Subgroups — C₇₃×#62597 #32972001

Order 18688.

1704 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×#3559	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₃×#3552	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₃×#3376	C₂	1	2	yes	maximal, complemented
4	C₇₃×#3372	C₂	1	2	yes	maximal, complemented
5	C₇₃×#3320	C₂	1	2	yes	maximal, complemented
6	C₇₃×#3320	C₂	1	2	yes	maximal, complemented
7	C₇₃×#3308	C₂	1	2	yes	maximal, complemented
8	C₇₃×#3307	C₂	1	2	yes	maximal, complemented
9	C₇₃×#3301	C₂	1	2	yes	maximal, complemented
10	C₇₃×#3298	C₂	1	2	yes	maximal, complemented
11	C₇₃×#3242	C₂	1	2	yes	maximal, complemented
12	C₇₃×#3232	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇₃×#3221	C₂	1	2	yes	maximal, complemented
14	C₇₃×#3206	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₃×#3180	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇₃×#3174	C₂	1	2	yes	maximal, complemented
17	C₇₃×#3137	C₂	1	2	yes	maximal, complemented
18	C₂×#491×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇₃×#2968	C₂	1	1	yes	maximal, characteristic, complemented
20	#563×C₇₃	—	2	2	no	—
21	#563×C₇₃	—	2	1	no	—
22	#562×C₇₃	—	2	1	no	—
23	#557×C₇₃	C₂²	1	1	yes	characteristic
24	#556×C₇₃	C₂²	1	1	yes	characteristic
25	#554×C₇₃	—	2	1	no	—
26	#554×C₇₃	C₂²	1	2	yes	—
27	#553×C₇₃	—	2	1	no	—
28	#553×C₇₃	C₂²	1	2	yes	—
29	#553×C₇₃	C₂²	1	2	yes	—
30	D₄×Q₈×C₇₃	C₂²	1	2	yes	—
31	D₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
32	#548×C₇₃	C₂²	1	2	yes	—
33	#547×C₇₃	—	2	2	no	—
34	#547×C₇₃	C₂²	1	1	yes	characteristic
35	#547×C₇₃	C₂²	1	2	yes	—
36	#544×C₇₃	—	2	1	no	—
37	#544×C₇₃	C₂²	1	2	yes	—
38	#542×C₇₃	—	2	1	no	—
39	#541×C₇₃	C₂²	1	2	yes	—
40	#540×C₇₃	C₂²	1	2	yes	—
41	#539×C₇₃	—	2	2	no	—
42	#539×C₇₃	—	2	2	no	—
43	#539×C₇₃	—	2	1	no	—
44	#537×C₇₃	—	2	1	no	—
45	#536×C₇₃	C₂²	1	2	yes	—
46	#532×C₇₃	C₂²	1	1	yes	characteristic
47	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
48	#529×C₇₃	C₂²	1	1	yes	characteristic
49	#529×C₇₃	C₂²	1	1	yes	characteristic
50	C₂×#125×C₇₃	C₂²	1	1	yes	characteristic
51	#501×C₇₃	C₂²	1	1	yes	characteristic
52	#499×C₇₃	C₂²	1	2	yes	—
53	#496×C₇₃	C₂²	1	1	yes	characteristic
54	#492×C₇₃	C₂²	1	2	yes	—
55	#491×C₇₃	C₂²	1	2	yes	—
56	#491×C₇₃	C₂²	1	2	yes	—
57	#491×C₇₃	C₂²	1	2	yes	—
58	#491×C₇₃	C₂²	1	2	yes	—
59	#491×C₇₃	C₂²	1	2	yes	—
60	#490×C₇₃	C₂²	1	1	yes	characteristic
61	#489×C₇₃	C₂²	1	2	yes	—
62	#489×C₇₃	C₂²	1	1	yes	characteristic
63	#488×C₇₃	C₂²	1	2	yes	—
64	#488×C₇₃	C₂²	1	2	yes	—
65	#487×C₇₃	C₂²	1	2	yes	—
66	#487×C₇₃	C₂²	1	2	yes	—
67	#485×C₇₃	C₂²	1	2	yes	—
68	#485×C₇₃	C₂²	1	2	yes	—
69	#484×C₇₃	C₂²	1	1	yes	characteristic
70	#484×C₇₃	C₂²	1	2	yes	—
71	#483×C₇₃	C₂²	1	1	yes	characteristic
72	#483×C₇₃	C₂²	1	2	yes	—
73	#481×C₇₃	C₂²	1	1	yes	characteristic
74	#480×C₇₃	C₂²	1	1	yes	characteristic
75	#479×C₇₃	C₂²	1	2	yes	—
76	#479×C₇₃	C₂²	1	2	yes	—
77	#479×C₇₃	C₂²	1	2	yes	—
78	#478×C₇₃	C₂²	1	2	yes	—
79	#477×C₇₃	C₂²	1	2	yes	—
80	#475×C₇₃	C₂²	1	2	yes	—
81	#468×C₇₃	C₂²	1	2	yes	—
82	#468×C₇₃	C₂²	1	2	yes	—
83	#466×C₇₃	C₂²	1	2	yes	—
84	#465×C₇₃	C₂²	1	2	yes	—
85	#465×C₇₃	C₂²	1	2	yes	—
86	#465×C₇₃	C₂²	1	2	yes	—
87	#463×C₇₃	C₂²	1	2	yes	—
88	#463×C₇₃	C₂²	1	2	yes	—
89	#461×C₇₃	C₂²	1	2	yes	—
90	#461×C₇₃	C₂²	1	2	yes	—
91	#461×C₇₃	C₂²	1	2	yes	—
92	#461×C₇₃	C₂²	1	2	yes	—
93	#449×C₇₃	C₂²	1	2	yes	—
94	#449×C₇₃	C₂²	1	2	yes	—
95	#448×C₇₃	C₂²	1	2	yes	—
96	#448×C₇₃	C₂²	1	2	yes	—
97	#448×C₇₃	C₂²	1	2	yes	—
98	#448×C₇₃	C₂²	1	2	yes	—
99	#446×C₇₃	C₂²	1	2	yes	—
100	#442×C₇₃	C₂²	1	2	yes	—
101	#440×C₇₃	C₂²	1	2	yes	—
102	#440×C₇₃	C₂²	1	2	yes	—
103	#440×C₇₃	C₂²	1	2	yes	—
104	C₄×SD₁₆×C₇₃	C₂²	1	2	yes	—
105	C₄×SD₁₆×C₇₃	C₂²	1	2	yes	—
106	#435×C₇₃	C₂²	1	2	yes	—
107	#435×C₇₃	C₂²	1	2	yes	—
108	C₈×D₄×C₇₃	C₂²	1	2	yes	—
109	#433×C₇₃	C₂²	1	2	yes	—
110	#431×C₇₃	C₂²	1	1	yes	characteristic
111	#419×C₇₃	C₂²	1	2	yes	—
112	#417×C₇₃	C₂²	1	2	yes	—
113	#416×C₇₃	C₂²	1	2	yes	—
114	C₂×#103×C₇₃	C₂²	1	2	yes	—
115	C₂×#103×C₇₃	C₂²	1	2	yes	—
116	C₂×#103×C₇₃	C₂²	1	2	yes	—
117	#405×C₇₃	C₂²	1	2	yes	—
118	C₂×#97×C₇₃	C₂²	1	1	yes	characteristic
119	C₂×#41×C₇₃	—	2	2	no	—
120	C₂×#41×C₇₃	—	2	1	no	—
121	C₂×#41×C₇₃	C₂³	1	2	yes	—
122	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
123	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
124	C₂×SD₁₆×C₇₃	C₂³	1	2	yes	—
125	C₂×SD₁₆×C₇₃	C₂³	1	2	yes	—
126	C₂×SD₁₆×C₇₃	C₂³	1	2	yes	—
127	C₂×SD₁₆×C₇₃	C₂³	1	2	yes	—
128	C₂×SD₁₆×C₇₃	C₂³	1	2	yes	—
129	C₂×D₈×C₇₃	C₂³	1	2	yes	—
130	C₂×M₁₆×C₇₃	C₂³	1	2	yes	—
131	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
132	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
133	C₄⋊Q₈×C₇₃	—	2	1	no	—
134	C₄⋊Q₈×C₇₃	—	2	2	no	—
135	C₄⋊Q₈×C₇₃	—	2	2	no	—
136	C₄⋊Q₈×C₇₃	—	2	1	no	—
137	C₄⋊Q₈×C₇₃	—	2	1	no	—
138	C₄⋊Q₈×C₇₃	C₂³	1	2	yes	—
139	C₄⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
140	C₄⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
141	C₄⋊Q₈×C₇₃	C₂³	1	2	yes	—
142	C₄⋊Q₈×C₇₃	C₂³	1	2	yes	—
143	C₄⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
144	#127×C₇₃	C₂³	1	1	yes	characteristic
145	#126×C₇₃	—	2	2	no	—
146	#126×C₇₃	—	2	2	no	—
147	#126×C₇₃	—	2	2	no	—
148	#126×C₇₃	—	2	2	no	—
149	#126×C₇₃	—	2	2	no	—
150	#126×C₇₃	—	2	1	no	—
151	#126×C₇₃	D₄	1	2	yes	—
152	#125×C₇₃	—	2	2	no	—
153	#125×C₇₃	—	2	2	no	—
154	#125×C₇₃	—	2	2	no	—
155	#125×C₇₃	—	2	2	no	—
156	#125×C₇₃	—	2	1	no	—
157	#125×C₇₃	—	2	1	no	—
158	#125×C₇₃	—	2	1	no	—
159	#125×C₇₃	D₄	1	1	yes	characteristic
160	#125×C₇₃	C₂³	1	2	yes	—
161	#125×C₇₃	C₂³	1	2	yes	—
162	#125×C₇₃	C₂³	1	2	yes	—
163	#125×C₇₃	C₂³	1	1	yes	characteristic
164	#124×C₇₃	—	2	2	no	—
165	#124×C₇₃	—	2	1	no	—
166	#124×C₇₃	D₄	1	1	yes	characteristic
167	#124×C₇₃	C₂³	1	2	yes	—
168	#124×C₇₃	C₂³	1	1	yes	characteristic
169	#123×C₇₃	—	2	1	no	—
170	#123×C₇₃	—	2	2	no	—
171	#123×C₇₃	—	2	2	no	—
172	#123×C₇₃	—	2	2	no	—
173	#123×C₇₃	—	2	2	no	—
174	#123×C₇₃	—	2	2	no	—
175	#123×C₇₃	—	2	2	no	—
176	#123×C₇₃	—	2	2	no	—
177	#123×C₇₃	—	2	2	no	—
178	#123×C₇₃	—	2	2	no	—
179	#123×C₇₃	D₄	1	2	yes	—
180	C₂²⋊Q₈×C₇₃	—	2	2	no	—
181	C₂²⋊Q₈×C₇₃	—	2	1	no	—
182	C₂²⋊Q₈×C₇₃	—	2	2	no	—
183	C₂²⋊Q₈×C₇₃	—	2	2	no	—
184	C₂²⋊Q₈×C₇₃	—	2	2	no	—
185	C₂²⋊Q₈×C₇₃	—	2	2	no	—
186	C₂²⋊Q₈×C₇₃	—	2	2	no	—
187	C₂²⋊Q₈×C₇₃	—	2	2	no	—
188	C₂²⋊Q₈×C₇₃	—	2	2	no	—
189	C₂²⋊Q₈×C₇₃	—	2	2	no	—
190	C₂²⋊Q₈×C₇₃	—	2	2	no	—
191	C₂²⋊Q₈×C₇₃	—	2	2	no	—
192	C₂²⋊Q₈×C₇₃	—	2	2	no	—
193	C₂²⋊Q₈×C₇₃	D₄	1	1	yes	characteristic
194	C₂²⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
195	C₂²⋊Q₈×C₇₃	C₂³	1	2	yes	—
196	C₂²⋊Q₈×C₇₃	C₂³	1	2	yes	—
197	#121×C₇₃	—	2	2	no	—
198	#121×C₇₃	—	2	2	no	—
199	#121×C₇₃	—	2	2	no	—
200	#121×C₇₃	—	2	1	no	—
201	#121×C₇₃	—	2	1	no	—
202	#121×C₇₃	—	2	2	no	—
203	#121×C₇₃	—	2	2	no	—
204	#121×C₇₃	D₄	1	1	yes	characteristic
205	#121×C₇₃	C₂³	1	2	yes	—
206	#121×C₇₃	C₂³	1	2	yes	—
207	#121×C₇₃	C₂³	1	2	yes	—
208	#121×C₇₃	C₂³	1	1	yes	characteristic
209	C₄×Q₈×C₇₃	—	2	1	no	—
210	C₄×Q₈×C₇₃	C₂³	1	2	yes	—
211	C₄×Q₈×C₇₃	C₂³	1	2	yes	—
212	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
213	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
214	C₄×D₄×C₇₃	—	2	2	no	—
215	C₄×D₄×C₇₃	—	2	1	no	—
216	C₄×D₄×C₇₃	—	2	1	no	—
217	C₄×D₄×C₇₃	—	2	2	no	—
218	C₄×D₄×C₇₃	—	2	2	no	—
219	C₄×D₄×C₇₃	—	2	2	no	—
220	C₄×D₄×C₇₃	—	2	1	no	—
221	C₄×D₄×C₇₃	C₂³	1	2	yes	—
222	C₄×D₄×C₇₃	C₂³	1	2	yes	—
223	C₄×D₄×C₇₃	C₂³	1	2	yes	—
224	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
225	C₄×D₄×C₇₃	C₂³	1	2	yes	—
226	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
227	#117×C₇₃	—	2	1	no	—
228	#117×C₇₃	—	2	1	no	—
229	#117×C₇₃	C₂³	1	2	yes	—
230	#117×C₇₃	C₂³	1	2	yes	—
231	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
232	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
233	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
234	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
235	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
236	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
237	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
238	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
239	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
240	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
241	#107×C₇₃	C₂³	1	2	yes	—
242	#107×C₇₃	C₂³	1	2	yes	—
243	#107×C₇₃	C₂³	1	2	yes	—
244	#106×C₇₃	C₂³	1	2	yes	—
245	#106×C₇₃	C₂³	1	2	yes	—
246	#106×C₇₃	C₂³	1	2	yes	—
247	C₄⋊C₈×C₇₃	C₂³	1	2	yes	—
248	C₄⋊C₈×C₇₃	C₂³	1	2	yes	—
249	C₄⋊C₈×C₇₃	C₂³	1	2	yes	—
250	#103×C₇₃	C₂³	1	2	yes	—
251	#103×C₇₃	C₂³	1	2	yes	—
252	#103×C₇₃	C₂³	1	2	yes	—
253	#103×C₇₃	C₂³	1	2	yes	—
254	#103×C₇₃	C₂³	1	2	yes	—
255	#103×C₇₃	C₂³	1	2	yes	—
256	#103×C₇₃	C₂³	1	2	yes	—
257	#103×C₇₃	C₂³	1	2	yes	—
258	#103×C₇₃	C₂³	1	2	yes	—
259	#103×C₇₃	C₂³	1	2	yes	—
260	#103×C₇₃	C₂³	1	2	yes	—
261	#103×C₇₃	C₂³	1	2	yes	—
262	#103×C₇₃	C₂³	1	2	yes	—
263	#103×C₇₃	C₂³	1	2	yes	—
264	#103×C₇₃	C₂³	1	2	yes	—
265	#102×C₇₃	C₂³	1	2	yes	—
266	#102×C₇₃	C₂³	1	2	yes	—
267	#102×C₇₃	C₂³	1	2	yes	—
268	#102×C₇₃	C₂³	1	2	yes	—
269	#102×C₇₃	C₂³	1	2	yes	—
270	C₂²⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
271	C₂²⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
272	C₂²⋊C₈×C₇₃	C₂³	1	2	yes	—
273	C₂²⋊C₈×C₇₃	C₂³	1	2	yes	—
274	#97×C₇₃	C₂³	1	1	yes	characteristic
275	#97×C₇₃	C₂³	1	1	yes	characteristic
276	#97×C₇₃	C₂³	1	2	yes	—
277	#97×C₇₃	C₂³	1	2	yes	—
278	C₄×C₈×C₇₃	C₂³	1	2	yes	—
279	C₄×C₈×C₇₃	C₂³	1	2	yes	—
280	#41×C₇₃	—	4	2	no	—
281	#41×C₇₃	—	4	2	no	—
282	#41×C₇₃	—	8	2	no	—
283	#41×C₇₃	—	8	4	no	—
284	C₂×Q₈×C₇₃	—	2	2	no	—
285	C₂×Q₈×C₇₃	—	2	2	no	—
286	C₂×Q₈×C₇₃	—	2	2	no	—
287	C₂×Q₈×C₇₃	—	2	1	no	—
288	C₂×Q₈×C₇₃	—	4	2	no	—
289	C₂×Q₈×C₇₃	—	4	2	no	—
290	C₂×Q₈×C₇₃	—	4	2	no	—
291	C₂×Q₈×C₇₃	—	4	2	no	—
292	C₂×Q₈×C₇₃	C₂×D₄	1	1	yes	characteristic
293	C₂×Q₈×C₇₃	C₂⁴	1	2	yes	—
294	C₂×Q₈×C₇₃	C₂⁴	1	1	yes	characteristic
295	C₂×Q₈×C₇₃	C₂⁴	1	2	yes	—
296	C₂×D₄×C₇₃	—	2	1	no	—
297	C₂×D₄×C₇₃	—	2	2	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	1	no	—
302	C₂×D₄×C₇₃	—	2	1	no	—
303	C₂×D₄×C₇₃	C₂×D₄	1	2	yes	—
304	C₂×D₄×C₇₃	C₂×D₄	1	1	yes	characteristic
305	C₂×D₄×C₇₃	C₂⁴	1	1	yes	characteristic
306	C₂×D₄×C₇₃	C₂⁴	1	2	yes	—
307	C₂²×C₄×C₇₃	—	2	1	no	—
308	C₂²×C₄×C₇₃	—	2	1	no	—
309	C₂²×C₄×C₇₃	—	2	2	no	—
310	C₂²×C₄×C₇₃	—	2	2	no	—
311	C₂²×C₄×C₇₃	—	2	2	no	—
312	C₂²×C₄×C₇₃	—	2	1	no	—
313	C₂²×C₄×C₇₃	—	2	2	no	—
314	C₂²×C₄×C₇₃	—	2	2	no	—
315	C₂²×C₄×C₇₃	—	2	2	no	—
316	C₂²×C₄×C₇₃	—	2	2	no	—
317	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
318	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
319	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
320	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
321	SD₁₆×C₇₃	—	4	2	no	—
322	SD₁₆×C₇₃	—	4	2	no	—
323	SD₁₆×C₇₃	—	4	2	no	—
324	SD₁₆×C₇₃	—	4	2	no	—
325	SD₁₆×C₇₃	—	4	2	no	—
326	D₈×C₇₃	—	4	2	no	—
327	M₁₆×C₇₃	—	4	2	no	—
328	C₂×C₈×C₇₃	—	4	2	no	—
329	C₂×C₈×C₇₃	—	4	2	no	—
330	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
331	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
332	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
333	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
334	C₄⋊C₄×C₇₃	—	2	2	no	—
335	C₄⋊C₄×C₇₃	—	2	1	no	—
336	C₄⋊C₄×C₇₃	—	2	1	no	—
337	C₄⋊C₄×C₇₃	—	2	2	no	—
338	C₄⋊C₄×C₇₃	—	2	2	no	—
339	C₄⋊C₄×C₇₃	—	2	2	no	—
340	C₄⋊C₄×C₇₃	—	2	2	no	—
341	C₄⋊C₄×C₇₃	—	2	2	no	—
342	C₄⋊C₄×C₇₃	—	2	1	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	—	2	1	no	—
347	C₄⋊C₄×C₇₃	—	2	1	no	—
348	C₄⋊C₄×C₇₃	—	2	2	no	—
349	C₄⋊C₄×C₇₃	—	2	1	no	—
350	C₄⋊C₄×C₇₃	—	2	1	no	—
351	C₄⋊C₄×C₇₃	—	2	1	no	—
352	C₄⋊C₄×C₇₃	—	2	1	no	—
353	C₄⋊C₄×C₇₃	—	2	2	no	—
354	C₄⋊C₄×C₇₃	—	2	2	no	—
355	C₄⋊C₄×C₇₃	—	2	2	no	—
356	C₄⋊C₄×C₇₃	—	2	1	no	—
357	C₄⋊C₄×C₇₃	—	2	2	no	—
358	C₄⋊C₄×C₇₃	—	2	2	no	—
359	C₄⋊C₄×C₇₃	—	2	2	no	—
360	C₄⋊C₄×C₇₃	—	2	1	no	—
361	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
362	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
363	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
364	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
365	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
366	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
367	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
368	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
369	C₄⋊C₄×C₇₃	C₂⁴	1	2	yes	—
370	C₄⋊C₄×C₇₃	C₂⁴	1	2	yes	—
371	C₄⋊C₄×C₇₃	C₂⁴	1	2	yes	—
372	C₂²⋊C₄×C₇₃	—	2	2	no	—
373	C₂²⋊C₄×C₇₃	—	2	1	no	—
374	C₂²⋊C₄×C₇₃	—	2	2	no	—
375	C₂²⋊C₄×C₇₃	—	2	2	no	—
376	C₂²⋊C₄×C₇₃	—	2	2	no	—
377	C₂²⋊C₄×C₇₃	—	2	1	no	—
378	C₂²⋊C₄×C₇₃	—	2	1	no	—
379	C₂²⋊C₄×C₇₃	—	2	2	no	—
380	C₂²⋊C₄×C₇₃	—	2	2	no	—
381	C₂²⋊C₄×C₇₃	—	2	2	no	—
382	C₂²⋊C₄×C₇₃	—	2	1	no	—
383	C₂²⋊C₄×C₇₃	—	2	2	no	—
384	C₂²⋊C₄×C₇₃	—	2	2	no	—
385	C₂²⋊C₄×C₇₃	—	2	2	no	—
386	C₂²⋊C₄×C₇₃	—	2	2	no	—
387	C₂²⋊C₄×C₇₃	—	2	1	no	—
388	C₂²⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
389	C₂²⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
390	C₂²⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
391	C₂²⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
392	C₂²⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
393	C₄²×C₇₃	—	2	1	no	—
394	C₄²×C₇₃	—	2	2	no	—
395	C₄²×C₇₃	—	2	2	no	—
396	C₄²×C₇₃	—	2	2	no	—
397	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
398	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
399	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
400	C₄²×C₇₃	C₂⁴	1	2	yes	—
401	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
402	C₂³×C₇₃	—	2	1	no	—
403	C₂³×C₇₃	—	2	2	no	—
404	C₂³×C₇₃	C₂²×D₄	1	2	yes	—
405	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
406	Q₈×C₇₃	—	2	2	no	—
407	Q₈×C₇₃	—	2	2	no	—
408	Q₈×C₇₃	—	2	2	no	—
409	Q₈×C₇₃	—	2	2	no	—
410	Q₈×C₇₃	—	2	2	no	—
411	Q₈×C₇₃	—	4	1	no	—
412	Q₈×C₇₃	—	8	2	no	—
413	Q₈×C₇₃	—	8	2	no	—
414	Q₈×C₇₃	—	8	1	no	—
415	Q₈×C₇₃	—	8	2	no	—
416	D₄×C₇₃	—	2	4	no	—
417	D₄×C₇₃	—	2	2	no	—
418	D₄×C₇₃	—	2	2	no	—
419	D₄×C₇₃	—	2	2	no	—
420	D₄×C₇₃	—	4	1	no	—
421	D₄×C₇₃	—	4	2	no	—
422	D₄×C₇₃	—	4	4	no	—
423	D₄×C₇₃	—	8	1	no	—
424	D₄×C₇₃	—	8	1	no	—
425	D₄×C₇₃	—	8	2	no	—
426	D₄×C₇₃	—	8	2	no	—
427	D₄×C₇₃	—	8	2	no	—
428	C₂×C₄×C₇₃	—	2	2	no	—
429	C₂×C₄×C₇₃	—	2	2	no	—
430	C₂×C₄×C₇₃	—	2	2	no	—
431	C₂×C₄×C₇₃	—	2	2	no	—
432	C₂×C₄×C₇₃	—	2	1	no	—
433	C₂×C₄×C₇₃	—	2	1	no	—
434	C₂×C₄×C₇₃	—	2	2	no	—
435	C₂×C₄×C₇₃	—	2	1	no	—
436	C₂×C₄×C₇₃	—	2	2	no	—
437	C₂×C₄×C₇₃	—	2	2	no	—
438	C₂×C₄×C₇₃	—	2	2	no	—
439	C₂×C₄×C₇₃	—	2	2	no	—
440	C₂×C₄×C₇₃	—	4	1	no	—
441	C₂×C₄×C₇₃	—	4	2	no	—
442	C₂×C₄×C₇₃	—	4	2	no	—
443	C₂×C₄×C₇₃	—	8	2	no	—
444	C₂×C₄×C₇₃	—	8	2	no	—
445	C₂×C₄×C₇₃	—	8	2	no	—
446	C₂×C₄×C₇₃	—	8	2	no	—
447	C₂×C₄×C₇₃	—	8	1	no	—
448	C₂×C₄×C₇₃	—	8	2	no	—
449	C₂×C₄×C₇₃	—	8	2	no	—
450	C₂×C₄×C₇₃	—	8	2	no	—
451	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
452	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
453	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
454	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
455	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
456	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
457	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
458	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
459	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
460	C₈×C₇₃	—	2	2	no	—
461	C₈×C₇₃	—	2	2	no	—
462	C₈×C₇₃	—	2	2	no	—
463	C₈×C₇₃	—	2	2	no	—
464	C₂²×C₇₃	—	2	1	no	—
465	C₂²×C₇₃	—	2	1	no	—
466	C₂²×C₇₃	—	2	2	no	—
467	C₂²×C₇₃	—	2	2	no	—
468	C₂²×C₇₃	—	2	2	no	—
469	C₂²×C₇₃	—	4	1	no	—
470	C₂²×C₇₃	—	4	2	no	—
471	C₂²×C₇₃	—	4	1	no	—
472	C₂²×C₇₃	—	4	2	no	—
473	C₂²×C₇₃	—	4	2	no	—
474	C₂²×C₇₃	—	4	1	no	—
475	C₂²×C₇₃	#577	1	2	yes	—
476	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
477	C₄×C₇₃	—	2	1	no	—
478	C₄×C₇₃	—	2	1	no	—
479	C₄×C₇₃	—	2	2	no	—
480	C₄×C₇₃	—	2	2	no	—
481	C₄×C₇₃	—	2	1	no	—
482	C₄×C₇₃	—	2	1	no	—
483	C₄×C₇₃	—	2	1	no	—
484	C₄×C₇₃	—	2	2	no	—
485	C₄×C₇₃	—	4	1	no	—
486	C₄×C₇₃	—	4	2	no	—
487	C₄×C₇₃	—	4	2	no	—
488	C₄×C₇₃	—	4	1	no	—
489	C₄×C₇₃	—	4	2	no	—
490	C₄×C₇₃	—	4	2	no	—
491	C₄×C₇₃	—	4	2	no	—
492	C₄×C₇₃	—	4	1	no	—
493	C₄×C₇₃	#585	1	2	yes	—
494	#62597	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
495	C₂×C₇₃	—	2	2	no	—
496	C₂×C₇₃	—	4	2	no	—
497	C₂×C₇₃	—	8	1	no	—
498	C₂×C₇₃	—	8	2	no	—
499	C₂×C₇₃	#3500	1	1	yes	characteristic
500	C₂×C₇₃	C₂×#577	1	1	yes	characteristic
501	C₂×C₇₃	#3586	1	1	yes	characteristic
502	#3559	C₂×C₇₃	1	1	yes	characteristic, complemented
503	#3552	C₂×C₇₃	1	1	yes	characteristic, complemented
504	#3376	C₂×C₇₃	1	2	yes	complemented
505	#3372	C₂×C₇₃	1	2	yes	complemented
506	#3320	C₂×C₇₃	1	2	yes	complemented
507	#3320	C₂×C₇₃	1	2	yes	complemented
508	#3308	C₂×C₇₃	1	2	yes	complemented
509	#3307	C₂×C₇₃	1	2	yes	complemented
510	#3301	C₂×C₇₃	1	2	yes	complemented
511	#3298	C₂×C₇₃	1	2	yes	complemented
512	#3242	C₂×C₇₃	1	2	yes	complemented
513	#3232	C₂×C₇₃	1	1	yes	characteristic, complemented
514	#3221	C₂×C₇₃	1	2	yes	complemented
515	#3206	C₂×C₇₃	1	1	yes	characteristic, complemented
516	#3180	C₂×C₇₃	1	1	yes	characteristic, complemented
517	#3174	C₂×C₇₃	1	2	yes	complemented
518	#3137	C₂×C₇₃	1	2	yes	complemented
519	C₂×#491	C₂×C₇₃	1	1	yes	characteristic, complemented
520	#2968	C₂×C₇₃	1	1	yes	characteristic, complemented
521	C₇₃	#62597	1	1	yes	characteristic, direct product factor, Sylow
522	#563	—	2	2	no	—
523	#563	—	2	1	no	—
524	#562	—	2	1	no	—
525	#557	C₂²×C₇₃	1	1	yes	characteristic
526	#556	C₂²×C₇₃	1	1	yes	characteristic
527	#554	—	2	1	no	—
528	#554	C₂²×C₇₃	1	2	yes	—
529	#553	—	2	1	no	—
530	#553	C₂²×C₇₃	1	2	yes	—
531	#553	C₂²×C₇₃	1	2	yes	—
532	D₄×Q₈	C₂²×C₇₃	1	2	yes	—
533	D₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
534	#548	C₂²×C₇₃	1	2	yes	—
535	#547	—	2	2	no	—
536	#547	C₂²×C₇₃	1	1	yes	characteristic
537	#547	C₂²×C₇₃	1	2	yes	—
538	#544	—	2	1	no	—
539	#544	C₂²×C₇₃	1	2	yes	—
540	#542	—	2	1	no	—
541	#541	C₂²×C₇₃	1	2	yes	—
542	#540	C₂²×C₇₃	1	2	yes	—
543	#539	—	2	2	no	—
544	#539	—	2	2	no	—
545	#539	—	2	1	no	—
546	#537	—	2	1	no	—
547	#536	C₂²×C₇₃	1	2	yes	—
548	#532	C₂²×C₇₃	1	1	yes	characteristic
549	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
550	#529	C₂²×C₇₃	1	1	yes	characteristic
551	#529	C₂²×C₇₃	1	1	yes	characteristic
552	C₂×#125	C₂²×C₇₃	1	1	yes	characteristic
553	#501	C₂²×C₇₃	1	1	yes	characteristic
554	#499	C₂²×C₇₃	1	2	yes	—
555	#496	C₂²×C₇₃	1	1	yes	characteristic
556	#492	C₂²×C₇₃	1	2	yes	—
557	#491	C₂²×C₇₃	1	2	yes	—
558	#491	C₂²×C₇₃	1	2	yes	—
559	#491	C₂²×C₇₃	1	2	yes	—
560	#491	C₂²×C₇₃	1	2	yes	—
561	#491	C₂²×C₇₃	1	2	yes	—
562	#490	C₂²×C₇₃	1	1	yes	characteristic
563	#489	C₂²×C₇₃	1	2	yes	—
564	#489	C₂²×C₇₃	1	1	yes	characteristic
565	#488	C₂²×C₇₃	1	2	yes	—
566	#488	C₂²×C₇₃	1	2	yes	—
567	#487	C₂²×C₇₃	1	2	yes	—
568	#487	C₂²×C₇₃	1	2	yes	—
569	#485	C₂²×C₇₃	1	2	yes	—
570	#485	C₂²×C₇₃	1	2	yes	—
571	#484	C₂²×C₇₃	1	1	yes	characteristic
572	#484	C₂²×C₇₃	1	2	yes	—
573	#483	C₂²×C₇₃	1	1	yes	characteristic
574	#483	C₂²×C₇₃	1	2	yes	—
575	#481	C₂²×C₇₃	1	1	yes	characteristic
576	#480	C₂²×C₇₃	1	1	yes	characteristic
577	#479	C₂²×C₇₃	1	2	yes	—
578	#479	C₂²×C₇₃	1	2	yes	—
579	#479	C₂²×C₇₃	1	2	yes	—
580	#478	C₂²×C₇₃	1	2	yes	—
581	#477	C₂²×C₇₃	1	2	yes	—
582	#475	C₂²×C₇₃	1	2	yes	—
583	#468	C₂²×C₇₃	1	2	yes	—
584	#468	C₂²×C₇₃	1	2	yes	—
585	#466	C₂²×C₇₃	1	2	yes	—
586	#465	C₂²×C₇₃	1	2	yes	—
587	#465	C₂²×C₇₃	1	2	yes	—
588	#465	C₂²×C₇₃	1	2	yes	—
589	#463	C₂²×C₇₃	1	2	yes	—
590	#463	C₂²×C₇₃	1	2	yes	—
591	#461	C₂²×C₇₃	1	2	yes	—
592	#461	C₂²×C₇₃	1	2	yes	—
593	#461	C₂²×C₇₃	1	2	yes	—
594	#461	C₂²×C₇₃	1	2	yes	—
595	#449	C₂²×C₇₃	1	2	yes	—
596	#449	C₂²×C₇₃	1	2	yes	—
597	#448	C₂²×C₇₃	1	2	yes	—
598	#448	C₂²×C₇₃	1	2	yes	—
599	#448	C₂²×C₇₃	1	2	yes	—
600	#448	C₂²×C₇₃	1	2	yes	—
601	#446	C₂²×C₇₃	1	2	yes	—
602	#442	C₂²×C₇₃	1	2	yes	—
603	#440	C₂²×C₇₃	1	2	yes	—
604	#440	C₂²×C₇₃	1	2	yes	—
605	#440	C₂²×C₇₃	1	2	yes	—
606	C₄×SD₁₆	C₂²×C₇₃	1	2	yes	—
607	C₄×SD₁₆	C₂²×C₇₃	1	2	yes	—
608	#435	C₂²×C₇₃	1	2	yes	—
609	#435	C₂²×C₇₃	1	2	yes	—
610	C₈×D₄	C₂²×C₇₃	1	2	yes	—
611	#433	C₂²×C₇₃	1	2	yes	—
612	#431	C₂²×C₇₃	1	1	yes	characteristic
613	#419	C₂²×C₇₃	1	2	yes	—
614	#417	C₂²×C₇₃	1	2	yes	—
615	#416	C₂²×C₇₃	1	2	yes	—
616	C₂×#103	C₂²×C₇₃	1	2	yes	—
617	C₂×#103	C₂²×C₇₃	1	2	yes	—
618	C₂×#103	C₂²×C₇₃	1	2	yes	—
619	#405	C₂²×C₇₃	1	2	yes	—
620	C₂×#97	C₂²×C₇₃	1	1	yes	characteristic
621	C₂×#41	—	2	2	no	—
622	C₂×#41	—	2	1	no	—
623	C₂×#41	C₂³×C₇₃	1	2	yes	—
624	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
625	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
626	C₂×SD₁₆	C₂³×C₇₃	1	2	yes	—
627	C₂×SD₁₆	C₂³×C₇₃	1	2	yes	—
628	C₂×SD₁₆	C₂³×C₇₃	1	2	yes	—
629	C₂×SD₁₆	C₂³×C₇₃	1	2	yes	—
630	C₂×SD₁₆	C₂³×C₇₃	1	2	yes	—
631	C₂×D₈	C₂³×C₇₃	1	2	yes	—
632	C₂×M₁₆	C₂³×C₇₃	1	2	yes	—
633	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
634	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
635	C₄⋊Q₈	—	2	1	no	—
636	C₄⋊Q₈	—	2	2	no	—
637	C₄⋊Q₈	—	2	2	no	—
638	C₄⋊Q₈	—	2	1	no	—
639	C₄⋊Q₈	—	2	1	no	—
640	C₄⋊Q₈	C₂³×C₇₃	1	2	yes	—
641	C₄⋊Q₈	C₂³×C₇₃	1	1	yes	characteristic
642	C₄⋊Q₈	C₂³×C₇₃	1	1	yes	characteristic
643	C₄⋊Q₈	C₂³×C₇₃	1	2	yes	—
644	C₄⋊Q₈	C₂³×C₇₃	1	1	yes	characteristic
645	C₄⋊Q₈	C₂³×C₇₃	1	2	yes	—
646	#127	C₂³×C₇₃	1	1	yes	characteristic
647	#126	—	2	2	no	—
648	#126	—	2	2	no	—
649	#126	—	2	2	no	—
650	#126	—	2	2	no	—
651	#126	—	2	2	no	—
652	#126	—	2	1	no	—
653	#126	D₄×C₇₃	1	2	yes	—
654	#125	—	2	2	no	—
655	#125	—	2	2	no	—
656	#125	—	2	2	no	—
657	#125	—	2	2	no	—
658	#125	—	2	1	no	—
659	#125	—	2	1	no	—
660	#125	—	2	1	no	—
661	#125	D₄×C₇₃	1	1	yes	characteristic
662	#125	C₂³×C₇₃	1	2	yes	—
663	#125	C₂³×C₇₃	1	2	yes	—
664	#125	C₂³×C₇₃	1	1	yes	characteristic
665	#125	C₂³×C₇₃	1	2	yes	—
666	#124	—	2	2	no	—
667	#124	—	2	1	no	—
668	#124	D₄×C₇₃	1	1	yes	characteristic
669	#124	C₂³×C₇₃	1	1	yes	characteristic
670	#124	C₂³×C₇₃	1	2	yes	—
671	#123	—	2	1	no	—
672	#123	—	2	2	no	—
673	#123	—	2	2	no	—
674	#123	—	2	2	no	—
675	#123	—	2	2	no	—
676	#123	—	2	2	no	—
677	#123	—	2	2	no	—
678	#123	—	2	2	no	—
679	#123	—	2	2	no	—
680	#123	—	2	2	no	—
681	#123	D₄×C₇₃	1	2	yes	—
682	C₂²⋊Q₈	—	2	2	no	—
683	C₂²⋊Q₈	—	2	1	no	—
684	C₂²⋊Q₈	—	2	2	no	—
685	C₂²⋊Q₈	—	2	2	no	—
686	C₂²⋊Q₈	—	2	2	no	—
687	C₂²⋊Q₈	—	2	2	no	—
688	C₂²⋊Q₈	—	2	2	no	—
689	C₂²⋊Q₈	—	2	2	no	—
690	C₂²⋊Q₈	—	2	2	no	—
691	C₂²⋊Q₈	—	2	2	no	—
692	C₂²⋊Q₈	—	2	2	no	—
693	C₂²⋊Q₈	—	2	2	no	—
694	C₂²⋊Q₈	—	2	2	no	—
695	C₂²⋊Q₈	D₄×C₇₃	1	1	yes	characteristic
696	C₂²⋊Q₈	C₂³×C₇₃	1	1	yes	characteristic
697	C₂²⋊Q₈	C₂³×C₇₃	1	2	yes	—
698	C₂²⋊Q₈	C₂³×C₇₃	1	2	yes	—
699	#121	—	2	2	no	—
700	#121	—	2	2	no	—
701	#121	—	2	2	no	—
702	#121	—	2	1	no	—
703	#121	—	2	1	no	—
704	#121	—	2	2	no	—
705	#121	—	2	2	no	—
706	#121	D₄×C₇₃	1	1	yes	characteristic
707	#121	C₂³×C₇₃	1	1	yes	characteristic
708	#121	C₂³×C₇₃	1	2	yes	—
709	#121	C₂³×C₇₃	1	2	yes	—
710	#121	C₂³×C₇₃	1	2	yes	—
711	C₄×Q₈	—	2	1	no	—
712	C₄×Q₈	C₂³×C₇₃	1	1	yes	characteristic
713	C₄×Q₈	C₂³×C₇₃	1	2	yes	—
714	C₄×Q₈	C₂³×C₇₃	1	2	yes	—
715	C₄×Q₈	C₂³×C₇₃	1	1	yes	characteristic
716	C₄×D₄	—	2	2	no	—
717	C₄×D₄	—	2	1	no	—
718	C₄×D₄	—	2	1	no	—
719	C₄×D₄	—	2	2	no	—
720	C₄×D₄	—	2	2	no	—
721	C₄×D₄	—	2	2	no	—
722	C₄×D₄	—	2	1	no	—
723	C₄×D₄	C₂³×C₇₃	1	1	yes	characteristic
724	C₄×D₄	C₂³×C₇₃	1	2	yes	—
725	C₄×D₄	C₂³×C₇₃	1	2	yes	—
726	C₄×D₄	C₂³×C₇₃	1	2	yes	—
727	C₄×D₄	C₂³×C₇₃	1	2	yes	—
728	C₄×D₄	C₂³×C₇₃	1	1	yes	characteristic
729	#117	—	2	1	no	—
730	#117	—	2	1	no	—
731	#117	C₂³×C₇₃	1	2	yes	—
732	#117	C₂³×C₇₃	1	2	yes	—
733	C₂×C₄⋊C₄	—	2	1	no	—
734	C₂×C₄⋊C₄	—	2	1	no	—
735	C₂×C₄⋊C₄	—	2	1	no	—
736	C₂×C₄⋊C₄	—	2	1	no	—
737	C₂×C₄⋊C₄	—	2	2	no	—
738	C₂×C₄⋊C₄	—	2	1	no	—
739	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
740	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
741	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
742	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
743	#107	C₂³×C₇₃	1	2	yes	—
744	#107	C₂³×C₇₃	1	2	yes	—
745	#107	C₂³×C₇₃	1	2	yes	—
746	#106	C₂³×C₇₃	1	2	yes	—
747	#106	C₂³×C₇₃	1	2	yes	—
748	#106	C₂³×C₇₃	1	2	yes	—
749	C₄⋊C₈	C₂³×C₇₃	1	2	yes	—
750	C₄⋊C₈	C₂³×C₇₃	1	2	yes	—
751	C₄⋊C₈	C₂³×C₇₃	1	2	yes	—
752	#103	C₂³×C₇₃	1	2	yes	—
753	#103	C₂³×C₇₃	1	2	yes	—
754	#103	C₂³×C₇₃	1	2	yes	—
755	#103	C₂³×C₇₃	1	2	yes	—
756	#103	C₂³×C₇₃	1	2	yes	—
757	#103	C₂³×C₇₃	1	2	yes	—
758	#103	C₂³×C₇₃	1	2	yes	—
759	#103	C₂³×C₇₃	1	2	yes	—
760	#103	C₂³×C₇₃	1	2	yes	—
761	#103	C₂³×C₇₃	1	2	yes	—
762	#103	C₂³×C₇₃	1	2	yes	—
763	#103	C₂³×C₇₃	1	2	yes	—
764	#103	C₂³×C₇₃	1	2	yes	—
765	#103	C₂³×C₇₃	1	2	yes	—
766	#103	C₂³×C₇₃	1	2	yes	—
767	#102	C₂³×C₇₃	1	2	yes	—
768	#102	C₂³×C₇₃	1	2	yes	—
769	#102	C₂³×C₇₃	1	2	yes	—
770	#102	C₂³×C₇₃	1	2	yes	—
771	#102	C₂³×C₇₃	1	2	yes	—
772	C₂²⋊C₈	C₂³×C₇₃	1	1	yes	characteristic
773	C₂²⋊C₈	C₂³×C₇₃	1	1	yes	characteristic
774	C₂²⋊C₈	C₂³×C₇₃	1	2	yes	—
775	C₂²⋊C₈	C₂³×C₇₃	1	2	yes	—
776	#97	C₂³×C₇₃	1	1	yes	characteristic
777	#97	C₂³×C₇₃	1	1	yes	characteristic
778	#97	C₂³×C₇₃	1	2	yes	—
779	#97	C₂³×C₇₃	1	2	yes	—
780	C₄×C₈	C₂³×C₇₃	1	2	yes	—
781	C₄×C₈	C₂³×C₇₃	1	2	yes	—
782	#41	—	4	2	no	—
783	#41	—	4	2	no	—
784	#41	—	8	2	no	—
785	#41	—	8	4	no	—
786	C₂×Q₈	—	2	2	no	—
787	C₂×Q₈	—	2	2	no	—
788	C₂×Q₈	—	2	2	no	—
789	C₂×Q₈	—	2	1	no	—
790	C₂×Q₈	—	4	2	no	—
791	C₂×Q₈	—	4	2	no	—
792	C₂×Q₈	—	4	2	no	—
793	C₂×Q₈	—	4	2	no	—
794	C₂×Q₈	C₂×D₄×C₇₃	1	1	yes	characteristic
795	C₂×Q₈	C₂⁴×C₇₃	1	2	yes	—
796	C₂×Q₈	C₂⁴×C₇₃	1	1	yes	characteristic
797	C₂×Q₈	C₂⁴×C₇₃	1	2	yes	—
798	C₂×D₄	—	2	1	no	—
799	C₂×D₄	—	2	2	no	—
800	C₂×D₄	—	2	2	no	—
801	C₂×D₄	—	2	2	no	—
802	C₂×D₄	—	2	2	no	—
803	C₂×D₄	—	2	1	no	—
804	C₂×D₄	—	2	1	no	—
805	C₂×D₄	C₂×D₄×C₇₃	1	2	yes	—
806	C₂×D₄	C₂×D₄×C₇₃	1	1	yes	characteristic
807	C₂×D₄	C₂⁴×C₇₃	1	1	yes	characteristic
808	C₂×D₄	C₂⁴×C₇₃	1	2	yes	—
809	C₂²×C₄	—	2	1	no	—
810	C₂²×C₄	—	2	1	no	—
811	C₂²×C₄	—	2	2	no	—
812	C₂²×C₄	—	2	2	no	—
813	C₂²×C₄	—	2	2	no	—
814	C₂²×C₄	—	2	1	no	—
815	C₂²×C₄	—	2	2	no	—
816	C₂²×C₄	—	2	2	no	—
817	C₂²×C₄	—	2	2	no	—
818	C₂²×C₄	—	2	2	no	—
819	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
820	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
821	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
822	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
823	SD₁₆	—	4	2	no	—
824	SD₁₆	—	4	2	no	—
825	SD₁₆	—	4	2	no	—
826	SD₁₆	—	4	2	no	—
827	SD₁₆	—	4	2	no	—
828	D₈	—	4	2	no	—
829	M₁₆	—	4	2	no	—
830	C₂×C₈	—	4	2	no	—
831	C₂×C₈	—	4	2	no	—
832	C₂×C₈	C₂⁴×C₇₃	1	2	yes	—
833	C₂×C₈	C₂⁴×C₇₃	1	2	yes	—
834	C₂×C₈	C₂⁴×C₇₃	1	2	yes	—
835	C₂×C₈	C₂⁴×C₇₃	1	2	yes	—
836	C₄⋊C₄	—	2	2	no	—
837	C₄⋊C₄	—	2	1	no	—
838	C₄⋊C₄	—	2	1	no	—
839	C₄⋊C₄	—	2	2	no	—
840	C₄⋊C₄	—	2	2	no	—
841	C₄⋊C₄	—	2	2	no	—
842	C₄⋊C₄	—	2	2	no	—
843	C₄⋊C₄	—	2	2	no	—
844	C₄⋊C₄	—	2	1	no	—
845	C₄⋊C₄	—	2	2	no	—
846	C₄⋊C₄	—	2	2	no	—
847	C₄⋊C₄	—	2	2	no	—
848	C₄⋊C₄	—	2	1	no	—
849	C₄⋊C₄	—	2	1	no	—
850	C₄⋊C₄	—	2	2	no	—
851	C₄⋊C₄	—	2	1	no	—
852	C₄⋊C₄	—	2	1	no	—
853	C₄⋊C₄	—	2	1	no	—
854	C₄⋊C₄	—	2	1	no	—
855	C₄⋊C₄	—	2	2	no	—
856	C₄⋊C₄	—	2	2	no	—
857	C₄⋊C₄	—	2	2	no	—
858	C₄⋊C₄	—	2	1	no	—
859	C₄⋊C₄	—	2	2	no	—
860	C₄⋊C₄	—	2	2	no	—
861	C₄⋊C₄	—	2	2	no	—
862	C₄⋊C₄	—	2	1	no	—
863	C₄⋊C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
864	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
865	C₄⋊C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
866	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
867	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
868	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
869	C₄⋊C₄	C₂⁴×C₇₃	1	1	yes	characteristic
870	C₄⋊C₄	C₂⁴×C₇₃	1	1	yes	characteristic
871	C₄⋊C₄	C₂⁴×C₇₃	1	2	yes	—
872	C₄⋊C₄	C₂⁴×C₇₃	1	2	yes	—
873	C₄⋊C₄	C₂⁴×C₇₃	1	2	yes	—
874	C₂²⋊C₄	—	2	2	no	—
875	C₂²⋊C₄	—	2	1	no	—
876	C₂²⋊C₄	—	2	2	no	—
877	C₂²⋊C₄	—	2	2	no	—
878	C₂²⋊C₄	—	2	2	no	—
879	C₂²⋊C₄	—	2	1	no	—
880	C₂²⋊C₄	—	2	1	no	—
881	C₂²⋊C₄	—	2	2	no	—
882	C₂²⋊C₄	—	2	2	no	—
883	C₂²⋊C₄	—	2	2	no	—
884	C₂²⋊C₄	—	2	1	no	—
885	C₂²⋊C₄	—	2	2	no	—
886	C₂²⋊C₄	—	2	2	no	—
887	C₂²⋊C₄	—	2	2	no	—
888	C₂²⋊C₄	—	2	2	no	—
889	C₂²⋊C₄	—	2	1	no	—
890	C₂²⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
891	C₂²⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
892	C₂²⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
893	C₂²⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
894	C₂²⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
895	C₄²	—	2	1	no	—
896	C₄²	—	2	2	no	—
897	C₄²	—	2	2	no	—
898	C₄²	—	2	2	no	—
899	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
900	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
901	C₄²	C₂⁴×C₇₃	1	1	yes	characteristic
902	C₄²	C₂⁴×C₇₃	1	2	yes	—
903	C₄²	C₂⁴×C₇₃	1	1	yes	characteristic
904	C₂³	—	2	1	no	—
905	C₂³	—	2	2	no	—
906	C₂³	C₂²×D₄×C₇₃	1	2	yes	—
907	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
908	Q₈	—	2	2	no	—
909	Q₈	—	2	2	no	—
910	Q₈	—	2	2	no	—
911	Q₈	—	2	2	no	—
912	Q₈	—	2	2	no	—
913	Q₈	—	4	1	no	—
914	Q₈	—	8	2	no	—
915	Q₈	—	8	2	no	—
916	Q₈	—	8	1	no	—
917	Q₈	—	8	2	no	—
918	D₄	—	2	4	no	—
919	D₄	—	2	2	no	—
920	D₄	—	2	2	no	—
921	D₄	—	2	2	no	—
922	D₄	—	4	1	no	—
923	D₄	—	4	4	no	—
924	D₄	—	4	2	no	—
925	D₄	—	8	1	no	—
926	D₄	—	8	1	no	—
927	D₄	—	8	2	no	—
928	D₄	—	8	2	no	—
929	D₄	—	8	2	no	—
930	C₂×C₄	—	2	2	no	—
931	C₂×C₄	—	2	2	no	—
932	C₂×C₄	—	2	2	no	—
933	C₂×C₄	—	2	2	no	—
934	C₂×C₄	—	2	1	no	—
935	C₂×C₄	—	2	1	no	—
936	C₂×C₄	—	2	2	no	—
937	C₂×C₄	—	2	1	no	—
938	C₂×C₄	—	2	2	no	—
939	C₂×C₄	—	2	2	no	—
940	C₂×C₄	—	2	2	no	—
941	C₂×C₄	—	2	2	no	—
942	C₂×C₄	—	4	1	no	—
943	C₂×C₄	—	4	2	no	—
944	C₂×C₄	—	4	2	no	—
945	C₂×C₄	—	8	2	no	—
946	C₂×C₄	—	8	2	no	—
947	C₂×C₄	—	8	2	no	—
948	C₂×C₄	—	8	2	no	—
949	C₂×C₄	—	8	2	no	—
950	C₂×C₄	—	8	2	no	—
951	C₂×C₄	—	8	2	no	—
952	C₂×C₄	—	8	1	no	—
953	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
954	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
955	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
956	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
957	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
958	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
959	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
960	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
961	C₂×C₄	C₂⁵×C₇₃	1	1	yes	characteristic
962	C₈	—	2	2	no	—
963	C₈	—	2	2	no	—
964	C₈	—	2	2	no	—
965	C₈	—	2	2	no	—
966	C₂²	—	2	1	no	—
967	C₂²	—	2	1	no	—
968	C₂²	—	2	2	no	—
969	C₂²	—	2	2	no	—
970	C₂²	—	2	2	no	—
971	C₂²	—	4	1	no	—
972	C₂²	—	4	2	no	—
973	C₂²	—	4	2	no	—
974	C₂²	—	4	1	no	—
975	C₂²	—	4	1	no	—
976	C₂²	—	4	2	no	—
977	C₂²	#577×C₇₃	1	2	yes	—
978	C₂²	C₂³×D₄×C₇₃	1	1	yes	characteristic
979	C₄	—	2	2	no	—
980	C₄	—	2	1	no	—
981	C₄	—	2	1	no	—
982	C₄	—	2	1	no	—
983	C₄	—	2	2	no	—
984	C₄	—	2	1	no	—
985	C₄	—	2	1	no	—
986	C₄	—	2	2	no	—
987	C₄	—	4	2	no	—
988	C₄	—	4	1	no	—
989	C₄	—	4	2	no	—
990	C₄	—	4	2	no	—
991	C₄	—	4	2	no	—
992	C₄	—	4	1	no	—
993	C₄	—	4	1	no	—
994	C₄	—	4	2	no	—
995	C₄	#585×C₇₃	1	2	yes	—
996	C₂	—	2	2	no	—
997	C₂	—	4	2	no	—
998	C₂	—	8	1	no	—
999	C₂	—	8	2	no	—
1000	C₂	C₇₃×#3500	1	1	yes	characteristic
1001	C₂	C₂×#577×C₇₃	1	1	yes	characteristic
1002	C₂	C₇₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇₃ ◁ #529×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇₃×#3559	C₂	semidirect
2. C₇₃×#3552	C₂	semidirect
3. C₇₃×#3376	C₂	semidirect
4. C₇₃×#3372	C₂	semidirect
5. C₇₃×#3320	C₂	semidirect
6. C₇₃×#3320	C₂	semidirect
7. C₇₃×#3308	C₂	semidirect
8. C₇₃×#3307	C₂	semidirect
9. C₇₃×#3301	C₂	semidirect
10. C₇₃×#3298	C₂	semidirect
11. C₇₃×#3242	C₂	semidirect
12. C₇₃×#3232	C₂	semidirect
13. C₇₃×#3221	C₂	semidirect
14. C₇₃×#3206	C₂	semidirect
15. C₇₃×#3180	C₂	semidirect
16. C₇₃×#3174	C₂	semidirect
17. C₇₃×#3137	C₂	semidirect
18. C₂×#491×C₇₃	C₂	semidirect
19. C₇₃×#2968	C₂	semidirect
494. #62597	C₇₃	direct (N × H)
502. #3559	C₂×C₇₃	semidirect
503. #3552	C₂×C₇₃	semidirect
504. #3376	C₂×C₇₃	semidirect
505. #3372	C₂×C₇₃	semidirect
506. #3320	C₂×C₇₃	semidirect
507. #3320	C₂×C₇₃	semidirect
508. #3308	C₂×C₇₃	semidirect
509. #3307	C₂×C₇₃	semidirect
510. #3301	C₂×C₇₃	semidirect
511. #3298	C₂×C₇₃	semidirect
512. #3242	C₂×C₇₃	semidirect
513. #3232	C₂×C₇₃	semidirect
514. #3221	C₂×C₇₃	semidirect
515. #3206	C₂×C₇₃	semidirect
516. #3180	C₂×C₇₃	semidirect
517. #3174	C₂×C₇₃	semidirect
518. #3137	C₂×C₇₃	semidirect
519. C₂×#491	C₂×C₇₃	semidirect
520. #2968	C₂×C₇₃	semidirect
521. C₇₃	#62597	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇₃×#3559	2
C₇₃×#3552	2
C₇₃×#3376	2
C₇₃×#3372	2
C₇₃×#3320	2
C₇₃×#3308	2
C₇₃×#3307	2
C₇₃×#3301	2
C₇₃×#3298	2
C₇₃×#3242	2
C₇₃×#3232	2
C₇₃×#3221	2
C₇₃×#3206	2
C₇₃×#3180	2
C₇₃×#3174	2
C₇₃×#3137	2
C₂×#491×C₇₃	2
C₇₃×#2968	2
#62597	73

Subgroups — C73×#62597 #32972001

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#62597 #32972001