Subgroups — #34306065

Order 20224.

744 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23765807	C₂	1	1	yes	maximal, characteristic
2	#23764118	C₂	1	1	yes	maximal, characteristic, complemented
3	#23764118	C₂	1	1	yes	maximal, characteristic, complemented
4	#23763963	C₂	1	2	yes	maximal, complemented
5	#23763956	C₂	1	2	yes	maximal, complemented
6	#23763382	C₂	1	2	yes	maximal
7	#23763380	C₂	1	1	yes	maximal, characteristic
8	#23763267	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈×C₄⋊Dic₇₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#23763168	C₂	1	2	yes	maximal
11	C₄×C₂²⋊C₈×C₇₉	C₂	1	1	yes	maximal, characteristic
12	C₂×#14579120	C₂²	1	2	yes	—
13	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
15	C₂×Dic₇₉⋊C₈	C₂²	1	2	yes	—
16	C₂×Dic₇₉⋊C₈	C₂²	1	2	yes	—
17	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
18	C₂×#14579071	C₂²	1	2	yes	—
19	C₂×C₈×Dic₇₉	C₂²	1	2	yes	—
20	#19098433	C₄	1	1	yes	characteristic
21	#19098433	C₄	1	1	yes	characteristic
22	#19098429	C₄	1	2	yes	—
23	#19098423	C₄	1	1	yes	characteristic
24	#19098423	C₄	1	1	yes	characteristic
25	#19098423	C₄	1	2	yes	—
26	C₄×C₄⋊Dic₇₉	C₂²	1	1	yes	characteristic
27	C₄×C₄⋊Dic₇₉	C₂²	1	1	yes	characteristic
28	C₄×C₄⋊Dic₇₉	C₂²	1	2	yes	—
29	#19098318	C₂²	1	2	yes	—
30	#19098317	C₂²	1	2	yes	—
31	#19098317	C₂²	1	2	yes	—
32	#19098317	C₂²	1	2	yes	—
33	#19098317	C₂²	1	2	yes	—
34	C₂²×C₄²×C₇₉	C₂²	1	1	yes	characteristic
35	C₂×C₂²⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
36	C₂×C₂²⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
39	#336×C₇₉	C₂²	1	1	yes	characteristic
40	#336×C₇₉	C₂²	1	1	yes	characteristic
41	C₂²×C₇₉⋊C₈	C₂³	1	2	yes	—
42	C₂²×C₇₉⋊C₈	C₂³	1	2	yes	—
43	#14579120	—	4	2	no	—
44	#14579120	—	4	2	no	—
45	C₂×C₄⋊Dic₇₉	C₂×C₄	1	2	yes	—
46	C₂×C₄⋊Dic₇₉	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄⋊Dic₇₉	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄⋊Dic₇₉	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄⋊Dic₇₉	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄⋊Dic₇₉	C₂×C₄	1	2	yes	—
51	C₂×C₄⋊Dic₇₉	C₂×C₄	1	2	yes	—
52	C₂×C₄⋊Dic₇₉	C₂×C₄	1	2	yes	—
53	C₂×C₂²⋊Dic₇₉	C₂×C₄	1	2	yes	—
54	C₂×C₂²⋊Dic₇₉	C₂×C₄	1	2	yes	—
55	C₂×C₄×Dic₇₉	C₂³	1	2	yes	—
56	C₂×C₄×Dic₇₉	C₂³	1	2	yes	—
57	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
58	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
59	Dic₇₉⋊C₈	—	4	2	no	—
60	Dic₇₉⋊C₈	—	4	2	no	—
61	C₂²⋊(C₇₉⋊C₈)	—	2	4	no	—
62	#14579071	—	4	2	no	—
63	C₈×Dic₇₉	—	4	2	no	—
64	C₇₉⋊#95	C₂×C₄	1	2	yes	—
65	C₇₉⋊#95	C₂×C₄	1	2	yes	—
66	C₇₉⋊#95	C₂×C₄	1	2	yes	—
67	C₇₉⋊#95	C₂×C₄	1	2	yes	—
68	C₂³×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
69	C₂³×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
70	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
73	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
75	C₂×C₄²×C₇₉	—	2	2	no	—
76	C₂×C₄²×C₇₉	—	2	2	no	—
77	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
78	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
79	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
80	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
81	C₂²⋊C₈×C₇₉	—	2	2	no	—
82	C₂²⋊C₈×C₇₉	Q₈	1	4	yes	—
83	C₄×C₈×C₇₉	—	2	2	no	—
84	C₄×C₈×C₇₉	—	2	2	no	—
85	C₂²×Dic₇₉	C₂²×C₄	1	2	yes	—
86	C₂²×Dic₇₉	C₂²×C₄	1	2	yes	—
87	C₂²×Dic₇₉	C₂²×C₄	1	2	yes	—
88	C₂²×Dic₇₉	C₂²×C₄	1	2	yes	—
89	C₂×C₇₉⋊C₈	—	2	2	no	—
90	C₂×C₇₉⋊C₈	—	2	2	no	—
91	C₂×C₇₉⋊C₈	—	2	2	no	—
92	C₂×C₇₉⋊C₈	—	2	2	no	—
93	C₂×C₇₉⋊C₈	—	2	2	no	—
94	C₂×C₇₉⋊C₈	—	2	2	no	—
95	C₄⋊Dic₇₉	—	2	4	no	—
96	C₄⋊Dic₇₉	—	2	2	no	—
97	C₄⋊Dic₇₉	—	2	2	no	—
98	C₄⋊Dic₇₉	—	2	2	no	—
99	C₄⋊Dic₇₉	—	2	2	no	—
100	C₄⋊Dic₇₉	—	4	2	no	—
101	C₄⋊Dic₇₉	—	4	2	no	—
102	C₄⋊Dic₇₉	—	4	2	no	—
103	C₂²⋊Dic₇₉	—	4	2	no	—
104	C₂²⋊Dic₇₉	—	4	2	no	—
105	C₄×Dic₇₉	—	2	2	no	—
106	C₄×Dic₇₉	—	2	2	no	—
107	C₄×Dic₇₉	—	2	2	no	—
108	C₄×Dic₇₉	—	2	2	no	—
109	C₂⁴×C₇₉	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₇₉	—	2	1	no	—
111	C₂²×C₄×C₇₉	—	2	1	no	—
112	C₂²×C₄×C₇₉	—	2	1	no	—
113	C₂²×C₄×C₇₉	—	2	1	no	—
114	C₂²×C₄×C₇₉	—	2	2	no	—
115	C₂²×C₄×C₇₉	—	2	2	no	—
116	C₂²×C₄×C₇₉	—	2	2	no	—
117	C₂²×C₄×C₇₉	—	2	2	no	—
118	C₂²×C₄×C₇₉	—	2	2	no	—
119	C₂²×C₄×C₇₉	—	4	1	no	—
120	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
121	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
123	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
124	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
125	C₂²×C₄×C₇₉	C₂×Q₈	1	2	yes	—
126	C₂²×C₄×C₇₉	#41	1	2	yes	—
127	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
128	C₂×C₈×C₇₉	—	2	1	no	—
129	C₂×C₈×C₇₉	—	2	1	no	—
130	C₂×C₈×C₇₉	—	2	1	no	—
131	C₂×C₈×C₇₉	—	2	1	no	—
132	C₂×C₈×C₇₉	—	2	1	no	—
133	C₂×C₈×C₇₉	—	2	1	no	—
134	C₂×C₈×C₇₉	—	2	1	no	—
135	C₂×C₈×C₇₉	—	2	1	no	—
136	C₂×C₈×C₇₉	—	2	1	no	—
137	C₂×C₈×C₇₉	—	2	1	no	—
138	C₂×C₈×C₇₉	C₂×Q₈	1	2	yes	—
139	C₂×C₈×C₇₉	C₂×Q₈	1	2	yes	—
140	C₄²×C₇₉	—	2	2	no	—
141	C₄²×C₇₉	—	2	2	no	—
142	C₄²×C₇₉	—	2	1	no	—
143	C₄²×C₇₉	—	2	1	no	—
144	C₄²×C₇₉	#41	1	2	yes	—
145	C₄²×C₇₉	#41	1	2	yes	—
146	C₂³×C₇₉	—	2	1	no	—
147	C₂³×C₇₉	—	2	1	no	—
148	C₂³×C₇₉	—	2	1	no	—
149	C₂³×C₇₉	—	2	1	no	—
150	C₂³×C₇₉	—	2	1	no	—
151	C₂³×C₇₉	—	2	1	no	—
152	C₂³×C₇₉	C₄×Q₈	1	2	yes	—
153	C₂³×C₇₉	C₂³×C₄	1	1	yes	characteristic
154	C₂×C₄×C₇₉	—	2	1	no	—
155	C₂×C₄×C₇₉	—	2	1	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	—	2	2	no	—
161	C₂×C₄×C₇₉	—	2	2	no	—
162	C₂×C₄×C₇₉	—	2	2	no	—
163	C₂×C₄×C₇₉	—	2	2	no	—
164	C₂×C₄×C₇₉	—	2	1	no	—
165	C₂×C₄×C₇₉	—	2	1	no	—
166	C₂×C₄×C₇₉	—	2	1	no	—
167	C₂×C₄×C₇₉	—	4	4	no	—
168	C₂×C₄×C₇₉	—	4	4	no	—
169	C₂×C₄×C₇₉	#117	1	2	yes	—
170	C₂×C₄×C₇₉	#117	1	2	yes	—
171	C₂×C₄×C₇₉	C₄×Q₈	1	2	yes	—
172	C₂×C₄×C₇₉	#131	1	2	yes	—
173	C₂×C₄×C₇₉	#131	1	2	yes	—
174	C₂×C₄×C₇₉	#131	1	2	yes	—
175	C₂×C₄×C₇₉	C₂²×Q₈	1	1	yes	characteristic
176	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
177	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
178	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
179	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
180	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
181	C₂×Dic₇₉	—	2	2	no	—
182	C₂×Dic₇₉	—	2	2	no	—
183	C₂×Dic₇₉	—	2	2	no	—
184	C₂×Dic₇₉	—	2	2	no	—
185	C₂×Dic₇₉	—	2	2	no	—
186	C₂×Dic₇₉	—	2	2	no	—
187	C₂×Dic₇₉	—	2	2	no	—
188	C₂×Dic₇₉	—	2	2	no	—
189	C₂×Dic₇₉	—	2	2	no	—
190	C₂×Dic₇₉	—	2	2	no	—
191	C₂×Dic₇₉	—	2	2	no	—
192	C₂×Dic₇₉	—	2	2	no	—
193	C₈×C₇₉	—	2	2	no	—
194	C₈×C₇₉	—	2	2	no	—
195	C₈×C₇₉	—	4	1	no	—
196	C₈×C₇₉	—	4	1	no	—
197	C₇₉⋊C₈	—	4	2	no	—
198	C₇₉⋊C₈	—	4	2	no	—
199	C₂²×C₇₉	—	2	2	no	—
200	C₂²×C₇₉	—	2	2	no	—
201	C₂²×C₇₉	—	2	2	no	—
202	C₂²×C₇₉	—	4	1	no	—
203	C₂²×C₇₉	—	4	1	no	—
204	C₂²×C₇₉	—	4	1	no	—
205	C₂²×C₇₉	—	4	1	no	—
206	C₂²×C₇₉	C₂×#117	1	1	yes	characteristic
207	C₂²×C₇₉	C₂×C₄×Q₈	1	1	yes	characteristic
208	C₂²×C₇₉	#518	1	1	yes	characteristic
209	C₂²×C₇₉	C₂×#131	1	1	yes	characteristic
210	C₂²×C₇₉	C₂×#131	1	1	yes	characteristic
211	C₂²×C₇₉	C₂×#131	1	1	yes	characteristic
212	C₂²×C₇₉	#568	1	1	yes	characteristic
213	C₄×C₇₉	—	2	2	no	—
214	C₄×C₇₉	—	2	2	no	—
215	C₄×C₇₉	—	2	2	no	—
216	C₄×C₇₉	—	4	1	no	—
217	C₄×C₇₉	#433	1	4	yes	—
218	C₄×C₇₉	#553	1	1	yes	characteristic
219	C₄×C₇₉	#553	1	1	yes	characteristic
220	C₄×C₇₉	#554	1	1	yes	characteristic
221	C₄×C₇₉	#554	1	1	yes	characteristic
222	Dic₇₉	—	4	2	no	—
223	Dic₇₉	—	4	2	no	—
224	Dic₇₉	—	4	2	no	—
225	Dic₇₉	—	4	2	no	—
226	#22626	—	79	1	no	maximal, Sylow
227	C₂×C₇₉	—	4	2	no	—
228	C₂×C₇₉	#2345	1	1	yes	characteristic
229	C₂×C₇₉	C₂×#433	1	1	yes	characteristic
230	C₂×C₇₉	#2924	1	1	yes	characteristic
231	C₂×C₇₉	#2960	1	1	yes	characteristic
232	C₂×C₇₉	#2962	1	1	yes	characteristic
233	C₂×C₇₉	#2979	1	1	yes	characteristic
234	C₂×C₇₉	#2981	1	1	yes	characteristic
235	#2285	—	79	1	no	—
236	#1939	—	79	1	no	—
237	#1939	—	79	1	no	—
238	#1917	—	79	2	no	—
239	#1916	—	79	2	no	—
240	#1798	—	79	2	no	—
241	#1797	—	79	1	no	—
242	#1770	—	79	1	no	—
243	C₈×C₄⋊C₄	—	79	1	no	—
244	#1750	—	79	2	no	—
245	C₄×C₂²⋊C₈	D₇₉	1	1	yes	characteristic
246	C₇₉	#22626	1	1	yes	characteristic, complemented, Sylow
247	C₂×#117	—	79	2	no	—
248	C₂²×C₄²	C₂×D₇₉	1	1	yes	characteristic
249	C₂×C₄⋊C₈	—	79	2	no	—
250	C₂×C₄⋊C₈	—	79	2	no	—
251	C₂×C₄⋊C₈	—	79	1	no	—
252	C₂×C₄⋊C₈	—	79	1	no	—
253	C₂×C₂²⋊C₈	—	79	2	no	—
254	C₂×C₂²⋊C₈	C₂×D₇₉	1	1	yes	characteristic
255	C₂×C₂²⋊C₈	C₂×D₇₉	1	1	yes	characteristic
256	C₂×#97	—	79	2	no	—
257	C₂×C₄×C₈	—	79	2	no	—
258	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
259	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
260	#384	—	79	1	no	—
261	#384	—	79	1	no	—
262	#382	—	79	2	no	—
263	#380	—	79	2	no	—
264	#380	—	79	1	no	—
265	#380	—	79	1	no	—
266	C₄×C₄⋊C₄	—	79	2	no	—
267	C₄×C₄⋊C₄	—	79	1	no	—
268	C₄×C₄⋊C₄	—	79	1	no	—
269	#336	—	79	2	no	—
270	#336	—	79	2	no	—
271	#336	—	79	2	no	—
272	#336	—	79	2	no	—
273	#336	—	79	2	no	—
274	#336	C₂×D₇₉	1	1	yes	characteristic
275	#336	C₂×D₇₉	1	1	yes	characteristic
276	C₂³×C₄	C₄×D₇₉	1	1	yes	characteristic
277	C₂³×C₄	C₄×D₇₉	1	1	yes	characteristic
278	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
279	C₂²×C₈	—	79	2	no	—
280	C₂²×C₈	—	79	2	no	—
281	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
282	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
283	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
284	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
285	#117	—	316	2	no	—
286	#117	—	316	2	no	—
287	C₂×C₄⋊C₄	—	79	2	no	—
288	C₂×C₄⋊C₄	—	79	2	no	—
289	C₂×C₄⋊C₄	—	79	2	no	—
290	C₂×C₄⋊C₄	—	79	2	no	—
291	C₂×C₄⋊C₄	—	79	1	no	—
292	C₂×C₄⋊C₄	—	79	1	no	—
293	C₂×C₄⋊C₄	—	79	1	no	—
294	C₂×C₄⋊C₄	—	79	1	no	—
295	C₂×C₂²⋊C₄	—	79	2	no	—
296	C₂×C₂²⋊C₄	—	79	2	no	—
297	C₂×C₄²	—	2	2	no	—
298	C₂×C₄²	—	2	2	no	—
299	C₂×C₄²	—	79	2	no	—
300	C₂×C₄²	—	79	2	no	—
301	C₂×C₄²	C₄×D₇₉	1	1	yes	characteristic
302	C₂×C₄²	C₄×D₇₉	1	1	yes	characteristic
303	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
304	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
305	C₄⋊C₈	—	316	2	no	—
306	C₄⋊C₈	—	316	2	no	—
307	C₄⋊C₈	—	158	2	no	—
308	C₄⋊C₈	—	158	2	no	—
309	C₂²⋊C₈	—	2	2	no	—
310	C₂²⋊C₈	—	158	4	no	—
311	C₂²⋊C₈	Dic₁₅₈	1	4	yes	—
312	#97	—	316	2	no	—
313	C₄×C₈	—	2	2	no	—
314	C₄×C₈	—	2	2	no	—
315	C₄×C₈	—	316	2	no	—
316	#95	—	79	2	no	—
317	#95	—	79	2	no	—
318	#95	—	79	2	no	—
319	#95	—	79	2	no	—
320	C₂⁴	C₂×C₄×D₇₉	1	1	yes	characteristic
321	C₂²×C₄	—	2	1	no	—
322	C₂²×C₄	—	2	1	no	—
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	4	1	no	—
331	C₂²×C₄	—	79	2	no	—
332	C₂²×C₄	—	79	2	no	—
333	C₂²×C₄	—	79	2	no	—
334	C₂²×C₄	—	79	2	no	—
335	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
336	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
337	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
338	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
339	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
340	C₂²×C₄	C₂×Dic₁₅₈	1	2	yes	—
341	C₂²×C₄	#11929624	1	2	yes	—
342	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
343	C₂×C₈	—	2	1	no	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	—	2	1	no	—
346	C₂×C₈	—	2	1	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	2	1	no	—
349	C₂×C₈	—	2	1	no	—
350	C₂×C₈	—	2	1	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	158	2	no	—
354	C₂×C₈	—	158	2	no	—
355	C₂×C₈	—	158	2	no	—
356	C₂×C₈	—	158	2	no	—
357	C₂×C₈	—	158	2	no	—
358	C₂×C₈	—	158	2	no	—
359	C₂×C₈	C₂×Dic₁₅₈	1	2	yes	—
360	C₂×C₈	C₂×Dic₁₅₈	1	2	yes	—
361	C₄⋊C₄	—	316	2	no	—
362	C₄⋊C₄	—	316	2	no	—
363	C₄⋊C₄	—	316	2	no	—
364	C₄⋊C₄	—	158	4	no	—
365	C₄⋊C₄	—	158	2	no	—
366	C₄⋊C₄	—	158	2	no	—
367	C₄⋊C₄	—	158	2	no	—
368	C₄⋊C₄	—	158	2	no	—
369	C₂²⋊C₄	—	316	2	no	—
370	C₂²⋊C₄	—	316	2	no	—
371	C₄²	—	2	1	no	—
372	C₄²	—	2	1	no	—
373	C₄²	—	2	2	no	—
374	C₄²	—	2	2	no	—
375	C₄²	—	158	2	no	—
376	C₄²	—	158	2	no	—
377	C₄²	—	158	2	no	—
378	C₄²	—	158	2	no	—
379	C₄²	#11929623	1	2	yes	—
380	C₄²	#11929623	1	2	yes	—
381	C₂³	—	2	1	no	—
382	C₂³	—	2	1	no	—
383	C₂³	—	2	1	no	—
384	C₂³	—	2	1	no	—
385	C₂³	—	2	1	no	—
386	C₂³	—	2	1	no	—
387	C₂³	C₄×Dic₁₅₈	1	2	yes	—
388	C₂³	C₂²×C₄×D₇₉	1	1	yes	characteristic
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	4	4	no	—
403	C₂×C₄	—	4	4	no	—
404	C₂×C₄	—	158	2	no	—
405	C₂×C₄	—	158	2	no	—
406	C₂×C₄	—	158	2	no	—
407	C₂×C₄	—	158	2	no	—
408	C₂×C₄	—	158	2	no	—
409	C₂×C₄	—	158	2	no	—
410	C₂×C₄	—	158	2	no	—
411	C₂×C₄	—	158	2	no	—
412	C₂×C₄	—	158	2	no	—
413	C₂×C₄	—	158	2	no	—
414	C₂×C₄	—	158	2	no	—
415	C₂×C₄	—	158	2	no	—
416	C₂×C₄	#14579117	1	2	yes	—
417	C₂×C₄	#14579117	1	2	yes	—
418	C₂×C₄	C₄×Dic₁₅₈	1	2	yes	—
419	C₂×C₄	#14579167	1	2	yes	—
420	C₂×C₄	#14579167	1	2	yes	—
421	C₂×C₄	#14579169	1	2	yes	—
422	C₂×C₄	C₂²×Dic₁₅₈	1	1	yes	characteristic
423	C₂×C₄	C₂×#11929623	1	1	yes	characteristic
424	C₂×C₄	C₂×#11929623	1	1	yes	characteristic
425	C₂×C₄	C₂×#11929624	1	1	yes	characteristic
426	C₂×C₄	#14579207	1	1	yes	characteristic
427	C₂×C₄	#14579207	1	1	yes	characteristic
428	C₈	—	2	2	no	—
429	C₈	—	2	2	no	—
430	C₈	—	4	1	no	—
431	C₈	—	4	1	no	—
432	C₈	—	316	2	no	—
433	C₈	—	316	2	no	—
434	C₂²	—	2	2	no	—
435	C₂²	—	2	2	no	—
436	C₂²	—	2	2	no	—
437	C₂²	—	4	1	no	—
438	C₂²	—	4	1	no	—
439	C₂²	—	4	1	no	—
440	C₂²	—	4	1	no	—
441	C₂²	C₂×#14579117	1	1	yes	characteristic
442	C₂²	C₂×C₄×Dic₁₅₈	1	1	yes	characteristic
443	C₂²	#19099037	1	1	yes	characteristic
444	C₂²	C₂×#14579167	1	1	yes	characteristic
445	C₂²	C₂×#14579167	1	1	yes	characteristic
446	C₂²	C₂×#14579169	1	1	yes	characteristic
447	C₂²	#19099329	1	1	yes	characteristic
448	C₄	—	2	2	no	—
449	C₄	—	2	2	no	—
450	C₄	—	2	2	no	—
451	C₄	—	4	1	no	—
452	C₄	—	316	2	no	—
453	C₄	—	316	2	no	—
454	C₄	—	316	2	no	—
455	C₄	—	316	2	no	—
456	C₄	#19098621	1	4	yes	—
457	C₄	#19099259	1	1	yes	characteristic
458	C₄	#19099259	1	1	yes	characteristic
459	C₄	#19099270	1	1	yes	characteristic
460	C₄	#19099270	1	1	yes	characteristic
461	C₂	—	4	2	no	—
462	C₂	#23766275	1	1	yes	characteristic
463	C₂	C₂×#19098621	1	1	yes	characteristic
464	C₂	#23772054	1	1	yes	characteristic
465	C₂	#23772334	1	1	yes	characteristic
466	C₂	#23772347	1	1	yes	characteristic
467	C₂	#23772466	1	1	yes	characteristic
468	C₂	#23772475	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₇₉
commutator, socle	C₂³×C₇₉	C₂³×C₄
Fitting	C₄×C₂²⋊C₈×C₇₉	C₂
prime radical	C₂⁴×C₇₉	C₂²×C₄
cosocle	C₂²×C₄×C₇₉	C₂⁴
hypercenter	C₄×C₂²⋊C₈	D₇₉
hypocenter	C₇₉	#22626
LCS	G ▷ C₂³×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₄×C₂²⋊C₈

Complements

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

N	H ≅ G/N	type
2. #23764118	C₂	semidirect
3. #23764118	C₂	semidirect
4. #23763963	C₂	semidirect
5. #23763956	C₂	semidirect
8. #23763267	C₂	semidirect
9. C₈×C₄⋊Dic₇₉	C₂	semidirect
246. C₇₉	#22626	semidirect

Maximal subgroups

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

subgroup	index
#23765807	2
#23764118	2
#23763963	2
#23763956	2
#23763382	2
#23763380	2
#23763267	2
C₈×C₄⋊Dic₇₉	2
#23763168	2
C₄×C₂²⋊C₈×C₇₉	2
#22626	79