Subgroups — #35168906

Order 20224.

1818 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23777201	C₂	1	2	yes	maximal, complemented
2	#23776360	C₂	1	4	yes	maximal, complemented
3	#23776301	C₂	1	4	yes	maximal, complemented
4	#23776268	C₂	1	2	yes	maximal, complemented
5	#23776268	C₂	1	4	yes	maximal, complemented
6	Q₈×D₆₃₂	C₂	1	2	yes	maximal, complemented
7	#23773939	C₂	1	2	yes	maximal, complemented
8	#23773914	C₂	1	1	yes	maximal, characteristic, complemented
9	#23773232	C₂	1	4	yes	maximal, complemented
10	#23773199	C₂	1	2	yes	maximal, complemented
11	#23772253	C₂	1	2	yes	maximal
12	C₂×C₄×D₆₃₂	C₂	1	1	yes	maximal, characteristic
13	C₇₉×#2960	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²×D₆₃₂	C₂²	1	1	yes	characteristic
15	#19099274	—	2	2	no	—
16	#19099273	C₂²	1	4	yes	complemented
17	#19099273	C₂²	1	8	yes	complemented
18	#19099269	—	2	4	no	—
19	Q₈×D₃₁₆	C₂²	1	4	yes	complemented
20	#19099228	—	2	2	no	—
21	#19099191	C₂²	1	4	yes	—
22	#19099188	—	2	4	no	—
23	#19099120	C₂²	1	2	yes	—
24	C₂²⋊Q₈×D₇₉	—	2	4	no	—
25	#19099037	C₂²	1	4	yes	—
26	C₂×C₄×D₃₁₆	C₂²	1	2	yes	—
27	#19098972	C₂²	1	8	yes	complemented
28	#19098968	C₂²	1	1	yes	characteristic, complemented
29	#19098968	C₂²	1	4	yes	complemented
30	#19098968	C₂²	1	1	yes	characteristic, complemented
31	#19098965	C₂²	1	2	yes	complemented
32	#19098965	C₂²	1	4	yes	complemented
33	#19098965	C₂²	1	2	yes	complemented
34	#19098961	C₂²	1	2	yes	complemented
35	#19098864	C₂²	1	8	yes	complemented
36	#19098864	C₂²	1	8	yes	complemented
37	#19098864	C₂²	1	8	yes	complemented
38	#19098854	C₂²	1	4	yes	complemented
39	#19098854	C₂²	1	8	yes	complemented
40	#19098844	C₂²	1	4	yes	complemented
41	#19098844	C₂²	1	8	yes	complemented
42	#19098676	C₂²	1	8	yes	—
43	C₄×D₆₃₂	C₂²	1	4	yes	—
44	C₄×D₆₃₂	C₂²	1	2	yes	—
45	C₄×D₆₃₂	C₂²	1	4	yes	—
46	C₄×D₆₃₂	C₂²	1	2	yes	—
47	C₄×D₆₃₂	C₂²	1	2	yes	—
48	C₄×D₆₃₂	C₂²	1	2	yes	—
49	#19098605	C₂²	1	4	yes	—
50	#19098601	C₂²	1	2	yes	—
51	#19098601	C₂²	1	2	yes	—
52	C₂×#14579095	C₂²	1	1	yes	characteristic
53	#19098569	C₂²	1	4	yes	—
54	C₂×#14579083	C₂²	1	2	yes	—
55	#533×C₇₉	C₂²	1	1	yes	characteristic
56	#446×C₇₉	C₂²	1	2	yes	complemented
57	#446×C₇₉	C₂²	1	2	yes	complemented
58	C₈×Q₈×C₇₉	C₂²	1	2	yes	complemented
59	C₈×Q₈×C₇₉	C₂²	1	2	yes	complemented
60	#424×C₇₉	C₂²	1	2	yes	—
61	#423×C₇₉	C₂²	1	1	yes	characteristic
62	#405×C₇₉	C₂²	1	2	yes	—
63	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
64	C₂×Q₈×D₇₉	—	2	4	no	—
65	C₂²×D₃₁₆	C₂³	1	2	yes	—
66	C₂²×C₄×D₇₉	—	2	2	no	—
67	C₂×D₆₃₂	Q₈	1	8	yes	complemented
68	C₂×D₆₃₂	C₂³	1	2	yes	—
69	C₂×D₆₃₂	C₂³	1	2	yes	—
70	#14579161	C₂³	1	8	yes	—
71	#14579161	C₂³	1	2	yes	—
72	#14579161	C₂³	1	2	yes	—
73	#14579160	—	2	4	no	—
74	#14579153	C₂³	1	8	yes	—
75	#14579153	C₂³	1	4	yes	—
76	#14579152	—	2	4	no	—
77	#14579141	—	2	8	no	—
78	#14579141	—	2	4	no	—
79	#14579140	—	2	2	no	—
80	#14579140	—	2	2	no	—
81	#14579139	—	2	8	no	—
82	#14579139	—	2	8	no	—
83	#14579139	—	2	8	no	—
84	#14579138	—	2	8	no	—
85	#14579137	—	2	8	no	—
86	#14579137	—	2	4	no	—
87	C₄×Dic₁₅₈	—	2	2	no	—
88	C₄×Dic₁₅₈	—	2	2	no	—
89	C₄×D₃₁₆	—	2	2	no	—
90	C₄×D₃₁₆	—	2	2	no	—
91	C₄×D₃₁₆	C₂³	1	4	yes	—
92	C₄×D₃₁₆	C₂³	1	4	yes	—
93	C₄×D₃₁₆	C₂³	1	8	yes	—
94	C₄×D₃₁₆	C₂³	1	8	yes	—
95	#14579123	—	2	4	no	—
96	#14579123	—	2	4	no	—
97	#14579120	C₂³	1	4	yes	—
98	C₂×C₄⋊Dic₇₉	C₂³	1	2	yes	—
99	C₄⋊C₄×D₇₉	—	2	8	no	—
100	C₄⋊C₄×D₇₉	—	2	4	no	—
101	C₂×(C₂×D₇₉)⋊C₄	—	2	2	no	—
102	C₂²⋊C₄×D₇₉	—	2	8	no	—
103	#14579095	C₂³	1	2	yes	—
104	#14579095	C₂³	1	2	yes	—
105	#14579095	C₂³	1	2	yes	—
106	#14579095	C₂³	1	2	yes	—
107	#14579095	C₂³	1	2	yes	—
108	#14579095	C₂³	1	2	yes	—
109	#14579095	C₂³	1	8	yes	—
110	#14579093	C₂³	1	4	yes	—
111	#14579093	C₂³	1	4	yes	—
112	#14579093	C₂³	1	8	yes	—
113	#14579083	C₂³	1	4	yes	—
114	#14579083	C₂³	1	4	yes	—
115	#14579083	C₂³	1	8	yes	—
116	#14579083	C₂³	1	8	yes	—
117	C₂×M₁₆×C₇₉	C₂³	1	2	yes	—
118	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
119	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
120	C₄⋊Q₈×C₇₉	D₄	1	1	yes	characteristic
121	C₄⋊Q₈×C₇₉	D₄	1	1	yes	characteristic
122	#125×C₇₉	D₄	1	2	yes	—
123	C₂²⋊Q₈×C₇₉	D₄	1	2	yes	—
124	C₂²⋊Q₈×C₇₉	D₄	1	2	yes	—
125	C₄×Q₈×C₇₉	C₂³	1	2	yes	—
126	C₄×Q₈×C₇₉	C₂³	1	2	yes	—
127	#117×C₇₉	C₂³	1	2	yes	—
128	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
129	C₄⋊C₈×C₇₉	C₂³	1	2	yes	—
130	C₄⋊C₈×C₇₉	C₂³	1	2	yes	—
131	C₄⋊C₈×C₇₉	C₂³	1	4	yes	—
132	C₄⋊C₈×C₇₉	C₂³	1	4	yes	—
133	#97×C₇₉	C₂³	1	4	yes	—
134	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
135	C₄×C₈×C₇₉	C₂³	1	4	yes	—
136	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
137	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
138	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
139	C₂³×D₇₉	—	2	2	no	—
140	C₂×Dic₁₅₈	—	2	2	no	—
141	C₂×Dic₁₅₈	—	2	8	no	—
142	C₂×Dic₁₅₈	—	2	2	no	—
143	Q₈×D₇₉	—	8	8	no	—
144	C₂×D₃₁₆	—	2	2	no	—
145	C₂×D₃₁₆	—	2	4	no	—
146	C₂×D₃₁₆	C₂×Q₈	1	8	yes	complemented
147	C₂×D₃₁₆	C₂⁴	1	4	yes	—
148	C₂²×Dic₇₉	—	2	2	no	—
149	C₂×C₄×D₇₉	—	2	4	no	—
150	C₂×C₄×D₇₉	—	2	8	no	—
151	C₂×C₄×D₇₉	—	2	8	no	—
152	C₂×C₄×D₇₉	—	2	4	no	—
153	C₂×C₄×D₇₉	—	8	4	no	—
154	D₆₃₂	C₂×Q₈	1	8	yes	complemented
155	D₆₃₂	C₂×Q₈	1	8	yes	complemented
156	C₄⋊Dic₇₉	—	2	2	no	—
157	C₄⋊Dic₇₉	—	2	8	no	—
158	C₄⋊Dic₇₉	—	2	2	no	—
159	C₄⋊Dic₇₉	—	2	2	no	—
160	C₄⋊Dic₇₉	C₂⁴	1	4	yes	—
161	C₄⋊Dic₇₉	C₂⁴	1	4	yes	—
162	C₄⋊Dic₇₉	C₂⁴	1	4	yes	—
163	Dic₇₉⋊C₄	—	2	4	no	—
164	Dic₇₉⋊C₄	—	2	8	no	—
165	Dic₇₉⋊C₄	—	2	8	no	—
166	Dic₇₉⋊C₄	—	2	4	no	—
167	C₂²⋊Dic₇₉	—	2	4	no	—
168	(C₂×D₇₉)⋊C₄	—	2	8	no	—
169	(C₂×D₇₉)⋊C₄	—	2	8	no	—
170	(C₂×D₇₉)⋊C₄	—	2	4	no	—
171	(C₂×D₇₉)⋊C₄	—	2	4	no	—
172	C₄×Dic₇₉	—	2	4	no	—
173	C₂×Q₈×C₇₉	C₂×D₄	1	2	yes	—
174	C₂×Q₈×C₇₉	C₂×D₄	1	2	yes	—
175	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
178	M₁₆×C₇₉	—	2	4	no	—
179	C₂×C₈×C₇₉	—	2	2	no	—
180	C₂×C₈×C₇₉	C₂×Q₈	1	4	yes	complemented
181	C₂×C₈×C₇₉	C₂⁴	1	1	yes	characteristic
182	C₂×C₈×C₇₉	C₂⁴	1	1	yes	characteristic
183	C₂×C₈×C₇₉	C₂⁴	1	4	yes	—
184	C₂×C₈×C₇₉	C₂⁴	1	1	yes	characteristic
185	C₂×C₈×C₇₉	C₂⁴	1	1	yes	characteristic
186	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
187	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
188	C₄⋊C₄×C₇₉	C₂×D₄	1	4	yes	—
189	C₄⋊C₄×C₇₉	C₂×D₄	1	4	yes	—
190	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
191	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
192	C₂²⋊C₄×C₇₉	C₂×D₄	1	4	yes	—
193	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
194	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
195	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
196	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
197	C₄²×C₇₉	C₂⁴	1	4	yes	—
198	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
199	C₂²×D₇₉	—	2	4	no	—
200	C₂²×D₇₉	—	2	8	no	—
201	C₂²×D₇₉	—	8	2	no	—
202	C₂²×D₇₉	—	8	2	no	—
203	Q₈×C₇₉	—	2	4	no	—
204	Q₈×C₇₉	—	4	2	no	—
205	C₂×C₄×C₇₉	—	2	2	no	—
206	C₂×C₄×C₇₉	—	4	1	no	—
207	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
208	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
209	C₂×C₄×C₇₉	C₂²×D₄	1	4	yes	—
210	C₂×C₄×C₇₉	C₂²×D₄	1	4	yes	—
211	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
212	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
213	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
214	C₂×C₄×C₇₉	C₂²×Q₈	1	2	yes	—
215	C₂×C₄×C₇₉	2₋¹⁺⁴	1	2	yes	—
216	C₂×C₄×C₇₉	C₂⁵	1	1	yes	characteristic
217	C₂×Dic₇₉	—	2	4	no	—
218	C₂×Dic₇₉	—	2	4	no	—
219	C₂×Dic₇₉	—	2	4	no	—
220	C₂×Dic₇₉	—	8	2	no	—
221	D₃₁₆	—	2	8	no	—
222	D₃₁₆	—	2	4	no	—
223	D₃₁₆	C₂²×Q₈	1	8	yes	—
224	C₄×D₇₉	—	4	8	no	—
225	C₄×D₇₉	—	8	8	no	—
226	C₄×D₇₉	—	8	4	no	—
227	C₄×D₇₉	—	8	8	no	—
228	Dic₁₅₈	—	4	4	no	—
229	Dic₁₅₈	—	8	8	no	—
230	Dic₁₅₈	—	8	2	no	—
231	C₈×C₇₉	—	2	1	no	—
232	C₈×C₇₉	—	2	1	no	—
233	C₈×C₇₉	—	2	4	no	—
234	C₈×C₇₉	C₂²×Q₈	1	2	yes	—
235	C₈×C₇₉	C₂²×Q₈	1	2	yes	—
236	C₂²×C₇₉	—	2	1	no	—
237	C₂²×C₇₉	—	2	1	no	—
238	C₂²×C₇₉	D₄×Q₈	1	2	yes	—
239	C₂²×C₇₉	C₂³×D₄	1	1	yes	characteristic
240	C₂×D₇₉	—	2	8	no	—
241	C₂×D₇₉	—	4	4	no	—
242	C₂×D₇₉	—	4	4	no	—
243	C₂×D₇₉	—	8	8	no	—
244	C₄×C₇₉	—	2	1	no	—
245	C₄×C₇₉	—	2	1	no	—
246	C₄×C₇₉	—	2	4	no	—
247	C₄×C₇₉	—	2	1	no	—
248	C₄×C₇₉	—	2	4	no	—
249	C₄×C₇₉	D₄×Q₈	1	2	yes	—
250	C₄×C₇₉	#576	1	2	yes	—
251	C₄×C₇₉	C₂³×Q₈	1	1	yes	characteristic
252	C₄×C₇₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
253	Dic₇₉	—	4	4	no	—
254	Dic₇₉	—	4	4	no	—
255	Dic₇₉	—	4	4	no	—
256	#61370	—	79	1	no	maximal, Sylow
257	C₂×C₇₉	—	2	2	no	—
258	C₂×C₇₉	C₂×D₄×Q₈	1	1	yes	characteristic
259	C₂×C₇₉	C₂×#576	1	1	yes	characteristic
260	C₂×C₇₉	#3584	1	1	yes	characteristic
261	D₇₉	—	4	8	no	—
262	#3501	—	79	2	no	—
263	#3389	—	79	4	no	—
264	#3384	—	79	4	no	—
265	#3380	—	79	2	no	—
266	#3380	—	79	4	no	—
267	Q₈×D₈	—	79	2	no	—
268	#3164	—	79	2	no	—
269	#3160	—	79	1	no	—
270	#3081	—	79	4	no	—
271	#3077	—	79	2	no	—
272	#2960	D₇₉	1	1	yes	characteristic, complemented
273	#2948	—	79	2	no	—
274	C₂×C₄×D₈	—	79	1	no	—
275	C₇₉	#61370	1	1	yes	characteristic, complemented, Sylow
276	C₂²×D₈	—	79	1	no	—
277	#554	—	79	4	no	—
278	#554	—	79	8	no	—
279	#554	—	158	2	no	—
280	#554	—	158	4	no	—
281	D₄×Q₈	—	79	4	no	—
282	D₄×Q₈	—	158	2	no	—
283	#544	—	79	4	no	—
284	#543	—	158	4	no	—
285	#533	—	79	2	no	—
286	#533	C₂×D₇₉	1	1	yes	characteristic
287	C₂×C₂²⋊Q₈	—	158	4	no	—
288	#518	—	79	4	no	—
289	C₂×C₄×D₄	—	79	2	no	—
290	#501	—	79	8	no	—
291	#500	—	79	1	no	—
292	#500	—	79	4	no	—
293	#500	—	79	1	no	—
294	#499	—	79	2	no	—
295	#499	—	79	4	no	—
296	#499	—	79	2	no	—
297	#498	—	79	2	no	—
298	#478	—	79	8	no	—
299	#478	—	79	8	no	—
300	#478	—	79	8	no	—
301	#476	—	79	4	no	—
302	#476	—	79	8	no	—
303	#474	—	79	4	no	—
304	#474	—	79	8	no	—
305	#446	C₂×D₇₉	1	2	yes	complemented
306	#446	C₂×D₇₉	1	2	yes	complemented
307	C₈×Q₈	C₂×D₇₉	1	2	yes	complemented
308	C₈×Q₈	C₂×D₇₉	1	2	yes	complemented
309	#442	—	79	8	no	—
310	C₄×D₈	—	79	2	no	—
311	C₄×D₈	—	79	4	no	—
312	C₄×D₈	—	79	2	no	—
313	C₄×D₈	—	79	4	no	—
314	C₄×D₈	—	79	2	no	—
315	C₄×D₈	—	79	2	no	—
316	#428	—	79	4	no	—
317	#427	—	79	2	no	—
318	#427	—	79	2	no	—
319	C₂×#107	—	79	1	no	—
320	#424	C₂×D₇₉	1	2	yes	—
321	#423	C₂×D₇₉	1	1	yes	characteristic
322	#418	—	79	4	no	—
323	C₂×#102	—	79	2	no	—
324	#405	C₂×D₇₉	1	2	yes	—
325	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
326	C₂²×Q₈	—	158	4	no	—
327	C₂²×D₄	—	79	2	no	—
328	C₂³×C₄	—	158	2	no	—
329	C₂×D₈	—	79	8	no	—
330	C₂×D₈	—	79	2	no	—
331	C₂×D₈	—	79	2	no	—
332	C₂×M₁₆	C₂²×D₇₉	1	2	yes	—
333	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
334	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
335	C₄⋊Q₈	—	79	2	no	—
336	C₄⋊Q₈	—	79	2	no	—
337	C₄⋊Q₈	—	79	8	no	—
338	C₄⋊Q₈	—	158	4	no	—
339	C₄⋊Q₈	D₃₁₆	1	1	yes	characteristic
340	C₄⋊Q₈	D₃₁₆	1	1	yes	characteristic
341	#125	—	79	4	no	—
342	#125	—	79	8	no	—
343	#125	—	158	4	no	—
344	#125	D₃₁₆	1	2	yes	—
345	C₂²⋊Q₈	—	158	4	no	—
346	C₂²⋊Q₈	—	158	8	no	—
347	C₂²⋊Q₈	—	158	2	no	—
348	C₂²⋊Q₈	—	158	2	no	—
349	C₂²⋊Q₈	—	158	4	no	—
350	C₂²⋊Q₈	—	158	8	no	—
351	C₂²⋊Q₈	—	158	8	no	—
352	C₂²⋊Q₈	—	158	8	no	—
353	C₂²⋊Q₈	—	158	8	no	—
354	C₂²⋊Q₈	—	158	8	no	—
355	C₂²⋊Q₈	D₃₁₆	1	2	yes	—
356	C₂²⋊Q₈	D₃₁₆	1	2	yes	—
357	C₄×Q₈	—	158	2	no	—
358	C₄×Q₈	—	158	2	no	—
359	C₄×Q₈	C₂²×D₇₉	1	2	yes	—
360	C₄×Q₈	C₂²×D₇₉	1	2	yes	—
361	C₄×D₄	—	79	4	no	—
362	C₄×D₄	—	79	4	no	—
363	C₄×D₄	—	79	8	no	—
364	C₄×D₄	—	79	8	no	—
365	C₄×D₄	—	158	4	no	—
366	C₄×D₄	—	158	4	no	—
367	C₄×D₄	—	158	2	no	—
368	C₄×D₄	—	158	2	no	—
369	#117	—	79	4	no	—
370	#117	C₂²×D₇₉	1	2	yes	—
371	C₂×C₄⋊C₄	—	79	2	no	—
372	C₂×C₄⋊C₄	—	158	8	no	—
373	C₂×C₄⋊C₄	—	158	4	no	—
374	C₂×C₂²⋊C₄	—	158	2	no	—
375	C₂×C₂²⋊C₄	—	158	8	no	—
376	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
377	#107	—	79	2	no	—
378	#107	—	79	2	no	—
379	#107	—	79	2	no	—
380	#107	—	79	2	no	—
381	#107	—	79	2	no	—
382	#107	—	79	2	no	—
383	#107	—	79	8	no	—
384	#106	—	79	4	no	—
385	#106	—	79	4	no	—
386	#106	—	79	8	no	—
387	C₄⋊C₈	C₂²×D₇₉	1	2	yes	—
388	C₄⋊C₈	C₂²×D₇₉	1	2	yes	—
389	C₄⋊C₈	C₂²×D₇₉	1	4	yes	—
390	C₄⋊C₈	C₂²×D₇₉	1	4	yes	—
391	#102	—	79	4	no	—
392	#102	—	79	4	no	—
393	#102	—	79	8	no	—
394	#102	—	79	8	no	—
395	#97	C₂²×D₇₉	1	4	yes	—
396	C₄×C₈	C₂²×D₇₉	1	1	yes	characteristic
397	C₄×C₈	C₂²×D₇₉	1	1	yes	characteristic
398	C₄×C₈	C₂²×D₇₉	1	1	yes	characteristic
399	C₄×C₈	C₂²×D₇₉	1	1	yes	characteristic
400	C₄×C₈	C₂²×D₇₉	1	4	yes	—
401	C₂⁴	—	158	2	no	—
402	C₂×Q₈	—	632	8	no	—
403	C₂×Q₈	—	158	2	no	—
404	C₂×Q₈	—	158	2	no	—
405	C₂×Q₈	—	158	8	no	—
406	C₂×Q₈	C₂×D₃₁₆	1	2	yes	—
407	C₂×Q₈	C₂×D₃₁₆	1	2	yes	—
408	C₂×D₄	—	79	8	no	—
409	C₂×D₄	—	79	4	no	—
410	C₂×D₄	—	158	4	no	—
411	C₂×D₄	—	158	2	no	—
412	C₂²×C₄	—	632	4	no	—
413	C₂²×C₄	—	158	4	no	—
414	C₂²×C₄	—	158	2	no	—
415	C₂²×C₄	—	158	8	no	—
416	C₂²×C₄	—	158	8	no	—
417	C₂²×C₄	—	158	4	no	—
418	C₂²×C₄	C₂×D₃₁₆	1	1	yes	characteristic
419	C₂²×C₄	C₂×D₃₁₆	1	1	yes	characteristic
420	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
421	D₈	—	79	8	no	—
422	D₈	—	79	8	no	—
423	M₁₆	—	2	4	no	—
424	C₂×C₈	—	2	2	no	—
425	C₂×C₈	Q₈×D₇₉	1	4	yes	complemented
426	C₂×C₈	C₂³×D₇₉	1	1	yes	characteristic
427	C₂×C₈	C₂³×D₇₉	1	1	yes	characteristic
428	C₂×C₈	C₂³×D₇₉	1	4	yes	—
429	C₂×C₈	C₂³×D₇₉	1	1	yes	characteristic
430	C₂×C₈	C₂³×D₇₉	1	1	yes	characteristic
431	C₄⋊C₄	—	79	4	no	—
432	C₄⋊C₄	—	79	4	no	—
433	C₄⋊C₄	—	79	4	no	—
434	C₄⋊C₄	—	158	4	no	—
435	C₄⋊C₄	—	158	8	no	—
436	C₄⋊C₄	—	158	8	no	—
437	C₄⋊C₄	—	158	4	no	—
438	C₄⋊C₄	—	158	2	no	—
439	C₄⋊C₄	—	158	2	no	—
440	C₄⋊C₄	—	158	8	no	—
441	C₄⋊C₄	—	158	2	no	—
442	C₄⋊C₄	C₂×D₃₁₆	1	4	yes	—
443	C₄⋊C₄	C₂×D₃₁₆	1	2	yes	—
444	C₄⋊C₄	C₂×D₃₁₆	1	2	yes	—
445	C₄⋊C₄	C₂×D₃₁₆	1	2	yes	—
446	C₄⋊C₄	C₂×D₃₁₆	1	4	yes	—
447	C₄⋊C₄	C₂×D₃₁₆	1	2	yes	—
448	C₂²⋊C₄	—	158	4	no	—
449	C₂²⋊C₄	—	158	8	no	—
450	C₂²⋊C₄	—	158	8	no	—
451	C₂²⋊C₄	—	158	4	no	—
452	C₂²⋊C₄	—	158	4	no	—
453	C₂²⋊C₄	C₂×D₃₁₆	1	4	yes	—
454	C₄²	—	158	4	no	—
455	C₄²	C₂×D₃₁₆	1	1	yes	characteristic
456	C₄²	C₂×D₃₁₆	1	1	yes	characteristic
457	C₄²	C₂³×D₇₉	1	1	yes	characteristic
458	C₄²	C₂³×D₇₉	1	1	yes	characteristic
459	C₄²	C₂³×D₇₉	1	4	yes	—
460	C₂³	—	632	2	no	—
461	C₂³	—	632	2	no	—
462	C₂³	—	158	4	no	—
463	C₂³	—	158	8	no	—
464	C₂³	C₂²×D₃₁₆	1	1	yes	characteristic
465	Q₈	—	2	4	no	—
466	Q₈	—	4	2	no	—
467	Q₈	—	316	4	no	—
468	Q₈	—	632	8	no	—
469	Q₈	—	632	2	no	—
470	D₄	—	79	8	no	—
471	D₄	—	158	4	no	—
472	D₄	—	158	8	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	4	1	no	—
475	C₂×C₄	—	316	8	no	—
476	C₂×C₄	—	632	4	no	—
477	C₂×C₄	—	632	8	no	—
478	C₂×C₄	—	632	8	no	—
479	C₂×C₄	—	632	2	no	—
480	C₂×C₄	—	158	4	no	—
481	C₂×C₄	—	158	4	no	—
482	C₂×C₄	—	158	4	no	—
483	C₂×C₄	C₂²×D₃₁₆	1	1	yes	characteristic
484	C₂×C₄	C₂²×D₃₁₆	1	1	yes	characteristic
485	C₂×C₄	C₂²×D₃₁₆	1	1	yes	characteristic
486	C₂×C₄	C₂²×D₃₁₆	1	4	yes	—
487	C₂×C₄	C₂²×D₃₁₆	1	4	yes	—
488	C₂×C₄	C₂²×D₃₁₆	1	1	yes	characteristic
489	C₂×C₄	C₂²×D₃₁₆	1	1	yes	characteristic
490	C₂×C₄	C₂×Q₈×D₇₉	1	2	yes	—
491	C₂×C₄	#14579208	1	2	yes	—
492	C₂×C₄	C₂⁴×D₇₉	1	1	yes	characteristic
493	C₈	—	2	1	no	—
494	C₈	—	2	1	no	—
495	C₈	—	2	4	no	—
496	C₈	C₂×Q₈×D₇₉	1	2	yes	—
497	C₈	C₂×Q₈×D₇₉	1	2	yes	—
498	C₂²	—	2	1	no	—
499	C₂²	—	2	1	no	—
500	C₂²	—	316	4	no	—
501	C₂²	—	316	4	no	—
502	C₂²	—	632	8	no	—
503	C₂²	—	158	8	no	—
504	C₂²	Q₈×D₃₁₆	1	2	yes	—
505	C₂²	C₂³×D₃₁₆	1	1	yes	characteristic
506	C₄	—	2	1	no	—
507	C₄	—	2	4	no	—
508	C₄	—	2	1	no	—
509	C₄	—	2	1	no	—
510	C₄	—	2	4	no	—
511	C₄	—	316	4	no	—
512	C₄	—	316	4	no	—
513	C₄	—	316	4	no	—
514	C₄	Q₈×D₃₁₆	1	2	yes	—
515	C₄	#19099368	1	2	yes	—
516	C₄	C₂²×Q₈×D₇₉	1	1	yes	characteristic
517	C₄	C₂×#14579208	1	1	yes	characteristic
518	C₂	—	2	2	no	—
519	C₂	—	316	8	no	—
520	C₂	C₂×Q₈×D₃₁₆	1	1	yes	characteristic
521	C₂	C₂×#19099368	1	1	yes	characteristic
522	C₂	#23778174	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂³×D₃₁₆
commutator, cosocle	C₂×C₄×C₇₉	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₇₉
Fitting	C₇₉×#2960	C₂
socle	C₂²×C₇₉	C₂³×D₄
prime radical	C₂²×D₆₃₂	C₂²
hypercenter	#2960	D₇₉
hypocenter	C₇₉	#61370
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ #533 ◁ #2960

Complements

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

N	H ≅ G/N	type
1. #23777201	C₂	semidirect
2. #23776360	C₂	semidirect
3. #23776301	C₂	semidirect
4. #23776268	C₂	semidirect
5. #23776268	C₂	semidirect
6. Q₈×D₆₃₂	C₂	semidirect
7. #23773939	C₂	semidirect
8. #23773914	C₂	semidirect
9. #23773232	C₂	semidirect
10. #23773199	C₂	semidirect
13. C₇₉×#2960	C₂	semidirect
16. #19099273	C₂²	semidirect
17. #19099273	C₂²	semidirect
19. Q₈×D₃₁₆	C₂²	semidirect
27. #19098972	C₂²	semidirect
28. #19098968	C₂²	semidirect
29. #19098968	C₂²	semidirect
30. #19098968	C₂²	semidirect
31. #19098965	C₂²	semidirect
32. #19098965	C₂²	semidirect
33. #19098965	C₂²	semidirect
34. #19098961	C₂²	semidirect
35. #19098864	C₂²	semidirect
36. #19098864	C₂²	semidirect
37. #19098864	C₂²	semidirect
38. #19098854	C₂²	semidirect
39. #19098854	C₂²	semidirect
40. #19098844	C₂²	semidirect
41. #19098844	C₂²	semidirect
56. #446×C₇₉	C₂²	semidirect
57. #446×C₇₉	C₂²	semidirect
58. C₈×Q₈×C₇₉	C₂²	semidirect
59. C₈×Q₈×C₇₉	C₂²	semidirect
67. C₂×D₆₃₂	Q₈	semidirect
146. C₂×D₃₁₆	C₂×Q₈	semidirect
154. D₆₃₂	C₂×Q₈	semidirect
155. D₆₃₂	C₂×Q₈	semidirect
180. C₂×C₈×C₇₉	C₂×Q₈	semidirect
272. #2960	D₇₉	semidirect
275. C₇₉	#61370	semidirect
305. #446	C₂×D₇₉	semidirect
306. #446	C₂×D₇₉	semidirect
307. C₈×Q₈	C₂×D₇₉	semidirect
308. C₈×Q₈	C₂×D₇₉	semidirect
425. C₂×C₈	Q₈×D₇₉	semidirect

Maximal subgroups

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

subgroup	index
#23777201	2
#23776360	2
#23776301	2
#23776268	2
Q₈×D₆₃₂	2
#23773939	2
#23773914	2
#23773232	2
#23773199	2
#23772253	2
C₂×C₄×D₆₃₂	2
C₇₉×#2960	2
#61370	79