Subgroups — #34254304

Order 20224.

984 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23772429	C₂	1	1	yes	maximal, characteristic, complemented
2	#23772424	C₂	1	1	yes	maximal, characteristic, complemented
3	#23761769	C₂	1	2	yes	maximal, complemented
4	#23761764	C₂	1	2	yes	maximal, complemented
5	#23761756	C₂	1	2	yes	maximal, complemented
6	#23761748	C₂	1	2	yes	maximal, complemented
7	#23761718	C₂	1	2	yes	maximal, complemented
8	C₂×#19098289	C₂	1	2	yes	maximal, complemented
9	C₂×#539×C₇₉	C₂	1	1	yes	maximal, characteristic
10	#19098635	—	2	4	no	—
11	D₄×C₇₉⋊C₈	—	2	4	no	—
12	#19098620	C₂²	1	2	yes	—
13	#19098616	C₂²	1	2	yes	—
14	#19098527	C₂²	1	2	yes	—
15	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
16	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
17	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
18	#19098289	C₂²	1	4	yes	—
19	#19098289	C₂²	1	4	yes	—
20	#19098289	C₂²	1	4	yes	—
21	#19098287	C₂²	1	4	yes	—
22	#539×C₇₉	—	2	4	no	—
23	#539×C₇₉	—	2	4	no	—
24	C₂×#126×C₇₉	C₄	1	1	yes	characteristic
25	C₂×#126×C₇₉	C₂²	1	1	yes	characteristic
26	C₂×#125×C₇₉	C₄	1	1	yes	characteristic
27	C₂×#125×C₇₉	C₂²	1	1	yes	characteristic
28	C₂×#123×C₇₉	C₄	1	1	yes	characteristic
29	C₂×#123×C₇₉	C₄	1	1	yes	characteristic
30	C₂×#123×C₇₉	C₄	1	1	yes	characteristic
31	C₂×#123×C₇₉	C₂²	1	1	yes	characteristic
32	C₂×C₂²⋊Q₈×C₇₉	C₄	1	1	yes	characteristic
33	C₂×C₂²⋊Q₈×C₇₉	C₄	1	1	yes	characteristic
34	C₂×C₂²⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
35	C₂×#121×C₇₉	C₄	1	1	yes	characteristic
36	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
38	C₂²×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
39	C₂×#11929608	—	2	2	no	—
40	C₂²×C₇₉⋊C₈	—	2	2	no	—
41	C₂²×C₇₉⋊C₈	—	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	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
46	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
47	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
48	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
49	C₂²⋊(C₇₉⋊C₈)	C₂³	1	4	yes	—
50	C₂²⋊(C₇₉⋊C₈)	C₂³	1	4	yes	—
51	#14579072	—	2	2	no	—
52	C₄×C₇₉⋊C₈	—	2	2	no	—
53	C₂²×Q₈×C₇₉	C₂×C₄	1	1	yes	characteristic
54	C₂²×D₄×C₇₉	C₂×C₄	1	1	yes	characteristic
55	C₂²×D₄×C₇₉	C₂×C₄	1	1	yes	characteristic
56	C₂²×D₄×C₇₉	C₂×C₄	1	1	yes	characteristic
57	C₂³×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
58	C₂³×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
59	C₂³×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
60	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
62	#126×C₇₉	—	2	4	no	—
63	#126×C₇₉	—	2	2	no	—
64	#126×C₇₉	—	2	2	no	—
65	#125×C₇₉	—	2	4	no	—
66	#125×C₇₉	—	2	2	no	—
67	#125×C₇₉	—	2	2	no	—
68	#123×C₇₉	—	2	4	no	—
69	#123×C₇₉	—	2	2	no	—
70	#123×C₇₉	—	2	2	no	—
71	#123×C₇₉	—	2	4	no	—
72	#123×C₇₉	—	2	4	no	—
73	C₂²⋊Q₈×C₇₉	—	2	2	no	—
74	C₂²⋊Q₈×C₇₉	—	2	2	no	—
75	C₂²⋊Q₈×C₇₉	—	2	4	no	—
76	C₂²⋊Q₈×C₇₉	—	2	4	no	—
77	#121×C₇₉	—	2	4	no	—
78	C₄×D₄×C₇₉	—	2	2	no	—
79	C₄×D₄×C₇₉	—	2	2	no	—
80	C₄×D₄×C₇₉	D₄	1	4	yes	—
81	C₄×D₄×C₇₉	D₄	1	4	yes	—
82	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
83	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
84	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
85	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
86	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
87	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
89	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
91	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
92	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
93	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
94	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
95	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
96	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
97	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
98	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
99	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
100	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
101	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
102	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
103	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
104	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
105	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
106	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
107	C₂×C₂²⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
108	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
109	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
110	#11929608	—	8	2	no	—
111	C₂×C₇₉⋊C₈	—	2	4	no	—
112	C₂×C₇₉⋊C₈	—	2	4	no	—
113	C₂×C₇₉⋊C₈	—	8	2	no	—
114	C₂×C₇₉⋊C₈	—	8	2	no	—
115	C₂×C₇₉⋊C₈	—	8	2	no	—
116	C₂⁴×C₇₉	C₂²×C₄	1	1	yes	characteristic
117	C₂⁴×C₇₉	C₂²×C₄	1	1	yes	characteristic
118	C₂⁴×C₇₉	C₂²×C₄	1	1	yes	characteristic
119	C₂×Q₈×C₇₉	—	2	2	no	—
120	C₂×Q₈×C₇₉	—	8	1	no	—
121	C₂×D₄×C₇₉	—	2	4	no	—
122	C₂×D₄×C₇₉	—	2	2	no	—
123	C₂×D₄×C₇₉	—	2	4	no	—
124	C₂×D₄×C₇₉	—	2	2	no	—
125	C₂×D₄×C₇₉	—	8	1	no	—
126	C₂×D₄×C₇₉	C₂²⋊C₄	1	4	yes	—
127	C₂²×C₄×C₇₉	—	2	2	no	—
128	C₂²×C₄×C₇₉	—	2	4	no	—
129	C₂²×C₄×C₇₉	—	2	2	no	—
130	C₂²×C₄×C₇₉	—	2	2	no	—
131	C₂²×C₄×C₇₉	—	8	1	no	—
132	C₂²×C₄×C₇₉	—	8	1	no	—
133	C₂²×C₄×C₇₉	—	8	1	no	—
134	C₂²×C₄×C₇₉	—	8	1	no	—
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	1	yes	characteristic
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	C₂×D₄	1	2	yes	—
147	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
148	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
149	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
150	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
151	C₄⋊C₄×C₇₉	—	2	2	no	—
152	C₄⋊C₄×C₇₉	—	2	2	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	—	2	2	no	—
158	C₄⋊C₄×C₇₉	—	2	2	no	—
159	C₄⋊C₄×C₇₉	—	2	2	no	—
160	C₄⋊C₄×C₇₉	—	2	2	no	—
161	C₄⋊C₄×C₇₉	—	2	1	no	—
162	C₄⋊C₄×C₇₉	—	2	1	no	—
163	C₄⋊C₄×C₇₉	—	2	1	no	—
164	C₄⋊C₄×C₇₉	—	2	1	no	—
165	C₄⋊C₄×C₇₉	—	2	1	no	—
166	C₄⋊C₄×C₇₉	—	2	1	no	—
167	C₄⋊C₄×C₇₉	C₂²⋊C₄	1	4	yes	—
168	C₂²⋊C₄×C₇₉	—	2	2	no	—
169	C₂²⋊C₄×C₇₉	—	2	2	no	—
170	C₂²⋊C₄×C₇₉	—	2	2	no	—
171	C₂²⋊C₄×C₇₉	—	2	2	no	—
172	C₂²⋊C₄×C₇₉	—	2	2	no	—
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	1	no	—
177	C₂²⋊C₄×C₇₉	C₂²⋊C₄	1	4	yes	—
178	C₂²⋊C₄×C₇₉	C₂²⋊C₄	1	4	yes	—
179	C₄²×C₇₉	—	2	2	no	—
180	C₄²×C₇₉	C₂×D₄	1	2	yes	—
181	C₄²×C₇₉	C₂×D₄	1	2	yes	—
182	C₂³×C₇₉	—	2	2	no	—
183	C₂³×C₇₉	—	2	1	no	—
184	C₂³×C₇₉	—	2	2	no	—
185	C₂³×C₇₉	—	4	1	no	—
186	C₂³×C₇₉	—	4	1	no	—
187	C₂³×C₇₉	—	4	1	no	—
188	C₂³×C₇₉	—	4	1	no	—
189	C₂³×C₇₉	—	4	1	no	—
190	C₂³×C₇₉	—	4	1	no	—
191	C₂³×C₇₉	C₂×C₂²⋊C₄	1	2	yes	—
192	C₂³×C₇₉	C₂×C₂²⋊C₄	1	2	yes	—
193	C₂³×C₇₉	#131	1	4	yes	—
194	C₂³×C₇₉	C₂³×C₄	1	1	yes	characteristic
195	Q₈×C₇₉	—	8	2	no	—
196	D₄×C₇₉	—	2	8	no	—
197	D₄×C₇₉	—	4	4	no	—
198	D₄×C₇₉	—	8	2	no	—
199	C₂×C₄×C₇₉	—	2	2	no	—
200	C₂×C₄×C₇₉	—	2	1	no	—
201	C₂×C₄×C₇₉	—	2	1	no	—
202	C₂×C₄×C₇₉	—	2	1	no	—
203	C₂×C₄×C₇₉	—	2	1	no	—
204	C₂×C₄×C₇₉	—	2	1	no	—
205	C₂×C₄×C₇₉	—	2	1	no	—
206	C₂×C₄×C₇₉	—	2	1	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	—	4	2	no	—
211	C₂×C₄×C₇₉	—	4	2	no	—
212	C₂×C₄×C₇₉	—	4	2	no	—
213	C₂×C₄×C₇₉	—	4	2	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	1	no	—
218	C₂×C₄×C₇₉	—	4	4	no	—
219	C₂×C₄×C₇₉	—	4	1	no	—
220	C₂×C₄×C₇₉	—	4	1	no	—
221	C₂×C₄×C₇₉	—	4	1	no	—
222	C₂×C₄×C₇₉	—	4	1	no	—
223	C₂×C₄×C₇₉	—	8	2	no	—
224	C₂×C₄×C₇₉	—	8	2	no	—
225	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	2	yes	—
226	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	2	yes	—
227	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	2	yes	—
228	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	2	yes	—
229	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
230	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
231	C₇₉⋊C₈	—	4	4	no	—
232	C₇₉⋊C₈	—	4	4	no	—
233	C₂²×C₇₉	—	2	1	no	—
234	C₂²×C₇₉	—	2	2	no	—
235	C₂²×C₇₉	—	2	1	no	—
236	C₂²×C₇₉	—	2	2	no	—
237	C₂²×C₇₉	—	2	2	no	—
238	C₂²×C₇₉	—	2	2	no	—
239	C₂²×C₇₉	—	2	2	no	—
240	C₂²×C₇₉	—	4	4	no	—
241	C₂²×C₇₉	—	4	1	no	—
242	C₂²×C₇₉	—	4	1	no	—
243	C₂²×C₇₉	—	4	1	no	—
244	C₂²×C₇₉	—	8	2	no	—
245	C₂²×C₇₉	—	8	2	no	—
246	C₂²×C₇₉	#408	1	4	yes	—
247	C₂²×C₇₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
248	C₂²×C₇₉	C₂×#131	1	2	yes	—
249	C₄×C₇₉	—	2	2	no	—
250	C₄×C₇₉	—	2	1	no	—
251	C₄×C₇₉	—	2	1	no	—
252	C₄×C₇₉	—	2	2	no	—
253	C₄×C₇₉	—	2	2	no	—
254	C₄×C₇₉	—	2	2	no	—
255	C₄×C₇₉	—	4	1	no	—
256	C₄×C₇₉	—	4	1	no	—
257	C₄×C₇₉	—	4	1	no	—
258	C₄×C₇₉	—	4	1	no	—
259	C₄×C₇₉	—	4	1	no	—
260	C₄×C₇₉	—	4	1	no	—
261	C₄×C₇₉	—	4	1	no	—
262	#17387	—	79	1	no	maximal, Sylow
263	C₂×C₇₉	—	2	2	no	—
264	C₂×C₇₉	—	2	4	no	—
265	C₂×C₇₉	—	4	2	no	—
266	C₂×C₇₉	—	8	1	no	—
267	C₂×C₇₉	C₂×#408	1	1	yes	characteristic
268	C₂×C₇₉	#2883	1	1	yes	characteristic
269	C₂×C₇₉	#2889	1	1	yes	characteristic
270	C₂×#539	D₇₉	1	1	yes	characteristic
271	#2973	—	79	1	no	—
272	#2972	—	79	1	no	—
273	#1473	—	79	2	no	—
274	#1472	—	79	2	no	—
275	#1470	—	79	2	no	—
276	#1468	—	79	2	no	—
277	#1459	—	79	2	no	—
278	C₂×#324	—	79	2	no	—
279	C₇₉	#17387	1	1	yes	characteristic, complemented, Sylow
280	#539	—	2	4	no	—
281	#539	—	2	4	no	—
282	C₂×#126	Dic₇₉	1	1	yes	characteristic
283	C₂×#126	C₂×D₇₉	1	1	yes	characteristic
284	C₂×#125	Dic₇₉	1	1	yes	characteristic
285	C₂×#125	C₂×D₇₉	1	1	yes	characteristic
286	C₂×#123	Dic₇₉	1	1	yes	characteristic
287	C₂×#123	Dic₇₉	1	1	yes	characteristic
288	C₂×#123	Dic₇₉	1	1	yes	characteristic
289	C₂×#123	C₂×D₇₉	1	1	yes	characteristic
290	C₂×C₂²⋊Q₈	Dic₇₉	1	1	yes	characteristic
291	C₂×C₂²⋊Q₈	Dic₇₉	1	1	yes	characteristic
292	C₂×C₂²⋊Q₈	C₂×D₇₉	1	1	yes	characteristic
293	C₂×#121	Dic₇₉	1	1	yes	characteristic
294	C₂×C₄×D₄	C₂×D₇₉	1	1	yes	characteristic
295	C₂×C₄×D₄	C₂×D₇₉	1	1	yes	characteristic
296	C₂²×C₄⋊C₄	C₂×D₇₉	1	1	yes	characteristic
297	#435	—	158	4	no	—
298	C₈×D₄	—	158	4	no	—
299	#432	—	79	2	no	—
300	#431	—	79	2	no	—
301	#407	—	79	2	no	—
302	C₂×C₂²⋊C₈	—	79	2	no	—
303	C₂×C₂²⋊C₈	—	79	2	no	—
304	C₂×C₂²⋊C₈	—	79	2	no	—
305	#324	—	79	4	no	—
306	#324	—	79	4	no	—
307	#324	—	79	4	no	—
308	#323	—	79	4	no	—
309	C₂²×Q₈	C₂×Dic₇₉	1	1	yes	characteristic
310	C₂²×D₄	C₂×Dic₇₉	1	1	yes	characteristic
311	C₂²×D₄	C₂×Dic₇₉	1	1	yes	characteristic
312	C₂²×D₄	C₂×Dic₇₉	1	1	yes	characteristic
313	C₂³×C₄	C₂×Dic₇₉	1	1	yes	characteristic
314	C₂³×C₄	C₂×Dic₇₉	1	1	yes	characteristic
315	C₂³×C₄	C₂×Dic₇₉	1	1	yes	characteristic
316	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
317	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
318	C₂×M₁₆	—	158	2	no	—
319	C₂²×C₈	—	158	2	no	—
320	C₂²×C₈	—	158	2	no	—
321	C₂²×C₈	—	158	2	no	—
322	#126	—	2	4	no	—
323	#126	—	2	2	no	—
324	#126	—	2	2	no	—
325	#125	—	2	4	no	—
326	#125	—	2	2	no	—
327	#125	—	2	2	no	—
328	#123	—	2	4	no	—
329	#123	—	2	2	no	—
330	#123	—	2	2	no	—
331	#123	—	2	4	no	—
332	#123	—	2	4	no	—
333	C₂²⋊Q₈	—	2	2	no	—
334	C₂²⋊Q₈	—	2	2	no	—
335	C₂²⋊Q₈	—	2	4	no	—
336	C₂²⋊Q₈	—	2	4	no	—
337	#121	—	2	4	no	—
338	C₄×D₄	—	2	2	no	—
339	C₄×D₄	—	2	2	no	—
340	C₄×D₄	C₂²⋊D₇₉	1	4	yes	—
341	C₄×D₄	C₂²⋊D₇₉	1	4	yes	—
342	C₂×C₄⋊C₄	—	2	2	no	—
343	C₂×C₄⋊C₄	—	2	2	no	—
344	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
345	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
346	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
347	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
348	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
349	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
350	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
351	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
352	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
353	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
354	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
355	C₂×C₄⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
356	C₂×C₄⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
357	C₂×C₄⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
358	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
359	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
360	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
361	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
362	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
363	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
364	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
365	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
366	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
367	C₂×C₂²⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
368	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
369	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
370	C₄⋊C₈	—	158	2	no	—
371	C₄⋊C₈	—	158	2	no	—
372	C₂²⋊C₈	—	79	4	no	—
373	C₂²⋊C₈	—	79	4	no	—
374	C₂²⋊C₈	—	158	2	no	—
375	C₂²⋊C₈	—	158	2	no	—
376	C₂²⋊C₈	—	158	2	no	—
377	C₂²⋊C₈	—	158	2	no	—
378	#97	—	158	2	no	—
379	C₄×C₈	—	158	2	no	—
380	C₂⁴	C₂²×Dic₇₉	1	1	yes	characteristic
381	C₂⁴	C₂²×Dic₇₉	1	1	yes	characteristic
382	C₂⁴	C₂²×Dic₇₉	1	1	yes	characteristic
383	C₂×Q₈	—	2	2	no	—
384	C₂×Q₈	—	8	1	no	—
385	C₂×D₄	—	2	4	no	—
386	C₂×D₄	—	2	2	no	—
387	C₂×D₄	—	2	4	no	—
388	C₂×D₄	—	2	2	no	—
389	C₂×D₄	—	8	1	no	—
390	C₂×D₄	C₂²⋊Dic₇₉	1	4	yes	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	2	4	no	—
393	C₂²×C₄	—	2	2	no	—
394	C₂²×C₄	—	2	2	no	—
395	C₂²×C₄	—	8	1	no	—
396	C₂²×C₄	—	8	1	no	—
397	C₂²×C₄	—	8	1	no	—
398	C₂²×C₄	—	8	1	no	—
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	1	yes	characteristic
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	1	yes	characteristic
408	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
409	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
410	C₂²×C₄	C₂×C₂²⋊D₇₉	1	2	yes	—
411	C₂²×C₄	C₂×C₂²⋊D₇₉	1	2	yes	—
412	C₂²×C₄	C₂×C₂²⋊D₇₉	1	2	yes	—
413	C₂²×C₄	C₂×C₂²⋊D₇₉	1	2	yes	—
414	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
415	M₁₆	—	632	2	no	—
416	C₂×C₈	—	632	2	no	—
417	C₂×C₈	—	632	2	no	—
418	C₂×C₈	—	632	2	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	2	no	—
426	C₄⋊C₄	—	2	2	no	—
427	C₄⋊C₄	—	2	2	no	—
428	C₄⋊C₄	—	2	2	no	—
429	C₄⋊C₄	—	2	2	no	—
430	C₄⋊C₄	—	2	2	no	—
431	C₄⋊C₄	—	2	1	no	—
432	C₄⋊C₄	—	2	1	no	—
433	C₄⋊C₄	—	2	1	no	—
434	C₄⋊C₄	—	2	1	no	—
435	C₄⋊C₄	—	2	1	no	—
436	C₄⋊C₄	—	2	1	no	—
437	C₄⋊C₄	C₂²⋊Dic₇₉	1	4	yes	—
438	C₂²⋊C₄	—	2	2	no	—
439	C₂²⋊C₄	—	2	2	no	—
440	C₂²⋊C₄	—	2	2	no	—
441	C₂²⋊C₄	—	2	2	no	—
442	C₂²⋊C₄	—	2	2	no	—
443	C₂²⋊C₄	—	2	2	no	—
444	C₂²⋊C₄	—	2	2	no	—
445	C₂²⋊C₄	—	2	1	no	—
446	C₂²⋊C₄	—	2	1	no	—
447	C₂²⋊C₄	C₂²⋊Dic₇₉	1	4	yes	—
448	C₂²⋊C₄	C₂²⋊Dic₇₉	1	4	yes	—
449	C₄²	—	2	2	no	—
450	C₄²	C₂×C₂²⋊D₇₉	1	2	yes	—
451	C₄²	C₂×C₂²⋊D₇₉	1	2	yes	—
452	C₂³	—	2	2	no	—
453	C₂³	—	2	1	no	—
454	C₂³	—	2	2	no	—
455	C₂³	—	4	1	no	—
456	C₂³	—	4	1	no	—
457	C₂³	—	4	1	no	—
458	C₂³	—	4	1	no	—
459	C₂³	—	4	1	no	—
460	C₂³	—	4	1	no	—
461	C₂³	C₂×C₂²⋊Dic₇₉	1	2	yes	—
462	C₂³	C₂×C₂²⋊Dic₇₉	1	2	yes	—
463	C₂³	#14579168	1	4	yes	—
464	C₂³	C₂³×Dic₇₉	1	1	yes	characteristic
465	Q₈	—	8	2	no	—
466	D₄	—	2	8	no	—
467	D₄	—	4	4	no	—
468	D₄	—	8	2	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	1	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	2	1	no	—
475	C₂×C₄	—	2	1	no	—
476	C₂×C₄	—	2	1	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	4	2	no	—
481	C₂×C₄	—	4	2	no	—
482	C₂×C₄	—	4	2	no	—
483	C₂×C₄	—	4	2	no	—
484	C₂×C₄	—	4	1	no	—
485	C₂×C₄	—	4	1	no	—
486	C₂×C₄	—	4	1	no	—
487	C₂×C₄	—	4	1	no	—
488	C₂×C₄	—	4	4	no	—
489	C₂×C₄	—	4	1	no	—
490	C₂×C₄	—	4	1	no	—
491	C₂×C₄	—	4	1	no	—
492	C₂×C₄	—	4	1	no	—
493	C₂×C₄	—	8	2	no	—
494	C₂×C₄	—	8	2	no	—
495	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	2	yes	—
496	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	2	yes	—
497	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	2	yes	—
498	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	2	yes	—
499	C₂×C₄	C₂²×C₂²⋊D₇₉	1	1	yes	characteristic
500	C₂×C₄	C₂²×C₂²⋊D₇₉	1	1	yes	characteristic
501	C₈	—	316	4	no	—
502	C₈	—	316	4	no	—
503	C₂²	—	2	1	no	—
504	C₂²	—	2	2	no	—
505	C₂²	—	2	1	no	—
506	C₂²	—	2	2	no	—
507	C₂²	—	2	2	no	—
508	C₂²	—	2	2	no	—
509	C₂²	—	2	2	no	—
510	C₂²	—	4	4	no	—
511	C₂²	—	4	1	no	—
512	C₂²	—	4	1	no	—
513	C₂²	—	4	1	no	—
514	C₂²	—	8	2	no	—
515	C₂²	—	8	2	no	—
516	C₂²	#19098530	1	4	yes	—
517	C₂²	C₂²×C₂²⋊Dic₇₉	1	1	yes	characteristic
518	C₂²	C₂×#14579168	1	2	yes	—
519	C₄	—	2	2	no	—
520	C₄	—	2	1	no	—
521	C₄	—	2	1	no	—
522	C₄	—	2	2	no	—
523	C₄	—	2	2	no	—
524	C₄	—	2	2	no	—
525	C₄	—	4	1	no	—
526	C₄	—	4	1	no	—
527	C₄	—	4	1	no	—
528	C₄	—	4	1	no	—
529	C₄	—	4	1	no	—
530	C₄	—	4	1	no	—
531	C₄	—	4	1	no	—
532	C₂	—	2	2	no	—
533	C₂	—	2	4	no	—
534	C₂	—	4	2	no	—
535	C₂	—	8	1	no	—
536	C₂	C₂×#19098530	1	1	yes	characteristic
537	C₂	#23771861	1	1	yes	characteristic
538	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×#539×C₇₉	C₂
socle	C₂²×C₇₉	C₂²×C₂²⋊C₄
prime radical	C₂×#121×C₇₉	C₄
cosocle	C₂²×C₄×C₇₉	C₂⁴
hypercenter	C₂×#539	D₇₉
hypocenter	C₇₉	#17387
LCS	G ▷ C₂³×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄×D₄ ◁ C₂×#539

Complements

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

N	H ≅ G/N	type
1. #23772429	C₂	semidirect
2. #23772424	C₂	semidirect
3. #23761769	C₂	semidirect
4. #23761764	C₂	semidirect
5. #23761756	C₂	semidirect
6. #23761748	C₂	semidirect
7. #23761718	C₂	semidirect
8. C₂×#19098289	C₂	semidirect
279. C₇₉	#17387	semidirect

Maximal subgroups

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

subgroup	index
#23772429	2
#23772424	2
#23761769	2
#23761764	2
#23761756	2
#23761748	2
#23761718	2
C₂×#19098289	2
C₂×#539×C₇₉	2
#17387	79