Subgroups — #34184512

Order 20224.

570 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19098764	C₂	1	1	yes	maximal, characteristic
2	C₂×#19098693	C₂	1	1	yes	maximal, characteristic, complemented
3	#23764206	C₂	1	1	yes	maximal, characteristic
4	#23763406	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#19098306	C₂	1	1	yes	maximal, characteristic
6	#23761284	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₉×#1277	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#11929613	—	2	1	no	—
9	C₂×#14579158	C₂²	1	1	yes	characteristic
10	C₂×C₄×Dic₁₅₈	C₂²	1	1	yes	characteristic
11	#19098764	—	2	2	no	—
12	#19098764	C₄	1	4	yes	complemented
13	#19098693	—	2	2	no	—
14	#19098693	—	2	2	no	—
15	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
16	C₂×Dic₇₉⋊C₈	—	2	1	no	—
17	C₂×#14579086	—	2	1	no	—
18	C₂×#14579083	—	2	1	no	—
19	C₂×#14579083	—	2	1	no	—
20	C₂×#14579083	—	2	1	no	—
21	C₂×#14579071	—	2	1	no	—
22	#19098433	C₂²	1	1	yes	characteristic
23	#19098326	—	2	1	no	—
24	#19098306	—	2	2	no	—
25	C₂×C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
28	C₂²×Dic₁₅₈	D₄	1	1	yes	characteristic
29	C₂²×D₃₁₆	—	2	1	no	—
30	C₂²×D₃₁₆	—	2	1	no	—
31	C₂²×D₃₁₆	—	2	1	no	—
32	C₂×#11929613	—	2	4	no	—
33	C₂×#11929613	—	4	2	no	—
34	C₂×#11929613	—	4	2	no	—
35	C₂²×C₇₉⋊C₈	—	2	1	no	—
36	#14579158	—	2	1	no	—
37	#14579158	—	2	1	no	—
38	#14579158	—	2	1	no	—
39	#14579158	C₂×C₄	1	2	yes	—
40	C₄×Dic₁₅₈	—	2	1	no	—
41	C₄×Dic₁₅₈	—	2	1	no	—
42	C₄×Dic₁₅₈	C₂×C₄	1	2	yes	—
43	C₄×Dic₁₅₈	D₄	1	2	yes	—
44	C₂×C₄⋊Dic₇₉	—	2	1	no	—
45	C₂×C₄⋊Dic₇₉	—	2	1	no	—
46	C₂×C₄⋊Dic₇₉	—	2	1	no	—
47	C₂×C₄⋊Dic₇₉	D₄	1	1	yes	characteristic
48	C₂×Dic₇₉⋊C₄	—	2	1	no	—
49	C₂×C₄×Dic₇₉	—	2	1	no	—
50	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
51	C₄⋊(C₇₉⋊C₈)	D₄	1	2	yes	—
52	Dic₇₉⋊C₈	—	2	4	no	—
53	#14579086	—	4	2	no	—
54	#14579083	—	2	4	no	—
55	#14579083	—	4	2	no	—
56	#14579083	—	4	2	no	—
57	#14579071	—	2	4	no	—
58	C₂²×C₈×C₇₉	—	2	1	no	—
59	C₂²×C₈×C₇₉	—	2	1	no	—
60	C₂²×C₈×C₇₉	D₄	1	1	yes	characteristic
61	C₂²×C₈×C₇₉	D₄	1	1	yes	characteristic
62	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
63	C₄⋊C₈×C₇₉	—	2	1	no	—
64	C₄⋊C₈×C₇₉	—	2	1	no	—
65	C₄⋊C₈×C₇₉	—	2	1	no	—
66	C₄⋊C₈×C₇₉	C₂×C₄	1	2	yes	—
67	C₄×C₈×C₇₉	—	2	1	no	—
68	C₄×C₈×C₇₉	—	2	1	no	—
69	C₂³×D₇₉	—	4	1	no	—
70	C₂×Dic₁₅₈	—	2	1	no	—
71	C₂×Dic₁₅₈	—	2	1	no	—
72	C₂×Dic₁₅₈	—	2	1	no	—
73	C₂×Dic₁₅₈	—	2	1	no	—
74	C₂×Dic₁₅₈	—	2	1	no	—
75	C₂×Dic₁₅₈	C₂²⋊C₄	1	2	yes	—
76	C₂×D₃₁₆	—	2	2	no	—
77	C₂×D₃₁₆	—	2	2	no	—
78	C₂×D₃₁₆	—	2	2	no	—
79	C₂×D₃₁₆	—	4	1	no	—
80	C₂×D₃₁₆	—	4	1	no	—
81	C₂×D₃₁₆	—	4	1	no	—
82	C₂×D₃₁₆	—	4	1	no	—
83	C₂×D₃₁₆	—	4	1	no	—
84	C₂×D₃₁₆	—	4	1	no	—
85	C₂×D₃₁₆	—	4	1	no	—
86	C₂×D₃₁₆	—	4	1	no	—
87	C₂×D₃₁₆	—	4	1	no	—
88	C₂×D₃₁₆	—	4	1	no	—
89	C₂×D₃₁₆	—	4	1	no	—
90	C₂×D₃₁₆	—	8	1	no	—
91	C₂×D₃₁₆	—	8	1	no	—
92	C₂²×Dic₇₉	—	2	1	no	—
93	C₂²×Dic₇₉	—	2	1	no	—
94	C₂²×Dic₇₉	—	4	1	no	—
95	#11929613	—	4	8	no	—
96	C₂×C₇₉⋊C₈	—	2	2	no	—
97	C₂×C₇₉⋊C₈	—	4	1	no	—
98	C₂×C₇₉⋊C₈	—	4	1	no	—
99	C₄⋊Dic₇₉	—	2	1	no	—
100	C₄⋊Dic₇₉	—	4	1	no	—
101	C₄⋊Dic₇₉	—	4	1	no	—
102	C₄⋊Dic₇₉	—	4	1	no	—
103	C₄⋊Dic₇₉	—	4	1	no	—
104	C₄⋊Dic₇₉	—	8	1	no	—
105	C₄⋊Dic₇₉	C₂²⋊C₄	1	2	yes	—
106	Dic₇₉⋊C₄	—	2	2	no	—
107	Dic₇₉⋊C₄	—	2	2	no	—
108	C₄×Dic₇₉	—	2	2	no	—
109	C₄×Dic₇₉	—	2	2	no	—
110	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
113	C₂×C₈×C₇₉	—	2	2	no	—
114	C₂×C₈×C₇₉	—	2	1	no	—
115	C₂×C₈×C₇₉	—	2	1	no	—
116	C₂×C₈×C₇₉	—	2	1	no	—
117	C₂×C₈×C₇₉	—	2	1	no	—
118	C₂×C₈×C₇₉	—	2	1	no	—
119	C₂×C₈×C₇₉	—	4	1	no	—
120	C₂×C₈×C₇₉	—	4	1	no	—
121	C₂×C₈×C₇₉	—	4	1	no	—
122	C₂×C₈×C₇₉	—	4	1	no	—
123	C₂×C₈×C₇₉	—	4	1	no	—
124	C₂×C₈×C₇₉	SD₁₆	1	2	yes	complemented
125	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
126	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
127	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
128	C₄²×C₇₉	#41	1	1	yes	characteristic
129	C₂³×C₇₉	#121	1	1	yes	characteristic
130	C₂²×D₇₉	—	4	2	no	—
131	C₂²×D₇₉	—	8	1	no	—
132	C₂²×D₇₉	—	8	1	no	—
133	C₂²×D₇₉	—	8	1	no	—
134	C₂²×D₇₉	—	8	1	no	—
135	C₂²×D₇₉	—	8	1	no	—
136	C₂²×D₇₉	—	8	1	no	—
137	C₂×C₄×C₇₉	—	2	1	no	—
138	C₂×C₄×C₇₉	—	2	1	no	—
139	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
140	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
141	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
142	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
143	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
144	C₂×C₄×C₇₉	#123	1	1	yes	characteristic
145	C₂×C₄×C₇₉	C₂×SD₁₆	1	1	yes	characteristic
146	C₂×C₄×C₇₉	#135	1	1	yes	characteristic
147	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
148	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
149	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
150	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
151	C₂×C₄×C₇₉	#137	1	1	yes	characteristic
152	C₂×C₄×C₇₉	#137	1	1	yes	characteristic
153	C₂×Dic₇₉	—	2	2	no	—
154	C₂×Dic₇₉	—	2	2	no	—
155	C₂×Dic₇₉	—	4	1	no	—
156	C₂×Dic₇₉	—	4	1	no	—
157	C₂×Dic₇₉	—	4	1	no	—
158	C₂×Dic₇₉	—	4	1	no	—
159	C₂×Dic₇₉	—	8	1	no	—
160	C₂×Dic₇₉	—	8	1	no	—
161	C₂×Dic₇₉	—	8	1	no	—
162	D₃₁₆	—	4	2	no	—
163	D₃₁₆	—	4	2	no	—
164	D₃₁₆	—	4	2	no	—
165	D₃₁₆	—	4	2	no	—
166	D₃₁₆	—	8	2	no	—
167	D₃₁₆	—	8	2	no	—
168	D₃₁₆	—	8	1	no	—
169	D₃₁₆	—	8	1	no	—
170	D₃₁₆	—	8	1	no	—
171	D₃₁₆	—	8	1	no	—
172	Dic₁₅₈	—	2	2	no	—
173	Dic₁₅₈	—	2	2	no	—
174	Dic₁₅₈	—	4	1	no	—
175	Dic₁₅₈	—	4	1	no	—
176	C₈×C₇₉	—	2	2	no	—
177	C₈×C₇₉	—	4	2	no	—
178	C₈×C₇₉	—	4	1	no	—
179	C₈×C₇₉	—	8	1	no	—
180	C₇₉⋊C₈	—	4	2	no	—
181	C₂²×C₇₉	#386	1	1	yes	characteristic
182	C₂²×C₇₉	#460	1	1	yes	characteristic
183	C₂²×C₇₉	#464	1	1	yes	characteristic
184	C₂²×C₇₉	#468	1	1	yes	characteristic
185	C₂²×C₇₉	#469	1	1	yes	characteristic
186	C₂²×C₇₉	#471	1	1	yes	characteristic
187	C₂²×C₇₉	#472	1	1	yes	characteristic
188	C₂×D₇₉	—	8	2	no	—
189	C₂×D₇₉	—	8	2	no	—
190	C₂×D₇₉	—	8	2	no	—
191	C₂×D₇₉	—	16	1	no	—
192	C₂×D₇₉	—	16	1	no	—
193	C₂×D₇₉	—	16	1	no	—
194	C₂×D₇₉	—	16	1	no	—
195	C₄×C₇₉	—	2	1	no	—
196	C₄×C₇₉	—	2	1	no	—
197	C₄×C₇₉	#417	1	1	yes	characteristic
198	C₄×C₇₉	#418	1	1	yes	characteristic
199	C₄×C₇₉	C₄×SD₁₆	1	1	yes	characteristic
200	C₄×C₇₉	#440	1	1	yes	characteristic
201	C₄×C₇₉	#448	1	1	yes	characteristic
202	C₄×C₇₉	#449	1	1	yes	characteristic
203	C₄×C₇₉	#468	1	1	yes	characteristic
204	C₄×C₇₉	#469	1	1	yes	characteristic
205	Dic₇₉	—	4	2	no	—
206	Dic₇₉	—	4	2	no	—
207	Dic₇₉	—	16	1	no	—
208	#9230	—	79	1	no	maximal, Sylow
209	C₂×C₇₉	#1686	1	1	yes	characteristic
210	C₂×C₇₉	#1688	1	1	yes	characteristic
211	C₂×C₇₉	#1698	1	1	yes	characteristic
212	C₂×C₇₉	#1702	1	1	yes	characteristic
213	C₂×C₇₉	#1880	1	1	yes	characteristic
214	C₂×C₇₉	#1895	1	1	yes	characteristic
215	C₂×C₇₉	#1907	1	1	yes	characteristic
216	D₇₉	—	16	2	no	—
217	C₂×#460	—	79	1	no	—
218	C₂×#446	—	79	1	no	—
219	#1957	—	79	1	no	—
220	#1803	—	79	1	no	—
221	C₂×#331	—	79	1	no	—
222	#1296	—	79	1	no	—
223	#1277	D₇₉	1	1	yes	characteristic, complemented
224	C₇₉	#9230	1	1	yes	characteristic, complemented, Sylow
225	C₂²×SD₁₆	—	158	1	no	—
226	C₂×#127	—	79	1	no	—
227	C₂×C₄×Q₈	—	79	1	no	—
228	#460	—	79	4	no	—
229	#460	—	158	2	no	—
230	#446	—	158	2	no	—
231	#446	—	158	2	no	—
232	C₂×C₄⋊C₈	—	79	1	no	—
233	C₂×C₄⋊C₈	—	158	1	no	—
234	C₂×C₄⋊C₈	C₂×D₇₉	1	1	yes	characteristic
235	C₂×C₄⋊C₈	C₂×D₇₉	1	1	yes	characteristic
236	C₂×#103	—	158	1	no	—
237	C₂×#102	—	158	1	no	—
238	C₂×#102	—	158	1	no	—
239	C₂×#102	—	158	1	no	—
240	C₂×#97	—	158	1	no	—
241	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
242	#384	—	79	1	no	—
243	#340	—	158	1	no	—
244	#331	—	158	2	no	—
245	C₂²×Q₈	—	79	1	no	—
246	C₂²×D₄	—	158	1	no	—
247	C₂²×D₄	—	158	1	no	—
248	C₂²×D₄	—	158	1	no	—
249	C₂×SD₁₆	—	316	2	no	—
250	C₂×SD₁₆	—	316	2	no	—
251	C₂×SD₁₆	—	158	4	no	—
252	C₂²×C₈	—	2	1	no	—
253	C₂²×C₈	—	2	1	no	—
254	C₂²×C₈	—	158	1	no	—
255	C₂²×C₈	D₃₁₆	1	1	yes	characteristic
256	C₂²×C₈	D₃₁₆	1	1	yes	characteristic
257	#127	—	79	2	no	—
258	#127	—	158	1	no	—
259	#127	—	158	1	no	—
260	#127	—	158	1	no	—
261	C₄×Q₈	—	79	2	no	—
262	C₄×Q₈	—	79	2	no	—
263	C₄×Q₈	—	158	1	no	—
264	C₄×Q₈	—	158	1	no	—
265	C₂×C₄⋊C₄	—	79	1	no	—
266	C₂×C₄⋊C₄	—	158	1	no	—
267	C₂×C₄⋊C₄	—	158	1	no	—
268	C₂×C₄⋊C₄	—	158	1	no	—
269	C₂×C₄⋊C₄	—	158	1	no	—
270	C₂×C₄²	—	158	1	no	—
271	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
272	C₄⋊C₈	—	2	1	no	—
273	C₄⋊C₈	—	2	1	no	—
274	C₄⋊C₈	—	2	1	no	—
275	C₄⋊C₈	—	79	2	no	—
276	C₄⋊C₈	—	158	4	no	—
277	C₄⋊C₈	—	158	1	no	—
278	C₄⋊C₈	C₄×D₇₉	1	2	yes	—
279	#103	—	316	2	no	—
280	#102	—	316	2	no	—
281	#102	—	316	2	no	—
282	#102	—	158	4	no	—
283	#97	—	158	4	no	—
284	C₄×C₈	—	2	1	no	—
285	C₄×C₈	—	2	1	no	—
286	C₂⁴	—	316	1	no	—
287	C₂×Q₈	—	79	2	no	—
288	C₂×Q₈	—	158	1	no	—
289	C₂×Q₈	—	158	1	no	—
290	C₂×Q₈	—	158	1	no	—
291	C₂×Q₈	—	158	1	no	—
292	C₂×Q₈	—	158	1	no	—
293	C₂×D₄	—	316	1	no	—
294	C₂×D₄	—	316	1	no	—
295	C₂×D₄	—	316	1	no	—
296	C₂×D₄	—	316	1	no	—
297	C₂×D₄	—	316	1	no	—
298	C₂×D₄	—	316	1	no	—
299	C₂×D₄	—	316	1	no	—
300	C₂×D₄	—	316	1	no	—
301	C₂×D₄	—	316	1	no	—
302	C₂×D₄	—	316	1	no	—
303	C₂×D₄	—	316	1	no	—
304	C₂×D₄	—	632	1	no	—
305	C₂×D₄	—	632	1	no	—
306	C₂×D₄	—	158	2	no	—
307	C₂×D₄	—	158	2	no	—
308	C₂×D₄	—	158	2	no	—
309	C₂²×C₄	—	316	1	no	—
310	C₂²×C₄	—	158	1	no	—
311	C₂²×C₄	—	158	1	no	—
312	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
313	C₂²×C₄	C₂×D₃₁₆	1	1	yes	characteristic
314	C₂²×C₄	#11929625	1	1	yes	characteristic
315	SD₁₆	—	316	8	no	—
316	C₂×C₈	—	2	1	no	—
317	C₂×C₈	—	2	1	no	—
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	—	2	1	no	—
320	C₂×C₈	—	2	1	no	—
321	C₂×C₈	—	2	1	no	—
322	C₂×C₈	—	4	1	no	—
323	C₂×C₈	—	4	1	no	—
324	C₂×C₈	—	4	1	no	—
325	C₂×C₈	—	4	1	no	—
326	C₂×C₈	—	4	1	no	—
327	C₂×C₈	—	316	1	no	—
328	C₂×C₈	—	316	1	no	—
329	C₂×C₈	—	158	2	no	—
330	C₂×C₈	#11929613	1	2	yes	complemented
331	C₄⋊C₄	—	316	1	no	—
332	C₄⋊C₄	—	316	1	no	—
333	C₄⋊C₄	—	316	1	no	—
334	C₄⋊C₄	—	316	1	no	—
335	C₄⋊C₄	—	79	2	no	—
336	C₄⋊C₄	—	632	1	no	—
337	C₄⋊C₄	—	158	2	no	—
338	C₄⋊C₄	—	158	1	no	—
339	C₄⋊C₄	—	158	2	no	—
340	C₄²	—	158	2	no	—
341	C₄²	—	158	2	no	—
342	C₄²	C₂×C₄×D₇₉	1	1	yes	characteristic
343	C₄²	D₄×D₇₉	1	1	yes	characteristic
344	C₄²	D₄×D₇₉	1	1	yes	characteristic
345	C₄²	#11929624	1	1	yes	characteristic
346	C₂³	—	316	2	no	—
347	C₂³	—	632	1	no	—
348	C₂³	—	632	1	no	—
349	C₂³	—	632	1	no	—
350	C₂³	—	632	1	no	—
351	C₂³	—	632	1	no	—
352	C₂³	—	632	1	no	—
353	C₂³	#14579136	1	1	yes	characteristic
354	Q₈	—	316	1	no	—
355	Q₈	—	316	1	no	—
356	Q₈	—	158	2	no	—
357	Q₈	—	158	2	no	—
358	D₄	—	316	2	no	—
359	D₄	—	316	2	no	—
360	D₄	—	316	2	no	—
361	D₄	—	316	2	no	—
362	D₄	—	632	2	no	—
363	D₄	—	632	2	no	—
364	D₄	—	632	1	no	—
365	D₄	—	632	1	no	—
366	D₄	—	632	1	no	—
367	D₄	—	632	1	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	316	1	no	—
371	C₂×C₄	—	316	1	no	—
372	C₂×C₄	—	316	1	no	—
373	C₂×C₄	—	316	1	no	—
374	C₂×C₄	—	632	1	no	—
375	C₂×C₄	—	632	1	no	—
376	C₂×C₄	—	632	1	no	—
377	C₂×C₄	—	158	2	no	—
378	C₂×C₄	—	158	2	no	—
379	C₂×C₄	C₂²⋊C₄×D₇₉	1	1	yes	characteristic
380	C₂×C₄	#14579123	1	1	yes	characteristic
381	C₂×C₄	C₄×D₃₁₆	1	1	yes	characteristic
382	C₂×C₄	#14579131	1	1	yes	characteristic
383	C₂×C₄	#14579134	1	1	yes	characteristic
384	C₂×C₄	#14579146	1	1	yes	characteristic
385	C₂×C₄	C₂×#11929613	1	1	yes	characteristic
386	C₂×C₄	#14579183	1	1	yes	characteristic
387	C₂×C₄	#14579185	1	1	yes	characteristic
388	C₂×C₄	#14579188	1	1	yes	characteristic
389	C₂×C₄	#14579188	1	1	yes	characteristic
390	C₂×C₄	#14579189	1	1	yes	characteristic
391	C₂×C₄	#14579193	1	1	yes	characteristic
392	C₂×C₄	#14579194	1	1	yes	characteristic
393	C₈	—	2	2	no	—
394	C₈	—	4	1	no	—
395	C₈	—	4	2	no	—
396	C₈	—	8	1	no	—
397	C₈	—	316	2	no	—
398	C₂²	—	632	2	no	—
399	C₂²	—	632	2	no	—
400	C₂²	—	632	2	no	—
401	C₂²	—	1264	1	no	—
402	C₂²	—	1264	1	no	—
403	C₂²	—	1264	1	no	—
404	C₂²	—	1264	1	no	—
405	C₂²	#19098441	1	1	yes	characteristic
406	C₂²	#19098764	1	1	yes	characteristic
407	C₂²	#19098786	1	1	yes	characteristic
408	C₂²	#19098810	1	1	yes	characteristic
409	C₂²	#19098817	1	1	yes	characteristic
410	C₂²	#19098827	1	1	yes	characteristic
411	C₂²	#19098834	1	1	yes	characteristic
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	316	2	no	—
415	C₄	—	316	2	no	—
416	C₄	—	1264	1	no	—
417	C₄	#19098563	1	1	yes	characteristic
418	C₄	#19098566	1	1	yes	characteristic
419	C₄	C₄×#11929613	1	1	yes	characteristic
420	C₄	#19098665	1	1	yes	characteristic
421	C₄	#19098704	1	1	yes	characteristic
422	C₄	#19098710	1	1	yes	characteristic
423	C₄	#19098812	1	1	yes	characteristic
424	C₄	#19098815	1	1	yes	characteristic
425	C₂	—	1264	2	no	—
426	C₂	#23762873	1	1	yes	characteristic
427	C₂	#23762885	1	1	yes	characteristic
428	C₂	#23762941	1	1	yes	characteristic
429	C₂	#23762969	1	1	yes	characteristic
430	C₂	#23763754	1	1	yes	characteristic
431	C₂	#23763837	1	1	yes	characteristic
432	C₂	#23763907	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#14579136
commutator	C₄²×C₇₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₇₉
Fitting	C₇₉×#1277	C₂
socle	C₂³×C₇₉	#121
prime radical	C₂×#14579158	C₂²
cosocle	C₂×C₄²×C₇₉	C₂³
hypercenter	#1277	D₇₉
hypocenter	C₇₉	#9230
LCS	G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1277

Complements

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

N	H ≅ G/N	type
2. C₂×#19098693	C₂	semidirect
4. #23763406	C₂	semidirect
6. #23761284	C₂	semidirect
7. C₇₉×#1277	C₂	semidirect
12. #19098764	C₄	semidirect
124. C₂×C₈×C₇₉	SD₁₆	semidirect
223. #1277	D₇₉	semidirect
224. C₇₉	#9230	semidirect
330. C₂×C₈	#11929613	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19098764	2
C₂×#19098693	2
#23764206	2
#23763406	2
C₂×#19098306	2
#23761284	2
C₇₉×#1277	2
#9230	79