Subgroups — #34256698

Order 20224.

972 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23772033	C₂	1	1	yes	maximal, characteristic
2	C₂×#19098616	C₂	1	1	yes	maximal, characteristic
3	#23762110	C₂	1	4	yes	maximal, complemented
4	#23762081	C₂	1	2	yes	maximal, complemented
5	#23762072	C₂	1	2	yes	maximal, complemented
6	#23762057	C₂	1	4	yes	maximal, complemented
7	C₂×#533×C₇₉	C₂	1	1	yes	maximal, characteristic
8	#19098620	—	2	1	no	—
9	#19098620	C₂²	1	2	yes	—
10	#19098616	—	2	1	no	—
11	#19098616	—	2	1	no	—
12	#19098616	—	2	1	no	—
13	#19098616	C₂²	1	2	yes	—
14	#19098616	C₂²	1	2	yes	—
15	#19098616	C₂²	1	2	yes	—
16	#19098587	C₂²	1	2	yes	—
17	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
18	#19098527	—	2	1	no	—
19	C₂×C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
20	C₄×#11929608	—	2	1	no	—
21	C₂×C₄×C₇₉⋊C₈	—	2	1	no	—
22	#19098312	C₂²	1	8	yes	complemented
23	#19098309	C₂²	1	8	yes	complemented
24	#533×C₇₉	—	2	1	no	—
25	#533×C₇₉	—	2	1	no	—
26	#533×C₇₉	—	2	1	no	—
27	#533×C₇₉	—	2	1	no	—
28	#533×C₇₉	C₄	1	2	yes	—
29	#533×C₇₉	C₄	1	2	yes	—
30	#533×C₇₉	C₂²	1	2	yes	—
31	#533×C₇₉	C₂²	1	2	yes	—
32	C₂×C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
33	C₂×C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
34	C₂×#125×C₇₉	—	2	1	no	—
35	C₂×C₂²⋊Q₈×C₇₉	—	2	1	no	—
36	C₂×C₂²⋊Q₈×C₇₉	C₄	1	2	yes	—
37	C₂×C₄×Q₈×C₇₉	—	2	1	no	—
38	C₂×C₄×Q₈×C₇₉	C₄	1	2	yes	—
39	C₂×#117×C₇₉	—	2	1	no	—
40	C₂²×C₄²×C₇₉	C₂²	1	1	yes	characteristic
41	C₂×#11929608	—	2	2	no	—
42	C₂²×C₇₉⋊C₈	—	2	2	no	—
43	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
44	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
45	C₄⋊(C₇₉⋊C₈)	C₂³	1	4	yes	—
46	C₄⋊(C₇₉⋊C₈)	C₂³	1	4	yes	—
47	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
48	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
49	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
50	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
51	#14579072	—	2	2	no	—
52	C₄×C₇₉⋊C₈	—	2	2	no	—
53	C₄×C₇₉⋊C₈	—	2	2	no	—
54	C₄×C₇₉⋊C₈	—	2	2	no	—
55	C₂²×Q₈×C₇₉	—	2	1	no	—
56	C₂²×Q₈×C₇₉	C₂×C₄	1	2	yes	—
57	C₂³×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
58	C₂³×C₄×C₇₉	D₄	1	1	yes	characteristic
59	C₂³×C₄×C₇₉	D₄	1	1	yes	characteristic
60	C₄⋊Q₈×C₇₉	—	2	1	no	—
61	C₄⋊Q₈×C₇₉	—	2	1	no	—
62	C₄⋊Q₈×C₇₉	—	2	1	no	—
63	C₄⋊Q₈×C₇₉	—	2	1	no	—
64	C₄⋊Q₈×C₇₉	C₂×C₄	1	2	yes	—
65	C₄⋊Q₈×C₇₉	C₂×C₄	1	2	yes	—
66	C₄⋊Q₈×C₇₉	C₂³	1	2	yes	—
67	C₄⋊Q₈×C₇₉	C₂³	1	2	yes	—
68	#125×C₇₉	—	2	2	no	—
69	#125×C₇₉	—	2	2	no	—
70	#125×C₇₉	—	2	2	no	—
71	#125×C₇₉	—	2	2	no	—
72	C₂²⋊Q₈×C₇₉	—	2	2	no	—
73	C₂²⋊Q₈×C₇₉	—	2	2	no	—
74	C₂²⋊Q₈×C₇₉	—	2	2	no	—
75	C₂²⋊Q₈×C₇₉	—	2	2	no	—
76	C₂²⋊Q₈×C₇₉	—	2	2	no	—
77	C₂²⋊Q₈×C₇₉	—	2	2	no	—
78	C₂²⋊Q₈×C₇₉	C₂×C₄	1	4	yes	—
79	C₂²⋊Q₈×C₇₉	C₂×C₄	1	4	yes	—
80	C₄×Q₈×C₇₉	—	2	2	no	—
81	C₄×Q₈×C₇₉	—	2	2	no	—
82	C₄×Q₈×C₇₉	—	2	2	no	—
83	C₄×Q₈×C₇₉	—	2	2	no	—
84	C₄×Q₈×C₇₉	—	2	2	no	—
85	C₄×Q₈×C₇₉	—	2	2	no	—
86	C₄×Q₈×C₇₉	C₂×C₄	1	4	yes	—
87	C₄×Q₈×C₇₉	C₂×C₄	1	4	yes	—
88	#117×C₇₉	—	2	2	no	—
89	#117×C₇₉	—	2	2	no	—
90	#117×C₇₉	—	2	2	no	—
91	#117×C₇₉	—	2	2	no	—
92	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
93	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
94	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
95	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
96	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
97	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
98	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
99	C₂×C₄²×C₇₉	—	2	2	no	—
100	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
101	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
102	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
103	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
104	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
105	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
106	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
107	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
108	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
109	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
110	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
111	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
112	#11929608	—	4	4	no	—
113	C₂×C₇₉⋊C₈	—	2	4	no	—
114	C₂×C₇₉⋊C₈	—	2	4	no	—
115	C₂×C₇₉⋊C₈	—	4	4	no	—
116	C₂⁴×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
117	C₂×Q₈×C₇₉	—	2	2	no	—
118	C₂×Q₈×C₇₉	—	2	2	no	—
119	C₂×Q₈×C₇₉	—	2	2	no	—
120	C₂×Q₈×C₇₉	—	4	4	no	—
121	C₂×Q₈×C₇₉	—	4	4	no	—
122	C₂×Q₈×C₇₉	C₂²×C₄	1	4	yes	—
123	C₂²×C₄×C₇₉	—	2	4	no	—
124	C₂²×C₄×C₇₉	—	2	4	no	—
125	C₂²×C₄×C₇₉	—	2	2	no	—
126	C₂²×C₄×C₇₉	—	2	2	no	—
127	C₂²×C₄×C₇₉	—	4	2	no	—
128	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
129	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
130	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
131	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
132	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
133	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
134	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
135	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
136	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
137	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
138	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
139	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
140	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
146	C₄⋊C₄×C₇₉	—	2	2	no	—
147	C₄⋊C₄×C₇₉	—	2	2	no	—
148	C₄⋊C₄×C₇₉	—	2	2	no	—
149	C₄⋊C₄×C₇₉	—	2	4	no	—
150	C₄⋊C₄×C₇₉	—	2	4	no	—
151	C₄⋊C₄×C₇₉	—	2	4	no	—
152	C₄⋊C₄×C₇₉	—	2	4	no	—
153	C₄⋊C₄×C₇₉	—	2	2	no	—
154	C₄⋊C₄×C₇₉	—	2	2	no	—
155	C₄⋊C₄×C₇₉	—	2	2	no	—
156	C₄⋊C₄×C₇₉	—	2	2	no	—
157	C₄⋊C₄×C₇₉	C₂²×C₄	1	4	yes	—
158	C₂²⋊C₄×C₇₉	—	2	4	no	—
159	C₂²⋊C₄×C₇₉	—	2	4	no	—
160	C₄²×C₇₉	—	2	4	no	—
161	C₄²×C₇₉	—	2	4	no	—
162	C₄²×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
163	C₄²×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
164	C₄²×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
165	C₄²×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
166	C₄²×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
167	C₄²×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
168	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
169	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
170	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
171	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
172	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
173	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
174	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
175	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
176	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
177	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
178	C₂³×C₇₉	—	2	2	no	—
179	C₂³×C₇₉	—	2	2	no	—
180	C₂³×C₇₉	—	4	1	no	—
181	C₂³×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
182	C₂³×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
183	C₂³×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
184	Q₈×C₇₉	—	4	4	no	—
185	Q₈×C₇₉	—	4	4	no	—
186	Q₈×C₇₉	—	4	4	no	—
187	Q₈×C₇₉	—	4	4	no	—
188	C₂×C₄×C₇₉	—	2	2	no	—
189	C₂×C₄×C₇₉	—	2	2	no	—
190	C₂×C₄×C₇₉	—	2	2	no	—
191	C₂×C₄×C₇₉	—	2	2	no	—
192	C₂×C₄×C₇₉	—	2	2	no	—
193	C₂×C₄×C₇₉	—	2	2	no	—
194	C₂×C₄×C₇₉	—	2	2	no	—
195	C₂×C₄×C₇₉	—	2	2	no	—
196	C₂×C₄×C₇₉	—	2	2	no	—
197	C₂×C₄×C₇₉	—	2	2	no	—
198	C₂×C₄×C₇₉	—	2	2	no	—
199	C₂×C₄×C₇₉	—	2	2	no	—
200	C₂×C₄×C₇₉	—	2	2	no	—
201	C₂×C₄×C₇₉	—	2	4	no	—
202	C₂×C₄×C₇₉	—	2	4	no	—
203	C₂×C₄×C₇₉	—	4	1	no	—
204	C₂×C₄×C₇₉	—	4	1	no	—
205	C₂×C₄×C₇₉	—	4	1	no	—
206	C₂×C₄×C₇₉	—	4	4	no	—
207	C₂×C₄×C₇₉	—	4	4	no	—
208	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
209	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
210	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
211	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
212	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
213	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
214	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
215	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
216	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
217	C₂×C₄×C₇₉	#135	1	4	yes	—
218	C₂×C₄×C₇₉	#137	1	4	yes	—
219	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
220	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
221	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
222	C₇₉⋊C₈	—	4	4	no	—
223	C₇₉⋊C₈	—	4	4	no	—
224	C₂²×C₇₉	—	2	1	no	—
225	C₂²×C₇₉	—	2	1	no	—
226	C₂²×C₇₉	—	2	1	no	—
227	C₂²×C₇₉	—	2	1	no	—
228	C₂²×C₇₉	—	2	1	no	—
229	C₂²×C₇₉	—	2	1	no	—
230	C₂²×C₇₉	—	2	1	no	—
231	C₂²×C₇₉	—	4	4	no	—
232	C₂²×C₇₉	#416	1	2	yes	—
233	C₂²×C₇₉	#419	1	2	yes	—
234	C₂²×C₇₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
235	C₄×C₇₉	—	2	1	no	—
236	C₄×C₇₉	—	2	1	no	—
237	C₄×C₇₉	—	2	1	no	—
238	C₄×C₇₉	—	2	1	no	—
239	C₄×C₇₉	—	2	1	no	—
240	C₄×C₇₉	—	2	1	no	—
241	C₄×C₇₉	—	2	1	no	—
242	C₄×C₇₉	—	4	4	no	—
243	C₄×C₇₉	—	4	4	no	—
244	C₄×C₇₉	#413	1	2	yes	—
245	C₄×C₇₉	#416	1	2	yes	—
246	C₄×C₇₉	#419	1	2	yes	—
247	C₄×C₇₉	C₂×#135	1	2	yes	—
248	C₄×C₇₉	C₂×#137	1	2	yes	—
249	#17718	—	79	1	no	maximal, Sylow
250	C₂×C₇₉	—	2	2	no	—
251	C₂×C₇₉	—	2	2	no	—
252	C₂×C₇₉	—	4	1	no	—
253	C₂×C₇₉	C₂×#413	1	1	yes	characteristic
254	C₂×C₇₉	C₂×#416	1	1	yes	characteristic
255	C₂×C₇₉	C₂×#419	1	1	yes	characteristic
256	C₂×#533	D₇₉	1	1	yes	characteristic
257	#2920	—	79	1	no	—
258	C₂×#431	—	79	1	no	—
259	#1554	—	79	4	no	—
260	#1548	—	79	2	no	—
261	#1546	—	79	2	no	—
262	#1542	—	79	4	no	—
263	C₇₉	#17718	1	1	yes	characteristic, complemented, Sylow
264	#533	—	2	1	no	—
265	#533	—	2	1	no	—
266	#533	—	2	1	no	—
267	#533	—	2	1	no	—
268	#533	Dic₇₉	1	2	yes	—
269	#533	Dic₇₉	1	2	yes	—
270	#533	C₂×D₇₉	1	2	yes	—
271	#533	C₂×D₇₉	1	2	yes	—
272	C₂×C₄⋊Q₈	C₂×D₇₉	1	1	yes	characteristic
273	C₂×C₄⋊Q₈	C₂×D₇₉	1	1	yes	characteristic
274	C₂×#125	—	2	1	no	—
275	C₂×C₂²⋊Q₈	—	2	1	no	—
276	C₂×C₂²⋊Q₈	Dic₇₉	1	2	yes	—
277	C₂×C₄×Q₈	—	2	1	no	—
278	C₂×C₄×Q₈	Dic₇₉	1	2	yes	—
279	C₂×#117	—	2	1	no	—
280	C₂²×C₄²	C₂×D₇₉	1	1	yes	characteristic
281	#432	—	79	2	no	—
282	#432	—	158	1	no	—
283	#431	—	79	2	no	—
284	#431	—	79	2	no	—
285	#431	—	79	2	no	—
286	#431	—	158	1	no	—
287	#431	—	158	1	no	—
288	#431	—	158	1	no	—
289	#423	—	79	2	no	—
290	C₂×C₄⋊C₈	—	79	2	no	—
291	#407	—	158	1	no	—
292	C₂×C₂²⋊C₈	—	158	1	no	—
293	C₄×M₁₆	—	158	1	no	—
294	C₂×C₄×C₈	—	158	1	no	—
295	#333	—	79	8	no	—
296	#332	—	79	8	no	—
297	C₂²×Q₈	—	2	1	no	—
298	C₂²×Q₈	C₂×Dic₇₉	1	2	yes	—
299	C₂³×C₄	C₂×Dic₇₉	1	1	yes	characteristic
300	C₂³×C₄	C₂²⋊D₇₉	1	1	yes	characteristic
301	C₂³×C₄	C₂²⋊D₇₉	1	1	yes	characteristic
302	C₂×M₁₆	—	158	2	no	—
303	C₂²×C₈	—	158	2	no	—
304	C₄⋊Q₈	—	2	1	no	—
305	C₄⋊Q₈	—	2	1	no	—
306	C₄⋊Q₈	—	2	1	no	—
307	C₄⋊Q₈	—	2	1	no	—
308	C₄⋊Q₈	C₂×Dic₇₉	1	2	yes	—
309	C₄⋊Q₈	C₂×Dic₇₉	1	2	yes	—
310	C₄⋊Q₈	C₂²×D₇₉	1	2	yes	—
311	C₄⋊Q₈	C₂²×D₇₉	1	2	yes	—
312	#125	—	2	2	no	—
313	#125	—	2	2	no	—
314	#125	—	2	2	no	—
315	#125	—	2	2	no	—
316	C₂²⋊Q₈	—	2	2	no	—
317	C₂²⋊Q₈	—	2	2	no	—
318	C₂²⋊Q₈	—	2	2	no	—
319	C₂²⋊Q₈	—	2	2	no	—
320	C₂²⋊Q₈	—	2	2	no	—
321	C₂²⋊Q₈	—	2	2	no	—
322	C₂²⋊Q₈	C₂×Dic₇₉	1	4	yes	—
323	C₂²⋊Q₈	C₂×Dic₇₉	1	4	yes	—
324	C₄×Q₈	—	2	2	no	—
325	C₄×Q₈	—	2	2	no	—
326	C₄×Q₈	—	2	2	no	—
327	C₄×Q₈	—	2	2	no	—
328	C₄×Q₈	—	2	2	no	—
329	C₄×Q₈	—	2	2	no	—
330	C₄×Q₈	C₂×Dic₇₉	1	4	yes	—
331	C₄×Q₈	C₂×Dic₇₉	1	4	yes	—
332	#117	—	2	2	no	—
333	#117	—	2	2	no	—
334	#117	—	2	2	no	—
335	#117	—	2	2	no	—
336	C₂×C₄⋊C₄	—	2	2	no	—
337	C₂×C₄⋊C₄	—	2	2	no	—
338	C₂×C₄⋊C₄	—	2	1	no	—
339	C₂×C₄⋊C₄	—	2	1	no	—
340	C₂×C₄⋊C₄	—	2	1	no	—
341	C₂×C₄⋊C₄	C₂×Dic₇₉	1	2	yes	—
342	C₂×C₂²⋊C₄	—	2	2	no	—
343	C₂×C₄²	—	2	2	no	—
344	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
345	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
346	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
347	C₂×C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
348	C₂×C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
349	C₂×C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
350	C₂×C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
351	C₂×C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
352	C₂×C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
353	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
354	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
355	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
356	C₄⋊C₈	—	79	4	no	—
357	C₄⋊C₈	—	79	4	no	—
358	C₄⋊C₈	—	158	2	no	—
359	C₄⋊C₈	—	158	2	no	—
360	C₂²⋊C₈	—	158	2	no	—
361	C₂²⋊C₈	—	158	2	no	—
362	C₂²⋊C₈	—	158	2	no	—
363	C₂²⋊C₈	—	158	2	no	—
364	#97	—	158	2	no	—
365	C₄×C₈	—	158	2	no	—
366	C₄×C₈	—	158	2	no	—
367	C₄×C₈	—	158	2	no	—
368	C₂⁴	C₂²⋊Dic₇₉	1	1	yes	characteristic
369	C₂×Q₈	—	2	2	no	—
370	C₂×Q₈	—	2	2	no	—
371	C₂×Q₈	—	2	2	no	—
372	C₂×Q₈	—	4	4	no	—
373	C₂×Q₈	—	4	4	no	—
374	C₂×Q₈	C₂²×Dic₇₉	1	4	yes	—
375	C₂²×C₄	—	2	4	no	—
376	C₂²×C₄	—	2	4	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	—	4	2	no	—
380	C₂²×C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
381	C₂²×C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
382	C₂²×C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
383	C₂²×C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
384	C₂²×C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
385	C₂²×C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
386	C₂²×C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
387	C₂²×C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
388	C₂²×C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
389	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
390	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
391	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
392	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
393	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
394	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
395	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
396	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
397	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
398	M₁₆	—	316	4	no	—
399	C₂×C₈	—	316	4	no	—
400	C₂×C₈	—	158	4	no	—
401	C₂×C₈	—	158	4	no	—
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	—	2	4	no	—
406	C₄⋊C₄	—	2	4	no	—
407	C₄⋊C₄	—	2	4	no	—
408	C₄⋊C₄	—	2	4	no	—
409	C₄⋊C₄	—	2	2	no	—
410	C₄⋊C₄	—	2	2	no	—
411	C₄⋊C₄	—	2	2	no	—
412	C₄⋊C₄	—	2	2	no	—
413	C₄⋊C₄	C₂²×Dic₇₉	1	4	yes	—
414	C₂²⋊C₄	—	2	4	no	—
415	C₂²⋊C₄	—	2	4	no	—
416	C₄²	—	2	4	no	—
417	C₄²	—	2	4	no	—
418	C₄²	C₂²⋊Dic₇₉	1	1	yes	characteristic
419	C₄²	C₂²⋊Dic₇₉	1	1	yes	characteristic
420	C₄²	C₂²⋊Dic₇₉	1	1	yes	characteristic
421	C₄²	C₂²⋊Dic₇₉	1	1	yes	characteristic
422	C₄²	C₂²⋊Dic₇₉	1	1	yes	characteristic
423	C₄²	C₂²⋊Dic₇₉	1	1	yes	characteristic
424	C₄²	C₂²×Dic₇₉	1	1	yes	characteristic
425	C₄²	C₂²×Dic₇₉	1	1	yes	characteristic
426	C₄²	C₂²×Dic₇₉	1	1	yes	characteristic
427	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
428	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
429	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
430	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
431	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
432	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
433	C₄²	C₂³×D₇₉	1	1	yes	characteristic
434	C₂³	—	2	2	no	—
435	C₂³	—	2	2	no	—
436	C₂³	—	4	1	no	—
437	C₂³	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
438	C₂³	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
439	C₂³	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
440	Q₈	—	4	4	no	—
441	Q₈	—	4	4	no	—
442	Q₈	—	4	4	no	—
443	Q₈	—	4	4	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	4	no	—
458	C₂×C₄	—	2	4	no	—
459	C₂×C₄	—	4	1	no	—
460	C₂×C₄	—	4	1	no	—
461	C₂×C₄	—	4	1	no	—
462	C₂×C₄	—	4	4	no	—
463	C₂×C₄	—	4	4	no	—
464	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
465	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
466	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
467	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
468	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
469	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
470	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
471	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
472	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
473	C₂×C₄	#14579181	1	4	yes	—
474	C₂×C₄	#14579192	1	4	yes	—
475	C₂×C₄	C₂³×Dic₇₉	1	1	yes	characteristic
476	C₂×C₄	C₂²×C₂²⋊D₇₉	1	1	yes	characteristic
477	C₂×C₄	C₂²×C₂²⋊D₇₉	1	1	yes	characteristic
478	C₈	—	316	4	no	—
479	C₈	—	316	4	no	—
480	C₂²	—	2	1	no	—
481	C₂²	—	2	1	no	—
482	C₂²	—	2	1	no	—
483	C₂²	—	2	1	no	—
484	C₂²	—	2	1	no	—
485	C₂²	—	2	1	no	—
486	C₂²	—	2	1	no	—
487	C₂²	—	4	4	no	—
488	C₂²	#19098559	1	2	yes	—
489	C₂²	#19098572	1	2	yes	—
490	C₂²	C₂²×C₂²⋊Dic₇₉	1	1	yes	characteristic
491	C₄	—	2	1	no	—
492	C₄	—	2	1	no	—
493	C₄	—	2	1	no	—
494	C₄	—	2	1	no	—
495	C₄	—	2	1	no	—
496	C₄	—	2	1	no	—
497	C₄	—	2	1	no	—
498	C₄	—	4	4	no	—
499	C₄	—	4	4	no	—
500	C₄	#19098547	1	2	yes	—
501	C₄	#19098559	1	2	yes	—
502	C₄	#19098572	1	2	yes	—
503	C₄	C₂×#14579181	1	2	yes	—
504	C₄	C₂×#14579192	1	2	yes	—
505	C₂	—	2	2	no	—
506	C₂	—	2	2	no	—
507	C₂	—	4	1	no	—
508	C₂	C₂×#19098547	1	1	yes	characteristic
509	C₂	C₂×#19098559	1	1	yes	characteristic
510	C₂	C₂×#19098572	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×C₂²⋊Dic₇₉
commutator	C₂×C₄×C₇₉	C₂³×C₄
Frattini	C₄²	C₂³×D₇₉
Fitting	C₂×#533×C₇₉	C₂
socle	C₂²×C₇₉	C₂²×C₂²⋊C₄
prime radical	C₂⁴×C₇₉	C₂²⋊C₄
cosocle	C₄²×C₇₉	C₂⁴
hypercenter	C₂×#533	D₇₉
hypocenter	C₇₉	#17718
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄² ◁ C₂×#533

Complements

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

N	H ≅ G/N	type
3. #23762110	C₂	semidirect
4. #23762081	C₂	semidirect
5. #23762072	C₂	semidirect
6. #23762057	C₂	semidirect
22. #19098312	C₂²	semidirect
23. #19098309	C₂²	semidirect
263. C₇₉	#17718	semidirect

Maximal subgroups

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

subgroup	index
#23772033	2
C₂×#19098616	2
#23762110	2
#23762081	2
#23762072	2
#23762057	2
C₂×#533×C₇₉	2
#17718	79