Subgroups — C₇₃×#59414 #32968818

Order 18688.

2834 conjugacy classes of subgroups.

The subgroup lattice has 1226 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#559×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#546×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₃×#2706	C₂	1	2	yes	maximal, complemented
4	C₇₃×#2670	C₂	1	2	yes	maximal, complemented
5	C₇₃×#2580	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₃×#2557	C₂	1	2	yes	maximal, complemented
7	C₇₃×#2539	C₂	1	2	yes	maximal, complemented
8	C₇₃×#2535	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₃×#2464	C₂	1	2	yes	maximal, complemented
10	C₇₃×#2456	C₂	1	2	yes	maximal, complemented
11	C₇₃×#2433	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇₃×#2431	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇₃×#2428	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇₃×#2426	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₃×#2423	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇₃×#2422	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇₃×#2418	C₂	1	2	yes	maximal, complemented
18	C₇₃×#2358	C₂	1	2	yes	maximal, complemented
19	C₇₃×#2341	C₂	1	1	yes	maximal, characteristic, complemented
20	D₄×C₂²⋊C₄×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×#127×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#124×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×#124×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41×C₇₃	C₂²	1	1	yes	characteristic
25	C₂³×D₄×C₇₃	C₂²	1	1	yes	characteristic
26	#559×C₇₃	—	2	8	no	—
27	#546×C₇₃	—	2	8	no	—
28	C₂×#127×C₇₃	C₂²	1	1	yes	characteristic
29	C₂×#127×C₇₃	C₂²	1	1	yes	characteristic
30	C₂×#124×C₇₃	C₂²	1	1	yes	characteristic
31	C₂×#124×C₇₃	C₂²	1	1	yes	characteristic
32	C₂×#124×C₇₃	C₂²	1	2	yes	complemented
33	C₂×#124×C₇₃	C₂²	1	1	yes	characteristic, complemented
34	C₂×#123×C₇₃	C₂²	1	2	yes	—
35	C₂×#123×C₇₃	C₂²	1	2	yes	complemented
36	C₂×#123×C₇₃	C₂²	1	2	yes	complemented
37	C₂×#123×C₇₃	C₂²	1	2	yes	complemented
38	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
39	C₂×#121×C₇₃	C₂²	1	2	yes	—
40	C₂×#121×C₇₃	C₂²	1	1	yes	characteristic
41	C₂×#121×C₇₃	C₂²	1	1	yes	characteristic
42	C₂×#121×C₇₃	C₂²	1	2	yes	complemented
43	C₂×#121×C₇₃	C₂²	1	1	yes	characteristic, complemented
44	C₂×#120×C₇₃	C₂²	1	2	yes	—
45	C₂×#120×C₇₃	C₂²	1	2	yes	—
46	C₂×#120×C₇₃	C₂²	1	2	yes	—
47	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
48	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
49	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
50	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
51	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
52	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
53	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
54	C₂×C₄×D₄×C₇₃	C₂²	1	2	yes	complemented
55	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic, complemented
56	C₂×C₄×D₄×C₇₃	C₂²	1	2	yes	complemented
57	C₂×C₄×D₄×C₇₃	C₂²	1	2	yes	complemented
58	C₂²×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
59	C₂²×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
60	#399×C₇₃	C₂²	1	2	yes	—
61	#399×C₇₃	C₂²	1	2	yes	complemented
62	#398×C₇₃	C₂²	1	2	yes	complemented
63	#397×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	—
67	#394×C₇₃	C₂²	1	2	yes	complemented
68	#394×C₇₃	C₂²	1	2	yes	complemented
69	#393×C₇₃	C₂²	1	2	yes	complemented
70	#392×C₇₃	C₂²	1	2	yes	—
71	#392×C₇₃	C₂²	1	2	yes	—
72	#392×C₇₃	C₂²	1	2	yes	—
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	#391×C₇₃	C₂²	1	1	yes	characteristic, complemented
77	#391×C₇₃	C₂²	1	1	yes	characteristic, complemented
78	#390×C₇₃	C₂²	1	1	yes	characteristic
79	#390×C₇₃	C₂²	1	2	yes	—
80	#390×C₇₃	C₂²	1	1	yes	characteristic
81	#390×C₇₃	C₂²	1	1	yes	characteristic
82	#390×C₇₃	C₂²	1	1	yes	characteristic
83	#390×C₇₃	C₂²	1	1	yes	characteristic
84	#390×C₇₃	C₂²	1	2	yes	complemented
85	#390×C₇₃	C₂²	1	2	yes	complemented
86	#390×C₇₃	C₂²	1	2	yes	complemented
87	#390×C₇₃	C₂²	1	2	yes	complemented
88	#390×C₇₃	C₂²	1	1	yes	characteristic, complemented
89	#389×C₇₃	C₂²	1	1	yes	characteristic, complemented
90	#389×C₇₃	C₂²	1	1	yes	characteristic, complemented
91	#388×C₇₃	C₂²	1	1	yes	characteristic
92	#388×C₇₃	C₂²	1	1	yes	characteristic
93	#388×C₇₃	C₂²	1	2	yes	—
94	#388×C₇₃	C₂²	1	2	yes	complemented
95	#388×C₇₃	C₂²	1	1	yes	characteristic, 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	#387×C₇₃	C₂²	1	2	yes	complemented
100	#386×C₇₃	C₂²	1	2	yes	—
101	#386×C₇₃	C₂²	1	2	yes	—
102	#386×C₇₃	C₂²	1	2	yes	—
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	2	yes	complemented
107	#385×C₇₃	C₂²	1	2	yes	complemented
108	#385×C₇₃	C₂²	1	2	yes	complemented
109	#385×C₇₃	C₂²	1	2	yes	complemented
110	#384×C₇₃	C₂²	1	1	yes	characteristic, complemented
111	#382×C₇₃	C₂²	1	1	yes	characteristic, complemented
112	#382×C₇₃	C₂²	1	1	yes	characteristic, complemented
113	#380×C₇₃	C₂²	1	1	yes	characteristic
114	#380×C₇₃	C₂²	1	2	yes	complemented
115	#380×C₇₃	C₂²	1	1	yes	characteristic, complemented
116	#379×C₇₃	C₂²	1	2	yes	—
117	C₄×C₂²⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
118	C₄×C₂²⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
119	C₄×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	complemented
120	C₄×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	complemented
121	C₄×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	complemented
122	C₄×C₂²⋊C₄×C₇₃	C₂²	1	1	yes	characteristic, complemented
123	C₄×C₂²⋊C₄×C₇₃	C₂²	1	1	yes	characteristic, complemented
124	C₄³×C₇₃	C₂²	1	1	yes	characteristic, complemented
125	C₂⁵×C₇₃	C₂³	1	2	yes	—
126	C₂×#41×C₇₃	—	2	4	no	—
127	C₂×#41×C₇₃	—	2	4	no	—
128	C₂×#41×C₇₃	—	4	2	no	—
129	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
130	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
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	C₂³	1	1	yes	characteristic
135	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
136	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
137	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
138	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
139	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
140	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
141	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
142	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
143	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
144	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
145	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
146	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
147	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
148	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
149	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
150	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
151	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
152	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
153	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
154	#127×C₇₃	—	2	4	no	—
155	#127×C₇₃	—	2	4	no	—
156	#124×C₇₃	—	2	4	no	—
157	#124×C₇₃	—	2	8	no	—
158	#124×C₇₃	—	2	4	no	—
159	#124×C₇₃	D₄	1	8	yes	complemented
160	#123×C₇₃	—	2	8	no	—
161	#123×C₇₃	—	2	8	no	—
162	#123×C₇₃	—	2	8	no	—
163	#123×C₇₃	—	4	4	no	—
164	C₂²⋊Q₈×C₇₃	—	2	4	no	—
165	#121×C₇₃	—	2	4	no	—
166	#121×C₇₃	—	2	8	no	—
167	#121×C₇₃	—	4	4	no	—
168	#121×C₇₃	—	4	2	no	—
169	#121×C₇₃	—	4	2	no	—
170	#120×C₇₃	—	2	8	no	—
171	#120×C₇₃	—	2	8	no	—
172	#120×C₇₃	—	4	4	no	—
173	C₄×Q₈×C₇₃	—	2	4	no	—
174	C₄×Q₈×C₇₃	—	2	4	no	—
175	C₄×Q₈×C₇₃	—	4	2	no	—
176	C₄×D₄×C₇₃	—	2	4	no	—
177	C₄×D₄×C₇₃	—	2	8	no	—
178	C₄×D₄×C₇₃	—	2	4	no	—
179	C₄×D₄×C₇₃	—	2	4	no	—
180	C₄×D₄×C₇₃	—	2	4	no	—
181	C₄×D₄×C₇₃	—	4	4	no	—
182	C₄×D₄×C₇₃	—	4	2	no	—
183	C₄×D₄×C₇₃	—	4	4	no	—
184	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
185	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
186	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
187	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
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	2	yes	—
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	2	yes	—
197	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
198	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
199	C₂×C₂²⋊C₄×C₇₃	—	2	8	no	—
200	C₂×C₂²⋊C₄×C₇₃	—	4	4	no	—
201	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
202	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
203	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
204	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
205	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
206	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
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	1	yes	characteristic
212	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
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	1	yes	characteristic
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	2	yes	—
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	2	yes	—
225	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
226	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
227	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
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	1	yes	characteristic
235	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
236	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
237	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
238	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
239	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
240	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
241	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
242	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
243	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
244	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
245	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
246	#95×C₇₃	C₂³	1	1	yes	characteristic
247	#95×C₇₃	C₂³	1	1	yes	characteristic
248	#95×C₇₃	C₂³	1	1	yes	characteristic
249	#95×C₇₃	C₂³	1	1	yes	characteristic
250	#95×C₇₃	C₂³	1	1	yes	characteristic
251	#95×C₇₃	C₂³	1	1	yes	characteristic
252	#95×C₇₃	C₂³	1	2	yes	—
253	#95×C₇₃	C₂³	1	2	yes	—
254	#95×C₇₃	C₂³	1	1	yes	characteristic
255	#95×C₇₃	C₂³	1	2	yes	—
256	#95×C₇₃	C₂³	1	1	yes	characteristic
257	#95×C₇₃	C₂³	1	2	yes	—
258	#95×C₇₃	C₂³	1	2	yes	—
259	#95×C₇₃	C₂³	1	2	yes	—
260	#95×C₇₃	C₂³	1	2	yes	—
261	#95×C₇₃	C₂³	1	2	yes	—
262	C₂⁴×C₇₃	—	2	4	no	—
263	C₂⁴×C₇₃	—	2	4	no	—
264	C₂⁴×C₇₃	—	2	4	no	—
265	C₂⁴×C₇₃	—	4	2	no	—
266	C₂⁴×C₇₃	—	4	2	no	—
267	C₂⁴×C₇₃	—	4	2	no	—
268	C₂⁴×C₇₃	—	4	2	no	—
269	C₂⁴×C₇₃	C₂⁴	1	2	yes	—
270	C₂⁴×C₇₃	C₂⁴	1	1	yes	characteristic
271	C₂⁴×C₇₃	C₂⁴	1	2	yes	—
272	C₂⁴×C₇₃	C₂⁴	1	1	yes	characteristic
273	C₂⁴×C₇₃	C₂⁴	1	2	yes	—
274	#41×C₇₃	—	4	16	no	—
275	C₂×Q₈×C₇₃	—	2	2	no	—
276	C₂×Q₈×C₇₃	—	2	2	no	—
277	C₂×Q₈×C₇₃	—	2	2	no	—
278	C₂×Q₈×C₇₃	—	2	2	no	—
279	C₂×Q₈×C₇₃	—	4	1	no	—
280	C₂×Q₈×C₇₃	C₂×D₄	1	4	yes	—
281	C₂×D₄×C₇₃	—	2	4	no	—
282	C₂×D₄×C₇₃	—	2	4	no	—
283	C₂×D₄×C₇₃	—	2	2	no	—
284	C₂×D₄×C₇₃	—	2	4	no	—
285	C₂×D₄×C₇₃	—	2	4	no	—
286	C₂×D₄×C₇₃	—	2	4	no	—
287	C₂×D₄×C₇₃	—	2	4	no	—
288	C₂×D₄×C₇₃	—	2	4	no	—
289	C₂×D₄×C₇₃	—	2	4	no	—
290	C₂×D₄×C₇₃	—	2	4	no	—
291	C₂×D₄×C₇₃	—	2	2	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	2	no	—
296	C₂×D₄×C₇₃	—	2	4	no	—
297	C₂×D₄×C₇₃	—	2	4	no	—
298	C₂×D₄×C₇₃	—	2	2	no	—
299	C₂×D₄×C₇₃	—	2	2	no	—
300	C₂×D₄×C₇₃	—	2	2	no	—
301	C₂×D₄×C₇₃	—	2	4	no	—
302	C₂×D₄×C₇₃	—	2	2	no	—
303	C₂×D₄×C₇₃	—	4	2	no	—
304	C₂×D₄×C₇₃	—	4	2	no	—
305	C₂×D₄×C₇₃	—	4	2	no	—
306	C₂×D₄×C₇₃	—	4	1	no	—
307	C₂×D₄×C₇₃	—	4	2	no	—
308	C₂×D₄×C₇₃	—	4	2	no	—
309	C₂×D₄×C₇₃	—	4	2	no	—
310	C₂×D₄×C₇₃	—	4	2	no	—
311	C₂×D₄×C₇₃	—	4	2	no	—
312	C₂×D₄×C₇₃	—	4	2	no	—
313	C₂×D₄×C₇₃	—	4	2	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	16	no	—
319	C₂×D₄×C₇₃	C₂×D₄	1	4	yes	—
320	C₂×D₄×C₇₃	#41	1	4	yes	—
321	C₂²×C₄×C₇₃	—	2	4	no	—
322	C₂²×C₄×C₇₃	—	2	4	no	—
323	C₂²×C₄×C₇₃	—	2	4	no	—
324	C₂²×C₄×C₇₃	—	2	2	no	—
325	C₂²×C₄×C₇₃	—	2	2	no	—
326	C₂²×C₄×C₇₃	—	2	2	no	—
327	C₂²×C₄×C₇₃	—	2	2	no	—
328	C₂²×C₄×C₇₃	—	2	2	no	—
329	C₂²×C₄×C₇₃	—	2	2	no	—
330	C₂²×C₄×C₇₃	—	2	4	no	—
331	C₂²×C₄×C₇₃	—	2	4	no	—
332	C₂²×C₄×C₇₃	—	2	4	no	—
333	C₂²×C₄×C₇₃	—	4	2	no	—
334	C₂²×C₄×C₇₃	—	4	2	no	—
335	C₂²×C₄×C₇₃	—	4	2	no	—
336	C₂²×C₄×C₇₃	—	4	2	no	—
337	C₂²×C₄×C₇₃	—	4	2	no	—
338	C₂²×C₄×C₇₃	—	4	2	no	—
339	C₂²×C₄×C₇₃	—	4	2	no	—
340	C₂²×C₄×C₇₃	—	4	2	no	—
341	C₂²×C₄×C₇₃	—	4	2	no	—
342	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
343	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
344	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
345	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
346	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
347	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
348	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
349	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
350	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
351	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
352	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
353	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
354	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
355	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
356	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
357	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
358	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
359	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
360	C₄⋊C₄×C₇₃	—	2	2	no	—
361	C₄⋊C₄×C₇₃	—	2	2	no	—
362	C₄⋊C₄×C₇₃	—	2	2	no	—
363	C₄⋊C₄×C₇₃	—	2	2	no	—
364	C₄⋊C₄×C₇₃	—	2	2	no	—
365	C₄⋊C₄×C₇₃	—	2	4	no	—
366	C₄⋊C₄×C₇₃	—	2	2	no	—
367	C₄⋊C₄×C₇₃	—	2	4	no	—
368	C₄⋊C₄×C₇₃	—	2	2	no	—
369	C₄⋊C₄×C₇₃	—	2	4	no	—
370	C₄⋊C₄×C₇₃	—	2	2	no	—
371	C₄⋊C₄×C₇₃	—	4	2	no	—
372	C₄⋊C₄×C₇₃	—	4	2	no	—
373	C₄⋊C₄×C₇₃	—	4	2	no	—
374	C₄⋊C₄×C₇₃	—	4	2	no	—
375	C₂²⋊C₄×C₇₃	—	2	4	no	—
376	C₂²⋊C₄×C₇₃	—	2	4	no	—
377	C₂²⋊C₄×C₇₃	—	2	2	no	—
378	C₂²⋊C₄×C₇₃	—	2	2	no	—
379	C₂²⋊C₄×C₇₃	—	2	4	no	—
380	C₂²⋊C₄×C₇₃	—	2	4	no	—
381	C₂²⋊C₄×C₇₃	—	2	2	no	—
382	C₂²⋊C₄×C₇₃	—	2	4	no	—
383	C₂²⋊C₄×C₇₃	—	2	4	no	—
384	C₂²⋊C₄×C₇₃	—	2	4	no	—
385	C₂²⋊C₄×C₇₃	—	2	4	no	—
386	C₂²⋊C₄×C₇₃	—	2	4	no	—
387	C₂²⋊C₄×C₇₃	—	2	2	no	—
388	C₂²⋊C₄×C₇₃	—	2	2	no	—
389	C₂²⋊C₄×C₇₃	—	2	2	no	—
390	C₂²⋊C₄×C₇₃	—	2	4	no	—
391	C₂²⋊C₄×C₇₃	—	2	4	no	—
392	C₂²⋊C₄×C₇₃	—	2	2	no	—
393	C₂²⋊C₄×C₇₃	—	2	4	no	—
394	C₂²⋊C₄×C₇₃	—	2	2	no	—
395	C₂²⋊C₄×C₇₃	—	2	2	no	—
396	C₂²⋊C₄×C₇₃	—	4	2	no	—
397	C₂²⋊C₄×C₇₃	—	4	2	no	—
398	C₂²⋊C₄×C₇₃	—	4	2	no	—
399	C₂²⋊C₄×C₇₃	—	4	2	no	—
400	C₂²⋊C₄×C₇₃	—	4	2	no	—
401	C₂²⋊C₄×C₇₃	—	4	2	no	—
402	C₂²⋊C₄×C₇₃	—	4	2	no	—
403	C₂²⋊C₄×C₇₃	—	4	2	no	—
404	C₂²⋊C₄×C₇₃	—	4	2	no	—
405	C₂²⋊C₄×C₇₃	—	4	2	no	—
406	C₂²⋊C₄×C₇₃	C₂×D₄	1	8	yes	—
407	C₂²⋊C₄×C₇₃	C₂×D₄	1	8	yes	—
408	C₂²⋊C₄×C₇₃	#41	1	4	yes	complemented
409	C₄²×C₇₃	—	2	4	no	—
410	C₄²×C₇₃	—	2	2	no	—
411	C₄²×C₇₃	—	2	2	no	—
412	C₄²×C₇₃	—	2	2	no	—
413	C₄²×C₇₃	—	2	2	no	—
414	C₄²×C₇₃	—	2	2	no	—
415	C₄²×C₇₃	—	2	2	no	—
416	C₄²×C₇₃	—	2	2	no	—
417	C₄²×C₇₃	—	4	1	no	—
418	C₄²×C₇₃	—	4	2	no	—
419	C₄²×C₇₃	C₂×D₄	1	4	yes	—
420	C₂³×C₇₃	—	2	1	no	—
421	C₂³×C₇₃	—	2	2	no	—
422	C₂³×C₇₃	—	2	2	no	—
423	C₂³×C₇₃	—	2	2	no	—
424	C₂³×C₇₃	—	2	1	no	—
425	C₂³×C₇₃	—	2	2	no	—
426	C₂³×C₇₃	—	2	1	no	—
427	C₂³×C₇₃	—	2	2	no	—
428	C₂³×C₇₃	—	2	2	no	—
429	C₂³×C₇₃	—	2	1	no	—
430	C₂³×C₇₃	—	2	2	no	—
431	C₂³×C₇₃	—	2	2	no	—
432	C₂³×C₇₃	—	2	2	no	—
433	C₂³×C₇₃	—	2	1	no	—
434	C₂³×C₇₃	—	2	2	no	—
435	C₂³×C₇₃	—	2	2	no	—
436	C₂³×C₇₃	—	2	2	no	—
437	C₂³×C₇₃	—	2	1	no	—
438	C₂³×C₇₃	—	2	2	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	1	no	—
447	C₂³×C₇₃	—	2	2	no	—
448	C₂³×C₇₃	—	2	2	no	—
449	C₂³×C₇₃	—	2	1	no	—
450	C₂³×C₇₃	—	2	2	no	—
451	C₂³×C₇₃	—	2	1	no	—
452	C₂³×C₇₃	—	4	8	no	—
453	C₂³×C₇₃	—	4	8	no	—
454	C₂³×C₇₃	—	4	8	no	—
455	C₂³×C₇₃	—	8	4	no	—
456	C₂³×C₇₃	—	8	4	no	—
457	C₂³×C₇₃	—	8	4	no	—
458	C₂³×C₇₃	—	8	4	no	—
459	C₂³×C₇₃	C₂²×D₄	1	4	yes	—
460	C₂³×C₇₃	C₂×#41	1	2	yes	—
461	C₂³×C₇₃	C₂×#41	1	4	yes	—
462	C₂³×C₇₃	C₂⁵	1	1	yes	characteristic
463	Q₈×C₇₃	—	2	8	no	—
464	Q₈×C₇₃	—	4	4	no	—
465	D₄×C₇₃	—	2	8	no	—
466	D₄×C₇₃	—	2	8	no	—
467	D₄×C₇₃	—	4	4	no	—
468	D₄×C₇₃	—	4	8	no	—
469	D₄×C₇₃	—	4	8	no	—
470	D₄×C₇₃	—	4	8	no	—
471	D₄×C₇₃	—	4	8	no	—
472	D₄×C₇₃	—	4	8	no	—
473	D₄×C₇₃	—	4	4	no	—
474	D₄×C₇₃	—	8	4	no	—
475	D₄×C₇₃	—	8	4	no	—
476	D₄×C₇₃	—	8	4	no	—
477	D₄×C₇₃	—	8	4	no	—
478	C₂×C₄×C₇₃	—	2	1	no	—
479	C₂×C₄×C₇₃	—	2	1	no	—
480	C₂×C₄×C₇₃	—	2	1	no	—
481	C₂×C₄×C₇₃	—	2	1	no	—
482	C₂×C₄×C₇₃	—	2	2	no	—
483	C₂×C₄×C₇₃	—	2	1	no	—
484	C₂×C₄×C₇₃	—	2	1	no	—
485	C₂×C₄×C₇₃	—	2	1	no	—
486	C₂×C₄×C₇₃	—	2	1	no	—
487	C₂×C₄×C₇₃	—	2	2	no	—
488	C₂×C₄×C₇₃	—	2	1	no	—
489	C₂×C₄×C₇₃	—	2	1	no	—
490	C₂×C₄×C₇₃	—	2	1	no	—
491	C₂×C₄×C₇₃	—	2	1	no	—
492	C₂×C₄×C₇₃	—	2	1	no	—
493	C₂×C₄×C₇₃	—	2	2	no	—
494	C₂×C₄×C₇₃	—	2	1	no	—
495	C₂×C₄×C₇₃	—	2	1	no	—
496	C₂×C₄×C₇₃	—	2	2	no	—
497	C₂×C₄×C₇₃	—	2	1	no	—
498	C₂×C₄×C₇₃	—	2	1	no	—
499	C₂×C₄×C₇₃	—	2	1	no	—
500	C₂×C₄×C₇₃	—	2	2	no	—
501	C₂×C₄×C₇₃	—	2	1	no	—
502	C₂×C₄×C₇₃	—	2	1	no	—
503	C₂×C₄×C₇₃	—	2	1	no	—
504	C₂×C₄×C₇₃	—	2	1	no	—
505	C₂×C₄×C₇₃	—	2	1	no	—
506	C₂×C₄×C₇₃	—	2	2	no	—
507	C₂×C₄×C₇₃	—	2	2	no	—
508	C₂×C₄×C₇₃	—	2	1	no	—
509	C₂×C₄×C₇₃	—	2	1	no	—
510	C₂×C₄×C₇₃	—	2	2	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	2	no	—
515	C₂×C₄×C₇₃	—	2	2	no	—
516	C₂×C₄×C₇₃	—	2	2	no	—
517	C₂×C₄×C₇₃	—	2	1	no	—
518	C₂×C₄×C₇₃	—	2	1	no	—
519	C₂×C₄×C₇₃	—	2	2	no	—
520	C₂×C₄×C₇₃	—	2	1	no	—
521	C₂×C₄×C₇₃	—	2	2	no	—
522	C₂×C₄×C₇₃	—	4	8	no	—
523	C₂×C₄×C₇₃	—	4	4	no	—
524	C₂×C₄×C₇₃	—	4	4	no	—
525	C₂×C₄×C₇₃	—	8	4	no	—
526	C₂×C₄×C₇₃	—	8	4	no	—
527	C₂×C₄×C₇₃	—	8	4	no	—
528	C₂×C₄×C₇₃	—	8	4	no	—
529	C₂×C₄×C₇₃	C₂²×D₄	1	4	yes	—
530	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
531	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
532	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
533	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
534	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
535	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
536	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
537	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
538	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
539	C₂²×C₇₃	—	2	4	no	—
540	C₂²×C₇₃	—	2	4	no	—
541	C₂²×C₇₃	—	2	2	no	—
542	C₂²×C₇₃	—	2	4	no	—
543	C₂²×C₇₃	—	2	4	no	—
544	C₂²×C₇₃	—	2	2	no	—
545	C₂²×C₇₃	—	2	4	no	—
546	C₂²×C₇₃	—	2	2	no	—
547	C₂²×C₇₃	—	2	4	no	—
548	C₂²×C₇₃	—	4	1	no	—
549	C₂²×C₇₃	—	4	2	no	—
550	C₂²×C₇₃	—	4	2	no	—
551	C₂²×C₇₃	—	4	2	no	—
552	C₂²×C₇₃	—	4	1	no	—
553	C₂²×C₇₃	—	4	2	no	—
554	C₂²×C₇₃	—	4	2	no	—
555	C₂²×C₇₃	—	4	2	no	—
556	C₂²×C₇₃	—	4	1	no	—
557	C₂²×C₇₃	—	4	2	no	—
558	C₂²×C₇₃	—	4	2	no	—
559	C₂²×C₇₃	—	4	1	no	—
560	C₂²×C₇₃	—	4	1	no	—
561	C₂²×C₇₃	—	4	2	no	—
562	C₂²×C₇₃	—	4	2	no	—
563	C₂²×C₇₃	—	4	1	no	—
564	C₂²×C₇₃	—	4	2	no	—
565	C₂²×C₇₃	—	4	1	no	—
566	C₂²×C₇₃	—	4	2	no	—
567	C₂²×C₇₃	—	4	1	no	—
568	C₂²×C₇₃	—	4	2	no	—
569	C₂²×C₇₃	—	4	1	no	—
570	C₂²×C₇₃	—	4	2	no	—
571	C₂²×C₇₃	—	4	1	no	—
572	C₂²×C₇₃	—	4	1	no	—
573	C₂²×C₇₃	—	4	2	no	—
574	C₂²×C₇₃	—	8	16	no	—
575	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
576	C₂²×C₇₃	C₂²×#41	1	1	yes	characteristic
577	C₂²×C₇₃	C₂²×#41	1	1	yes	characteristic
578	C₂²×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
579	C₂²×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
580	C₂²×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
581	C₂²×C₇₃	#585	1	1	yes	characteristic
582	C₄×C₇₃	—	2	4	no	—
583	C₄×C₇₃	—	2	2	no	—
584	C₄×C₇₃	—	2	2	no	—
585	C₄×C₇₃	—	2	2	no	—
586	C₄×C₇₃	—	2	2	no	—
587	C₄×C₇₃	—	2	2	no	—
588	C₄×C₇₃	—	2	2	no	—
589	C₄×C₇₃	—	4	1	no	—
590	C₄×C₇₃	—	4	1	no	—
591	C₄×C₇₃	—	4	1	no	—
592	C₄×C₇₃	—	4	1	no	—
593	C₄×C₇₃	—	4	2	no	—
594	C₄×C₇₃	—	4	2	no	—
595	C₄×C₇₃	—	4	1	no	—
596	C₄×C₇₃	—	4	1	no	—
597	C₄×C₇₃	—	4	2	no	—
598	C₄×C₇₃	—	4	2	no	—
599	C₄×C₇₃	#546	1	4	yes	—
600	#59414	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
601	C₂×C₇₃	—	4	4	no	—
602	C₂×C₇₃	—	4	4	no	—
603	C₂×C₇₃	—	4	2	no	—
604	C₂×C₇₃	—	8	1	no	—
605	C₂×C₇₃	—	8	2	no	—
606	C₂×C₇₃	C₂×#546	1	1	yes	characteristic
607	C₂×C₇₃	D₄×#41	1	1	yes	characteristic
608	C₂×C₇₃	#3481	1	1	yes	characteristic
609	C₂×C₇₃	#3498	1	1	yes	characteristic
610	C₂×C₇₃	#3508	1	1	yes	characteristic
611	C₂×C₇₃	#3513	1	1	yes	characteristic
612	C₂×C₇₃	#3558	1	1	yes	characteristic
613	C₂×#559	C₂×C₇₃	1	1	yes	characteristic, complemented
614	C₂×#546	C₂×C₇₃	1	1	yes	characteristic, complemented
615	#2706	C₂×C₇₃	1	2	yes	complemented
616	#2670	C₂×C₇₃	1	2	yes	complemented
617	#2580	C₂×C₇₃	1	1	yes	characteristic, complemented
618	#2557	C₂×C₇₃	1	2	yes	complemented
619	#2539	C₂×C₇₃	1	2	yes	complemented
620	#2535	C₂×C₇₃	1	1	yes	characteristic, complemented
621	#2464	C₂×C₇₃	1	2	yes	complemented
622	#2456	C₂×C₇₃	1	2	yes	complemented
623	#2433	C₂×C₇₃	1	1	yes	characteristic, complemented
624	#2431	C₂×C₇₃	1	1	yes	characteristic, complemented
625	#2428	C₂×C₇₃	1	1	yes	characteristic, complemented
626	#2426	C₂×C₇₃	1	1	yes	characteristic, complemented
627	#2423	C₂×C₇₃	1	1	yes	characteristic, complemented
628	#2422	C₂×C₇₃	1	1	yes	characteristic, complemented
629	#2418	C₂×C₇₃	1	2	yes	complemented
630	#2358	C₂×C₇₃	1	2	yes	complemented
631	#2341	C₂×C₇₃	1	1	yes	characteristic, complemented
632	D₄×C₂²⋊C₄	C₂×C₇₃	1	1	yes	characteristic, complemented
633	C₄×#127	C₂×C₇₃	1	1	yes	characteristic, complemented
634	C₄×#124	C₂×C₇₃	1	1	yes	characteristic, complemented
635	C₄×#124	C₂×C₇₃	1	1	yes	characteristic, complemented
636	C₇₃	#59414	1	1	yes	characteristic, direct product factor, Sylow
637	C₂²×#41	C₂²×C₇₃	1	1	yes	characteristic
638	C₂³×D₄	C₂²×C₇₃	1	1	yes	characteristic
639	#559	—	2	8	no	—
640	#546	—	2	8	no	—
641	C₂×#127	C₂²×C₇₃	1	1	yes	characteristic
642	C₂×#127	C₂²×C₇₃	1	1	yes	characteristic
643	C₂×#124	C₂²×C₇₃	1	1	yes	characteristic
644	C₂×#124	C₂²×C₇₃	1	1	yes	characteristic
645	C₂×#124	C₂²×C₇₃	1	2	yes	complemented
646	C₂×#124	C₂²×C₇₃	1	1	yes	characteristic, complemented
647	C₂×#123	C₂²×C₇₃	1	2	yes	—
648	C₂×#123	C₂²×C₇₃	1	2	yes	complemented
649	C₂×#123	C₂²×C₇₃	1	2	yes	complemented
650	C₂×#123	C₂²×C₇₃	1	2	yes	complemented
651	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
652	C₂×#121	C₂²×C₇₃	1	1	yes	characteristic
653	C₂×#121	C₂²×C₇₃	1	2	yes	—
654	C₂×#121	C₂²×C₇₃	1	1	yes	characteristic
655	C₂×#121	C₂²×C₇₃	1	1	yes	characteristic, complemented
656	C₂×#121	C₂²×C₇₃	1	2	yes	complemented
657	C₂×#120	C₂²×C₇₃	1	2	yes	—
658	C₂×#120	C₂²×C₇₃	1	2	yes	—
659	C₂×#120	C₂²×C₇₃	1	2	yes	—
660	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic, complemented
661	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic, complemented
662	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic, complemented
663	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
664	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
665	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
666	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
667	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic, complemented
668	C₂×C₄×D₄	C₂²×C₇₃	1	2	yes	complemented
669	C₂×C₄×D₄	C₂²×C₇₃	1	2	yes	complemented
670	C₂×C₄×D₄	C₂²×C₇₃	1	2	yes	complemented
671	C₂²×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
672	C₂²×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
673	#399	C₂²×C₇₃	1	2	yes	—
674	#399	C₂²×C₇₃	1	2	yes	complemented
675	#398	C₂²×C₇₃	1	2	yes	complemented
676	#397	C₂²×C₇₃	1	2	yes	complemented
677	#397	C₂²×C₇₃	1	2	yes	complemented
678	#396	C₂²×C₇₃	1	2	yes	complemented
679	#394	C₂²×C₇₃	1	2	yes	—
680	#394	C₂²×C₇₃	1	2	yes	complemented
681	#394	C₂²×C₇₃	1	2	yes	complemented
682	#393	C₂²×C₇₃	1	2	yes	complemented
683	#392	C₂²×C₇₃	1	2	yes	—
684	#392	C₂²×C₇₃	1	2	yes	—
685	#392	C₂²×C₇₃	1	2	yes	—
686	#392	C₂²×C₇₃	1	2	yes	complemented
687	#392	C₂²×C₇₃	1	2	yes	complemented
688	#392	C₂²×C₇₃	1	2	yes	complemented
689	#391	C₂²×C₇₃	1	1	yes	characteristic, complemented
690	#391	C₂²×C₇₃	1	1	yes	characteristic, complemented
691	#390	C₂²×C₇₃	1	1	yes	characteristic
692	#390	C₂²×C₇₃	1	1	yes	characteristic
693	#390	C₂²×C₇₃	1	1	yes	characteristic
694	#390	C₂²×C₇₃	1	2	yes	—
695	#390	C₂²×C₇₃	1	1	yes	characteristic
696	#390	C₂²×C₇₃	1	1	yes	characteristic
697	#390	C₂²×C₇₃	1	2	yes	complemented
698	#390	C₂²×C₇₃	1	1	yes	characteristic, complemented
699	#390	C₂²×C₇₃	1	2	yes	complemented
700	#390	C₂²×C₇₃	1	2	yes	complemented
701	#390	C₂²×C₇₃	1	2	yes	complemented
702	#389	C₂²×C₇₃	1	1	yes	characteristic, complemented
703	#389	C₂²×C₇₃	1	1	yes	characteristic, complemented
704	#388	C₂²×C₇₃	1	1	yes	characteristic
705	#388	C₂²×C₇₃	1	2	yes	—
706	#388	C₂²×C₇₃	1	1	yes	characteristic
707	#388	C₂²×C₇₃	1	2	yes	complemented
708	#388	C₂²×C₇₃	1	2	yes	complemented
709	#388	C₂²×C₇₃	1	2	yes	complemented
710	#388	C₂²×C₇₃	1	1	yes	characteristic, complemented
711	#388	C₂²×C₇₃	1	1	yes	characteristic, complemented
712	#387	C₂²×C₇₃	1	2	yes	complemented
713	#386	C₂²×C₇₃	1	2	yes	—
714	#386	C₂²×C₇₃	1	2	yes	—
715	#386	C₂²×C₇₃	1	2	yes	—
716	#386	C₂²×C₇₃	1	2	yes	complemented
717	#386	C₂²×C₇₃	1	2	yes	complemented
718	#386	C₂²×C₇₃	1	2	yes	complemented
719	#386	C₂²×C₇₃	1	2	yes	complemented
720	#385	C₂²×C₇₃	1	2	yes	complemented
721	#385	C₂²×C₇₃	1	2	yes	complemented
722	#385	C₂²×C₇₃	1	2	yes	complemented
723	#384	C₂²×C₇₃	1	1	yes	characteristic, complemented
724	#382	C₂²×C₇₃	1	1	yes	characteristic, complemented
725	#382	C₂²×C₇₃	1	1	yes	characteristic, complemented
726	#380	C₂²×C₇₃	1	1	yes	characteristic
727	#380	C₂²×C₇₃	1	2	yes	complemented
728	#380	C₂²×C₇₃	1	1	yes	characteristic, complemented
729	#379	C₂²×C₇₃	1	2	yes	—
730	C₄×C₂²⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
731	C₄×C₂²⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
732	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	complemented
733	C₄×C₂²⋊C₄	C₂²×C₇₃	1	1	yes	characteristic, complemented
734	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	complemented
735	C₄×C₂²⋊C₄	C₂²×C₇₃	1	1	yes	characteristic, complemented
736	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	complemented
737	C₄³	C₂²×C₇₃	1	1	yes	characteristic, complemented
738	C₂⁵	C₂³×C₇₃	1	2	yes	—
739	C₂×#41	—	2	4	no	—
740	C₂×#41	—	2	4	no	—
741	C₂×#41	—	4	2	no	—
742	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
743	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
744	C₂²×D₄	—	2	4	no	—
745	C₂²×D₄	—	2	4	no	—
746	C₂²×D₄	—	4	2	no	—
747	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
748	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
749	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
750	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
751	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
752	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
753	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
754	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
755	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
756	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
757	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
758	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
759	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
760	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
761	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
762	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
763	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
764	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
765	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
766	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
767	#127	—	2	4	no	—
768	#127	—	2	4	no	—
769	#124	—	2	4	no	—
770	#124	—	2	8	no	—
771	#124	—	2	4	no	—
772	#124	D₄×C₇₃	1	8	yes	complemented
773	#123	—	2	8	no	—
774	#123	—	2	8	no	—
775	#123	—	2	8	no	—
776	#123	—	4	4	no	—
777	C₂²⋊Q₈	—	2	4	no	—
778	#121	—	2	4	no	—
779	#121	—	2	8	no	—
780	#121	—	4	4	no	—
781	#121	—	4	2	no	—
782	#121	—	4	2	no	—
783	#120	—	2	8	no	—
784	#120	—	2	8	no	—
785	#120	—	4	4	no	—
786	C₄×Q₈	—	2	4	no	—
787	C₄×Q₈	—	2	4	no	—
788	C₄×Q₈	—	4	2	no	—
789	C₄×D₄	—	2	4	no	—
790	C₄×D₄	—	2	8	no	—
791	C₄×D₄	—	2	4	no	—
792	C₄×D₄	—	2	4	no	—
793	C₄×D₄	—	2	4	no	—
794	C₄×D₄	—	4	4	no	—
795	C₄×D₄	—	4	2	no	—
796	C₄×D₄	—	4	4	no	—
797	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
798	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
799	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
800	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
801	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
802	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
803	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
804	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
805	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
806	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
807	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
808	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
809	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
810	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
811	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
812	C₂×C₂²⋊C₄	—	2	8	no	—
813	C₂×C₂²⋊C₄	—	4	4	no	—
814	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
815	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
816	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
817	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
818	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
819	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
820	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
821	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
822	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
823	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
824	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
825	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
826	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
827	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
828	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
829	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
830	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
831	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
832	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
833	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
834	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
835	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
836	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
837	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
838	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
839	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
840	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
841	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
842	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
843	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
844	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
845	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
846	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
847	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
848	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
849	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
850	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
851	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
852	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
853	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
854	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
855	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
856	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
857	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
858	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
859	#95	C₂³×C₇₃	1	1	yes	characteristic
860	#95	C₂³×C₇₃	1	1	yes	characteristic
861	#95	C₂³×C₇₃	1	1	yes	characteristic
862	#95	C₂³×C₇₃	1	1	yes	characteristic
863	#95	C₂³×C₇₃	1	1	yes	characteristic
864	#95	C₂³×C₇₃	1	1	yes	characteristic
865	#95	C₂³×C₇₃	1	2	yes	—
866	#95	C₂³×C₇₃	1	2	yes	—
867	#95	C₂³×C₇₃	1	1	yes	characteristic
868	#95	C₂³×C₇₃	1	2	yes	—
869	#95	C₂³×C₇₃	1	1	yes	characteristic
870	#95	C₂³×C₇₃	1	2	yes	—
871	#95	C₂³×C₇₃	1	2	yes	—
872	#95	C₂³×C₇₃	1	2	yes	—
873	#95	C₂³×C₇₃	1	2	yes	—
874	#95	C₂³×C₇₃	1	2	yes	—
875	C₂⁴	—	2	4	no	—
876	C₂⁴	—	2	4	no	—
877	C₂⁴	—	2	4	no	—
878	C₂⁴	—	4	2	no	—
879	C₂⁴	—	4	2	no	—
880	C₂⁴	—	4	2	no	—
881	C₂⁴	—	4	2	no	—
882	C₂⁴	C₂⁴×C₇₃	1	2	yes	—
883	C₂⁴	C₂⁴×C₇₃	1	1	yes	characteristic
884	C₂⁴	C₂⁴×C₇₃	1	2	yes	—
885	C₂⁴	C₂⁴×C₇₃	1	1	yes	characteristic
886	C₂⁴	C₂⁴×C₇₃	1	2	yes	—
887	#41	—	4	16	no	—
888	C₂×Q₈	—	2	2	no	—
889	C₂×Q₈	—	2	2	no	—
890	C₂×Q₈	—	2	2	no	—
891	C₂×Q₈	—	2	2	no	—
892	C₂×Q₈	—	4	1	no	—
893	C₂×Q₈	C₂×D₄×C₇₃	1	4	yes	—
894	C₂×D₄	—	2	4	no	—
895	C₂×D₄	—	2	4	no	—
896	C₂×D₄	—	2	2	no	—
897	C₂×D₄	—	2	4	no	—
898	C₂×D₄	—	2	4	no	—
899	C₂×D₄	—	2	4	no	—
900	C₂×D₄	—	2	4	no	—
901	C₂×D₄	—	2	4	no	—
902	C₂×D₄	—	2	4	no	—
903	C₂×D₄	—	2	4	no	—
904	C₂×D₄	—	2	2	no	—
905	C₂×D₄	—	2	2	no	—
906	C₂×D₄	—	2	2	no	—
907	C₂×D₄	—	2	4	no	—
908	C₂×D₄	—	2	2	no	—
909	C₂×D₄	—	2	4	no	—
910	C₂×D₄	—	2	4	no	—
911	C₂×D₄	—	2	2	no	—
912	C₂×D₄	—	2	2	no	—
913	C₂×D₄	—	2	2	no	—
914	C₂×D₄	—	2	4	no	—
915	C₂×D₄	—	2	2	no	—
916	C₂×D₄	—	4	2	no	—
917	C₂×D₄	—	4	2	no	—
918	C₂×D₄	—	4	2	no	—
919	C₂×D₄	—	4	1	no	—
920	C₂×D₄	—	4	2	no	—
921	C₂×D₄	—	4	2	no	—
922	C₂×D₄	—	4	2	no	—
923	C₂×D₄	—	4	2	no	—
924	C₂×D₄	—	4	2	no	—
925	C₂×D₄	—	4	2	no	—
926	C₂×D₄	—	4	2	no	—
927	C₂×D₄	—	4	2	no	—
928	C₂×D₄	—	4	2	no	—
929	C₂×D₄	—	4	2	no	—
930	C₂×D₄	—	4	2	no	—
931	C₂×D₄	—	4	16	no	—
932	C₂×D₄	C₂×D₄×C₇₃	1	4	yes	—
933	C₂×D₄	#41×C₇₃	1	4	yes	—
934	C₂²×C₄	—	2	4	no	—
935	C₂²×C₄	—	2	4	no	—
936	C₂²×C₄	—	2	4	no	—
937	C₂²×C₄	—	2	2	no	—
938	C₂²×C₄	—	2	2	no	—
939	C₂²×C₄	—	2	2	no	—
940	C₂²×C₄	—	2	2	no	—
941	C₂²×C₄	—	2	2	no	—
942	C₂²×C₄	—	2	2	no	—
943	C₂²×C₄	—	2	4	no	—
944	C₂²×C₄	—	2	4	no	—
945	C₂²×C₄	—	2	4	no	—
946	C₂²×C₄	—	4	2	no	—
947	C₂²×C₄	—	4	2	no	—
948	C₂²×C₄	—	4	2	no	—
949	C₂²×C₄	—	4	2	no	—
950	C₂²×C₄	—	4	2	no	—
951	C₂²×C₄	—	4	2	no	—
952	C₂²×C₄	—	4	2	no	—
953	C₂²×C₄	—	4	2	no	—
954	C₂²×C₄	—	4	2	no	—
955	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
956	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
957	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
958	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
959	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
960	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
961	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
962	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
963	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
964	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
965	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
966	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
967	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
968	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
969	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
970	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
971	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
972	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
973	C₄⋊C₄	—	2	2	no	—
974	C₄⋊C₄	—	2	2	no	—
975	C₄⋊C₄	—	2	2	no	—
976	C₄⋊C₄	—	2	2	no	—
977	C₄⋊C₄	—	2	2	no	—
978	C₄⋊C₄	—	2	4	no	—
979	C₄⋊C₄	—	2	2	no	—
980	C₄⋊C₄	—	2	4	no	—
981	C₄⋊C₄	—	2	2	no	—
982	C₄⋊C₄	—	2	4	no	—
983	C₄⋊C₄	—	2	2	no	—
984	C₄⋊C₄	—	4	2	no	—
985	C₄⋊C₄	—	4	2	no	—
986	C₄⋊C₄	—	4	2	no	—
987	C₄⋊C₄	—	4	2	no	—
988	C₂²⋊C₄	—	2	4	no	—
989	C₂²⋊C₄	—	2	4	no	—
990	C₂²⋊C₄	—	2	2	no	—
991	C₂²⋊C₄	—	2	2	no	—
992	C₂²⋊C₄	—	2	4	no	—
993	C₂²⋊C₄	—	2	4	no	—
994	C₂²⋊C₄	—	2	2	no	—
995	C₂²⋊C₄	—	2	4	no	—
996	C₂²⋊C₄	—	2	4	no	—
997	C₂²⋊C₄	—	2	4	no	—
998	C₂²⋊C₄	—	2	4	no	—
999	C₂²⋊C₄	—	2	4	no	—
1000	C₂²⋊C₄	—	2	2	no	—
1001	C₂²⋊C₄	—	2	2	no	—
1002	C₂²⋊C₄	—	2	2	no	—
1003	C₂²⋊C₄	—	2	4	no	—
1004	C₂²⋊C₄	—	2	4	no	—
1005	C₂²⋊C₄	—	2	2	no	—
1006	C₂²⋊C₄	—	2	4	no	—
1007	C₂²⋊C₄	—	2	2	no	—
1008	C₂²⋊C₄	—	2	2	no	—
1009	C₂²⋊C₄	—	4	2	no	—
1010	C₂²⋊C₄	—	4	2	no	—
1011	C₂²⋊C₄	—	4	2	no	—
1012	C₂²⋊C₄	—	4	2	no	—
1013	C₂²⋊C₄	—	4	2	no	—
1014	C₂²⋊C₄	—	4	2	no	—
1015	C₂²⋊C₄	—	4	2	no	—
1016	C₂²⋊C₄	—	4	2	no	—
1017	C₂²⋊C₄	—	4	2	no	—
1018	C₂²⋊C₄	—	4	2	no	—
1019	C₂²⋊C₄	C₂×D₄×C₇₃	1	8	yes	—
1020	C₂²⋊C₄	C₂×D₄×C₇₃	1	8	yes	—
1021	C₂²⋊C₄	#41×C₇₃	1	4	yes	complemented
1022	C₄²	—	2	4	no	—
1023	C₄²	—	2	2	no	—
1024	C₄²	—	2	2	no	—
1025	C₄²	—	2	2	no	—
1026	C₄²	—	2	2	no	—
1027	C₄²	—	2	2	no	—
1028	C₄²	—	2	2	no	—
1029	C₄²	—	2	2	no	—
1030	C₄²	—	4	1	no	—
1031	C₄²	—	4	2	no	—
1032	C₄²	C₂×D₄×C₇₃	1	4	yes	—
1033	C₂³	—	2	1	no	—
1034	C₂³	—	2	2	no	—
1035	C₂³	—	2	2	no	—
1036	C₂³	—	2	2	no	—
1037	C₂³	—	2	1	no	—
1038	C₂³	—	2	2	no	—
1039	C₂³	—	2	1	no	—
1040	C₂³	—	2	2	no	—
1041	C₂³	—	2	2	no	—
1042	C₂³	—	2	1	no	—
1043	C₂³	—	2	2	no	—
1044	C₂³	—	2	2	no	—
1045	C₂³	—	2	2	no	—
1046	C₂³	—	2	1	no	—
1047	C₂³	—	2	2	no	—
1048	C₂³	—	2	2	no	—
1049	C₂³	—	2	2	no	—
1050	C₂³	—	2	1	no	—
1051	C₂³	—	2	2	no	—
1052	C₂³	—	2	1	no	—
1053	C₂³	—	2	1	no	—
1054	C₂³	—	2	1	no	—
1055	C₂³	—	2	2	no	—
1056	C₂³	—	2	2	no	—
1057	C₂³	—	2	1	no	—
1058	C₂³	—	2	2	no	—
1059	C₂³	—	2	1	no	—
1060	C₂³	—	2	2	no	—
1061	C₂³	—	2	2	no	—
1062	C₂³	—	2	1	no	—
1063	C₂³	—	2	2	no	—
1064	C₂³	—	2	1	no	—
1065	C₂³	—	4	8	no	—
1066	C₂³	—	4	8	no	—
1067	C₂³	—	4	8	no	—
1068	C₂³	—	8	4	no	—
1069	C₂³	—	8	4	no	—
1070	C₂³	—	8	4	no	—
1071	C₂³	—	8	4	no	—
1072	C₂³	C₂²×D₄×C₇₃	1	4	yes	—
1073	C₂³	C₂×#41×C₇₃	1	2	yes	—
1074	C₂³	C₂×#41×C₇₃	1	4	yes	—
1075	C₂³	C₂⁵×C₇₃	1	1	yes	characteristic
1076	Q₈	—	2	8	no	—
1077	Q₈	—	4	4	no	—
1078	D₄	—	2	8	no	—
1079	D₄	—	2	8	no	—
1080	D₄	—	4	8	no	—
1081	D₄	—	4	4	no	—
1082	D₄	—	4	8	no	—
1083	D₄	—	4	8	no	—
1084	D₄	—	4	8	no	—
1085	D₄	—	4	8	no	—
1086	D₄	—	4	4	no	—
1087	D₄	—	8	4	no	—
1088	D₄	—	8	4	no	—
1089	D₄	—	8	4	no	—
1090	D₄	—	8	4	no	—
1091	C₂×C₄	—	2	1	no	—
1092	C₂×C₄	—	2	1	no	—
1093	C₂×C₄	—	2	1	no	—
1094	C₂×C₄	—	2	1	no	—
1095	C₂×C₄	—	2	2	no	—
1096	C₂×C₄	—	2	1	no	—
1097	C₂×C₄	—	2	1	no	—
1098	C₂×C₄	—	2	1	no	—
1099	C₂×C₄	—	2	1	no	—
1100	C₂×C₄	—	2	2	no	—
1101	C₂×C₄	—	2	1	no	—
1102	C₂×C₄	—	2	1	no	—
1103	C₂×C₄	—	2	1	no	—
1104	C₂×C₄	—	2	1	no	—
1105	C₂×C₄	—	2	1	no	—
1106	C₂×C₄	—	2	2	no	—
1107	C₂×C₄	—	2	1	no	—
1108	C₂×C₄	—	2	1	no	—
1109	C₂×C₄	—	2	2	no	—
1110	C₂×C₄	—	2	1	no	—
1111	C₂×C₄	—	2	1	no	—
1112	C₂×C₄	—	2	1	no	—
1113	C₂×C₄	—	2	2	no	—
1114	C₂×C₄	—	2	1	no	—
1115	C₂×C₄	—	2	1	no	—
1116	C₂×C₄	—	2	1	no	—
1117	C₂×C₄	—	2	1	no	—
1118	C₂×C₄	—	2	1	no	—
1119	C₂×C₄	—	2	2	no	—
1120	C₂×C₄	—	2	2	no	—
1121	C₂×C₄	—	2	1	no	—
1122	C₂×C₄	—	2	1	no	—
1123	C₂×C₄	—	2	2	no	—
1124	C₂×C₄	—	2	1	no	—
1125	C₂×C₄	—	2	2	no	—
1126	C₂×C₄	—	2	1	no	—
1127	C₂×C₄	—	2	2	no	—
1128	C₂×C₄	—	2	2	no	—
1129	C₂×C₄	—	2	2	no	—
1130	C₂×C₄	—	2	1	no	—
1131	C₂×C₄	—	2	1	no	—
1132	C₂×C₄	—	2	2	no	—
1133	C₂×C₄	—	2	1	no	—
1134	C₂×C₄	—	2	2	no	—
1135	C₂×C₄	—	4	8	no	—
1136	C₂×C₄	—	4	4	no	—
1137	C₂×C₄	—	4	4	no	—
1138	C₂×C₄	—	8	4	no	—
1139	C₂×C₄	—	8	4	no	—
1140	C₂×C₄	—	8	4	no	—
1141	C₂×C₄	—	8	4	no	—
1142	C₂×C₄	C₂²×D₄×C₇₃	1	4	yes	—
1143	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
1144	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
1145	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
1146	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
1147	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
1148	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
1149	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
1150	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
1151	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
1152	C₂²	—	2	4	no	—
1153	C₂²	—	2	4	no	—
1154	C₂²	—	2	2	no	—
1155	C₂²	—	2	4	no	—
1156	C₂²	—	2	4	no	—
1157	C₂²	—	2	2	no	—
1158	C₂²	—	2	4	no	—
1159	C₂²	—	2	2	no	—
1160	C₂²	—	2	4	no	—
1161	C₂²	—	4	1	no	—
1162	C₂²	—	4	2	no	—
1163	C₂²	—	4	2	no	—
1164	C₂²	—	4	2	no	—
1165	C₂²	—	4	1	no	—
1166	C₂²	—	4	2	no	—
1167	C₂²	—	4	2	no	—
1168	C₂²	—	4	1	no	—
1169	C₂²	—	4	2	no	—
1170	C₂²	—	4	2	no	—
1171	C₂²	—	4	1	no	—
1172	C₂²	—	4	2	no	—
1173	C₂²	—	4	1	no	—
1174	C₂²	—	4	2	no	—
1175	C₂²	—	4	2	no	—
1176	C₂²	—	4	1	no	—
1177	C₂²	—	4	2	no	—
1178	C₂²	—	4	1	no	—
1179	C₂²	—	4	2	no	—
1180	C₂²	—	4	1	no	—
1181	C₂²	—	4	2	no	—
1182	C₂²	—	4	1	no	—
1183	C₂²	—	4	2	no	—
1184	C₂²	—	4	1	no	—
1185	C₂²	—	4	1	no	—
1186	C₂²	—	4	2	no	—
1187	C₂²	—	8	16	no	—
1188	C₂²	C₂³×D₄×C₇₃	1	1	yes	characteristic
1189	C₂²	C₂²×#41×C₇₃	1	1	yes	characteristic
1190	C₂²	C₂²×#41×C₇₃	1	1	yes	characteristic
1191	C₂²	C₂×H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
1192	C₂²	C₂×H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
1193	C₂²	C₂×H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
1194	C₂²	#585×C₇₃	1	1	yes	characteristic
1195	C₄	—	2	4	no	—
1196	C₄	—	2	2	no	—
1197	C₄	—	2	2	no	—
1198	C₄	—	2	2	no	—
1199	C₄	—	2	2	no	—
1200	C₄	—	2	2	no	—
1201	C₄	—	2	2	no	—
1202	C₄	—	4	1	no	—
1203	C₄	—	4	1	no	—
1204	C₄	—	4	1	no	—
1205	C₄	—	4	1	no	—
1206	C₄	—	4	2	no	—
1207	C₄	—	4	2	no	—
1208	C₄	—	4	1	no	—
1209	C₄	—	4	2	no	—
1210	C₄	—	4	1	no	—
1211	C₄	—	4	2	no	—
1212	C₄	#546×C₇₃	1	4	yes	—
1213	C₂	—	4	2	no	—
1214	C₂	—	4	4	no	—
1215	C₂	—	4	4	no	—
1216	C₂	—	8	1	no	—
1217	C₂	—	8	2	no	—
1218	C₂	C₂×#546×C₇₃	1	1	yes	characteristic
1219	C₂	D₄×#41×C₇₃	1	1	yes	characteristic
1220	C₂	C₇₃×#3481	1	1	yes	characteristic
1221	C₂	C₇₃×#3498	1	1	yes	characteristic
1222	C₂	C₇₃×#3508	1	1	yes	characteristic
1223	C₂	C₇₃×#3513	1	1	yes	characteristic
1224	C₂	C₇₃×#3558	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×#559×C₇₃	C₂	semidirect
2. C₂×#546×C₇₃	C₂	semidirect
3. C₇₃×#2706	C₂	semidirect
4. C₇₃×#2670	C₂	semidirect
5. C₇₃×#2580	C₂	semidirect
6. C₇₃×#2557	C₂	semidirect
7. C₇₃×#2539	C₂	semidirect
8. C₇₃×#2535	C₂	semidirect
9. C₇₃×#2464	C₂	semidirect
10. C₇₃×#2456	C₂	semidirect
11. C₇₃×#2433	C₂	semidirect
12. C₇₃×#2431	C₂	semidirect
13. C₇₃×#2428	C₂	semidirect
14. C₇₃×#2426	C₂	semidirect
15. C₇₃×#2423	C₂	semidirect
16. C₇₃×#2422	C₂	semidirect
17. C₇₃×#2418	C₂	semidirect
18. C₇₃×#2358	C₂	semidirect
19. C₇₃×#2341	C₂	semidirect
20. D₄×C₂²⋊C₄×C₇₃	C₂	semidirect
21. C₄×#127×C₇₃	C₂	semidirect
22. C₄×#124×C₇₃	C₂	semidirect
23. C₄×#124×C₇₃	C₂	semidirect
32. C₂×#124×C₇₃	C₂²	semidirect
33. C₂×#124×C₇₃	C₂²	semidirect
35. C₂×#123×C₇₃	C₂²	semidirect
36. C₂×#123×C₇₃	C₂²	semidirect
37. C₂×#123×C₇₃	C₂²	semidirect
42. C₂×#121×C₇₃	C₂²	semidirect
43. C₂×#121×C₇₃	C₂²	semidirect
47. C₂×C₄×Q₈×C₇₃	C₂²	semidirect
48. C₂×C₄×Q₈×C₇₃	C₂²	semidirect
49. C₂×C₄×Q₈×C₇₃	C₂²	semidirect
54. C₂×C₄×D₄×C₇₃	C₂²	semidirect
55. C₂×C₄×D₄×C₇₃	C₂²	semidirect
56. C₂×C₄×D₄×C₇₃	C₂²	semidirect
57. C₂×C₄×D₄×C₇₃	C₂²	semidirect
61. #399×C₇₃	C₂²	semidirect
62. #398×C₇₃	C₂²	semidirect
63. #397×C₇₃	C₂²	semidirect
64. #397×C₇₃	C₂²	semidirect
65. #396×C₇₃	C₂²	semidirect
67. #394×C₇₃	C₂²	semidirect
68. #394×C₇₃	C₂²	semidirect
69. #393×C₇₃	C₂²	semidirect
73. #392×C₇₃	C₂²	semidirect
74. #392×C₇₃	C₂²	semidirect
75. #392×C₇₃	C₂²	semidirect
76. #391×C₇₃	C₂²	semidirect
77. #391×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. #389×C₇₃	C₂²	semidirect
90. #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. #387×C₇₃	C₂²	semidirect
103. #386×C₇₃	C₂²	semidirect
104. #386×C₇₃	C₂²	semidirect
105. #386×C₇₃	C₂²	semidirect
106. #386×C₇₃	C₂²	semidirect
107. #385×C₇₃	C₂²	semidirect
108. #385×C₇₃	C₂²	semidirect
109. #385×C₇₃	C₂²	semidirect
110. #384×C₇₃	C₂²	semidirect
111. #382×C₇₃	C₂²	semidirect
112. #382×C₇₃	C₂²	semidirect
114. #380×C₇₃	C₂²	semidirect
115. #380×C₇₃	C₂²	semidirect
119. C₄×C₂²⋊C₄×C₇₃	C₂²	semidirect
120. C₄×C₂²⋊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. C₄³×C₇₃	C₂²	semidirect
159. #124×C₇₃	D₄	semidirect
408. C₂²⋊C₄×C₇₃	#41	semidirect
600. #59414	C₇₃	direct (N × H)
613. C₂×#559	C₂×C₇₃	semidirect
614. C₂×#546	C₂×C₇₃	semidirect
615. #2706	C₂×C₇₃	semidirect
616. #2670	C₂×C₇₃	semidirect
617. #2580	C₂×C₇₃	semidirect
618. #2557	C₂×C₇₃	semidirect
619. #2539	C₂×C₇₃	semidirect
620. #2535	C₂×C₇₃	semidirect
621. #2464	C₂×C₇₃	semidirect
622. #2456	C₂×C₇₃	semidirect
623. #2433	C₂×C₇₃	semidirect
624. #2431	C₂×C₇₃	semidirect
625. #2428	C₂×C₇₃	semidirect
626. #2426	C₂×C₇₃	semidirect
627. #2423	C₂×C₇₃	semidirect
628. #2422	C₂×C₇₃	semidirect
629. #2418	C₂×C₇₃	semidirect
630. #2358	C₂×C₇₃	semidirect
631. #2341	C₂×C₇₃	semidirect
632. D₄×C₂²⋊C₄	C₂×C₇₃	semidirect
633. C₄×#127	C₂×C₇₃	semidirect
634. C₄×#124	C₂×C₇₃	semidirect
635. C₄×#124	C₂×C₇₃	semidirect
636. C₇₃	#59414	direct (N × H)
645. C₂×#124	C₂²×C₇₃	semidirect
646. C₂×#124	C₂²×C₇₃	semidirect
648. C₂×#123	C₂²×C₇₃	semidirect
649. C₂×#123	C₂²×C₇₃	semidirect
650. C₂×#123	C₂²×C₇₃	semidirect
655. C₂×#121	C₂²×C₇₃	semidirect
656. C₂×#121	C₂²×C₇₃	semidirect
660. C₂×C₄×Q₈	C₂²×C₇₃	semidirect
661. C₂×C₄×Q₈	C₂²×C₇₃	semidirect
662. C₂×C₄×Q₈	C₂²×C₇₃	semidirect
667. C₂×C₄×D₄	C₂²×C₇₃	semidirect
668. C₂×C₄×D₄	C₂²×C₇₃	semidirect
669. C₂×C₄×D₄	C₂²×C₇₃	semidirect
670. C₂×C₄×D₄	C₂²×C₇₃	semidirect
674. #399	C₂²×C₇₃	semidirect
675. #398	C₂²×C₇₃	semidirect
676. #397	C₂²×C₇₃	semidirect
677. #397	C₂²×C₇₃	semidirect
678. #396	C₂²×C₇₃	semidirect
680. #394	C₂²×C₇₃	semidirect
681. #394	C₂²×C₇₃	semidirect
682. #393	C₂²×C₇₃	semidirect
686. #392	C₂²×C₇₃	semidirect
687. #392	C₂²×C₇₃	semidirect
688. #392	C₂²×C₇₃	semidirect
689. #391	C₂²×C₇₃	semidirect
690. #391	C₂²×C₇₃	semidirect
697. #390	C₂²×C₇₃	semidirect
698. #390	C₂²×C₇₃	semidirect
699. #390	C₂²×C₇₃	semidirect
700. #390	C₂²×C₇₃	semidirect
701. #390	C₂²×C₇₃	semidirect
702. #389	C₂²×C₇₃	semidirect
703. #389	C₂²×C₇₃	semidirect
707. #388	C₂²×C₇₃	semidirect
708. #388	C₂²×C₇₃	semidirect
709. #388	C₂²×C₇₃	semidirect
710. #388	C₂²×C₇₃	semidirect
711. #388	C₂²×C₇₃	semidirect
712. #387	C₂²×C₇₃	semidirect
716. #386	C₂²×C₇₃	semidirect
717. #386	C₂²×C₇₃	semidirect
718. #386	C₂²×C₇₃	semidirect
719. #386	C₂²×C₇₃	semidirect
720. #385	C₂²×C₇₃	semidirect
721. #385	C₂²×C₇₃	semidirect
722. #385	C₂²×C₇₃	semidirect
723. #384	C₂²×C₇₃	semidirect
724. #382	C₂²×C₇₃	semidirect
725. #382	C₂²×C₇₃	semidirect
727. #380	C₂²×C₇₃	semidirect
728. #380	C₂²×C₇₃	semidirect
732. C₄×C₂²⋊C₄	C₂²×C₇₃	semidirect
733. C₄×C₂²⋊C₄	C₂²×C₇₃	semidirect
734. C₄×C₂²⋊C₄	C₂²×C₇₃	semidirect
735. C₄×C₂²⋊C₄	C₂²×C₇₃	semidirect
736. C₄×C₂²⋊C₄	C₂²×C₇₃	semidirect
737. C₄³	C₂²×C₇₃	semidirect
772. #124	D₄×C₇₃	semidirect
1021. C₂²⋊C₄	#41×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#559×C₇₃	2
C₂×#546×C₇₃	2
C₇₃×#2706	2
C₇₃×#2670	2
C₇₃×#2580	2
C₇₃×#2557	2
C₇₃×#2539	2
C₇₃×#2535	2
C₇₃×#2464	2
C₇₃×#2456	2
C₇₃×#2433	2
C₇₃×#2431	2
C₇₃×#2428	2
C₇₃×#2426	2
C₇₃×#2423	2
C₇₃×#2422	2
C₇₃×#2418	2
C₇₃×#2358	2
C₇₃×#2341	2
D₄×C₂²⋊C₄×C₇₃	2
C₄×#127×C₇₃	2
C₄×#124×C₇₃	2
#59414	73

Subgroups — C73×#59414 #32968818

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#59414 #32968818