Subgroups — #34306349

Order 20224.

992 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19098641	C₂	1	1	yes	maximal, characteristic
2	C₂×D₄×C₇₉⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₂×#19098590	C₂	1	2	yes	maximal, complemented
4	#23764119	C₂	1	1	yes	maximal, characteristic, complemented
5	#23764119	C₂	1	1	yes	maximal, characteristic, complemented
6	#23763585	C₂	1	2	yes	maximal, complemented
7	#23763580	C₂	1	2	yes	maximal, complemented
8	#23763552	C₂	1	1	yes	maximal, characteristic, complemented
9	#23763384	C₂	1	2	yes	maximal, complemented
10	C₄×C₄⋊(C₇₉⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₉×#2293	C₂	1	1	yes	maximal, characteristic
12	C₂²×#11929608	C₂²	1	2	yes	—
13	C₂³×C₇₉⋊C₈	C₂²	1	2	yes	—
14	#19098641	—	2	4	no	—
15	D₄×C₇₉⋊C₈	—	2	4	no	—
16	#19098590	—	2	8	no	—
17	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
19	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
20	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
21	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
24	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
25	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
26	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
27	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
29	#19098318	C₂²	1	1	yes	characteristic
30	#19098318	C₂²	1	1	yes	characteristic
31	#19098318	C₂²	1	2	yes	—
32	#19098318	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
34	C₂×#117×C₇₉	C₂²	1	2	yes	—
35	#390×C₇₉	C₄	1	1	yes	characteristic
36	#390×C₇₉	C₄	1	1	yes	characteristic
37	#389×C₇₉	C₄	1	1	yes	characteristic
38	#389×C₇₉	C₄	1	1	yes	characteristic
39	#388×C₇₉	C₄	1	2	yes	—
40	#388×C₇₉	C₄	1	2	yes	—
41	C₄×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
42	C₄×C₂²⋊C₄×C₇₉	C₂²	1	2	yes	—
43	C₄³×C₇₉	C₂²	1	1	yes	characteristic
44	C₂×#11929608	—	2	4	no	—
45	C₂×#11929608	—	2	4	no	—
46	C₂×#11929608	—	4	2	no	—
47	C₂²×C₇₉⋊C₈	—	2	4	no	—
48	C₂²×C₇₉⋊C₈	—	2	4	no	—
49	C₂²×C₇₉⋊C₈	—	4	2	no	—
50	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
51	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
52	C₂²×C₇₉⋊C₈	C₂³	1	2	yes	—
53	C₂²×C₇₉⋊C₈	C₂³	1	2	yes	—
54	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
55	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
56	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
57	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
58	C₄⋊(C₇₉⋊C₈)	—	2	4	no	—
59	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
60	C₄⋊(C₇₉⋊C₈)	—	2	4	no	—
61	C₄⋊(C₇₉⋊C₈)	—	2	4	no	—
62	C₄⋊(C₇₉⋊C₈)	—	4	2	no	—
63	C₄⋊(C₇₉⋊C₈)	D₄	1	4	yes	complemented
64	C₂²⋊(C₇₉⋊C₈)	—	2	4	no	—
65	C₂²⋊(C₇₉⋊C₈)	—	2	4	no	—
66	C₄×C₇₉⋊C₈	—	2	2	no	—
67	C₄×C₇₉⋊C₈	—	2	2	no	—
68	C₂²×D₄×C₇₉	C₂×C₄	1	1	yes	characteristic
69	C₂³×C₄×C₇₉	C₂³	1	2	yes	—
70	C₄×D₄×C₇₉	D₄	1	4	yes	—
71	C₄×D₄×C₇₉	Q₈	1	4	yes	—
72	#117×C₇₉	—	2	4	no	—
73	#117×C₇₉	—	2	4	no	—
74	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
75	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
76	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
78	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
79	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
80	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
81	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
82	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
83	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
84	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
85	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
86	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
87	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
88	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
89	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
90	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
91	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
92	#95×C₇₉	C₂×C₄	1	2	yes	—
93	#95×C₇₉	C₂×C₄	1	2	yes	—
94	#95×C₇₉	C₂×C₄	1	2	yes	—
95	#11929608	—	4	8	no	—
96	C₂×C₇₉⋊C₈	—	2	1	no	—
97	C₂×C₇₉⋊C₈	—	2	1	no	—
98	C₂×C₇₉⋊C₈	—	2	1	no	—
99	C₂×C₇₉⋊C₈	—	2	1	no	—
100	C₂×C₇₉⋊C₈	—	2	2	no	—
101	C₂×C₇₉⋊C₈	—	2	2	no	—
102	C₂×C₇₉⋊C₈	—	2	2	no	—
103	C₂×C₇₉⋊C₈	—	2	2	no	—
104	C₂×C₇₉⋊C₈	—	2	1	no	—
105	C₂×C₇₉⋊C₈	—	2	1	no	—
106	C₂×C₇₉⋊C₈	—	2	1	no	—
107	C₂×C₇₉⋊C₈	—	2	1	no	—
108	C₂×C₇₉⋊C₈	—	2	2	no	—
109	C₂×C₇₉⋊C₈	—	2	2	no	—
110	C₂×C₇₉⋊C₈	—	2	1	no	—
111	C₂×C₇₉⋊C₈	—	2	1	no	—
112	C₂×C₇₉⋊C₈	—	4	8	no	—
113	C₂×C₇₉⋊C₈	C₂×D₄	1	2	yes	—
114	C₂×C₇₉⋊C₈	C₂×D₄	1	2	yes	—
115	C₂⁴×C₇₉	C₂²×C₄	1	2	yes	—
116	C₂×D₄×C₇₉	—	2	2	no	—
117	C₂×D₄×C₇₉	—	2	2	no	—
118	C₂×D₄×C₇₉	C₄⋊C₄	1	4	yes	—
119	C₂²×C₄×C₇₉	—	2	2	no	—
120	C₂²×C₄×C₇₉	—	2	2	no	—
121	C₂²×C₄×C₇₉	—	2	2	no	—
122	C₂²×C₄×C₇₉	—	2	2	no	—
123	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
124	C₂²×C₄×C₇₉	C₂²×C₄	1	2	yes	—
125	C₂²×C₄×C₇₉	C₂²×C₄	1	2	yes	—
126	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
127	C₂²×C₄×C₇₉	C₂²×C₄	1	2	yes	—
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	C₂×D₄	1	4	yes	—
133	C₂²×C₄×C₇₉	C₂×Q₈	1	4	yes	—
134	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
135	C₄⋊C₄×C₇₉	—	2	4	no	—
136	C₄⋊C₄×C₇₉	—	2	4	no	—
137	C₄⋊C₄×C₇₉	—	2	2	no	—
138	C₄⋊C₄×C₇₉	—	2	2	no	—
139	C₄⋊C₄×C₇₉	C₄⋊C₄	1	4	yes	—
140	C₂²⋊C₄×C₇₉	—	2	4	no	—
141	C₂²⋊C₄×C₇₉	—	2	4	no	—
142	C₂²⋊C₄×C₇₉	—	2	4	no	—
143	C₂²⋊C₄×C₇₉	—	4	2	no	—
144	C₂²⋊C₄×C₇₉	C₄⋊C₄	1	8	yes	—
145	C₄²×C₇₉	—	2	2	no	—
146	C₄²×C₇₉	—	2	2	no	—
147	C₄²×C₇₉	—	2	2	no	—
148	C₄²×C₇₉	—	2	2	no	—
149	C₄²×C₇₉	—	2	2	no	—
150	C₄²×C₇₉	—	2	1	no	—
151	C₄²×C₇₉	—	2	1	no	—
152	C₄²×C₇₉	—	4	1	no	—
153	C₄²×C₇₉	C₂×D₄	1	2	yes	—
154	C₄²×C₇₉	C₂×D₄	1	2	yes	—
155	C₄²×C₇₉	C₂×Q₈	1	2	yes	—
156	C₄²×C₇₉	#41	1	2	yes	—
157	C₂³×C₇₉	—	2	2	no	—
158	C₂³×C₇₉	—	2	2	no	—
159	C₂³×C₇₉	—	2	2	no	—
160	C₂³×C₇₉	—	2	2	no	—
161	C₂³×C₇₉	—	2	2	no	—
162	C₂³×C₇₉	—	2	2	no	—
163	C₂³×C₇₉	C₂×C₄⋊C₄	1	4	yes	—
164	C₂³×C₇₉	C₂³×C₄	1	1	yes	characteristic
165	D₄×C₇₉	—	2	8	no	—
166	C₂×C₄×C₇₉	—	2	2	no	—
167	C₂×C₄×C₇₉	—	2	1	no	—
168	C₂×C₄×C₇₉	—	2	2	no	—
169	C₂×C₄×C₇₉	—	2	1	no	—
170	C₂×C₄×C₇₉	—	2	1	no	—
171	C₂×C₄×C₇₉	—	2	1	no	—
172	C₂×C₄×C₇₉	—	2	1	no	—
173	C₂×C₄×C₇₉	—	2	1	no	—
174	C₂×C₄×C₇₉	—	2	1	no	—
175	C₂×C₄×C₇₉	—	2	1	no	—
176	C₂×C₄×C₇₉	—	2	4	no	—
177	C₂×C₄×C₇₉	—	2	4	no	—
178	C₂×C₄×C₇₉	—	2	4	no	—
179	C₂×C₄×C₇₉	—	2	4	no	—
180	C₂×C₄×C₇₉	—	2	2	no	—
181	C₂×C₄×C₇₉	—	2	2	no	—
182	C₂×C₄×C₇₉	—	2	1	no	—
183	C₂×C₄×C₇₉	—	2	1	no	—
184	C₂×C₄×C₇₉	—	2	2	no	—
185	C₂×C₄×C₇₉	—	2	2	no	—
186	C₂×C₄×C₇₉	—	2	2	no	—
187	C₂×C₄×C₇₉	—	2	1	no	—
188	C₂×C₄×C₇₉	—	2	2	no	—
189	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	2	yes	—
190	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	4	yes	—
191	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	2	yes	—
192	C₂×C₄×C₇₉	C₄×D₄	1	2	yes	—
193	C₂×C₄×C₇₉	C₄×D₄	1	2	yes	—
194	C₂×C₄×C₇₉	#131	1	2	yes	—
195	C₂×C₄×C₇₉	#131	1	2	yes	—
196	C₂×C₄×C₇₉	#131	1	2	yes	—
197	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
198	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
199	C₂×C₄×C₇₉	C₂²×Q₈	1	1	yes	characteristic
200	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
201	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
202	C₂×C₄×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
203	C₇₉⋊C₈	—	2	2	no	—
204	C₇₉⋊C₈	—	2	2	no	—
205	C₇₉⋊C₈	—	4	2	no	—
206	C₇₉⋊C₈	—	4	2	no	—
207	C₇₉⋊C₈	—	4	1	no	—
208	C₇₉⋊C₈	—	4	1	no	—
209	C₂²×C₇₉	—	2	4	no	—
210	C₂²×C₇₉	—	2	4	no	—
211	C₂²×C₇₉	—	2	4	no	—
212	C₂²×C₇₉	—	4	2	no	—
213	C₂²×C₇₉	—	4	2	no	—
214	C₂²×C₇₉	—	4	2	no	—
215	C₂²×C₇₉	—	4	2	no	—
216	C₂²×C₇₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
217	C₂²×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
218	C₂²×C₇₉	#520	1	1	yes	characteristic
219	C₂²×C₇₉	C₂×#131	1	1	yes	characteristic
220	C₂²×C₇₉	C₂×#131	1	1	yes	characteristic
221	C₂²×C₇₉	C₂×#131	1	1	yes	characteristic
222	C₂²×C₇₉	#568	1	1	yes	characteristic
223	C₄×C₇₉	—	2	4	no	—
224	C₄×C₇₉	—	2	2	no	—
225	C₄×C₇₉	—	2	2	no	—
226	C₄×C₇₉	—	2	2	no	—
227	C₄×C₇₉	—	2	2	no	—
228	C₄×C₇₉	—	4	2	no	—
229	C₄×C₇₉	—	4	2	no	—
230	C₄×C₇₉	—	4	1	no	—
231	C₄×C₇₉	#424	1	4	yes	complemented
232	C₄×C₇₉	D₄²	1	1	yes	characteristic
233	C₄×C₇₉	#547	1	1	yes	characteristic
234	C₄×C₇₉	D₄×Q₈	1	1	yes	characteristic
235	C₄×C₇₉	#554	1	1	yes	characteristic
236	#22651	—	79	1	no	maximal, Sylow
237	C₂×C₇₉	—	4	4	no	—
238	C₂×C₇₉	D₄×C₄⋊C₄	1	1	yes	characteristic
239	C₂×C₇₉	C₂×#424	1	1	yes	characteristic
240	C₂×C₇₉	#2906	1	1	yes	characteristic
241	C₂×C₇₉	#2931	1	1	yes	characteristic
242	C₂×C₇₉	#2935	1	1	yes	characteristic
243	C₂×C₇₉	#2993	1	1	yes	characteristic
244	C₂×C₇₉	#2994	1	1	yes	characteristic
245	C₂×#436	—	79	1	no	—
246	C₂×C₈×D₄	—	79	1	no	—
247	C₂×#424	—	79	2	no	—
248	#2293	D₇₉	1	1	yes	characteristic
249	#1939	—	79	1	no	—
250	#1939	—	79	1	no	—
251	#1851	—	79	2	no	—
252	#1850	—	79	2	no	—
253	#1842	—	79	1	no	—
254	#1798	—	79	2	no	—
255	C₄×C₄⋊C₈	—	79	1	no	—
256	C₇₉	#22651	1	1	yes	characteristic, complemented, Sylow
257	C₂²×M₁₆	—	79	2	no	—
258	C₂³×C₈	—	79	2	no	—
259	C₂×C₄×D₄	C₂×D₇₉	1	1	yes	characteristic
260	C₂×#117	C₂×D₇₉	1	2	yes	—
261	#436	—	158	4	no	—
262	C₈×D₄	—	158	4	no	—
263	#424	—	158	8	no	—
264	C₂×C₄⋊C₈	—	79	2	no	—
265	C₂×C₄⋊C₈	—	79	1	no	—
266	C₂×C₄⋊C₈	—	79	1	no	—
267	C₂×C₄⋊C₈	—	79	2	no	—
268	C₂×C₄⋊C₈	—	79	1	no	—
269	C₂×C₄⋊C₈	—	79	1	no	—
270	C₂×C₄⋊C₈	—	79	2	no	—
271	C₂×C₄⋊C₈	—	79	2	no	—
272	C₂×C₂²⋊C₈	—	79	2	no	—
273	C₂×C₂²⋊C₈	—	79	2	no	—
274	C₂×C₄×C₈	—	79	1	no	—
275	C₂×C₄×C₈	—	79	1	no	—
276	#390	Dic₇₉	1	1	yes	characteristic
277	#390	Dic₇₉	1	1	yes	characteristic
278	#389	Dic₇₉	1	1	yes	characteristic
279	#389	Dic₇₉	1	1	yes	characteristic
280	#388	Dic₇₉	1	2	yes	—
281	#388	Dic₇₉	1	2	yes	—
282	C₄×C₄⋊C₄	C₂×D₇₉	1	1	yes	characteristic
283	C₄×C₂²⋊C₄	C₂×D₇₉	1	2	yes	—
284	C₄³	C₂×D₇₉	1	1	yes	characteristic
285	#336	—	79	2	no	—
286	#336	—	79	2	no	—
287	#336	—	79	1	no	—
288	#336	—	79	1	no	—
289	C₂²×D₄	C₂×Dic₇₉	1	1	yes	characteristic
290	C₂³×C₄	C₂²×D₇₉	1	2	yes	—
291	C₂×M₁₆	—	316	2	no	—
292	C₂×M₁₆	—	158	4	no	—
293	C₂×M₁₆	—	158	4	no	—
294	C₂²×C₈	—	316	2	no	—
295	C₂²×C₈	—	79	1	no	—
296	C₂²×C₈	—	79	1	no	—
297	C₂²×C₈	—	79	2	no	—
298	C₂²×C₈	—	79	2	no	—
299	C₂²×C₈	—	79	1	no	—
300	C₂²×C₈	—	79	1	no	—
301	C₂²×C₈	—	158	4	no	—
302	C₂²×C₈	—	158	4	no	—
303	C₄×D₄	Dic₁₅₈	1	4	yes	—
304	C₄×D₄	D₃₁₆	1	4	yes	—
305	#117	—	2	4	no	—
306	#117	—	2	4	no	—
307	C₂×C₄⋊C₄	C₂×Dic₇₉	1	2	yes	—
308	C₂×C₄⋊C₄	C₂×Dic₇₉	1	2	yes	—
309	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
310	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
311	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
312	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	2	yes	—
313	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	2	yes	—
314	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	2	yes	—
315	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	2	yes	—
316	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	2	yes	—
317	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
318	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
319	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
320	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
321	C₂×C₄²	C₂²×D₇₉	1	2	yes	—
322	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
323	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
324	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
325	C₄⋊C₈	—	316	2	no	—
326	C₄⋊C₈	—	79	4	no	—
327	C₄⋊C₈	—	158	4	no	—
328	C₄⋊C₈	—	158	4	no	—
329	C₄⋊C₈	—	158	4	no	—
330	C₄⋊C₈	—	158	2	no	—
331	C₄⋊C₈	—	158	2	no	—
332	C₄⋊C₈	—	158	2	no	—
333	C₂²⋊C₈	—	158	4	no	—
334	C₂²⋊C₈	—	158	4	no	—
335	C₄×C₈	—	158	2	no	—
336	C₄×C₈	—	158	2	no	—
337	#95	C₂×Dic₇₉	1	2	yes	—
338	#95	C₂×Dic₇₉	1	2	yes	—
339	#95	C₂×Dic₇₉	1	2	yes	—
340	C₂⁴	C₂²×Dic₇₉	1	2	yes	—
341	C₂×D₄	—	2	2	no	—
342	C₂×D₄	—	2	2	no	—
343	C₂×D₄	C₄⋊Dic₇₉	1	4	yes	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
349	C₂²×C₄	C₂²×Dic₇₉	1	2	yes	—
350	C₂²×C₄	C₂²×Dic₇₉	1	2	yes	—
351	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
352	C₂²×C₄	C₂²×Dic₇₉	1	2	yes	—
353	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
354	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
355	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
356	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
357	C₂²×C₄	C₂×D₃₁₆	1	4	yes	—
358	C₂²×C₄	C₂×Dic₁₅₈	1	4	yes	—
359	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
360	M₁₆	—	316	8	no	—
361	C₂×C₈	—	316	8	no	—
362	C₂×C₈	—	79	2	no	—
363	C₂×C₈	—	79	2	no	—
364	C₂×C₈	—	158	1	no	—
365	C₂×C₈	—	158	1	no	—
366	C₂×C₈	—	158	2	no	—
367	C₂×C₈	—	158	2	no	—
368	C₂×C₈	—	158	1	no	—
369	C₂×C₈	—	158	1	no	—
370	C₂×C₈	—	158	2	no	—
371	C₂×C₈	—	158	2	no	—
372	C₂×C₈	—	158	1	no	—
373	C₂×C₈	—	158	1	no	—
374	C₂×C₈	—	158	2	no	—
375	C₂×C₈	—	158	2	no	—
376	C₂×C₈	—	158	1	no	—
377	C₂×C₈	—	158	1	no	—
378	C₂×C₈	—	158	1	no	—
379	C₂×C₈	—	158	1	no	—
380	C₄⋊C₄	—	2	4	no	—
381	C₄⋊C₄	—	2	4	no	—
382	C₄⋊C₄	—	2	2	no	—
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	C₄⋊Dic₇₉	1	4	yes	—
385	C₂²⋊C₄	—	2	4	no	—
386	C₂²⋊C₄	—	2	4	no	—
387	C₂²⋊C₄	—	2	4	no	—
388	C₂²⋊C₄	—	4	2	no	—
389	C₂²⋊C₄	C₄⋊Dic₇₉	1	8	yes	—
390	C₄²	—	2	2	no	—
391	C₄²	—	2	1	no	—
392	C₄²	—	2	1	no	—
393	C₄²	—	2	2	no	—
394	C₄²	—	2	2	no	—
395	C₄²	—	2	2	no	—
396	C₄²	—	2	2	no	—
397	C₄²	—	4	1	no	—
398	C₄²	D₄×D₇₉	1	2	yes	—
399	C₄²	C₂×D₃₁₆	1	2	yes	—
400	C₄²	C₂×Dic₁₅₈	1	2	yes	—
401	C₄²	#11929623	1	2	yes	—
402	C₂³	—	2	2	no	—
403	C₂³	—	2	2	no	—
404	C₂³	—	2	2	no	—
405	C₂³	—	2	2	no	—
406	C₂³	—	2	2	no	—
407	C₂³	—	2	2	no	—
408	C₂³	C₂×C₄⋊Dic₇₉	1	4	yes	—
409	C₂³	C₂³×Dic₇₉	1	1	yes	characteristic
410	D₄	—	2	8	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	4	no	—
422	C₂×C₄	—	2	4	no	—
423	C₂×C₄	—	2	4	no	—
424	C₂×C₄	—	2	4	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	C₂×C₄⋊Dic₇₉	1	2	yes	—
435	C₂×C₄	C₂×C₄⋊Dic₇₉	1	4	yes	—
436	C₂×C₄	C₂×C₄⋊Dic₇₉	1	2	yes	—
437	C₂×C₄	D₄×Dic₇₉	1	2	yes	—
438	C₂×C₄	D₄×Dic₇₉	1	2	yes	—
439	C₂×C₄	#14579168	1	2	yes	—
440	C₂×C₄	#14579168	1	2	yes	—
441	C₂×C₄	#14579168	1	2	yes	—
442	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
443	C₂×C₄	C₂²×D₃₁₆	1	1	yes	characteristic
444	C₂×C₄	C₂²×Dic₁₅₈	1	1	yes	characteristic
445	C₂×C₄	C₂×#11929623	1	1	yes	characteristic
446	C₂×C₄	#14579207	1	1	yes	characteristic
447	C₂×C₄	#14579208	1	1	yes	characteristic
448	C₈	—	316	2	no	—
449	C₈	—	316	2	no	—
450	C₈	—	316	1	no	—
451	C₈	—	316	1	no	—
452	C₈	—	158	2	no	—
453	C₈	—	158	2	no	—
454	C₂²	—	2	4	no	—
455	C₂²	—	2	4	no	—
456	C₂²	—	2	4	no	—
457	C₂²	—	4	2	no	—
458	C₂²	—	4	2	no	—
459	C₂²	—	4	2	no	—
460	C₂²	—	4	2	no	—
461	C₂²	C₂²×C₄⋊Dic₇₉	1	1	yes	characteristic
462	C₂²	C₂×D₄×Dic₇₉	1	1	yes	characteristic
463	C₂²	#19099046	1	1	yes	characteristic
464	C₂²	C₂×#14579168	1	1	yes	characteristic
465	C₂²	C₂×#14579168	1	1	yes	characteristic
466	C₂²	C₂×#14579168	1	1	yes	characteristic
467	C₂²	#19099330	1	1	yes	characteristic
468	C₄	—	2	4	no	—
469	C₄	—	2	2	no	—
470	C₄	—	2	2	no	—
471	C₄	—	2	2	no	—
472	C₄	—	2	2	no	—
473	C₄	—	4	1	no	—
474	C₄	—	4	2	no	—
475	C₄	—	4	2	no	—
476	C₄	#19098590	1	4	yes	complemented
477	C₄	D₄×D₃₁₆	1	1	yes	characteristic
478	C₄	#19099217	1	1	yes	characteristic
479	C₄	D₄×Dic₁₅₈	1	1	yes	characteristic
480	C₄	#19099270	1	1	yes	characteristic
481	C₂	—	4	4	no	—
482	C₂	D₄×C₄⋊Dic₇₉	1	1	yes	characteristic
483	C₂	C₂×#19098590	1	1	yes	characteristic
484	C₂	#23771968	1	1	yes	characteristic
485	C₂	#23772112	1	1	yes	characteristic
486	C₂	#23772144	1	1	yes	characteristic
487	C₂	#23772549	1	1	yes	characteristic
488	C₂	#23772560	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₇₉
commutator, socle	C₂³×C₇₉	C₂³×C₄
Fitting	C₇₉×#2293	C₂
prime radical	C₂²×D₄×C₇₉	C₂×C₄
cosocle	C₂²×C₄×C₇₉	C₂⁴
hypercenter	#2293	D₇₉
hypocenter	C₇₉	#22651
LCS	G ▷ C₂³×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂²×C₄ ◁ #2293

Complements

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

N	H ≅ G/N	type
3. C₂×#19098590	C₂	semidirect
4. #23764119	C₂	semidirect
5. #23764119	C₂	semidirect
6. #23763585	C₂	semidirect
7. #23763580	C₂	semidirect
8. #23763552	C₂	semidirect
9. #23763384	C₂	semidirect
10. C₄×C₄⋊(C₇₉⋊C₈)	C₂	semidirect
63. C₄⋊(C₇₉⋊C₈)	D₄	semidirect
231. C₄×C₇₉	#424	semidirect
256. C₇₉	#22651	semidirect
476. C₄	#19098590	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19098641	2
C₂×D₄×C₇₉⋊C₈	2
C₂×#19098590	2
#23764119	2
#23763585	2
#23763580	2
#23763552	2
#23763384	2
C₄×C₄⋊(C₇₉⋊C₈)	2
C₇₉×#2293	2
#22651	79