Subgroups — #34254504

Order 20224.

944 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23772058	C₂	1	2	yes	maximal, complemented
2	#23761769	C₂	1	2	yes	maximal, complemented
3	#23761756	C₂	1	2	yes	maximal, complemented
4	#23761748	C₂	1	2	yes	maximal
5	#23761744	C₂	1	1	yes	maximal, characteristic, complemented
6	#23761734	C₂	1	1	yes	maximal, characteristic, complemented
7	#23761730	C₂	1	1	yes	maximal, characteristic, complemented
8	#23761724	C₂	1	1	yes	maximal, characteristic, complemented
9	#23761714	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#19098289	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#552×C₇₉	C₂	1	1	yes	maximal, characteristic
12	#19098624	—	2	2	no	—
13	#19098624	—	2	2	no	—
14	#19098620	C₂²	1	2	yes	—
15	#19098620	C₂²	1	2	yes	—
16	#19098616	C₂²	1	2	yes	—
17	#19098616	C₂²	1	2	yes	—
18	#19098590	—	2	2	no	—
19	#19098527	C₂²	1	2	yes	—
20	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
21	#19098519	—	2	2	no	—
22	#19098289	C₂²	1	1	yes	characteristic
23	#19098289	C₂²	1	1	yes	characteristic
24	#19098289	C₂²	1	2	yes	—
25	#19098289	C₂²	1	1	yes	characteristic
26	#19098289	C₂²	1	1	yes	characteristic
27	#19098289	C₂²	1	2	yes	—
28	#19098289	C₂²	1	2	yes	—
29	#19098289	C₂²	1	2	yes	—
30	#19098287	C₂²	1	2	yes	—
31	#19098287	C₂²	1	2	yes	—
32	#552×C₇₉	—	2	2	no	—
33	#552×C₇₉	—	2	2	no	—
34	#552×C₇₉	—	2	2	no	—
35	#552×C₇₉	—	2	2	no	—
36	C₂×#126×C₇₉	C₄	1	1	yes	characteristic
37	C₂×#126×C₇₉	C₂²	1	1	yes	characteristic
38	C₂×#125×C₇₉	C₄	1	1	yes	characteristic
39	C₂×#125×C₇₉	C₄	1	1	yes	characteristic
40	C₂×#125×C₇₉	C₂²	1	1	yes	characteristic
41	C₂×#123×C₇₉	C₄	1	1	yes	characteristic
42	C₂×#123×C₇₉	C₂²	1	1	yes	characteristic
43	C₂×C₂²⋊Q₈×C₇₉	C₄	1	1	yes	characteristic
44	C₂×C₂²⋊Q₈×C₇₉	C₄	1	1	yes	characteristic
45	C₂×C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₇₉	C₄	1	1	yes	characteristic
47	C₂×#117×C₇₉	C₄	1	1	yes	characteristic
48	C₂×#117×C₇₉	C₂²	1	1	yes	characteristic
49	C₂×#117×C₇₉	C₂²	1	1	yes	characteristic
50	C₂²×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
51	C₂×#11929608	—	2	2	no	—
52	C₂²×C₇₉⋊C₈	—	2	2	no	—
53	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
54	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
55	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
56	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
57	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
58	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
59	C₂²⋊(C₇₉⋊C₈)	C₂³	1	2	yes	—
60	C₂²⋊(C₇₉⋊C₈)	C₂³	1	2	yes	—
61	C₂²⋊(C₇₉⋊C₈)	C₂³	1	2	yes	—
62	C₂²⋊(C₇₉⋊C₈)	C₂³	1	2	yes	—
63	#14579072	—	2	2	no	—
64	#14579072	—	2	2	no	—
65	C₄×C₇₉⋊C₈	—	2	2	no	—
66	C₄×C₇₉⋊C₈	—	2	2	no	—
67	C₂²×Q₈×C₇₉	C₂×C₄	1	1	yes	characteristic
68	C₂²×D₄×C₇₉	C₂×C₄	1	1	yes	characteristic
69	C₂³×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
70	C₂³×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
71	C₂³×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
72	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
73	#126×C₇₉	—	2	2	no	—
74	#126×C₇₉	—	2	2	no	—
75	#126×C₇₉	—	2	2	no	—
76	#126×C₇₉	—	2	2	no	—
77	#125×C₇₉	—	2	2	no	—
78	#125×C₇₉	—	2	2	no	—
79	#125×C₇₉	—	2	2	no	—
80	#125×C₇₉	—	2	2	no	—
81	#125×C₇₉	—	2	2	no	—
82	#125×C₇₉	—	2	2	no	—
83	#123×C₇₉	—	2	2	no	—
84	#123×C₇₉	—	2	2	no	—
85	#123×C₇₉	—	2	2	no	—
86	#123×C₇₉	—	2	2	no	—
87	C₂²⋊Q₈×C₇₉	—	2	2	no	—
88	C₂²⋊Q₈×C₇₉	—	2	2	no	—
89	C₂²⋊Q₈×C₇₉	—	2	2	no	—
90	C₂²⋊Q₈×C₇₉	—	2	2	no	—
91	C₄×Q₈×C₇₉	—	2	2	no	—
92	C₄×Q₈×C₇₉	—	2	2	no	—
93	C₄×D₄×C₇₉	—	2	1	no	—
94	C₄×D₄×C₇₉	—	2	1	no	—
95	C₄×D₄×C₇₉	—	2	1	no	—
96	C₄×D₄×C₇₉	—	2	1	no	—
97	#117×C₇₉	—	2	1	no	—
98	#117×C₇₉	—	2	1	no	—
99	#117×C₇₉	—	2	1	no	—
100	#117×C₇₉	—	2	1	no	—
101	#117×C₇₉	—	2	2	no	—
102	#117×C₇₉	—	2	2	no	—
103	#117×C₇₉	D₄	1	2	yes	—
104	#117×C₇₉	D₄	1	2	yes	—
105	#117×C₇₉	D₄	1	2	yes	—
106	#117×C₇₉	D₄	1	2	yes	—
107	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
108	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
109	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
110	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
111	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
112	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
113	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
114	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
115	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
116	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
117	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
118	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
119	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
120	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
121	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
122	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
123	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
124	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
125	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
126	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
127	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
128	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
129	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
130	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
131	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
132	C₂×C₂²⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
133	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
134	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
135	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
136	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
137	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
138	#11929608	—	4	4	no	—
139	C₂×C₇₉⋊C₈	—	2	2	no	—
140	C₂×C₇₉⋊C₈	—	2	2	no	—
141	C₂×C₇₉⋊C₈	—	2	2	no	—
142	C₂×C₇₉⋊C₈	—	2	2	no	—
143	C₂×C₇₉⋊C₈	—	4	4	no	—
144	C₂⁴×C₇₉	C₂²×C₄	1	1	yes	characteristic
145	C₂⁴×C₇₉	C₂²×C₄	1	1	yes	characteristic
146	C₂×Q₈×C₇₉	—	2	2	no	—
147	C₂×Q₈×C₇₉	—	2	2	no	—
148	C₂×Q₈×C₇₉	—	4	1	no	—
149	C₂×D₄×C₇₉	—	2	1	no	—
150	C₂×D₄×C₇₉	—	2	1	no	—
151	C₂×D₄×C₇₉	—	4	2	no	—
152	C₂²×C₄×C₇₉	—	2	1	no	—
153	C₂²×C₄×C₇₉	—	2	1	no	—
154	C₂²×C₄×C₇₉	—	2	1	no	—
155	C₂²×C₄×C₇₉	—	2	1	no	—
156	C₂²×C₄×C₇₉	—	2	1	no	—
157	C₂²×C₄×C₇₉	—	2	1	no	—
158	C₂²×C₄×C₇₉	—	2	2	no	—
159	C₂²×C₄×C₇₉	—	2	2	no	—
160	C₂²×C₄×C₇₉	—	4	1	no	—
161	C₂²×C₄×C₇₉	—	4	1	no	—
162	C₂²×C₄×C₇₉	—	4	2	no	—
163	C₂²×C₄×C₇₉	—	4	2	no	—
164	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
165	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
166	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
167	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
168	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
169	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
170	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
171	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
172	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
173	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
174	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
175	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
176	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
177	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
178	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
179	C₄⋊C₄×C₇₉	—	2	2	no	—
180	C₄⋊C₄×C₇₉	—	2	2	no	—
181	C₄⋊C₄×C₇₉	—	2	2	no	—
182	C₄⋊C₄×C₇₉	—	2	1	no	—
183	C₄⋊C₄×C₇₉	—	2	1	no	—
184	C₄⋊C₄×C₇₉	—	2	1	no	—
185	C₄⋊C₄×C₇₉	—	2	1	no	—
186	C₄⋊C₄×C₇₉	—	2	1	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	2	no	—
191	C₄⋊C₄×C₇₉	—	2	2	no	—
192	C₄⋊C₄×C₇₉	—	2	2	no	—
193	C₄⋊C₄×C₇₉	—	2	2	no	—
194	C₄⋊C₄×C₇₉	—	2	2	no	—
195	C₄⋊C₄×C₇₉	—	2	2	no	—
196	C₄⋊C₄×C₇₉	C₂²⋊C₄	1	2	yes	—
197	C₄⋊C₄×C₇₉	C₂²⋊C₄	1	2	yes	—
198	C₄⋊C₄×C₇₉	C₂²⋊C₄	1	2	yes	—
199	C₄⋊C₄×C₇₉	C₂²⋊C₄	1	2	yes	—
200	C₂²⋊C₄×C₇₉	—	2	1	no	—
201	C₂²⋊C₄×C₇₉	—	2	1	no	—
202	C₂²⋊C₄×C₇₉	—	2	2	no	—
203	C₂²⋊C₄×C₇₉	—	2	1	no	—
204	C₂²⋊C₄×C₇₉	—	2	1	no	—
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	C₂²⋊C₄	1	1	yes	characteristic
209	C₂²⋊C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
210	C₂²⋊C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
211	C₂²⋊C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
212	C₂²⋊C₄×C₇₉	C₂²⋊C₄	1	2	yes	—
213	C₂²⋊C₄×C₇₉	C₂²⋊C₄	1	2	yes	—
214	C₄²×C₇₉	—	2	1	no	—
215	C₄²×C₇₉	—	2	1	no	—
216	C₄²×C₇₉	—	2	1	no	—
217	C₄²×C₇₉	—	2	1	no	—
218	C₄²×C₇₉	—	2	1	no	—
219	C₄²×C₇₉	—	2	1	no	—
220	C₄²×C₇₉	C₂×D₄	1	2	yes	—
221	C₄²×C₇₉	C₂×D₄	1	2	yes	—
222	C₄²×C₇₉	C₂×D₄	1	2	yes	—
223	C₄²×C₇₉	C₂×D₄	1	2	yes	—
224	C₂³×C₇₉	—	2	1	no	—
225	C₂³×C₇₉	—	2	1	no	—
226	C₂³×C₇₉	—	2	2	no	—
227	C₂³×C₇₉	—	2	1	no	—
228	C₂³×C₇₉	—	2	1	no	—
229	C₂³×C₇₉	—	2	1	no	—
230	C₂³×C₇₉	—	4	1	no	—
231	C₂³×C₇₉	—	4	1	no	—
232	C₂³×C₇₉	—	4	1	no	—
233	C₂³×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
234	C₂³×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
235	C₂³×C₇₉	C₂³×C₄	1	1	yes	characteristic
236	Q₈×C₇₉	—	4	4	no	—
237	D₄×C₇₉	—	4	2	no	—
238	D₄×C₇₉	—	4	2	no	—
239	C₂×C₄×C₇₉	—	2	1	no	—
240	C₂×C₄×C₇₉	—	2	1	no	—
241	C₂×C₄×C₇₉	—	2	1	no	—
242	C₂×C₄×C₇₉	—	2	1	no	—
243	C₂×C₄×C₇₉	—	2	1	no	—
244	C₂×C₄×C₇₉	—	2	1	no	—
245	C₂×C₄×C₇₉	—	2	4	no	—
246	C₂×C₄×C₇₉	—	2	1	no	—
247	C₂×C₄×C₇₉	—	2	1	no	—
248	C₂×C₄×C₇₉	—	2	1	no	—
249	C₂×C₄×C₇₉	—	2	1	no	—
250	C₂×C₄×C₇₉	—	2	1	no	—
251	C₂×C₄×C₇₉	—	2	1	no	—
252	C₂×C₄×C₇₉	—	2	1	no	—
253	C₂×C₄×C₇₉	—	2	1	no	—
254	C₂×C₄×C₇₉	—	2	1	no	—
255	C₂×C₄×C₇₉	—	2	1	no	—
256	C₂×C₄×C₇₉	—	4	1	no	—
257	C₂×C₄×C₇₉	—	4	2	no	—
258	C₂×C₄×C₇₉	—	4	1	no	—
259	C₂×C₄×C₇₉	—	4	1	no	—
260	C₂×C₄×C₇₉	—	4	1	no	—
261	C₂×C₄×C₇₉	—	4	2	no	—
262	C₂×C₄×C₇₉	—	4	2	no	—
263	C₂×C₄×C₇₉	—	4	2	no	—
264	C₂×C₄×C₇₉	—	4	2	no	—
265	C₂×C₄×C₇₉	—	4	2	no	—
266	C₂×C₄×C₇₉	—	4	2	no	—
267	C₂×C₄×C₇₉	—	4	1	no	—
268	C₂×C₄×C₇₉	—	4	1	no	—
269	C₂×C₄×C₇₉	—	4	1	no	—
270	C₂×C₄×C₇₉	—	4	1	no	—
271	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
272	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
273	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
274	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
275	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	2	yes	—
276	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	2	yes	—
277	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	2	yes	—
278	C₂×C₄×C₇₉	#131	1	2	yes	—
279	C₂×C₄×C₇₉	C₂²×D₄	1	2	yes	—
280	C₇₉⋊C₈	—	4	2	no	—
281	C₇₉⋊C₈	—	4	2	no	—
282	C₇₉⋊C₈	—	4	2	no	—
283	C₇₉⋊C₈	—	4	2	no	—
284	C₂²×C₇₉	—	2	1	no	—
285	C₂²×C₇₉	—	2	1	no	—
286	C₂²×C₇₉	—	2	1	no	—
287	C₂²×C₇₉	—	2	1	no	—
288	C₂²×C₇₉	—	2	1	no	—
289	C₂²×C₇₉	—	2	1	no	—
290	C₂²×C₇₉	—	2	1	no	—
291	C₂²×C₇₉	—	4	2	no	—
292	C₂²×C₇₉	—	4	2	no	—
293	C₂²×C₇₉	—	4	1	no	—
294	C₂²×C₇₉	—	4	1	no	—
295	C₂²×C₇₉	—	4	1	no	—
296	C₂²×C₇₉	—	8	1	no	—
297	C₂²×C₇₉	—	8	1	no	—
298	C₂²×C₇₉	#410	1	2	yes	—
299	C₂²×C₇₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
300	C₂²×C₇₉	C₂×#131	1	1	yes	characteristic
301	C₂²×C₇₉	#568	1	1	yes	characteristic
302	C₄×C₇₉	—	2	2	no	—
303	C₄×C₇₉	—	2	1	no	—
304	C₄×C₇₉	—	2	1	no	—
305	C₄×C₇₉	—	2	2	no	—
306	C₄×C₇₉	—	2	2	no	—
307	C₄×C₇₉	—	2	2	no	—
308	C₄×C₇₉	—	2	1	no	—
309	C₄×C₇₉	—	2	1	no	—
310	C₄×C₇₉	—	2	2	no	—
311	C₄×C₇₉	—	4	1	no	—
312	C₄×C₇₉	—	4	1	no	—
313	C₄×C₇₉	—	4	1	no	—
314	C₄×C₇₉	—	4	1	no	—
315	C₄×C₇₉	—	4	1	no	—
316	C₄×C₇₉	—	4	1	no	—
317	#17417	—	79	1	no	maximal, Sylow
318	C₂×C₇₉	—	2	1	no	—
319	C₂×C₇₉	—	2	1	no	—
320	C₂×C₇₉	—	2	2	no	—
321	C₂×C₇₉	—	4	1	no	—
322	C₂×C₇₉	—	8	1	no	—
323	C₂×C₇₉	#2880	1	1	yes	characteristic
324	C₂×C₇₉	C₂×#410	1	1	yes	characteristic
325	C₂×C₇₉	#2889	1	1	yes	characteristic
326	C₂×#552	D₇₉	1	1	yes	characteristic
327	#2924	—	79	2	no	—
328	#1473	—	79	2	no	—
329	#1470	—	79	2	no	—
330	#1468	—	79	2	no	—
331	#1467	—	79	1	no	—
332	#1464	—	79	1	no	—
333	#1463	—	79	1	no	—
334	#1461	—	79	1	no	—
335	#1458	—	79	1	no	—
336	C₂×#324	—	79	1	no	—
337	C₇₉	#17417	1	1	yes	characteristic, complemented, Sylow
338	#552	—	2	2	no	—
339	#552	—	2	2	no	—
340	#552	—	2	2	no	—
341	#552	—	2	2	no	—
342	C₂×#126	Dic₇₉	1	1	yes	characteristic
343	C₂×#126	C₂×D₇₉	1	1	yes	characteristic
344	C₂×#125	Dic₇₉	1	1	yes	characteristic
345	C₂×#125	Dic₇₉	1	1	yes	characteristic
346	C₂×#125	C₂×D₇₉	1	1	yes	characteristic
347	C₂×#123	Dic₇₉	1	1	yes	characteristic
348	C₂×#123	C₂×D₇₉	1	1	yes	characteristic
349	C₂×C₂²⋊Q₈	Dic₇₉	1	1	yes	characteristic
350	C₂×C₂²⋊Q₈	Dic₇₉	1	1	yes	characteristic
351	C₂×C₄×Q₈	C₂×D₇₉	1	1	yes	characteristic
352	C₂×C₄×D₄	Dic₇₉	1	1	yes	characteristic
353	C₂×#117	Dic₇₉	1	1	yes	characteristic
354	C₂×#117	C₂×D₇₉	1	1	yes	characteristic
355	C₂×#117	C₂×D₇₉	1	1	yes	characteristic
356	C₂²×C₄⋊C₄	C₂×D₇₉	1	1	yes	characteristic
357	#433	—	158	2	no	—
358	#433	—	158	2	no	—
359	#432	—	79	2	no	—
360	#432	—	79	2	no	—
361	#431	—	79	2	no	—
362	#431	—	79	2	no	—
363	#424	—	158	2	no	—
364	#407	—	79	2	no	—
365	C₂×C₂²⋊C₈	—	79	2	no	—
366	#405	—	158	2	no	—
367	#324	—	79	1	no	—
368	#324	—	79	1	no	—
369	#324	—	79	2	no	—
370	#324	—	79	1	no	—
371	#324	—	79	1	no	—
372	#324	—	79	2	no	—
373	#324	—	79	2	no	—
374	#324	—	79	2	no	—
375	#323	—	79	2	no	—
376	#323	—	79	2	no	—
377	C₂²×Q₈	C₂×Dic₇₉	1	1	yes	characteristic
378	C₂²×D₄	C₂×Dic₇₉	1	1	yes	characteristic
379	C₂³×C₄	C₂×Dic₇₉	1	1	yes	characteristic
380	C₂³×C₄	C₂×Dic₇₉	1	1	yes	characteristic
381	C₂³×C₄	C₂×Dic₇₉	1	1	yes	characteristic
382	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
383	C₂×M₁₆	—	158	2	no	—
384	C₂²×C₈	—	158	2	no	—
385	#126	—	2	2	no	—
386	#126	—	2	2	no	—
387	#126	—	2	2	no	—
388	#126	—	2	2	no	—
389	#125	—	2	2	no	—
390	#125	—	2	2	no	—
391	#125	—	2	2	no	—
392	#125	—	2	2	no	—
393	#125	—	2	2	no	—
394	#125	—	2	2	no	—
395	#123	—	2	2	no	—
396	#123	—	2	2	no	—
397	#123	—	2	2	no	—
398	#123	—	2	2	no	—
399	C₂²⋊Q₈	—	2	2	no	—
400	C₂²⋊Q₈	—	2	2	no	—
401	C₂²⋊Q₈	—	2	2	no	—
402	C₂²⋊Q₈	—	2	2	no	—
403	C₄×Q₈	—	2	2	no	—
404	C₄×Q₈	—	2	2	no	—
405	C₄×D₄	—	2	1	no	—
406	C₄×D₄	—	2	1	no	—
407	C₄×D₄	—	2	1	no	—
408	C₄×D₄	—	2	1	no	—
409	#117	—	2	1	no	—
410	#117	—	2	1	no	—
411	#117	—	2	1	no	—
412	#117	—	2	1	no	—
413	#117	—	2	2	no	—
414	#117	—	2	2	no	—
415	#117	C₂²⋊D₇₉	1	2	yes	—
416	#117	C₂²⋊D₇₉	1	2	yes	—
417	#117	C₂²⋊D₇₉	1	2	yes	—
418	#117	C₂²⋊D₇₉	1	2	yes	—
419	C₂×C₄⋊C₄	—	2	2	no	—
420	C₂×C₄⋊C₄	—	2	2	no	—
421	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
422	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
423	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
424	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
425	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
426	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
427	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
428	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
429	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
430	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
431	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
432	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
433	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
434	C₂×C₄⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
435	C₂×C₄⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
436	C₂×C₄⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
437	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
438	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
439	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
440	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
441	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
442	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
443	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
444	C₂×C₂²⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
445	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
446	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
447	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
448	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
449	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
450	C₄⋊C₈	—	158	2	no	—
451	C₄⋊C₈	—	158	2	no	—
452	C₄⋊C₈	—	158	2	no	—
453	C₄⋊C₈	—	158	2	no	—
454	C₂²⋊C₈	—	79	2	no	—
455	C₂²⋊C₈	—	79	2	no	—
456	C₂²⋊C₈	—	79	2	no	—
457	C₂²⋊C₈	—	79	2	no	—
458	C₂²⋊C₈	—	158	2	no	—
459	C₂²⋊C₈	—	158	2	no	—
460	#97	—	158	2	no	—
461	#97	—	158	2	no	—
462	C₄×C₈	—	158	2	no	—
463	C₄×C₈	—	158	2	no	—
464	C₂⁴	C₂²×Dic₇₉	1	1	yes	characteristic
465	C₂⁴	C₂²×Dic₇₉	1	1	yes	characteristic
466	C₂×Q₈	—	2	2	no	—
467	C₂×Q₈	—	2	2	no	—
468	C₂×Q₈	—	4	1	no	—
469	C₂×D₄	—	2	1	no	—
470	C₂×D₄	—	2	1	no	—
471	C₂×D₄	—	4	2	no	—
472	C₂²×C₄	—	2	1	no	—
473	C₂²×C₄	—	2	1	no	—
474	C₂²×C₄	—	2	1	no	—
475	C₂²×C₄	—	2	1	no	—
476	C₂²×C₄	—	2	1	no	—
477	C₂²×C₄	—	2	1	no	—
478	C₂²×C₄	—	2	2	no	—
479	C₂²×C₄	—	2	2	no	—
480	C₂²×C₄	—	4	2	no	—
481	C₂²×C₄	—	4	1	no	—
482	C₂²×C₄	—	4	1	no	—
483	C₂²×C₄	—	4	2	no	—
484	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
485	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
486	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
487	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
488	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
489	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
490	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
491	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
492	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
493	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
494	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
495	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
496	C₂²×C₄	C₂×C₂²⋊D₇₉	1	2	yes	—
497	C₂²×C₄	C₂×C₂²⋊D₇₉	1	2	yes	—
498	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
499	M₁₆	—	316	4	no	—
500	C₂×C₈	—	316	4	no	—
501	C₂×C₈	—	158	2	no	—
502	C₂×C₈	—	158	2	no	—
503	C₂×C₈	—	158	2	no	—
504	C₂×C₈	—	158	2	no	—
505	C₄⋊C₄	—	2	2	no	—
506	C₄⋊C₄	—	2	2	no	—
507	C₄⋊C₄	—	2	2	no	—
508	C₄⋊C₄	—	2	1	no	—
509	C₄⋊C₄	—	2	1	no	—
510	C₄⋊C₄	—	2	1	no	—
511	C₄⋊C₄	—	2	1	no	—
512	C₄⋊C₄	—	2	1	no	—
513	C₄⋊C₄	—	2	1	no	—
514	C₄⋊C₄	—	2	2	no	—
515	C₄⋊C₄	—	2	2	no	—
516	C₄⋊C₄	—	2	2	no	—
517	C₄⋊C₄	—	2	2	no	—
518	C₄⋊C₄	—	2	2	no	—
519	C₄⋊C₄	—	2	2	no	—
520	C₄⋊C₄	—	2	2	no	—
521	C₄⋊C₄	—	2	2	no	—
522	C₄⋊C₄	C₂²⋊Dic₇₉	1	2	yes	—
523	C₄⋊C₄	C₂²⋊Dic₇₉	1	2	yes	—
524	C₄⋊C₄	C₂²⋊Dic₇₉	1	2	yes	—
525	C₄⋊C₄	C₂²⋊Dic₇₉	1	2	yes	—
526	C₂²⋊C₄	—	2	1	no	—
527	C₂²⋊C₄	—	2	1	no	—
528	C₂²⋊C₄	—	2	2	no	—
529	C₂²⋊C₄	—	2	1	no	—
530	C₂²⋊C₄	—	2	1	no	—
531	C₂²⋊C₄	—	2	2	no	—
532	C₂²⋊C₄	—	2	2	no	—
533	C₂²⋊C₄	—	2	2	no	—
534	C₂²⋊C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
535	C₂²⋊C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
536	C₂²⋊C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
537	C₂²⋊C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
538	C₂²⋊C₄	C₂²⋊Dic₇₉	1	2	yes	—
539	C₂²⋊C₄	C₂²⋊Dic₇₉	1	2	yes	—
540	C₄²	—	2	1	no	—
541	C₄²	—	2	1	no	—
542	C₄²	—	2	1	no	—
543	C₄²	—	2	1	no	—
544	C₄²	—	2	1	no	—
545	C₄²	—	2	1	no	—
546	C₄²	C₂×C₂²⋊D₇₉	1	2	yes	—
547	C₄²	C₂×C₂²⋊D₇₉	1	2	yes	—
548	C₄²	C₂×C₂²⋊D₇₉	1	2	yes	—
549	C₄²	C₂×C₂²⋊D₇₉	1	2	yes	—
550	C₂³	—	2	2	no	—
551	C₂³	—	2	1	no	—
552	C₂³	—	2	1	no	—
553	C₂³	—	2	1	no	—
554	C₂³	—	2	1	no	—
555	C₂³	—	2	1	no	—
556	C₂³	—	4	1	no	—
557	C₂³	—	4	1	no	—
558	C₂³	—	4	1	no	—
559	C₂³	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
560	C₂³	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
561	C₂³	C₂³×Dic₇₉	1	1	yes	characteristic
562	Q₈	—	4	4	no	—
563	D₄	—	4	2	no	—
564	D₄	—	4	2	no	—
565	C₂×C₄	—	2	1	no	—
566	C₂×C₄	—	2	4	no	—
567	C₂×C₄	—	2	1	no	—
568	C₂×C₄	—	2	1	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	1	no	—
571	C₂×C₄	—	2	1	no	—
572	C₂×C₄	—	2	1	no	—
573	C₂×C₄	—	2	1	no	—
574	C₂×C₄	—	2	1	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	2	1	no	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	2	1	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	4	1	no	—
583	C₂×C₄	—	4	2	no	—
584	C₂×C₄	—	4	1	no	—
585	C₂×C₄	—	4	1	no	—
586	C₂×C₄	—	4	1	no	—
587	C₂×C₄	—	4	2	no	—
588	C₂×C₄	—	4	2	no	—
589	C₂×C₄	—	4	2	no	—
590	C₂×C₄	—	4	2	no	—
591	C₂×C₄	—	4	2	no	—
592	C₂×C₄	—	4	2	no	—
593	C₂×C₄	—	4	1	no	—
594	C₂×C₄	—	4	1	no	—
595	C₂×C₄	—	4	1	no	—
596	C₂×C₄	—	4	1	no	—
597	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
598	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
599	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
600	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
601	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	2	yes	—
602	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	2	yes	—
603	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	2	yes	—
604	C₂×C₄	#14579168	1	2	yes	—
605	C₂×C₄	C₂²×C₂²⋊D₇₉	1	2	yes	—
606	C₈	—	316	2	no	—
607	C₈	—	316	2	no	—
608	C₈	—	316	2	no	—
609	C₈	—	316	2	no	—
610	C₂²	—	2	1	no	—
611	C₂²	—	2	1	no	—
612	C₂²	—	2	1	no	—
613	C₂²	—	2	1	no	—
614	C₂²	—	2	1	no	—
615	C₂²	—	2	1	no	—
616	C₂²	—	2	1	no	—
617	C₂²	—	4	2	no	—
618	C₂²	—	4	2	no	—
619	C₂²	—	4	1	no	—
620	C₂²	—	4	1	no	—
621	C₂²	—	4	1	no	—
622	C₂²	—	8	1	no	—
623	C₂²	—	8	1	no	—
624	C₂²	#19098537	1	2	yes	—
625	C₂²	C₂²×C₂²⋊Dic₇₉	1	1	yes	characteristic
626	C₂²	C₂×#14579168	1	1	yes	characteristic
627	C₂²	#19099330	1	1	yes	characteristic
628	C₄	—	2	2	no	—
629	C₄	—	2	1	no	—
630	C₄	—	2	1	no	—
631	C₄	—	2	2	no	—
632	C₄	—	2	2	no	—
633	C₄	—	2	2	no	—
634	C₄	—	2	1	no	—
635	C₄	—	2	1	no	—
636	C₄	—	2	2	no	—
637	C₄	—	4	1	no	—
638	C₄	—	4	1	no	—
639	C₄	—	4	1	no	—
640	C₄	—	4	1	no	—
641	C₄	—	4	1	no	—
642	C₄	—	4	1	no	—
643	C₂	—	2	1	no	—
644	C₂	—	2	1	no	—
645	C₂	—	2	2	no	—
646	C₂	—	4	1	no	—
647	C₂	—	8	1	no	—
648	C₂	#23771849	1	1	yes	characteristic
649	C₂	C₂×#19098537	1	1	yes	characteristic
650	C₂	#23771883	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×C₂²⋊Dic₇₉
commutator	C₂³×C₇₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₇₉
Fitting	C₂×#552×C₇₉	C₂
socle	C₂²×C₇₉	C₂²×C₂²⋊C₄
prime radical	C₂²×D₄×C₇₉	C₂×C₄
cosocle	C₂²×C₄×C₇₉	C₂⁴
hypercenter	C₂×#552	D₇₉
hypocenter	C₇₉	#17417
LCS	G ▷ C₂³×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂×#117 ◁ C₂×#552

Complements

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

N	H ≅ G/N	type
1. #23772058	C₂	semidirect
2. #23761769	C₂	semidirect
3. #23761756	C₂	semidirect
5. #23761744	C₂	semidirect
6. #23761734	C₂	semidirect
7. #23761730	C₂	semidirect
8. #23761724	C₂	semidirect
9. #23761714	C₂	semidirect
10. C₂×#19098289	C₂	semidirect
337. C₇₉	#17417	semidirect

Maximal subgroups

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

subgroup	index
#23772058	2
#23761769	2
#23761756	2
#23761748	2
#23761744	2
#23761734	2
#23761730	2
#23761724	2
#23761714	2
C₂×#19098289	2
C₂×#552×C₇₉	2
#17417	79