Subgroups — #34302183

Order 20224.

772 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23773889	C₂	1	1	yes	maximal, characteristic
2	#23772318	C₂	1	1	yes	maximal, characteristic
3	#23764316	C₂	1	1	yes	maximal, characteristic, complemented
4	#23764296	C₂	1	1	yes	maximal, characteristic
5	#23763937	C₂	1	2	yes	maximal, complemented
6	#23763919	C₂	1	2	yes	maximal, complemented
7	#23763894	C₂	1	2	yes	maximal, complemented
8	#23763870	C₂	1	2	yes	maximal, complemented
9	#23763523	C₂	1	1	yes	maximal, characteristic, complemented
10	#23763155	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₉×#2950	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14579192	C₂²	1	2	yes	—
13	C₂×#14579183	C₂²	1	1	yes	characteristic
14	#19099329	C₂²	1	2	yes	—
15	#19099137	C₂²	1	2	yes	—
16	#19098956	C₄	1	4	yes	complemented
17	#19098948	C₄	1	2	yes	complemented
18	#19098941	C₄	1	2	yes	complemented
19	#19098686	—	2	2	no	—
20	#19098681	—	2	2	no	—
21	C₂×#14579097	C₂²	1	1	yes	characteristic
22	#19098581	C₂²	1	2	yes	—
23	#19098581	C₂²	1	2	yes	—
24	#19098572	C₂²	1	2	yes	—
25	C₂×#14579080	C₂²	1	2	yes	—
26	#19098536	C₂²	1	2	yes	—
27	#19098518	C₂²	1	1	yes	characteristic
28	#19098518	C₂²	1	1	yes	characteristic
29	#19098333	C₂²	1	2	yes	—
30	C₇₉⋊#338	C₂²	1	1	yes	characteristic
31	#19098320	C₂²	1	1	yes	characteristic
32	#19098319	C₂²	1	2	yes	—
33	#19098319	C₂²	1	1	yes	characteristic
34	#19098319	C₂²	1	1	yes	characteristic
35	C₂²×Q₁₆×C₇₉	C₂²	1	1	yes	characteristic
36	#519×C₇₉	C₂²	1	2	yes	—
37	#441×C₇₉	—	2	2	no	—
38	C₄×Q₁₆×C₇₉	—	2	2	no	—
39	#427×C₇₉	C₂²	1	1	yes	characteristic
40	#419×C₇₉	C₂²	1	2	yes	—
41	#405×C₇₉	C₂²	1	1	yes	characteristic
42	C₂×#11929624	C₂³	1	2	yes	—
43	#14579192	—	4	2	no	—
44	#14579192	—	4	2	no	—
45	#14579183	—	2	1	no	—
46	#14579183	—	2	1	no	—
47	#14579183	—	2	1	no	—
48	#14579183	—	2	1	no	—
49	C₂×Dic₃₁₆	C₂×C₄	1	1	yes	characteristic
50	C₂×#11929614	C₂×C₄	1	4	yes	—
51	C₂×#11929613	C₂×C₄	1	2	yes	—
52	C₂×#11929611	C₂×C₄	1	4	yes	—
53	C₂×D₆₃₂	C₂×C₄	1	1	yes	characteristic
54	#14579169	—	4	2	no	—
55	#14579167	—	2	4	no	—
56	C₂×#11929608	C₂³	1	1	yes	characteristic
57	C₂×#11929608	C₂³	1	2	yes	—
58	C₂×#11929608	C₂³	1	1	yes	characteristic
59	M₁₆×D₇₉	—	4	2	no	—
60	#14579159	C₂×C₄	1	4	yes	—
61	#14579150	C₂×C₄	1	4	yes	—
62	#14579144	—	4	2	no	—
63	#14579137	—	4	2	no	—
64	#14579120	C₂³	1	1	yes	characteristic
65	#14579120	C₂³	1	1	yes	characteristic
66	#14579097	—	2	1	no	—
67	#14579097	—	2	1	no	—
68	#14579089	—	2	4	no	—
69	#14579089	—	4	2	no	—
70	#14579085	—	4	2	no	—
71	#14579080	—	4	2	no	—
72	#14579075	—	4	2	no	—
73	#14579071	—	2	1	no	—
74	#14579071	C₂×C₄	1	2	yes	—
75	C₈×Dic₇₉	—	2	1	no	—
76	C₈×Dic₇₉	C₂×C₄	1	2	yes	—
77	C₂²×Q₈×C₇₉	C₂³	1	2	yes	—
78	C₂×Q₁₆×C₇₉	—	2	1	no	—
79	C₂×Q₁₆×C₇₉	—	2	1	no	—
80	C₂×Q₁₆×C₇₉	—	2	1	no	—
81	C₂×Q₁₆×C₇₉	—	2	1	no	—
82	C₂×Q₁₆×C₇₉	C₂×C₄	1	2	yes	—
83	C₂×Q₁₆×C₇₉	C₂×C₄	1	2	yes	—
84	C₂×M₁₆×C₇₉	C₂³	1	1	yes	characteristic
85	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
86	C₄×Q₈×C₇₉	—	2	4	no	—
87	C₄×Q₈×C₇₉	—	4	2	no	—
88	#117×C₇₉	—	4	2	no	—
89	#117×C₇₉	C₂³	1	2	yes	—
90	#117×C₇₉	C₂³	1	1	yes	characteristic
91	#107×C₇₉	—	2	1	no	—
92	#106×C₇₉	—	2	1	no	—
93	#103×C₇₉	—	2	4	no	—
94	#97×C₇₉	D₄	1	2	yes	—
95	C₄×C₈×C₇₉	D₄	1	2	yes	—
96	#11929624	—	2	2	no	—
97	#11929624	—	2	2	no	—
98	#11929624	—	2	2	no	—
99	#11929624	—	2	2	no	—
100	C₂×Dic₁₅₈	C₂²×C₄	1	2	yes	—
101	C₂×D₃₁₆	C₂²×C₄	1	2	yes	—
102	C₂×C₂²⋊D₇₉	—	2	2	no	—
103	C₂×C₄×D₇₉	—	2	2	no	—
104	Dic₃₁₆	—	2	1	no	—
105	Dic₃₁₆	—	2	1	no	—
106	#11929614	—	4	4	no	—
107	#11929613	—	2	2	no	—
108	#11929613	—	2	2	no	—
109	#11929611	—	4	4	no	—
110	D₆₃₂	—	2	1	no	—
111	D₆₃₂	—	2	1	no	—
112	#11929608	—	2	2	no	—
113	#11929608	—	2	1	no	—
114	#11929608	—	2	1	no	—
115	#11929608	—	2	1	no	—
116	#11929608	—	2	2	no	—
117	#11929608	—	2	1	no	—
118	#11929607	—	4	4	no	—
119	C₂×C₇₉⋊C₈	—	2	1	no	—
120	C₂×C₇₉⋊C₈	—	2	2	no	—
121	C₂×C₇₉⋊C₈	C₂²×C₄	1	2	yes	—
122	C₈×D₇₉	—	4	4	no	—
123	C₄⋊Dic₇₉	—	2	1	no	—
124	C₄⋊Dic₇₉	—	2	1	no	—
125	Dic₇₉⋊C₄	—	4	4	no	—
126	C₂²⋊Dic₇₉	—	2	1	no	—
127	C₂²⋊Dic₇₉	—	2	1	no	—
128	(C₂×D₇₉)⋊C₄	—	4	4	no	—
129	C₄×Dic₇₉	—	2	1	no	—
130	C₄×Dic₇₉	C₂²×C₄	1	2	yes	—
131	C₂×Q₈×C₇₉	—	2	2	no	—
132	C₂×Q₈×C₇₉	—	2	2	no	—
133	C₂×Q₈×C₇₉	—	2	2	no	—
134	C₂×Q₈×C₇₉	—	2	2	no	—
135	C₂×Q₈×C₇₉	—	2	2	no	—
136	C₂×Q₈×C₇₉	C₂²×C₄	1	4	yes	—
137	C₂²×C₄×C₇₉	—	2	2	no	—
138	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
139	Q₁₆×C₇₉	—	2	2	no	—
140	Q₁₆×C₇₉	—	2	2	no	—
141	Q₁₆×C₇₉	—	2	2	no	—
142	Q₁₆×C₇₉	—	2	2	no	—
143	M₁₆×C₇₉	—	2	1	no	—
144	M₁₆×C₇₉	—	2	1	no	—
145	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
146	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
147	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
148	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
149	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
150	C₂×C₈×C₇₉	#41	1	1	yes	characteristic
151	C₂×C₈×C₇₉	#41	1	1	yes	characteristic
152	C₄⋊C₄×C₇₉	—	2	1	no	—
153	C₄⋊C₄×C₇₉	—	2	2	no	—
154	C₄⋊C₄×C₇₉	—	4	4	no	—
155	C₂²⋊C₄×C₇₉	—	2	1	no	—
156	C₂²⋊C₄×C₇₉	—	2	2	no	—
157	C₄²×C₇₉	—	2	2	no	—
158	C₄²×C₇₉	—	4	4	no	—
159	C₄²×C₇₉	C₂×D₄	1	2	yes	—
160	C₂³×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
161	C₂²×D₇₉	—	2	2	no	—
162	Q₈×C₇₉	—	2	4	no	—
163	Q₈×C₇₉	—	2	4	no	—
164	Q₈×C₇₉	—	4	2	no	—
165	Q₈×C₇₉	—	4	2	no	—
166	C₂×C₄×C₇₉	—	2	4	no	—
167	C₂×C₄×C₇₉	—	2	2	no	—
168	C₂×C₄×C₇₉	—	4	2	no	—
169	C₂×C₄×C₇₉	—	4	2	no	—
170	C₂×C₄×C₇₉	—	4	2	no	—
171	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
172	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
173	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
174	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
175	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
176	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
177	C₂²⋊D₇₉	—	4	2	no	—
178	C₂²⋊D₇₉	—	4	2	no	—
179	C₂×Dic₇₉	—	2	2	no	—
180	C₂×Dic₇₉	—	2	2	no	—
181	C₂×Dic₇₉	—	4	1	no	—
182	D₃₁₆	—	2	2	no	—
183	D₃₁₆	—	2	2	no	—
184	C₄×D₇₉	—	4	2	no	—
185	C₄×D₇₉	—	4	2	no	—
186	Dic₁₅₈	—	2	2	no	—
187	Dic₁₅₈	—	2	2	no	—
188	C₈×C₇₉	—	2	2	no	—
189	C₈×C₇₉	C₄×D₄	1	1	yes	characteristic
190	C₈×C₇₉	C₄×D₄	1	1	yes	characteristic
191	C₈×C₇₉	C₄×D₄	1	1	yes	characteristic
192	C₈×C₇₉	C₄×D₄	1	1	yes	characteristic
193	C₇₉⋊C₈	—	2	2	no	—
194	C₇₉⋊C₈	—	4	2	no	—
195	C₇₉⋊C₈	—	4	1	no	—
196	C₂²×C₇₉	—	4	1	no	—
197	C₂²×C₇₉	#518	1	1	yes	characteristic
198	C₂²×C₇₉	#535	1	1	yes	characteristic
199	C₂²×C₇₉	#540	1	1	yes	characteristic
200	C₂×D₇₉	—	4	2	no	—
201	C₂×D₇₉	—	8	2	no	—
202	C₄×C₇₉	—	4	2	no	—
203	C₄×C₇₉	—	4	4	no	—
204	C₄×C₇₉	—	8	2	no	—
205	C₄×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
206	C₄×C₇₉	#518	1	1	yes	characteristic
207	C₄×C₇₉	#535	1	1	yes	characteristic
208	C₄×C₇₉	#540	1	1	yes	characteristic
209	Dic₇₉	—	4	2	no	—
210	Dic₇₉	—	4	2	no	—
211	Dic₇₉	—	8	1	no	—
212	#22285	—	79	1	no	maximal, Sylow
213	C₂×C₇₉	—	2	1	no	—
214	C₂×C₇₉	—	2	1	no	—
215	C₂×C₇₉	—	2	1	no	—
216	C₂×C₇₉	#2328	1	1	yes	characteristic
217	D₇₉	—	8	2	no	—
218	#3156	—	79	1	no	—
219	#2957	—	79	1	no	—
220	#2950	D₇₉	1	1	yes	characteristic, complemented
221	#1979	—	79	1	no	—
222	#1976	—	79	1	no	—
223	#1912	—	79	2	no	—
224	#1909	—	79	2	no	—
225	#1905	—	79	2	no	—
226	#1902	—	79	2	no	—
227	#1833	—	79	1	no	—
228	#1747	—	79	1	no	—
229	C₇₉	#22285	1	1	yes	characteristic, complemented, Sylow
230	C₂×#137	—	79	2	no	—
231	C₂×#135	—	79	1	no	—
232	C₂²×Q₁₆	C₂×D₇₉	1	1	yes	characteristic
233	#568	—	79	2	no	—
234	#536	—	79	2	no	—
235	#519	C₂×D₇₉	1	2	yes	—
236	#497	—	79	4	no	—
237	#495	—	79	2	no	—
238	#494	—	79	2	no	—
239	#444	—	158	2	no	—
240	#443	—	158	2	no	—
241	#441	—	2	2	no	—
242	C₄×Q₁₆	—	2	2	no	—
243	C₂×#108	—	79	1	no	—
244	#427	C₂×D₇₉	1	1	yes	characteristic
245	#421	—	79	2	no	—
246	#421	—	79	2	no	—
247	#419	—	79	2	no	—
248	#419	C₂×D₇₉	1	2	yes	—
249	C₂×#101	—	79	2	no	—
250	#410	—	79	2	no	—
251	#405	—	79	1	no	—
252	#405	—	79	1	no	—
253	#405	C₂×D₇₉	1	1	yes	characteristic
254	#344	—	79	2	no	—
255	#338	—	79	1	no	—
256	H(3,ℤ/4)	—	79	1	no	—
257	H(3,ℤ/4)	—	79	2	no	—
258	H(3,ℤ/4)	—	79	1	no	—
259	H(3,ℤ/4)	—	79	1	no	—
260	C₂×#41	—	79	2	no	—
261	C₂²×Q₈	C₂²×D₇₉	1	2	yes	—
262	#137	—	316	2	no	—
263	#137	—	316	2	no	—
264	#135	—	158	1	no	—
265	#135	—	158	1	no	—
266	#135	—	158	1	no	—
267	#135	—	158	1	no	—
268	C₂×Q₁₆	—	2	1	no	—
269	C₂×Q₁₆	—	2	1	no	—
270	C₂×Q₁₆	—	2	1	no	—
271	C₂×Q₁₆	—	2	1	no	—
272	C₂×Q₁₆	—	79	4	no	—
273	C₂×Q₁₆	—	79	1	no	—
274	C₂×Q₁₆	C₄×D₇₉	1	2	yes	—
275	C₂×Q₁₆	C₄×D₇₉	1	2	yes	—
276	C₂×SD₁₆	—	79	4	no	—
277	C₂×SD₁₆	—	79	2	no	—
278	C₂×D₈	—	79	1	no	—
279	#131	—	316	2	no	—
280	#131	—	158	4	no	—
281	C₂×M₁₆	—	316	2	no	—
282	C₂×M₁₆	—	79	1	no	—
283	C₂×M₁₆	—	79	2	no	—
284	C₂×M₁₆	—	79	1	no	—
285	C₂×M₁₆	C₂²×D₇₉	1	1	yes	characteristic
286	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
287	C₄⋊Q₈	—	79	4	no	—
288	#124	—	79	4	no	—
289	#123	—	316	2	no	—
290	C₂²⋊Q₈	—	316	2	no	—
291	C₄×Q₈	—	2	4	no	—
292	C₄×Q₈	—	4	2	no	—
293	#117	—	4	2	no	—
294	#117	—	79	1	no	—
295	#117	—	79	1	no	—
296	#117	C₂²×D₇₉	1	2	yes	—
297	#117	C₂²×D₇₉	1	1	yes	characteristic
298	#108	—	158	1	no	—
299	#108	—	158	1	no	—
300	#107	—	2	1	no	—
301	#106	—	2	1	no	—
302	#104	—	316	2	no	—
303	#104	—	158	4	no	—
304	#103	—	2	4	no	—
305	#103	—	316	2	no	—
306	#101	—	316	2	no	—
307	#99	—	316	2	no	—
308	#97	—	79	2	no	—
309	#97	—	158	1	no	—
310	#97	C₂²⋊D₇₉	1	2	yes	—
311	C₄×C₈	—	79	2	no	—
312	C₄×C₈	—	158	1	no	—
313	C₄×C₈	C₂²⋊D₇₉	1	2	yes	—
314	#41	—	158	2	no	—
315	#41	—	158	2	no	—
316	#41	—	158	2	no	—
317	#41	—	158	2	no	—
318	C₂×Q₈	—	2	2	no	—
319	C₂×Q₈	—	2	2	no	—
320	C₂×Q₈	—	2	2	no	—
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	—	2	2	no	—
323	C₂×Q₈	—	79	2	no	—
324	C₂×Q₈	C₂×C₄×D₇₉	1	4	yes	—
325	C₂×D₄	—	79	2	no	—
326	C₂×D₄	—	158	2	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	158	2	no	—
329	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
330	Q₁₆	—	2	2	no	—
331	Q₁₆	—	2	2	no	—
332	Q₁₆	—	2	2	no	—
333	Q₁₆	—	2	2	no	—
334	Q₁₆	—	316	4	no	—
335	Q₁₆	—	158	1	no	—
336	Q₁₆	—	158	1	no	—
337	SD₁₆	—	316	4	no	—
338	SD₁₆	—	158	2	no	—
339	SD₁₆	—	158	2	no	—
340	D₈	—	158	1	no	—
341	D₈	—	158	1	no	—
342	M₁₆	—	2	1	no	—
343	M₁₆	—	2	1	no	—
344	M₁₆	—	316	4	no	—
345	M₁₆	—	158	1	no	—
346	M₁₆	—	158	1	no	—
347	M₁₆	—	158	2	no	—
348	M₁₆	—	158	2	no	—
349	M₁₆	—	158	1	no	—
350	M₁₆	—	158	1	no	—
351	C₂×C₈	—	316	4	no	—
352	C₂×C₈	—	79	2	no	—
353	C₂×C₈	—	158	1	no	—
354	C₂×C₈	—	158	2	no	—
355	C₂×C₈	C₂×C₄×D₇₉	1	1	yes	characteristic
356	C₂×C₈	C₂×C₄×D₇₉	1	1	yes	characteristic
357	C₂×C₈	C₂×C₂²⋊D₇₉	1	2	yes	—
358	C₂×C₈	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
359	C₂×C₈	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
360	C₂×C₈	#11929624	1	1	yes	characteristic
361	C₂×C₈	#11929624	1	1	yes	characteristic
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	4	4	no	—
365	C₄⋊C₄	—	316	4	no	—
366	C₄⋊C₄	—	158	1	no	—
367	C₄⋊C₄	—	158	1	no	—
368	C₂²⋊C₄	—	2	1	no	—
369	C₂²⋊C₄	—	2	2	no	—
370	C₂²⋊C₄	—	316	4	no	—
371	C₂²⋊C₄	—	158	1	no	—
372	C₂²⋊C₄	—	158	1	no	—
373	C₄²	—	2	2	no	—
374	C₄²	—	4	4	no	—
375	C₄²	—	79	2	no	—
376	C₄²	—	158	1	no	—
377	C₄²	C₂×C₂²⋊D₇₉	1	2	yes	—
378	C₂³	—	158	2	no	—
379	C₂³	#14579206	1	1	yes	characteristic
380	Q₈	—	2	4	no	—
381	Q₈	—	2	4	no	—
382	Q₈	—	4	2	no	—
383	Q₈	—	4	2	no	—
384	Q₈	—	158	2	no	—
385	Q₈	—	158	2	no	—
386	D₄	—	316	2	no	—
387	D₄	—	316	2	no	—
388	D₄	—	158	2	no	—
389	D₄	—	158	2	no	—
390	C₂×C₄	—	2	4	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	316	2	no	—
396	C₂×C₄	—	316	2	no	—
397	C₂×C₄	—	316	1	no	—
398	C₂×C₄	—	158	2	no	—
399	C₂×C₄	—	158	2	no	—
400	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
401	C₂×C₄	C₂²×C₂²⋊D₇₉	1	1	yes	characteristic
402	C₂×C₄	C₂×#11929624	1	1	yes	characteristic
403	C₂×C₄	#14579206	1	1	yes	characteristic
404	C₂×C₄	#14579207	1	1	yes	characteristic
405	C₂×C₄	#14579207	1	1	yes	characteristic
406	C₈	—	2	2	no	—
407	C₈	—	316	1	no	—
408	C₈	—	316	2	no	—
409	C₈	—	158	2	no	—
410	C₈	C₄×C₂²⋊D₇₉	1	1	yes	characteristic
411	C₈	C₄×C₂²⋊D₇₉	1	1	yes	characteristic
412	C₈	C₄×C₂²⋊D₇₉	1	1	yes	characteristic
413	C₈	C₄×C₂²⋊D₇₉	1	1	yes	characteristic
414	C₂²	—	4	1	no	—
415	C₂²	—	316	2	no	—
416	C₂²	—	632	2	no	—
417	C₂²	#19099035	1	1	yes	characteristic
418	C₂²	#19099130	1	1	yes	characteristic
419	C₂²	#19099164	1	1	yes	characteristic
420	C₄	—	4	2	no	—
421	C₄	—	4	4	no	—
422	C₄	—	8	2	no	—
423	C₄	—	316	2	no	—
424	C₄	—	316	2	no	—
425	C₄	—	632	1	no	—
426	C₄	C₂×C₄×C₂²⋊D₇₉	1	1	yes	characteristic
427	C₄	#19099035	1	1	yes	characteristic
428	C₄	#19099127	1	1	yes	characteristic
429	C₄	#19099164	1	1	yes	characteristic
430	C₂	—	2	1	no	—
431	C₂	—	2	1	no	—
432	C₂	—	2	1	no	—
433	C₂	—	632	2	no	—
434	C₂	#23766122	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#23766122
commutator	C₂×C₄×C₇₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₇₉
Fitting	C₇₉×#2950	C₂
socle	C₂×C₇₉	#2328
prime radical	C₂×#14579183	C₂²
cosocle	C₂²×C₄×C₇₉	C₂⁴
hypercenter	#2950	D₇₉
hypocenter	C₇₉	#22285
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #2950

Complements

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

N	H ≅ G/N	type
3. #23764316	C₂	semidirect
5. #23763937	C₂	semidirect
6. #23763919	C₂	semidirect
7. #23763894	C₂	semidirect
8. #23763870	C₂	semidirect
9. #23763523	C₂	semidirect
10. #23763155	C₂	semidirect
11. C₇₉×#2950	C₂	semidirect
16. #19098956	C₄	semidirect
17. #19098948	C₄	semidirect
18. #19098941	C₄	semidirect
220. #2950	D₇₉	semidirect
229. C₇₉	#22285	semidirect

Maximal subgroups

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

subgroup	index
#23773889	2
#23772318	2
#23764316	2
#23764296	2
#23763937	2
#23763919	2
#23763894	2
#23763870	2
#23763523	2
#23763155	2
C₇₉×#2950	2
#22285	79