₃	—	4	2	no	—
275	C₂⁴×C₇₃	—	4	2	no	—
276	C₂⁴×C₇₃	—	4	2	no	—
277	C₂⁴×C₇₃	—	4	2	no	—
278	C₂⁴×C₇₃	—	4	2	no	—
279	C₂⁴×C₇₃	C₂⁴	1	2	yes	—
280	C₂⁴×C₇₃	C₂⁴	1	1	yes	characteristic
281	C₂⁴×C₇₃	C₂⁴	1	2	yes	—
282	C₂⁴×C₇₃	C₂⁴	1	2	yes	—
283	C₂⁴×C₇₃	C₂⁴	1	1	yes	characteristic
284	C₂⁴×C₇₃	C₂⁴	1	1	yes	characteristic
285	C₂×D₄×C₇₃	—	2	2	no	—
286	C₂×D₄×C₇₃	—	2	4	no	—
287	C₂×D₄×C₇₃	—	2	4	no	—
288	C₂×D₄×C₇₃	—	2	2	no	—
289	C₂×D₄×C₇₃	—	2	2	no	—
290	C₂×D₄×C₇₃	—	2	4	no	—
291	C₂×D₄×C₇₃	—	2	4	no	—
292	C₂×D₄×C₇₃	—	2	2	no	—
293	C₂×D₄×C₇₃	—	2	2	no	—
294	C₂×D₄×C₇₃	—	2	4	no	—
295	C₂×D₄×C₇₃	—	2	4	no	—
296	C₂×D₄×C₇₃	—	2	4	no	—
297	C₂×D₄×C₇₃	—	2	2	no	—
298	C₂×D₄×C₇₃	—	2	4	no	—
299	C₂×D₄×C₇₃	—	2	4	no	—
300	C₂×D₄×C₇₃	—	2	4	no	—
301	C₂×D₄×C₇₃	—	2	2	no	—
302	C₂×D₄×C₇₃	—	2	4	no	—
303	C₂×D₄×C₇₃	—	2	4	no	—
304	C₂×D₄×C₇₃	—	2	2	no	—
305	C₂×D₄×C₇₃	—	2	2	no	—
306	C₂×D₄×C₇₃	—	2	4	no	—
307	C₂×D₄×C₇₃	—	2	2	no	—
308	C₂×D₄×C₇₃	—	2	2	no	—
309	C₂×D₄×C₇₃	—	2	2	no	—
310	C₂×D₄×C₇₃	—	2	2	no	—
311	C₂×D₄×C₇₃	—	2	2	no	—
312	C₂×D₄×C₇₃	—	4	16	no	—
313	C₂×D₄×C₇₃	—	4	1	no	—
314	C₂×D₄×C₇₃	—	4	2	no	—
315	C₂×D₄×C₇₃	—	4	2	no	—
316	C₂×D₄×C₇₃	—	4	2	no	—
317	C₂×D₄×C₇₃	—	4	2	no	—
318	C₂×D₄×C₇₃	—	4	2	no	—
319	C₂×D₄×C₇₃	—	4	2	no	—
320	C₂×D₄×C₇₃	—	4	2	no	—
321	C₂×D₄×C₇₃	—	4	2	no	—
322	C₂×D₄×C₇₃	—	4	2	no	—
323	C₂×D₄×C₇₃	—	4	2	no	—
324	C₂×D₄×C₇₃	—	4	2	no	—
325	C₂×D₄×C₇₃	—	4	2	no	—
326	C₂×D₄×C₇₃	—	4	2	no	—
327	C₂×D₄×C₇₃	—	4	32	no	—
328	C₂×D₄×C₇₃	—	4	16	no	—
329	C₂×D₄×C₇₃	C₂×D₄	1	8	yes	—
330	C₂×D₄×C₇₃	C₂×D₄	1	4	yes	—
331	C₂×D₄×C₇₃	#41	1	4	yes	—
332	C₂×D₄×C₇₃	#41	1	4	yes	—
333	C₂²×C₄×C₇₃	—	2	2	no	—
334	C₂²×C₄×C₇₃	—	2	2	no	—
335	C₂²×C₄×C₇₃	—	2	2	no	—
336	C₂²×C₄×C₇₃	—	2	2	no	—
337	C₂²×C₄×C₇₃	—	2	4	no	—
338	C₂²×C₄×C₇₃	—	2	4	no	—
339	C₂²×C₄×C₇₃	—	2	2	no	—
340	C₂²×C₄×C₇₃	—	2	4	no	—
341	C₂²×C₄×C₇₃	—	2	2	no	—
342	C₂²×C₄×C₇₃	—	2	2	no	—
343	C₂²×C₄×C₇₃	—	2	4	no	—
344	C₂²×C₄×C₇₃	—	2	2	no	—
345	C₂²×C₄×C₇₃	—	2	2	no	—
346	C₂²×C₄×C₇₃	—	2	2	no	—
347	C₂²×C₄×C₇₃	—	2	2	no	—
348	C₂²×C₄×C₇₃	—	2	2	no	—
349	C₂²×C₄×C₇₃	—	2	4	no	—
350	C₂²×C₄×C₇₃	—	4	1	no	—
351	C₂²×C₄×C₇₃	—	4	1	no	—
352	C₂²×C₄×C₇₃	—	4	2	no	—
353	C₂²×C₄×C₇₃	—	4	2	no	—
354	C₂²×C₄×C₇₃	—	4	2	no	—
355	C₂²×C₄×C₇₃	—	4	2	no	—
356	C₂²×C₄×C₇₃	—	4	2	no	—
357	C₂²×C₄×C₇₃	—	4	2	no	—
358	C₂²×C₄×C₇₃	—	4	2	no	—
359	C₂²×C₄×C₇₃	C₂×D₄	1	4	yes	—
360	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
361	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
362	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
363	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
364	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
365	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
366	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
367	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
368	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
369	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
370	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
371	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
372	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
373	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
374	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
375	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
376	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
377	C₄⋊C₄×C₇₃	—	2	2	no	—
378	C₄⋊C₄×C₇₃	—	2	2	no	—
379	C₄⋊C₄×C₇₃	—	2	4	no	—
380	C₄⋊C₄×C₇₃	—	2	2	no	—
381	C₄⋊C₄×C₇₃	—	2	4	no	—
382	C₄⋊C₄×C₇₃	—	2	2	no	—
383	C₄⋊C₄×C₇₃	—	2	4	no	—
384	C₄⋊C₄×C₇₃	—	2	2	no	—
385	C₄⋊C₄×C₇₃	—	2	2	no	—
386	C₄⋊C₄×C₇₃	—	2	2	no	—
387	C₄⋊C₄×C₇₃	—	2	2	no	—
388	C₄⋊C₄×C₇₃	—	4	1	no	—
389	C₄⋊C₄×C₇₃	—	4	2	no	—
390	C₄⋊C₄×C₇₃	—	4	2	no	—
391	C₄⋊C₄×C₇₃	—	4	2	no	—
392	C₄⋊C₄×C₇₃	C₂×D₄	1	4	yes	—
393	C₂²⋊C₄×C₇₃	—	2	2	no	—
394	C₂²⋊C₄×C₇₃	—	2	2	no	—
395	C₂²⋊C₄×C₇₃	—	2	4	no	—
396	C₂²⋊C₄×C₇₃	—	2	4	no	—
397	C₂²⋊C₄×C₇₃	—	2	4	no	—
398	C₂²⋊C₄×C₇₃	—	2	2	no	—
399	C₂²⋊C₄×C₇₃	—	2	4	no	—
400	C₂²⋊C₄×C₇₃	—	2	4	no	—
401	C₂²⋊C₄×C₇₃	—	2	4	no	—
402	C₂²⋊C₄×C₇₃	—	2	2	no	—
403	C₂²⋊C₄×C₇₃	—	2	2	no	—
404	C₂²⋊C₄×C₇₃	—	2	4	no	—
405	C₂²⋊C₄×C₇₃	—	2	2	no	—
406	C₂²⋊C₄×C₇₃	—	2	2	no	—
407	C₂²⋊C₄×C₇₃	—	2	4	no	—
408	C₂²⋊C₄×C₇₃	—	2	4	no	—
409	C₂²⋊C₄×C₇₃	—	2	4	no	—
410	C₂²⋊C₄×C₇₃	—	2	4	no	—
411	C₂²⋊C₄×C₇₃	—	2	4	no	—
412	C₂²⋊C₄×C₇₃	—	2	2	no	—
413	C₂²⋊C₄×C₇₃	—	4	2	no	—
414	C₂²⋊C₄×C₇₃	—	4	2	no	—
415	C₂²⋊C₄×C₇₃	—	4	2	no	—
416	C₂²⋊C₄×C₇₃	—	4	2	no	—
417	C₂²⋊C₄×C₇₃	—	4	2	no	—
418	C₂²⋊C₄×C₇₃	—	4	2	no	—
419	C₂²⋊C₄×C₇₃	—	4	1	no	—
420	C₂²⋊C₄×C₇₃	—	4	2	no	—
421	C₂²⋊C₄×C₇₃	—	4	1	no	—
422	C₂²⋊C₄×C₇₃	—	4	2	no	—
423	C₂²⋊C₄×C₇₃	—	4	2	no	—
424	C₂²⋊C₄×C₇₃	—	4	2	no	—
425	C₂²⋊C₄×C₇₃	—	4	2	no	—
426	C₂²⋊C₄×C₇₃	—	4	2	no	—
427	C₂²⋊C₄×C₇₃	—	4	2	no	—
428	C₂²⋊C₄×C₇₃	C₂×D₄	1	8	yes	—
429	C₄²×C₇₃	—	2	4	no	—
430	C₄²×C₇₃	—	2	2	no	—
431	C₄²×C₇₃	—	2	2	no	—
432	C₄²×C₇₃	—	2	2	no	—
433	C₄²×C₇₃	—	2	2	no	—
434	C₄²×C₇₃	—	4	1	no	—
435	C₄²×C₇₃	—	4	1	no	—
436	C₄²×C₇₃	—	4	2	no	—
437	C₂³×C₇₃	—	2	1	no	—
438	C₂³×C₇₃	—	2	1	no	—
439	C₂³×C₇₃	—	2	1	no	—
440	C₂³×C₇₃	—	2	1	no	—
441	C₂³×C₇₃	—	2	1	no	—
442	C₂³×C₇₃	—	2	2	no	—
443	C₂³×C₇₃	—	2	2	no	—
444	C₂³×C₇₃	—	2	1	no	—
445	C₂³×C₇₃	—	2	2	no	—
446	C₂³×C₇₃	—	2	2	no	—
447	C₂³×C₇₃	—	2	2	no	—
448	C₂³×C₇₃	—	2	1	no	—
449	C₂³×C₇₃	—	2	2	no	—
450	C₂³×C₇₃	—	2	2	no	—
451	C₂³×C₇₃	—	2	1	no	—
452	C₂³×C₇₃	—	2	1	no	—
453	C₂³×C₇₃	—	2	2	no	—
454	C₂³×C₇₃	—	2	2	no	—
455	C₂³×C₇₃	—	2	2	no	—
456	C₂³×C₇₃	—	2	2	no	—
457	C₂³×C₇₃	—	2	1	no	—
458	C₂³×C₇₃	—	2	2	no	—
459	C₂³×C₇₃	—	2	1	no	—
460	C₂³×C₇₃	—	2	2	no	—
461	C₂³×C₇₃	—	2	1	no	—
462	C₂³×C₇₃	—	2	1	no	—
463	C₂³×C₇₃	—	2	2	no	—
464	C₂³×C₇₃	—	2	2	no	—
465	C₂³×C₇₃	—	2	2	no	—
466	C₂³×C₇₃	—	2	2	no	—
467	C₂³×C₇₃	—	2	1	no	—
468	C₂³×C₇₃	—	2	1	no	—
469	C₂³×C₇₃	—	2	2	no	—
470	C₂³×C₇₃	—	2	2	no	—
471	C₂³×C₇₃	—	2	1	no	—
472	C₂³×C₇₃	—	2	1	no	—
473	C₂³×C₇₃	—	4	8	no	—
474	C₂³×C₇₃	—	4	8	no	—
475	C₂³×C₇₃	—	4	8	no	—
476	C₂³×C₇₃	—	4	8	no	—
477	C₂³×C₇₃	—	4	8	no	—
478	C₂³×C₇₃	—	4	8	no	—
479	C₂³×C₇₃	—	4	8	no	—
480	C₂³×C₇₃	—	8	4	no	—
481	C₂³×C₇₃	—	8	4	no	—
482	C₂³×C₇₃	—	8	4	no	—
483	C₂³×C₇₃	—	8	4	no	—
484	C₂³×C₇₃	—	8	4	no	—
485	C₂³×C₇₃	—	8	4	no	—
486	C₂³×C₇₃	—	8	4	no	—
487	C₂³×C₇₃	C₂²×D₄	1	4	yes	—
488	C₂³×C₇₃	C₂²×D₄	1	2	yes	—
489	C₂³×C₇₃	C₂×#41	1	2	yes	—
490	C₂³×C₇₃	C₂×#41	1	4	yes	—
491	C₂³×C₇₃	C₂×#41	1	2	yes	—
492	C₂³×C₇₃	H(5,𝔽₂)	1	2	yes	—
493	C₂³×C₇₃	C₂⁵	1	1	yes	characteristic
494	D₄×C₇₃	—	2	8	no	—
495	D₄×C₇₃	—	2	16	no	—
496	D₄×C₇₃	—	2	8	no	—
497	D₄×C₇₃	—	2	8	no	—
498	D₄×C₇₃	—	4	4	no	—
499	D₄×C₇₃	—	4	8	no	—
500	D₄×C₇₃	—	4	8	no	—
501	D₄×C₇₃	—	4	8	no	—
502	D₄×C₇₃	—	4	8	no	—
503	D₄×C₇₃	—	4	4	no	—
504	D₄×C₇₃	—	4	4	no	—
505	D₄×C₇₃	—	8	4	no	—
506	D₄×C₇₃	—	8	4	no	—
507	D₄×C₇₃	—	8	4	no	—
508	D₄×C₇₃	—	8	4	no	—
509	C₂×C₄×C₇₃	—	2	1	no	—
510	C₂×C₄×C₇₃	—	2	1	no	—
511	C₂×C₄×C₇₃	—	2	1	no	—
512	C₂×C₄×C₇₃	—	2	2	no	—
513	C₂×C₄×C₇₃	—	2	1	no	—
514	C₂×C₄×C₇₃	—	2	1	no	—
515	C₂×C₄×C₇₃	—	2	1	no	—
516	C₂×C₄×C₇₃	—	2	1	no	—
517	C₂×C₄×C₇₃	—	2	2	no	—
518	C₂×C₄×C₇₃	—	2	1	no	—
519	C₂×C₄×C₇₃	—	2	8	no	—
520	C₂×C₄×C₇₃	—	2	1	no	—
521	C₂×C₄×C₇₃	—	2	1	no	—
522	C₂×C₄×C₇₃	—	2	1	no	—
523	C₂×C₄×C₇₃	—	2	2	no	—
524	C₂×C₄×C₇₃	—	2	1	no	—
525	C₂×C₄×C₇₃	—	2	1	no	—
526	C₂×C₄×C₇₃	—	2	2	no	—
527	C₂×C₄×C₇₃	—	2	1	no	—
528	C₂×C₄×C₇₃	—	2	1	no	—
529	C₂×C₄×C₇₃	—	2	1	no	—
530	C₂×C₄×C₇₃	—	2	2	no	—
531	C₂×C₄×C₇₃	—	2	1	no	—
532	C₂×C₄×C₇₃	—	2	1	no	—
533	C₂×C₄×C₇₃	—	2	1	no	—
534	C₂×C₄×C₇₃	—	2	2	no	—
535	C₂×C₄×C₇₃	—	2	2	no	—
536	C₂×C₄×C₇₃	—	2	2	no	—
537	C₂×C₄×C₇₃	—	2	1	no	—
538	C₂×C₄×C₇₃	—	2	2	no	—
539	C₂×C₄×C₇₃	—	2	2	no	—
540	C₂×C₄×C₇₃	—	2	2	no	—
541	C₂×C₄×C₇₃	—	2	2	no	—
542	C₂×C₄×C₇₃	—	2	1	no	—
543	C₂×C₄×C₇₃	—	2	1	no	—
544	C₂×C₄×C₇₃	—	2	1	no	—
545	C₂×C₄×C₇₃	—	2	1	no	—
546	C₂×C₄×C₇₃	—	2	1	no	—
547	C₂×C₄×C₇₃	—	2	1	no	—
548	C₂×C₄×C₇₃	—	2	2	no	—
549	C₂×C₄×C₇₃	—	2	1	no	—
550	C₂×C₄×C₇₃	—	2	2	no	—
551	C₂×C₄×C₇₃	—	2	1	no	—
552	C₂×C₄×C₇₃	—	2	1	no	—
553	C₂×C₄×C₇₃	—	4	8	no	—
554	C₂×C₄×C₇₃	—	4	4	no	—
555	C₂×C₄×C₇₃	—	4	4	no	—
556	C₂×C₄×C₇₃	—	4	4	no	—
557	C₂×C₄×C₇₃	—	4	4	no	—
558	C₂×C₄×C₇₃	—	8	4	no	—
559	C₂×C₄×C₇₃	—	8	4	no	—
560	C₂×C₄×C₇₃	—	8	4	no	—
561	C₂×C₄×C₇₃	C₂²×D₄	1	4	yes	—
562	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
563	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
564	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
565	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
566	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
567	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
568	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
569	C₂²×C₇₃	—	2	2	no	—
570	C₂²×C₇₃	—	2	2	no	—
571	C₂²×C₇₃	—	2	2	no	—
572	C₂²×C₇₃	—	2	2	no	—
573	C₂²×C₇₃	—	2	2	no	—
574	C₂²×C₇₃	—	2	2	no	—
575	C₂²×C₇₃	—	2	2	no	—
576	C₂²×C₇₃	—	2	4	no	—
577	C₂²×C₇₃	—	2	4	no	—
578	C₂²×C₇₃	—	2	4	no	—
579	C₂²×C₇₃	—	2	2	no	—
580	C₂²×C₇₃	—	2	4	no	—
581	C₂²×C₇₃	—	2	4	no	—
582	C₂²×C₇₃	—	2	2	no	—
583	C₂²×C₇₃	—	2	4	no	—
584	C₂²×C₇₃	—	4	2	no	—
585	C₂²×C₇₃	—	4	1	no	—
586	C₂²×C₇₃	—	4	2	no	—
587	C₂²×C₇₃	—	4	2	no	—
588	C₂²×C₇₃	—	4	1	no	—
589	C₂²×C₇₃	—	4	2	no	—
590	C₂²×C₇₃	—	4	2	no	—
591	C₂²×C₇₃	—	4	2	no	—
592	C₂²×C₇₃	—	4	1	no	—
593	C₂²×C₇₃	—	4	2	no	—
594	C₂²×C₇₃	—	4	1	no	—
595	C₂²×C₇₃	—	4	2	no	—
596	C₂²×C₇₃	—	4	1	no	—
597	C₂²×C₇₃	—	4	2	no	—
598	C₂²×C₇₃	—	4	2	no	—
599	C₂²×C₇₃	—	4	1	no	—
600	C₂²×C₇₃	—	4	1	no	—
601	C₂²×C₇₃	—	4	2	no	—
602	C₂²×C₇₃	—	4	1	no	—
603	C₂²×C₇₃	—	4	2	no	—
604	C₂²×C₇₃	—	4	1	no	—
605	C₂²×C₇₃	—	4	1	no	—
606	C₂²×C₇₃	—	4	2	no	—
607	C₂²×C₇₃	—	4	2	no	—
608	C₂²×C₇₃	—	4	1	no	—
609	C₂²×C₇₃	—	4	2	no	—
610	C₂²×C₇₃	—	8	16	no	—
611	C₂²×C₇₃	—	8	16	no	—
612	C₂²×C₇₃	#546	1	4	yes	—
613	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
614	C₂²×C₇₃	C₂²×#41	1	1	yes	characteristic
615	C₂²×C₇₃	C₂²×#41	1	1	yes	characteristic
616	C₂²×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
617	C₂²×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
618	C₂²×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
619	C₂²×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
620	C₄×C₇₃	—	2	2	no	—
621	C₄×C₇₃	—	2	2	no	—
622	C₄×C₇₃	—	2	4	no	—
623	C₄×C₇₃	—	2	2	no	—
624	C₄×C₇₃	—	2	2	no	—
625	C₄×C₇₃	—	4	1	no	—
626	C₄×C₇₃	—	4	1	no	—
627	C₄×C₇₃	—	4	1	no	—
628	C₄×C₇₃	—	4	2	no	—
629	C₄×C₇₃	—	4	1	no	—
630	C₄×C₇₃	—	4	2	no	—
631	C₄×C₇₃	—	4	1	no	—
632	C₄×C₇₃	—	4	1	no	—
633	C₄×C₇₃	—	4	2	no	—
634	C₄×C₇₃	—	4	1	no	—
635	C₄×C₇₃	—	4	2	no	—
636	C₄×C₇₃	#546	1	4	yes	—
637	#59408	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
638	C₂×C₇₃	—	2	4	no	—
639	C₂×C₇₃	—	4	4	no	—
640	C₂×C₇₃	—	4	2	no	—
641	C₂×C₇₃	—	4	4	no	—
642	C₂×C₇₃	—	8	1	no	—
643	C₂×C₇₃	—	8	2	no	—
644	C₂×C₇₃	C₂×#546	1	1	yes	characteristic
645	C₂×C₇₃	C₂×#546	1	1	yes	characteristic
646	C₂×C₇₃	#3481	1	1	yes	characteristic
647	C₂×C₇₃	#3498	1	1	yes	characteristic
648	C₂×C₇₃	#3519	1	1	yes	characteristic
649	C₂×C₇₃	#3519	1	1	yes	characteristic
650	C₂×C₇₃	#3537	1	1	yes	characteristic
651	C₂×#553	C₂×C₇₃	1	1	yes	characteristic, complemented
652	C₂×D₄²	C₂×C₇₃	1	1	yes	characteristic, complemented
653	#2703	C₂×C₇₃	1	2	yes	complemented
654	#2685	C₂×C₇₃	1	2	yes	complemented
655	#2559	C₂×C₇₃	1	2	yes	complemented
656	#2539	C₂×C₇₃	1	2	yes	complemented
657	#2490	C₂×C₇₃	1	1	yes	characteristic, complemented
658	#2487	C₂×C₇₃	1	1	yes	characteristic, complemented
659	#2454	C₂×C₇₃	1	1	yes	characteristic, complemented
660	#2445	C₂×C₇₃	1	1	yes	characteristic, complemented
661	#2428	C₂×C₇₃	1	1	yes	characteristic, complemented
662	#2424	C₂×C₇₃	1	2	yes	complemented
663	#2418	C₂×C₇₃	1	2	yes	complemented
664	#2414	C₂×C₇₃	1	1	yes	characteristic, complemented
665	#2410	C₂×C₇₃	1	2	yes	complemented
666	#2408	C₂×C₇₃	1	1	yes	characteristic, complemented
667	#2408	C₂×C₇₃	1	1	yes	characteristic, complemented
668	#2363	C₂×C₇₃	1	1	yes	characteristic, complemented
669	D₄×C₂²⋊C₄	C₂×C₇₃	1	2	yes	complemented
670	D₄×C₂²⋊C₄	C₂×C₇₃	1	1	yes	characteristic, complemented
671	C₄×#121	C₂×C₇₃	1	1	yes	characteristic, complemented
672	C₄×#121	C₂×C₇₃	1	1	yes	characteristic, complemented
673	C₂×#390	C₂×C₇₃	1	1	yes	characteristic, complemented
674	C₇₃	#59408	1	1	yes	characteristic, direct product factor, Sylow
675	C₂³×D₄	C₂²×C₇₃	1	1	yes	characteristic
676	C₂³×D₄	C₂²×C₇₃	1	2	yes	—
677	C₂³×D₄	C₂²×C₇₃	1	1	yes	characteristic
678	#553	—	2	8	no	—
679	D₄²	—	2	8	no	—
680	C₂×#127	C₂²×C₇₃	1	1	yes	characteristic
681	C₂×#126	C₂²×C₇₃	1	2	yes	complemented
682	C₂×#125	C₂²×C₇₃	1	1	yes	characteristic, complemented
683	C₂×#123	C₂²×C₇₃	1	2	yes	complemented
684	C₂×#123	C₂²×C₇₃	1	2	yes	complemented
685	C₂×#121	C₂²×C₇₃	1	1	yes	characteristic
686	C₂×#121	C₂²×C₇₃	1	1	yes	characteristic
687	C₂×#121	C₂²×C₇₃	1	1	yes	characteristic
688	C₂×#121	C₂²×C₇₃	1	2	yes	—
689	C₂×#121	C₂²×C₇₃	1	1	yes	characteristic
690	C₂×#121	C₂²×C₇₃	1	1	yes	characteristic, complemented
691	C₂×#121	C₂²×C₇₃	1	2	yes	complemented
692	C₂×#121	C₂²×C₇₃	1	1	yes	characteristic, complemented
693	C₂×#121	C₂²×C₇₃	1	2	yes	complemented
694	C₂×#120	C₂²×C₇₃	1	2	yes	—
695	C₂×#120	C₂²×C₇₃	1	2	yes	—
696	C₂×#120	C₂²×C₇₃	1	2	yes	complemented
697	C₂×#120	C₂²×C₇₃	1	2	yes	complemented
698	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
699	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
700	C₂×C₄×D₄	C₂²×C₇₃	1	2	yes	complemented
701	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic, complemented
702	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic, complemented
703	C₂×C₄×D₄	C₂²×C₇₃	1	2	yes	complemented
704	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic, complemented
705	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic, complemented
706	C₂×#117	C₂²×C₇₃	1	1	yes	characteristic, complemented
707	C₂²×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic, complemented
708	C₂²×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	complemented
709	C₂²×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	complemented
710	C₂²×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	complemented
711	C₂²×C₄²	C₂²×C₇₃	1	1	yes	characteristic, complemented
712	#400	C₂²×C₇₃	1	2	yes	complemented
713	#399	C₂²×C₇₃	1	2	yes	complemented
714	#399	C₂²×C₇₃	1	2	yes	complemented
715	#397	C₂²×C₇₃	1	2	yes	complemented
716	#396	C₂²×C₇₃	1	2	yes	complemented
717	#394	C₂²×C₇₃	1	2	yes	complemented
718	#394	C₂²×C₇₃	1	2	yes	complemented
719	#394	C₂²×C₇₃	1	2	yes	complemented
720	#394	C₂²×C₇₃	1	2	yes	complemented
721	#394	C₂²×C₇₃	1	2	yes	complemented
722	#394	C₂²×C₇₃	1	2	yes	complemented
723	#394	C₂²×C₇₃	1	2	yes	complemented
724	#392	C₂²×C₇₃	1	2	yes	complemented
725	#392	C₂²×C₇₃	1	2	yes	complemented
726	#392	C₂²×C₇₃	1	2	yes	complemented
727	#392	C₂²×C₇₃	1	2	yes	complemented
728	#390	C₂²×C₇₃	1	1	yes	characteristic
729	#390	C₂²×C₇₃	1	1	yes	characteristic
730	#390	C₂²×C₇₃	1	1	yes	characteristic
731	#390	C₂²×C₇₃	1	2	yes	complemented
732	#390	C₂²×C₇₃	1	2	yes	complemented
733	#390	C₂²×C₇₃	1	2	yes	complemented
734	#390	C₂²×C₇₃	1	1	yes	characteristic, complemented
735	#390	C₂²×C₇₃	1	1	yes	characteristic, complemented
736	#390	C₂²×C₇₃	1	1	yes	characteristic, complemented
737	#390	C₂²×C₇₃	1	1	yes	characteristic, complemented
738	#390	C₂²×C₇₃	1	2	yes	complemented
739	#390	C₂²×C₇₃	1	1	yes	characteristic, complemented
740	#390	C₂²×C₇₃	1	2	yes	complemented
741	#389	C₂²×C₇₃	1	1	yes	characteristic, complemented
742	#389	C₂²×C₇₃	1	1	yes	characteristic, complemented
743	#389	C₂²×C₇₃	1	1	yes	characteristic, complemented
744	#389	C₂²×C₇₃	1	1	yes	characteristic, complemented
745	#388	C₂²×C₇₃	1	2	yes	complemented
746	#388	C₂²×C₇₃	1	2	yes	complemented
747	#388	C₂²×C₇₃	1	2	yes	complemented
748	#388	C₂²×C₇₃	1	1	yes	characteristic, complemented
749	#388	C₂²×C₇₃	1	2	yes	complemented
750	#388	C₂²×C₇₃	1	1	yes	characteristic, complemented
751	#386	C₂²×C₇₃	1	1	yes	characteristic
752	#386	C₂²×C₇₃	1	2	yes	—
753	#386	C₂²×C₇₃	1	2	yes	complemented
754	#386	C₂²×C₇₃	1	2	yes	complemented
755	#386	C₂²×C₇₃	1	2	yes	complemented
756	#386	C₂²×C₇₃	1	2	yes	complemented
757	#386	C₂²×C₇₃	1	2	yes	complemented
758	#386	C₂²×C₇₃	1	2	yes	complemented
759	#386	C₂²×C₇₃	1	1	yes	characteristic, complemented
760	#385	C₂²×C₇₃	1	2	yes	complemented
761	#385	C₂²×C₇₃	1	2	yes	complemented
762	#380	C₂²×C₇₃	1	1	yes	characteristic, complemented
763	#380	C₂²×C₇₃	1	2	yes	complemented
764	#380	C₂²×C₇₃	1	1	yes	characteristic, complemented
765	#380	C₂²×C₇₃	1	1	yes	characteristic, complemented
766	#380	C₂²×C₇₃	1	1	yes	characteristic, complemented
767	#379	C₂²×C₇₃	1	2	yes	complemented
768	#379	C₂²×C₇₃	1	2	yes	complemented
769	#379	C₂²×C₇₃	1	2	yes	complemented
770	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic, complemented
771	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic, complemented
772	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	complemented
773	C₄×C₂²⋊C₄	C₂²×C₇₃	1	1	yes	characteristic, complemented
774	C₄×C₂²⋊C₄	C₂²×C₇₃	1	1	yes	characteristic, complemented
775	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	complemented
776	C₂⁵	C₂³×C₇₃	1	2	yes	—
777	C₂⁵	C₂³×C₇₃	1	2	yes	—
778	C₂²×D₄	—	2	8	no	—
779	C₂²×D₄	—	2	4	no	—
780	C₂²×D₄	—	2	4	no	—
781	C₂²×D₄	—	2	8	no	—
782	C₂²×D₄	—	2	4	no	—
783	C₂²×D₄	—	2	4	no	—
784	C₂²×D₄	—	4	2	no	—
785	C₂²×D₄	—	4	2	no	—
786	C₂²×D₄	—	4	4	no	—
787	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
788	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
789	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
790	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
791	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
792	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
793	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
794	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
795	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
796	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
797	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
798	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
799	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
800	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
801	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
802	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
803	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
804	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
805	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
806	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
807	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
808	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
809	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
810	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
811	#127	—	2	4	no	—
812	#126	—	2	8	no	—
813	#125	—	2	4	no	—
814	#123	—	2	8	no	—
815	#123	—	4	4	no	—
816	#121	—	2	4	no	—
817	#121	—	2	8	no	—
818	#121	—	2	4	no	—
819	#121	—	2	4	no	—
820	#121	—	2	4	no	—
821	#121	—	2	8	no	—
822	#121	—	4	4	no	—
823	#121	—	4	2	no	—
824	#121	D₄×C₇₃	1	8	yes	complemented
825	#120	—	2	8	no	—
826	#120	—	2	8	no	—
827	#120	—	4	4	no	—
828	#120	—	4	4	no	—
829	C₄×D₄	—	2	8	no	—
830	C₄×D₄	—	2	4	no	—
831	C₄×D₄	—	2	4	no	—
832	C₄×D₄	—	2	4	no	—
833	C₄×D₄	—	2	4	no	—
834	C₄×D₄	—	4	2	no	—
835	C₄×D₄	—	4	2	no	—
836	C₄×D₄	—	4	4	no	—
837	#117	—	2	4	no	—
838	C₂×C₄⋊C₄	—	2	4	no	—
839	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
840	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
841	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
842	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
843	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
844	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
845	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
846	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
847	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
848	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
849	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
850	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
851	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
852	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
853	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
854	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
855	C₂×C₂²⋊C₄	—	4	4	no	—
856	C₂×C₂²⋊C₄	—	4	4	no	—
857	C₂×C₂²⋊C₄	—	4	4	no	—
858	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
859	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
860	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
861	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
862	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
863	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
864	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
865	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
866	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
867	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
868	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
869	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
870	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
871	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
872	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
873	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
874	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
875	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
876	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
877	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
878	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
879	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
880	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
881	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
882	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
883	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
884	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
885	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
886	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
887	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
888	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
889	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
890	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
891	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
892	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
893	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
894	C₂×C₄²	—	4	2	no	—
895	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
896	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
897	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
898	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
899	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
900	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
901	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
902	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
903	#95	C₂³×C₇₃	1	1	yes	characteristic
904	#95	C₂³×C₇₃	1	1	yes	characteristic
905	#95	C₂³×C₇₃	1	1	yes	characteristic
906	#95	C₂³×C₇₃	1	2	yes	—
907	#95	C₂³×C₇₃	1	2	yes	—
908	#95	C₂³×C₇₃	1	2	yes	—
909	#95	C₂³×C₇₃	1	1	yes	characteristic
910	#95	C₂³×C₇₃	1	1	yes	characteristic
911	#95	C₂³×C₇₃	1	2	yes	—
912	#95	C₂³×C₇₃	1	1	yes	characteristic
913	#95	C₂³×C₇₃	1	2	yes	—
914	#95	C₂³×C₇₃	1	2	yes	—
915	#95	C₂³×C₇₃	1	2	yes	—
916	C₂⁴	—	2	4	no	—
917	C₂⁴	—	2	4	no	—
918	C₂⁴	—	2	4	no	—
919	C₂⁴	—	2	4	no	—
920	C₂⁴	—	2	4	no	—
921	C₂⁴	—	2	4	no	—
922	C₂⁴	—	2	4	no	—
923	C₂⁴	—	4	2	no	—
924	C₂⁴	—	4	2	no	—
925	C₂⁴	—	4	2	no	—
926	C₂⁴	—	4	2	no	—
927	C₂⁴	—	4	2	no	—
928	C₂⁴	—	4	2	no	—
929	C₂⁴	—	4	2	no	—
930	C₂⁴	C₂⁴×C₇₃	1	2	yes	—
931	C₂⁴	C₂⁴×C₇₃	1	1	yes	characteristic
932	C₂⁴	C₂⁴×C₇₃	1	2	yes	—
933	C₂⁴	C₂⁴×C₇₃	1	2	yes	—
934	C₂⁴	C₂⁴×C₇₃	1	1	yes	characteristic
935	C₂⁴	C₂⁴×C₇₃	1	1	yes	characteristic
936	C₂×D₄	—	2	2	no	—
937	C₂×D₄	—	2	4	no	—
938	C₂×D₄	—	2	4	no	—
939	C₂×D₄	—	2	2	no	—
940	C₂×D₄	—	2	2	no	—
941	C₂×D₄	—	2	4	no	—
942	C₂×D₄	—	2	4	no	—
943	C₂×D₄	—	2	2	no	—
944	C₂×D₄	—	2	2	no	—
945	C₂×D₄	—	2	4	no	—
946	C₂×D₄	—	2	4	no	—
947	C₂×D₄	—	2	4	no	—
948	C₂×D₄	—	2	2	no	—
949	C₂×D₄	—	2	4	no	—
950	C₂×D₄	—	2	4	no	—
951	C₂×D₄	—	2	4	no	—
952	C₂×D₄	—	2	2	no	—
953	C₂×D₄	—	2	4	no	—
954	C₂×D₄	—	2	4	no	—
955	C₂×D₄	—	2	2	no	—
956	C₂×D₄	—	2	2	no	—
957	C₂×D₄	—	2	4	no	—
958	C₂×D₄	—	2	2	no	—
959	C₂×D₄	—	2	2	no	—
960	C₂×D₄	—	2	2	no	—
961	C₂×D₄	—	2	2	no	—
962	C₂×D₄	—	2	2	no	—
963	C₂×D₄	—	4	16	no	—
964	C₂×D₄	—	4	1	no	—
965	C₂×D₄	—	4	2	no	—
966	C₂×D₄	—	4	2	no	—
967	C₂×D₄	—	4	2	no	—
968	C₂×D₄	—	4	2	no	—
969	C₂×D₄	—	4	2	no	—
970	C₂×D₄	—	4	2	no	—
971	C₂×D₄	—	4	2	no	—
972	C₂×D₄	—	4	2	no	—
973	C₂×D₄	—	4	2	no	—
974	C₂×D₄	—	4	2	no	—
975	C₂×D₄	—	4	2	no	—
976	C₂×D₄	—	4	2	no	—
977	C₂×D₄	—	4	2	no	—
978	C₂×D₄	—	4	32	no	—
979	C₂×D₄	—	4	16	no	—
980	C₂×D₄	C₂×D₄×C₇₃	1	8	yes	—
981	C₂×D₄	C₂×D₄×C₇₃	1	4	yes	—
982	C₂×D₄	#41×C₇₃	1	4	yes	—
983	C₂×D₄	#41×C₇₃	1	4	yes	—
984	C₂²×C₄	—	2	2	no	—
985	C₂²×C₄	—	2	2	no	—
986	C₂²×C₄	—	2	2	no	—
987	C₂²×C₄	—	2	2	no	—
988	C₂²×C₄	—	2	4	no	—
989	C₂²×C₄	—	2	4	no	—
990	C₂²×C₄	—	2	2	no	—
991	C₂²×C₄	—	2	4	no	—
992	C₂²×C₄	—	2	2	no	—
993	C₂²×C₄	—	2	2	no	—
994	C₂²×C₄	—	2	4	no	—
995	C₂²×C₄	—	2	2	no	—
996	C₂²×C₄	—	2	2	no	—
997	C₂²×C₄	—	2	2	no	—
998	C₂²×C₄	—	2	2	no	—
999	C₂²×C₄	—	2	2	no	—
1000	C₂²×C₄	—	2	4	no	—
1001	C₂²×C₄	—	4	1	no	—
1002	C₂²×C₄	—	4	1	no	—
1003	C₂²×C₄	—	4	2	no	—
1004	C₂²×C₄	—	4	2	no	—
1005	C₂²×C₄	—	4	2	no	—
1006	C₂²×C₄	—	4	2	no	—
1007	C₂²×C₄	—	4	2	no	—
1008	C₂²×C₄	—	4	2	no	—
1009	C₂²×C₄	—	4	2	no	—
1010	C₂²×C₄	C₂×D₄×C₇₃	1	4	yes	—
1011	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
1012	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
1013	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
1014	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
1015	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
1016	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
1017	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
1018	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
1019	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
1020	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
1021	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
1022	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
1023	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
1024	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
1025	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
1026	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
1027	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
1028	C₄⋊C₄	—	2	2	no	—
1029	C₄⋊C₄	—	2	2	no	—
1030	C₄⋊C₄	—	2	4	no	—
1031	C₄⋊C₄	—	2	2	no	—
1032	C₄⋊C₄	—	2	4	no	—
1033	C₄⋊C₄	—	2	2	no	—
1034	C₄⋊C₄	—	2	4	no	—
1035	C₄⋊C₄	—	2	2	no	—
1036	C₄⋊C₄	—	2	2	no	—
1037	C₄⋊C₄	—	2	2	no	—
1038	C₄⋊C₄	—	2	2	no	—
1039	C₄⋊C₄	—	4	1	no	—
1040	C₄⋊C₄	—	4	2	no	—
1041	C₄⋊C₄	—	4	2	no	—
1042	C₄⋊C₄	—	4	2	no	—
1043	C₄⋊C₄	C₂×D₄×C₇₃	1	4	yes	—
1044	C₂²⋊C₄	—	2	2	no	—
1045	C₂²⋊C₄	—	2	2	no	—
1046	C₂²⋊C₄	—	2	4	no	—
1047	C₂²⋊C₄	—	2	4	no	—
1048	C₂²⋊C₄	—	2	4	no	—
1049	C₂²⋊C₄	—	2	2	no	—
1050	C₂²⋊C₄	—	2	4	no	—
1051	C₂²⋊C₄	—	2	4	no	—
1052	C₂²⋊C₄	—	2	4	no	—
1053	C₂²⋊C₄	—	2	2	no	—
1054	C₂²⋊C₄	—	2	2	no	—
1055	C₂²⋊C₄	—	2	4	no	—
1056	C₂²⋊C₄	—	2	2	no	—
1057	C₂²⋊C₄	—	2	2	no	—
1058	C₂²⋊C₄	—	2	4	no	—
1059	C₂²⋊C₄	—	2	4	no	—
1060	C₂²⋊C₄	—	2	4	no	—
1061	C₂²⋊C₄	—	2	4	no	—
1062	C₂²⋊C₄	—	2	4	no	—
1063	C₂²⋊C₄	—	2	2	no	—
1064	C₂²⋊C₄	—	4	2	no	—
1065	C₂²⋊C₄	—	4	2	no	—
1066	C₂²⋊C₄	—	4	2	no	—
1067	C₂²⋊C₄	—	4	2	no	—
1068	C₂²⋊C₄	—	4	2	no	—
1069	C₂²⋊C₄	—	4	2	no	—
1070	C₂²⋊C₄	—	4	1	no	—
1071	C₂²⋊C₄	—	4	2	no	—
1072	C₂²⋊C₄	—	4	1	no	—
1073	C₂²⋊C₄	—	4	2	no	—
1074	C₂²⋊C₄	—	4	2	no	—
1075	C₂²⋊C₄	—	4	2	no	—
1076	C₂²⋊C₄	—	4	2	no	—
1077	C₂²⋊C₄	—	4	2	no	—
1078	C₂²⋊C₄	—	4	2	no	—
1079	C₂²⋊C₄	C₂×D₄×C₇₃	1	8	yes	—
1080	C₄²	—	2	4	no	—
1081	C₄²	—	2	2	no	—
1082	C₄²	—	2	2	no	—
1083	C₄²	—	2	2	no	—
1084	C₄²	—	2	2	no	—
1085	C₄²	—	4	1	no	—
1086	C₄²	—	4	1	no	—
1087	C₄²	—	4	2	no	—
1088	C₂³	—	2	1	no	—
1089	C₂³	—	2	1	no	—
1090	C₂³	—	2	1	no	—
1091	C₂³	—	2	1	no	—
1092	C₂³	—	2	1	no	—
1093	C₂³	—	2	2	no	—
1094	C₂³	—	2	2	no	—
1095	C₂³	—	2	1	no	—
1096	C₂³	—	2	2	no	—
1097	C₂³	—	2	2	no	—
1098	C₂³	—	2	2	no	—
1099	C₂³	—	2	1	no	—
1100	C₂³	—	2	2	no	—
1101	C₂³	—	2	2	no	—
1102	C₂³	—	2	1	no	—
1103	C₂³	—	2	1	no	—
1104	C₂³	—	2	2	no	—
1105	C₂³	—	2	2	no	—
1106	C₂³	—	2	2	no	—
1107	C₂³	—	2	2	no	—
1108	C₂³	—	2	1	no	—
1109	C₂³	—	2	2	no	—
1110	C₂³	—	2	1	no	—
1111	C₂³	—	2	2	no	—
1112	C₂³	—	2	1	no	—
1113	C₂³	—	2	1	no	—
1114	C₂³	—	2	2	no	—
1115	C₂³	—	2	2	no	—
1116	C₂³	—	2	2	no	—
1117	C₂³	—	2	2	no	—
1118	C₂³	—	2	1	no	—
1119	C₂³	—	2	1	no	—
1120	C₂³	—	2	2	no	—
1121	C₂³	—	2	2	no	—
1122	C₂³	—	2	1	no	—
1123	C₂³	—	2	1	no	—
1124	C₂³	—	4	8	no	—
1125	C₂³	—	4	8	no	—
1126	C₂³	—	4	8	no	—
1127	C₂³	—	4	8	no	—
1128	C₂³	—	4	8	no	—
1129	C₂³	—	4	8	no	—
1130	C₂³	—	4	8	no	—
1131	C₂³	—	8	4	no	—
1132	C₂³	—	8	4	no	—
1133	C₂³	—	8	4	no	—
1134	C₂³	—	8	4	no	—
1135	C₂³	—	8	4	no	—
1136	C₂³	—	8	4	no	—
1137	C₂³	—	8	4	no	—
1138	C₂³	C₂²×D₄×C₇₃	1	4	yes	—
1139	C₂³	C₂²×D₄×C₇₃	1	2	yes	—
1140	C₂³	C₂×#41×C₇₃	1	2	yes	—
1141	C₂³	C₂×#41×C₇₃	1	4	yes	—
1142	C₂³	C₂×#41×C₇₃	1	2	yes	—
1143	C₂³	H(5,𝔽₂)×C₇₃	1	2	yes	—
1144	C₂³	C₂⁵×C₇₃	1	1	yes	characteristic
1145	D₄	—	2	8	no	—
1146	D₄	—	2	16	no	—
1147	D₄	—	2	8	no	—
1148	D₄	—	2	8	no	—
1149	D₄	—	4	8	no	—
1150	D₄	—	4	8	no	—
1151	D₄	—	4	8	no	—
1152	D₄	—	4	4	no	—
1153	D₄	—	4	8	no	—
1154	D₄	—	4	4	no	—
1155	D₄	—	4	4	no	—
1156	D₄	—	8	4	no	—
1157	D₄	—	8	4	no	—
1158	D₄	—	8	4	no	—
1159	D₄	—	8	4	no	—
1160	C₂×C₄	—	2	1	no	—
1161	C₂×C₄	—	2	1	no	—
1162	C₂×C₄	—	2	1	no	—
1163	C₂×C₄	—	2	2	no	—
1164	C₂×C₄	—	2	1	no	—
1165	C₂×C₄	—	2	1	no	—
1166	C₂×C₄	—	2	1	no	—
1167	C₂×C₄	—	2	1	no	—
1168	C₂×C₄	—	2	2	no	—
1169	C₂×C₄	—	2	1	no	—
1170	C₂×C₄	—	2	8	no	—
1171	C₂×C₄	—	2	1	no	—
1172	C₂×C₄	—	2	1	no	—
1173	C₂×C₄	—	2	1	no	—
1174	C₂×C₄	—	2	2	no	—
1175	C₂×C₄	—	2	1	no	—
1176	C₂×C₄	—	2	1	no	—
1177	C₂×C₄	—	2	2	no	—
1178	C₂×C₄	—	2	1	no	—
1179	C₂×C₄	—	2	1	no	—
1180	C₂×C₄	—	2	1	no	—
1181	C₂×C₄	—	2	2	no	—
1182	C₂×C₄	—	2	1	no	—
1183	C₂×C₄	—	2	1	no	—
1184	C₂×C₄	—	2	1	no	—
1185	C₂×C₄	—	2	2	no	—
1186	C₂×C₄	—	2	2	no	—
1187	C₂×C₄	—	2	2	no	—
1188	C₂×C₄	—	2	1	no	—
1189	C₂×C₄	—	2	2	no	—
1190	C₂×C₄	—	2	2	no	—
1191	C₂×C₄	—	2	2	no	—
1192	C₂×C₄	—	2	2	no	—
1193	C₂×C₄	—	2	1	no	—
1194	C₂×C₄	—	2	1	no	—
1195	C₂×C₄	—	2	1	no	—
1196	C₂×C₄	—	2	1	no	—
1197	C₂×C₄	—	2	1	no	—
1198	C₂×C₄	—	2	1	no	—
1199	C₂×C₄	—	2	2	no	—
1200	C₂×C₄	—	2	1	no	—
1201	C₂×C₄	—	2	2	no	—
1202	C₂×C₄	—	2	1	no	—
1203	C₂×C₄	—	2	1	no	—
1204	C₂×C₄	—	4	8	no	—
1205	C₂×C₄	—	4	4	no	—
1206	C₂×C₄	—	4	4	no	—
1207	C₂×C₄	—	4	4	no	—
1208	C₂×C₄	—	4	4	no	—
1209	C₂×C₄	—	8	4	no	—
1210	C₂×C₄	—	8	4	no	—
1211	C₂×C₄	—	8	4	no	—
1212	C₂×C₄	C₂²×D₄×C₇₃	1	4	yes	—
1213	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
1214	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
1215	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
1216	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
1217	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
1218	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
1219	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
1220	C₂²	—	2	2	no	—
1221	C₂²	—	2	2	no	—
1222	C₂²	—	2	2	no	—
1223	C₂²	—	2	2	no	—
1224	C₂²	—	2	2	no	—
1225	C₂²	—	2	2	no	—
1226	C₂²	—	2	2	no	—
1227	C₂²	—	2	4	no	—
1228	C₂²	—	2	4	no	—
1229	C₂²	—	2	4	no	—
1230	C₂²	—	2	2	no	—
1231	C₂²	—	2	4	no	—
1232	C₂²	—	2	4	no	—
1233	C₂²	—	2	2	no	—
1234	C₂²	—	2	4	no	—
1235	C₂²	—	4	2	no	—
1236	C₂²	—	4	1	no	—
1237	C₂²	—	4	2	no	—
1238	C₂²	—	4	2	no	—
1239	C₂²	—	4	1	no	—
1240	C₂²	—	4	2	no	—
1241	C₂²	—	4	1	no	—
1242	C₂²	—	4	2	no	—
1243	C₂²	—	4	2	no	—
1244	C₂²	—	4	2	no	—
1245	C₂²	—	4	1	no	—
1246	C₂²	—	4	2	no	—
1247	C₂²	—	4	1	no	—
1248	C₂²	—	4	2	no	—
1249	C₂²	—	4	2	no	—
1250	C₂²	—	4	1	no	—
1251	C₂²	—	4	2	no	—
1252	C₂²	—	4	1	no	—
1253	C₂²	—	4	1	no	—
1254	C₂²	—	4	2	no	—
1255	C₂²	—	4	1	no	—
1256	C₂²	—	4	1	no	—
1257	C₂²	—	4	2	no	—
1258	C₂²	—	4	2	no	—
1259	C₂²	—	4	1	no	—
1260	C₂²	—	4	2	no	—
1261	C₂²	—	8	16	no	—
1262	C₂²	—	8	16	no	—
1263	C₂²	#546×C₇₃	1	4	yes	—
1264	C₂²	C₂³×D₄×C₇₃	1	1	yes	characteristic
1265	C₂²	C₂²×#41×C₇₃	1	1	yes	characteristic
1266	C₂²	C₂²×#41×C₇₃	1	1	yes	characteristic
1267	C₂²	C₂×H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
1268	C₂²	C₂×H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
1269	C₂²	C₂×H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
1270	C₂²	C₂×H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
1271	C₄	—	2	2	no	—
1272	C₄	—	2	2	no	—
1273	C₄	—	2	4	no	—
1274	C₄	—	2	2	no	—
1275	C₄	—	2	2	no	—
1276	C₄	—	4	1	no	—
1277	C₄	—	4	1	no	—
1278	C₄	—	4	1	no	—
1279	C₄	—	4	2	no	—
1280	C₄	—	4	1	no	—
1281	C₄	—	4	2	no	—
1282	C₄	—	4	1	no	—
1283	C₄	—	4	1	no	—
1284	C₄	—	4	2	no	—
1285	C₄	—	4	1	no	—
1286	C₄	—	4	2	no	—
1287	C₄	#546×C₇₃	1	4	yes	—
1288	C₂	—	2	4	no	—
1289	C₂	—	4	2	no	—
1290	C₂	—	4	4	no	—
1291	C₂	—	4	4	no	—
1292	C₂	—	8	2	no	—
1293	C₂	—	8	1	no	—
1294	C₂	C₂×#546×C₇₃	1	1	yes	characteristic
1295	C₂	C₂×#546×C₇₃	1	1	yes	characteristic
1296	C₂	C₇₃×#3481	1	1	yes	characteristic
1297	C₂	C₇₃×#3498	1	1	yes	characteristic
1298	C₂	C₇₃×#3519	1	1	yes	characteristic
1299	C₂	C₇₃×#3519	1	1	yes	characteristic
1300	C₂	C₇₃×#3537	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇₃
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×#553×C₇₃	C₂	semidirect
2. C₂×D₄²×C₇₃	C₂	semidirect
3. C₇₃×#2703	C₂	semidirect
4. C₇₃×#2685	C₂	semidirect
5. C₇₃×#2559	C₂	semidirect
6. C₇₃×#2539	C₂	semidirect
7. C₇₃×#2490	C₂	semidirect
8. C₇₃×#2487	C₂	semidirect
9. C₇₃×#2454	C₂	semidirect
10. C₇₃×#2445	C₂	semidirect
11. C₇₃×#2428	C₂	semidirect
12. C₇₃×#2424	C₂	semidirect
13. C₇₃×#2418	C₂	semidirect
14. C₇₃×#2414	C₂	semidirect
15. C₇₃×#2410	C₂	semidirect
16. C₇₃×#2408	C₂	semidirect
17. C₇₃×#2408	C₂	semidirect
18. C₇₃×#2363	C₂	semidirect
19. D₄×C₂²⋊C₄×C₇₃	C₂	semidirect
20. D₄×C₂²⋊C₄×C₇₃	C₂	semidirect
21. C₄×#121×C₇₃	C₂	semidirect
22. C₄×#121×C₇₃	C₂	semidirect
23. C₂×#390×C₇₃	C₂	semidirect
30. C₂×#126×C₇₃	C₂²	semidirect
31. C₂×#125×C₇₃	C₂²	semidirect
32. C₂×#123×C₇₃	C₂²	semidirect
33. C₂×#123×C₇₃	C₂²	semidirect
39. C₂×#121×C₇₃	C₂²	semidirect
40. C₂×#121×C₇₃	C₂²	semidirect
41. C₂×#121×C₇₃	C₂²	semidirect
42. C₂×#121×C₇₃	C₂²	semidirect
45. C₂×#120×C₇₃	C₂²	semidirect
46. C₂×#120×C₇₃	C₂²	semidirect
49. C₂×C₄×D₄×C₇₃	C₂²	semidirect
50. C₂×C₄×D₄×C₇₃	C₂²	semidirect
51. C₂×C₄×D₄×C₇₃	C₂²	semidirect
52. C₂×C₄×D₄×C₇₃	C₂²	semidirect
53. C₂×C₄×D₄×C₇₃	C₂²	semidirect
54. C₂×C₄×D₄×C₇₃	C₂²	semidirect
55. C₂×#117×C₇₃	C₂²	semidirect
56. C₂²×C₄⋊C₄×C₇₃	C₂²	semidirect
57. C₂²×C₂²⋊C₄×C₇₃	C₂²	semidirect
58. C₂²×C₂²⋊C₄×C₇₃	C₂²	semidirect
59. C₂²×C₂²⋊C₄×C₇₃	C₂²	semidirect
60. C₂²×C₄²×C₇₃	C₂²	semidirect
61. #400×C₇₃	C₂²	semidirect
62. #399×C₇₃	C₂²	semidirect
63. #399×C₇₃	C₂²	semidirect
64. #397×C₇₃	C₂²	semidirect
65. #396×C₇₃	C₂²	semidirect
66. #394×C₇₃	C₂²	semidirect
67. #394×C₇₃	C₂²	semidirect
68. #394×C₇₃	C₂²	semidirect
69. #394×C₇₃	C₂²	semidirect
70. #394×C₇₃	C₂²	semidirect
71. #394×C₇₃	C₂²	semidirect
72. #394×C₇₃	C₂²	semidirect
73. #392×C₇₃	C₂²	semidirect
74. #392×C₇₃	C₂²	semidirect
75. #392×C₇₃	C₂²	semidirect
76. #392×C₇₃	C₂²	semidirect
80. #390×C₇₃	C₂²	semidirect
81. #390×C₇₃	C₂²	semidirect
82. #390×C₇₃	C₂²	semidirect
83. #390×C₇₃	C₂²	semidirect
84. #390×C₇₃	C₂²	semidirect
85. #390×C₇₃	C₂²	semidirect
86. #390×C₇₃	C₂²	semidirect
87. #390×C₇₃	C₂²	semidirect
88. #390×C₇₃	C₂²	semidirect
89. #390×C₇₃	C₂²	semidirect
90. #389×C₇₃	C₂²	semidirect
91. #389×C₇₃	C₂²	semidirect
92. #389×C₇₃	C₂²	semidirect
93. #389×C₇₃	C₂²	semidirect
94. #388×C₇₃	C₂²	semidirect
95. #388×C₇₃	C₂²	semidirect
96. #388×C₇₃	C₂²	semidirect
97. #388×C₇₃	C₂²	semidirect
98. #388×C₇₃	C₂²	semidirect
99. #388×C₇₃	C₂²	semidirect
102. #386×C₇₃	C₂²	semidirect
103. #386×C₇₃	C₂²	semidirect
104. #386×C₇₃	C₂²	semidirect
105. #386×C₇₃	C₂²	semidirect
106. #386×C₇₃	C₂²	semidirect
107. #386×C₇₃	C₂²	semidirect
108. #386×C₇₃	C₂²	semidirect
109. #385×C₇₃	C₂²	semidirect
110. #385×C₇₃	C₂²	semidirect
111. #380×C₇₃	C₂²	semidirect
112. #380×C₇₃	C₂²	semidirect
113. #380×C₇₃	C₂²	semidirect
114. #380×C₇₃	C₂²	semidirect
115. #380×C₇₃	C₂²	semidirect
116. #379×C₇₃	C₂²	semidirect
117. #379×C₇₃	C₂²	semidirect
118. #379×C₇₃	C₂²	semidirect
119. C₄×C₄⋊C₄×C₇₃	C₂²	semidirect
120. C₄×C₄⋊C₄×C₇₃	C₂²	semidirect
121. C₄×C₂²⋊C₄×C₇₃	C₂²	semidirect
122. C₄×C₂²⋊C₄×C₇₃	C₂²	semidirect
123. C₄×C₂²⋊C₄×C₇₃	C₂²	semidirect
124. C₄×C₂²⋊C₄×C₇₃	C₂²	semidirect
173. #121×C₇₃	D₄	semidirect
637. #59408	C₇₃	direct (N × H)
651. C₂×#553	C₂×C₇₃	semidirect
652. C₂×D₄²	C₂×C₇₃	semidirect
653. #2703	C₂×C₇₃	semidirect
654. #2685	C₂×C₇₃	semidirect
655. #2559	C₂×C₇₃	semidirect
656. #2539	C₂×C₇₃	semidirect
657. #2490	C₂×C₇₃	semidirect
658. #2487	C₂×C₇₃	semidirect
659. #2454	C₂×C₇₃	semidirect
660. #2445	C₂×C₇₃	semidirect
661. #2428	C₂×C₇₃	semidirect
662. #2424	C₂×C₇₃	semidirect
663. #2418	C₂×C₇₃	semidirect
664. #2414	C₂×C₇₃	semidirect
665. #2410	C₂×C₇₃	semidirect
666. #2408	C₂×C₇₃	semidirect
667. #2408	C₂×C₇₃	semidirect
668. #2363	C₂×C₇₃	semidirect
669. D₄×C₂²⋊C₄	C₂×C₇₃	semidirect
670. D₄×C₂²⋊C₄	C₂×C₇₃	semidirect
671. C₄×#121	C₂×C₇₃	semidirect
672. C₄×#121	C₂×C₇₃	semidirect
673. C₂×#390	C₂×C₇₃	semidirect
674. C₇₃	#59408	direct (N × H)
681. C₂×#126	C₂²×C₇₃	semidirect
682. C₂×#125	C₂²×C₇₃	semidirect
683. C₂×#123	C₂²×C₇₃	semidirect
684. C₂×#123	C₂²×C₇₃	semidirect
690. C₂×#121	C₂²×C₇₃	semidirect
691. C₂×#121	C₂²×C₇₃	semidirect
692. C₂×#121	C₂²×C₇₃	semidirect
693. C₂×#121	C₂²×C₇₃	semidirect
696. C₂×#120	C₂²×C₇₃	semidirect
697. C₂×#120	C₂²×C₇₃	semidirect
700. C₂×C₄×D₄	C₂²×C₇₃	semidirect
701. C₂×C₄×D₄	C₂²×C₇₃	semidirect
702. C₂×C₄×D₄	C₂²×C₇₃	semidirect
703. C₂×C₄×D₄	C₂²×C₇₃	semidirect
704. C₂×C₄×D₄	C₂²×C₇₃	semidirect
705. C₂×C₄×D₄	C₂²×C₇₃	semidirect
706. C₂×#117	C₂²×C₇₃	semidirect
707. C₂²×C₄⋊C₄	C₂²×C₇₃	semidirect
708. C₂²×C₂²⋊C₄	C₂²×C₇₃	semidirect
709. C₂²×C₂²⋊C₄	C₂²×C₇₃	semidirect
710. C₂²×C₂²⋊C₄	C₂²×C₇₃	semidirect
711. C₂²×C₄²	C₂²×C₇₃	semidirect
712. #400	C₂²×C₇₃	semidirect
713. #399	C₂²×C₇₃	semidirect
714. #399	C₂²×C₇₃	semidirect
715. #397	C₂²×C₇₃	semidirect
716. #396	C₂²×C₇₃	semidirect
717. #394	C₂²×C₇₃	semidirect
718. #394	C₂²×C₇₃	semidirect
719. #394	C₂²×C₇₃	semidirect
720. #394	C₂²×C₇₃	semidirect
721. #394	C₂²×C₇₃	semidirect
722. #394	C₂²×C₇₃	semidirect
723. #394	C₂²×C₇₃	semidirect
724. #392	C₂²×C₇₃	semidirect
725. #392	C₂²×C₇₃	semidirect
726. #392	C₂²×C₇₃	semidirect
727. #392	C₂²×C₇₃	semidirect
731. #390	C₂²×C₇₃	semidirect
732. #390	C₂²×C₇₃	semidirect
733. #390	C₂²×C₇₃	semidirect
734. #390	C₂²×C₇₃	semidirect
735. #390	C₂²×C₇₃	semidirect
736. #390	C₂²×C₇₃	semidirect
737. #390	C₂²×C₇₃	semidirect
738. #390	C₂²×C₇₃	semidirect
739. #390	C₂²×C₇₃	semidirect
740. #390	C₂²×C₇₃	semidirect
741. #389	C₂²×C₇₃	semidirect
742. #389	C₂²×C₇₃	semidirect
743. #389	C₂²×C₇₃	semidirect
744. #389	C₂²×C₇₃	semidirect
745. #388	C₂²×C₇₃	semidirect
746. #388	C₂²×C₇₃	semidirect
747. #388	C₂²×C₇₃	semidirect
748. #388	C₂²×C₇₃	semidirect
749. #388	C₂²×C₇₃	semidirect
750. #388	C₂²×C₇₃	semidirect
753. #386	C₂²×C₇₃	semidirect
754. #386	C₂²×C₇₃	semidirect
755. #386	C₂²×C₇₃	semidirect
756. #386	C₂²×C₇₃	semidirect
757. #386	C₂²×C₇₃	semidirect
758. #386	C₂²×C₇₃	semidirect
759. #386	C₂²×C₇₃	semidirect
760. #385	C₂²×C₇₃	semidirect
761. #385	C₂²×C₇₃	semidirect
762. #380	C₂²×C₇₃	semidirect
763. #380	C₂²×C₇₃	semidirect
764. #380	C₂²×C₇₃	semidirect
765. #380	C₂²×C₇₃	semidirect
766. #380	C₂²×C₇₃	semidirect
767. #379	C₂²×C₇₃	semidirect
768. #379	C₂²×C₇₃	semidirect
769. #379	C₂²×C₇₃	semidirect
770. C₄×C₄⋊C₄	C₂²×C₇₃	semidirect
771. C₄×C₄⋊C₄	C₂²×C₇₃	semidirect
772. C₄×C₂²⋊C₄	C₂²×C₇₃	semidirect
773. C₄×C₂²⋊C₄	C₂²×C₇₃	semidirect
774. C₄×C₂²⋊C₄	C₂²×C₇₃	semidirect
775. C₄×C₂²⋊C₄	C₂²×C₇₃	semidirect
824. #121	D₄×C₇₃	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#553×C₇₃	2
C₂×D₄²×C₇₃	2
C₇₃×#2703	2
C₇₃×#2685	2
C₇₃×#2559	2
C₇₃×#2539	2
C₇₃×#2490	2
C₇₃×#2487	2
C₇₃×#2454	2
C₇₃×#2445	2
C₇₃×#2428	2
C₇₃×#2424	2
C₇₃×#2418	2
C₇₃×#2414	2
C₇₃×#2410	2
C₇₃×#2408	2
C₇₃×#2363	2
D₄×C₂²⋊C₄×C₇₃	2
C₄×#121×C₇₃	2
C₂×#390×C₇₃	2
#59408	73

Subgroups — C73×#59408 #32968812

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#59408 #32968812