Subgroups — #34255477

Order 20224.

1102 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23772435	C₂	1	1	yes	maximal, characteristic, complemented
2	#23765761	C₂	1	1	yes	maximal, characteristic, complemented
3	#23761925	C₂	1	1	yes	maximal, characteristic, complemented
4	#23761920	C₂	1	2	yes	maximal, complemented
5	#23761912	C₂	1	1	yes	maximal, characteristic, complemented
6	#23761904	C₂	1	2	yes	maximal, complemented
7	#23761899	C₂	1	1	yes	maximal, characteristic, complemented
8	#23761891	C₂	1	2	yes	maximal, complemented
9	#23761886	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#19098300	C₂	1	2	yes	maximal, complemented
11	C₇₉×#3520	C₂	1	1	yes	maximal, characteristic
12	C₂×D₄×Dic₇₉	—	2	1	no	—
13	#19098641	—	2	1	no	—
14	#19098635	—	2	2	no	—
15	D₄×C₇₉⋊C₈	—	2	1	no	—
16	#19098620	C₂²	1	1	yes	characteristic
17	#19098616	C₂²	1	1	yes	characteristic
18	#19098527	C₂²	1	2	yes	—
19	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
20	C₄⋊C₄×Dic₇₉	—	2	1	no	—
21	C₄×C₄⋊Dic₇₉	C₂²	1	1	yes	characteristic
22	C₂²⋊C₄×Dic₇₉	—	2	2	no	—
23	C₄×C₂²⋊Dic₇₉	C₂²	1	2	yes	—
24	#19098409	C₂²	1	1	yes	characteristic
25	C₂×C₇₉⋊#95	C₂²	1	2	yes	—
26	#19098300	C₂²	1	1	yes	characteristic
27	#19098300	C₂²	1	2	yes	—
28	#19098300	C₂²	1	2	yes	—
29	#19098300	C₂²	1	2	yes	—
30	#19098300	C₂²	1	1	yes	characteristic
31	#19098300	C₂²	1	2	yes	—
32	#19098300	C₂²	1	2	yes	—
33	#19098297	C₂²	1	2	yes	—
34	#19098297	C₂²	1	1	yes	characteristic
35	#19098297	C₂²	1	1	yes	characteristic
36	#556×C₇₉	C₄	1	1	yes	characteristic, complemented
37	#554×C₇₉	—	2	1	no	—
38	#552×C₇₉	C₄	1	2	yes	complemented
39	#551×C₇₉	—	2	2	no	—
40	D₄×Q₈×C₇₉	C₄	1	1	yes	characteristic, complemented
41	#548×C₇₉	C₄	1	2	yes	complemented
42	#547×C₇₉	C₄	1	1	yes	characteristic, complemented
43	#547×C₇₉	C₄	1	1	yes	characteristic, complemented
44	#546×C₇₉	—	2	1	no	—
45	#542×C₇₉	—	2	1	no	—
46	#539×C₇₉	—	2	2	no	—
47	#533×C₇₉	C₂²	1	1	yes	characteristic
48	#529×C₇₉	C₂²	1	1	yes	characteristic
49	#525×C₇₉	C₂²	1	2	yes	—
50	C₂×C₂²⋊Q₈×C₇₉	C₂²	1	2	yes	—
51	#520×C₇₉	—	2	1	no	—
52	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
53	C₂³×Dic₇₉	—	2	2	no	—
54	C₂×#11929608	—	2	2	no	—
55	C₂²×C₇₉⋊C₈	—	2	2	no	—
56	D₄×Dic₇₉	—	2	8	no	—
57	C₂×C₄⋊Dic₇₉	—	2	1	no	—
58	C₂×C₂²⋊Dic₇₉	—	2	2	no	—
59	C₂×C₄×Dic₇₉	—	2	1	no	—
60	C₂×C₄×Dic₇₉	—	2	2	no	—
61	C₂×C₄×Dic₇₉	—	2	1	no	—
62	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
63	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
64	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
65	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
66	C₂²⋊(C₇₉⋊C₈)	C₂³	1	1	yes	characteristic
67	C₂²⋊(C₇₉⋊C₈)	C₂³	1	2	yes	—
68	C₂²⋊(C₇₉⋊C₈)	C₂³	1	1	yes	characteristic
69	#14579072	—	2	1	no	—
70	C₄×C₇₉⋊C₈	—	2	1	no	—
71	C₇₉⋊#95	—	2	2	no	—
72	C₇₉⋊#95	—	2	1	no	—
73	C₇₉⋊#95	C₂³	1	1	yes	characteristic
74	C₇₉⋊#95	C₂³	1	2	yes	—
75	C₇₉⋊#95	C₂³	1	1	yes	characteristic
76	C₂×#41×C₇₉	—	2	1	no	—
77	C₂×#41×C₇₉	C₂×C₄	1	2	yes	complemented
78	C₂²×Q₈×C₇₉	C₂×C₄	1	2	yes	complemented
79	C₂²×D₄×C₇₉	D₄	1	1	yes	characteristic
80	C₂³×C₄×C₇₉	C₂³	1	2	yes	—
81	C₄⋊Q₈×C₇₉	—	2	1	no	—
82	C₄⋊Q₈×C₇₉	C₂×C₄	1	1	yes	characteristic, complemented
83	C₄⋊Q₈×C₇₉	C₂×C₄	1	1	yes	characteristic, complemented
84	#126×C₇₉	—	2	2	no	—
85	#126×C₇₉	—	2	2	no	—
86	#126×C₇₉	—	2	1	no	—
87	#125×C₇₉	—	2	2	no	—
88	#125×C₇₉	—	2	1	no	—
89	#125×C₇₉	C₂×C₄	1	1	yes	characteristic, complemented
90	#124×C₇₉	—	2	1	no	—
91	#124×C₇₉	—	2	2	no	—
92	#124×C₇₉	C₂×C₄	1	1	yes	characteristic, complemented
93	#123×C₇₉	—	2	2	no	—
94	#123×C₇₉	—	2	2	no	—
95	#123×C₇₉	—	2	1	no	—
96	#123×C₇₉	—	2	2	no	—
97	#123×C₇₉	—	2	2	no	—
98	C₂²⋊Q₈×C₇₉	—	2	2	no	—
99	C₂²⋊Q₈×C₇₉	—	2	2	no	—
100	C₂²⋊Q₈×C₇₉	—	2	1	no	—
101	C₂²⋊Q₈×C₇₉	—	2	2	no	—
102	C₂²⋊Q₈×C₇₉	—	2	1	no	—
103	C₂²⋊Q₈×C₇₉	—	2	2	no	—
104	C₂²⋊Q₈×C₇₉	C₂×C₄	1	2	yes	complemented
105	C₂²⋊Q₈×C₇₉	C₂×C₄	1	2	yes	complemented
106	C₂²⋊Q₈×C₇₉	C₂×C₄	1	2	yes	complemented
107	C₂²⋊Q₈×C₇₉	C₂³	1	1	yes	characteristic
108	C₂²⋊Q₈×C₇₉	C₂³	1	2	yes	—
109	#121×C₇₉	—	2	2	no	—
110	#121×C₇₉	—	2	1	no	—
111	#121×C₇₉	C₂×C₄	1	2	yes	complemented
112	#121×C₇₉	C₂³	1	1	yes	characteristic
113	#120×C₇₉	—	2	2	no	—
114	C₄×Q₈×C₇₉	—	2	1	no	—
115	C₄×Q₈×C₇₉	—	2	1	no	—
116	C₄×Q₈×C₇₉	C₂×C₄	1	1	yes	characteristic, complemented
117	C₄×Q₈×C₇₉	C₂×C₄	1	2	yes	complemented
118	C₄×D₄×C₇₉	—	2	1	no	—
119	C₄×D₄×C₇₉	—	2	2	no	—
120	C₄×D₄×C₇₉	—	2	2	no	—
121	C₄×D₄×C₇₉	—	2	1	no	—
122	C₄×D₄×C₇₉	—	2	2	no	—
123	C₄×D₄×C₇₉	C₂×C₄	1	1	yes	characteristic
124	C₄×D₄×C₇₉	C₂×C₄	1	1	yes	characteristic
125	C₄×D₄×C₇₉	C₂×C₄	1	2	yes	—
126	C₄×D₄×C₇₉	C₂×C₄	1	1	yes	characteristic, complemented
127	C₄×D₄×C₇₉	D₄	1	1	yes	characteristic
128	C₄×D₄×C₇₉	D₄	1	2	yes	—
129	C₄×D₄×C₇₉	D₄	1	1	yes	characteristic
130	#117×C₇₉	—	2	1	no	—
131	#117×C₇₉	—	2	2	no	—
132	#117×C₇₉	—	2	1	no	—
133	#117×C₇₉	C₂×C₄	1	2	yes	complemented
134	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
135	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
136	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	2	yes	complemented
137	C₂×C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
138	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
139	C₂×C₂²⋊C₄×C₇₉	D₄	1	2	yes	—
140	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
141	C₂²×Dic₇₉	—	2	8	no	—
142	C₂²×Dic₇₉	—	2	1	no	—
143	C₂²×Dic₇₉	—	2	1	no	—
144	C₂²×Dic₇₉	—	2	2	no	—
145	C₂²×Dic₇₉	—	8	2	no	—
146	C₂²×Dic₇₉	—	8	2	no	—
147	#11929608	—	8	2	no	—
148	C₂×C₇₉⋊C₈	—	2	1	no	—
149	C₂×C₇₉⋊C₈	—	2	1	no	—
150	C₂×C₇₉⋊C₈	—	2	2	no	—
151	C₂×C₇₉⋊C₈	—	8	2	no	—
152	C₄⋊Dic₇₉	—	2	4	no	—
153	C₂²⋊Dic₇₉	—	2	8	no	—
154	C₄×Dic₇₉	—	2	4	no	—
155	C₄×Dic₇₉	—	8	1	no	—
156	C₄×Dic₇₉	—	8	2	no	—
157	C₂⁴×C₇₉	C₂×D₄	1	2	yes	—
158	#41×C₇₉	—	4	4	no	—
159	#41×C₇₉	—	8	2	no	—
160	C₂×Q₈×C₇₉	—	2	1	no	—
161	C₂×Q₈×C₇₉	—	2	2	no	—
162	C₂×Q₈×C₇₉	—	8	2	no	—
163	C₂×Q₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
164	C₂×Q₈×C₇₉	C₂²×C₄	1	2	yes	—
165	C₂×D₄×C₇₉	—	2	4	no	—
166	C₂×D₄×C₇₉	—	2	2	no	—
167	C₂×D₄×C₇₉	—	2	1	no	—
168	C₂×D₄×C₇₉	—	2	2	no	—
169	C₂×D₄×C₇₉	C₂²⋊C₄	1	2	yes	—
170	C₂×D₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
171	C₂×D₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
172	C₂×D₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
173	C₂²×C₄×C₇₉	—	2	2	no	—
174	C₂²×C₄×C₇₉	—	2	2	no	—
175	C₂²×C₄×C₇₉	—	2	1	no	—
176	C₂²×C₄×C₇₉	—	2	2	no	—
177	C₂²×C₄×C₇₉	—	8	2	no	—
178	C₂²×C₄×C₇₉	C₂²×C₄	1	2	yes	—
179	C₂²×C₄×C₇₉	C₂²×C₄	1	2	yes	—
180	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
181	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
182	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
183	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
184	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
185	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
186	C₄⋊C₄×C₇₉	—	2	2	no	—
187	C₄⋊C₄×C₇₉	—	2	1	no	—
188	C₄⋊C₄×C₇₉	—	2	2	no	—
189	C₄⋊C₄×C₇₉	—	2	2	no	—
190	C₄⋊C₄×C₇₉	—	2	1	no	—
191	C₄⋊C₄×C₇₉	—	2	1	no	—
192	C₄⋊C₄×C₇₉	—	2	1	no	—
193	C₄⋊C₄×C₇₉	—	2	2	no	—
194	C₄⋊C₄×C₇₉	—	2	1	no	—
195	C₄⋊C₄×C₇₉	—	2	2	no	—
196	C₄⋊C₄×C₇₉	—	2	1	no	—
197	C₄⋊C₄×C₇₉	—	2	1	no	—
198	C₄⋊C₄×C₇₉	—	2	2	no	—
199	C₄⋊C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
200	C₄⋊C₄×C₇₉	C₂²⋊C₄	1	2	yes	—
201	C₄⋊C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
202	C₄⋊C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
203	C₄⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
204	C₄⋊C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
205	C₂²⋊C₄×C₇₉	—	2	2	no	—
206	C₂²⋊C₄×C₇₉	—	2	2	no	—
207	C₂²⋊C₄×C₇₉	—	2	2	no	—
208	C₂²⋊C₄×C₇₉	—	2	2	no	—
209	C₂²⋊C₄×C₇₉	—	2	1	no	—
210	C₂²⋊C₄×C₇₉	—	2	2	no	—
211	C₂²⋊C₄×C₇₉	—	2	1	no	—
212	C₂²⋊C₄×C₇₉	—	2	1	no	—
213	C₂²⋊C₄×C₇₉	—	2	2	no	—
214	C₂²⋊C₄×C₇₉	—	2	1	no	—
215	C₂²⋊C₄×C₇₉	—	2	1	no	—
216	C₂²⋊C₄×C₇₉	C₂²⋊C₄	1	2	yes	—
217	C₂²⋊C₄×C₇₉	C₂²⋊C₄	1	2	yes	—
218	C₂²⋊C₄×C₇₉	C₂²⋊C₄	1	2	yes	—
219	C₂²⋊C₄×C₇₉	C₂²⋊C₄	1	2	yes	—
220	C₄²×C₇₉	—	2	2	no	—
221	C₄²×C₇₉	—	2	2	no	—
222	C₄²×C₇₉	—	2	1	no	—
223	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
224	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
225	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
226	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
227	C₂³×C₇₉	—	2	2	no	—
228	C₂³×C₇₉	—	2	2	no	—
229	C₂³×C₇₉	—	2	4	no	—
230	C₂³×C₇₉	—	2	1	no	—
231	C₂³×C₇₉	—	4	2	no	—
232	C₂³×C₇₉	C₂×C₂²⋊C₄	1	2	yes	—
233	C₂³×C₇₉	C₂×C₂²⋊C₄	1	2	yes	—
234	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
235	Q₈×C₇₉	—	4	1	no	—
236	Q₈×C₇₉	—	4	2	no	—
237	Q₈×C₇₉	—	4	2	no	—
238	Q₈×C₇₉	—	8	2	no	—
239	D₄×C₇₉	—	2	4	no	—
240	D₄×C₇₉	—	2	2	no	—
241	D₄×C₇₉	—	4	1	no	—
242	D₄×C₇₉	—	4	1	no	—
243	D₄×C₇₉	—	4	1	no	—
244	D₄×C₇₉	—	4	4	no	—
245	D₄×C₇₉	—	8	2	no	—
246	D₄×C₇₉	#104	1	4	yes	—
247	C₂×C₄×C₇₉	—	2	1	no	—
248	C₂×C₄×C₇₉	—	2	1	no	—
249	C₂×C₄×C₇₉	—	2	2	no	—
250	C₂×C₄×C₇₉	—	2	1	no	—
251	C₂×C₄×C₇₉	—	2	2	no	—
252	C₂×C₄×C₇₉	—	2	1	no	—
253	C₂×C₄×C₇₉	—	2	2	no	—
254	C₂×C₄×C₇₉	—	2	1	no	—
255	C₂×C₄×C₇₉	—	4	2	no	—
256	C₂×C₄×C₇₉	—	4	2	no	—
257	C₂×C₄×C₇₉	—	4	2	no	—
258	C₂×C₄×C₇₉	—	4	1	no	—
259	C₂×C₄×C₇₉	—	4	2	no	—
260	C₂×C₄×C₇₉	—	4	2	no	—
261	C₂×C₄×C₇₉	—	4	4	no	—
262	C₂×C₄×C₇₉	—	4	2	no	—
263	C₂×C₄×C₇₉	—	8	2	no	—
264	C₂×C₄×C₇₉	—	8	2	no	—
265	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
266	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	2	yes	—
267	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
268	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
269	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	2	yes	—
270	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
271	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
272	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
273	C₂×Dic₇₉	—	2	2	no	—
274	C₂×Dic₇₉	—	2	2	no	—
275	C₂×Dic₇₉	—	2	4	no	—
276	C₂×Dic₇₉	—	4	1	no	—
277	C₂×Dic₇₉	—	4	2	no	—
278	C₂×Dic₇₉	—	4	1	no	—
279	C₂×Dic₇₉	—	4	2	no	—
280	C₂×Dic₇₉	—	4	1	no	—
281	C₂×Dic₇₉	—	4	1	no	—
282	C₂×Dic₇₉	—	8	8	no	—
283	C₇₉⋊C₈	—	4	1	no	—
284	C₇₉⋊C₈	—	4	2	no	—
285	C₇₉⋊C₈	—	4	1	no	—
286	C₂²×C₇₉	—	2	1	no	—
287	C₂²×C₇₉	—	2	2	no	—
288	C₂²×C₇₉	—	2	2	no	—
289	C₂²×C₇₉	—	2	1	no	—
290	C₂²×C₇₉	—	2	2	no	—
291	C₂²×C₇₉	—	2	2	no	—
292	C₂²×C₇₉	—	2	2	no	—
293	C₂²×C₇₉	—	4	4	no	—
294	C₂²×C₇₉	—	4	4	no	—
295	C₂²×C₇₉	—	4	1	no	—
296	C₂²×C₇₉	—	4	1	no	—
297	C₂²×C₇₉	—	4	1	no	—
298	C₂²×C₇₉	C₂×#104	1	4	yes	—
299	C₂²×C₇₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
300	C₂²×C₇₉	#577	1	1	yes	characteristic
301	C₂²×C₇₉	#578	1	1	yes	characteristic
302	C₄×C₇₉	—	2	1	no	—
303	C₄×C₇₉	—	2	1	no	—
304	C₄×C₇₉	—	2	2	no	—
305	C₄×C₇₉	—	2	2	no	—
306	C₄×C₇₉	—	2	1	no	—
307	C₄×C₇₉	—	2	1	no	—
308	C₄×C₇₉	—	2	1	no	—
309	C₄×C₇₉	—	4	2	no	—
310	C₄×C₇₉	—	4	1	no	—
311	C₄×C₇₉	—	4	1	no	—
312	C₄×C₇₉	—	4	1	no	—
313	C₄×C₇₉	—	4	2	no	—
314	C₄×C₇₉	C₂×#104	1	2	yes	—
315	Dic₇₉	—	4	2	no	—
316	Dic₇₉	—	4	4	no	—
317	Dic₇₉	—	4	2	no	—
318	#17548	—	79	1	no	maximal, Sylow
319	C₂×C₇₉	—	2	1	no	—
320	C₂×C₇₉	—	2	1	no	—
321	C₂×C₇₉	—	2	4	no	—
322	C₂×C₇₉	—	4	2	no	—
323	C₂×C₇₉	—	8	1	no	—
324	C₂×C₇₉	#2883	1	1	yes	characteristic
325	C₂×C₇₉	#2898	1	1	yes	characteristic
326	C₂×C₇₉	C₂²×#104	1	1	yes	characteristic
327	#3520	D₇₉	1	1	yes	characteristic
328	#2974	—	79	1	no	—
329	#2275	—	79	1	no	—
330	#1509	—	79	1	no	—
331	#1508	—	79	2	no	—
332	#1506	—	79	1	no	—
333	#1504	—	79	2	no	—
334	#1503	—	79	1	no	—
335	#1501	—	79	2	no	—
336	#1500	—	79	1	no	—
337	C₂×#328	—	79	2	no	—
338	C₇₉	#17548	1	1	yes	characteristic, complemented, Sylow
339	#556	Dic₇₉	1	1	yes	characteristic, complemented
340	#554	—	2	1	no	—
341	#552	Dic₇₉	1	2	yes	complemented
342	#551	—	2	2	no	—
343	D₄×Q₈	Dic₇₉	1	1	yes	characteristic, complemented
344	#548	Dic₇₉	1	2	yes	complemented
345	#547	Dic₇₉	1	1	yes	characteristic, complemented
346	#547	Dic₇₉	1	1	yes	characteristic, complemented
347	#546	—	2	1	no	—
348	#542	—	2	1	no	—
349	#539	—	2	2	no	—
350	#533	C₂×D₇₉	1	1	yes	characteristic
351	#529	C₂×D₇₉	1	1	yes	characteristic
352	#525	C₂×D₇₉	1	2	yes	—
353	C₂×C₂²⋊Q₈	C₂×D₇₉	1	2	yes	—
354	#520	—	2	1	no	—
355	C₂×C₄×D₄	—	158	1	no	—
356	C₂×C₄×D₄	C₂×D₇₉	1	1	yes	characteristic
357	#436	—	158	1	no	—
358	#435	—	158	2	no	—
359	C₈×D₄	—	158	1	no	—
360	#432	—	79	1	no	—
361	#431	—	79	1	no	—
362	#407	—	79	2	no	—
363	C₂×C₂²⋊C₈	—	79	2	no	—
364	C₄×C₄⋊C₄	—	79	1	no	—
365	C₄×C₄⋊C₄	—	158	1	no	—
366	C₄×C₂²⋊C₄	—	79	2	no	—
367	C₄×C₂²⋊C₄	—	158	2	no	—
368	#376	—	79	1	no	—
369	C₂×#95	—	79	2	no	—
370	#328	—	79	1	no	—
371	#328	—	79	2	no	—
372	#328	—	79	2	no	—
373	#328	—	79	2	no	—
374	#328	—	79	1	no	—
375	#328	—	79	2	no	—
376	#328	—	79	2	no	—
377	#327	—	79	1	no	—
378	#327	—	79	1	no	—
379	#327	—	79	2	no	—
380	C₂×#41	—	2	1	no	—
381	C₂×#41	C₂×Dic₇₉	1	2	yes	complemented
382	C₂²×Q₈	C₂×Dic₇₉	1	2	yes	complemented
383	C₂²×D₄	C₂²⋊D₇₉	1	1	yes	characteristic
384	C₂³×C₄	—	158	2	no	—
385	C₂³×C₄	C₂²×D₇₉	1	2	yes	—
386	C₂×M₁₆	—	158	2	no	—
387	C₂²×C₈	—	158	2	no	—
388	C₄⋊Q₈	—	2	1	no	—
389	C₄⋊Q₈	C₂×Dic₇₉	1	1	yes	characteristic, complemented
390	C₄⋊Q₈	C₂×Dic₇₉	1	1	yes	characteristic, complemented
391	#126	—	2	2	no	—
392	#126	—	2	2	no	—
393	#126	—	2	1	no	—
394	#125	—	2	2	no	—
395	#125	—	2	1	no	—
396	#125	C₂×Dic₇₉	1	1	yes	characteristic, complemented
397	#124	—	2	1	no	—
398	#124	—	2	2	no	—
399	#124	C₂×Dic₇₉	1	1	yes	characteristic, complemented
400	#123	—	2	2	no	—
401	#123	—	2	2	no	—
402	#123	—	2	1	no	—
403	#123	—	2	2	no	—
404	#123	—	2	2	no	—
405	C₂²⋊Q₈	—	2	2	no	—
406	C₂²⋊Q₈	—	2	2	no	—
407	C₂²⋊Q₈	—	2	1	no	—
408	C₂²⋊Q₈	—	2	2	no	—
409	C₂²⋊Q₈	—	2	1	no	—
410	C₂²⋊Q₈	—	2	2	no	—
411	C₂²⋊Q₈	C₂×Dic₇₉	1	2	yes	complemented
412	C₂²⋊Q₈	C₂×Dic₇₉	1	2	yes	complemented
413	C₂²⋊Q₈	C₂×Dic₇₉	1	2	yes	complemented
414	C₂²⋊Q₈	C₂²×D₇₉	1	1	yes	characteristic
415	C₂²⋊Q₈	C₂²×D₇₉	1	2	yes	—
416	#121	—	2	2	no	—
417	#121	—	2	1	no	—
418	#121	C₂×Dic₇₉	1	2	yes	complemented
419	#121	C₂²×D₇₉	1	1	yes	characteristic
420	#120	—	2	2	no	—
421	C₄×Q₈	—	2	1	no	—
422	C₄×Q₈	—	2	1	no	—
423	C₄×Q₈	C₂×Dic₇₉	1	1	yes	characteristic, complemented
424	C₄×Q₈	C₂×Dic₇₉	1	2	yes	complemented
425	C₄×D₄	—	2	1	no	—
426	C₄×D₄	—	2	2	no	—
427	C₄×D₄	—	2	2	no	—
428	C₄×D₄	—	2	1	no	—
429	C₄×D₄	—	2	2	no	—
430	C₄×D₄	—	158	8	no	—
431	C₄×D₄	C₂×Dic₇₉	1	1	yes	characteristic
432	C₄×D₄	C₂×Dic₇₉	1	1	yes	characteristic
433	C₄×D₄	C₂×Dic₇₉	1	2	yes	—
434	C₄×D₄	C₂×Dic₇₉	1	1	yes	characteristic, complemented
435	C₄×D₄	C₂²⋊D₇₉	1	1	yes	characteristic
436	C₄×D₄	C₂²⋊D₇₉	1	2	yes	—
437	C₄×D₄	C₂²⋊D₇₉	1	1	yes	characteristic
438	#117	—	2	1	no	—
439	#117	—	2	2	no	—
440	#117	—	2	1	no	—
441	#117	C₂×Dic₇₉	1	2	yes	complemented
442	C₂×C₄⋊C₄	—	2	2	no	—
443	C₂×C₄⋊C₄	—	2	1	no	—
444	C₂×C₄⋊C₄	—	158	1	no	—
445	C₂×C₄⋊C₄	C₂×Dic₇₉	1	2	yes	complemented
446	C₂×C₄⋊C₄	C₂²⋊D₇₉	1	1	yes	characteristic
447	C₂×C₂²⋊C₄	—	2	2	no	—
448	C₂×C₂²⋊C₄	—	158	2	no	—
449	C₂×C₂²⋊C₄	C₂²⋊D₇₉	1	2	yes	—
450	C₂×C₄²	—	158	2	no	—
451	C₂×C₄²	—	158	1	no	—
452	C₂×C₄²	—	158	1	no	—
453	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
454	C₄⋊C₈	—	158	1	no	—
455	C₄⋊C₈	—	158	1	no	—
456	C₂²⋊C₈	—	79	1	no	—
457	C₂²⋊C₈	—	79	2	no	—
458	C₂²⋊C₈	—	79	1	no	—
459	C₂²⋊C₈	—	158	2	no	—
460	C₂²⋊C₈	—	158	2	no	—
461	#97	—	158	1	no	—
462	C₄×C₈	—	158	1	no	—
463	#95	—	79	1	no	—
464	#95	—	79	2	no	—
465	#95	—	79	1	no	—
466	#95	—	158	2	no	—
467	#95	—	158	1	no	—
468	C₂⁴	C₂×C₂²⋊D₇₉	1	2	yes	—
469	#41	—	4	4	no	—
470	#41	—	8	2	no	—
471	C₂×Q₈	—	2	1	no	—
472	C₂×Q₈	—	2	2	no	—
473	C₂×Q₈	—	8	2	no	—
474	C₂×Q₈	C₂²×Dic₇₉	1	1	yes	characteristic
475	C₂×Q₈	C₂²×Dic₇₉	1	2	yes	—
476	C₂×D₄	—	2	4	no	—
477	C₂×D₄	—	2	2	no	—
478	C₂×D₄	—	2	1	no	—
479	C₂×D₄	—	2	2	no	—
480	C₂×D₄	C₂²⋊Dic₇₉	1	2	yes	—
481	C₂×D₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
482	C₂×D₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
483	C₂×D₄	C₂²×Dic₇₉	1	1	yes	characteristic
484	C₂²×C₄	—	2	2	no	—
485	C₂²×C₄	—	2	2	no	—
486	C₂²×C₄	—	2	1	no	—
487	C₂²×C₄	—	2	2	no	—
488	C₂²×C₄	—	8	2	no	—
489	C₂²×C₄	—	632	2	no	—
490	C₂²×C₄	—	632	2	no	—
491	C₂²×C₄	—	158	1	no	—
492	C₂²×C₄	—	158	1	no	—
493	C₂²×C₄	—	158	2	no	—
494	C₂²×C₄	—	158	8	no	—
495	C₂²×C₄	C₂²×Dic₇₉	1	2	yes	—
496	C₂²×C₄	C₂²×Dic₇₉	1	2	yes	—
497	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
498	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
499	C₂²×C₄	C₂×C₂²⋊D₇₉	1	2	yes	—
500	C₂²×C₄	C₂×C₂²⋊D₇₉	1	2	yes	—
501	C₂²×C₄	C₂×C₂²⋊D₇₉	1	2	yes	—
502	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
503	M₁₆	—	632	2	no	—
504	C₂×C₈	—	632	2	no	—
505	C₂×C₈	—	158	1	no	—
506	C₂×C₈	—	158	1	no	—
507	C₂×C₈	—	158	2	no	—
508	C₄⋊C₄	—	2	2	no	—
509	C₄⋊C₄	—	2	1	no	—
510	C₄⋊C₄	—	2	2	no	—
511	C₄⋊C₄	—	2	2	no	—
512	C₄⋊C₄	—	2	1	no	—
513	C₄⋊C₄	—	2	1	no	—
514	C₄⋊C₄	—	2	1	no	—
515	C₄⋊C₄	—	2	2	no	—
516	C₄⋊C₄	—	2	1	no	—
517	C₄⋊C₄	—	2	2	no	—
518	C₄⋊C₄	—	2	1	no	—
519	C₄⋊C₄	—	2	1	no	—
520	C₄⋊C₄	—	2	2	no	—
521	C₄⋊C₄	—	158	4	no	—
522	C₄⋊C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
523	C₄⋊C₄	C₂²⋊Dic₇₉	1	2	yes	—
524	C₄⋊C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
525	C₄⋊C₄	C₂²×Dic₇₉	1	1	yes	characteristic
526	C₄⋊C₄	C₂²×Dic₇₉	1	2	yes	—
527	C₄⋊C₄	C₂²×Dic₇₉	1	1	yes	characteristic
528	C₂²⋊C₄	—	2	2	no	—
529	C₂²⋊C₄	—	2	2	no	—
530	C₂²⋊C₄	—	2	2	no	—
531	C₂²⋊C₄	—	2	2	no	—
532	C₂²⋊C₄	—	2	1	no	—
533	C₂²⋊C₄	—	2	2	no	—
534	C₂²⋊C₄	—	2	1	no	—
535	C₂²⋊C₄	—	2	1	no	—
536	C₂²⋊C₄	—	2	2	no	—
537	C₂²⋊C₄	—	2	1	no	—
538	C₂²⋊C₄	—	2	1	no	—
539	C₂²⋊C₄	—	158	8	no	—
540	C₂²⋊C₄	C₂²⋊Dic₇₉	1	2	yes	—
541	C₂²⋊C₄	C₂²⋊Dic₇₉	1	2	yes	—
542	C₂²⋊C₄	C₂²⋊Dic₇₉	1	2	yes	—
543	C₂²⋊C₄	C₂²⋊Dic₇₉	1	2	yes	—
544	C₄²	—	2	2	no	—
545	C₄²	—	2	2	no	—
546	C₄²	—	2	1	no	—
547	C₄²	—	632	1	no	—
548	C₄²	—	632	2	no	—
549	C₄²	—	158	4	no	—
550	C₄²	C₂²×Dic₇₉	1	1	yes	characteristic
551	C₄²	C₂²×Dic₇₉	1	1	yes	characteristic
552	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
553	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
554	C₂³	—	2	4	no	—
555	C₂³	—	2	2	no	—
556	C₂³	—	2	2	no	—
557	C₂³	—	2	1	no	—
558	C₂³	—	4	2	no	—
559	C₂³	C₂×C₂²⋊Dic₇₉	1	2	yes	—
560	C₂³	C₂×C₂²⋊Dic₇₉	1	2	yes	—
561	C₂³	C₂²×C₂²⋊D₇₉	1	1	yes	characteristic
562	Q₈	—	4	1	no	—
563	Q₈	—	4	2	no	—
564	Q₈	—	4	2	no	—
565	Q₈	—	8	2	no	—
566	D₄	—	2	4	no	—
567	D₄	—	2	2	no	—
568	D₄	—	4	1	no	—
569	D₄	—	4	4	no	—
570	D₄	—	4	1	no	—
571	D₄	—	4	1	no	—
572	D₄	—	8	2	no	—
573	D₄	#14579088	1	4	yes	—
574	C₂×C₄	—	2	1	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	2	2	no	—
577	C₂×C₄	—	2	1	no	—
578	C₂×C₄	—	2	2	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	2	2	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	4	2	no	—
583	C₂×C₄	—	4	2	no	—
584	C₂×C₄	—	4	2	no	—
585	C₂×C₄	—	4	1	no	—
586	C₂×C₄	—	4	2	no	—
587	C₂×C₄	—	4	2	no	—
588	C₂×C₄	—	4	4	no	—
589	C₂×C₄	—	4	2	no	—
590	C₂×C₄	—	8	2	no	—
591	C₂×C₄	—	8	2	no	—
592	C₂×C₄	—	316	1	no	—
593	C₂×C₄	—	316	2	no	—
594	C₂×C₄	—	316	1	no	—
595	C₂×C₄	—	316	2	no	—
596	C₂×C₄	—	316	1	no	—
597	C₂×C₄	—	316	1	no	—
598	C₂×C₄	—	632	8	no	—
599	C₂×C₄	—	158	2	no	—
600	C₂×C₄	—	158	2	no	—
601	C₂×C₄	—	158	4	no	—
602	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
603	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	2	yes	—
604	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
605	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
606	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	2	yes	—
607	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
608	C₂×C₄	C₂³×Dic₇₉	1	1	yes	characteristic
609	C₂×C₄	C₂²×C₂²⋊D₇₉	1	1	yes	characteristic
610	C₈	—	316	1	no	—
611	C₈	—	316	2	no	—
612	C₈	—	316	1	no	—
613	C₂²	—	2	2	no	—
614	C₂²	—	2	1	no	—
615	C₂²	—	2	1	no	—
616	C₂²	—	2	2	no	—
617	C₂²	—	2	2	no	—
618	C₂²	—	2	2	no	—
619	C₂²	—	2	2	no	—
620	C₂²	—	4	4	no	—
621	C₂²	—	4	4	no	—
622	C₂²	—	4	1	no	—
623	C₂²	—	4	1	no	—
624	C₂²	—	4	1	no	—
625	C₂²	C₂×#14579088	1	4	yes	—
626	C₂²	C₂²×C₂²⋊Dic₇₉	1	1	yes	characteristic
627	C₂²	#19099371	1	1	yes	characteristic
628	C₂²	#19099378	1	1	yes	characteristic
629	C₄	—	2	1	no	—
630	C₄	—	2	1	no	—
631	C₄	—	2	1	no	—
632	C₄	—	2	1	no	—
633	C₄	—	2	1	no	—
634	C₄	—	2	2	no	—
635	C₄	—	2	2	no	—
636	C₄	—	4	1	no	—
637	C₄	—	4	1	no	—
638	C₄	—	4	2	no	—
639	C₄	—	4	2	no	—
640	C₄	—	4	1	no	—
641	C₄	—	316	2	no	—
642	C₄	—	316	4	no	—
643	C₄	—	316	2	no	—
644	C₄	C₂×#14579088	1	2	yes	—
645	C₂	—	2	1	no	—
646	C₂	—	2	1	no	—
647	C₂	—	2	4	no	—
648	C₂	—	4	2	no	—
649	C₂	—	8	1	no	—
650	C₂	#23771861	1	1	yes	characteristic
651	C₂	#23771933	1	1	yes	characteristic
652	C₂	C₂²×#14579088	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×C₂²⋊Dic₇₉
commutator	C₂×C₄×C₇₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₇₉
Fitting, prime radical	C₇₉×#3520	C₂
socle	C₂²×C₇₉	C₂²×C₂²⋊C₄
cosocle	C₂²×C₄×C₇₉	C₂⁴
hypercenter	#3520	D₇₉
hypocenter	C₇₉	#17548
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄×D₄ ◁ #3520

Complements

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

N	H ≅ G/N	type
1. #23772435	C₂	semidirect
2. #23765761	C₂	semidirect
3. #23761925	C₂	semidirect
4. #23761920	C₂	semidirect
5. #23761912	C₂	semidirect
6. #23761904	C₂	semidirect
7. #23761899	C₂	semidirect
8. #23761891	C₂	semidirect
9. #23761886	C₂	semidirect
10. C₂×#19098300	C₂	semidirect
36. #556×C₇₉	C₄	semidirect
38. #552×C₇₉	C₄	semidirect
40. D₄×Q₈×C₇₉	C₄	semidirect
41. #548×C₇₉	C₄	semidirect
42. #547×C₇₉	C₄	semidirect
43. #547×C₇₉	C₄	semidirect
77. C₂×#41×C₇₉	C₂×C₄	semidirect
78. C₂²×Q₈×C₇₉	C₂×C₄	semidirect
82. C₄⋊Q₈×C₇₉	C₂×C₄	semidirect
83. C₄⋊Q₈×C₇₉	C₂×C₄	semidirect
89. #125×C₇₉	C₂×C₄	semidirect
92. #124×C₇₉	C₂×C₄	semidirect
104. C₂²⋊Q₈×C₇₉	C₂×C₄	semidirect
105. C₂²⋊Q₈×C₇₉	C₂×C₄	semidirect
106. C₂²⋊Q₈×C₇₉	C₂×C₄	semidirect
111. #121×C₇₉	C₂×C₄	semidirect
116. C₄×Q₈×C₇₉	C₂×C₄	semidirect
117. C₄×Q₈×C₇₉	C₂×C₄	semidirect
126. C₄×D₄×C₇₉	C₂×C₄	semidirect
133. #117×C₇₉	C₂×C₄	semidirect
136. C₂×C₄⋊C₄×C₇₉	C₂×C₄	semidirect
338. C₇₉	#17548	semidirect
339. #556	Dic₇₉	semidirect
341. #552	Dic₇₉	semidirect
343. D₄×Q₈	Dic₇₉	semidirect
344. #548	Dic₇₉	semidirect
345. #547	Dic₇₉	semidirect
346. #547	Dic₇₉	semidirect
381. C₂×#41	C₂×Dic₇₉	semidirect
382. C₂²×Q₈	C₂×Dic₇₉	semidirect
389. C₄⋊Q₈	C₂×Dic₇₉	semidirect
390. C₄⋊Q₈	C₂×Dic₇₉	semidirect
396. #125	C₂×Dic₇₉	semidirect
399. #124	C₂×Dic₇₉	semidirect
411. C₂²⋊Q₈	C₂×Dic₇₉	semidirect
412. C₂²⋊Q₈	C₂×Dic₇₉	semidirect
413. C₂²⋊Q₈	C₂×Dic₇₉	semidirect
418. #121	C₂×Dic₇₉	semidirect
423. C₄×Q₈	C₂×Dic₇₉	semidirect
424. C₄×Q₈	C₂×Dic₇₉	semidirect
434. C₄×D₄	C₂×Dic₇₉	semidirect
441. #117	C₂×Dic₇₉	semidirect
445. C₂×C₄⋊C₄	C₂×Dic₇₉	semidirect

Maximal subgroups

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

subgroup	index
#23772435	2
#23765761	2
#23761925	2
#23761920	2
#23761912	2
#23761904	2
#23761899	2
#23761891	2
#23761886	2
C₂×#19098300	2
C₇₉×#3520	2
#17548	79