Subgroups — #34330880

Order 20224.

810 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23773139	C₂	1	2	yes	maximal
2	C₂×#19098838	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#19098838	C₂	1	1	yes	maximal, characteristic, complemented
4	#23772011	C₂	1	1	yes	maximal, characteristic, complemented
5	#23764800	C₂	1	2	yes	maximal, complemented
6	#23764681	C₂	1	2	yes	maximal, complemented
7	#23764315	C₂	1	1	yes	maximal, characteristic, complemented
8	#23764190	C₂	1	1	yes	maximal, characteristic, complemented
9	#23763871	C₂	1	2	yes	maximal, complemented
10	#23763450	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₉×#2955	C₂	1	1	yes	maximal, characteristic
12	C₂×#14579191	C₂²	1	2	yes	—
13	C₂×#14579191	C₂²	1	2	yes	—
14	C₂²×Dic₃₁₆	C₂²	1	1	yes	characteristic
15	#19099330	C₂²	1	2	yes	—
16	#19098838	—	2	2	no	—
17	#19098838	—	2	2	no	—
18	#19098838	—	2	2	no	—
19	#19098838	—	2	2	no	—
20	#19098836	—	2	4	no	—
21	#19098824	—	2	4	no	—
22	#19098612	—	2	2	no	—
23	#19098612	C₂²	1	2	yes	—
24	#19098611	C₂²	1	2	yes	—
25	C₂×#14579097	—	2	2	no	—
26	C₂×#14579097	C₂²	1	1	yes	characteristic
27	C₂×#14579097	C₂²	1	1	yes	characteristic
28	C₂×#14579097	C₂²	1	1	yes	characteristic
29	#19098571	C₂²	1	2	yes	—
30	#19098547	C₂²	1	2	yes	—
31	C₂×#14579079	C₂²	1	2	yes	—
32	C₂×#14579079	C₂²	1	2	yes	—
33	C₂×#14579079	C₂²	1	2	yes	—
34	#19098333	C₂²	1	2	yes	—
35	C₇₉⋊#338	C₂²	1	2	yes	—
36	#575×C₇₉	C₂²	1	1	yes	characteristic
37	C₂×#131×C₇₉	C₂²	1	1	yes	characteristic
38	C₂×#131×C₇₉	C₂²	1	1	yes	characteristic
39	#444×C₇₉	—	2	2	no	—
40	#443×C₇₉	—	2	2	no	—
41	#430×C₇₉	C₂²	1	1	yes	characteristic
42	#421×C₇₉	C₂²	1	1	yes	characteristic
43	#421×C₇₉	C₂²	1	1	yes	characteristic
44	#405×C₇₉	C₂²	1	1	yes	characteristic
45	C₂²×Dic₁₅₈	C₂³	1	2	yes	—
46	#14579191	—	2	4	no	—
47	#14579191	—	2	4	no	—
48	#14579191	—	2	4	no	—
49	#14579191	—	4	2	no	—
50	C₂×Dic₃₁₆	—	2	1	no	—
51	C₂×Dic₃₁₆	—	2	1	no	—
52	C₂×Dic₃₁₆	—	2	1	no	—
53	C₂×Dic₃₁₆	—	2	1	no	—
54	C₂×Dic₃₁₆	—	2	1	no	—
55	C₂×Dic₃₁₆	—	2	1	no	—
56	C₂×#11929614	—	2	2	no	—
57	C₂×#11929614	—	2	2	no	—
58	C₂×#11929612	—	2	2	no	—
59	C₂×#11929612	—	2	2	no	—
60	#14579168	—	2	4	no	—
61	#14579168	—	4	2	no	—
62	C₂×#11929608	—	2	4	no	—
63	C₂×#11929608	C₂³	1	2	yes	—
64	C₂×#11929608	C₂³	1	2	yes	—
65	C₂×#11929608	C₂³	1	2	yes	—
66	#14579097	—	2	1	no	—
67	#14579097	—	2	1	no	—
68	#14579097	—	2	1	no	—
69	#14579097	—	2	1	no	—
70	#14579097	—	2	4	no	—
71	#14579097	D₄	1	2	yes	—
72	#14579097	D₄	1	2	yes	—
73	#14579096	—	2	4	no	—
74	#14579084	—	4	2	no	—
75	#14579080	—	2	2	no	—
76	#14579079	—	2	4	no	—
77	#14579079	—	2	4	no	—
78	#14579079	—	2	4	no	—
79	#14579078	—	2	2	no	—
80	C₂×#41×C₇₉	C₂³	1	1	yes	characteristic
81	C₂×#41×C₇₉	C₂³	1	1	yes	characteristic
82	#137×C₇₉	—	2	1	no	—
83	#137×C₇₉	D₄	1	2	yes	—
84	AGL(1,ℤ/8)×C₇₉	—	2	1	no	—
85	AGL(1,ℤ/8)×C₇₉	D₄	1	2	yes	—
86	#135×C₇₉	—	2	2	no	—
87	#131×C₇₉	—	2	1	no	—
88	#131×C₇₉	—	2	1	no	—
89	#131×C₇₉	—	2	1	no	—
90	#131×C₇₉	—	2	1	no	—
91	#131×C₇₉	—	2	1	no	—
92	#131×C₇₉	—	2	1	no	—
93	#131×C₇₉	D₄	1	2	yes	—
94	#131×C₇₉	D₄	1	2	yes	—
95	C₂×M₁₆×C₇₉	—	2	1	no	—
96	C₂×M₁₆×C₇₉	—	2	1	no	—
97	C₂×M₁₆×C₇₉	C₂³	1	1	yes	characteristic
98	C₂×M₁₆×C₇₉	C₂³	1	1	yes	characteristic
99	C₂×M₁₆×C₇₉	C₂³	1	1	yes	characteristic
100	C₂²×C₈×C₇₉	—	2	1	no	—
101	C₂²×C₈×C₇₉	—	2	1	no	—
102	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
103	#117×C₇₉	C₂³	1	1	yes	characteristic
104	#108×C₇₉	—	2	2	no	—
105	#104×C₇₉	—	2	2	no	—
106	#104×C₇₉	—	2	2	no	—
107	#97×C₇₉	—	2	1	no	—
108	C₄×C₈×C₇₉	—	2	1	no	—
109	C₂×Dic₁₅₈	—	2	2	no	—
110	C₂×Dic₁₅₈	—	2	2	no	—
111	C₂×Dic₁₅₈	—	2	2	no	—
112	C₂×Dic₁₅₈	—	2	2	no	—
113	C₂×Dic₁₅₈	—	2	2	no	—
114	C₂×Dic₁₅₈	—	2	2	no	—
115	C₂²×Dic₇₉	—	2	2	no	—
116	Dic₃₁₆	—	4	1	no	—
117	Dic₃₁₆	—	4	1	no	—
118	Dic₃₁₆	—	4	1	no	—
119	Dic₃₁₆	—	4	1	no	—
120	#11929614	—	4	4	no	—
121	#11929614	—	4	4	no	—
122	#11929612	—	4	4	no	—
123	#11929612	—	4	4	no	—
124	#11929608	—	2	2	no	—
125	#11929608	—	2	2	no	—
126	#11929608	—	2	2	no	—
127	#11929608	—	2	2	no	—
128	#11929608	—	2	2	no	—
129	#11929608	—	4	4	no	—
130	#11929608	C₂×D₄	1	4	yes	—
131	C₂×C₇₉⋊C₈	—	2	2	no	—
132	C₂×C₇₉⋊C₈	—	2	2	no	—
133	C₂×C₇₉⋊C₈	—	2	2	no	—
134	C₂×C₇₉⋊C₈	—	4	4	no	—
135	#41×C₇₉	—	2	1	no	—
136	#41×C₇₉	—	2	1	no	—
137	#41×C₇₉	—	2	1	no	—
138	#41×C₇₉	—	2	1	no	—
139	#41×C₇₉	—	2	1	no	—
140	#41×C₇₉	—	2	1	no	—
141	#41×C₇₉	C₂×D₄	1	2	yes	—
142	#41×C₇₉	C₂×D₄	1	2	yes	—
143	C₂×Q₈×C₇₉	C₂×D₄	1	1	yes	characteristic
144	C₂×Q₈×C₇₉	#41	1	1	yes	characteristic
145	C₂×D₄×C₇₉	—	2	1	no	—
146	C₂×D₄×C₇₉	—	2	1	no	—
147	C₂×D₄×C₇₉	C₂×D₄	1	1	yes	characteristic
148	C₂×D₄×C₇₉	#41	1	1	yes	characteristic
149	C₂²×C₄×C₇₉	—	2	1	no	—
150	C₂²×C₄×C₇₉	—	2	1	no	—
151	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
152	Q₁₆×C₇₉	—	2	2	no	—
153	SD₁₆×C₇₉	—	2	2	no	—
154	SD₁₆×C₇₉	—	2	2	no	—
155	D₈×C₇₉	—	2	2	no	—
156	M₁₆×C₇₉	—	2	2	no	—
157	M₁₆×C₇₉	—	2	2	no	—
158	M₁₆×C₇₉	—	2	1	no	—
159	M₁₆×C₇₉	—	2	1	no	—
160	M₁₆×C₇₉	—	2	1	no	—
161	M₁₆×C₇₉	—	2	1	no	—
162	M₁₆×C₇₉	—	4	1	no	—
163	M₁₆×C₇₉	—	4	1	no	—
164	M₁₆×C₇₉	C₂×D₄	1	2	yes	—
165	M₁₆×C₇₉	C₂×D₄	1	2	yes	—
166	C₂×C₈×C₇₉	—	2	2	no	—
167	C₂×C₈×C₇₉	—	2	2	no	—
168	C₂×C₈×C₇₉	—	2	1	no	—
169	C₂×C₈×C₇₉	—	2	1	no	—
170	C₂×C₈×C₇₉	—	2	1	no	—
171	C₂×C₈×C₇₉	—	4	1	no	—
172	C₂×C₈×C₇₉	—	4	1	no	—
173	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
174	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
175	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
176	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
177	C₂×C₈×C₇₉	#41	1	1	yes	characteristic
178	C₂×C₈×C₇₉	#41	1	1	yes	characteristic
179	C₄⋊C₄×C₇₉	—	2	1	no	—
180	C₂²⋊C₄×C₇₉	—	2	1	no	—
181	C₄²×C₇₉	—	2	1	no	—
182	C₂³×C₇₉	—	2	1	no	—
183	C₂³×C₇₉	—	2	1	no	—
184	C₂³×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
185	Q₈×C₇₉	—	2	1	no	—
186	Q₈×C₇₉	—	2	1	no	—
187	Q₈×C₇₉	—	2	1	no	—
188	Q₈×C₇₉	#121	1	2	yes	—
189	D₄×C₇₉	—	2	2	no	—
190	D₄×C₇₉	—	2	2	no	—
191	D₄×C₇₉	—	2	1	no	—
192	D₄×C₇₉	—	2	1	no	—
193	D₄×C₇₉	—	2	1	no	—
194	D₄×C₇₉	—	4	1	no	—
195	D₄×C₇₉	—	4	1	no	—
196	D₄×C₇₉	#121	1	2	yes	—
197	C₂×C₄×C₇₉	—	2	1	no	—
198	C₂×C₄×C₇₉	—	2	2	no	—
199	C₂×C₄×C₇₉	—	2	2	no	—
200	C₂×C₄×C₇₉	—	2	1	no	—
201	C₂×C₄×C₇₉	—	4	1	no	—
202	C₂×C₄×C₇₉	—	4	1	no	—
203	C₂×C₄×C₇₉	—	4	1	no	—
204	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
205	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
206	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
207	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
208	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
209	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
210	C₂×Dic₇₉	—	4	2	no	—
211	C₂×Dic₇₉	—	4	2	no	—
212	C₂×Dic₇₉	—	4	2	no	—
213	Dic₁₅₈	—	4	2	no	—
214	Dic₁₅₈	—	4	2	no	—
215	Dic₁₅₈	—	4	2	no	—
216	Dic₁₅₈	—	4	2	no	—
217	C₈×C₇₉	—	2	2	no	—
218	C₈×C₇₉	—	2	2	no	—
219	C₈×C₇₉	—	4	1	no	—
220	C₈×C₇₉	#121	1	1	yes	characteristic
221	C₈×C₇₉	#121	1	1	yes	characteristic
222	C₈×C₇₉	#121	1	1	yes	characteristic
223	C₈×C₇₉	#121	1	1	yes	characteristic
224	C₇₉⋊C₈	—	2	4	no	—
225	C₇₉⋊C₈	—	4	2	no	—
226	C₇₉⋊C₈	—	4	2	no	—
227	C₂²×C₇₉	—	2	2	no	—
228	C₂²×C₇₉	—	4	1	no	—
229	C₂²×C₇₉	—	4	1	no	—
230	C₂²×C₇₉	—	8	1	no	—
231	C₂²×C₇₉	—	8	1	no	—
232	C₂²×C₇₉	#537	1	1	yes	characteristic
233	C₂²×C₇₉	#547	1	1	yes	characteristic
234	C₂²×C₇₉	#548	1	1	yes	characteristic
235	C₄×C₇₉	—	2	2	no	—
236	C₄×C₇₉	—	4	1	no	—
237	C₄×C₇₉	—	8	1	no	—
238	C₄×C₇₉	C₂×#121	1	1	yes	characteristic
239	C₄×C₇₉	C₂×#121	1	1	yes	characteristic
240	C₄×C₇₉	D₄²	1	1	yes	characteristic
241	C₄×C₇₉	#553	1	1	yes	characteristic
242	Dic₇₉	—	8	2	no	—
243	#24810	—	79	1	no	maximal, Sylow
244	C₂×C₇₉	—	2	1	no	—
245	C₂×C₇₉	—	2	1	no	—
246	C₂×C₇₉	—	2	1	no	—
247	C₂×C₇₉	—	4	2	no	—
248	C₂×C₇₉	—	8	1	no	—
249	C₂×C₇₉	#2416	1	1	yes	characteristic
250	#3069	—	79	2	no	—
251	C₂×#473	—	79	1	no	—
252	C₂×#473	—	79	1	no	—
253	#2955	D₇₉	1	1	yes	characteristic
254	#2916	—	79	1	no	—
255	#2070	—	79	2	no	—
256	#2049	—	79	2	no	—
257	#1979	—	79	1	no	—
258	#1953	—	79	1	no	—
259	#1902	—	79	2	no	—
260	#1813	—	79	1	no	—
261	C₇₉	#24810	1	1	yes	characteristic, complemented, Sylow
262	#575	C₂×D₇₉	1	1	yes	characteristic
263	C₂×#137	—	79	2	no	—
264	C₂×#137	—	79	2	no	—
265	C₂²×Q₁₆	—	79	1	no	—
266	#568	—	79	2	no	—
267	C₂×#131	C₂×D₇₉	1	1	yes	characteristic
268	C₂×#131	C₂×D₇₉	1	1	yes	characteristic
269	#473	—	158	2	no	—
270	#473	—	158	2	no	—
271	#473	—	158	4	no	—
272	#473	—	158	2	no	—
273	#473	—	158	2	no	—
274	#471	—	158	4	no	—
275	#444	—	2	2	no	—
276	#443	—	2	2	no	—
277	#430	—	79	2	no	—
278	#430	—	79	2	no	—
279	#430	—	158	2	no	—
280	#430	C₂×D₇₉	1	1	yes	characteristic
281	C₂×#108	—	79	1	no	—
282	C₂×#108	—	79	1	no	—
283	C₂×#108	—	79	1	no	—
284	C₂×#108	—	158	2	no	—
285	#421	C₂×D₇₉	1	1	yes	characteristic
286	#421	C₂×D₇₉	1	1	yes	characteristic
287	#419	—	79	2	no	—
288	#413	—	79	2	no	—
289	C₂×#101	—	79	2	no	—
290	C₂×#101	—	79	2	no	—
291	C₂×#101	—	79	2	no	—
292	#405	C₂×D₇₉	1	1	yes	characteristic
293	#344	—	79	2	no	—
294	#338	—	79	2	no	—
295	C₂×#41	C₂²×D₇₉	1	1	yes	characteristic
296	C₂×#41	C₂²×D₇₉	1	1	yes	characteristic
297	C₂²×Q₈	—	79	2	no	—
298	#137	—	2	1	no	—
299	#137	—	316	2	no	—
300	#137	—	158	4	no	—
301	#137	—	158	4	no	—
302	#137	—	158	4	no	—
303	#137	D₃₁₆	1	2	yes	—
304	AGL(1,ℤ/8)	—	2	1	no	—
305	AGL(1,ℤ/8)	D₃₁₆	1	2	yes	—
306	#135	—	2	2	no	—
307	C₂×Q₁₆	—	158	2	no	—
308	C₂×Q₁₆	—	158	2	no	—
309	C₂×Q₁₆	—	158	1	no	—
310	C₂×Q₁₆	—	158	1	no	—
311	C₂×Q₁₆	—	158	1	no	—
312	C₂×Q₁₆	—	158	1	no	—
313	C₂×Q₁₆	—	158	1	no	—
314	C₂×Q₁₆	—	158	1	no	—
315	C₂×SD₁₆	—	158	2	no	—
316	C₂×SD₁₆	—	158	2	no	—
317	#131	—	2	1	no	—
318	#131	—	2	1	no	—
319	#131	—	2	1	no	—
320	#131	—	2	1	no	—
321	#131	—	2	1	no	—
322	#131	—	2	1	no	—
323	#131	—	316	2	no	—
324	#131	—	158	4	no	—
325	#131	C₂²⋊D₇₉	1	2	yes	—
326	#131	C₂²⋊D₇₉	1	2	yes	—
327	C₂×M₁₆	—	2	1	no	—
328	C₂×M₁₆	—	2	1	no	—
329	C₂×M₁₆	—	79	2	no	—
330	C₂×M₁₆	—	79	2	no	—
331	C₂×M₁₆	—	79	2	no	—
332	C₂×M₁₆	—	158	4	no	—
333	C₂×M₁₆	C₂²×D₇₉	1	1	yes	characteristic
334	C₂×M₁₆	C₂²×D₇₉	1	1	yes	characteristic
335	C₂×M₁₆	C₂²×D₇₉	1	1	yes	characteristic
336	C₂²×C₈	—	2	1	no	—
337	C₂²×C₈	—	2	1	no	—
338	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
339	#117	C₂²×D₇₉	1	1	yes	characteristic
340	#108	—	2	2	no	—
341	#108	—	79	2	no	—
342	#108	—	79	2	no	—
343	#108	—	158	4	no	—
344	#108	—	158	4	no	—
345	#108	—	158	1	no	—
346	#108	—	158	1	no	—
347	#108	—	158	1	no	—
348	#108	—	158	1	no	—
349	#104	—	2	2	no	—
350	#104	—	2	2	no	—
351	#103	—	316	2	no	—
352	#101	—	158	4	no	—
353	#101	—	158	2	no	—
354	#101	—	158	4	no	—
355	#101	—	158	4	no	—
356	#100	—	158	2	no	—
357	#97	—	2	1	no	—
358	C₄×C₈	—	2	1	no	—
359	#41	—	2	1	no	—
360	#41	—	2	1	no	—
361	#41	—	2	1	no	—
362	#41	—	2	1	no	—
363	#41	—	2	1	no	—
364	#41	—	2	1	no	—
365	#41	C₂×C₂²⋊D₇₉	1	2	yes	—
366	#41	C₂×D₃₁₆	1	2	yes	—
367	C₂×Q₈	—	158	2	no	—
368	C₂×Q₈	—	158	2	no	—
369	C₂×Q₈	—	158	2	no	—
370	C₂×Q₈	—	158	2	no	—
371	C₂×Q₈	—	158	2	no	—
372	C₂×Q₈	—	158	2	no	—
373	C₂×Q₈	C₂×D₃₁₆	1	1	yes	characteristic
374	C₂×Q₈	#11929624	1	1	yes	characteristic
375	C₂×D₄	—	2	1	no	—
376	C₂×D₄	—	2	1	no	—
377	C₂×D₄	C₂×D₃₁₆	1	1	yes	characteristic
378	C₂×D₄	#11929624	1	1	yes	characteristic
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	—	158	2	no	—
382	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
383	Q₁₆	—	2	2	no	—
384	Q₁₆	—	316	4	no	—
385	Q₁₆	—	316	4	no	—
386	Q₁₆	—	316	1	no	—
387	Q₁₆	—	316	1	no	—
388	Q₁₆	—	316	1	no	—
389	Q₁₆	—	316	1	no	—
390	SD₁₆	—	2	2	no	—
391	SD₁₆	—	2	2	no	—
392	SD₁₆	—	316	4	no	—
393	SD₁₆	—	316	4	no	—
394	D₈	—	2	2	no	—
395	M₁₆	—	2	1	no	—
396	M₁₆	—	2	1	no	—
397	M₁₆	—	2	2	no	—
398	M₁₆	—	2	2	no	—
399	M₁₆	—	2	1	no	—
400	M₁₆	—	2	1	no	—
401	M₁₆	—	4	1	no	—
402	M₁₆	—	4	1	no	—
403	M₁₆	—	316	4	no	—
404	M₁₆	—	79	4	no	—
405	M₁₆	—	158	2	no	—
406	M₁₆	—	158	2	no	—
407	M₁₆	—	158	2	no	—
408	M₁₆	—	158	2	no	—
409	M₁₆	—	158	2	no	—
410	M₁₆	C₂×C₂²⋊D₇₉	1	2	yes	—
411	M₁₆	C₂×D₃₁₆	1	2	yes	—
412	C₂×C₈	—	2	1	no	—
413	C₂×C₈	—	2	1	no	—
414	C₂×C₈	—	2	2	no	—
415	C₂×C₈	—	2	2	no	—
416	C₂×C₈	—	2	1	no	—
417	C₂×C₈	—	4	1	no	—
418	C₂×C₈	—	4	1	no	—
419	C₂×C₈	—	316	4	no	—
420	C₂×C₈	—	158	2	no	—
421	C₂×C₈	—	158	2	no	—
422	C₂×C₈	—	158	2	no	—
423	C₂×C₈	D₄×D₇₉	1	1	yes	characteristic
424	C₂×C₈	D₄×D₇₉	1	1	yes	characteristic
425	C₂×C₈	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
426	C₂×C₈	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
427	C₂×C₈	#11929623	1	1	yes	characteristic
428	C₂×C₈	#11929623	1	1	yes	characteristic
429	C₄⋊C₄	—	2	1	no	—
430	C₂²⋊C₄	—	2	1	no	—
431	C₄²	—	2	1	no	—
432	C₂³	—	2	1	no	—
433	C₂³	—	2	1	no	—
434	C₂³	#14579208	1	1	yes	characteristic
435	Q₈	—	2	1	no	—
436	Q₈	—	2	1	no	—
437	Q₈	—	2	1	no	—
438	Q₈	—	316	2	no	—
439	Q₈	—	316	2	no	—
440	Q₈	—	316	2	no	—
441	Q₈	—	316	2	no	—
442	Q₈	#14579135	1	2	yes	—
443	D₄	—	2	2	no	—
444	D₄	—	2	2	no	—
445	D₄	—	2	1	no	—
446	D₄	—	2	1	no	—
447	D₄	—	2	1	no	—
448	D₄	—	4	1	no	—
449	D₄	—	4	1	no	—
450	D₄	#14579135	1	2	yes	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	4	1	no	—
456	C₂×C₄	—	4	1	no	—
457	C₂×C₄	—	4	1	no	—
458	C₂×C₄	—	316	2	no	—
459	C₂×C₄	—	316	2	no	—
460	C₂×C₄	—	316	2	no	—
461	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
462	C₂×C₄	C₂²×C₂²⋊D₇₉	1	1	yes	characteristic
463	C₂×C₄	C₂²×D₃₁₆	1	1	yes	characteristic
464	C₂×C₄	C₂×#11929623	1	1	yes	characteristic
465	C₂×C₄	C₂×#11929624	1	1	yes	characteristic
466	C₂×C₄	#14579207	1	1	yes	characteristic
467	C₈	—	2	2	no	—
468	C₈	—	2	2	no	—
469	C₈	—	4	1	no	—
470	C₈	—	316	2	no	—
471	C₈	—	316	2	no	—
472	C₈	—	158	4	no	—
473	C₈	#14579133	1	1	yes	characteristic
474	C₈	#14579133	1	1	yes	characteristic
475	C₈	#14579133	1	1	yes	characteristic
476	C₈	#14579133	1	1	yes	characteristic
477	C₂²	—	2	2	no	—
478	C₂²	—	4	1	no	—
479	C₂²	—	4	1	no	—
480	C₂²	—	8	1	no	—
481	C₂²	—	8	1	no	—
482	C₂²	#19099141	1	1	yes	characteristic
483	C₂²	#19099217	1	1	yes	characteristic
484	C₂²	#19099222	1	1	yes	characteristic
485	C₄	—	2	2	no	—
486	C₄	—	4	1	no	—
487	C₄	—	8	1	no	—
488	C₄	—	632	2	no	—
489	C₄	C₂×#14579133	1	1	yes	characteristic
490	C₄	C₂×#14579135	1	1	yes	characteristic
491	C₄	D₄×D₃₁₆	1	1	yes	characteristic
492	C₄	#19099259	1	1	yes	characteristic
493	C₂	—	2	1	no	—
494	C₂	—	2	1	no	—
495	C₂	—	2	1	no	—
496	C₂	—	4	2	no	—
497	C₂	—	8	1	no	—
498	C₂	#23766840	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#23766840
commutator, cosocle	C₂²×C₄×C₇₉	C₂⁴
Frattini	C₂²×C₄	C₂³×D₇₉
Fitting	C₇₉×#2955	C₂
socle	C₂×C₇₉	#2416
prime radical	#575×C₇₉	C₂²
hypercenter	#2955	D₇₉
hypocenter	C₇₉	#24810
LCS	G ▷ C₂²×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #2955

Complements

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

N	H ≅ G/N	type
2. C₂×#19098838	C₂	semidirect
3. C₂×#19098838	C₂	semidirect
4. #23772011	C₂	semidirect
5. #23764800	C₂	semidirect
6. #23764681	C₂	semidirect
7. #23764315	C₂	semidirect
8. #23764190	C₂	semidirect
9. #23763871	C₂	semidirect
10. #23763450	C₂	semidirect
261. C₇₉	#24810	semidirect

Maximal subgroups

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

subgroup	index
#23773139	2
C₂×#19098838	2
#23772011	2
#23764800	2
#23764681	2
#23764315	2
#23764190	2
#23763871	2
#23763450	2
C₇₉×#2955	2
#24810	79