Subgroups — C₇₃×#59820 #32969224

Order 18688.

2650 conjugacy classes of subgroups.

The subgroup lattice has 1152 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#551×C₇₃	C₂	1	2	yes	maximal, complemented
2	C₇₃×#2730	C₂	1	2	yes	maximal, complemented
3	C₇₃×#2705	C₂	1	2	yes	maximal, complemented
4	C₇₃×#2548	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₃×#2538	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₃×#2534	C₂	1	2	yes	maximal, complemented
7	C₇₃×#2512	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₃×#2512	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₃×#2501	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₃×#2471	C₂	1	2	yes	maximal, complemented
11	C₇₃×#2467	C₂	1	2	yes	maximal, complemented
12	C₇₃×#2445	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇₃×#2445	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇₃×#2433	C₂	1	1	yes	maximal, characteristic
15	C₇₃×#2412	C₂	1	2	yes	maximal, complemented
16	C₇₃×#2411	C₂	1	2	yes	maximal, complemented
17	C₇₃×#2366	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇₃×#2354	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇₃×#2344	C₂	1	1	yes	maximal, characteristic, complemented
20	D₄×C₂²⋊C₄×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×C₂²⋊Q₈×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	#551×C₇₃	—	2	16	no	—
26	C₂×#127×C₇₃	C₂²	1	1	yes	characteristic
27	C₂×#127×C₇₃	C₂²	1	1	yes	characteristic
28	C₂×#126×C₇₃	C₂²	1	2	yes	complemented
29	C₂×#126×C₇₃	C₂²	1	2	yes	complemented
30	C₂×#124×C₇₃	C₂²	1	2	yes	complemented
31	C₂×#123×C₇₃	C₂²	1	2	yes	—
32	C₂×#123×C₇₃	C₂²	1	2	yes	—
33	C₂×#123×C₇₃	C₂²	1	2	yes	complemented
34	C₂×#123×C₇₃	C₂²	1	2	yes	complemented
35	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
36	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	2	yes	complemented
37	C₂×#121×C₇₃	C₂²	1	1	yes	characteristic
38	C₂×#120×C₇₃	C₂²	1	2	yes	—
39	C₂×#120×C₇₃	C₂²	1	2	yes	—
40	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₇₃	C₂²	1	2	yes	—
43	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
44	C₂×C₄×D₄×C₇₃	C₂²	1	2	yes	complemented
45	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic, complemented
46	C₂×#117×C₇₃	C₂²	1	2	yes	—
47	C₂×#117×C₇₃	C₂²	1	2	yes	complemented
48	C₂²×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
49	C₂²×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
50	C₂²×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
51	C₂²×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
52	C₂²×C₄²×C₇₃	C₂²	1	1	yes	characteristic
53	#399×C₇₃	C₂²	1	2	yes	complemented
54	#399×C₇₃	C₂²	1	2	yes	complemented
55	#397×C₇₃	C₂²	1	2	yes	complemented
56	#397×C₇₃	C₂²	1	2	yes	complemented
57	#396×C₇₃	C₂²	1	2	yes	complemented
58	#396×C₇₃	C₂²	1	2	yes	complemented
59	#396×C₇₃	C₂²	1	2	yes	complemented
60	#396×C₇₃	C₂²	1	2	yes	complemented
61	#394×C₇₃	C₂²	1	2	yes	complemented
62	#394×C₇₃	C₂²	1	2	yes	complemented
63	#394×C₇₃	C₂²	1	2	yes	complemented
64	#394×C₇₃	C₂²	1	2	yes	complemented
65	#394×C₇₃	C₂²	1	2	yes	complemented
66	#394×C₇₃	C₂²	1	2	yes	complemented
67	#392×C₇₃	C₂²	1	2	yes	—
68	#392×C₇₃	C₂²	1	2	yes	—
69	#391×C₇₃	C₂²	1	1	yes	characteristic, complemented
70	#390×C₇₃	C₂²	1	1	yes	characteristic
71	#390×C₇₃	C₂²	1	1	yes	characteristic
72	#390×C₇₃	C₂²	1	1	yes	characteristic
73	#390×C₇₃	C₂²	1	2	yes	—
74	#390×C₇₃	C₂²	1	2	yes	—
75	#390×C₇₃	C₂²	1	1	yes	characteristic
76	#390×C₇₃	C₂²	1	1	yes	characteristic
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	2	yes	complemented
83	#390×C₇₃	C₂²	1	2	yes	complemented
84	#390×C₇₃	C₂²	1	1	yes	characteristic, complemented
85	#389×C₇₃	C₂²	1	1	yes	characteristic, complemented
86	#389×C₇₃	C₂²	1	1	yes	characteristic, complemented
87	#389×C₇₃	C₂²	1	1	yes	characteristic, complemented
88	#389×C₇₃	C₂²	1	1	yes	characteristic, complemented
89	#388×C₇₃	C₂²	1	2	yes	complemented
90	#388×C₇₃	C₂²	1	2	yes	complemented
91	#388×C₇₃	C₂²	1	2	yes	complemented
92	#388×C₇₃	C₂²	1	2	yes	complemented
93	#388×C₇₃	C₂²	1	2	yes	complemented
94	#387×C₇₃	C₂²	1	2	yes	complemented
95	#387×C₇₃	C₂²	1	1	yes	characteristic, complemented
96	#387×C₇₃	C₂²	1	1	yes	characteristic, complemented
97	#387×C₇₃	C₂²	1	2	yes	complemented
98	#386×C₇₃	C₂²	1	2	yes	—
99	#386×C₇₃	C₂²	1	2	yes	—
100	#386×C₇₃	C₂²	1	2	yes	—
101	#386×C₇₃	C₂²	1	2	yes	complemented
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	#385×C₇₃	C₂²	1	1	yes	characteristic
106	#385×C₇₃	C₂²	1	1	yes	characteristic
107	#384×C₇₃	C₂²	1	1	yes	characteristic, complemented
108	#384×C₇₃	C₂²	1	1	yes	characteristic, complemented
109	#381×C₇₃	C₂²	1	2	yes	—
110	#380×C₇₃	C₂²	1	1	yes	characteristic
111	#380×C₇₃	C₂²	1	1	yes	characteristic
112	#380×C₇₃	C₂²	1	2	yes	complemented
113	#380×C₇₃	C₂²	1	2	yes	complemented
114	#379×C₇₃	C₂²	1	2	yes	—
115	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic, complemented
116	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic, complemented
117	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic, complemented
118	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic, 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
122	C₄×C₂²⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
123	C₄×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	complemented
124	C₂⁵×C₇₃	C₂³	1	2	yes	—
125	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
126	C₂²×D₄×C₇₃	—	2	4	no	—
127	C₂²×D₄×C₇₃	—	2	4	no	—
128	C₂²×D₄×C₇₃	—	4	2	no	—
129	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
130	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
131	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
132	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
133	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
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	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
139	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
140	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
141	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
142	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
143	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
144	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
145	#127×C₇₃	—	2	4	no	—
146	#127×C₇₃	—	4	2	no	—
147	#126×C₇₃	—	2	8	no	—
148	#126×C₇₃	—	2	8	no	—
149	#124×C₇₃	—	2	8	no	—
150	#123×C₇₃	—	2	8	no	—
151	#123×C₇₃	—	2	8	no	—
152	#123×C₇₃	—	2	8	no	—
153	#123×C₇₃	—	4	4	no	—
154	C₂²⋊Q₈×C₇₃	—	2	8	no	—
155	C₂²⋊Q₈×C₇₃	D₄	1	8	yes	complemented
156	#121×C₇₃	—	2	4	no	—
157	#120×C₇₃	—	2	8	no	—
158	#120×C₇₃	—	4	4	no	—
159	C₄×Q₈×C₇₃	—	4	2	no	—
160	C₄×D₄×C₇₃	—	2	4	no	—
161	C₄×D₄×C₇₃	—	2	8	no	—
162	C₄×D₄×C₇₃	—	2	8	no	—
163	C₄×D₄×C₇₃	—	4	2	no	—
164	C₄×D₄×C₇₃	—	4	2	no	—
165	#117×C₇₃	—	2	8	no	—
166	#117×C₇₃	—	2	8	no	—
167	C₂×C₄⋊C₄×C₇₃	—	2	4	no	—
168	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
169	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
170	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
171	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
172	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
173	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
174	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
175	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
176	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
177	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
178	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
179	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
180	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
181	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
182	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
183	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
184	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
185	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
186	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
187	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
188	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
189	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
190	C₂×C₂²⋊C₄×C₇₃	—	2	8	no	—
191	C₂×C₂²⋊C₄×C₇₃	—	2	8	no	—
192	C₂×C₂²⋊C₄×C₇₃	—	4	4	no	—
193	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
194	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
195	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
196	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
197	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
198	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
199	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
200	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
201	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
202	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
203	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
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	2	yes	—
208	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
209	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
210	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
211	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
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	2	yes	—
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	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	1	yes	characteristic
223	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
224	C₂×C₄²×C₇₃	—	4	2	no	—
225	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
226	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
227	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
228	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
229	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
230	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
231	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
232	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
233	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
234	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
235	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
236	#95×C₇₃	C₂³	1	1	yes	characteristic
237	#95×C₇₃	C₂³	1	1	yes	characteristic
238	#95×C₇₃	C₂³	1	1	yes	characteristic
239	#95×C₇₃	C₂³	1	1	yes	characteristic
240	#95×C₇₃	C₂³	1	2	yes	—
241	#95×C₇₃	C₂³	1	2	yes	—
242	#95×C₇₃	C₂³	1	1	yes	characteristic
243	#95×C₇₃	C₂³	1	1	yes	characteristic
244	#95×C₇₃	C₂³	1	2	yes	—
245	#95×C₇₃	C₂³	1	2	yes	—
246	#95×C₇₃	C₂³	1	2	yes	—
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	2	yes	—
252	#95×C₇₃	C₂³	1	2	yes	—
253	C₂⁴×C₇₃	—	2	4	no	—
254	C₂⁴×C₇₃	—	2	4	no	—
255	C₂⁴×C₇₃	—	2	4	no	—
256	C₂⁴×C₇₃	—	2	4	no	—
257	C₂⁴×C₇₃	—	4	2	no	—
258	C₂⁴×C₇₃	—	4	2	no	—
259	C₂⁴×C₇₃	—	4	2	no	—
260	C₂⁴×C₇₃	C₂⁴	1	2	yes	—
261	C₂⁴×C₇₃	C₂⁴	1	2	yes	—
262	C₂⁴×C₇₃	C₂⁴	1	2	yes	—
263	C₂⁴×C₇₃	C₂⁴	1	1	yes	characteristic
264	C₂×Q₈×C₇₃	—	4	1	no	—
265	C₂×Q₈×C₇₃	—	4	1	no	—
266	C₂×Q₈×C₇₃	C₂×D₄	1	4	yes	complemented
267	C₂×D₄×C₇₃	—	2	4	no	—
268	C₂×D₄×C₇₃	—	2	4	no	—
269	C₂×D₄×C₇₃	—	2	4	no	—
270	C₂×D₄×C₇₃	—	2	4	no	—
271	C₂×D₄×C₇₃	—	2	4	no	—
272	C₂×D₄×C₇₃	—	2	4	no	—
273	C₂×D₄×C₇₃	—	2	4	no	—
274	C₂×D₄×C₇₃	—	2	4	no	—
275	C₂×D₄×C₇₃	—	2	2	no	—
276	C₂×D₄×C₇₃	—	2	2	no	—
277	C₂×D₄×C₇₃	—	2	2	no	—
278	C₂×D₄×C₇₃	—	2	4	no	—
279	C₂×D₄×C₇₃	—	2	2	no	—
280	C₂×D₄×C₇₃	—	2	2	no	—
281	C₂×D₄×C₇₃	—	2	2	no	—
282	C₂×D₄×C₇₃	—	2	2	no	—
283	C₂×D₄×C₇₃	—	2	2	no	—
284	C₂×D₄×C₇₃	—	4	16	no	—
285	C₂×D₄×C₇₃	—	4	2	no	—
286	C₂×D₄×C₇₃	—	4	2	no	—
287	C₂×D₄×C₇₃	—	4	2	no	—
288	C₂×D₄×C₇₃	—	4	2	no	—
289	C₂×D₄×C₇₃	—	4	2	no	—
290	C₂×D₄×C₇₃	—	4	2	no	—
291	C₂×D₄×C₇₃	—	4	2	no	—
292	C₂×D₄×C₇₃	—	4	2	no	—
293	C₂×D₄×C₇₃	—	4	2	no	—
294	C₂×D₄×C₇₃	#41	1	4	yes	—
295	C₂²×C₄×C₇₃	—	2	2	no	—
296	C₂²×C₄×C₇₃	—	2	2	no	—
297	C₂²×C₄×C₇₃	—	2	4	no	—
298	C₂²×C₄×C₇₃	—	2	4	no	—
299	C₂²×C₄×C₇₃	—	2	4	no	—
300	C₂²×C₄×C₇₃	—	2	2	no	—
301	C₂²×C₄×C₇₃	—	2	4	no	—
302	C₂²×C₄×C₇₃	—	2	4	no	—
303	C₂²×C₄×C₇₃	—	2	4	no	—
304	C₂²×C₄×C₇₃	—	2	4	no	—
305	C₂²×C₄×C₇₃	—	4	1	no	—
306	C₂²×C₄×C₇₃	—	4	1	no	—
307	C₂²×C₄×C₇₃	—	4	2	no	—
308	C₂²×C₄×C₇₃	—	4	1	no	—
309	C₂²×C₄×C₇₃	—	4	1	no	—
310	C₂²×C₄×C₇₃	—	4	2	no	—
311	C₂²×C₄×C₇₃	—	4	2	no	—
312	C₂²×C₄×C₇₃	—	4	2	no	—
313	C₂²×C₄×C₇₃	—	4	2	no	—
314	C₂²×C₄×C₇₃	C₂×D₄	1	4	yes	—
315	C₂²×C₄×C₇₃	#41	1	4	yes	—
316	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
317	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
318	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
319	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
320	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
321	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
322	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
323	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
324	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
325	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
326	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
327	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
328	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
329	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
330	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
331	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
332	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
333	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
334	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
335	C₄⋊C₄×C₇₃	—	2	4	no	—
336	C₄⋊C₄×C₇₃	—	2	4	no	—
337	C₄⋊C₄×C₇₃	—	2	4	no	—
338	C₄⋊C₄×C₇₃	—	2	4	no	—
339	C₄⋊C₄×C₇₃	—	2	4	no	—
340	C₄⋊C₄×C₇₃	—	2	4	no	—
341	C₄⋊C₄×C₇₃	—	2	2	no	—
342	C₄⋊C₄×C₇₃	—	2	2	no	—
343	C₄⋊C₄×C₇₃	—	2	2	no	—
344	C₄⋊C₄×C₇₃	—	2	2	no	—
345	C₄⋊C₄×C₇₃	—	2	2	no	—
346	C₄⋊C₄×C₇₃	—	4	1	no	—
347	C₄⋊C₄×C₇₃	—	4	1	no	—
348	C₄⋊C₄×C₇₃	—	4	1	no	—
349	C₄⋊C₄×C₇₃	—	4	1	no	—
350	C₄⋊C₄×C₇₃	—	4	1	no	—
351	C₄⋊C₄×C₇₃	—	4	1	no	—
352	C₄⋊C₄×C₇₃	—	4	2	no	—
353	C₄⋊C₄×C₇₃	—	4	2	no	—
354	C₄⋊C₄×C₇₃	C₂×D₄	1	4	yes	complemented
355	C₄⋊C₄×C₇₃	C₂×D₄	1	4	yes	complemented
356	C₄⋊C₄×C₇₃	C₂×D₄	1	4	yes	complemented
357	C₂²⋊C₄×C₇₃	—	2	4	no	—
358	C₂²⋊C₄×C₇₃	—	2	4	no	—
359	C₂²⋊C₄×C₇₃	—	2	2	no	—
360	C₂²⋊C₄×C₇₃	—	2	2	no	—
361	C₂²⋊C₄×C₇₃	—	2	4	no	—
362	C₂²⋊C₄×C₇₃	—	2	4	no	—
363	C₂²⋊C₄×C₇₃	—	2	4	no	—
364	C₂²⋊C₄×C₇₃	—	2	4	no	—
365	C₂²⋊C₄×C₇₃	—	2	4	no	—
366	C₂²⋊C₄×C₇₃	—	2	4	no	—
367	C₂²⋊C₄×C₇₃	—	2	4	no	—
368	C₂²⋊C₄×C₇₃	—	2	4	no	—
369	C₂²⋊C₄×C₇₃	—	2	4	no	—
370	C₂²⋊C₄×C₇₃	—	2	4	no	—
371	C₂²⋊C₄×C₇₃	—	2	4	no	—
372	C₂²⋊C₄×C₇₃	—	2	4	no	—
373	C₂²⋊C₄×C₇₃	—	4	2	no	—
374	C₂²⋊C₄×C₇₃	—	4	2	no	—
375	C₂²⋊C₄×C₇₃	—	4	2	no	—
376	C₂²⋊C₄×C₇₃	—	4	2	no	—
377	C₂²⋊C₄×C₇₃	—	4	2	no	—
378	C₂²⋊C₄×C₇₃	—	4	2	no	—
379	C₂²⋊C₄×C₇₃	—	4	2	no	—
380	C₂²⋊C₄×C₇₃	—	4	2	no	—
381	C₂²⋊C₄×C₇₃	—	4	2	no	—
382	C₂²⋊C₄×C₇₃	—	4	2	no	—
383	C₂²⋊C₄×C₇₃	—	4	2	no	—
384	C₂²⋊C₄×C₇₃	—	4	2	no	—
385	C₂²⋊C₄×C₇₃	—	4	2	no	—
386	C₂²⋊C₄×C₇₃	C₂×D₄	1	4	yes	—
387	C₂²⋊C₄×C₇₃	C₂×D₄	1	4	yes	—
388	C₄²×C₇₃	—	2	4	no	—
389	C₄²×C₇₃	—	2	4	no	—
390	C₄²×C₇₃	—	2	4	no	—
391	C₄²×C₇₃	—	2	2	no	—
392	C₄²×C₇₃	—	2	2	no	—
393	C₄²×C₇₃	—	2	2	no	—
394	C₄²×C₇₃	—	2	2	no	—
395	C₄²×C₇₃	—	2	2	no	—
396	C₄²×C₇₃	—	2	2	no	—
397	C₄²×C₇₃	—	4	1	no	—
398	C₄²×C₇₃	—	4	1	no	—
399	C₂³×C₇₃	—	2	1	no	—
400	C₂³×C₇₃	—	2	1	no	—
401	C₂³×C₇₃	—	2	1	no	—
402	C₂³×C₇₃	—	2	1	no	—
403	C₂³×C₇₃	—	2	2	no	—
404	C₂³×C₇₃	—	2	2	no	—
405	C₂³×C₇₃	—	2	2	no	—
406	C₂³×C₇₃	—	2	2	no	—
407	C₂³×C₇₃	—	2	2	no	—
408	C₂³×C₇₃	—	2	2	no	—
409	C₂³×C₇₃	—	2	2	no	—
410	C₂³×C₇₃	—	2	2	no	—
411	C₂³×C₇₃	—	2	2	no	—
412	C₂³×C₇₃	—	2	2	no	—
413	C₂³×C₇₃	—	2	2	no	—
414	C₂³×C₇₃	—	2	2	no	—
415	C₂³×C₇₃	—	2	2	no	—
416	C₂³×C₇₃	—	2	2	no	—
417	C₂³×C₇₃	—	2	2	no	—
418	C₂³×C₇₃	—	2	2	no	—
419	C₂³×C₇₃	—	2	2	no	—
420	C₂³×C₇₃	—	2	2	no	—
421	C₂³×C₇₃	—	2	2	no	—
422	C₂³×C₇₃	—	2	2	no	—
423	C₂³×C₇₃	—	4	8	no	—
424	C₂³×C₇₃	—	4	8	no	—
425	C₂³×C₇₃	—	4	8	no	—
426	C₂³×C₇₃	—	4	8	no	—
427	C₂³×C₇₃	—	8	4	no	—
428	C₂³×C₇₃	—	8	4	no	—
429	C₂³×C₇₃	—	8	4	no	—
430	C₂³×C₇₃	C₂²×D₄	1	2	yes	—
431	C₂³×C₇₃	C₂×#41	1	4	yes	—
432	C₂³×C₇₃	C₂×#41	1	2	yes	—
433	C₂³×C₇₃	H(5,𝔽₂)	1	2	yes	—
434	C₂³×C₇₃	C₂⁵	1	1	yes	characteristic
435	Q₈×C₇₃	—	4	4	no	—
436	D₄×C₇₃	—	2	8	no	—
437	D₄×C₇₃	—	4	8	no	—
438	D₄×C₇₃	—	4	8	no	—
439	D₄×C₇₃	—	4	8	no	—
440	D₄×C₇₃	—	4	4	no	—
441	D₄×C₇₃	—	4	4	no	—
442	D₄×C₇₃	—	8	4	no	—
443	D₄×C₇₃	—	8	4	no	—
444	D₄×C₇₃	—	8	4	no	—
445	C₂×C₄×C₇₃	—	2	1	no	—
446	C₂×C₄×C₇₃	—	2	1	no	—
447	C₂×C₄×C₇₃	—	2	1	no	—
448	C₂×C₄×C₇₃	—	2	1	no	—
449	C₂×C₄×C₇₃	—	2	1	no	—
450	C₂×C₄×C₇₃	—	2	1	no	—
451	C₂×C₄×C₇₃	—	2	1	no	—
452	C₂×C₄×C₇₃	—	2	1	no	—
453	C₂×C₄×C₇₃	—	2	1	no	—
454	C₂×C₄×C₇₃	—	2	1	no	—
455	C₂×C₄×C₇₃	—	2	1	no	—
456	C₂×C₄×C₇₃	—	2	1	no	—
457	C₂×C₄×C₇₃	—	2	1	no	—
458	C₂×C₄×C₇₃	—	2	1	no	—
459	C₂×C₄×C₇₃	—	2	8	no	—
460	C₂×C₄×C₇₃	—	2	2	no	—
461	C₂×C₄×C₇₃	—	2	2	no	—
462	C₂×C₄×C₇₃	—	2	2	no	—
463	C₂×C₄×C₇₃	—	2	2	no	—
464	C₂×C₄×C₇₃	—	2	2	no	—
465	C₂×C₄×C₇₃	—	2	1	no	—
466	C₂×C₄×C₇₃	—	2	1	no	—
467	C₂×C₄×C₇₃	—	2	2	no	—
468	C₂×C₄×C₇₃	—	2	2	no	—
469	C₂×C₄×C₇₃	—	2	2	no	—
470	C₂×C₄×C₇₃	—	2	2	no	—
471	C₂×C₄×C₇₃	—	2	1	no	—
472	C₂×C₄×C₇₃	—	2	1	no	—
473	C₂×C₄×C₇₃	—	2	1	no	—
474	C₂×C₄×C₇₃	—	2	1	no	—
475	C₂×C₄×C₇₃	—	2	1	no	—
476	C₂×C₄×C₇₃	—	2	1	no	—
477	C₂×C₄×C₇₃	—	2	1	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	2	no	—
482	C₂×C₄×C₇₃	—	2	2	no	—
483	C₂×C₄×C₇₃	—	2	2	no	—
484	C₂×C₄×C₇₃	—	2	2	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	2	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	—	4	4	no	—
494	C₂×C₄×C₇₃	—	4	8	no	—
495	C₂×C₄×C₇₃	—	4	4	no	—
496	C₂×C₄×C₇₃	—	4	8	no	—
497	C₂×C₄×C₇₃	—	8	4	no	—
498	C₂×C₄×C₇₃	—	8	4	no	—
499	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
500	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
501	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
502	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
503	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
504	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
505	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
506	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
507	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
508	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
509	C₂²×C₇₃	—	2	2	no	—
510	C₂²×C₇₃	—	2	2	no	—
511	C₂²×C₇₃	—	2	2	no	—
512	C₂²×C₇₃	—	2	2	no	—
513	C₂²×C₇₃	—	2	2	no	—
514	C₂²×C₇₃	—	2	2	no	—
515	C₂²×C₇₃	—	2	4	no	—
516	C₂²×C₇₃	—	2	4	no	—
517	C₂²×C₇₃	—	2	4	no	—
518	C₂²×C₇₃	—	4	2	no	—
519	C₂²×C₇₃	—	4	2	no	—
520	C₂²×C₇₃	—	4	2	no	—
521	C₂²×C₇₃	—	4	2	no	—
522	C₂²×C₇₃	—	4	2	no	—
523	C₂²×C₇₃	—	4	2	no	—
524	C₂²×C₇₃	—	4	2	no	—
525	C₂²×C₇₃	—	4	2	no	—
526	C₂²×C₇₃	—	4	2	no	—
527	C₂²×C₇₃	—	4	2	no	—
528	C₂²×C₇₃	—	4	2	no	—
529	C₂²×C₇₃	—	4	2	no	—
530	C₂²×C₇₃	—	4	2	no	—
531	C₂²×C₇₃	—	4	2	no	—
532	C₂²×C₇₃	—	4	2	no	—
533	C₂²×C₇₃	—	4	2	no	—
534	C₂²×C₇₃	—	4	2	no	—
535	C₂²×C₇₃	—	4	2	no	—
536	C₂²×C₇₃	—	8	16	no	—
537	C₂²×C₇₃	#550	1	4	yes	—
538	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
539	C₂²×C₇₃	C₂²×#41	1	1	yes	characteristic
540	C₂²×C₇₃	C₂²×#41	1	1	yes	characteristic
541	C₂²×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
542	C₂²×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
543	C₂²×C₇₃	#585	1	1	yes	characteristic
544	C₂²×C₇₃	#585	1	1	yes	characteristic
545	C₄×C₇₃	—	2	2	no	—
546	C₄×C₇₃	—	2	2	no	—
547	C₄×C₇₃	—	2	2	no	—
548	C₄×C₇₃	—	2	2	no	—
549	C₄×C₇₃	—	2	2	no	—
550	C₄×C₇₃	—	2	2	no	—
551	C₄×C₇₃	—	2	2	no	—
552	C₄×C₇₃	—	4	2	no	—
553	C₄×C₇₃	—	4	2	no	—
554	C₄×C₇₃	—	4	2	no	—
555	C₄×C₇₃	—	4	2	no	—
556	C₄×C₇₃	—	4	2	no	—
557	C₄×C₇₃	—	4	1	no	—
558	C₄×C₇₃	—	4	1	no	—
559	C₄×C₇₃	—	4	1	no	—
560	C₄×C₇₃	—	4	1	no	—
561	C₄×C₇₃	—	4	1	no	—
562	C₄×C₇₃	—	4	1	no	—
563	C₄×C₇₃	#551	1	4	yes	complemented
564	#59820	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
565	C₂×C₇₃	—	2	4	no	—
566	C₂×C₇₃	—	4	4	no	—
567	C₂×C₇₃	—	8	2	no	—
568	C₂×C₇₃	—	8	2	no	—
569	C₂×C₇₃	C₂×#550	1	1	yes	characteristic
570	C₂×C₇₃	D₄×#41	1	1	yes	characteristic
571	C₂×C₇₃	C₂×#551	1	1	yes	characteristic
572	C₂×C₇₃	#3496	1	1	yes	characteristic
573	C₂×C₇₃	#3510	1	1	yes	characteristic
574	C₂×C₇₃	#3513	1	1	yes	characteristic
575	C₂×C₇₃	#3542	1	1	yes	characteristic
576	C₂×#551	C₂×C₇₃	1	2	yes	complemented
577	#2730	C₂×C₇₃	1	2	yes	complemented
578	#2705	C₂×C₇₃	1	2	yes	complemented
579	#2548	C₂×C₇₃	1	1	yes	characteristic, complemented
580	#2538	C₂×C₇₃	1	1	yes	characteristic, complemented
581	#2534	C₂×C₇₃	1	2	yes	complemented
582	#2512	C₂×C₇₃	1	1	yes	characteristic, complemented
583	#2512	C₂×C₇₃	1	1	yes	characteristic, complemented
584	#2501	C₂×C₇₃	1	1	yes	characteristic, complemented
585	#2471	C₂×C₇₃	1	2	yes	complemented
586	#2467	C₂×C₇₃	1	2	yes	complemented
587	#2445	C₂×C₇₃	1	1	yes	characteristic, complemented
588	#2445	C₂×C₇₃	1	1	yes	characteristic, complemented
589	#2433	C₂×C₇₃	1	1	yes	characteristic
590	#2412	C₂×C₇₃	1	2	yes	complemented
591	#2411	C₂×C₇₃	1	2	yes	complemented
592	#2366	C₂×C₇₃	1	1	yes	characteristic, complemented
593	#2354	C₂×C₇₃	1	1	yes	characteristic, complemented
594	#2344	C₂×C₇₃	1	1	yes	characteristic, complemented
595	D₄×C₂²⋊C₄	C₂×C₇₃	1	1	yes	characteristic, complemented
596	C₄×C₂²⋊Q₈	C₂×C₇₃	1	1	yes	characteristic, complemented
597	C₄×#121	C₂×C₇₃	1	1	yes	characteristic, complemented
598	C₂×#390	C₂×C₇₃	1	1	yes	characteristic, complemented
599	C₇₃	#59820	1	1	yes	characteristic, direct product factor, Sylow
600	C₂³×D₄	C₂²×C₇₃	1	1	yes	characteristic
601	#551	—	2	16	no	—
602	C₂×#127	C₂²×C₇₃	1	1	yes	characteristic
603	C₂×#127	C₂²×C₇₃	1	1	yes	characteristic
604	C₂×#126	C₂²×C₇₃	1	2	yes	complemented
605	C₂×#126	C₂²×C₇₃	1	2	yes	complemented
606	C₂×#124	C₂²×C₇₃	1	2	yes	complemented
607	C₂×#123	C₂²×C₇₃	1	2	yes	—
608	C₂×#123	C₂²×C₇₃	1	2	yes	—
609	C₂×#123	C₂²×C₇₃	1	2	yes	complemented
610	C₂×#123	C₂²×C₇₃	1	2	yes	complemented
611	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
612	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	2	yes	complemented
613	C₂×#121	C₂²×C₇₃	1	1	yes	characteristic
614	C₂×#120	C₂²×C₇₃	1	2	yes	—
615	C₂×#120	C₂²×C₇₃	1	2	yes	—
616	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic, complemented
617	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
618	C₂×C₄×D₄	C₂²×C₇₃	1	2	yes	—
619	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
620	C₂×C₄×D₄	C₂²×C₇₃	1	2	yes	complemented
621	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic, complemented
622	C₂×#117	C₂²×C₇₃	1	2	yes	—
623	C₂×#117	C₂²×C₇₃	1	2	yes	complemented
624	C₂²×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
625	C₂²×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
626	C₂²×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
627	C₂²×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
628	C₂²×C₄²	C₂²×C₇₃	1	1	yes	characteristic
629	#399	C₂²×C₇₃	1	2	yes	complemented
630	#399	C₂²×C₇₃	1	2	yes	complemented
631	#397	C₂²×C₇₃	1	2	yes	complemented
632	#397	C₂²×C₇₃	1	2	yes	complemented
633	#396	C₂²×C₇₃	1	2	yes	complemented
634	#396	C₂²×C₇₃	1	2	yes	complemented
635	#396	C₂²×C₇₃	1	2	yes	complemented
636	#396	C₂²×C₇₃	1	2	yes	complemented
637	#394	C₂²×C₇₃	1	2	yes	complemented
638	#394	C₂²×C₇₃	1	2	yes	complemented
639	#394	C₂²×C₇₃	1	2	yes	complemented
640	#394	C₂²×C₇₃	1	2	yes	complemented
641	#394	C₂²×C₇₃	1	2	yes	complemented
642	#394	C₂²×C₇₃	1	2	yes	complemented
643	#392	C₂²×C₇₃	1	2	yes	—
644	#392	C₂²×C₇₃	1	2	yes	—
645	#391	C₂²×C₇₃	1	1	yes	characteristic, complemented
646	#390	C₂²×C₇₃	1	1	yes	characteristic
647	#390	C₂²×C₇₃	1	1	yes	characteristic
648	#390	C₂²×C₇₃	1	1	yes	characteristic
649	#390	C₂²×C₇₃	1	1	yes	characteristic
650	#390	C₂²×C₇₃	1	1	yes	characteristic
651	#390	C₂²×C₇₃	1	1	yes	characteristic
652	#390	C₂²×C₇₃	1	1	yes	characteristic
653	#390	C₂²×C₇₃	1	2	yes	—
654	#390	C₂²×C₇₃	1	2	yes	—
655	#390	C₂²×C₇₃	1	1	yes	characteristic
656	#390	C₂²×C₇₃	1	2	yes	complemented
657	#390	C₂²×C₇₃	1	1	yes	characteristic, complemented
658	#390	C₂²×C₇₃	1	2	yes	complemented
659	#390	C₂²×C₇₃	1	1	yes	characteristic, complemented
660	#390	C₂²×C₇₃	1	1	yes	characteristic, complemented
661	#389	C₂²×C₇₃	1	1	yes	characteristic, complemented
662	#389	C₂²×C₇₃	1	1	yes	characteristic, complemented
663	#389	C₂²×C₇₃	1	1	yes	characteristic, complemented
664	#389	C₂²×C₇₃	1	1	yes	characteristic, complemented
665	#388	C₂²×C₇₃	1	2	yes	complemented
666	#388	C₂²×C₇₃	1	2	yes	complemented
667	#388	C₂²×C₇₃	1	2	yes	complemented
668	#388	C₂²×C₇₃	1	2	yes	complemented
669	#388	C₂²×C₇₃	1	2	yes	complemented
670	#387	C₂²×C₇₃	1	2	yes	complemented
671	#387	C₂²×C₇₃	1	2	yes	complemented
672	#387	C₂²×C₇₃	1	1	yes	characteristic, complemented
673	#387	C₂²×C₇₃	1	1	yes	characteristic, complemented
674	#386	C₂²×C₇₃	1	2	yes	—
675	#386	C₂²×C₇₃	1	2	yes	—
676	#386	C₂²×C₇₃	1	2	yes	—
677	#386	C₂²×C₇₃	1	2	yes	complemented
678	#386	C₂²×C₇₃	1	2	yes	complemented
679	#386	C₂²×C₇₃	1	2	yes	complemented
680	#386	C₂²×C₇₃	1	2	yes	complemented
681	#385	C₂²×C₇₃	1	1	yes	characteristic
682	#385	C₂²×C₇₃	1	1	yes	characteristic
683	#384	C₂²×C₇₃	1	1	yes	characteristic, complemented
684	#384	C₂²×C₇₃	1	1	yes	characteristic, complemented
685	#381	C₂²×C₇₃	1	2	yes	—
686	#380	C₂²×C₇₃	1	1	yes	characteristic
687	#380	C₂²×C₇₃	1	1	yes	characteristic
688	#380	C₂²×C₇₃	1	2	yes	complemented
689	#380	C₂²×C₇₃	1	2	yes	complemented
690	#379	C₂²×C₇₃	1	2	yes	—
691	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic, complemented
692	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic, complemented
693	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic, complemented
694	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic, complemented
695	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic, complemented
696	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic, complemented
697	C₄×C₂²⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
698	C₄×C₂²⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
699	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	complemented
700	C₂⁵	C₂³×C₇₃	1	2	yes	—
701	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
702	C₂²×D₄	—	2	4	no	—
703	C₂²×D₄	—	2	4	no	—
704	C₂²×D₄	—	4	2	no	—
705	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
706	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
707	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
708	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
709	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
710	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
711	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
712	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
713	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
714	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
715	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
716	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
717	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
718	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
719	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
720	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
721	#127	—	2	4	no	—
722	#127	—	4	2	no	—
723	#126	—	2	8	no	—
724	#126	—	2	8	no	—
725	#124	—	2	8	no	—
726	#123	—	2	8	no	—
727	#123	—	2	8	no	—
728	#123	—	2	8	no	—
729	#123	—	4	4	no	—
730	C₂²⋊Q₈	—	2	8	no	—
731	C₂²⋊Q₈	D₄×C₇₃	1	8	yes	complemented
732	#121	—	2	4	no	—
733	#120	—	2	8	no	—
734	#120	—	4	4	no	—
735	C₄×Q₈	—	4	2	no	—
736	C₄×D₄	—	2	4	no	—
737	C₄×D₄	—	2	8	no	—
738	C₄×D₄	—	2	8	no	—
739	C₄×D₄	—	4	2	no	—
740	C₄×D₄	—	4	2	no	—
741	#117	—	2	8	no	—
742	#117	—	2	8	no	—
743	C₂×C₄⋊C₄	—	2	4	no	—
744	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
745	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
746	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
747	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
748	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
749	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
750	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
751	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
752	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
753	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
754	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
755	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
756	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
757	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
758	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
759	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
760	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
761	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
762	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
763	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
764	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
765	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
766	C₂×C₂²⋊C₄	—	2	8	no	—
767	C₂×C₂²⋊C₄	—	2	8	no	—
768	C₂×C₂²⋊C₄	—	4	4	no	—
769	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
770	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
771	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
772	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
773	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
774	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
775	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
776	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
777	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
778	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
779	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
780	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
781	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
782	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
783	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
784	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
785	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
786	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
787	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
788	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
789	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
790	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
791	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
792	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
793	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
794	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
795	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
796	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
797	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
798	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
799	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
800	C₂×C₄²	—	4	2	no	—
801	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
802	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
803	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
804	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
805	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
806	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
807	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
808	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
809	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
810	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
811	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
812	#95	C₂³×C₇₃	1	1	yes	characteristic
813	#95	C₂³×C₇₃	1	1	yes	characteristic
814	#95	C₂³×C₇₃	1	1	yes	characteristic
815	#95	C₂³×C₇₃	1	1	yes	characteristic
816	#95	C₂³×C₇₃	1	2	yes	—
817	#95	C₂³×C₇₃	1	2	yes	—
818	#95	C₂³×C₇₃	1	1	yes	characteristic
819	#95	C₂³×C₇₃	1	1	yes	characteristic
820	#95	C₂³×C₇₃	1	2	yes	—
821	#95	C₂³×C₇₃	1	2	yes	—
822	#95	C₂³×C₇₃	1	2	yes	—
823	#95	C₂³×C₇₃	1	1	yes	characteristic
824	#95	C₂³×C₇₃	1	1	yes	characteristic
825	#95	C₂³×C₇₃	1	1	yes	characteristic
826	#95	C₂³×C₇₃	1	1	yes	characteristic
827	#95	C₂³×C₇₃	1	2	yes	—
828	#95	C₂³×C₇₃	1	2	yes	—
829	C₂⁴	—	2	4	no	—
830	C₂⁴	—	2	4	no	—
831	C₂⁴	—	2	4	no	—
832	C₂⁴	—	2	4	no	—
833	C₂⁴	—	4	2	no	—
834	C₂⁴	—	4	2	no	—
835	C₂⁴	—	4	2	no	—
836	C₂⁴	C₂⁴×C₇₃	1	2	yes	—
837	C₂⁴	C₂⁴×C₇₃	1	2	yes	—
838	C₂⁴	C₂⁴×C₇₃	1	2	yes	—
839	C₂⁴	C₂⁴×C₇₃	1	1	yes	characteristic
840	C₂×Q₈	—	4	1	no	—
841	C₂×Q₈	—	4	1	no	—
842	C₂×Q₈	C₂×D₄×C₇₃	1	4	yes	complemented
843	C₂×D₄	—	2	4	no	—
844	C₂×D₄	—	2	4	no	—
845	C₂×D₄	—	2	4	no	—
846	C₂×D₄	—	2	4	no	—
847	C₂×D₄	—	2	4	no	—
848	C₂×D₄	—	2	4	no	—
849	C₂×D₄	—	2	4	no	—
850	C₂×D₄	—	2	4	no	—
851	C₂×D₄	—	2	2	no	—
852	C₂×D₄	—	2	2	no	—
853	C₂×D₄	—	2	2	no	—
854	C₂×D₄	—	2	4	no	—
855	C₂×D₄	—	2	2	no	—
856	C₂×D₄	—	2	2	no	—
857	C₂×D₄	—	2	2	no	—
858	C₂×D₄	—	2	2	no	—
859	C₂×D₄	—	2	2	no	—
860	C₂×D₄	—	4	16	no	—
861	C₂×D₄	—	4	2	no	—
862	C₂×D₄	—	4	2	no	—
863	C₂×D₄	—	4	2	no	—
864	C₂×D₄	—	4	2	no	—
865	C₂×D₄	—	4	2	no	—
866	C₂×D₄	—	4	2	no	—
867	C₂×D₄	—	4	2	no	—
868	C₂×D₄	—	4	2	no	—
869	C₂×D₄	—	4	2	no	—
870	C₂×D₄	#41×C₇₃	1	4	yes	—
871	C₂²×C₄	—	2	2	no	—
872	C₂²×C₄	—	2	2	no	—
873	C₂²×C₄	—	2	4	no	—
874	C₂²×C₄	—	2	4	no	—
875	C₂²×C₄	—	2	4	no	—
876	C₂²×C₄	—	2	2	no	—
877	C₂²×C₄	—	2	4	no	—
878	C₂²×C₄	—	2	4	no	—
879	C₂²×C₄	—	2	4	no	—
880	C₂²×C₄	—	2	4	no	—
881	C₂²×C₄	—	4	1	no	—
882	C₂²×C₄	—	4	1	no	—
883	C₂²×C₄	—	4	2	no	—
884	C₂²×C₄	—	4	1	no	—
885	C₂²×C₄	—	4	1	no	—
886	C₂²×C₄	—	4	2	no	—
887	C₂²×C₄	—	4	2	no	—
888	C₂²×C₄	—	4	2	no	—
889	C₂²×C₄	—	4	2	no	—
890	C₂²×C₄	C₂×D₄×C₇₃	1	4	yes	—
891	C₂²×C₄	#41×C₇₃	1	4	yes	—
892	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
893	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
894	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
895	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
896	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
897	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
898	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
899	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
900	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
901	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
902	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
903	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
904	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
905	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
906	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
907	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
908	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
909	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
910	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
911	C₄⋊C₄	—	2	4	no	—
912	C₄⋊C₄	—	2	4	no	—
913	C₄⋊C₄	—	2	4	no	—
914	C₄⋊C₄	—	2	4	no	—
915	C₄⋊C₄	—	2	4	no	—
916	C₄⋊C₄	—	2	4	no	—
917	C₄⋊C₄	—	2	2	no	—
918	C₄⋊C₄	—	2	2	no	—
919	C₄⋊C₄	—	2	2	no	—
920	C₄⋊C₄	—	2	2	no	—
921	C₄⋊C₄	—	2	2	no	—
922	C₄⋊C₄	—	4	1	no	—
923	C₄⋊C₄	—	4	1	no	—
924	C₄⋊C₄	—	4	1	no	—
925	C₄⋊C₄	—	4	1	no	—
926	C₄⋊C₄	—	4	1	no	—
927	C₄⋊C₄	—	4	1	no	—
928	C₄⋊C₄	—	4	2	no	—
929	C₄⋊C₄	—	4	2	no	—
930	C₄⋊C₄	C₂×D₄×C₇₃	1	4	yes	complemented
931	C₄⋊C₄	C₂×D₄×C₇₃	1	4	yes	complemented
932	C₄⋊C₄	C₂×D₄×C₇₃	1	4	yes	complemented
933	C₂²⋊C₄	—	2	4	no	—
934	C₂²⋊C₄	—	2	4	no	—
935	C₂²⋊C₄	—	2	2	no	—
936	C₂²⋊C₄	—	2	2	no	—
937	C₂²⋊C₄	—	2	4	no	—
938	C₂²⋊C₄	—	2	4	no	—
939	C₂²⋊C₄	—	2	4	no	—
940	C₂²⋊C₄	—	2	4	no	—
941	C₂²⋊C₄	—	2	4	no	—
942	C₂²⋊C₄	—	2	4	no	—
943	C₂²⋊C₄	—	2	4	no	—
944	C₂²⋊C₄	—	2	4	no	—
945	C₂²⋊C₄	—	2	4	no	—
946	C₂²⋊C₄	—	2	4	no	—
947	C₂²⋊C₄	—	2	4	no	—
948	C₂²⋊C₄	—	2	4	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	—	4	2	no	—
956	C₂²⋊C₄	—	4	2	no	—
957	C₂²⋊C₄	—	4	2	no	—
958	C₂²⋊C₄	—	4	2	no	—
959	C₂²⋊C₄	—	4	2	no	—
960	C₂²⋊C₄	—	4	2	no	—
961	C₂²⋊C₄	—	4	2	no	—
962	C₂²⋊C₄	C₂×D₄×C₇₃	1	4	yes	—
963	C₂²⋊C₄	C₂×D₄×C₇₃	1	4	yes	—
964	C₄²	—	2	4	no	—
965	C₄²	—	2	4	no	—
966	C₄²	—	2	4	no	—
967	C₄²	—	2	2	no	—
968	C₄²	—	2	2	no	—
969	C₄²	—	2	2	no	—
970	C₄²	—	2	2	no	—
971	C₄²	—	2	2	no	—
972	C₄²	—	2	2	no	—
973	C₄²	—	4	1	no	—
974	C₄²	—	4	1	no	—
975	C₂³	—	2	1	no	—
976	C₂³	—	2	1	no	—
977	C₂³	—	2	1	no	—
978	C₂³	—	2	1	no	—
979	C₂³	—	2	2	no	—
980	C₂³	—	2	2	no	—
981	C₂³	—	2	2	no	—
982	C₂³	—	2	2	no	—
983	C₂³	—	2	2	no	—
984	C₂³	—	2	2	no	—
985	C₂³	—	2	2	no	—
986	C₂³	—	2	2	no	—
987	C₂³	—	2	2	no	—
988	C₂³	—	2	2	no	—
989	C₂³	—	2	2	no	—
990	C₂³	—	2	2	no	—
991	C₂³	—	2	2	no	—
992	C₂³	—	2	2	no	—
993	C₂³	—	2	2	no	—
994	C₂³	—	2	2	no	—
995	C₂³	—	2	2	no	—
996	C₂³	—	2	2	no	—
997	C₂³	—	2	2	no	—
998	C₂³	—	2	2	no	—
999	C₂³	—	4	8	no	—
1000	C₂³	—	4	8	no	—
1001	C₂³	—	4	8	no	—
1002	C₂³	—	4	8	no	—
1003	C₂³	—	8	4	no	—
1004	C₂³	—	8	4	no	—
1005	C₂³	—	8	4	no	—
1006	C₂³	C₂²×D₄×C₇₃	1	2	yes	—
1007	C₂³	C₂×#41×C₇₃	1	4	yes	—
1008	C₂³	C₂×#41×C₇₃	1	2	yes	—
1009	C₂³	H(5,𝔽₂)×C₇₃	1	2	yes	—
1010	C₂³	C₂⁵×C₇₃	1	1	yes	characteristic
1011	Q₈	—	4	4	no	—
1012	D₄	—	2	8	no	—
1013	D₄	—	4	8	no	—
1014	D₄	—	4	8	no	—
1015	D₄	—	4	8	no	—
1016	D₄	—	4	4	no	—
1017	D₄	—	4	4	no	—
1018	D₄	—	8	4	no	—
1019	D₄	—	8	4	no	—
1020	D₄	—	8	4	no	—
1021	C₂×C₄	—	2	1	no	—
1022	C₂×C₄	—	2	1	no	—
1023	C₂×C₄	—	2	1	no	—
1024	C₂×C₄	—	2	1	no	—
1025	C₂×C₄	—	2	1	no	—
1026	C₂×C₄	—	2	1	no	—
1027	C₂×C₄	—	2	1	no	—
1028	C₂×C₄	—	2	1	no	—
1029	C₂×C₄	—	2	1	no	—
1030	C₂×C₄	—	2	1	no	—
1031	C₂×C₄	—	2	1	no	—
1032	C₂×C₄	—	2	1	no	—
1033	C₂×C₄	—	2	1	no	—
1034	C₂×C₄	—	2	1	no	—
1035	C₂×C₄	—	2	8	no	—
1036	C₂×C₄	—	2	2	no	—
1037	C₂×C₄	—	2	2	no	—
1038	C₂×C₄	—	2	2	no	—
1039	C₂×C₄	—	2	2	no	—
1040	C₂×C₄	—	2	2	no	—
1041	C₂×C₄	—	2	1	no	—
1042	C₂×C₄	—	2	1	no	—
1043	C₂×C₄	—	2	2	no	—
1044	C₂×C₄	—	2	2	no	—
1045	C₂×C₄	—	2	2	no	—
1046	C₂×C₄	—	2	2	no	—
1047	C₂×C₄	—	2	1	no	—
1048	C₂×C₄	—	2	1	no	—
1049	C₂×C₄	—	2	1	no	—
1050	C₂×C₄	—	2	1	no	—
1051	C₂×C₄	—	2	1	no	—
1052	C₂×C₄	—	2	1	no	—
1053	C₂×C₄	—	2	1	no	—
1054	C₂×C₄	—	2	1	no	—
1055	C₂×C₄	—	2	1	no	—
1056	C₂×C₄	—	2	1	no	—
1057	C₂×C₄	—	2	2	no	—
1058	C₂×C₄	—	2	2	no	—
1059	C₂×C₄	—	2	2	no	—
1060	C₂×C₄	—	2	2	no	—
1061	C₂×C₄	—	2	1	no	—
1062	C₂×C₄	—	2	1	no	—
1063	C₂×C₄	—	2	2	no	—
1064	C₂×C₄	—	2	1	no	—
1065	C₂×C₄	—	2	2	no	—
1066	C₂×C₄	—	2	1	no	—
1067	C₂×C₄	—	2	1	no	—
1068	C₂×C₄	—	2	1	no	—
1069	C₂×C₄	—	4	4	no	—
1070	C₂×C₄	—	4	8	no	—
1071	C₂×C₄	—	4	4	no	—
1072	C₂×C₄	—	4	8	no	—
1073	C₂×C₄	—	8	4	no	—
1074	C₂×C₄	—	8	4	no	—
1075	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
1076	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
1077	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
1078	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
1079	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
1080	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
1081	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
1082	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
1083	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
1084	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
1085	C₂²	—	2	2	no	—
1086	C₂²	—	2	2	no	—
1087	C₂²	—	2	2	no	—
1088	C₂²	—	2	2	no	—
1089	C₂²	—	2	2	no	—
1090	C₂²	—	2	2	no	—
1091	C₂²	—	2	4	no	—
1092	C₂²	—	2	4	no	—
1093	C₂²	—	2	4	no	—
1094	C₂²	—	4	2	no	—
1095	C₂²	—	4	2	no	—
1096	C₂²	—	4	2	no	—
1097	C₂²	—	4	2	no	—
1098	C₂²	—	4	2	no	—
1099	C₂²	—	4	2	no	—
1100	C₂²	—	4	2	no	—
1101	C₂²	—	4	2	no	—
1102	C₂²	—	4	2	no	—
1103	C₂²	—	4	2	no	—
1104	C₂²	—	4	2	no	—
1105	C₂²	—	4	2	no	—
1106	C₂²	—	4	2	no	—
1107	C₂²	—	4	2	no	—
1108	C₂²	—	4	2	no	—
1109	C₂²	—	4	2	no	—
1110	C₂²	—	4	2	no	—
1111	C₂²	—	4	2	no	—
1112	C₂²	—	8	16	no	—
1113	C₂²	#550×C₇₃	1	4	yes	—
1114	C₂²	C₂³×D₄×C₇₃	1	1	yes	characteristic
1115	C₂²	C₂²×#41×C₇₃	1	1	yes	characteristic
1116	C₂²	C₂²×#41×C₇₃	1	1	yes	characteristic
1117	C₂²	C₂×H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
1118	C₂²	C₂×H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
1119	C₂²	#585×C₇₃	1	1	yes	characteristic
1120	C₂²	#585×C₇₃	1	1	yes	characteristic
1121	C₄	—	2	2	no	—
1122	C₄	—	2	2	no	—
1123	C₄	—	2	2	no	—
1124	C₄	—	2	2	no	—
1125	C₄	—	2	2	no	—
1126	C₄	—	2	2	no	—
1127	C₄	—	2	2	no	—
1128	C₄	—	4	2	no	—
1129	C₄	—	4	2	no	—
1130	C₄	—	4	2	no	—
1131	C₄	—	4	2	no	—
1132	C₄	—	4	2	no	—
1133	C₄	—	4	1	no	—
1134	C₄	—	4	1	no	—
1135	C₄	—	4	1	no	—
1136	C₄	—	4	1	no	—
1137	C₄	—	4	1	no	—
1138	C₄	—	4	1	no	—
1139	C₄	#551×C₇₃	1	4	yes	complemented
1140	C₂	—	2	4	no	—
1141	C₂	—	4	4	no	—
1142	C₂	—	8	2	no	—
1143	C₂	—	8	2	no	—
1144	C₂	C₂×#550×C₇₃	1	1	yes	characteristic
1145	C₂	D₄×#41×C₇₃	1	1	yes	characteristic
1146	C₂	C₂×#551×C₇₃	1	1	yes	characteristic
1147	C₂	C₇₃×#3496	1	1	yes	characteristic
1148	C₂	C₇₃×#3510	1	1	yes	characteristic
1149	C₂	C₇₃×#3513	1	1	yes	characteristic
1150	C₂	C₇₃×#3542	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇₃
prime radical	C₇₃×#2433	C₂
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×#551×C₇₃	C₂	semidirect
2. C₇₃×#2730	C₂	semidirect
3. C₇₃×#2705	C₂	semidirect
4. C₇₃×#2548	C₂	semidirect
5. C₇₃×#2538	C₂	semidirect
6. C₇₃×#2534	C₂	semidirect
7. C₇₃×#2512	C₂	semidirect
8. C₇₃×#2512	C₂	semidirect
9. C₇₃×#2501	C₂	semidirect
10. C₇₃×#2471	C₂	semidirect
11. C₇₃×#2467	C₂	semidirect
12. C₇₃×#2445	C₂	semidirect
13. C₇₃×#2445	C₂	semidirect
15. C₇₃×#2412	C₂	semidirect
16. C₇₃×#2411	C₂	semidirect
17. C₇₃×#2366	C₂	semidirect
18. C₇₃×#2354	C₂	semidirect
19. C₇₃×#2344	C₂	semidirect
20. D₄×C₂²⋊C₄×C₇₃	C₂	semidirect
21. C₄×C₂²⋊Q₈×C₇₃	C₂	semidirect
22. C₄×#121×C₇₃	C₂	semidirect
23. C₂×#390×C₇₃	C₂	semidirect
28. C₂×#126×C₇₃	C₂²	semidirect
29. C₂×#126×C₇₃	C₂²	semidirect
30. C₂×#124×C₇₃	C₂²	semidirect
33. C₂×#123×C₇₃	C₂²	semidirect
34. C₂×#123×C₇₃	C₂²	semidirect
36. C₂×C₂²⋊Q₈×C₇₃	C₂²	semidirect
40. C₂×C₄×Q₈×C₇₃	C₂²	semidirect
44. C₂×C₄×D₄×C₇₃	C₂²	semidirect
45. C₂×C₄×D₄×C₇₃	C₂²	semidirect
47. C₂×#117×C₇₃	C₂²	semidirect
53. #399×C₇₃	C₂²	semidirect
54. #399×C₇₃	C₂²	semidirect
55. #397×C₇₃	C₂²	semidirect
56. #397×C₇₃	C₂²	semidirect
57. #396×C₇₃	C₂²	semidirect
58. #396×C₇₃	C₂²	semidirect
59. #396×C₇₃	C₂²	semidirect
60. #396×C₇₃	C₂²	semidirect
61. #394×C₇₃	C₂²	semidirect
62. #394×C₇₃	C₂²	semidirect
63. #394×C₇₃	C₂²	semidirect
64. #394×C₇₃	C₂²	semidirect
65. #394×C₇₃	C₂²	semidirect
66. #394×C₇₃	C₂²	semidirect
69. #391×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. #389×C₇₃	C₂²	semidirect
86. #389×C₇₃	C₂²	semidirect
87. #389×C₇₃	C₂²	semidirect
88. #389×C₇₃	C₂²	semidirect
89. #388×C₇₃	C₂²	semidirect
90. #388×C₇₃	C₂²	semidirect
91. #388×C₇₃	C₂²	semidirect
92. #388×C₇₃	C₂²	semidirect
93. #388×C₇₃	C₂²	semidirect
94. #387×C₇₃	C₂²	semidirect
95. #387×C₇₃	C₂²	semidirect
96. #387×C₇₃	C₂²	semidirect
97. #387×C₇₃	C₂²	semidirect
101. #386×C₇₃	C₂²	semidirect
102. #386×C₇₃	C₂²	semidirect
103. #386×C₇₃	C₂²	semidirect
104. #386×C₇₃	C₂²	semidirect
107. #384×C₇₃	C₂²	semidirect
108. #384×C₇₃	C₂²	semidirect
112. #380×C₇₃	C₂²	semidirect
113. #380×C₇₃	C₂²	semidirect
115. C₄×C₄⋊C₄×C₇₃	C₂²	semidirect
116. C₄×C₄⋊C₄×C₇₃	C₂²	semidirect
117. C₄×C₄⋊C₄×C₇₃	C₂²	semidirect
118. C₄×C₄⋊C₄×C₇₃	C₂²	semidirect
119. C₄×C₄⋊C₄×C₇₃	C₂²	semidirect
120. C₄×C₄⋊C₄×C₇₃	C₂²	semidirect
123. C₄×C₂²⋊C₄×C₇₃	C₂²	semidirect
155. C₂²⋊Q₈×C₇₃	D₄	semidirect
266. C₂×Q₈×C₇₃	C₂×D₄	semidirect
354. C₄⋊C₄×C₇₃	C₂×D₄	semidirect
355. C₄⋊C₄×C₇₃	C₂×D₄	semidirect
356. C₄⋊C₄×C₇₃	C₂×D₄	semidirect
563. C₄×C₇₃	#551	semidirect
564. #59820	C₇₃	direct (N × H)
576. C₂×#551	C₂×C₇₃	semidirect
577. #2730	C₂×C₇₃	semidirect
578. #2705	C₂×C₇₃	semidirect
579. #2548	C₂×C₇₃	semidirect
580. #2538	C₂×C₇₃	semidirect
581. #2534	C₂×C₇₃	semidirect
582. #2512	C₂×C₇₃	semidirect
583. #2512	C₂×C₇₃	semidirect
584. #2501	C₂×C₇₃	semidirect
585. #2471	C₂×C₇₃	semidirect
586. #2467	C₂×C₇₃	semidirect
587. #2445	C₂×C₇₃	semidirect
588. #2445	C₂×C₇₃	semidirect
590. #2412	C₂×C₇₃	semidirect
591. #2411	C₂×C₇₃	semidirect
592. #2366	C₂×C₇₃	semidirect
593. #2354	C₂×C₇₃	semidirect
594. #2344	C₂×C₇₃	semidirect
595. D₄×C₂²⋊C₄	C₂×C₇₃	semidirect
596. C₄×C₂²⋊Q₈	C₂×C₇₃	semidirect
597. C₄×#121	C₂×C₇₃	semidirect
598. C₂×#390	C₂×C₇₃	semidirect
599. C₇₃	#59820	direct (N × H)
604. C₂×#126	C₂²×C₇₃	semidirect
605. C₂×#126	C₂²×C₇₃	semidirect
606. C₂×#124	C₂²×C₇₃	semidirect
609. C₂×#123	C₂²×C₇₃	semidirect
610. C₂×#123	C₂²×C₇₃	semidirect
612. C₂×C₂²⋊Q₈	C₂²×C₇₃	semidirect
616. C₂×C₄×Q₈	C₂²×C₇₃	semidirect
620. C₂×C₄×D₄	C₂²×C₇₃	semidirect
621. C₂×C₄×D₄	C₂²×C₇₃	semidirect
623. C₂×#117	C₂²×C₇₃	semidirect
629. #399	C₂²×C₇₃	semidirect
630. #399	C₂²×C₇₃	semidirect
631. #397	C₂²×C₇₃	semidirect
632. #397	C₂²×C₇₃	semidirect
633. #396	C₂²×C₇₃	semidirect
634. #396	C₂²×C₇₃	semidirect
635. #396	C₂²×C₇₃	semidirect
636. #396	C₂²×C₇₃	semidirect
637. #394	C₂²×C₇₃	semidirect
638. #394	C₂²×C₇₃	semidirect
639. #394	C₂²×C₇₃	semidirect
640. #394	C₂²×C₇₃	semidirect
641. #394	C₂²×C₇₃	semidirect
642. #394	C₂²×C₇₃	semidirect
645. #391	C₂²×C₇₃	semidirect
656. #390	C₂²×C₇₃	semidirect
657. #390	C₂²×C₇₃	semidirect
658. #390	C₂²×C₇₃	semidirect
659. #390	C₂²×C₇₃	semidirect
660. #390	C₂²×C₇₃	semidirect
661. #389	C₂²×C₇₃	semidirect
662. #389	C₂²×C₇₃	semidirect
663. #389	C₂²×C₇₃	semidirect
664. #389	C₂²×C₇₃	semidirect
665. #388	C₂²×C₇₃	semidirect
666. #388	C₂²×C₇₃	semidirect
667. #388	C₂²×C₇₃	semidirect
668. #388	C₂²×C₇₃	semidirect
669. #388	C₂²×C₇₃	semidirect
670. #387	C₂²×C₇₃	semidirect
671. #387	C₂²×C₇₃	semidirect
672. #387	C₂²×C₇₃	semidirect
673. #387	C₂²×C₇₃	semidirect
677. #386	C₂²×C₇₃	semidirect
678. #386	C₂²×C₇₃	semidirect
679. #386	C₂²×C₇₃	semidirect
680. #386	C₂²×C₇₃	semidirect
683. #384	C₂²×C₇₃	semidirect
684. #384	C₂²×C₇₃	semidirect
688. #380	C₂²×C₇₃	semidirect
689. #380	C₂²×C₇₃	semidirect
691. C₄×C₄⋊C₄	C₂²×C₇₃	semidirect
692. C₄×C₄⋊C₄	C₂²×C₇₃	semidirect
693. C₄×C₄⋊C₄	C₂²×C₇₃	semidirect
694. C₄×C₄⋊C₄	C₂²×C₇₃	semidirect
695. C₄×C₄⋊C₄	C₂²×C₇₃	semidirect
696. C₄×C₄⋊C₄	C₂²×C₇₃	semidirect
699. C₄×C₂²⋊C₄	C₂²×C₇₃	semidirect
731. C₂²⋊Q₈	D₄×C₇₃	semidirect
842. C₂×Q₈	C₂×D₄×C₇₃	semidirect
930. C₄⋊C₄	C₂×D₄×C₇₃	semidirect
931. C₄⋊C₄	C₂×D₄×C₇₃	semidirect
932. C₄⋊C₄	C₂×D₄×C₇₃	semidirect
1139. C₄	#551×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#551×C₇₃	2
C₇₃×#2730	2
C₇₃×#2705	2
C₇₃×#2548	2
C₇₃×#2538	2
C₇₃×#2534	2
C₇₃×#2512	2
C₇₃×#2501	2
C₇₃×#2471	2
C₇₃×#2467	2
C₇₃×#2445	2
C₇₃×#2433	2
C₇₃×#2412	2
C₇₃×#2411	2
C₇₃×#2366	2
C₇₃×#2354	2
C₇₃×#2344	2
D₄×C₂²⋊C₄×C₇₃	2
C₄×C₂²⋊Q₈×C₇₃	2
C₄×#121×C₇₃	2
C₂×#390×C₇₃	2
#59820	73

Subgroups — C73×#59820 #32969224

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#59820 #32969224