Subgroups — #33950653

Order 18688.

1920 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22623498	C₂	1	1	yes	maximal, characteristic
2	#22618944	C₂	1	2	yes	maximal, complemented
3	#22618937	C₂	1	2	yes	maximal, complemented
4	#22618924	C₂	1	2	yes	maximal, complemented
5	#22618924	C₂	1	2	yes	maximal, complemented
6	#22618915	C₂	1	2	yes	maximal, complemented
7	#22618915	C₂	1	2	yes	maximal, complemented
8	#22618905	C₂	1	2	yes	maximal, complemented
9	#22618896	C₂	1	2	yes	maximal, complemented
10	#22618880	C₂	1	1	yes	maximal, characteristic, complemented
11	#22618666	C₂	1	1	yes	maximal, characteristic, complemented
12	#22618655	C₂	1	1	yes	maximal, characteristic, complemented
13	#22618655	C₂	1	1	yes	maximal, characteristic, complemented
14	#22618636	C₂	1	1	yes	maximal, characteristic, complemented
15	#22618627	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#17988660	C₂	1	1	yes	maximal, characteristic, complemented
17	#22618599	C₂	1	1	yes	maximal, characteristic, complemented
18	#22618588	C₂	1	1	yes	maximal, characteristic, complemented
19	#22618588	C₂	1	1	yes	maximal, characteristic, complemented
20	#22618356	C₂	1	1	yes	maximal, characteristic, complemented
21	#22618347	C₂	1	1	yes	maximal, characteristic, complemented
22	#405×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
23	C₇₃×#2961	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#14556597	C₂²	1	1	yes	characteristic
25	C₂×#14556597	C₂²	1	1	yes	characteristic
26	C₂²×#11924011	C₂²	1	1	yes	characteristic
27	C₂×M₁₆×D₇₃	C₂²	1	1	yes	characteristic
28	C₂×M₁₆×D₇₃	C₂²	1	1	yes	characteristic
29	C₂²×C₈×D₇₃	C₂²	1	1	yes	characteristic
30	#17989311	C₄	1	1	yes	characteristic
31	#17989303	C₄	1	1	yes	characteristic
32	#17989298	C₄	1	1	yes	characteristic
33	#17989290	C₄	1	1	yes	characteristic
34	#17989290	C₄	1	1	yes	characteristic
35	#17989279	C₄	1	2	yes	—
36	#17989275	C₄	1	1	yes	characteristic
37	#17989275	C₄	1	1	yes	characteristic
38	#17989264	C₄	1	2	yes	—
39	#17989264	C₄	1	2	yes	—
40	#17989240	C₄	1	1	yes	characteristic
41	#17989228	C₄	1	2	yes	—
42	#17989124	C₂²	1	2	yes	—
43	#17989124	C₂²	1	2	yes	—
44	#17989124	C₂²	1	2	yes	—
45	#17989099	C₂²	1	1	yes	characteristic
46	#17989099	C₂²	1	1	yes	characteristic
47	C₄×#11924029	C₂²	1	2	yes	—
48	C₄×#11924028	C₂²	1	1	yes	characteristic
49	C₂×C₄×D₂₉₂	C₂²	1	1	yes	characteristic
50	#117×D₇₃	C₂²	1	1	yes	characteristic
51	#117×D₇₃	C₂²	1	1	yes	characteristic
52	#17988718	C₂²	1	2	yes	complemented
53	#17988718	C₂²	1	2	yes	complemented
54	#17988718	C₂²	1	2	yes	complemented
55	Q₈×#10596831	C₂²	1	2	yes	complemented
56	#17988666	C₂²	1	2	yes	complemented
57	#17988666	C₂²	1	2	yes	complemented
58	#17988664	C₂²	1	2	yes	—
59	#17988664	C₂²	1	2	yes	complemented
60	#17988664	C₂²	1	2	yes	complemented
61	#17988660	C₂²	1	1	yes	characteristic
62	#17988660	C₂²	1	1	yes	characteristic
63	#17988660	C₂²	1	1	yes	characteristic
64	#17988660	C₂²	1	1	yes	characteristic
65	#17988660	C₂²	1	1	yes	characteristic
66	#17988660	C₂²	1	1	yes	characteristic
67	#17988660	C₂²	1	1	yes	characteristic
68	#17988660	C₂²	1	1	yes	characteristic
69	#17988660	C₂²	1	2	yes	complemented
70	#17988660	C₂²	1	2	yes	complemented
71	#17988660	C₂²	1	2	yes	complemented
72	#17988660	C₂²	1	2	yes	complemented
73	#17988657	C₂²	1	2	yes	—
74	#17988657	C₂²	1	2	yes	—
75	#17988657	C₂²	1	2	yes	complemented
76	#17988657	C₂²	1	2	yes	complemented
77	#17988657	C₂²	1	2	yes	complemented
78	#17988657	C₂²	1	2	yes	complemented
79	C₈×D₂₉₂	C₂²	1	2	yes	complemented
80	C₈×D₂₉₂	C₂²	1	2	yes	complemented
81	#17988652	C₂²	1	2	yes	—
82	#17988652	C₂²	1	2	yes	complemented
83	#17988652	C₂²	1	2	yes	complemented
84	#17988647	C₂²	1	2	yes	complemented
85	#17988647	C₂²	1	2	yes	complemented
86	#17988647	C₂²	1	2	yes	complemented
87	#17988647	C₂²	1	2	yes	complemented
88	#17988647	C₂²	1	2	yes	complemented
89	#17988647	C₂²	1	2	yes	complemented
90	#17988643	C₂²	1	2	yes	complemented
91	#17988643	C₂²	1	2	yes	complemented
92	#17988643	C₂²	1	2	yes	complemented
93	#17988639	C₂²	1	2	yes	complemented
94	#17988639	C₂²	1	2	yes	complemented
95	#17988639	C₂²	1	2	yes	complemented
96	#17988614	C₂²	1	1	yes	characteristic
97	#17988614	C₂²	1	1	yes	characteristic
98	C₂×C₄⋊#10596831	C₂²	1	1	yes	characteristic
99	#17988555	C₂²	1	1	yes	characteristic
100	#17988555	C₂²	1	1	yes	characteristic
101	#17988550	C₂²	1	1	yes	characteristic
102	#17988550	C₂²	1	1	yes	characteristic
103	C₂×#14556503	C₂²	1	1	yes	characteristic
104	C₂×#14556503	C₂²	1	1	yes	characteristic
105	#17988545	C₂²	1	1	yes	characteristic
106	#17988545	C₂²	1	1	yes	characteristic
107	#17988544	C₂²	1	2	yes	complemented
108	#17988544	C₂²	1	2	yes	complemented
109	#17988544	C₂²	1	2	yes	complemented
110	#17988544	C₂²	1	2	yes	complemented
111	#17988543	C₂²	1	1	yes	characteristic
112	#17988543	C₂²	1	1	yes	characteristic
113	#17988542	C₂²	1	1	yes	characteristic
114	#17988542	C₂²	1	1	yes	characteristic
115	#17988541	C₂²	1	2	yes	complemented
116	#17988541	C₂²	1	2	yes	complemented
117	C₄×#11924012	C₂²	1	1	yes	characteristic
118	#17988539	C₂²	1	2	yes	complemented
119	#17988539	C₂²	1	2	yes	complemented
120	C₄×#11924011	C₂²	1	2	yes	complemented
121	#97×D₇₃	C₂²	1	2	yes	complemented
122	#97×D₇₃	C₂²	1	2	yes	complemented
123	C₄×C₈×D₇₃	C₂²	1	2	yes	complemented
124	#533×C₇₃	C₂²	1	1	yes	characteristic
125	#446×C₇₃	C₂²	1	2	yes	complemented
126	#446×C₇₃	C₂²	1	2	yes	complemented
127	#446×C₇₃	C₂²	1	2	yes	complemented
128	#446×C₇₃	C₂²	1	2	yes	complemented
129	#424×C₇₃	C₂²	1	1	yes	characteristic
130	#424×C₇₃	C₂²	1	1	yes	characteristic
131	#423×C₇₃	C₂²	1	1	yes	characteristic
132	#405×C₇₃	C₂²	1	1	yes	characteristic
133	#405×C₇₃	C₂²	1	1	yes	characteristic
134	C₂×#97×C₇₃	C₂²	1	1	yes	characteristic
135	C₂×#11924029	C₂×C₄	1	2	yes	—
136	C₂×#11924028	C₂³	1	1	yes	characteristic
137	C₂²×D₂₉₂	C₂×C₄	1	1	yes	characteristic
138	C₂²×C₄×D₇₃	C₂³	1	1	yes	characteristic
139	C₂²×C₄×D₇₃	C₂³	1	1	yes	characteristic
140	#14556597	—	2	4	no	—
141	#14556597	—	2	4	no	—
142	C₂×#11924012	C₂³	1	1	yes	characteristic
143	C₂×#11924012	C₂³	1	1	yes	characteristic
144	C₂×#11924011	—	2	4	no	—
145	C₂×#11924011	C₂³	1	2	yes	—
146	C₂×#11924011	C₂³	1	2	yes	—
147	C₂×#11924011	C₂³	1	2	yes	—
148	C₂×#11924011	C₂³	1	1	yes	characteristic
149	C₂×#11924011	C₂³	1	1	yes	characteristic
150	C₂×#11924011	C₂³	1	1	yes	characteristic
151	C₂×#11924011	C₂³	1	1	yes	characteristic
152	C₂×#11924011	C₂³	1	2	yes	—
153	M₁₆×D₇₃	—	2	4	no	—
154	M₁₆×D₇₃	—	2	4	no	—
155	C₂²×#10596831	C₂³	1	1	yes	characteristic
156	C₂²×#10596831	C₂³	1	1	yes	characteristic
157	C₂×C₈×D₇₃	—	2	4	no	—
158	C₂×C₈×D₇₃	C₂³	1	2	yes	—
159	C₂×C₈×D₇₃	C₂³	1	2	yes	—
160	C₂×C₈×D₇₃	C₂³	1	2	yes	—
161	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
162	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
163	C₂×C₈×D₇₃	C₂³	1	2	yes	—
164	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
165	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
166	#14556586	C₂×C₄	1	2	yes	—
167	#14556586	C₂×C₄	1	2	yes	—
168	#14556586	C₂×C₄	1	2	yes	—
169	#14556586	C₂×C₄	1	2	yes	—
170	#14556586	C₂×C₄	1	2	yes	—
171	#14556586	C₂×C₄	1	2	yes	—
172	#14556582	C₂×C₄	1	2	yes	—
173	#14556582	C₂×C₄	1	2	yes	—
174	#14556582	C₂×C₄	1	2	yes	—
175	#14556580	C₂×C₄	1	2	yes	—
176	#14556580	C₂×C₄	1	2	yes	—
177	#14556580	C₂×C₄	1	2	yes	—
178	#14556576	C₂×C₄	1	2	yes	—
179	#14556576	C₂×C₄	1	2	yes	—
180	#14556576	C₂×C₄	1	2	yes	—
181	#14556576	C₂×C₄	1	2	yes	—
182	#14556576	C₂×C₄	1	2	yes	—
183	#14556576	C₂×C₄	1	2	yes	—
184	#14556575	C₂×C₄	1	2	yes	—
185	#14556575	C₂×C₄	1	2	yes	—
186	#14556571	C₂×C₄	1	1	yes	characteristic
187	#14556571	C₂×C₄	1	1	yes	characteristic
188	#14556571	C₂×C₄	1	1	yes	characteristic
189	#14556571	C₂×C₄	1	1	yes	characteristic
190	#14556567	C₂×C₄	1	2	yes	—
191	#14556567	C₂×C₄	1	2	yes	—
192	#14556567	C₂×C₄	1	2	yes	—
193	#14556566	C₂×C₄	1	2	yes	—
194	#14556566	C₂×C₄	1	2	yes	—
195	#14556566	C₂×C₄	1	2	yes	—
196	#14556566	C₂×C₄	1	1	yes	characteristic
197	#14556566	C₂×C₄	1	1	yes	characteristic
198	#14556566	C₂×C₄	1	1	yes	characteristic
199	#14556566	C₂×C₄	1	1	yes	characteristic
200	#14556561	C₂×C₄	1	2	yes	—
201	#14556561	C₂×C₄	1	2	yes	—
202	Q₈×Dic₇₃	C₂×C₄	1	2	yes	—
203	C₄×Dic₁₄₆	C₂×C₄	1	1	yes	characteristic
204	C₄×Dic₁₄₆	C₂×C₄	1	1	yes	characteristic
205	C₄×D₂₉₂	C₂×C₄	1	1	yes	characteristic
206	C₄×D₂₉₂	C₂×C₄	1	1	yes	characteristic
207	C₄×D₂₉₂	C₂×C₄	1	1	yes	characteristic
208	C₄×D₂₉₂	C₂×C₄	1	1	yes	characteristic
209	C₄×D₂₉₂	C₂×C₄	1	1	yes	characteristic
210	C₄×D₂₉₂	C₂×C₄	1	1	yes	characteristic
211	C₄×D₂₉₂	C₂³	1	1	yes	characteristic
212	C₄×D₂₉₂	C₂³	1	2	yes	—
213	C₄×D₂₉₂	C₂³	1	2	yes	—
214	C₄×D₂₉₂	C₂³	1	1	yes	characteristic
215	C₄×D₂₉₂	C₂³	1	1	yes	characteristic
216	C₄×D₂₉₂	C₂³	1	2	yes	—
217	C₄×D₂₉₂	C₂³	1	2	yes	—
218	C₄×D₂₉₂	C₂³	1	1	yes	characteristic
219	#14556553	C₂×C₄	1	2	yes	—
220	#14556553	C₂×C₄	1	2	yes	—
221	#14556553	C₂×C₄	1	2	yes	—
222	C₄×C₂²⋊D₇₃	C₂×C₄	1	2	yes	—
223	C₄×C₂²⋊D₇₃	C₂×C₄	1	2	yes	—
224	#14556550	C₂³	1	1	yes	characteristic
225	#14556549	C₂×C₄	1	2	yes	—
226	#14556549	C₂×C₄	1	2	yes	—
227	#14556549	C₂×C₄	1	1	yes	characteristic
228	#14556549	C₂×C₄	1	1	yes	characteristic
229	#14556549	C₂×C₄	1	2	yes	—
230	#14556549	C₂×C₄	1	1	yes	characteristic
231	#14556549	C₂×C₄	1	1	yes	characteristic
232	#14556548	C₂³	1	2	yes	—
233	#14556548	C₂³	1	2	yes	—
234	#14556548	C₂³	1	2	yes	—
235	#14556547	C₂×C₄	1	2	yes	—
236	#14556547	C₂×C₄	1	2	yes	—
237	C₂×C₄⋊Dic₇₃	C₂×C₄	1	1	yes	characteristic
238	C₄⋊C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
239	C₄⋊C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
240	C₄⋊C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
241	C₄⋊C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
242	C₂×#11924005	C₂×C₄	1	1	yes	characteristic
243	C₂×#11924005	C₂×C₄	1	1	yes	characteristic
244	C₂²⋊C₄×D₇₃	C₂×C₄	1	2	yes	—
245	C₂²⋊C₄×D₇₃	C₂×C₄	1	2	yes	—
246	C₄²×D₇₃	C₂³	1	2	yes	—
247	C₄²×D₇₃	C₂³	1	2	yes	—
248	C₄²×D₇₃	C₂³	1	2	yes	—
249	C₄⋊#10596831	C₂³	1	1	yes	characteristic
250	C₄⋊#10596831	C₂³	1	1	yes	characteristic
251	C₄⋊#10596831	C₂³	1	1	yes	characteristic
252	C₄⋊#10596831	C₂³	1	1	yes	characteristic
253	C₄⋊#10596831	C₂³	1	2	yes	—
254	C₄⋊#10596831	C₂³	1	2	yes	—
255	C₄⋊#10596831	C₂³	1	2	yes	—
256	C₄⋊#10596831	C₂³	1	2	yes	—
257	#14556503	C₂³	1	1	yes	characteristic
258	#14556503	C₂³	1	1	yes	characteristic
259	#14556503	C₂³	1	2	yes	—
260	#14556503	C₂³	1	2	yes	—
261	#14556503	C₂³	1	2	yes	—
262	#14556503	C₂³	1	2	yes	—
263	#14556503	C₂³	1	1	yes	characteristic
264	#14556503	C₂³	1	1	yes	characteristic
265	#14556503	C₂³	1	2	yes	—
266	#14556503	C₂³	1	2	yes	—
267	#14556503	C₂³	1	2	yes	—
268	#14556503	C₂³	1	1	yes	characteristic
269	#14556503	C₂³	1	2	yes	—
270	#14556503	C₂³	1	1	yes	characteristic
271	#14556503	C₂³	1	1	yes	characteristic
272	#14556503	C₂³	1	1	yes	characteristic
273	#14556502	C₂³	1	2	yes	—
274	#14556502	C₂³	1	2	yes	—
275	#14556502	C₂³	1	2	yes	—
276	#14556501	C₂³	1	2	yes	—
277	#14556501	C₂³	1	2	yes	—
278	#14556501	C₂³	1	2	yes	—
279	#14556501	C₂³	1	2	yes	—
280	C₄×#10596831	C₂³	1	2	yes	—
281	C₄×#10596831	C₂³	1	2	yes	—
282	C₄×#10596831	C₂³	1	2	yes	—
283	C₈×Dic₇₃	C₂³	1	2	yes	—
284	C₈×Dic₇₃	C₂³	1	2	yes	—
285	C₈×Dic₇₃	C₂³	1	2	yes	—
286	C₈×Dic₇₃	C₂³	1	2	yes	—
287	C₂×M₁₆×C₇₃	C₂³	1	1	yes	characteristic
288	C₂×M₁₆×C₇₃	C₂³	1	1	yes	characteristic
289	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
290	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
291	C₄⋊Q₈×C₇₃	C₂×C₄	1	1	yes	characteristic
292	C₄⋊Q₈×C₇₃	C₂×C₄	1	1	yes	characteristic
293	#125×C₇₃	C₂×C₄	1	1	yes	characteristic
294	#125×C₇₃	C₂×C₄	1	1	yes	characteristic
295	C₂²⋊Q₈×C₇₃	C₂×C₄	1	2	yes	—
296	C₂²⋊Q₈×C₇₃	C₂×C₄	1	2	yes	—
297	C₄×Q₈×C₇₃	C₂³	1	2	yes	—
298	C₄×Q₈×C₇₃	C₂³	1	2	yes	—
299	#117×C₇₃	C₂³	1	1	yes	characteristic
300	#117×C₇₃	C₂³	1	1	yes	characteristic
301	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
302	C₄⋊C₈×C₇₃	C₂³	1	2	yes	—
303	C₄⋊C₈×C₇₃	C₂³	1	2	yes	—
304	C₄⋊C₈×C₇₃	C₂³	1	2	yes	—
305	C₄⋊C₈×C₇₃	C₂³	1	2	yes	—
306	C₄⋊C₈×C₇₃	C₂³	1	2	yes	—
307	C₄⋊C₈×C₇₃	C₂³	1	2	yes	—
308	#97×C₇₃	C₂³	1	1	yes	characteristic
309	#97×C₇₃	C₂³	1	1	yes	characteristic
310	#97×C₇₃	C₂³	1	1	yes	characteristic
311	#97×C₇₃	C₂³	1	1	yes	characteristic
312	#97×C₇₃	C₂³	1	2	yes	—
313	#97×C₇₃	C₂³	1	2	yes	—
314	C₄×C₈×C₇₃	C₂³	1	2	yes	—
315	C₄×C₈×C₇₃	C₂³	1	2	yes	—
316	C₂³×D₇₃	C₂²×C₄	1	1	yes	characteristic
317	C₂³×D₇₃	C₂²×C₄	1	1	yes	characteristic
318	#11924029	—	4	4	no	—
319	#11924028	—	2	2	no	—
320	#11924028	—	2	2	no	—
321	C₂×Dic₁₄₆	C₂²×C₄	1	1	yes	characteristic
322	C₂×D₂₉₂	—	4	2	no	—
323	C₂×D₂₉₂	C₂²×C₄	1	1	yes	characteristic
324	C₂×D₂₉₂	C₂²×C₄	1	2	yes	—
325	C₂×D₂₉₂	C₂²×C₄	1	1	yes	characteristic
326	C₂×D₂₉₂	C₂²×C₄	1	1	yes	characteristic
327	C₂×D₂₉₂	C₂²×C₄	1	2	yes	—
328	C₂×D₂₉₂	C₂²×C₄	1	1	yes	characteristic
329	C₂×D₂₉₂	C₂²×C₄	1	1	yes	characteristic
330	C₂×D₂₉₂	C₂²×C₄	1	2	yes	—
331	C₂×D₂₉₂	C₂²×C₄	1	2	yes	—
332	C₂×C₂²⋊D₇₃	C₂²×C₄	1	2	yes	—
333	C₂²×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
334	C₂²×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
335	C₂×C₄×D₇₃	—	2	2	no	—
336	C₂×C₄×D₇₃	—	2	2	no	—
337	C₂×C₄×D₇₃	—	2	2	no	—
338	C₂×C₄×D₇₃	—	2	2	no	—
339	C₂×C₄×D₇₃	C₂²×C₄	1	2	yes	—
340	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
341	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
342	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
343	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
344	C₂×C₄×D₇₃	C₂²×C₄	1	2	yes	—
345	C₂×C₄×D₇₃	C₂²×C₄	1	2	yes	—
346	C₂×C₄×D₇₃	C₂²×C₄	1	2	yes	—
347	C₂×C₄×D₇₃	C₂²×C₄	1	2	yes	—
348	C₂×C₄×D₇₃	C₂²×C₄	1	2	yes	—
349	C₂×C₄×D₇₃	C₂⁴	1	1	yes	characteristic
350	C₂×C₄×D₇₃	C₂⁴	1	1	yes	characteristic
351	C₂×C₄×D₇₃	C₂⁴	1	2	yes	—
352	C₂×C₄×D₇₃	C₂⁴	1	1	yes	characteristic
353	C₂×C₄×D₇₃	C₂⁴	1	1	yes	characteristic
354	#11924012	—	2	2	no	—
355	#11924012	#41	1	4	yes	complemented
356	#11924011	—	2	2	no	—
357	#11924011	—	2	2	no	—
358	#11924011	—	2	2	no	—
359	#11924011	—	2	2	no	—
360	#11924011	—	2	4	no	—
361	#11924011	—	2	4	no	—
362	#11924011	—	2	4	no	—
363	#11924011	—	2	4	no	—
364	C₂×#10596831	—	2	2	no	—
365	C₂×#10596831	—	2	2	no	—
366	C₂×#10596831	C₂⁴	1	1	yes	characteristic
367	C₂×#10596831	C₂⁴	1	1	yes	characteristic
368	C₂×#10596831	C₂⁴	1	2	yes	—
369	C₂×#10596831	C₂⁴	1	1	yes	characteristic
370	C₂×#10596831	C₂⁴	1	1	yes	characteristic
371	C₂×#10596831	C₂⁴	1	2	yes	—
372	C₈×D₇₃	—	2	2	no	—
373	C₈×D₇₃	—	2	2	no	—
374	C₈×D₇₃	—	2	2	no	—
375	C₈×D₇₃	—	2	2	no	—
376	C₈×D₇₃	—	2	4	no	—
377	C₈×D₇₃	—	2	4	no	—
378	C₈×D₇₃	—	2	4	no	—
379	C₈×D₇₃	—	2	4	no	—
380	C₄⋊Dic₇₃	C₂²×C₄	1	1	yes	characteristic
381	C₄⋊Dic₇₃	C₂²×C₄	1	1	yes	characteristic
382	C₄⋊Dic₇₃	C₂²×C₄	1	1	yes	characteristic
383	C₄⋊Dic₇₃	C₂²×C₄	1	1	yes	characteristic
384	C₄⋊Dic₇₃	C₂²×C₄	1	1	yes	characteristic
385	C₄⋊Dic₇₃	C₂²×C₄	1	1	yes	characteristic
386	C₄⋊Dic₇₃	C₂²×C₄	1	2	yes	—
387	C₄⋊Dic₇₃	C₂²×C₄	1	2	yes	—
388	C₄⋊Dic₇₃	C₂²×C₄	1	2	yes	—
389	C₄⋊Dic₇₃	C₂²×C₄	1	2	yes	—
390	#11924007	C₂²×C₄	1	2	yes	—
391	#11924007	C₂²×C₄	1	2	yes	—
392	#11924007	C₂²×C₄	1	2	yes	—
393	#11924007	C₂²×C₄	1	2	yes	—
394	#11924007	C₂²×C₄	1	2	yes	—
395	#11924007	C₂²×C₄	1	2	yes	—
396	C₂²⋊Dic₇₃	C₂²×C₄	1	2	yes	—
397	#11924005	C₂²×C₄	1	2	yes	—
398	#11924005	C₂²×C₄	1	2	yes	—
399	#11924005	C₂²×C₄	1	2	yes	—
400	#11924005	C₂²×C₄	1	2	yes	—
401	#11924005	C₂²×C₄	1	1	yes	characteristic
402	#11924005	C₂²×C₄	1	1	yes	characteristic
403	#11924005	C₂²×C₄	1	1	yes	characteristic
404	#11924005	C₂²×C₄	1	1	yes	characteristic
405	#11924005	C₂²×C₄	1	1	yes	characteristic
406	#11924005	C₂²×C₄	1	1	yes	characteristic
407	#11924005	C₂²×C₄	1	1	yes	characteristic
408	#11924005	C₂²×C₄	1	1	yes	characteristic
409	#11924005	C₂²×C₄	1	2	yes	—
410	#11924005	C₂²×C₄	1	2	yes	—
411	#11924005	C₂²×C₄	1	2	yes	—
412	#11924005	C₂²×C₄	1	2	yes	—
413	#11924005	C₂²×C₄	1	2	yes	—
414	#11924005	C₂²×C₄	1	2	yes	—
415	#11924005	C₂²×C₄	1	2	yes	—
416	#11924005	C₂²×C₄	1	2	yes	—
417	#11924005	C₂²×C₄	1	2	yes	—
418	#11924005	C₂²×C₄	1	2	yes	—
419	C₄×Dic₇₃	C₂²×C₄	1	2	yes	—
420	C₄×Dic₇₃	C₂²×C₄	1	2	yes	—
421	C₄×Dic₇₃	C₂²×C₄	1	2	yes	—
422	C₄×Dic₇₃	C₂²×C₄	1	2	yes	—
423	C₄×Dic₇₃	C₂²×C₄	1	2	yes	—
424	C₄×Dic₇₃	C₂²×C₄	1	2	yes	—
425	C₄×Dic₇₃	C₂⁴	1	2	yes	—
426	C₂×Q₈×C₇₃	C₂²×C₄	1	2	yes	—
427	C₂×Q₈×C₇₃	C₂²×C₄	1	2	yes	—
428	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
429	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
430	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
431	M₁₆×C₇₃	—	2	2	no	—
432	M₁₆×C₇₃	—	2	2	no	—
433	C₂×C₈×C₇₃	—	2	2	no	—
434	C₂×C₈×C₇₃	#41	1	4	yes	complemented
435	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
436	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
437	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
438	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
439	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
440	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
441	C₄⋊C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
442	C₄⋊C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
443	C₄⋊C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
444	C₄⋊C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
445	C₄⋊C₄×C₇₃	C₂²×C₄	1	2	yes	—
446	C₄⋊C₄×C₇₃	C₂²×C₄	1	2	yes	—
447	C₄⋊C₄×C₇₃	C₂²×C₄	1	2	yes	—
448	C₄⋊C₄×C₇₃	C₂²×C₄	1	2	yes	—
449	C₄⋊C₄×C₇₃	C₂²×C₄	1	2	yes	—
450	C₄⋊C₄×C₇₃	C₂²×C₄	1	2	yes	—
451	C₂²⋊C₄×C₇₃	C₂²×C₄	1	2	yes	—
452	C₂²⋊C₄×C₇₃	C₂²×C₄	1	2	yes	—
453	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
454	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
455	C₄²×C₇₃	C₂⁴	1	2	yes	—
456	C₄²×C₇₃	C₂⁴	1	2	yes	—
457	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
458	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
459	C₂³×C₇₃	C₂³×C₄	1	1	yes	characteristic
460	C₂²×D₇₃	—	2	2	no	—
461	C₂²×D₇₃	—	2	2	no	—
462	C₂²×D₇₃	—	2	2	no	—
463	C₂²×D₇₃	—	4	1	no	—
464	C₂²×D₇₃	—	4	1	no	—
465	C₂²×D₇₃	—	4	1	no	—
466	C₂²×D₇₃	C₂³×C₄	1	1	yes	characteristic
467	C₂²×D₇₃	C₂³×C₄	1	1	yes	characteristic
468	C₂²×D₇₃	C₂³×C₄	1	2	yes	—
469	C₂²×D₇₃	C₂³×C₄	1	1	yes	characteristic
470	C₂²×D₇₃	C₂³×C₄	1	1	yes	characteristic
471	Q₈×C₇₃	—	4	2	no	—
472	Q₈×C₇₃	—	4	2	no	—
473	C₂×C₄×C₇₃	—	4	1	no	—
474	C₂×C₄×C₇₃	—	4	1	no	—
475	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
476	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
477	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
478	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
479	C₂×C₄×C₇₃	C₂³×C₄	1	2	yes	—
480	C₂×C₄×C₇₃	C₂³×C₄	1	2	yes	—
481	C₂×C₄×C₇₃	C₂³×C₄	1	2	yes	—
482	C₂×C₄×C₇₃	C₂³×C₄	1	2	yes	—
483	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
484	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
485	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
486	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
487	C₂²⋊D₇₃	—	2	4	no	—
488	C₂×Dic₇₃	—	2	2	no	—
489	C₂×Dic₇₃	—	2	2	no	—
490	C₂×Dic₇₃	C₂³×C₄	1	1	yes	characteristic
491	C₂×Dic₇₃	C₂³×C₄	1	1	yes	characteristic
492	C₂×Dic₇₃	C₂³×C₄	1	2	yes	—
493	C₂×Dic₇₃	C₂³×C₄	1	2	yes	—
494	C₂×Dic₇₃	C₂³×C₄	1	2	yes	—
495	C₂×Dic₇₃	C₂³×C₄	1	1	yes	characteristic
496	C₂×Dic₇₃	C₂³×C₄	1	1	yes	characteristic
497	D₂₉₂	—	2	2	no	—
498	D₂₉₂	—	2	2	no	—
499	D₂₉₂	—	2	4	no	—
500	D₂₉₂	—	2	2	no	—
501	D₂₉₂	—	4	1	no	—
502	D₂₉₂	—	4	1	no	—
503	D₂₉₂	—	4	2	no	—
504	D₂₉₂	—	4	2	no	—
505	D₂₉₂	—	4	2	no	—
506	C₄×D₇₃	—	2	4	no	—
507	C₄×D₇₃	—	2	2	no	—
508	C₄×D₇₃	—	2	2	no	—
509	C₄×D₇₃	—	2	2	no	—
510	C₄×D₇₃	—	2	2	no	—
511	C₄×D₇₃	—	2	1	no	—
512	C₄×D₇₃	—	2	1	no	—
513	C₄×D₇₃	—	2	1	no	—
514	C₄×D₇₃	—	2	1	no	—
515	C₄×D₇₃	—	2	2	no	—
516	C₄×D₇₃	—	2	2	no	—
517	C₄×D₇₃	—	2	1	no	—
518	C₄×D₇₃	—	2	1	no	—
519	C₄×D₇₃	—	2	1	no	—
520	C₄×D₇₃	—	2	1	no	—
521	C₄×D₇₃	—	4	2	no	—
522	C₄×D₇₃	—	4	2	no	—
523	C₄×D₇₃	—	4	2	no	—
524	C₄×D₇₃	—	4	2	no	—
525	C₄×D₇₃	—	4	2	no	—
526	Dic₁₄₆	—	2	2	no	—
527	C₈×C₇₃	—	2	1	no	—
528	C₈×C₇₃	—	2	1	no	—
529	C₈×C₇₃	—	2	2	no	—
530	C₈×C₇₃	—	2	2	no	—
531	C₈×C₇₃	C₂×#41	1	2	yes	—
532	C₈×C₇₃	C₂×#41	1	2	yes	—
533	#10596831	—	2	1	no	—
534	#10596831	—	2	1	no	—
535	#10596831	—	2	2	no	—
536	#10596831	—	2	1	no	—
537	#10596831	—	2	1	no	—
538	#10596831	C₂×#41	1	4	yes	—
539	C₂²×C₇₃	—	2	1	no	—
540	C₂²×C₇₃	—	2	1	no	—
541	C₂²×C₇₃	C₄×#41	1	2	yes	—
542	C₂²×C₇₃	C₂⁴×C₄	1	1	yes	characteristic
543	C₂×D₇₃	—	2	1	no	—
544	C₂×D₇₃	—	2	1	no	—
545	C₂×D₇₃	—	2	1	no	—
546	C₂×D₇₃	—	2	1	no	—
547	C₂×D₇₃	—	2	1	no	—
548	C₂×D₇₃	—	2	2	no	—
549	C₂×D₇₃	—	2	1	no	—
550	C₂×D₇₃	—	2	2	no	—
551	C₂×D₇₃	—	2	1	no	—
552	C₂×D₇₃	—	2	1	no	—
553	C₂×D₇₃	—	2	1	no	—
554	C₂×D₇₃	—	2	2	no	—
555	C₂×D₇₃	—	2	1	no	—
556	C₂×D₇₃	—	2	1	no	—
557	C₂×D₇₃	—	4	4	no	—
558	C₂×D₇₃	—	8	2	no	—
559	C₂×D₇₃	#568	1	2	yes	—
560	C₄×C₇₃	—	2	2	no	—
561	C₄×C₇₃	—	2	1	no	—
562	C₄×C₇₃	—	2	2	no	—
563	C₄×C₇₃	—	2	1	no	—
564	C₄×C₇₃	—	2	1	no	—
565	C₄×C₇₃	—	2	2	no	—
566	C₄×C₇₃	—	2	2	no	—
567	C₄×C₇₃	—	2	1	no	—
568	C₄×C₇₃	C₄×#41	1	2	yes	—
569	C₄×C₇₃	C₂²×#41	1	1	yes	characteristic
570	C₄×C₇₃	C₂²×#41	1	1	yes	characteristic
571	Dic₇₃	—	2	2	no	—
572	Dic₇₃	—	2	1	no	—
573	Dic₇₃	—	2	1	no	—
574	Dic₇₃	—	2	1	no	—
575	Dic₇₃	—	2	1	no	—
576	Dic₇₃	—	2	2	no	—
577	Dic₇₃	—	2	2	no	—
578	#60216	—	73	1	no	maximal, Sylow
579	C₂×C₇₃	—	2	2	no	—
580	C₂×C₇₃	C₂×C₄×#41	1	1	yes	characteristic
581	C₂×C₇₃	C₂×#568	1	1	yes	characteristic
582	C₂×C₇₃	#3573	1	1	yes	characteristic
583	D₇₃	—	2	2	no	—
584	D₇₃	—	4	2	no	—
585	D₇₃	—	4	1	no	—
586	D₇₃	—	4	1	no	—
587	D₇₃	—	4	1	no	—
588	#3475	—	73	1	no	—
589	#2970	—	73	2	no	—
590	#2969	—	73	2	no	—
591	#2968	—	73	2	no	—
592	#2968	—	73	2	no	—
593	#2967	—	73	2	no	—
594	#2967	—	73	2	no	—
595	#2966	—	73	2	no	—
596	#2965	—	73	2	no	—
597	#2962	—	73	1	no	—
598	#2961	D₇₃	1	1	yes	characteristic, complemented
599	D₄×M₁₆	—	73	1	no	—
600	#2933	—	73	1	no	—
601	#2933	—	73	1	no	—
602	#2930	—	73	1	no	—
603	#2929	—	73	1	no	—
604	C₂×#435	—	73	1	no	—
605	#2925	—	73	1	no	—
606	#2924	—	73	1	no	—
607	#2924	—	73	1	no	—
608	#2875	—	73	1	no	—
609	#2873	—	73	1	no	—
610	C₂×#405	—	73	1	no	—
611	C₇₃	#60216	1	1	yes	characteristic, complemented, Sylow
612	C₂×#131	—	73	1	no	—
613	C₂×#131	—	73	1	no	—
614	C₂²×M₁₆	—	73	1	no	—
615	C₂²×M₁₆	—	73	1	no	—
616	C₂²×M₁₆	—	73	1	no	—
617	C₂³×C₈	—	73	1	no	—
618	#556	—	73	1	no	—
619	#555	—	73	1	no	—
620	#554	—	73	1	no	—
621	#553	—	73	1	no	—
622	#553	—	73	1	no	—
623	#552	—	73	1	no	—
624	#552	—	73	1	no	—
625	#552	—	73	2	no	—
626	#551	—	73	2	no	—
627	#551	—	73	2	no	—
628	#547	—	73	1	no	—
629	#546	—	73	2	no	—
630	#533	C₂×D₇₃	1	1	yes	characteristic
631	#529	—	73	2	no	—
632	#529	—	73	2	no	—
633	#529	—	73	2	no	—
634	#525	—	73	1	no	—
635	#525	—	73	1	no	—
636	C₄×#41	—	73	2	no	—
637	C₄×#41	—	73	1	no	—
638	C₂×C₄×D₄	—	73	1	no	—
639	C₂×#117	—	73	1	no	—
640	C₂×#117	—	73	1	no	—
641	#446	—	73	2	no	—
642	#446	—	73	2	no	—
643	#446	—	73	2	no	—
644	#446	C₂×D₇₃	1	2	yes	complemented
645	#446	C₂×D₇₃	1	2	yes	complemented
646	#446	C₂×D₇₃	1	2	yes	complemented
647	#446	C₂×D₇₃	1	2	yes	complemented
648	C₈×Q₈	—	73	2	no	—
649	#436	—	73	2	no	—
650	#436	—	73	2	no	—
651	#436	—	73	2	no	—
652	#436	—	73	2	no	—
653	#436	—	73	2	no	—
654	#435	—	73	2	no	—
655	#435	—	73	2	no	—
656	#435	—	73	2	no	—
657	#435	—	73	2	no	—
658	#435	—	73	2	no	—
659	#435	—	73	2	no	—
660	#435	—	73	1	no	—
661	#435	—	73	1	no	—
662	#435	—	73	1	no	—
663	#435	—	73	1	no	—
664	#435	—	73	1	no	—
665	#435	—	73	1	no	—
666	#435	—	73	1	no	—
667	#435	—	73	1	no	—
668	#435	—	73	2	no	—
669	#435	—	73	2	no	—
670	#435	—	73	2	no	—
671	#435	—	73	2	no	—
672	C₈×D₄	—	73	2	no	—
673	C₈×D₄	—	73	2	no	—
674	C₈×D₄	—	73	2	no	—
675	C₈×D₄	—	73	2	no	—
676	C₈×D₄	—	73	2	no	—
677	#433	—	73	2	no	—
678	#433	—	73	2	no	—
679	#433	—	73	2	no	—
680	#433	—	73	2	no	—
681	#433	—	73	2	no	—
682	#433	—	73	2	no	—
683	#432	—	73	2	no	—
684	#432	—	73	2	no	—
685	#432	—	73	2	no	—
686	#431	—	73	2	no	—
687	#431	—	73	2	no	—
688	#431	—	73	2	no	—
689	#424	—	73	1	no	—
690	#424	—	73	1	no	—
691	#424	C₂×D₇₃	1	1	yes	characteristic
692	#424	C₂×D₇₃	1	1	yes	characteristic
693	#423	C₂×D₇₃	1	1	yes	characteristic
694	C₂×C₄⋊C₈	—	73	1	no	—
695	#408	—	73	1	no	—
696	#408	—	73	1	no	—
697	#407	—	73	1	no	—
698	#407	—	73	1	no	—
699	C₂×C₂²⋊C₈	—	73	1	no	—
700	C₂×C₂²⋊C₈	—	73	1	no	—
701	#405	—	73	1	no	—
702	#405	—	73	1	no	—
703	#405	—	73	1	no	—
704	#405	—	73	1	no	—
705	#405	—	73	1	no	—
706	#405	—	73	1	no	—
707	#405	—	73	2	no	—
708	#405	—	73	2	no	—
709	#405	—	73	2	no	—
710	#405	—	73	2	no	—
711	#405	—	73	2	no	—
712	#405	—	73	2	no	—
713	#405	C₂×D₇₃	1	1	yes	characteristic
714	#405	C₂×D₇₃	1	1	yes	characteristic
715	C₄×M₁₆	—	73	1	no	—
716	C₄×M₁₆	—	73	2	no	—
717	C₄×M₁₆	—	73	2	no	—
718	C₄×M₁₆	—	73	2	no	—
719	C₂×#97	—	73	2	no	—
720	C₂×#97	—	73	2	no	—
721	C₂×#97	C₂×D₇₃	1	1	yes	characteristic
722	C₂×C₄×C₈	—	73	2	no	—
723	C₂×#41	—	73	2	no	—
724	C₂×#41	—	73	1	no	—
725	C₂²×D₄	—	73	1	no	—
726	C₂³×C₄	—	73	1	no	—
727	C₂³×C₄	—	73	1	no	—
728	#131	—	146	4	no	—
729	#131	—	146	4	no	—
730	C₂×M₁₆	—	73	1	no	—
731	C₂×M₁₆	—	73	1	no	—
732	C₂×M₁₆	—	73	1	no	—
733	C₂×M₁₆	—	73	2	no	—
734	C₂×M₁₆	—	73	1	no	—
735	C₂×M₁₆	—	73	1	no	—
736	C₂×M₁₆	—	73	2	no	—
737	C₂×M₁₆	—	73	1	no	—
738	C₂×M₁₆	—	73	2	no	—
739	C₂×M₁₆	—	73	2	no	—
740	C₂×M₁₆	—	146	4	no	—
741	C₂×M₁₆	—	146	4	no	—
742	C₂×M₁₆	—	146	4	no	—
743	C₂×M₁₆	C₂²×D₇₃	1	1	yes	characteristic
744	C₂×M₁₆	C₂²×D₇₃	1	1	yes	characteristic
745	C₂²×C₈	—	73	1	no	—
746	C₂²×C₈	—	73	1	no	—
747	C₂²×C₈	—	73	1	no	—
748	C₂²×C₈	—	73	1	no	—
749	C₂²×C₈	—	73	1	no	—
750	C₂²×C₈	—	73	1	no	—
751	C₂²×C₈	—	73	2	no	—
752	C₂²×C₈	—	73	2	no	—
753	C₂²×C₈	—	73	2	no	—
754	C₂²×C₈	—	73	2	no	—
755	C₂²×C₈	—	146	4	no	—
756	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
757	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
758	C₄⋊Q₈	C₄×D₇₃	1	1	yes	characteristic
759	C₄⋊Q₈	C₄×D₇₃	1	1	yes	characteristic
760	#126	—	73	2	no	—
761	#126	—	73	2	no	—
762	#126	—	73	2	no	—
763	#126	—	73	2	no	—
764	#126	—	73	2	no	—
765	#126	—	73	2	no	—
766	#125	—	73	2	no	—
767	#125	—	73	2	no	—
768	#125	—	73	2	no	—
769	#125	C₄×D₇₃	1	1	yes	characteristic
770	#125	C₄×D₇₃	1	1	yes	characteristic
771	#124	—	73	2	no	—
772	#124	—	73	2	no	—
773	#124	—	73	2	no	—
774	#123	—	73	2	no	—
775	#123	—	73	2	no	—
776	#123	—	73	2	no	—
777	#123	—	73	2	no	—
778	#123	—	73	2	no	—
779	#123	—	73	2	no	—
780	#123	—	73	2	no	—
781	#123	—	73	2	no	—
782	C₂²⋊Q₈	—	73	2	no	—
783	C₂²⋊Q₈	—	73	2	no	—
784	C₂²⋊Q₈	—	73	2	no	—
785	C₂²⋊Q₈	—	73	1	no	—
786	C₂²⋊Q₈	—	73	1	no	—
787	C₂²⋊Q₈	—	73	1	no	—
788	C₂²⋊Q₈	—	73	1	no	—
789	C₂²⋊Q₈	C₄×D₇₃	1	2	yes	—
790	C₂²⋊Q₈	C₄×D₇₃	1	2	yes	—
791	#121	—	73	1	no	—
792	#121	—	73	1	no	—
793	#121	—	73	1	no	—
794	#121	—	73	1	no	—
795	#121	—	73	2	no	—
796	#121	—	73	2	no	—
797	#121	—	73	2	no	—
798	#120	—	73	2	no	—
799	#120	—	73	2	no	—
800	C₄×Q₈	—	73	2	no	—
801	C₄×Q₈	—	73	1	no	—
802	C₄×Q₈	—	73	1	no	—
803	C₄×Q₈	C₂²×D₇₃	1	2	yes	—
804	C₄×Q₈	C₂²×D₇₃	1	2	yes	—
805	C₄×D₄	—	73	2	no	—
806	C₄×D₄	—	73	2	no	—
807	C₄×D₄	—	73	2	no	—
808	C₄×D₄	—	73	2	no	—
809	C₄×D₄	—	73	2	no	—
810	C₄×D₄	—	73	1	no	—
811	C₄×D₄	—	73	1	no	—
812	C₄×D₄	—	73	1	no	—
813	C₄×D₄	—	73	1	no	—
814	C₄×D₄	—	73	1	no	—
815	C₄×D₄	—	73	1	no	—
816	C₄×D₄	—	73	1	no	—
817	C₄×D₄	—	73	1	no	—
818	C₄×D₄	—	73	1	no	—
819	C₄×D₄	—	73	1	no	—
820	C₄×D₄	—	73	2	no	—
821	C₄×D₄	—	73	2	no	—
822	C₄×D₄	—	73	2	no	—
823	C₄×D₄	—	73	2	no	—
824	#117	—	73	1	no	—
825	#117	—	73	1	no	—
826	#117	—	73	1	no	—
827	#117	—	73	1	no	—
828	#117	—	73	1	no	—
829	#117	—	73	2	no	—
830	#117	—	73	2	no	—
831	#117	—	73	2	no	—
832	#117	—	73	2	no	—
833	#117	—	73	2	no	—
834	#117	—	73	2	no	—
835	#117	—	73	2	no	—
836	#117	—	73	2	no	—
837	#117	C₂²×D₇₃	1	1	yes	characteristic
838	#117	C₂²×D₇₃	1	1	yes	characteristic
839	C₂×C₄⋊C₄	—	73	1	no	—
840	C₂×C₄⋊C₄	—	73	1	no	—
841	C₂×C₄⋊C₄	—	73	1	no	—
842	C₂×C₄⋊C₄	—	73	1	no	—
843	C₂×C₄⋊C₄	—	73	1	no	—
844	C₂×C₂²⋊C₄	—	73	1	no	—
845	C₂×C₂²⋊C₄	—	73	1	no	—
846	C₂×C₂²⋊C₄	—	73	2	no	—
847	C₂×C₂²⋊C₄	—	73	2	no	—
848	C₂×C₄²	—	73	2	no	—
849	C₂×C₄²	—	73	2	no	—
850	C₂×C₄²	—	73	2	no	—
851	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
852	C₄⋊C₈	—	73	1	no	—
853	C₄⋊C₈	—	73	1	no	—
854	C₄⋊C₈	—	73	1	no	—
855	C₄⋊C₈	—	73	1	no	—
856	C₄⋊C₈	—	73	2	no	—
857	C₄⋊C₈	—	73	2	no	—
858	C₄⋊C₈	—	73	2	no	—
859	C₄⋊C₈	—	73	2	no	—
860	C₄⋊C₈	C₂²×D₇₃	1	2	yes	—
861	C₄⋊C₈	C₂²×D₇₃	1	2	yes	—
862	C₄⋊C₈	C₂²×D₇₃	1	2	yes	—
863	C₄⋊C₈	C₂²×D₇₃	1	2	yes	—
864	C₄⋊C₈	C₂²×D₇₃	1	2	yes	—
865	C₄⋊C₈	C₂²×D₇₃	1	2	yes	—
866	C₂²⋊C₈	—	73	1	no	—
867	C₂²⋊C₈	—	73	1	no	—
868	C₂²⋊C₈	—	73	1	no	—
869	C₂²⋊C₈	—	73	1	no	—
870	C₂²⋊C₈	—	73	1	no	—
871	C₂²⋊C₈	—	73	1	no	—
872	C₂²⋊C₈	—	73	1	no	—
873	C₂²⋊C₈	—	73	1	no	—
874	C₂²⋊C₈	—	73	2	no	—
875	C₂²⋊C₈	—	73	2	no	—
876	C₂²⋊C₈	—	73	2	no	—
877	C₂²⋊C₈	—	73	2	no	—
878	C₂²⋊C₈	—	73	2	no	—
879	C₂²⋊C₈	—	73	2	no	—
880	C₂²⋊C₈	—	73	2	no	—
881	C₂²⋊C₈	—	73	2	no	—
882	#97	—	73	2	no	—
883	#97	—	73	2	no	—
884	#97	—	73	2	no	—
885	#97	—	73	2	no	—
886	#97	—	73	2	no	—
887	#97	—	73	2	no	—
888	#97	—	73	2	no	—
889	#97	C₂²×D₇₃	1	1	yes	characteristic
890	#97	C₂²×D₇₃	1	2	yes	—
891	#97	C₂²×D₇₃	1	1	yes	characteristic
892	#97	C₂²×D₇₃	1	1	yes	characteristic
893	#97	C₂²×D₇₃	1	1	yes	characteristic
894	#97	C₂²×D₇₃	1	2	yes	—
895	C₄×C₈	—	73	2	no	—
896	C₄×C₈	—	73	2	no	—
897	C₄×C₈	—	73	2	no	—
898	C₄×C₈	—	73	2	no	—
899	C₄×C₈	—	73	2	no	—
900	C₄×C₈	—	73	2	no	—
901	C₄×C₈	—	73	2	no	—
902	C₄×C₈	C₂²×D₇₃	1	2	yes	—
903	C₄×C₈	C₂²×D₇₃	1	2	yes	—
904	C₂⁴	—	73	1	no	—
905	C₂⁴	—	73	1	no	—
906	#41	—	292	4	no	—
907	#41	—	146	2	no	—
908	#41	—	146	2	no	—
909	C₂×Q₈	—	73	1	no	—
910	C₂×Q₈	C₂×C₄×D₇₃	1	2	yes	—
911	C₂×Q₈	C₂×C₄×D₇₃	1	2	yes	—
912	C₂×D₄	—	292	2	no	—
913	C₂×D₄	—	73	2	no	—
914	C₂×D₄	—	73	2	no	—
915	C₂×D₄	—	73	1	no	—
916	C₂×D₄	—	73	1	no	—
917	C₂×D₄	—	73	2	no	—
918	C₂×D₄	—	73	2	no	—
919	C₂×D₄	—	73	1	no	—
920	C₂×D₄	—	73	2	no	—
921	C₂×D₄	—	73	1	no	—
922	C₂×D₄	—	73	1	no	—
923	C₂²×C₄	—	73	2	no	—
924	C₂²×C₄	—	73	2	no	—
925	C₂²×C₄	—	73	2	no	—
926	C₂²×C₄	—	73	2	no	—
927	C₂²×C₄	—	73	2	no	—
928	C₂²×C₄	—	73	1	no	—
929	C₂²×C₄	—	73	1	no	—
930	C₂²×C₄	—	73	2	no	—
931	C₂²×C₄	—	73	1	no	—
932	C₂²×C₄	—	73	1	no	—
933	C₂²×C₄	—	73	1	no	—
934	C₂²×C₄	—	73	1	no	—
935	C₂²×C₄	—	73	1	no	—
936	C₂²×C₄	—	73	1	no	—
937	C₂²×C₄	—	73	2	no	—
938	C₂²×C₄	—	73	1	no	—
939	C₂²×C₄	—	73	1	no	—
940	C₂²×C₄	—	146	2	no	—
941	C₂²×C₄	—	146	2	no	—
942	C₂²×C₄	—	146	2	no	—
943	C₂²×C₄	—	146	2	no	—
944	C₂²×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
945	C₂²×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
946	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
947	M₁₆	—	2	2	no	—
948	M₁₆	—	2	2	no	—
949	M₁₆	—	73	4	no	—
950	M₁₆	—	146	4	no	—
951	M₁₆	—	146	4	no	—
952	M₁₆	—	146	4	no	—
953	M₁₆	—	146	2	no	—
954	M₁₆	—	146	2	no	—
955	M₁₆	—	146	2	no	—
956	M₁₆	—	146	2	no	—
957	M₁₆	—	146	2	no	—
958	M₁₆	—	146	4	no	—
959	C₂×C₈	—	2	2	no	—
960	C₂×C₈	—	73	2	no	—
961	C₂×C₈	—	73	1	no	—
962	C₂×C₈	—	73	1	no	—
963	C₂×C₈	—	73	2	no	—
964	C₂×C₈	—	73	1	no	—
965	C₂×C₈	—	73	1	no	—
966	C₂×C₈	—	146	4	no	—
967	C₂×C₈	—	146	4	no	—
968	C₂×C₈	—	146	4	no	—
969	C₂×C₈	—	146	2	no	—
970	C₂×C₈	—	146	2	no	—
971	C₂×C₈	—	146	2	no	—
972	C₂×C₈	—	146	2	no	—
973	C₂×C₈	—	146	2	no	—
974	C₂×C₈	—	146	2	no	—
975	C₂×C₈	—	146	4	no	—
976	C₂×C₈	#11924029	1	4	yes	complemented
977	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
978	C₂×C₈	C₂³×D₇₃	1	2	yes	—
979	C₂×C₈	C₂³×D₇₃	1	2	yes	—
980	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
981	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
982	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
983	C₄⋊C₄	—	73	2	no	—
984	C₄⋊C₄	—	73	2	no	—
985	C₄⋊C₄	—	73	2	no	—
986	C₄⋊C₄	—	73	2	no	—
987	C₄⋊C₄	—	73	2	no	—
988	C₄⋊C₄	—	73	2	no	—
989	C₄⋊C₄	—	73	1	no	—
990	C₄⋊C₄	—	73	1	no	—
991	C₄⋊C₄	—	73	1	no	—
992	C₄⋊C₄	—	73	1	no	—
993	C₄⋊C₄	—	73	1	no	—
994	C₄⋊C₄	—	73	1	no	—
995	C₄⋊C₄	—	73	2	no	—
996	C₄⋊C₄	—	73	2	no	—
997	C₄⋊C₄	—	73	2	no	—
998	C₄⋊C₄	—	73	2	no	—
999	C₄⋊C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
1000	C₄⋊C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
1001	C₄⋊C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
1002	C₄⋊C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
1003	C₄⋊C₄	C₂×C₄×D₇₃	1	2	yes	—
1004	C₄⋊C₄	C₂×C₄×D₇₃	1	2	yes	—
1005	C₄⋊C₄	C₂×C₄×D₇₃	1	2	yes	—
1006	C₄⋊C₄	C₂×C₄×D₇₃	1	2	yes	—
1007	C₄⋊C₄	C₂×C₄×D₇₃	1	2	yes	—
1008	C₄⋊C₄	C₂×C₄×D₇₃	1	2	yes	—
1009	C₂²⋊C₄	—	73	2	no	—
1010	C₂²⋊C₄	—	73	1	no	—
1011	C₂²⋊C₄	—	73	1	no	—
1012	C₂²⋊C₄	—	73	2	no	—
1013	C₂²⋊C₄	—	73	2	no	—
1014	C₂²⋊C₄	—	73	2	no	—
1015	C₂²⋊C₄	—	73	2	no	—
1016	C₂²⋊C₄	—	73	1	no	—
1017	C₂²⋊C₄	—	73	1	no	—
1018	C₂²⋊C₄	—	73	1	no	—
1019	C₂²⋊C₄	—	73	1	no	—
1020	C₂²⋊C₄	—	73	1	no	—
1021	C₂²⋊C₄	—	73	1	no	—
1022	C₂²⋊C₄	—	73	2	no	—
1023	C₂²⋊C₄	—	73	2	no	—
1024	C₂²⋊C₄	—	73	2	no	—
1025	C₂²⋊C₄	—	73	2	no	—
1026	C₂²⋊C₄	—	73	2	no	—
1027	C₂²⋊C₄	—	73	2	no	—
1028	C₂²⋊C₄	—	73	2	no	—
1029	C₂²⋊C₄	—	73	2	no	—
1030	C₂²⋊C₄	—	73	2	no	—
1031	C₂²⋊C₄	—	73	2	no	—
1032	C₂²⋊C₄	C₂×C₄×D₇₃	1	2	yes	—
1033	C₂²⋊C₄	C₂×C₄×D₇₃	1	2	yes	—
1034	C₄²	—	73	2	no	—
1035	C₄²	—	73	2	no	—
1036	C₄²	—	73	2	no	—
1037	C₄²	—	73	2	no	—
1038	C₄²	—	73	2	no	—
1039	C₄²	—	73	2	no	—
1040	C₄²	—	73	2	no	—
1041	C₄²	C₂×C₄×D₇₃	1	1	yes	characteristic
1042	C₄²	C₂×C₄×D₇₃	1	1	yes	characteristic
1043	C₄²	C₂³×D₇₃	1	1	yes	characteristic
1044	C₄²	C₂³×D₇₃	1	2	yes	—
1045	C₄²	C₂³×D₇₃	1	2	yes	—
1046	C₄²	C₂³×D₇₃	1	1	yes	characteristic
1047	C₂³	—	292	1	no	—
1048	C₂³	—	292	1	no	—
1049	C₂³	—	292	1	no	—
1050	C₂³	—	73	1	no	—
1051	C₂³	—	73	1	no	—
1052	C₂³	—	73	1	no	—
1053	C₂³	—	73	2	no	—
1054	C₂³	—	73	1	no	—
1055	C₂³	—	146	2	no	—
1056	C₂³	—	146	2	no	—
1057	C₂³	—	146	2	no	—
1058	C₂³	C₂²×C₄×D₇₃	1	1	yes	characteristic
1059	Q₈	—	4	2	no	—
1060	Q₈	—	4	2	no	—
1061	Q₈	—	146	2	no	—
1062	D₄	—	292	1	no	—
1063	D₄	—	292	1	no	—
1064	D₄	—	292	2	no	—
1065	D₄	—	292	2	no	—
1066	D₄	—	292	2	no	—
1067	D₄	—	146	2	no	—
1068	D₄	—	146	2	no	—
1069	D₄	—	146	4	no	—
1070	D₄	—	146	4	no	—
1071	D₄	—	146	2	no	—
1072	C₂×C₄	—	4	1	no	—
1073	C₂×C₄	—	4	1	no	—
1074	C₂×C₄	—	292	2	no	—
1075	C₂×C₄	—	292	2	no	—
1076	C₂×C₄	—	292	2	no	—
1077	C₂×C₄	—	292	2	no	—
1078	C₂×C₄	—	292	2	no	—
1079	C₂×C₄	—	73	2	no	—
1080	C₂×C₄	—	73	2	no	—
1081	C₂×C₄	—	73	1	no	—
1082	C₂×C₄	—	73	1	no	—
1083	C₂×C₄	—	73	2	no	—
1084	C₂×C₄	—	73	1	no	—
1085	C₂×C₄	—	73	1	no	—
1086	C₂×C₄	—	146	4	no	—
1087	C₂×C₄	—	146	2	no	—
1088	C₂×C₄	—	146	2	no	—
1089	C₂×C₄	—	146	1	no	—
1090	C₂×C₄	—	146	1	no	—
1091	C₂×C₄	—	146	2	no	—
1092	C₂×C₄	—	146	1	no	—
1093	C₂×C₄	—	146	1	no	—
1094	C₂×C₄	—	146	1	no	—
1095	C₂×C₄	—	146	1	no	—
1096	C₂×C₄	—	146	2	no	—
1097	C₂×C₄	—	146	1	no	—
1098	C₂×C₄	—	146	1	no	—
1099	C₂×C₄	—	146	2	no	—
1100	C₂×C₄	—	146	2	no	—
1101	C₂×C₄	—	146	2	no	—
1102	C₂×C₄	—	146	2	no	—
1103	C₂×C₄	C₂²×C₄×D₇₃	1	1	yes	characteristic
1104	C₂×C₄	C₂²×C₄×D₇₃	1	1	yes	characteristic
1105	C₂×C₄	C₂²×C₄×D₇₃	1	2	yes	—
1106	C₂×C₄	C₂²×C₄×D₇₃	1	2	yes	—
1107	C₂×C₄	C₂²×C₄×D₇₃	1	2	yes	—
1108	C₂×C₄	C₂²×C₄×D₇₃	1	2	yes	—
1109	C₂×C₄	C₂²×C₄×D₇₃	1	1	yes	characteristic
1110	C₂×C₄	C₂²×C₄×D₇₃	1	1	yes	characteristic
1111	C₂×C₄	C₂²×C₄×D₇₃	1	1	yes	characteristic
1112	C₂×C₄	#41×D₇₃	1	2	yes	—
1113	C₂×C₄	C₂×#11924029	1	2	yes	—
1114	C₂×C₄	C₂⁴×D₇₃	1	1	yes	characteristic
1115	C₈	—	2	1	no	—
1116	C₈	—	2	1	no	—
1117	C₈	—	2	2	no	—
1118	C₈	—	2	2	no	—
1119	C₈	—	73	4	no	—
1120	C₈	—	146	1	no	—
1121	C₈	—	146	1	no	—
1122	C₈	—	146	1	no	—
1123	C₈	—	146	1	no	—
1124	C₈	—	146	2	no	—
1125	C₈	C₂×#11924029	1	2	yes	—
1126	C₈	C₂×#11924029	1	2	yes	—
1127	C₂²	—	2	1	no	—
1128	C₂²	—	2	1	no	—
1129	C₂²	—	292	4	no	—
1130	C₂²	—	584	2	no	—
1131	C₂²	—	73	2	no	—
1132	C₂²	—	146	1	no	—
1133	C₂²	—	146	2	no	—
1134	C₂²	—	146	1	no	—
1135	C₂²	—	146	1	no	—
1136	C₂²	—	146	1	no	—
1137	C₂²	—	146	2	no	—
1138	C₂²	—	146	1	no	—
1139	C₂²	—	146	1	no	—
1140	C₂²	—	146	1	no	—
1141	C₂²	—	146	1	no	—
1142	C₂²	—	146	1	no	—
1143	C₂²	—	146	2	no	—
1144	C₂²	—	146	1	no	—
1145	C₂²	—	146	1	no	—
1146	C₂²	C₄×#11924029	1	2	yes	—
1147	C₂²	C₂³×C₄×D₇₃	1	1	yes	characteristic
1148	C₄	—	2	1	no	—
1149	C₄	—	2	1	no	—
1150	C₄	—	2	2	no	—
1151	C₄	—	2	2	no	—
1152	C₄	—	2	1	no	—
1153	C₄	—	2	1	no	—
1154	C₄	—	2	2	no	—
1155	C₄	—	2	2	no	—
1156	C₄	—	146	2	no	—
1157	C₄	—	146	2	no	—
1158	C₄	—	146	1	no	—
1159	C₄	—	146	1	no	—
1160	C₄	—	146	1	no	—
1161	C₄	—	146	1	no	—
1162	C₄	—	146	2	no	—
1163	C₄	C₄×#11924029	1	2	yes	—
1164	C₄	C₂×#41×D₇₃	1	1	yes	characteristic
1165	C₄	C₂²×#11924029	1	1	yes	characteristic
1166	C₂	—	2	2	no	—
1167	C₂	—	292	1	no	—
1168	C₂	—	292	1	no	—
1169	C₂	—	292	1	no	—
1170	C₂	—	292	2	no	—
1171	C₂	—	146	2	no	—
1172	C₂	C₂×C₄×#11924029	1	1	yes	characteristic
1173	C₂	#568×D₇₃	1	1	yes	characteristic
1174	C₂	#22624644	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂⁴×D₇₃
commutator, socle	C₂²×C₇₃	C₂⁴×C₄
Fitting	C₇₃×#2961	C₂
prime radical	#22623498	C₂
cosocle	C₂×C₄×C₇₃	C₂⁵
hypercenter	#2961	D₇₃
hypocenter	C₇₃	#60216
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ #2961

Complements

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

N	H ≅ G/N	type
2. #22618944	C₂	semidirect
3. #22618937	C₂	semidirect
4. #22618924	C₂	semidirect
5. #22618924	C₂	semidirect
6. #22618915	C₂	semidirect
7. #22618915	C₂	semidirect
8. #22618905	C₂	semidirect
9. #22618896	C₂	semidirect
10. #22618880	C₂	semidirect
11. #22618666	C₂	semidirect
12. #22618655	C₂	semidirect
13. #22618655	C₂	semidirect
14. #22618636	C₂	semidirect
15. #22618627	C₂	semidirect
16. C₂×#17988660	C₂	semidirect
17. #22618599	C₂	semidirect
18. #22618588	C₂	semidirect
19. #22618588	C₂	semidirect
20. #22618356	C₂	semidirect
21. #22618347	C₂	semidirect
22. #405×D₇₃	C₂	semidirect
23. C₇₃×#2961	C₂	semidirect
52. #17988718	C₂²	semidirect
53. #17988718	C₂²	semidirect
54. #17988718	C₂²	semidirect
55. Q₈×#10596831	C₂²	semidirect
56. #17988666	C₂²	semidirect
57. #17988666	C₂²	semidirect
59. #17988664	C₂²	semidirect
60. #17988664	C₂²	semidirect
69. #17988660	C₂²	semidirect
70. #17988660	C₂²	semidirect
71. #17988660	C₂²	semidirect
72. #17988660	C₂²	semidirect
75. #17988657	C₂²	semidirect
76. #17988657	C₂²	semidirect
77. #17988657	C₂²	semidirect
78. #17988657	C₂²	semidirect
79. C₈×D₂₉₂	C₂²	semidirect
80. C₈×D₂₉₂	C₂²	semidirect
82. #17988652	C₂²	semidirect
83. #17988652	C₂²	semidirect
84. #17988647	C₂²	semidirect
85. #17988647	C₂²	semidirect
86. #17988647	C₂²	semidirect
87. #17988647	C₂²	semidirect
88. #17988647	C₂²	semidirect
89. #17988647	C₂²	semidirect
90. #17988643	C₂²	semidirect
91. #17988643	C₂²	semidirect
92. #17988643	C₂²	semidirect
93. #17988639	C₂²	semidirect
94. #17988639	C₂²	semidirect
95. #17988639	C₂²	semidirect
107. #17988544	C₂²	semidirect
108. #17988544	C₂²	semidirect
109. #17988544	C₂²	semidirect
110. #17988544	C₂²	semidirect
115. #17988541	C₂²	semidirect
116. #17988541	C₂²	semidirect
118. #17988539	C₂²	semidirect
119. #17988539	C₂²	semidirect
120. C₄×#11924011	C₂²	semidirect
121. #97×D₇₃	C₂²	semidirect
122. #97×D₇₃	C₂²	semidirect
123. C₄×C₈×D₇₃	C₂²	semidirect
125. #446×C₇₃	C₂²	semidirect
126. #446×C₇₃	C₂²	semidirect
127. #446×C₇₃	C₂²	semidirect
128. #446×C₇₃	C₂²	semidirect
355. #11924012	#41	semidirect
434. C₂×C₈×C₇₃	#41	semidirect
598. #2961	D₇₃	semidirect
611. C₇₃	#60216	semidirect
644. #446	C₂×D₇₃	semidirect
645. #446	C₂×D₇₃	semidirect
646. #446	C₂×D₇₃	semidirect
647. #446	C₂×D₇₃	semidirect
976. C₂×C₈	#11924029	semidirect

Maximal subgroups

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

subgroup	index
#22623498	2
#22618944	2
#22618937	2
#22618924	2
#22618915	2
#22618905	2
#22618896	2
#22618880	2
#22618666	2
#22618655	2
#22618636	2
#22618627	2
C₂×#17988660	2
#22618599	2
#22618588	2
#22618356	2
#22618347	2
#405×D₇₃	2
C₇₃×#2961	2
#60216	73