Subgroups — #33950617

Order 18688.

1970 conjugacy classes of subgroups.

The subgroup lattice has 1148 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22623493	C₂	1	1	yes	maximal, characteristic
2	#22618945	C₂	1	1	yes	maximal, characteristic, complemented
3	#22618939	C₂	1	1	yes	maximal, characteristic, complemented
4	#22618934	C₂	1	1	yes	maximal, characteristic, complemented
5	#22618929	C₂	1	1	yes	maximal, characteristic, complemented
6	#22618920	C₂	1	2	yes	maximal, complemented
7	#22618919	C₂	1	2	yes	maximal, complemented
8	#22618908	C₂	1	1	yes	maximal, characteristic, complemented
9	#22618906	C₂	1	2	yes	maximal, complemented
10	#22618906	C₂	1	1	yes	maximal, characteristic, complemented
11	#22618899	C₂	1	2	yes	maximal, complemented
12	C₈×#11924027	C₂	1	1	yes	maximal, characteristic, complemented
13	#22618873	C₂	1	1	yes	maximal, characteristic, complemented
14	#22618860	C₂	1	1	yes	maximal, characteristic, complemented
15	D₄×#11924011	C₂	1	1	yes	maximal, characteristic, complemented
16	#22618651	C₂	1	2	yes	maximal, complemented
17	#22618620	C₂	1	2	yes	maximal, complemented
18	C₈×D₄×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
19	#22618592	C₂	1	1	yes	maximal, characteristic, complemented
20	#22618584	C₂	1	2	yes	maximal, complemented
21	C₄×#14556597	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#17988541	C₂	1	2	yes	maximal, complemented
23	C₈×#41×C₇₃	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	2	yes	—
27	C₂²×C₈×D₇₃	C₂²	1	2	yes	—
28	#17989309	C₄	1	1	yes	characteristic
29	#17989300	C₄	1	1	yes	characteristic
30	#17989296	C₄	1	1	yes	characteristic
31	#17989286	C₄	1	2	yes	—
32	#17989278	C₄	1	1	yes	characteristic
33	#17989276	C₄	1	1	yes	characteristic
34	#17989270	C₄	1	2	yes	—
35	#17989266	C₄	1	2	yes	—
36	#17989261	C₄	1	2	yes	—
37	#17989236	C₄	1	1	yes	characteristic
38	#17989232	C₄	1	1	yes	characteristic
39	#17989225	C₄	1	1	yes	characteristic
40	#17989141	C₂²	1	1	yes	characteristic
41	#17989124	C₂²	1	1	yes	characteristic
42	#17989121	C₂²	1	2	yes	—
43	#17989121	C₂²	1	1	yes	characteristic
44	#17989117	C₂²	1	2	yes	—
45	#17989096	C₂²	1	2	yes	—
46	C₄×#11924028	C₂²	1	1	yes	characteristic
47	C₄×#11924027	C₂²	1	1	yes	characteristic
48	C₄×D₄×D₇₃	C₂²	1	1	yes	characteristic
49	C₂×#14556548	C₂²	1	2	yes	—
50	#17988718	C₂²	1	1	yes	characteristic, complemented
51	#17988718	C₂²	1	1	yes	characteristic, complemented
52	#17988717	C₂²	1	2	yes	complemented
53	#17988717	C₂²	1	1	yes	characteristic, complemented
54	#17988716	C₂²	1	2	yes	complemented
55	#17988716	C₂²	1	2	yes	complemented
56	#17988714	C₂²	1	1	yes	characteristic, complemented
57	C₈×Dic₁₄₆	C₂²	1	1	yes	characteristic, complemented
58	C₈×Dic₁₄₆	C₂²	1	2	yes	complemented
59	#17988711	C₂²	1	1	yes	characteristic, complemented
60	#17988666	C₂²	1	1	yes	characteristic
61	#17988666	C₂²	1	2	yes	complemented
62	#17988664	C₂²	1	1	yes	characteristic
63	#17988662	C₂²	1	2	yes	complemented
64	#17988661	C₂²	1	2	yes	complemented
65	#17988659	C₂²	1	2	yes	complemented
66	#17988659	C₂²	1	2	yes	complemented
67	#17988658	C₂²	1	2	yes	—
68	#17988658	C₂²	1	2	yes	complemented
69	#17988658	C₂²	1	2	yes	complemented
70	#17988657	C₂²	1	2	yes	complemented
71	#17988657	C₂²	1	2	yes	complemented
72	#17988655	C₂²	1	2	yes	—
73	#17988655	C₂²	1	2	yes	complemented
74	C₈×D₂₉₂	C₂²	1	1	yes	characteristic
75	C₈×D₂₉₂	C₂²	1	2	yes	complemented
76	D₄×#10596831	C₂²	1	1	yes	characteristic
77	D₄×#10596831	C₂²	1	1	yes	characteristic
78	#17988652	C₂²	1	1	yes	characteristic
79	C₈×C₂²⋊D₇₃	C₂²	1	2	yes	—
80	C₈×C₂²⋊D₇₃	C₂²	1	2	yes	complemented
81	C₈×C₂²⋊D₇₃	C₂²	1	2	yes	complemented
82	#17988650	C₂²	1	2	yes	—
83	#17988650	C₂²	1	2	yes	complemented
84	#17988647	C₂²	1	2	yes	complemented
85	#17988647	C₂²	1	2	yes	complemented
86	#17988646	C₂²	1	2	yes	complemented
87	#17988646	C₂²	1	2	yes	complemented
88	#17988646	C₂²	1	2	yes	complemented
89	#17988645	C₂²	1	2	yes	complemented
90	#17988644	C₂²	1	2	yes	complemented
91	#17988644	C₂²	1	1	yes	characteristic, complemented
92	#17988643	C₂²	1	1	yes	characteristic, complemented
93	#17988641	C₂²	1	2	yes	complemented
94	#17988639	C₂²	1	1	yes	characteristic, complemented
95	#17988637	C₂²	1	2	yes	complemented
96	#17988612	C₂²	1	2	yes	—
97	#17988612	C₂²	1	2	yes	—
98	#17988609	C₂²	1	1	yes	characteristic
99	C₄⋊C₈×D₇₃	C₂²	1	1	yes	characteristic
100	#17988552	C₂²	1	2	yes	—
101	#17988549	C₂²	1	2	yes	—
102	C₂²⋊C₈×D₇₃	C₂²	1	2	yes	—
103	#17988542	C₂²	1	1	yes	characteristic, complemented
104	#17988542	C₂²	1	1	yes	characteristic, complemented
105	#17988541	C₂²	1	2	yes	—
106	#17988541	C₂²	1	1	yes	characteristic
107	#17988541	C₂²	1	2	yes	—
108	#17988541	C₂²	1	1	yes	characteristic
109	#17988541	C₂²	1	2	yes	—
110	#17988541	C₂²	1	2	yes	complemented
111	#17988541	C₂²	1	2	yes	complemented
112	#17988541	C₂²	1	1	yes	characteristic, complemented
113	#17988541	C₂²	1	2	yes	complemented
114	#17988541	C₂²	1	1	yes	characteristic, complemented
115	#17988541	C₂²	1	2	yes	complemented
116	C₄×#11924012	C₂²	1	1	yes	characteristic, complemented
117	C₄×#11924011	C₂²	1	1	yes	characteristic
118	C₄×#11924011	C₂²	1	1	yes	characteristic, complemented
119	C₂×#14556502	C₂²	1	2	yes	complemented
120	C₂×#14556501	C₂²	1	2	yes	complemented
121	C₂×C₈×Dic₇₃	C₂²	1	2	yes	complemented
122	C₄×C₈×D₇₃	C₂²	1	1	yes	characteristic
123	C₄×C₈×D₇₃	C₂²	1	1	yes	characteristic, complemented
124	C₄×#41×C₇₃	C₂²	1	1	yes	characteristic
125	C₈×Q₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
126	C₈×Q₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
127	C₈×D₄×C₇₃	C₂²	1	1	yes	characteristic
128	C₈×D₄×C₇₃	C₂²	1	1	yes	characteristic
129	C₈×D₄×C₇₃	C₂²	1	2	yes	complemented
130	C₈×D₄×C₇₃	C₂²	1	2	yes	complemented
131	#431×C₇₃	C₂²	1	2	yes	complemented
132	#431×C₇₃	C₂²	1	1	yes	characteristic, complemented
133	C₂×C₄×C₈×C₇₃	C₂²	1	2	yes	complemented
134	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
135	C₂×#11924028	C₂³	1	1	yes	characteristic
136	C₂×#11924027	C₂×C₄	1	1	yes	characteristic
137	C₂×D₄×D₇₃	C₂×C₄	1	1	yes	characteristic
138	C₂²×C₄×D₇₃	C₂³	1	2	yes	—
139	#14556597	—	2	4	no	—
140	#14556597	—	2	4	no	—
141	C₂×#11924012	C₂³	1	1	yes	characteristic
142	C₂×#11924012	C₂³	1	1	yes	characteristic
143	C₂×#11924011	—	2	8	no	—
144	C₂×#11924011	C₂³	1	2	yes	—
145	C₂×#11924011	C₂³	1	1	yes	characteristic
146	C₂×#11924011	C₂³	1	2	yes	—
147	C₂×#11924011	C₂³	1	1	yes	characteristic
148	C₂×#11924011	C₂³	1	2	yes	—
149	C₂×#11924011	C₂³	1	1	yes	characteristic
150	C₂×#11924011	C₂³	1	1	yes	characteristic
151	C₂²×#10596831	C₂³	1	2	yes	—
152	C₂²×#10596831	C₂³	1	2	yes	—
153	C₂×C₈×D₇₃	—	2	8	no	—
154	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
155	C₂×C₈×D₇₃	C₂³	1	2	yes	—
156	C₂×C₈×D₇₃	C₂³	1	2	yes	—
157	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
158	C₂×C₈×D₇₃	C₂³	1	2	yes	—
159	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
160	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
161	#14556590	C₂×C₄	1	1	yes	characteristic
162	#14556589	C₂×C₄	1	1	yes	characteristic
163	#14556586	C₂×C₄	1	2	yes	—
164	#14556586	C₂×C₄	1	2	yes	—
165	#14556585	C₂×C₄	1	2	yes	—
166	#14556585	C₂×C₄	1	2	yes	—
167	#14556585	C₂×C₄	1	2	yes	—
168	#14556584	C₂×C₄	1	2	yes	—
169	#14556583	C₂×C₄	1	2	yes	—
170	#14556583	C₂×C₄	1	1	yes	characteristic
171	#14556582	C₂×C₄	1	1	yes	characteristic
172	#14556581	C₂×C₄	1	2	yes	—
173	#14556581	C₂×C₄	1	2	yes	—
174	#14556580	C₂×C₄	1	1	yes	characteristic
175	#14556579	C₂×C₄	1	1	yes	characteristic
176	#14556579	C₂×C₄	1	2	yes	—
177	#14556577	C₂×C₄	1	2	yes	—
178	#14556576	C₂×C₄	1	2	yes	—
179	#14556576	C₂×C₄	1	2	yes	—
180	#14556575	C₂×C₄	1	2	yes	—
181	#14556574	C₂×C₄	1	2	yes	—
182	#14556574	C₂×C₄	1	2	yes	—
183	#14556574	C₂×C₄	1	2	yes	—
184	#14556573	C₂×C₄	1	2	yes	—
185	#14556572	C₂×C₄	1	2	yes	—
186	#14556571	C₂×C₄	1	1	yes	characteristic
187	#14556570	C₂×C₄	1	1	yes	characteristic
188	#14556570	C₂×C₄	1	2	yes	—
189	#14556569	C₂×C₄	1	2	yes	—
190	#14556569	C₂×C₄	1	2	yes	—
191	#14556568	C₂×C₄	1	2	yes	—
192	#14556568	C₂×C₄	1	2	yes	—
193	#14556567	C₂×C₄	1	1	yes	characteristic
194	#14556567	C₂×C₄	1	1	yes	characteristic
195	#14556566	C₂×C₄	1	1	yes	characteristic
196	#14556565	C₂×C₄	1	1	yes	characteristic
197	#14556565	C₂×C₄	1	2	yes	—
198	#14556564	C₂×C₄	1	2	yes	—
199	#14556563	C₂×C₄	1	2	yes	—
200	#14556563	C₂×C₄	1	2	yes	—
201	#14556561	C₂×C₄	1	2	yes	—
202	#14556559	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×Dic₁₄₆	C₂³	1	1	yes	characteristic
206	C₄×Dic₁₄₆	C₂³	1	2	yes	—
207	#14556556	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	C₂³	1	1	yes	characteristic
211	C₄×D₂₉₂	C₂³	1	2	yes	—
212	D₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
213	D₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
214	#14556553	C₂×C₄	1	1	yes	characteristic
215	C₄×C₂²⋊D₇₃	C₂×C₄	1	1	yes	characteristic
216	C₄×C₂²⋊D₇₃	C₂×C₄	1	1	yes	characteristic
217	C₄×C₂²⋊D₇₃	C₂×C₄	1	1	yes	characteristic
218	C₄×C₂²⋊D₇₃	C₂×C₄	1	1	yes	characteristic
219	C₄×C₂²⋊D₇₃	C₂³	1	2	yes	—
220	C₄×C₂²⋊D₇₃	C₂³	1	2	yes	—
221	C₄×C₂²⋊D₇₃	C₂³	1	2	yes	—
222	#14556551	C₂×C₄	1	2	yes	—
223	#14556551	C₂×C₄	1	2	yes	—
224	#14556550	C₂³	1	1	yes	characteristic
225	#14556549	C₂×C₄	1	1	yes	characteristic
226	#14556548	C₂×C₄	1	2	yes	—
227	#14556548	C₂×C₄	1	2	yes	—
228	#14556548	C₂×C₄	1	2	yes	—
229	#14556548	C₂×C₄	1	2	yes	—
230	#14556548	C₂³	1	2	yes	—
231	#14556548	C₂³	1	1	yes	characteristic
232	#14556548	C₂³	1	2	yes	—
233	#14556548	C₂³	1	2	yes	—
234	#14556548	C₂³	1	1	yes	characteristic
235	#14556547	C₂×C₄	1	2	yes	—
236	C₂×#11924007	C₂×C₄	1	2	yes	—
237	C₂×#11924007	C₂×C₄	1	2	yes	—
238	C₄⋊C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
239	C₂×#11924005	C₂×C₄	1	2	yes	—
240	C₂×#11924005	C₂×C₄	1	2	yes	—
241	C₂²⋊C₄×D₇₃	C₂×C₄	1	2	yes	—
242	C₂×C₄×Dic₇₃	C₂³	1	2	yes	—
243	C₄²×D₇₃	C₂³	1	1	yes	characteristic
244	C₄²×D₇₃	C₂³	1	1	yes	characteristic
245	C₄⋊#10596831	C₂³	1	1	yes	characteristic
246	C₄⋊#10596831	C₂³	1	2	yes	—
247	C₄⋊#10596831	C₂³	1	2	yes	—
248	C₄⋊#10596831	C₂³	1	1	yes	characteristic
249	#14556520	C₂³	1	2	yes	—
250	#14556520	C₂³	1	2	yes	—
251	#14556520	C₂³	1	2	yes	—
252	#14556520	C₂³	1	2	yes	—
253	#14556520	C₂³	1	2	yes	—
254	#14556520	C₂³	1	2	yes	—
255	C₂²⋊#10596831	C₂³	1	2	yes	—
256	C₂²⋊#10596831	C₂³	1	2	yes	—
257	C₂²⋊#10596831	C₂³	1	2	yes	—
258	#14556503	C₂³	1	2	yes	—
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	2	yes	—
264	#14556502	C₂³	1	2	yes	—
265	#14556502	C₂³	1	1	yes	characteristic
266	#14556502	C₂³	1	2	yes	—
267	#14556502	C₂³	1	2	yes	—
268	#14556502	C₂³	1	1	yes	characteristic
269	#14556501	C₂³	1	1	yes	characteristic
270	#14556501	C₂³	1	2	yes	—
271	#14556501	C₂³	1	1	yes	characteristic
272	#14556501	C₂³	1	2	yes	—
273	#14556501	C₂³	1	1	yes	characteristic
274	#14556501	C₂³	1	2	yes	—
275	#14556501	C₂³	1	1	yes	characteristic
276	C₄×#10596831	C₂³	1	1	yes	characteristic
277	C₄×#10596831	C₂³	1	1	yes	characteristic
278	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
279	C₈×Dic₇₃	C₂³	1	2	yes	—
280	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
281	C₈×Dic₇₃	C₂³	1	2	yes	—
282	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
283	C₈×Dic₇₃	C₂³	1	2	yes	—
284	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
285	C₂×#41×C₇₃	C₂×C₄	1	1	yes	characteristic
286	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
287	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
288	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
289	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
290	C₄×Q₈×C₇₃	C₂×C₄	1	1	yes	characteristic
291	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
292	C₄×D₄×C₇₃	C₂×C₄	1	1	yes	characteristic
293	C₄×D₄×C₇₃	C₂×C₄	1	2	yes	—
294	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
295	C₄×D₄×C₇₃	C₂³	1	2	yes	—
296	#117×C₇₃	C₂×C₄	1	2	yes	—
297	#117×C₇₃	C₂×C₄	1	1	yes	characteristic
298	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
299	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
300	C₄⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
301	C₄⋊C₈×C₇₃	C₂³	1	2	yes	—
302	C₄⋊C₈×C₇₃	C₂³	1	2	yes	—
303	C₄⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
304	C₂²⋊C₈×C₇₃	C₂³	1	2	yes	—
305	C₂²⋊C₈×C₇₃	C₂³	1	2	yes	—
306	C₂²⋊C₈×C₇₃	C₂³	1	2	yes	—
307	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
308	C₄×C₈×C₇₃	C₂³	1	2	yes	—
309	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₇₃	C₂³	1	2	yes	—
312	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₇₃	C₂³	1	2	yes	—
314	C₂³×D₇₃	C₂²×C₄	1	2	yes	—
315	#11924028	—	2	2	no	—
316	#11924028	—	2	2	no	—
317	#11924027	—	2	4	no	—
318	C₂×Dic₁₄₆	C₂²×C₄	1	1	yes	characteristic
319	C₂×Dic₁₄₆	C₂²×C₄	1	1	yes	characteristic
320	C₂×Dic₁₄₆	C₂²×C₄	1	2	yes	—
321	C₂×D₂₉₂	C₂²×C₄	1	1	yes	characteristic
322	C₂×D₂₉₂	C₂²×C₄	1	1	yes	characteristic
323	C₂×D₂₉₂	C₂²×C₄	1	2	yes	—
324	C₂×C₂²⋊D₇₃	C₂²×C₄	1	2	yes	—
325	C₂×C₂²⋊D₇₃	C₂²×C₄	1	2	yes	—
326	C₂×C₂²⋊D₇₃	C₂²×C₄	1	1	yes	characteristic
327	C₂×C₂²⋊D₇₃	C₂²×C₄	1	1	yes	characteristic
328	C₂×C₂²⋊D₇₃	C₂²×C₄	1	2	yes	—
329	D₄×D₇₃	—	2	4	no	—
330	C₂²×Dic₇₃	C₂²×C₄	1	2	yes	—
331	C₂²×Dic₇₃	C₂²×C₄	1	2	yes	—
332	C₂²×Dic₇₃	C₂²×C₄	1	2	yes	—
333	C₂×C₄×D₇₃	—	2	4	no	—
334	C₂×C₄×D₇₃	—	2	4	no	—
335	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
336	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
337	C₂×C₄×D₇₃	C₂²×C₄	1	2	yes	—
338	C₂×C₄×D₇₃	C₂²×C₄	1	2	yes	—
339	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
340	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
341	C₂×C₄×D₇₃	C₂⁴	1	1	yes	characteristic
342	C₂×C₄×D₇₃	C₂⁴	1	2	yes	—
343	C₂×C₄×D₇₃	C₂⁴	1	1	yes	characteristic
344	#11924012	—	2	2	no	—
345	#11924012	—	2	2	no	—
346	#11924011	—	2	4	no	—
347	#11924011	—	2	2	no	—
348	#11924011	—	2	4	no	—
349	#11924011	—	2	2	no	—
350	#11924011	—	2	4	no	—
351	#11924011	—	2	2	no	—
352	#11924011	#41	1	4	yes	complemented
353	C₂×#10596831	—	2	4	no	—
354	C₂×#10596831	—	2	4	no	—
355	C₂×#10596831	C₂⁴	1	2	yes	—
356	C₂×#10596831	C₂⁴	1	1	yes	characteristic
357	C₂×#10596831	C₂⁴	1	1	yes	characteristic
358	C₂×#10596831	C₂⁴	1	2	yes	—
359	C₂×#10596831	C₂⁴	1	1	yes	characteristic
360	C₂×#10596831	C₂⁴	1	1	yes	characteristic
361	C₈×D₇₃	—	2	4	no	—
362	C₈×D₇₃	—	2	2	no	—
363	C₈×D₇₃	—	2	4	no	—
364	C₈×D₇₃	—	2	2	no	—
365	C₈×D₇₃	—	2	4	no	—
366	C₈×D₇₃	—	2	2	no	—
367	C₈×D₇₃	#41	1	4	yes	complemented
368	C₄⋊Dic₇₃	C₂²×C₄	1	1	yes	characteristic
369	C₄⋊Dic₇₃	C₂²×C₄	1	1	yes	characteristic
370	C₄⋊Dic₇₃	C₂²×C₄	1	1	yes	characteristic
371	C₄⋊Dic₇₃	C₂²×C₄	1	1	yes	characteristic
372	C₄⋊Dic₇₃	C₂²×C₄	1	2	yes	—
373	C₄⋊Dic₇₃	C₂²×C₄	1	2	yes	—
374	#11924007	C₂²×C₄	1	2	yes	—
375	#11924007	C₂²×C₄	1	1	yes	characteristic
376	#11924007	C₂²×C₄	1	1	yes	characteristic
377	#11924007	C₂²×C₄	1	2	yes	—
378	#11924007	C₂²×C₄	1	2	yes	—
379	#11924007	C₂²×C₄	1	2	yes	—
380	#11924007	C₂²×C₄	1	2	yes	—
381	#11924007	C₂²×C₄	1	2	yes	—
382	#11924007	C₂²×C₄	1	2	yes	—
383	#11924007	C₂²×C₄	1	2	yes	—
384	#11924007	C₂²×C₄	1	2	yes	—
385	#11924007	C₂²×C₄	1	1	yes	characteristic
386	#11924007	C₂²×C₄	1	1	yes	characteristic
387	#11924007	C₂²×C₄	1	2	yes	—
388	#11924007	C₂²×C₄	1	2	yes	—
389	#11924007	C₂²×C₄	1	2	yes	—
390	C₂²⋊Dic₇₃	C₂²×C₄	1	2	yes	—
391	C₂²⋊Dic₇₃	C₂²×C₄	1	2	yes	—
392	C₂²⋊Dic₇₃	C₂²×C₄	1	1	yes	characteristic
393	C₂²⋊Dic₇₃	C₂²×C₄	1	1	yes	characteristic
394	C₂²⋊Dic₇₃	C₂²×C₄	1	2	yes	—
395	#11924005	C₂²×C₄	1	2	yes	—
396	#11924005	C₂²×C₄	1	2	yes	—
397	#11924005	C₂²×C₄	1	1	yes	characteristic
398	#11924005	C₂²×C₄	1	1	yes	characteristic
399	#11924005	C₂²×C₄	1	2	yes	—
400	#11924005	C₂²×C₄	1	2	yes	—
401	#11924005	C₂²×C₄	1	2	yes	—
402	#11924005	C₂²×C₄	1	2	yes	—
403	#11924005	C₂²×C₄	1	2	yes	—
404	#11924005	C₂²×C₄	1	2	yes	—
405	#11924005	C₂²×C₄	1	1	yes	characteristic
406	#11924005	C₂²×C₄	1	1	yes	characteristic
407	#11924005	C₂²×C₄	1	2	yes	—
408	#11924005	C₂²×C₄	1	2	yes	—
409	#11924005	C₂²×C₄	1	2	yes	—
410	#11924005	C₂²×C₄	1	2	yes	—
411	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
412	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
413	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
414	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
415	C₄×Dic₇₃	C₂²×C₄	1	2	yes	—
416	C₄×Dic₇₃	C₂²×C₄	1	2	yes	—
417	C₄×Dic₇₃	C₂⁴	1	1	yes	characteristic
418	C₄×Dic₇₃	C₂⁴	1	1	yes	characteristic
419	C₄×Dic₇₃	C₂⁴	1	2	yes	—
420	#41×C₇₃	—	2	4	no	—
421	C₂×Q₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
422	C₂×D₄×C₇₃	C₂²×C₄	1	2	yes	—
423	C₂×D₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
424	C₂²×C₄×C₇₃	C₂²×C₄	1	2	yes	—
425	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
426	C₂²×C₄×C₇₃	C₂²×C₄	1	2	yes	—
427	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
428	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
429	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
430	C₂×C₈×C₇₃	—	2	4	no	—
431	C₂×C₈×C₇₃	—	2	4	no	—
432	C₂×C₈×C₇₃	—	2	2	no	—
433	C₂×C₈×C₇₃	—	2	2	no	—
434	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
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	C₄⋊C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
441	C₄⋊C₄×C₇₃	C₂²×C₄	1	2	yes	—
442	C₄⋊C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
443	C₄⋊C₄×C₇₃	C₂²×C₄	1	2	yes	—
444	C₂²⋊C₄×C₇₃	C₂²×C₄	1	2	yes	—
445	C₂²⋊C₄×C₇₃	C₂²×C₄	1	2	yes	—
446	C₂²⋊C₄×C₇₃	C₂²×C₄	1	2	yes	—
447	C₄²×C₇₃	C₂²×C₄	1	2	yes	—
448	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
449	C₄²×C₇₃	C₂²×C₄	1	2	yes	—
450	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
451	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
452	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
453	C₄²×C₇₃	C₂⁴	1	2	yes	—
454	C₂³×C₇₃	C₂³×C₄	1	1	yes	characteristic
455	C₂³×C₇₃	C₂³×C₄	1	2	yes	—
456	C₂²×D₇₃	—	2	4	no	—
457	C₂²×D₇₃	—	2	4	no	—
458	C₂²×D₇₃	—	4	2	no	—
459	C₂²×D₇₃	C₂³×C₄	1	2	yes	—
460	C₂²×D₇₃	C₂³×C₄	1	1	yes	characteristic
461	C₂²×D₇₃	C₂³×C₄	1	1	yes	characteristic
462	Q₈×C₇₃	—	2	2	no	—
463	D₄×C₇₃	—	2	4	no	—
464	D₄×C₇₃	#131	1	4	yes	complemented
465	C₂×C₄×C₇₃	—	2	4	no	—
466	C₂×C₄×C₇₃	—	2	2	no	—
467	C₂×C₄×C₇₃	—	2	2	no	—
468	C₂×C₄×C₇₃	—	2	2	no	—
469	C₂×C₄×C₇₃	—	2	1	no	—
470	C₂×C₄×C₇₃	—	2	1	no	—
471	C₂×C₄×C₇₃	—	4	2	no	—
472	C₂×C₄×C₇₃	—	4	1	no	—
473	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
474	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
475	C₂×C₄×C₇₃	C₂³×C₄	1	2	yes	—
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	2	yes	—
479	C₂×C₄×C₇₃	C₂³×C₄	1	2	yes	—
480	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
481	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
482	C₂²⋊D₇₃	—	2	4	no	—
483	C₂²⋊D₇₃	—	2	4	no	—
484	C₂²⋊D₇₃	—	2	2	no	—
485	C₂²⋊D₇₃	—	2	2	no	—
486	C₂²⋊D₇₃	—	4	2	no	—
487	C₂×Dic₇₃	—	2	4	no	—
488	C₂×Dic₇₃	—	2	4	no	—
489	C₂×Dic₇₃	—	4	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	1	yes	characteristic
493	C₂×Dic₇₃	C₂³×C₄	1	1	yes	characteristic
494	C₂×Dic₇₃	C₂³×C₄	1	2	yes	—
495	C₂×Dic₇₃	C₂³×C₄	1	2	yes	—
496	C₂×Dic₇₃	C₂³×C₄	1	1	yes	characteristic
497	C₂×Dic₇₃	C₂³×C₄	1	2	yes	—
498	C₂×Dic₇₃	C₂³×C₄	1	1	yes	characteristic
499	D₂₉₂	—	2	2	no	—
500	D₂₉₂	—	2	2	no	—
501	D₂₉₂	—	4	2	no	—
502	C₄×D₇₃	—	2	4	no	—
503	C₄×D₇₃	—	2	2	no	—
504	C₄×D₇₃	—	2	2	no	—
505	C₄×D₇₃	—	2	2	no	—
506	C₄×D₇₃	—	2	1	no	—
507	C₄×D₇₃	—	2	1	no	—
508	C₄×D₇₃	—	2	2	no	—
509	C₄×D₇₃	—	2	4	no	—
510	C₄×D₇₃	—	4	1	no	—
511	C₄×D₇₃	—	4	1	no	—
512	C₄×D₇₃	C₂×#41	1	2	yes	—
513	C₄×D₇₃	C₂×#41	1	2	yes	—
514	Dic₁₄₆	—	2	2	no	—
515	Dic₁₄₆	—	2	2	no	—
516	Dic₁₄₆	—	4	2	no	—
517	C₈×C₇₃	—	2	2	no	—
518	C₈×C₇₃	—	2	1	no	—
519	C₈×C₇₃	—	2	2	no	—
520	C₈×C₇₃	—	2	1	no	—
521	C₈×C₇₃	C₂×#41	1	2	yes	—
522	C₈×C₇₃	C₂×#41	1	2	yes	—
523	#10596831	—	2	2	no	—
524	#10596831	—	2	1	no	—
525	#10596831	—	2	1	no	—
526	#10596831	—	2	2	no	—
527	#10596831	C₂×#41	1	2	yes	—
528	#10596831	C₂×#41	1	2	yes	—
529	C₂²×C₇₃	—	2	2	no	—
530	C₂²×C₇₃	—	2	2	no	—
531	C₂²×C₇₃	—	2	1	no	—
532	C₂²×C₇₃	—	2	1	no	—
533	C₂²×C₇₃	—	2	1	no	—
534	C₂²×C₇₃	C₂×#131	1	4	yes	—
535	C₂²×C₇₃	C₂⁴×C₄	1	1	yes	characteristic
536	C₂×D₇₃	—	2	1	no	—
537	C₂×D₇₃	—	2	1	no	—
538	C₂×D₇₃	—	2	2	no	—
539	C₂×D₇₃	—	2	1	no	—
540	C₂×D₇₃	—	2	1	no	—
541	C₂×D₇₃	—	2	2	no	—
542	C₂×D₇₃	—	2	1	no	—
543	C₂×D₇₃	—	2	2	no	—
544	C₂×D₇₃	—	4	8	no	—
545	C₂×D₇₃	C₄×#41	1	2	yes	—
546	C₄×C₇₃	—	2	1	no	—
547	C₄×C₇₃	—	2	2	no	—
548	C₄×C₇₃	—	2	1	no	—
549	C₄×C₇₃	—	2	2	no	—
550	C₄×C₇₃	—	2	2	no	—
551	C₄×C₇₃	—	2	1	no	—
552	C₄×C₇₃	—	2	1	no	—
553	C₄×C₇₃	C₂×#131	1	2	yes	—
554	C₄×C₇₃	C₂²×#41	1	1	yes	characteristic
555	C₄×C₇₃	C₂²×#41	1	1	yes	characteristic
556	Dic₇₃	—	2	1	no	—
557	Dic₇₃	—	2	2	no	—
558	Dic₇₃	—	2	2	no	—
559	Dic₇₃	—	2	1	no	—
560	Dic₇₃	—	2	1	no	—
561	Dic₇₃	—	2	1	no	—
562	Dic₇₃	—	2	2	no	—
563	Dic₇₃	—	2	1	no	—
564	Dic₇₃	C₄×#41	1	2	yes	—
565	#60215	—	73	1	no	maximal, Sylow
566	C₂×C₇₃	—	2	4	no	—
567	C₂×C₇₃	—	4	1	no	—
568	C₂×C₇₃	C₂×C₄×#41	1	1	yes	characteristic
569	C₂×C₇₃	C₂²×#131	1	1	yes	characteristic
570	C₂×C₇₃	#3573	1	1	yes	characteristic
571	D₇₃	—	2	2	no	—
572	D₇₃	—	4	1	no	—
573	D₇₃	—	4	2	no	—
574	#3475	—	73	1	no	—
575	#2970	—	73	1	no	—
576	#2970	—	73	1	no	—
577	#2969	—	73	1	no	—
578	#2969	—	73	1	no	—
579	#2968	—	73	2	no	—
580	#2968	—	73	2	no	—
581	#2966	—	73	1	no	—
582	#2966	—	73	2	no	—
583	#2966	—	73	2	no	—
584	#2966	—	73	1	no	—
585	C₈×#41	—	73	1	no	—
586	C₈×#41	D₇₃	1	1	yes	characteristic, complemented
587	#2962	—	73	1	no	—
588	#2960	—	73	1	no	—
589	D₄×M₁₆	—	73	1	no	—
590	#2933	—	73	2	no	—
591	#2929	—	73	2	no	—
592	C₂×C₈×D₄	—	73	1	no	—
593	#2925	—	73	1	no	—
594	#2924	—	73	2	no	—
595	C₄×#131	—	73	1	no	—
596	C₂×#405	—	73	2	no	—
597	C₇₃	#60215	1	1	yes	characteristic, complemented, Sylow
598	C₂×#131	—	73	1	no	—
599	C₂×#131	—	73	1	no	—
600	C₂²×M₁₆	—	73	2	no	—
601	C₂³×C₈	—	73	2	no	—
602	#556	—	73	1	no	—
603	#555	—	73	1	no	—
604	#554	—	73	1	no	—
605	#553	—	73	2	no	—
606	#552	—	73	1	no	—
607	#552	—	73	2	no	—
608	#552	—	73	1	no	—
609	#551	—	73	2	no	—
610	#551	—	73	2	no	—
611	#547	—	73	1	no	—
612	#546	—	73	1	no	—
613	#546	—	73	1	no	—
614	#533	—	73	1	no	—
615	#529	—	73	1	no	—
616	#529	—	73	2	no	—
617	#529	—	73	2	no	—
618	#529	—	73	1	no	—
619	#525	—	73	2	no	—
620	C₄×#41	—	73	1	no	—
621	C₄×#41	—	73	1	no	—
622	C₄×#41	C₂×D₇₃	1	1	yes	characteristic
623	C₂×C₄×D₄	—	73	1	no	—
624	C₂×#117	—	73	2	no	—
625	#446	—	73	1	no	—
626	#446	—	73	1	no	—
627	#446	—	73	1	no	—
628	#446	—	73	2	no	—
629	#446	—	73	2	no	—
630	#446	—	73	2	no	—
631	#446	—	73	1	no	—
632	C₈×Q₈	—	73	1	no	—
633	C₈×Q₈	—	73	1	no	—
634	C₈×Q₈	—	73	2	no	—
635	C₈×Q₈	C₂×D₇₃	1	1	yes	characteristic, complemented
636	C₈×Q₈	C₂×D₇₃	1	1	yes	characteristic, complemented
637	#436	—	73	1	no	—
638	#436	—	73	2	no	—
639	#436	—	73	1	no	—
640	#436	—	73	2	no	—
641	#435	—	73	2	no	—
642	#435	—	73	2	no	—
643	#435	—	73	2	no	—
644	#435	—	73	2	no	—
645	#435	—	73	2	no	—
646	#435	—	73	2	no	—
647	#435	—	73	2	no	—
648	#435	—	73	2	no	—
649	#435	—	73	2	no	—
650	#435	—	73	2	no	—
651	C₈×D₄	—	73	2	no	—
652	C₈×D₄	—	73	2	no	—
653	C₈×D₄	—	73	2	no	—
654	C₈×D₄	—	73	1	no	—
655	C₈×D₄	—	73	1	no	—
656	C₈×D₄	—	73	1	no	—
657	C₈×D₄	—	73	2	no	—
658	C₈×D₄	—	73	2	no	—
659	C₈×D₄	—	73	1	no	—
660	C₈×D₄	—	73	2	no	—
661	C₈×D₄	C₂×D₇₃	1	1	yes	characteristic
662	C₈×D₄	C₂×D₇₃	1	1	yes	characteristic
663	C₈×D₄	C₂×D₇₃	1	2	yes	complemented
664	C₈×D₄	C₂×D₇₃	1	2	yes	complemented
665	#433	—	73	2	no	—
666	#433	—	73	2	no	—
667	#433	—	73	2	no	—
668	#433	—	73	2	no	—
669	#433	—	73	2	no	—
670	#433	—	73	2	no	—
671	#432	—	73	2	no	—
672	#432	—	73	1	no	—
673	#432	—	73	1	no	—
674	#432	—	73	2	no	—
675	#431	—	73	1	no	—
676	#431	—	73	2	no	—
677	#431	C₂×D₇₃	1	2	yes	complemented
678	#431	C₂×D₇₃	1	1	yes	characteristic, complemented
679	#424	—	73	2	no	—
680	#424	—	73	2	no	—
681	#423	—	73	1	no	—
682	C₂×C₄⋊C₈	—	73	1	no	—
683	#408	—	73	2	no	—
684	#407	—	73	2	no	—
685	C₂×C₂²⋊C₈	—	73	2	no	—
686	#405	—	73	1	no	—
687	#405	—	73	1	no	—
688	#405	—	73	1	no	—
689	#405	—	73	2	no	—
690	#405	—	73	2	no	—
691	#405	—	73	2	no	—
692	#405	—	73	2	no	—
693	#405	—	73	2	no	—
694	#405	—	73	2	no	—
695	#405	—	73	2	no	—
696	#405	—	73	1	no	—
697	#405	—	73	1	no	—
698	#405	—	73	1	no	—
699	C₄×M₁₆	—	73	1	no	—
700	C₄×M₁₆	—	73	1	no	—
701	C₄×M₁₆	—	73	1	no	—
702	C₂×#97	—	73	2	no	—
703	C₂×#97	—	73	2	no	—
704	C₂×C₄×C₈	—	73	2	no	—
705	C₂×C₄×C₈	—	73	1	no	—
706	C₂×C₄×C₈	—	73	1	no	—
707	C₂×C₄×C₈	C₂×D₇₃	1	2	yes	complemented
708	C₂×C₄×C₈	C₂×D₇₃	1	1	yes	characteristic, complemented
709	C₂×#41	—	73	1	no	—
710	C₂×#41	—	73	1	no	—
711	C₂×#41	C₄×D₇₃	1	1	yes	characteristic
712	C₂²×D₄	—	73	1	no	—
713	C₂³×C₄	—	73	2	no	—
714	#131	—	146	4	no	—
715	#131	—	146	4	no	—
716	C₂×M₁₆	—	73	1	no	—
717	C₂×M₁₆	—	73	1	no	—
718	C₂×M₁₆	—	73	1	no	—
719	C₂×M₁₆	—	73	2	no	—
720	C₂×M₁₆	—	73	2	no	—
721	C₂×M₁₆	—	73	2	no	—
722	C₂×M₁₆	—	73	1	no	—
723	C₂×M₁₆	—	73	1	no	—
724	C₂×M₁₆	—	73	1	no	—
725	C₂×M₁₆	—	146	8	no	—
726	C₂²×C₈	—	73	1	no	—
727	C₂²×C₈	—	73	2	no	—
728	C₂²×C₈	—	73	2	no	—
729	C₂²×C₈	—	73	2	no	—
730	C₂²×C₈	—	73	2	no	—
731	C₂²×C₈	—	73	1	no	—
732	C₂²×C₈	—	73	1	no	—
733	C₂²×C₈	—	73	2	no	—
734	C₂²×C₈	—	73	1	no	—
735	C₂²×C₈	—	146	8	no	—
736	C₂²×C₈	C₂²×D₇₃	1	2	yes	—
737	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
738	C₂²×C₈	C₂²×D₇₃	1	2	yes	—
739	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
740	C₄⋊Q₈	—	73	1	no	—
741	C₄⋊Q₈	—	73	1	no	—
742	#126	—	73	2	no	—
743	#126	—	73	2	no	—
744	#126	—	73	2	no	—
745	#126	—	73	2	no	—
746	#126	—	73	2	no	—
747	#126	—	73	2	no	—
748	#125	—	73	2	no	—
749	#125	—	73	1	no	—
750	#125	—	73	2	no	—
751	#125	—	73	2	no	—
752	#125	—	73	1	no	—
753	#124	—	73	1	no	—
754	#124	—	73	2	no	—
755	#124	—	73	1	no	—
756	#124	—	73	2	no	—
757	#123	—	73	2	no	—
758	#123	—	73	2	no	—
759	#123	—	73	2	no	—
760	#123	—	73	2	no	—
761	#123	—	73	2	no	—
762	#123	—	73	2	no	—
763	#123	—	73	2	no	—
764	#123	—	73	2	no	—
765	C₂²⋊Q₈	—	73	1	no	—
766	C₂²⋊Q₈	—	73	1	no	—
767	C₂²⋊Q₈	—	73	1	no	—
768	C₂²⋊Q₈	—	73	2	no	—
769	C₂²⋊Q₈	—	73	2	no	—
770	C₂²⋊Q₈	—	73	1	no	—
771	C₂²⋊Q₈	—	73	2	no	—
772	C₂²⋊Q₈	—	73	2	no	—
773	C₂²⋊Q₈	—	73	2	no	—
774	#121	—	73	2	no	—
775	#121	—	73	2	no	—
776	#121	—	73	2	no	—
777	#121	—	73	1	no	—
778	#121	—	73	1	no	—
779	#121	—	73	2	no	—
780	#120	—	73	2	no	—
781	#120	—	73	2	no	—
782	C₄×Q₈	—	73	1	no	—
783	C₄×Q₈	—	73	1	no	—
784	C₄×Q₈	—	73	1	no	—
785	C₄×Q₈	—	73	1	no	—
786	C₄×Q₈	—	73	2	no	—
787	C₄×Q₈	C₄×D₇₃	1	1	yes	characteristic
788	C₄×Q₈	C₂²×D₇₃	1	1	yes	characteristic
789	C₄×D₄	—	73	1	no	—
790	C₄×D₄	—	73	1	no	—
791	C₄×D₄	—	73	1	no	—
792	C₄×D₄	—	73	1	no	—
793	C₄×D₄	—	73	1	no	—
794	C₄×D₄	—	73	1	no	—
795	C₄×D₄	—	73	2	no	—
796	C₄×D₄	—	73	2	no	—
797	C₄×D₄	—	73	2	no	—
798	C₄×D₄	—	73	1	no	—
799	C₄×D₄	—	73	2	no	—
800	C₄×D₄	—	73	2	no	—
801	C₄×D₄	—	73	1	no	—
802	C₄×D₄	—	73	1	no	—
803	C₄×D₄	—	73	1	no	—
804	C₄×D₄	—	73	2	no	—
805	C₄×D₄	C₄×D₇₃	1	1	yes	characteristic
806	C₄×D₄	C₄×D₇₃	1	2	yes	—
807	C₄×D₄	C₂²×D₇₃	1	1	yes	characteristic
808	C₄×D₄	C₂²×D₇₃	1	2	yes	—
809	#117	—	73	1	no	—
810	#117	—	73	1	no	—
811	#117	—	73	2	no	—
812	#117	—	73	2	no	—
813	#117	—	73	2	no	—
814	#117	—	73	2	no	—
815	#117	—	73	2	no	—
816	#117	—	73	1	no	—
817	#117	—	73	2	no	—
818	#117	—	73	2	no	—
819	#117	—	73	2	no	—
820	#117	—	73	1	no	—
821	#117	C₄×D₇₃	1	2	yes	—
822	#117	C₄×D₇₃	1	1	yes	characteristic
823	C₂×C₄⋊C₄	—	73	2	no	—
824	C₂×C₄⋊C₄	—	73	2	no	—
825	C₂×C₄⋊C₄	—	73	1	no	—
826	C₂×C₂²⋊C₄	—	73	2	no	—
827	C₂×C₂²⋊C₄	—	73	2	no	—
828	C₂×C₂²⋊C₄	—	73	2	no	—
829	C₂×C₄²	—	73	2	no	—
830	C₂×C₄²	—	73	1	no	—
831	C₂×C₄²	—	73	1	no	—
832	C₂×C₄²	C₂²×D₇₃	1	2	yes	—
833	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
834	C₄⋊C₈	—	73	2	no	—
835	C₄⋊C₈	—	73	2	no	—
836	C₄⋊C₈	—	73	2	no	—
837	C₄⋊C₈	—	73	2	no	—
838	C₄⋊C₈	—	73	2	no	—
839	C₄⋊C₈	—	73	2	no	—
840	C₄⋊C₈	—	73	1	no	—
841	C₄⋊C₈	—	73	1	no	—
842	C₄⋊C₈	—	73	2	no	—
843	C₄⋊C₈	—	73	2	no	—
844	C₄⋊C₈	C₂²×D₇₃	1	1	yes	characteristic
845	C₄⋊C₈	C₂²×D₇₃	1	1	yes	characteristic
846	C₄⋊C₈	C₂²×D₇₃	1	2	yes	—
847	C₄⋊C₈	C₂²×D₇₃	1	2	yes	—
848	C₂²⋊C₈	—	73	2	no	—
849	C₂²⋊C₈	—	73	2	no	—
850	C₂²⋊C₈	—	73	2	no	—
851	C₂²⋊C₈	—	73	2	no	—
852	C₂²⋊C₈	—	73	2	no	—
853	C₂²⋊C₈	—	73	2	no	—
854	C₂²⋊C₈	—	73	2	no	—
855	C₂²⋊C₈	—	73	2	no	—
856	C₂²⋊C₈	—	73	2	no	—
857	C₂²⋊C₈	C₂²×D₇₃	1	2	yes	—
858	C₂²⋊C₈	C₂²×D₇₃	1	2	yes	—
859	C₂²⋊C₈	C₂²×D₇₃	1	2	yes	—
860	#97	—	73	1	no	—
861	#97	—	73	2	no	—
862	#97	—	73	2	no	—
863	#97	—	73	2	no	—
864	#97	—	73	1	no	—
865	#97	—	73	1	no	—
866	#97	—	73	1	no	—
867	#97	—	73	1	no	—
868	#97	—	73	2	no	—
869	#97	—	73	2	no	—
870	#97	—	73	2	no	—
871	#97	—	73	1	no	—
872	C₄×C₈	—	73	1	no	—
873	C₄×C₈	—	73	2	no	—
874	C₄×C₈	—	73	1	no	—
875	C₄×C₈	—	73	2	no	—
876	C₄×C₈	—	73	1	no	—
877	C₄×C₈	—	73	1	no	—
878	C₄×C₈	—	73	2	no	—
879	C₄×C₈	—	73	1	no	—
880	C₄×C₈	—	73	1	no	—
881	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
882	C₄×C₈	C₂²×D₇₃	1	2	yes	—
883	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
884	C₄×C₈	C₂²×D₇₃	1	2	yes	—
885	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
886	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
887	C₄×C₈	C₂²×D₇₃	1	2	yes	—
888	C₂⁴	—	73	2	no	—
889	#41	—	2	4	no	—
890	#41	—	146	2	no	—
891	#41	—	146	2	no	—
892	#41	—	146	4	no	—
893	C₂×Q₈	—	73	2	no	—
894	C₂×Q₈	—	73	1	no	—
895	C₂×Q₈	—	73	1	no	—
896	C₂×Q₈	C₂×C₄×D₇₃	1	1	yes	characteristic
897	C₂×D₄	—	73	2	no	—
898	C₂×D₄	—	73	1	no	—
899	C₂×D₄	—	73	2	no	—
900	C₂×D₄	—	73	1	no	—
901	C₂×D₄	—	73	2	no	—
902	C₂×D₄	—	73	2	no	—
903	C₂×D₄	—	73	1	no	—
904	C₂×D₄	—	73	1	no	—
905	C₂×D₄	—	146	4	no	—
906	C₂×D₄	C₂×C₄×D₇₃	1	2	yes	—
907	C₂×D₄	C₂×C₄×D₇₃	1	1	yes	characteristic
908	C₂²×C₄	—	73	2	no	—
909	C₂²×C₄	—	73	1	no	—
910	C₂²×C₄	—	73	1	no	—
911	C₂²×C₄	—	73	1	no	—
912	C₂²×C₄	—	73	2	no	—
913	C₂²×C₄	—	73	2	no	—
914	C₂²×C₄	—	73	1	no	—
915	C₂²×C₄	—	73	1	no	—
916	C₂²×C₄	—	73	2	no	—
917	C₂²×C₄	—	73	2	no	—
918	C₂²×C₄	—	73	1	no	—
919	C₂²×C₄	—	73	2	no	—
920	C₂²×C₄	—	146	4	no	—
921	C₂²×C₄	—	146	4	no	—
922	C₂²×C₄	C₂×C₄×D₇₃	1	2	yes	—
923	C₂²×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
924	C₂²×C₄	C₂×C₄×D₇₃	1	2	yes	—
925	C₂²×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
926	C₂²×C₄	C₂³×D₇₃	1	2	yes	—
927	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
928	M₁₆	—	73	4	no	—
929	M₁₆	—	146	4	no	—
930	M₁₆	—	146	2	no	—
931	M₁₆	—	146	4	no	—
932	M₁₆	—	146	2	no	—
933	M₁₆	—	146	2	no	—
934	M₁₆	—	146	2	no	—
935	M₁₆	—	146	4	no	—
936	M₁₆	—	146	2	no	—
937	C₂×C₈	—	2	4	no	—
938	C₂×C₈	—	2	4	no	—
939	C₂×C₈	—	2	2	no	—
940	C₂×C₈	—	2	2	no	—
941	C₂×C₈	—	73	1	no	—
942	C₂×C₈	—	73	1	no	—
943	C₂×C₈	—	73	4	no	—
944	C₂×C₈	—	73	2	no	—
945	C₂×C₈	—	73	1	no	—
946	C₂×C₈	—	73	1	no	—
947	C₂×C₈	—	73	2	no	—
948	C₂×C₈	—	146	4	no	—
949	C₂×C₈	—	146	2	no	—
950	C₂×C₈	—	146	4	no	—
951	C₂×C₈	—	146	2	no	—
952	C₂×C₈	—	146	4	no	—
953	C₂×C₈	—	146	4	no	—
954	C₂×C₈	—	146	4	no	—
955	C₂×C₈	—	146	2	no	—
956	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
957	C₂×C₈	C₂³×D₇₃	1	2	yes	—
958	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
959	C₂×C₈	C₂³×D₇₃	1	2	yes	—
960	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
961	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
962	C₄⋊C₄	—	73	1	no	—
963	C₄⋊C₄	—	73	1	no	—
964	C₄⋊C₄	—	73	2	no	—
965	C₄⋊C₄	—	73	2	no	—
966	C₄⋊C₄	—	73	2	no	—
967	C₄⋊C₄	—	73	2	no	—
968	C₄⋊C₄	—	73	2	no	—
969	C₄⋊C₄	—	73	2	no	—
970	C₄⋊C₄	—	73	2	no	—
971	C₄⋊C₄	—	73	1	no	—
972	C₄⋊C₄	—	73	2	no	—
973	C₄⋊C₄	—	73	2	no	—
974	C₄⋊C₄	—	73	1	no	—
975	C₄⋊C₄	—	73	2	no	—
976	C₄⋊C₄	—	73	2	no	—
977	C₄⋊C₄	—	73	2	no	—
978	C₄⋊C₄	—	73	1	no	—
979	C₄⋊C₄	—	73	1	no	—
980	C₄⋊C₄	—	73	1	no	—
981	C₄⋊C₄	—	73	1	no	—
982	C₄⋊C₄	—	73	2	no	—
983	C₄⋊C₄	—	73	2	no	—
984	C₄⋊C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
985	C₄⋊C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
986	C₄⋊C₄	C₂×C₄×D₇₃	1	2	yes	—
987	C₄⋊C₄	C₂×C₄×D₇₃	1	2	yes	—
988	C₂²⋊C₄	—	73	2	no	—
989	C₂²⋊C₄	—	73	2	no	—
990	C₂²⋊C₄	—	73	1	no	—
991	C₂²⋊C₄	—	73	1	no	—
992	C₂²⋊C₄	—	73	2	no	—
993	C₂²⋊C₄	—	73	1	no	—
994	C₂²⋊C₄	—	73	1	no	—
995	C₂²⋊C₄	—	73	2	no	—
996	C₂²⋊C₄	—	73	2	no	—
997	C₂²⋊C₄	—	73	2	no	—
998	C₂²⋊C₄	—	73	2	no	—
999	C₂²⋊C₄	—	73	2	no	—
1000	C₂²⋊C₄	—	73	2	no	—
1001	C₂²⋊C₄	—	73	2	no	—
1002	C₂²⋊C₄	—	73	2	no	—
1003	C₂²⋊C₄	—	73	1	no	—
1004	C₂²⋊C₄	—	73	2	no	—
1005	C₂²⋊C₄	—	73	1	no	—
1006	C₂²⋊C₄	—	73	2	no	—
1007	C₂²⋊C₄	—	73	2	no	—
1008	C₂²⋊C₄	—	73	2	no	—
1009	C₂²⋊C₄	C₂×C₄×D₇₃	1	2	yes	—
1010	C₂²⋊C₄	C₂×C₄×D₇₃	1	2	yes	—
1011	C₂²⋊C₄	C₂×C₄×D₇₃	1	2	yes	—
1012	C₄²	—	73	2	no	—
1013	C₄²	—	73	2	no	—
1014	C₄²	—	73	1	no	—
1015	C₄²	—	73	1	no	—
1016	C₄²	—	73	1	no	—
1017	C₄²	—	73	1	no	—
1018	C₄²	—	73	1	no	—
1019	C₄²	—	73	1	no	—
1020	C₄²	—	73	2	no	—
1021	C₄²	C₂×C₄×D₇₃	1	2	yes	—
1022	C₄²	C₂×C₄×D₇₃	1	2	yes	—
1023	C₄²	C₂×C₄×D₇₃	1	1	yes	characteristic
1024	C₄²	C₂×C₄×D₇₃	1	1	yes	characteristic
1025	C₄²	C₂³×D₇₃	1	1	yes	characteristic
1026	C₄²	C₂³×D₇₃	1	1	yes	characteristic
1027	C₄²	C₂³×D₇₃	1	2	yes	—
1028	C₂³	—	292	2	no	—
1029	C₂³	—	73	1	no	—
1030	C₂³	—	73	2	no	—
1031	C₂³	—	73	1	no	—
1032	C₂³	—	146	4	no	—
1033	C₂³	—	146	4	no	—
1034	C₂³	C₂²×C₄×D₇₃	1	1	yes	characteristic
1035	C₂³	C₂²×C₄×D₇₃	1	2	yes	—
1036	Q₈	—	2	2	no	—
1037	Q₈	—	292	2	no	—
1038	Q₈	—	146	2	no	—
1039	Q₈	—	146	2	no	—
1040	D₄	—	2	4	no	—
1041	D₄	—	292	2	no	—
1042	D₄	—	292	2	no	—
1043	D₄	—	146	2	no	—
1044	D₄	—	146	2	no	—
1045	D₄	—	146	2	no	—
1046	D₄	—	146	4	no	—
1047	D₄	—	146	4	no	—
1048	D₄	—	146	2	no	—
1049	D₄	#14556597	1	4	yes	complemented
1050	C₂×C₄	—	2	4	no	—
1051	C₂×C₄	—	2	2	no	—
1052	C₂×C₄	—	2	2	no	—
1053	C₂×C₄	—	2	1	no	—
1054	C₂×C₄	—	2	1	no	—
1055	C₂×C₄	—	2	2	no	—
1056	C₂×C₄	—	4	1	no	—
1057	C₂×C₄	—	4	2	no	—
1058	C₂×C₄	—	292	1	no	—
1059	C₂×C₄	—	292	1	no	—
1060	C₂×C₄	—	292	2	no	—
1061	C₂×C₄	—	73	1	no	—
1062	C₂×C₄	—	73	2	no	—
1063	C₂×C₄	—	73	2	no	—
1064	C₂×C₄	—	73	1	no	—
1065	C₂×C₄	—	73	1	no	—
1066	C₂×C₄	—	73	1	no	—
1067	C₂×C₄	—	73	2	no	—
1068	C₂×C₄	—	73	2	no	—
1069	C₂×C₄	—	73	1	no	—
1070	C₂×C₄	—	73	1	no	—
1071	C₂×C₄	—	73	2	no	—
1072	C₂×C₄	—	146	4	no	—
1073	C₂×C₄	—	146	4	no	—
1074	C₂×C₄	—	146	4	no	—
1075	C₂×C₄	—	146	4	no	—
1076	C₂×C₄	—	146	2	no	—
1077	C₂×C₄	—	146	1	no	—
1078	C₂×C₄	—	146	1	no	—
1079	C₂×C₄	—	146	2	no	—
1080	C₂×C₄	—	146	2	no	—
1081	C₂×C₄	—	146	2	no	—
1082	C₂×C₄	C₂²×C₄×D₇₃	1	2	yes	—
1083	C₂×C₄	C₂²×C₄×D₇₃	1	1	yes	characteristic
1084	C₂×C₄	C₂²×C₄×D₇₃	1	1	yes	characteristic
1085	C₂×C₄	C₂²×C₄×D₇₃	1	1	yes	characteristic
1086	C₂×C₄	C₂²×C₄×D₇₃	1	1	yes	characteristic
1087	C₂×C₄	C₂²×C₄×D₇₃	1	2	yes	—
1088	C₂×C₄	C₂²×C₄×D₇₃	1	2	yes	—
1089	C₂×C₄	C₂²×C₄×D₇₃	1	1	yes	characteristic
1090	C₂×C₄	C₂⁴×D₇₃	1	1	yes	characteristic
1091	C₈	—	2	2	no	—
1092	C₈	—	2	1	no	—
1093	C₈	—	2	2	no	—
1094	C₈	—	2	1	no	—
1095	C₈	—	73	2	no	—
1096	C₈	—	73	2	no	—
1097	C₈	—	146	2	no	—
1098	C₈	—	146	1	no	—
1099	C₈	—	146	2	no	—
1100	C₈	—	146	1	no	—
1101	C₈	#41×D₇₃	1	2	yes	—
1102	C₈	#41×D₇₃	1	2	yes	—
1103	C₂²	—	2	2	no	—
1104	C₂²	—	2	2	no	—
1105	C₂²	—	2	1	no	—
1106	C₂²	—	2	1	no	—
1107	C₂²	—	2	1	no	—
1108	C₂²	—	292	8	no	—
1109	C₂²	—	73	2	no	—
1110	C₂²	—	146	1	no	—
1111	C₂²	—	146	2	no	—
1112	C₂²	—	146	1	no	—
1113	C₂²	—	146	2	no	—
1114	C₂²	—	146	2	no	—
1115	C₂²	—	146	1	no	—
1116	C₂²	—	146	1	no	—
1117	C₂²	—	146	1	no	—
1118	C₂²	C₂×#14556597	1	4	yes	—
1119	C₂²	C₂³×C₄×D₇₃	1	1	yes	characteristic
1120	C₄	—	2	1	no	—
1121	C₄	—	2	2	no	—
1122	C₄	—	2	1	no	—
1123	C₄	—	2	1	no	—
1124	C₄	—	2	2	no	—
1125	C₄	—	2	2	no	—
1126	C₄	—	2	1	no	—
1127	C₄	—	73	2	no	—
1128	C₄	—	146	1	no	—
1129	C₄	—	146	1	no	—
1130	C₄	—	146	2	no	—
1131	C₄	—	146	1	no	—
1132	C₄	—	146	2	no	—
1133	C₄	—	146	1	no	—
1134	C₄	—	146	2	no	—
1135	C₄	—	146	1	no	—
1136	C₄	C₂×#14556597	1	2	yes	—
1137	C₄	C₂×#41×D₇₃	1	1	yes	characteristic
1138	C₄	C₂×#41×D₇₃	1	1	yes	characteristic
1139	C₂	—	2	4	no	—
1140	C₂	—	4	1	no	—
1141	C₂	—	292	2	no	—
1142	C₂	—	292	1	no	—
1143	C₂	—	146	2	no	—
1144	C₂	C₄×#41×D₇₃	1	1	yes	characteristic
1145	C₂	C₂²×#14556597	1	1	yes	characteristic
1146	C₂	#22624642	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂³×D₇₃
commutator, socle	C₂²×C₇₃	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₇₃
Fitting	C₈×#41×C₇₃	C₂
prime radical	#22623493	C₂
cosocle	C₂×C₄×C₇₃	C₂⁵
hypercenter	C₈×#41	D₇₃
hypocenter	C₇₃	#60215
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₈ ◁ C₈×#41

Complements

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

N	H ≅ G/N	type
2. #22618945	C₂	semidirect
3. #22618939	C₂	semidirect
4. #22618934	C₂	semidirect
5. #22618929	C₂	semidirect
6. #22618920	C₂	semidirect
7. #22618919	C₂	semidirect
8. #22618908	C₂	semidirect
9. #22618906	C₂	semidirect
10. #22618906	C₂	semidirect
11. #22618899	C₂	semidirect
12. C₈×#11924027	C₂	semidirect
13. #22618873	C₂	semidirect
14. #22618860	C₂	semidirect
15. D₄×#11924011	C₂	semidirect
16. #22618651	C₂	semidirect
17. #22618620	C₂	semidirect
18. C₈×D₄×D₇₃	C₂	semidirect
19. #22618592	C₂	semidirect
20. #22618584	C₂	semidirect
21. C₄×#14556597	C₂	semidirect
22. C₂×#17988541	C₂	semidirect
23. C₈×#41×C₇₃	C₂	semidirect
50. #17988718	C₂²	semidirect
51. #17988718	C₂²	semidirect
52. #17988717	C₂²	semidirect
53. #17988717	C₂²	semidirect
54. #17988716	C₂²	semidirect
55. #17988716	C₂²	semidirect
56. #17988714	C₂²	semidirect
57. C₈×Dic₁₄₆	C₂²	semidirect
58. C₈×Dic₁₄₆	C₂²	semidirect
59. #17988711	C₂²	semidirect
61. #17988666	C₂²	semidirect
63. #17988662	C₂²	semidirect
64. #17988661	C₂²	semidirect
65. #17988659	C₂²	semidirect
66. #17988659	C₂²	semidirect
68. #17988658	C₂²	semidirect
69. #17988658	C₂²	semidirect
70. #17988657	C₂²	semidirect
71. #17988657	C₂²	semidirect
73. #17988655	C₂²	semidirect
75. C₈×D₂₉₂	C₂²	semidirect
80. C₈×C₂²⋊D₇₃	C₂²	semidirect
81. C₈×C₂²⋊D₇₃	C₂²	semidirect
83. #17988650	C₂²	semidirect
84. #17988647	C₂²	semidirect
85. #17988647	C₂²	semidirect
86. #17988646	C₂²	semidirect
87. #17988646	C₂²	semidirect
88. #17988646	C₂²	semidirect
89. #17988645	C₂²	semidirect
90. #17988644	C₂²	semidirect
91. #17988644	C₂²	semidirect
92. #17988643	C₂²	semidirect
93. #17988641	C₂²	semidirect
94. #17988639	C₂²	semidirect
95. #17988637	C₂²	semidirect
103. #17988542	C₂²	semidirect
104. #17988542	C₂²	semidirect
110. #17988541	C₂²	semidirect
111. #17988541	C₂²	semidirect
112. #17988541	C₂²	semidirect
113. #17988541	C₂²	semidirect
114. #17988541	C₂²	semidirect
115. #17988541	C₂²	semidirect
116. C₄×#11924012	C₂²	semidirect
118. C₄×#11924011	C₂²	semidirect
119. C₂×#14556502	C₂²	semidirect
120. C₂×#14556501	C₂²	semidirect
121. C₂×C₈×Dic₇₃	C₂²	semidirect
123. C₄×C₈×D₇₃	C₂²	semidirect
125. C₈×Q₈×C₇₃	C₂²	semidirect
126. C₈×Q₈×C₇₃	C₂²	semidirect
129. C₈×D₄×C₇₃	C₂²	semidirect
130. C₈×D₄×C₇₃	C₂²	semidirect
131. #431×C₇₃	C₂²	semidirect
132. #431×C₇₃	C₂²	semidirect
133. C₂×C₄×C₈×C₇₃	C₂²	semidirect
134. C₂×C₄×C₈×C₇₃	C₂²	semidirect
352. #11924011	#41	semidirect
367. C₈×D₇₃	#41	semidirect
464. D₄×C₇₃	#131	semidirect
586. C₈×#41	D₇₃	semidirect
597. C₇₃	#60215	semidirect
635. C₈×Q₈	C₂×D₇₃	semidirect
636. C₈×Q₈	C₂×D₇₃	semidirect
663. C₈×D₄	C₂×D₇₃	semidirect
664. C₈×D₄	C₂×D₇₃	semidirect
677. #431	C₂×D₇₃	semidirect
678. #431	C₂×D₇₃	semidirect
707. C₂×C₄×C₈	C₂×D₇₃	semidirect
708. C₂×C₄×C₈	C₂×D₇₃	semidirect
1049. D₄	#14556597	semidirect

Maximal subgroups

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

subgroup	index
#22623493	2
#22618945	2
#22618939	2
#22618934	2
#22618929	2
#22618920	2
#22618919	2
#22618908	2
#22618906	2
#22618899	2
C₈×#11924027	2
#22618873	2
#22618860	2
D₄×#11924011	2
#22618651	2
#22618620	2
C₈×D₄×D₇₃	2
#22618592	2
#22618584	2
C₄×#14556597	2
C₂×#17988541	2
C₈×#41×C₇₃	2
#60215	73