Subgroups — #34272208

Order 20224.

608 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23773556	C₂	1	2	yes	maximal
2	C₈×#11929624	C₂	1	1	yes	maximal, characteristic
3	#23762801	C₂	1	1	yes	maximal, characteristic, complemented
4	#23762796	C₂	1	1	yes	maximal, characteristic, complemented
5	#23762791	C₂	1	1	yes	maximal, characteristic, complemented
6	#23762786	C₂	1	1	yes	maximal, characteristic, complemented
7	#23762779	C₂	1	2	yes	maximal, complemented
8	#23762772	C₂	1	2	yes	maximal, complemented
9	#23762163	C₂	1	1	yes	maximal, characteristic, complemented
10	#23762110	C₂	1	2	yes	maximal, complemented
11	C₇₉×#3160	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×#11929624	C₂²	1	1	yes	characteristic
13	#19098901	—	2	2	no	—
14	#19098855	C₂²	1	2	yes	—
15	#19098850	C₂²	1	2	yes	—
16	#19098770	C₂²	1	2	yes	—
17	#19098765	C₂²	1	2	yes	—
18	#19098723	—	2	2	no	—
19	C₈×Dic₁₅₈	C₂²	1	1	yes	characteristic
20	C₈×Dic₁₅₈	C₂²	1	1	yes	characteristic
21	#19098668	—	2	2	no	—
22	#19098661	—	2	2	no	—
23	C₈×D₃₁₆	C₂²	1	1	yes	characteristic
24	C₈×D₃₁₆	C₂²	1	1	yes	characteristic
25	C₈×C₂²⋊D₇₉	—	2	1	no	—
26	C₈×C₂²⋊D₇₉	—	2	1	no	—
27	#19098620	C₂²	1	2	yes	—
28	#19098616	C₂²	1	1	yes	characteristic
29	#19098614	—	2	1	no	—
30	C₄×C₈×D₇₉	—	2	1	no	—
31	#19098316	C₂²	1	1	yes	characteristic
32	#19098316	C₂²	1	1	yes	characteristic
33	#19098314	C₂²	1	2	yes	—
34	#19098312	C₂²	1	2	yes	—
35	#19098312	C₂²	1	2	yes	—
36	#19098309	C₂²	1	2	yes	—
37	#19098309	C₂²	1	2	yes	—
38	#533×C₇₉	C₂²	1	2	yes	—
39	#500×C₇₉	C₂²	1	1	yes	characteristic
40	#500×C₇₉	C₂²	1	1	yes	characteristic
41	#499×C₇₉	—	2	1	no	—
42	#499×C₇₉	—	2	1	no	—
43	#498×C₇₉	C₂²	1	2	yes	—
44	#427×C₇₉	—	2	1	no	—
45	#427×C₇₉	—	2	1	no	—
46	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
47	C₂×#11929624	D₄	1	1	yes	characteristic
48	C₂×#11929614	—	2	2	no	—
49	C₂×#11929611	—	2	2	no	—
50	C₂×C₈×D₇₉	—	2	1	no	—
51	C₂×C₈×D₇₉	—	2	1	no	—
52	C₄×Dic₁₅₈	D₄	1	1	yes	characteristic
53	C₄×Dic₁₅₈	C₂³	1	1	yes	characteristic
54	C₄×D₃₁₆	D₄	1	1	yes	characteristic
55	C₄×D₃₁₆	C₂³	1	1	yes	characteristic
56	C₄×C₂²⋊D₇₉	—	2	1	no	—
57	C₄×C₂²⋊D₇₉	—	2	1	no	—
58	#14579120	D₄	1	1	yes	characteristic
59	#14579118	—	2	1	no	—
60	C₄²×D₇₉	—	2	1	no	—
61	#14579094	—	2	2	no	—
62	#14579092	—	2	2	no	—
63	C₄⋊(C₇₉⋊C₈)	C₂³	1	1	yes	characteristic
64	C₄⋊(C₇₉⋊C₈)	C₂³	1	1	yes	characteristic
65	C₄⋊(C₇₉⋊C₈)	C₂³	1	2	yes	—
66	C₄⋊(C₇₉⋊C₈)	C₂³	1	2	yes	—
67	Dic₇₉⋊C₈	—	2	1	no	—
68	Dic₇₉⋊C₈	—	2	1	no	—
69	#14579085	—	2	2	no	—
70	#14579085	—	2	2	no	—
71	#14579084	—	2	2	no	—
72	#14579081	—	2	2	no	—
73	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
74	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
75	(C₂×D₇₉)⋊C₈	—	2	1	no	—
76	(C₂×D₇₉)⋊C₈	—	2	1	no	—
77	#14579072	—	2	2	no	—
78	C₄×C₇₉⋊C₈	—	2	1	no	—
79	C₈×Dic₇₉	—	2	1	no	—
80	C₈×Dic₇₉	—	2	1	no	—
81	C₂²×C₈×C₇₉	D₄	1	1	yes	characteristic
82	C₂²×C₈×C₇₉	D₄	1	1	yes	characteristic
83	C₄⋊Q₈×C₇₉	C₂³	1	2	yes	—
84	C₄⋊Q₈×C₇₉	C₂³	1	2	yes	—
85	#125×C₇₉	—	2	2	no	—
86	C₂²⋊Q₈×C₇₉	—	2	2	no	—
87	C₂²⋊Q₈×C₇₉	—	2	2	no	—
88	C₄×Q₈×C₇₉	—	2	2	no	—
89	C₄×Q₈×C₇₉	—	2	2	no	—
90	#117×C₇₉	—	2	2	no	—
91	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
92	#107×C₇₉	—	2	1	no	—
93	#107×C₇₉	—	2	1	no	—
94	#107×C₇₉	—	2	1	no	—
95	#107×C₇₉	—	2	1	no	—
96	#106×C₇₉	—	2	2	no	—
97	#106×C₇₉	—	2	2	no	—
98	C₄×C₈×C₇₉	D₄	1	1	yes	characteristic
99	C₄×C₈×C₇₉	D₄	1	1	yes	characteristic
100	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
101	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
102	#11929624	—	2	2	no	—
103	#11929624	—	2	2	no	—
104	C₂×Dic₁₅₈	C₂×D₄	1	1	yes	characteristic
105	C₂×D₃₁₆	C₂×D₄	1	1	yes	characteristic
106	C₂×C₂²⋊D₇₉	—	2	1	no	—
107	C₂×C₄×D₇₉	—	2	1	no	—
108	C₂×C₄×D₇₉	—	2	1	no	—
109	C₂×C₄×D₇₉	—	2	1	no	—
110	#11929614	—	4	4	no	—
111	#11929611	—	4	4	no	—
112	C₂×C₇₉⋊C₈	—	2	1	no	—
113	C₂×C₇₉⋊C₈	—	2	1	no	—
114	C₂×C₇₉⋊C₈	—	2	2	no	—
115	C₂×C₇₉⋊C₈	—	2	2	no	—
116	C₈×D₇₉	—	4	2	no	—
117	C₈×D₇₉	—	4	2	no	—
118	C₄⋊Dic₇₉	C₂×D₄	1	1	yes	characteristic
119	C₄⋊Dic₇₉	C₂×D₄	1	1	yes	characteristic
120	Dic₇₉⋊C₄	—	2	1	no	—
121	Dic₇₉⋊C₄	—	2	1	no	—
122	C₂²⋊Dic₇₉	—	2	1	no	—
123	(C₂×D₇₉)⋊C₄	—	2	1	no	—
124	(C₂×D₇₉)⋊C₄	—	2	1	no	—
125	C₄×Dic₇₉	—	2	1	no	—
126	C₄×Dic₇₉	—	2	1	no	—
127	C₄×Dic₇₉	—	2	1	no	—
128	C₂×Q₈×C₇₉	—	2	2	no	—
129	C₂×Q₈×C₇₉	—	2	2	no	—
130	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
133	C₂×C₈×C₇₉	—	2	2	no	—
134	C₂×C₈×C₇₉	—	2	2	no	—
135	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
136	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
137	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
138	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
139	C₄⋊C₄×C₇₉	—	2	2	no	—
140	C₄⋊C₄×C₇₉	—	2	2	no	—
141	C₄⋊C₄×C₇₉	—	2	2	no	—
142	C₄⋊C₄×C₇₉	—	2	2	no	—
143	C₄⋊C₄×C₇₉	—	4	2	no	—
144	C₄⋊C₄×C₇₉	—	4	2	no	—
145	C₂²⋊C₄×C₇₉	—	4	2	no	—
146	C₄²×C₇₉	—	4	2	no	—
147	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
148	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
149	C₄²×C₇₉	#41	1	1	yes	characteristic
150	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
151	C₂³×C₇₉	#121	1	1	yes	characteristic
152	C₂²×D₇₉	—	2	1	no	—
153	Q₈×C₇₉	—	4	2	no	—
154	Q₈×C₇₉	—	4	2	no	—
155	Q₈×C₇₉	—	8	2	no	—
156	C₂×C₄×C₇₉	—	2	1	no	—
157	C₂×C₄×C₇₉	—	2	1	no	—
158	C₂×C₄×C₇₉	—	2	1	no	—
159	C₂×C₄×C₇₉	—	2	1	no	—
160	C₂×C₄×C₇₉	—	4	1	no	—
161	C₂×C₄×C₇₉	—	4	2	no	—
162	C₂×C₄×C₇₉	—	4	2	no	—
163	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
164	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
165	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
166	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
167	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
168	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
169	C₂²⋊D₇₉	—	2	4	no	—
170	C₂×Dic₇₉	—	2	1	no	—
171	C₂×Dic₇₉	—	2	1	no	—
172	C₂×Dic₇₉	—	2	1	no	—
173	D₃₁₆	—	2	1	no	—
174	D₃₁₆	#135	1	2	yes	—
175	C₄×D₇₉	—	2	4	no	—
176	C₄×D₇₉	—	4	2	no	—
177	C₄×D₇₉	—	4	1	no	—
178	C₄×D₇₉	—	4	1	no	—
179	Dic₁₅₈	—	2	1	no	—
180	Dic₁₅₈	#135	1	2	yes	—
181	C₈×C₇₉	—	2	1	no	—
182	C₈×C₇₉	—	2	1	no	—
183	C₈×C₇₉	#137	1	2	yes	—
184	C₈×C₇₉	#137	1	2	yes	—
185	C₇₉⋊C₈	—	4	2	no	—
186	C₇₉⋊C₈	—	4	2	no	—
187	C₇₉⋊C₈	—	4	1	no	—
188	C₇₉⋊C₈	—	4	1	no	—
189	C₂²×C₇₉	—	2	1	no	—
190	C₂²×C₇₉	—	2	1	no	—
191	C₂²×C₇₉	—	2	1	no	—
192	C₂²×C₇₉	C₂×#121	1	1	yes	characteristic
193	C₂×D₇₉	—	2	2	no	—
194	C₂×D₇₉	—	4	1	no	—
195	C₂×D₇₉	—	4	1	no	—
196	C₄×C₇₉	—	2	1	no	—
197	C₄×C₇₉	—	2	1	no	—
198	C₄×C₇₉	—	2	1	no	—
199	C₄×C₇₉	—	2	1	no	—
200	C₄×C₇₉	—	8	2	no	—
201	C₄×C₇₉	—	8	2	no	—
202	C₄×C₇₉	C₂×#135	1	1	yes	characteristic
203	C₄×C₇₉	C₂×#135	1	1	yes	characteristic
204	C₄×C₇₉	C₂×#137	1	1	yes	characteristic
205	C₄×C₇₉	C₂×#137	1	1	yes	characteristic
206	Dic₇₉	—	2	2	no	—
207	Dic₇₉	—	4	1	no	—
208	Dic₇₉	—	4	1	no	—
209	#19273	—	79	1	no	maximal, Sylow
210	C₂×C₇₉	—	4	1	no	—
211	C₂×C₇₉	#3039	1	1	yes	characteristic
212	C₂×C₇₉	#3050	1	1	yes	characteristic
213	C₂×C₇₉	#3067	1	1	yes	characteristic
214	D₇₉	—	4	2	no	—
215	#3160	D₇₉	1	1	yes	characteristic, complemented
216	#3116	—	79	2	no	—
217	C₈×#41	—	79	1	no	—
218	#1676	—	79	1	no	—
219	#1675	—	79	1	no	—
220	#1674	—	79	1	no	—
221	#1673	—	79	1	no	—
222	#1672	—	79	2	no	—
223	#1671	—	79	2	no	—
224	#1568	—	79	1	no	—
225	#1554	—	79	2	no	—
226	C₇₉	#19273	1	1	yes	characteristic, complemented, Sylow
227	#533	C₂×D₇₉	1	2	yes	—
228	C₄×#41	—	79	1	no	—
229	#500	C₂×D₇₉	1	1	yes	characteristic
230	#500	C₂×D₇₉	1	1	yes	characteristic
231	#499	—	2	1	no	—
232	#499	—	2	1	no	—
233	#498	C₂×D₇₉	1	2	yes	—
234	#485	—	158	2	no	—
235	#477	—	79	2	no	—
236	#476	—	79	2	no	—
237	#462	—	79	2	no	—
238	#461	—	79	2	no	—
239	#452	—	158	2	no	—
240	C₈×Q₈	—	79	1	no	—
241	C₈×Q₈	—	79	1	no	—
242	#441	—	158	2	no	—
243	#440	—	158	2	no	—
244	C₈×D₄	—	79	1	no	—
245	C₈×D₄	—	79	1	no	—
246	C₈×D₄	—	158	1	no	—
247	C₈×D₄	—	158	1	no	—
248	#432	—	79	2	no	—
249	#431	—	79	1	no	—
250	#431	—	158	1	no	—
251	#427	—	2	1	no	—
252	#427	—	2	1	no	—
253	C₂×C₄×C₈	—	158	1	no	—
254	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
255	#335	—	79	1	no	—
256	#335	—	79	1	no	—
257	#334	—	79	2	no	—
258	#333	—	79	2	no	—
259	#333	—	79	2	no	—
260	#332	—	79	2	no	—
261	#332	—	79	2	no	—
262	C₂×#41	—	79	1	no	—
263	C₂×Q₁₆	—	158	2	no	—
264	C₂×SD₁₆	—	158	2	no	—
265	C₂²×C₈	—	158	1	no	—
266	C₂²×C₈	—	158	1	no	—
267	C₂²×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
268	C₂²×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
269	C₄⋊Q₈	C₂²×D₇₉	1	2	yes	—
270	C₄⋊Q₈	C₂²×D₇₉	1	2	yes	—
271	#125	—	2	2	no	—
272	C₂²⋊Q₈	—	2	2	no	—
273	C₂²⋊Q₈	—	2	2	no	—
274	C₄×Q₈	—	2	2	no	—
275	C₄×Q₈	—	2	2	no	—
276	C₄×Q₈	—	79	1	no	—
277	C₄×Q₈	—	79	1	no	—
278	C₄×D₄	—	79	1	no	—
279	C₄×D₄	—	79	1	no	—
280	C₄×D₄	—	158	1	no	—
281	C₄×D₄	—	158	1	no	—
282	#117	—	2	2	no	—
283	#117	—	79	1	no	—
284	#117	—	158	1	no	—
285	C₂×C₄²	—	158	1	no	—
286	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
287	#107	—	2	1	no	—
288	#107	—	2	1	no	—
289	#107	—	2	1	no	—
290	#107	—	2	1	no	—
291	#107	—	158	2	no	—
292	#106	—	2	2	no	—
293	#106	—	2	2	no	—
294	#106	—	158	2	no	—
295	C₄⋊C₈	—	79	1	no	—
296	C₄⋊C₈	—	79	1	no	—
297	C₄⋊C₈	—	79	2	no	—
298	C₄⋊C₈	—	79	2	no	—
299	C₄⋊C₈	—	158	1	no	—
300	C₄⋊C₈	—	158	1	no	—
301	#103	—	158	2	no	—
302	#103	—	158	2	no	—
303	#103	—	158	2	no	—
304	#102	—	158	2	no	—
305	C₂²⋊C₈	—	158	2	no	—
306	C₂²⋊C₈	—	158	1	no	—
307	C₂²⋊C₈	—	158	1	no	—
308	C₂²⋊C₈	—	158	1	no	—
309	#97	—	158	2	no	—
310	C₄×C₈	—	158	1	no	—
311	C₄×C₈	—	158	1	no	—
312	C₄×C₈	—	158	1	no	—
313	C₄×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
314	C₄×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
315	C₄×C₈	C₂²×D₇₉	1	1	yes	characteristic
316	C₄×C₈	C₂²×D₇₉	1	1	yes	characteristic
317	#41	—	158	2	no	—
318	#41	—	158	2	no	—
319	C₂×Q₈	—	2	2	no	—
320	C₂×Q₈	—	2	2	no	—
321	C₂×Q₈	—	79	1	no	—
322	C₂×D₄	—	79	1	no	—
323	C₂×D₄	—	158	1	no	—
324	C₂²×C₄	—	158	1	no	—
325	C₂²×C₄	—	158	1	no	—
326	C₂²×C₄	—	158	1	no	—
327	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
328	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
329	C₂²×C₄	#11929623	1	1	yes	characteristic
330	Q₁₆	—	316	4	no	—
331	SD₁₆	—	316	4	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	316	2	no	—
335	C₂×C₈	—	316	2	no	—
336	C₂×C₈	—	158	2	no	—
337	C₂×C₈	—	158	2	no	—
338	C₂×C₈	—	158	1	no	—
339	C₂×C₈	—	158	1	no	—
340	C₂×C₈	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
341	C₂×C₈	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
342	C₂×C₈	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
343	C₂×C₈	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
344	C₄⋊C₄	—	2	2	no	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	4	2	no	—
349	C₄⋊C₄	—	4	2	no	—
350	C₄⋊C₄	—	79	1	no	—
351	C₄⋊C₄	—	79	1	no	—
352	C₄⋊C₄	—	158	1	no	—
353	C₄⋊C₄	—	158	1	no	—
354	C₂²⋊C₄	—	4	2	no	—
355	C₂²⋊C₄	—	158	1	no	—
356	C₂²⋊C₄	—	158	1	no	—
357	C₂²⋊C₄	—	158	1	no	—
358	C₄²	—	4	2	no	—
359	C₄²	—	158	1	no	—
360	C₄²	—	158	1	no	—
361	C₄²	—	158	1	no	—
362	C₄²	D₄×D₇₉	1	1	yes	characteristic
363	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
364	C₄²	#11929623	1	1	yes	characteristic
365	C₄²	C₂³×D₇₉	1	1	yes	characteristic
366	C₂³	—	158	1	no	—
367	C₂³	#14579132	1	1	yes	characteristic
368	Q₈	—	4	2	no	—
369	Q₈	—	4	2	no	—
370	Q₈	—	8	2	no	—
371	Q₈	—	79	2	no	—
372	Q₈	—	158	1	no	—
373	D₄	—	79	2	no	—
374	D₄	—	158	4	no	—
375	D₄	—	158	1	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	316	2	no	—
384	C₂×C₄	—	316	1	no	—
385	C₂×C₄	—	316	1	no	—
386	C₂×C₄	—	158	4	no	—
387	C₂×C₄	—	158	1	no	—
388	C₂×C₄	—	158	1	no	—
389	C₂×C₄	—	158	1	no	—
390	C₂×C₄	#14579132	1	1	yes	characteristic
391	C₂×C₄	#14579132	1	1	yes	characteristic
392	C₂×C₄	#14579132	1	1	yes	characteristic
393	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
394	C₂×C₄	C₂²×C₂²⋊D₇₉	1	1	yes	characteristic
395	C₂×C₄	C₂×#11929623	1	1	yes	characteristic
396	C₈	—	2	1	no	—
397	C₈	—	2	1	no	—
398	C₈	—	316	2	no	—
399	C₈	—	316	2	no	—
400	C₈	—	316	1	no	—
401	C₈	—	316	1	no	—
402	C₈	#14579192	1	2	yes	—
403	C₈	#14579192	1	2	yes	—
404	C₂²	—	2	1	no	—
405	C₂²	—	2	1	no	—
406	C₂²	—	2	1	no	—
407	C₂²	—	316	1	no	—
408	C₂²	—	316	1	no	—
409	C₂²	—	158	2	no	—
410	C₂²	C₂×#14579132	1	1	yes	characteristic
411	C₄	—	2	1	no	—
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	2	1	no	—
415	C₄	—	8	2	no	—
416	C₄	—	8	2	no	—
417	C₄	—	316	1	no	—
418	C₄	—	316	1	no	—
419	C₄	—	158	2	no	—
420	C₄	#135×D₇₉	1	1	yes	characteristic
421	C₄	#135×D₇₉	1	1	yes	characteristic
422	C₄	C₂×#14579192	1	1	yes	characteristic
423	C₄	C₂×#14579192	1	1	yes	characteristic
424	C₂	—	4	1	no	—
425	C₂	—	316	2	no	—
426	C₂	#23772883	1	1	yes	characteristic
427	C₂	#23772977	1	1	yes	characteristic
428	C₂	#23773116	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#14579132
commutator, cosocle	C₄²×C₇₉	C₂⁴
Frattini	C₄²	C₂³×D₇₉
Fitting	C₇₉×#3160	C₂
socle	C₂²×C₇₉	C₂×#121
prime radical	C₂×#11929624	D₄
hypercenter	#3160	D₇₉
hypocenter	C₇₉	#19273
LCS	G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3160

Complements

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

N	H ≅ G/N	type
3. #23762801	C₂	semidirect
4. #23762796	C₂	semidirect
5. #23762791	C₂	semidirect
6. #23762786	C₂	semidirect
7. #23762779	C₂	semidirect
8. #23762772	C₂	semidirect
9. #23762163	C₂	semidirect
10. #23762110	C₂	semidirect
11. C₇₉×#3160	C₂	semidirect
215. #3160	D₇₉	semidirect
226. C₇₉	#19273	semidirect

Maximal subgroups

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

subgroup	index
#23773556	2
C₈×#11929624	2
#23762801	2
#23762796	2
#23762791	2
#23762786	2
#23762779	2
#23762772	2
#23762163	2
#23762110	2
C₇₉×#3160	2
#19273	79