Subgroups — #34298110

Order 20224.

1044 conjugacy classes of subgroups.

The subgroup lattice has 536 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×#19098587	C₂	1	1	yes	maximal, characteristic
3	#23764390	C₂	1	2	yes	maximal, complemented
4	#23764245	C₂	1	2	yes	maximal, complemented
5	#23763869	C₂	1	4	yes	maximal
6	#23763396	C₂	1	4	yes	maximal, complemented
7	C₂×#533×C₇₉	C₂	1	1	yes	maximal, characteristic
8	C₂²×#11929608	C₂²	1	2	yes	—
9	#19098620	—	2	1	no	—
10	#19098620	—	2	1	no	—
11	#19098616	—	2	1	no	—
12	#19098616	—	2	1	no	—
13	#19098587	—	2	1	no	—
14	#19098587	—	2	1	no	—
15	#19098587	C₂²	1	2	yes	—
16	#19098587	C₂²	1	2	yes	—
17	#19098587	C₂²	1	2	yes	—
18	C₂×C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
19	C₂×C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
20	C₂×#14579080	C₂²	1	8	yes	—
21	#19098527	C₂²	1	2	yes	—
22	C₄×#11929608	C₂²	1	2	yes	—
23	#19098332	C₂²	1	8	yes	—
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	—	2	1	no	—
29	#533×C₇₉	—	2	1	no	—
30	#533×C₇₉	—	2	1	no	—
31	#533×C₇₉	—	2	1	no	—
32	C₂×C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
33	C₂×C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
34	C₂×#125×C₇₉	C₄	1	2	yes	—
35	C₂×C₂²⋊Q₈×C₇₉	C₄	1	2	yes	—
36	C₂×C₂²⋊Q₈×C₇₉	C₂²	1	2	yes	—
37	C₂×C₄×Q₈×C₇₉	C₄	1	2	yes	—
38	C₂×C₄×Q₈×C₇₉	C₂²	1	2	yes	—
39	C₂×#117×C₇₉	C₄	1	2	yes	—
40	C₂²×C₄²×C₇₉	C₂²	1	1	yes	characteristic
41	C₂×#11929608	—	2	2	no	—
42	C₂×#11929608	—	4	4	no	—
43	C₂×#11929608	C₂³	1	4	yes	—
44	C₂×#11929608	C₂³	1	4	yes	—
45	C₂²×C₇₉⋊C₈	—	2	2	no	—
46	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
47	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
48	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
49	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
50	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
51	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
52	#14579080	—	4	8	no	—
53	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
54	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
55	#14579072	—	2	2	no	—
56	C₄×C₇₉⋊C₈	—	2	2	no	—
57	C₂²×Q₈×C₇₉	C₂×C₄	1	2	yes	—
58	C₂²×Q₈×C₇₉	C₂³	1	2	yes	—
59	C₂³×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
60	C₂³×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
61	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
62	C₄⋊Q₈×C₇₉	—	2	1	no	—
63	C₄⋊Q₈×C₇₉	—	2	1	no	—
64	C₄⋊Q₈×C₇₉	—	2	1	no	—
65	C₄⋊Q₈×C₇₉	—	2	1	no	—
66	C₄⋊Q₈×C₇₉	—	2	1	no	—
67	C₄⋊Q₈×C₇₉	—	2	1	no	—
68	C₄⋊Q₈×C₇₉	—	2	1	no	—
69	C₄⋊Q₈×C₇₉	—	2	1	no	—
70	#125×C₇₉	—	2	2	no	—
71	#125×C₇₉	—	2	2	no	—
72	#125×C₇₉	—	2	2	no	—
73	#125×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	—	2	2	no	—
79	C₂²⋊Q₈×C₇₉	—	2	2	no	—
80	C₂²⋊Q₈×C₇₉	—	2	2	no	—
81	C₂²⋊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	—	2	2	no	—
87	C₄×Q₈×C₇₉	—	2	2	no	—
88	C₄×Q₈×C₇₉	—	2	2	no	—
89	C₄×Q₈×C₇₉	—	2	2	no	—
90	#117×C₇₉	—	2	2	no	—
91	#117×C₇₉	—	2	2	no	—
92	#117×C₇₉	—	2	2	no	—
93	#117×C₇₉	—	2	2	no	—
94	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
95	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
96	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
97	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	4	yes	—
98	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	4	yes	—
99	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
100	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	4	yes	—
101	C₂×C₄²×C₇₉	C₂×C₄	1	4	yes	—
102	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
103	C₂×C₄²×C₇₉	C₂×C₄	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	D₄	1	1	yes	characteristic
110	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
111	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
112	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
113	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
114	#11929608	—	2	4	no	—
115	#11929608	—	2	8	no	—
116	#11929608	—	2	4	no	—
117	#11929608	—	4	4	no	—
118	C₂×C₇₉⋊C₈	—	2	4	no	—
119	C₂×C₇₉⋊C₈	—	2	4	no	—
120	C₂×C₇₉⋊C₈	—	4	4	no	—
121	C₂⁴×C₇₉	C₂²×C₄	1	1	yes	characteristic
122	C₂×Q₈×C₇₉	—	2	2	no	—
123	C₂×Q₈×C₇₉	—	2	2	no	—
124	C₂×Q₈×C₇₉	—	2	2	no	—
125	C₂×Q₈×C₇₉	—	2	2	no	—
126	C₂×Q₈×C₇₉	—	2	4	no	—
127	C₂×Q₈×C₇₉	—	2	4	no	—
128	C₂×Q₈×C₇₉	—	4	4	no	—
129	C₂²×C₄×C₇₉	—	2	4	no	—
130	C₂²×C₄×C₇₉	—	2	2	no	—
131	C₂²×C₄×C₇₉	—	2	2	no	—
132	C₂²×C₄×C₇₉	—	4	2	no	—
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	C₂²⋊C₄	1	1	yes	characteristic
141	C₂²×C₄×C₇₉	C₂²×C₄	1	4	yes	—
142	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
143	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
144	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
145	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
146	C₂²×C₄×C₇₉	C₂²×C₄	1	4	yes	—
147	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
148	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
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	—	2	4	no	—
158	C₄⋊C₄×C₇₉	—	2	4	no	—
159	C₄⋊C₄×C₇₉	—	2	4	no	—
160	C₄⋊C₄×C₇₉	—	2	4	no	—
161	C₄⋊C₄×C₇₉	—	2	2	no	—
162	C₄⋊C₄×C₇₉	—	2	2	no	—
163	C₄⋊C₄×C₇₉	—	2	2	no	—
164	C₄⋊C₄×C₇₉	—	2	2	no	—
165	C₂²⋊C₄×C₇₉	—	2	4	no	—
166	C₂²⋊C₄×C₇₉	—	2	4	no	—
167	C₄²×C₇₉	—	2	4	no	—
168	C₄²×C₇₉	—	2	4	no	—
169	C₄²×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
170	C₄²×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
171	C₄²×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
172	C₄²×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
173	C₄²×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
174	C₄²×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
175	C₄²×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
176	C₄²×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
177	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
178	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
179	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
180	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
181	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
182	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
183	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
184	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
185	C₂³×C₇₉	—	2	2	no	—
186	C₂³×C₇₉	—	2	2	no	—
187	C₂³×C₇₉	—	4	1	no	—
188	C₂³×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
189	C₂³×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
190	C₂³×C₇₉	C₂³×C₄	1	1	yes	characteristic
191	Q₈×C₇₉	—	4	4	no	—
192	Q₈×C₇₉	—	4	2	no	—
193	Q₈×C₇₉	—	4	2	no	—
194	Q₈×C₇₉	—	4	4	no	—
195	Q₈×C₇₉	—	4	4	no	—
196	C₂×C₄×C₇₉	—	2	2	no	—
197	C₂×C₄×C₇₉	—	2	2	no	—
198	C₂×C₄×C₇₉	—	2	1	no	—
199	C₂×C₄×C₇₉	—	2	1	no	—
200	C₂×C₄×C₇₉	—	2	1	no	—
201	C₂×C₄×C₇₉	—	2	1	no	—
202	C₂×C₄×C₇₉	—	2	2	no	—
203	C₂×C₄×C₇₉	—	2	2	no	—
204	C₂×C₄×C₇₉	—	2	2	no	—
205	C₂×C₄×C₇₉	—	2	2	no	—
206	C₂×C₄×C₇₉	—	2	2	no	—
207	C₂×C₄×C₇₉	—	2	2	no	—
208	C₂×C₄×C₇₉	—	2	2	no	—
209	C₂×C₄×C₇₉	—	2	2	no	—
210	C₂×C₄×C₇₉	—	2	2	no	—
211	C₂×C₄×C₇₉	—	2	4	no	—
212	C₂×C₄×C₇₉	—	2	4	no	—
213	C₂×C₄×C₇₉	—	2	8	no	—
214	C₂×C₄×C₇₉	—	4	1	no	—
215	C₂×C₄×C₇₉	—	4	1	no	—
216	C₂×C₄×C₇₉	—	4	1	no	—
217	C₂×C₄×C₇₉	—	4	4	no	—
218	C₂×C₄×C₇₉	#101	1	4	yes	complemented
219	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
220	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
221	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
222	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
223	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
224	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
225	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
226	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
227	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
228	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
229	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
230	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
231	C₂×C₄×C₇₉	H(5,𝔽₂)	1	2	yes	—
232	C₂×C₄×C₇₉	2₋¹⁺⁴	1	2	yes	—
233	C₇₉⋊C₈	—	4	4	no	—
234	C₇₉⋊C₈	—	4	4	no	—
235	C₂²×C₇₉	—	2	1	no	—
236	C₂²×C₇₉	—	2	1	no	—
237	C₂²×C₇₉	—	2	1	no	—
238	C₂²×C₇₉	—	2	1	no	—
239	C₂²×C₇₉	—	2	1	no	—
240	C₂²×C₇₉	—	2	1	no	—
241	C₂²×C₇₉	—	2	1	no	—
242	C₂²×C₇₉	—	4	4	no	—
243	C₂²×C₇₉	C₂×#101	1	2	yes	—
244	C₂²×C₇₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
245	C₂²×C₇₉	#520	1	2	yes	—
246	C₄×C₇₉	—	2	1	no	—
247	C₄×C₇₉	—	2	1	no	—
248	C₄×C₇₉	—	2	1	no	—
249	C₄×C₇₉	—	2	1	no	—
250	C₄×C₇₉	—	2	1	no	—
251	C₄×C₇₉	—	2	1	no	—
252	C₄×C₇₉	—	2	1	no	—
253	C₄×C₇₉	—	4	4	no	—
254	C₄×C₇₉	—	4	4	no	—
255	C₄×C₇₉	C₂×#101	1	2	yes	—
256	C₄×C₇₉	C₂×#101	1	2	yes	—
257	C₄×C₇₉	#413	1	2	yes	—
258	C₄×C₇₉	#535	1	1	yes	characteristic
259	C₄×C₇₉	#536	1	1	yes	characteristic
260	C₄×C₇₉	#537	1	2	yes	—
261	#21879	—	79	1	no	maximal, Sylow
262	C₂×C₇₉	—	2	2	no	—
263	C₂×C₇₉	—	2	2	no	—
264	C₂×C₇₉	—	4	1	no	—
265	C₂×C₇₉	#2311	1	1	yes	characteristic
266	C₂×C₇₉	C₂²×#101	1	1	yes	characteristic
267	C₂×C₇₉	C₂×#413	1	1	yes	characteristic
268	C₂×#533	D₇₉	1	1	yes	characteristic
269	#2920	—	79	1	no	—
270	C₂×#423	—	79	1	no	—
271	#1997	—	79	2	no	—
272	#1966	—	79	2	no	—
273	#1901	—	79	4	no	—
274	#1801	—	79	4	no	—
275	C₇₉	#21879	1	1	yes	characteristic, complemented, Sylow
276	C₂²×M₁₆	—	79	2	no	—
277	#533	—	2	1	no	—
278	#533	—	2	1	no	—
279	#533	—	2	1	no	—
280	#533	—	2	1	no	—
281	#533	—	2	1	no	—
282	#533	—	2	1	no	—
283	#533	—	2	1	no	—
284	#533	—	2	1	no	—
285	C₂×C₄⋊Q₈	C₂×D₇₉	1	1	yes	characteristic
286	C₂×C₄⋊Q₈	C₂×D₇₉	1	1	yes	characteristic
287	C₂×#125	Dic₇₉	1	2	yes	—
288	C₂×C₂²⋊Q₈	Dic₇₉	1	2	yes	—
289	C₂×C₂²⋊Q₈	C₂×D₇₉	1	2	yes	—
290	C₂×C₄×Q₈	Dic₇₉	1	2	yes	—
291	C₂×C₄×Q₈	C₂×D₇₉	1	2	yes	—
292	C₂×#117	Dic₇₉	1	2	yes	—
293	C₂²×C₄²	C₂×D₇₉	1	1	yes	characteristic
294	#432	—	158	1	no	—
295	#432	—	158	1	no	—
296	#431	—	158	1	no	—
297	#431	—	158	1	no	—
298	#423	—	79	2	no	—
299	#423	—	79	2	no	—
300	#423	—	79	2	no	—
301	#423	—	158	1	no	—
302	#423	—	158	1	no	—
303	C₂×C₄⋊C₈	—	158	1	no	—
304	C₂×C₄⋊C₈	—	158	1	no	—
305	C₂×#101	—	79	8	no	—
306	#407	—	79	2	no	—
307	C₄×M₁₆	—	79	2	no	—
308	#343	—	79	8	no	—
309	C₂²×Q₈	C₂×Dic₇₉	1	2	yes	—
310	C₂²×Q₈	C₂²×D₇₉	1	2	yes	—
311	C₂³×C₄	C₂×Dic₇₉	1	1	yes	characteristic
312	C₂³×C₄	C₂×Dic₇₉	1	1	yes	characteristic
313	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
314	C₂×M₁₆	—	316	4	no	—
315	C₂×M₁₆	—	79	4	no	—
316	C₂×M₁₆	—	79	4	no	—
317	C₂×M₁₆	—	158	2	no	—
318	C₂²×C₈	—	158	2	no	—
319	C₄⋊Q₈	—	2	1	no	—
320	C₄⋊Q₈	—	2	1	no	—
321	C₄⋊Q₈	—	2	1	no	—
322	C₄⋊Q₈	—	2	1	no	—
323	C₄⋊Q₈	—	2	1	no	—
324	C₄⋊Q₈	—	2	1	no	—
325	C₄⋊Q₈	—	2	1	no	—
326	C₄⋊Q₈	—	2	1	no	—
327	#125	—	2	2	no	—
328	#125	—	2	2	no	—
329	#125	—	2	2	no	—
330	#125	—	2	2	no	—
331	C₂²⋊Q₈	—	2	2	no	—
332	C₂²⋊Q₈	—	2	2	no	—
333	C₂²⋊Q₈	—	2	2	no	—
334	C₂²⋊Q₈	—	2	2	no	—
335	C₂²⋊Q₈	—	2	2	no	—
336	C₂²⋊Q₈	—	2	2	no	—
337	C₂²⋊Q₈	—	2	2	no	—
338	C₂²⋊Q₈	—	2	2	no	—
339	C₄×Q₈	—	2	2	no	—
340	C₄×Q₈	—	2	2	no	—
341	C₄×Q₈	—	2	2	no	—
342	C₄×Q₈	—	2	2	no	—
343	C₄×Q₈	—	2	2	no	—
344	C₄×Q₈	—	2	2	no	—
345	C₄×Q₈	—	2	2	no	—
346	C₄×Q₈	—	2	2	no	—
347	#117	—	2	2	no	—
348	#117	—	2	2	no	—
349	#117	—	2	2	no	—
350	#117	—	2	2	no	—
351	C₂×C₄⋊C₄	C₂×Dic₇₉	1	2	yes	—
352	C₂×C₄⋊C₄	C₂×Dic₇₉	1	2	yes	—
353	C₂×C₄⋊C₄	C₂×Dic₇₉	1	2	yes	—
354	C₂×C₄⋊C₄	C₂×Dic₇₉	1	4	yes	—
355	C₂×C₄⋊C₄	C₂×Dic₇₉	1	4	yes	—
356	C₂×C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
357	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	4	yes	—
358	C₂×C₄²	C₂×Dic₇₉	1	4	yes	—
359	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
360	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
361	C₂×C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
362	C₂×C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
363	C₂×C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
364	C₂×C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
365	C₂×C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
366	C₂×C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
367	C₂×C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
368	C₂×C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
369	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
370	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
371	C₄⋊C₈	—	158	2	no	—
372	C₄⋊C₈	—	158	2	no	—
373	C₄⋊C₈	—	158	2	no	—
374	C₄⋊C₈	—	158	2	no	—
375	C₄⋊C₈	—	158	2	no	—
376	C₄⋊C₈	—	158	2	no	—
377	#101	—	316	8	no	—
378	C₂²⋊C₈	—	158	2	no	—
379	C₂²⋊C₈	—	158	2	no	—
380	#97	—	158	2	no	—
381	C₄×C₈	—	158	2	no	—
382	C₂⁴	C₂²×Dic₇₉	1	1	yes	characteristic
383	C₂×Q₈	—	2	4	no	—
384	C₂×Q₈	—	2	4	no	—
385	C₂×Q₈	—	2	2	no	—
386	C₂×Q₈	—	2	2	no	—
387	C₂×Q₈	—	2	2	no	—
388	C₂×Q₈	—	2	2	no	—
389	C₂×Q₈	—	4	4	no	—
390	C₂²×C₄	—	2	2	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	2	4	no	—
393	C₂²×C₄	—	4	2	no	—
394	C₂²×C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
395	C₂²×C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
396	C₂²×C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
397	C₂²×C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
398	C₂²×C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
399	C₂²×C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
400	C₂²×C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
401	C₂²×C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
402	C₂²×C₄	C₂²×Dic₇₉	1	4	yes	—
403	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
404	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
405	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
406	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
407	C₂²×C₄	C₂²×Dic₇₉	1	4	yes	—
408	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
409	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
410	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
411	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
412	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
413	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
414	M₁₆	—	316	4	no	—
415	M₁₆	—	158	4	no	—
416	M₁₆	—	158	8	no	—
417	M₁₆	—	158	4	no	—
418	C₂×C₈	—	316	4	no	—
419	C₂×C₈	—	158	4	no	—
420	C₂×C₈	—	158	4	no	—
421	C₄⋊C₄	—	2	2	no	—
422	C₄⋊C₄	—	2	2	no	—
423	C₄⋊C₄	—	2	2	no	—
424	C₄⋊C₄	—	2	2	no	—
425	C₄⋊C₄	—	2	4	no	—
426	C₄⋊C₄	—	2	4	no	—
427	C₄⋊C₄	—	2	4	no	—
428	C₄⋊C₄	—	2	4	no	—
429	C₄⋊C₄	—	2	2	no	—
430	C₄⋊C₄	—	2	2	no	—
431	C₄⋊C₄	—	2	2	no	—
432	C₄⋊C₄	—	2	2	no	—
433	C₂²⋊C₄	—	2	4	no	—
434	C₂²⋊C₄	—	2	4	no	—
435	C₄²	—	2	4	no	—
436	C₄²	—	2	4	no	—
437	C₄²	C₂²⋊Dic₇₉	1	1	yes	characteristic
438	C₄²	C₂²⋊Dic₇₉	1	1	yes	characteristic
439	C₄²	C₂²⋊Dic₇₉	1	1	yes	characteristic
440	C₄²	C₂²⋊Dic₇₉	1	1	yes	characteristic
441	C₄²	C₂²⋊Dic₇₉	1	1	yes	characteristic
442	C₄²	C₂²⋊Dic₇₉	1	1	yes	characteristic
443	C₄²	C₂²⋊Dic₇₉	1	1	yes	characteristic
444	C₄²	C₂²⋊Dic₇₉	1	1	yes	characteristic
445	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
446	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
447	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
448	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
449	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
450	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
451	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
452	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
453	C₂³	—	2	2	no	—
454	C₂³	—	2	2	no	—
455	C₂³	—	4	1	no	—
456	C₂³	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
457	C₂³	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
458	C₂³	C₂³×Dic₇₉	1	1	yes	characteristic
459	Q₈	—	4	4	no	—
460	Q₈	—	4	4	no	—
461	Q₈	—	4	4	no	—
462	Q₈	—	4	2	no	—
463	Q₈	—	4	2	no	—
464	C₂×C₄	—	2	2	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	1	no	—
476	C₂×C₄	—	2	1	no	—
477	C₂×C₄	—	2	1	no	—
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	2	4	no	—
480	C₂×C₄	—	2	4	no	—
481	C₂×C₄	—	2	8	no	—
482	C₂×C₄	—	4	1	no	—
483	C₂×C₄	—	4	1	no	—
484	C₂×C₄	—	4	1	no	—
485	C₂×C₄	—	4	4	no	—
486	C₂×C₄	#14579080	1	4	yes	complemented
487	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
488	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
489	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
490	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
491	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
492	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
493	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
494	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
495	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
496	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
497	C₂×C₄	C₂²×C₂²⋊D₇₉	1	1	yes	characteristic
498	C₂×C₄	C₂²×C₂²⋊D₇₉	1	1	yes	characteristic
499	C₂×C₄	#14579207	1	2	yes	—
500	C₂×C₄	#14579208	1	2	yes	—
501	C₈	—	316	4	no	—
502	C₈	—	316	4	no	—
503	C₂²	—	2	1	no	—
504	C₂²	—	2	1	no	—
505	C₂²	—	2	1	no	—
506	C₂²	—	2	1	no	—
507	C₂²	—	2	1	no	—
508	C₂²	—	2	1	no	—
509	C₂²	—	2	1	no	—
510	C₂²	—	4	4	no	—
511	C₂²	C₂×#14579080	1	2	yes	—
512	C₂²	C₂²×C₂²⋊Dic₇₉	1	1	yes	characteristic
513	C₂²	#19099046	1	2	yes	—
514	C₄	—	2	1	no	—
515	C₄	—	2	1	no	—
516	C₄	—	2	1	no	—
517	C₄	—	2	1	no	—
518	C₄	—	2	1	no	—
519	C₄	—	2	1	no	—
520	C₄	—	2	1	no	—
521	C₄	—	4	4	no	—
522	C₄	—	4	4	no	—
523	C₄	C₂×#14579080	1	2	yes	—
524	C₄	C₂×#14579080	1	2	yes	—
525	C₄	#19098547	1	2	yes	—
526	C₄	#19099127	1	1	yes	characteristic
527	C₄	#19099134	1	1	yes	characteristic
528	C₄	#19099141	1	2	yes	—
529	C₂	—	2	2	no	—
530	C₂	—	2	2	no	—
531	C₂	—	4	1	no	—
532	C₂	#23765992	1	1	yes	characteristic
533	C₂	C₂²×#14579080	1	1	yes	characteristic
534	C₂	C₂×#19098547	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×C₂²⋊Dic₇₉
commutator	C₂³×C₇₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₇₉
Fitting	C₂×#533×C₇₉	C₂
socle	C₂²×C₇₉	C₂²×C₂²⋊C₄
prime radical	C₂⁴×C₇₉	C₂²×C₄
cosocle	C₂²×C₄×C₇₉	C₂⁴
hypercenter	C₂×#533	D₇₉
hypocenter	C₇₉	#21879
LCS	G ▷ C₂³×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄² ◁ C₂×#533

Complements

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

N	H ≅ G/N	type
3. #23764390	C₂	semidirect
4. #23764245	C₂	semidirect
6. #23763396	C₂	semidirect
218. C₂×C₄×C₇₉	#101	semidirect
275. C₇₉	#21879	semidirect
486. C₂×C₄	#14579080	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×#19098587	2
#23764390	2
#23764245	2
#23763869	2
#23763396	2
C₂×#533×C₇₉	2
#21879	79