Subgroups — #34288850

Order 20224.

810 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23766009	C₂	1	2	yes	maximal
2	#23763568	C₂	1	2	yes	maximal, complemented
3	#23763531	C₂	1	1	yes	maximal, characteristic, complemented
4	#23763528	C₂	1	1	yes	maximal, characteristic, complemented
5	#23763433	C₂	1	2	yes	maximal
6	#23763429	C₂	1	1	yes	maximal, characteristic
7	#23763425	C₂	1	1	yes	maximal, characteristic
8	#23763297	C₂	1	2	yes	maximal, complemented
9	C₄×#14579095	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×#14579093	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#405×C₇₉	C₂	1	1	yes	maximal, characteristic
12	C₂×#14579095	C₂²	1	2	yes	—
13	C₂×#14579095	C₂²	1	2	yes	—
14	C₂×#14579093	C₂²	1	2	yes	—
15	C₂×#14579093	C₂²	1	2	yes	—
16	#19098456	—	2	2	no	—
17	#19098456	—	2	2	no	—
18	#19098449	—	2	2	no	—
19	#19098449	—	2	2	no	—
20	#19098433	C₂²	1	2	yes	—
21	#19098429	C₂²	1	2	yes	—
22	#19098423	C₂²	1	2	yes	—
23	#19098423	C₂²	1	2	yes	—
24	C₄×C₄⋊Dic₇₉	C₂²	1	2	yes	—
25	C₄×C₄⋊Dic₇₉	C₂²	1	2	yes	—
26	#19098326	C₂²	1	1	yes	characteristic
27	#19098326	C₂²	1	1	yes	characteristic
28	#19098326	C₂²	1	2	yes	—
29	#19098326	C₂²	1	1	yes	characteristic
30	#19098326	C₂²	1	1	yes	characteristic
31	#19098326	C₂²	1	2	yes	—
32	C₂²×M₁₆×C₇₉	C₂²	1	1	yes	characteristic
33	C₂³×C₈×C₇₉	C₂²	1	1	yes	characteristic
34	C₂×#117×C₇₉	C₂²	1	1	yes	characteristic
35	#405×C₇₉	C₄	1	8	yes	complemented
36	C₂×#97×C₇₉	C₂²	1	1	yes	characteristic
37	C₂×#97×C₇₉	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
40	C₂×C₄⋊Dic₇₉	—	2	2	no	—
41	C₂×C₄⋊Dic₇₉	—	2	2	no	—
42	C₂×C₄⋊Dic₇₉	C₂³	1	2	yes	—
43	C₂×C₄⋊Dic₇₉	C₂³	1	2	yes	—
44	C₂×C₄⋊Dic₇₉	C₂³	1	2	yes	—
45	C₂×C₄⋊Dic₇₉	C₂³	1	2	yes	—
46	C₂×C₂²⋊Dic₇₉	—	2	2	no	—
47	C₂×C₂²⋊Dic₇₉	—	2	2	no	—
48	C₂×C₄×Dic₇₉	—	2	2	no	—
49	C₂×C₄×Dic₇₉	—	2	2	no	—
50	#14579095	—	2	4	no	—
51	#14579095	—	2	4	no	—
52	#14579093	—	2	4	no	—
53	#14579093	—	2	4	no	—
54	C₇₉⋊#95	—	2	2	no	—
55	C₇₉⋊#95	—	2	2	no	—
56	C₇₉⋊#95	—	2	2	no	—
57	C₇₉⋊#95	—	2	2	no	—
58	C₇₉⋊#95	—	2	2	no	—
59	C₇₉⋊#95	—	2	2	no	—
60	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
61	C₂×M₁₆×C₇₉	—	2	4	no	—
62	C₂×M₁₆×C₇₉	C₂×C₄	1	4	yes	—
63	C₂²×C₈×C₇₉	—	2	4	no	—
64	C₂²×C₈×C₇₉	C₂×C₄	1	4	yes	—
65	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
66	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
67	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
68	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
69	#117×C₇₉	C₂×C₄	1	4	yes	—
70	#117×C₇₉	Q₈	1	4	yes	—
71	C₂×C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
72	C₂×C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
73	C₂×C₂²⋊C₄×C₇₉	D₄	1	1	yes	characteristic
74	C₂×C₂²⋊C₄×C₇₉	D₄	1	1	yes	characteristic
75	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
77	#97×C₇₉	C₂×C₄	1	4	yes	—
78	#97×C₇₉	C₂×C₄	1	4	yes	—
79	C₄×C₈×C₇₉	C₂×C₄	1	4	yes	—
80	C₄×C₈×C₇₉	C₂×C₄	1	4	yes	—
81	C₂²×Dic₇₉	—	2	2	no	—
82	C₂²×Dic₇₉	—	2	2	no	—
83	C₂²×Dic₇₉	—	2	2	no	—
84	C₂²×Dic₇₉	—	2	2	no	—
85	C₄⋊Dic₇₉	—	2	2	no	—
86	C₄⋊Dic₇₉	—	2	2	no	—
87	C₄⋊Dic₇₉	—	2	2	no	—
88	C₄⋊Dic₇₉	—	2	2	no	—
89	C₄⋊Dic₇₉	—	2	2	no	—
90	C₄⋊Dic₇₉	—	2	2	no	—
91	C₄⋊Dic₇₉	—	2	2	no	—
92	C₄⋊Dic₇₉	—	2	2	no	—
93	C₄⋊Dic₇₉	—	8	2	no	—
94	C₄⋊Dic₇₉	—	8	2	no	—
95	C₂²⋊Dic₇₉	—	8	2	no	—
96	C₂²⋊Dic₇₉	—	8	2	no	—
97	C₄×Dic₇₉	—	8	2	no	—
98	C₄×Dic₇₉	—	8	2	no	—
99	C₂⁴×C₇₉	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₇₉	—	2	2	no	—
101	C₂²×C₄×C₇₉	—	2	2	no	—
102	C₂²×C₄×C₇₉	C₂²×C₄	1	2	yes	—
103	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₇₉	C₂×Q₈	1	2	yes	—
109	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
110	M₁₆×C₇₉	—	2	8	no	—
111	C₂×C₈×C₇₉	—	2	8	no	—
112	C₂×C₈×C₇₉	—	2	2	no	—
113	C₂×C₈×C₇₉	—	2	2	no	—
114	C₂×C₈×C₇₉	C₂²×C₄	1	2	yes	—
115	C₂×C₈×C₇₉	C₂²×C₄	1	2	yes	—
116	C₂×C₈×C₇₉	C₂²×C₄	1	2	yes	—
117	C₂×C₈×C₇₉	C₂²×C₄	1	2	yes	—
118	C₂×C₈×C₇₉	#41	1	4	yes	—
119	C₂×C₈×C₇₉	#41	1	4	yes	—
120	C₄⋊C₄×C₇₉	C₄⋊C₄	1	4	yes	—
121	C₄⋊C₄×C₇₉	C₄⋊C₄	1	4	yes	—
122	C₂²⋊C₄×C₇₉	C₄⋊C₄	1	4	yes	—
123	C₂²⋊C₄×C₇₉	C₄⋊C₄	1	4	yes	—
124	C₄²×C₇₉	C₂²×C₄	1	2	yes	—
125	C₄²×C₇₉	C₂²×C₄	1	2	yes	—
126	C₄²×C₇₉	C₂×Q₈	1	2	yes	—
127	C₄²×C₇₉	C₂×Q₈	1	2	yes	—
128	C₂³×C₇₉	—	2	2	no	—
129	C₂³×C₇₉	—	2	1	no	—
130	C₂³×C₇₉	—	2	2	no	—
131	C₂³×C₇₉	—	2	1	no	—
132	C₂³×C₇₉	C₂×C₄⋊C₄	1	2	yes	—
133	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
134	C₂×C₄×C₇₉	—	2	2	no	—
135	C₂×C₄×C₇₉	—	2	1	no	—
136	C₂×C₄×C₇₉	—	2	1	no	—
137	C₂×C₄×C₇₉	—	2	2	no	—
138	C₂×C₄×C₇₉	—	2	2	no	—
139	C₂×C₄×C₇₉	—	2	1	no	—
140	C₂×C₄×C₇₉	—	2	1	no	—
141	C₂×C₄×C₇₉	—	2	2	no	—
142	C₂×C₄×C₇₉	—	2	2	no	—
143	C₂×C₄×C₇₉	—	2	4	no	—
144	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	2	yes	—
145	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	2	yes	—
146	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	2	yes	—
147	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	2	yes	—
148	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	2	yes	—
149	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
150	C₂×C₄×C₇₉	C₂²×Q₈	1	1	yes	characteristic
151	C₂×C₄×C₇₉	C₂×#41	1	2	yes	—
152	C₂×C₄×C₇₉	C₂×#41	1	2	yes	—
153	C₂×Dic₇₉	—	4	2	no	—
154	C₂×Dic₇₉	—	4	2	no	—
155	C₂×Dic₇₉	—	4	2	no	—
156	C₂×Dic₇₉	—	4	2	no	—
157	C₂×Dic₇₉	—	4	2	no	—
158	C₂×Dic₇₉	—	4	2	no	—
159	C₂×Dic₇₉	—	4	2	no	—
160	C₂×Dic₇₉	—	4	2	no	—
161	C₂×Dic₇₉	—	4	2	no	—
162	C₂×Dic₇₉	—	4	2	no	—
163	C₂×Dic₇₉	—	4	2	no	—
164	C₂×Dic₇₉	—	4	2	no	—
165	C₈×C₇₉	—	2	2	no	—
166	C₈×C₇₉	—	2	2	no	—
167	C₈×C₇₉	#117	1	4	yes	—
168	C₈×C₇₉	#117	1	4	yes	—
169	C₂²×C₇₉	—	2	2	no	—
170	C₂²×C₇₉	—	2	2	no	—
171	C₂²×C₇₉	—	2	2	no	—
172	C₂²×C₇₉	—	4	2	no	—
173	C₂²×C₇₉	—	4	2	no	—
174	C₂²×C₇₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
175	C₂²×C₇₉	#532	1	2	yes	—
176	C₂²×C₇₉	#576	1	1	yes	characteristic
177	C₂²×C₇₉	#577	1	2	yes	—
178	C₂²×C₇₉	#578	1	1	yes	characteristic
179	C₄×C₇₉	—	2	2	no	—
180	C₄×C₇₉	—	2	2	no	—
181	C₄×C₇₉	—	2	2	no	—
182	C₄×C₇₉	—	2	2	no	—
183	C₄×C₇₉	—	2	2	no	—
184	C₄×C₇₉	C₂×#117	1	1	yes	characteristic
185	C₄×C₇₉	C₂×#117	1	1	yes	characteristic
186	C₄×C₇₉	#533	1	2	yes	—
187	Dic₇₉	—	8	2	no	—
188	Dic₇₉	—	8	2	no	—
189	Dic₇₉	—	8	2	no	—
190	Dic₇₉	—	8	2	no	—
191	#20822	—	79	1	no	maximal, Sylow
192	C₂×C₇₉	—	4	2	no	—
193	C₂×C₇₉	#2285	1	1	yes	characteristic
194	C₂×C₇₉	#2912	1	1	yes	characteristic
195	C₂×C₇₉	#2913	1	1	yes	characteristic
196	C₂×C₇₉	#3178	1	2	yes	—
197	C₂×C₇₉	#3179	1	2	yes	—
198	C₂×#405	D₇₉	1	1	yes	characteristic
199	#2314	—	79	2	no	—
200	#1847	—	79	2	no	—
201	#1835	—	79	1	no	—
202	#1834	—	79	1	no	—
203	#1809	—	79	2	no	—
204	#1808	—	79	1	no	—
205	#1807	—	79	1	no	—
206	#1776	—	79	2	no	—
207	C₄×#107	—	79	1	no	—
208	C₄×#106	—	79	1	no	—
209	C₇₉	#20822	1	1	yes	characteristic, complemented, Sylow
210	C₂²×M₁₆	C₂×D₇₉	1	1	yes	characteristic
211	C₂³×C₈	C₂×D₇₉	1	1	yes	characteristic
212	C₂×#117	C₂×D₇₉	1	1	yes	characteristic
213	C₂×#107	—	79	2	no	—
214	C₂×#107	—	79	2	no	—
215	C₂×#106	—	79	2	no	—
216	C₂×#106	—	79	2	no	—
217	#405	Dic₇₉	1	8	yes	complemented
218	C₂×#97	C₂×D₇₉	1	1	yes	characteristic
219	C₂×#97	C₂×D₇₉	1	1	yes	characteristic
220	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
221	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
222	#388	—	158	2	no	—
223	#388	—	158	2	no	—
224	#387	—	158	2	no	—
225	#387	—	158	2	no	—
226	#384	—	79	2	no	—
227	#382	—	79	2	no	—
228	#380	—	79	2	no	—
229	#380	—	79	2	no	—
230	C₄×C₄⋊C₄	—	79	2	no	—
231	C₄×C₄⋊C₄	—	79	2	no	—
232	#340	—	79	1	no	—
233	#340	—	79	1	no	—
234	#340	—	79	1	no	—
235	#340	—	79	1	no	—
236	#340	—	79	2	no	—
237	#340	—	79	2	no	—
238	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
239	C₂×M₁₆	—	2	4	no	—
240	C₂×M₁₆	C₂×Dic₇₉	1	4	yes	—
241	C₂²×C₈	—	2	4	no	—
242	C₂²×C₈	C₂×Dic₇₉	1	4	yes	—
243	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
244	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
245	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
246	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
247	#117	Dic₁₅₈	1	4	yes	—
248	#117	C₂×Dic₇₉	1	4	yes	—
249	C₂×C₄⋊C₄	—	79	2	no	—
250	C₂×C₄⋊C₄	—	79	2	no	—
251	C₂×C₄⋊C₄	—	79	2	no	—
252	C₂×C₄⋊C₄	—	79	2	no	—
253	C₂×C₄⋊C₄	—	158	2	no	—
254	C₂×C₄⋊C₄	—	158	2	no	—
255	C₂×C₄⋊C₄	D₃₁₆	1	1	yes	characteristic
256	C₂×C₄⋊C₄	D₃₁₆	1	1	yes	characteristic
257	C₂×C₂²⋊C₄	—	158	2	no	—
258	C₂×C₂²⋊C₄	—	158	2	no	—
259	C₂×C₂²⋊C₄	D₃₁₆	1	1	yes	characteristic
260	C₂×C₂²⋊C₄	D₃₁₆	1	1	yes	characteristic
261	C₂×C₄²	—	158	2	no	—
262	C₂×C₄²	—	158	2	no	—
263	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
264	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
265	#107	—	158	4	no	—
266	#107	—	158	4	no	—
267	#106	—	158	4	no	—
268	#106	—	158	4	no	—
269	#97	C₂×Dic₇₉	1	4	yes	—
270	#97	C₂×Dic₇₉	1	4	yes	—
271	C₄×C₈	C₂×Dic₇₉	1	4	yes	—
272	C₄×C₈	C₂×Dic₇₉	1	4	yes	—
273	#95	—	158	2	no	—
274	#95	—	158	2	no	—
275	#95	—	158	2	no	—
276	#95	—	158	2	no	—
277	#95	—	158	2	no	—
278	#95	—	158	2	no	—
279	C₂⁴	C₂×D₃₁₆	1	1	yes	characteristic
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	158	2	no	—
283	C₂²×C₄	—	158	2	no	—
284	C₂²×C₄	—	158	2	no	—
285	C₂²×C₄	—	158	2	no	—
286	C₂²×C₄	C₂²×Dic₇₉	1	2	yes	—
287	C₂²×C₄	C₂×D₃₁₆	1	1	yes	characteristic
288	C₂²×C₄	C₂×D₃₁₆	1	1	yes	characteristic
289	C₂²×C₄	C₂×D₃₁₆	1	1	yes	characteristic
290	C₂²×C₄	C₂×D₃₁₆	1	1	yes	characteristic
291	C₂²×C₄	C₂×D₃₁₆	1	1	yes	characteristic
292	C₂²×C₄	C₂×Dic₁₅₈	1	2	yes	—
293	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
294	M₁₆	—	2	8	no	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	—	2	8	no	—
298	C₂×C₈	C₂²×Dic₇₉	1	2	yes	—
299	C₂×C₈	C₂²×Dic₇₉	1	2	yes	—
300	C₂×C₈	C₂²×Dic₇₉	1	2	yes	—
301	C₂×C₈	C₂²×Dic₇₉	1	2	yes	—
302	C₂×C₈	#11929624	1	4	yes	—
303	C₂×C₈	#11929624	1	4	yes	—
304	C₄⋊C₄	—	632	2	no	—
305	C₄⋊C₄	—	632	2	no	—
306	C₄⋊C₄	—	158	2	no	—
307	C₄⋊C₄	—	158	2	no	—
308	C₄⋊C₄	—	158	2	no	—
309	C₄⋊C₄	—	158	2	no	—
310	C₄⋊C₄	—	158	2	no	—
311	C₄⋊C₄	—	158	2	no	—
312	C₄⋊C₄	—	158	2	no	—
313	C₄⋊C₄	—	158	2	no	—
314	C₄⋊C₄	C₄⋊Dic₇₉	1	4	yes	—
315	C₄⋊C₄	C₄⋊Dic₇₉	1	4	yes	—
316	C₂²⋊C₄	—	632	2	no	—
317	C₂²⋊C₄	—	632	2	no	—
318	C₂²⋊C₄	C₄⋊Dic₇₉	1	4	yes	—
319	C₂²⋊C₄	C₄⋊Dic₇₉	1	4	yes	—
320	C₄²	—	632	2	no	—
321	C₄²	—	632	2	no	—
322	C₄²	C₂²×Dic₇₉	1	2	yes	—
323	C₄²	C₂²×Dic₇₉	1	2	yes	—
324	C₄²	C₂×Dic₁₅₈	1	2	yes	—
325	C₄²	C₂×Dic₁₅₈	1	2	yes	—
326	C₂³	—	2	1	no	—
327	C₂³	—	2	2	no	—
328	C₂³	—	2	2	no	—
329	C₂³	—	2	1	no	—
330	C₂³	C₂×C₄⋊Dic₇₉	1	2	yes	—
331	C₂³	C₂²×D₃₁₆	1	1	yes	characteristic
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	4	no	—
342	C₂×C₄	—	316	2	no	—
343	C₂×C₄	—	316	2	no	—
344	C₂×C₄	—	316	2	no	—
345	C₂×C₄	—	316	2	no	—
346	C₂×C₄	—	316	2	no	—
347	C₂×C₄	—	316	2	no	—
348	C₂×C₄	—	316	2	no	—
349	C₂×C₄	—	316	2	no	—
350	C₂×C₄	—	316	2	no	—
351	C₂×C₄	—	316	2	no	—
352	C₂×C₄	—	316	2	no	—
353	C₂×C₄	—	316	2	no	—
354	C₂×C₄	C₂×C₄⋊Dic₇₉	1	2	yes	—
355	C₂×C₄	C₂×C₄⋊Dic₇₉	1	2	yes	—
356	C₂×C₄	C₂×C₄⋊Dic₇₉	1	2	yes	—
357	C₂×C₄	C₂×C₄⋊Dic₇₉	1	2	yes	—
358	C₂×C₄	C₂×C₄⋊Dic₇₉	1	2	yes	—
359	C₂×C₄	C₂³×Dic₇₉	1	1	yes	characteristic
360	C₂×C₄	C₂²×Dic₁₅₈	1	1	yes	characteristic
361	C₂×C₄	C₂×#11929624	1	2	yes	—
362	C₂×C₄	C₂×#11929624	1	2	yes	—
363	C₈	—	2	2	no	—
364	C₈	—	2	2	no	—
365	C₈	#14579120	1	4	yes	—
366	C₈	#14579120	1	4	yes	—
367	C₂²	—	2	2	no	—
368	C₂²	—	2	2	no	—
369	C₂²	—	2	2	no	—
370	C₂²	—	4	2	no	—
371	C₂²	—	4	2	no	—
372	C₂²	C₂²×C₄⋊Dic₇₉	1	1	yes	characteristic
373	C₂²	#19099113	1	2	yes	—
374	C₂²	#19099368	1	1	yes	characteristic
375	C₂²	#19099375	1	2	yes	—
376	C₂²	#19099380	1	1	yes	characteristic
377	C₄	—	2	2	no	—
378	C₄	—	2	2	no	—
379	C₄	—	2	2	no	—
380	C₄	—	2	2	no	—
381	C₄	—	2	2	no	—
382	C₄	—	632	2	no	—
383	C₄	—	632	2	no	—
384	C₄	—	632	2	no	—
385	C₄	—	632	2	no	—
386	C₄	C₂×#14579120	1	1	yes	characteristic
387	C₄	C₂×#14579120	1	1	yes	characteristic
388	C₄	#19099120	1	2	yes	—
389	C₂	—	4	2	no	—
390	C₂	#23765807	1	1	yes	characteristic
391	C₂	#23771995	1	1	yes	characteristic
392	C₂	#23772000	1	1	yes	characteristic
393	C₂	#23774068	1	2	yes	—
394	C₂	#23774083	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂²×D₃₁₆
commutator	C₂×C₄×C₇₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₇₉
Fitting	C₂×#405×C₇₉	C₂
socle	C₂³×C₇₉	C₂²×D₄
prime radical	C₂⁴×C₇₉	C₂×D₄
cosocle	C₂²×C₄×C₇₉	C₂⁴
hypercenter	C₂×#405	D₇₉
hypocenter	C₇₉	#20822
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂×#117 ◁ C₂×#405

Complements

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

N	H ≅ G/N	type
2. #23763568	C₂	semidirect
3. #23763531	C₂	semidirect
4. #23763528	C₂	semidirect
8. #23763297	C₂	semidirect
9. C₄×#14579095	C₂	semidirect
10. C₄×#14579093	C₂	semidirect
35. #405×C₇₉	C₄	semidirect
209. C₇₉	#20822	semidirect
217. #405	Dic₇₉	semidirect

Maximal subgroups

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

subgroup	index
#23766009	2
#23763568	2
#23763531	2
#23763528	2
#23763433	2
#23763429	2
#23763425	2
#23763297	2
C₄×#14579095	2
C₄×#14579093	2
C₂×#405×C₇₉	2
#20822	79