Subgroups — #34306340

Order 20224.

1096 conjugacy classes of subgroups.

The subgroup lattice has 438 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	2	yes	maximal
2	C₂×#19098587	C₂	1	2	yes	maximal, complemented
3	#23764119	C₂	1	2	yes	maximal, complemented
4	#23763585	C₂	1	4	yes	maximal, complemented
5	#23763552	C₂	1	1	yes	maximal, characteristic, complemented
6	#23763380	C₂	1	2	yes	maximal, complemented
7	C₄×C₄⋊(C₇₉⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄²×D₄×C₇₉	C₂	1	1	yes	maximal, characteristic
9	C₂²×#11929608	C₂²	1	4	yes	—
10	#19098641	—	2	8	no	—
11	#19098587	—	2	8	no	—
12	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
14	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	4	yes	—
15	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
16	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
17	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
18	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	4	yes	—
19	C₂×C₄×C₇₉⋊C₈	C₂²	1	2	yes	—
20	#19098318	C₂²	1	2	yes	—
21	#19098318	C₂²	1	4	yes	—
22	C₂×C₄×D₄×C₇₉	C₄	1	1	yes	characteristic
23	C₂×C₄×D₄×C₇₉	C₄	1	1	yes	characteristic
24	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
25	C₂²×C₄²×C₇₉	C₂²	1	2	yes	—
26	C₄×C₄⋊C₄×C₇₉	C₄	1	1	yes	characteristic
27	C₄×C₄⋊C₄×C₇₉	C₄	1	1	yes	characteristic
28	C₄×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
29	C₄×C₂²⋊C₄×C₇₉	C₄	1	2	yes	—
30	C₄×C₂²⋊C₄×C₇₉	C₄	1	2	yes	—
31	C₄×C₂²⋊C₄×C₇₉	C₂²	1	2	yes	—
32	C₄³×C₇₉	C₂²	1	1	yes	characteristic
33	C₂×#11929608	—	2	8	no	—
34	C₂×#11929608	—	2	8	no	—
35	C₂×#11929608	—	4	4	no	—
36	C₂²×C₇₉⋊C₈	C₂³	1	2	yes	—
37	C₂²×C₇₉⋊C₈	C₂³	1	4	yes	—
38	C₂²×C₇₉⋊C₈	C₂³	1	2	yes	—
39	C₄⋊(C₇₉⋊C₈)	—	2	4	no	—
40	C₄⋊(C₇₉⋊C₈)	—	2	4	no	—
41	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
42	C₄⋊(C₇₉⋊C₈)	—	2	8	no	—
43	C₄⋊(C₇₉⋊C₈)	—	4	2	no	—
44	C₄⋊(C₇₉⋊C₈)	D₄	1	4	yes	complemented
45	C₂²⋊(C₇₉⋊C₈)	—	2	8	no	—
46	C₄×C₇₉⋊C₈	—	2	4	no	—
47	C₂²×D₄×C₇₉	C₂×C₄	1	1	yes	characteristic
48	C₂³×C₄×C₇₉	C₂×C₄	1	2	yes	—
49	C₂³×C₄×C₇₉	C₂×C₄	1	2	yes	—
50	C₂³×C₄×C₇₉	C₂³	1	2	yes	—
51	C₄×D₄×C₇₉	—	2	4	no	—
52	C₄×D₄×C₇₉	—	2	4	no	—
53	C₄×D₄×C₇₉	D₄	1	4	yes	—
54	C₄×D₄×C₇₉	Q₈	1	4	yes	—
55	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
58	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
59	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
60	C₂×C₂²⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
61	C₂×C₄²×C₇₉	—	2	4	no	—
62	C₂×C₄²×C₇₉	—	2	4	no	—
63	C₂×C₄²×C₇₉	C₂×C₄	1	2	yes	—
64	C₂×C₄²×C₇₉	C₂×C₄	1	2	yes	—
65	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
70	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
71	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
72	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
73	#95×C₇₉	C₂×C₄	1	2	yes	—
74	#95×C₇₉	C₂×C₄	1	2	yes	—
75	#95×C₇₉	C₂×C₄	1	2	yes	—
76	#11929608	—	4	16	no	—
77	C₂×C₇₉⋊C₈	—	2	2	no	—
78	C₂×C₇₉⋊C₈	—	2	2	no	—
79	C₂×C₇₉⋊C₈	—	2	4	no	—
80	C₂×C₇₉⋊C₈	—	2	4	no	—
81	C₂×C₇₉⋊C₈	—	2	2	no	—
82	C₂×C₇₉⋊C₈	—	2	2	no	—
83	C₂×C₇₉⋊C₈	—	2	4	no	—
84	C₂×C₇₉⋊C₈	—	2	2	no	—
85	C₂×C₇₉⋊C₈	C₂×D₄	1	4	yes	—
86	C₂⁴×C₇₉	C₂²×C₄	1	2	yes	—
87	C₂×D₄×C₇₉	—	2	2	no	—
88	C₂×D₄×C₇₉	—	2	2	no	—
89	C₂×D₄×C₇₉	C₄⋊C₄	1	4	yes	—
90	C₂²×C₄×C₇₉	—	2	2	no	—
91	C₂²×C₄×C₇₉	—	2	2	no	—
92	C₂²×C₄×C₇₉	—	2	2	no	—
93	C₂²×C₄×C₇₉	—	2	2	no	—
94	C₂²×C₄×C₇₉	—	2	4	no	—
95	C₂²×C₄×C₇₉	—	2	4	no	—
96	C₂²×C₄×C₇₉	—	2	4	no	—
97	C₂²×C₄×C₇₉	—	2	4	no	—
98	C₂²×C₄×C₇₉	—	2	4	no	—
99	C₂²×C₄×C₇₉	—	4	2	no	—
100	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₇₉	C₂²×C₄	1	2	yes	—
102	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₇₉	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₇₉	C₂²×C₄	1	2	yes	—
107	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₄×C₇₉	C₂×D₄	1	4	yes	—
110	C₂²×C₄×C₇₉	C₂×Q₈	1	4	yes	—
111	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
112	C₄⋊C₄×C₇₉	—	2	2	no	—
113	C₄⋊C₄×C₇₉	C₄⋊C₄	1	4	yes	—
114	C₄⋊C₄×C₇₉	M₁₆	1	4	yes	complemented
115	C₂²⋊C₄×C₇₉	—	2	4	no	—
116	C₂²⋊C₄×C₇₉	—	2	4	no	—
117	C₂²⋊C₄×C₇₉	C₄⋊C₄	1	8	yes	—
118	C₄²×C₇₉	—	2	4	no	—
119	C₄²×C₇₉	—	2	4	no	—
120	C₄²×C₇₉	—	2	2	no	—
121	C₄²×C₇₉	—	2	2	no	—
122	C₄²×C₇₉	—	2	2	no	—
123	C₄²×C₇₉	—	2	2	no	—
124	C₄²×C₇₉	—	2	1	no	—
125	C₄²×C₇₉	—	2	1	no	—
126	C₄²×C₇₉	—	4	1	no	—
127	C₄²×C₇₉	M₁₆	1	4	yes	complemented
128	C₄²×C₇₉	C₂×D₄	1	2	yes	—
129	C₄²×C₇₉	C₂×D₄	1	2	yes	—
130	C₄²×C₇₉	C₂×Q₈	1	2	yes	—
131	C₄²×C₇₉	#41	1	2	yes	—
132	C₂³×C₇₉	—	2	2	no	—
133	C₂³×C₇₉	—	2	2	no	—
134	C₂³×C₇₉	—	2	2	no	—
135	C₂³×C₇₉	—	2	2	no	—
136	C₂³×C₇₉	—	2	2	no	—
137	C₂³×C₇₉	—	2	2	no	—
138	C₂³×C₇₉	C₂×C₄⋊C₄	1	4	yes	—
139	C₂³×C₇₉	C₂³×C₄	1	1	yes	characteristic
140	D₄×C₇₉	—	2	8	no	—
141	C₂×C₄×C₇₉	—	2	2	no	—
142	C₂×C₄×C₇₉	—	2	2	no	—
143	C₂×C₄×C₇₉	—	2	1	no	—
144	C₂×C₄×C₇₉	—	2	2	no	—
145	C₂×C₄×C₇₉	—	2	1	no	—
146	C₂×C₄×C₇₉	—	2	1	no	—
147	C₂×C₄×C₇₉	—	2	1	no	—
148	C₂×C₄×C₇₉	—	2	1	no	—
149	C₂×C₄×C₇₉	—	2	1	no	—
150	C₂×C₄×C₇₉	—	2	2	no	—
151	C₂×C₄×C₇₉	—	2	4	no	—
152	C₂×C₄×C₇₉	—	2	4	no	—
153	C₂×C₄×C₇₉	—	2	4	no	—
154	C₂×C₄×C₇₉	—	2	4	no	—
155	C₂×C₄×C₇₉	—	2	2	no	—
156	C₂×C₄×C₇₉	—	2	1	no	—
157	C₂×C₄×C₇₉	—	2	1	no	—
158	C₂×C₄×C₇₉	—	2	2	no	—
159	C₂×C₄×C₇₉	—	2	1	no	—
160	C₂×C₄×C₇₉	—	2	2	no	—
161	C₂×C₄×C₇₉	—	4	8	no	—
162	C₂×C₄×C₇₉	—	4	8	no	—
163	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	2	yes	—
164	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	4	yes	—
165	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	2	yes	—
166	C₂×C₄×C₇₉	C₄×D₄	1	2	yes	—
167	C₂×C₄×C₇₉	C₄×D₄	1	2	yes	—
168	C₂×C₄×C₇₉	C₂×M₁₆	1	2	yes	—
169	C₂×C₄×C₇₉	C₂×M₁₆	1	4	yes	—
170	C₂×C₄×C₇₉	C₂×M₁₆	1	2	yes	—
171	C₂×C₄×C₇₉	C₂×M₁₆	1	2	yes	—
172	C₂×C₄×C₇₉	C₂×M₁₆	1	2	yes	—
173	C₂×C₄×C₇₉	#131	1	2	yes	—
174	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
175	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
176	C₂×C₄×C₇₉	C₂²×Q₈	1	1	yes	characteristic
177	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
178	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
179	C₂×C₄×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
180	C₇₉⋊C₈	—	2	4	no	—
181	C₇₉⋊C₈	—	4	4	no	—
182	C₇₉⋊C₈	—	4	2	no	—
183	C₂²×C₇₉	—	2	4	no	—
184	C₂²×C₇₉	—	2	4	no	—
185	C₂²×C₇₉	—	2	4	no	—
186	C₂²×C₇₉	—	4	2	no	—
187	C₂²×C₇₉	—	4	2	no	—
188	C₂²×C₇₉	—	4	2	no	—
189	C₂²×C₇₉	—	4	2	no	—
190	C₂²×C₇₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
191	C₂²×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
192	C₂²×C₇₉	#520	1	1	yes	characteristic
193	C₂²×C₇₉	C₂²×M₁₆	1	1	yes	characteristic
194	C₂²×C₇₉	C₂²×M₁₆	1	1	yes	characteristic
195	C₂²×C₇₉	C₂×#131	1	1	yes	characteristic
196	C₂²×C₇₉	#568	1	1	yes	characteristic
197	C₄×C₇₉	—	2	4	no	—
198	C₄×C₇₉	—	2	2	no	—
199	C₄×C₇₉	—	2	2	no	—
200	C₄×C₇₉	—	2	4	no	—
201	C₄×C₇₉	—	2	2	no	—
202	C₄×C₇₉	—	4	2	no	—
203	C₄×C₇₉	—	4	1	no	—
204	C₄×C₇₉	#423	1	4	yes	complemented
205	C₄×C₇₉	#436	1	4	yes	complemented
206	C₄×C₇₉	D₄²	1	1	yes	characteristic
207	C₄×C₇₉	#547	1	1	yes	characteristic
208	C₄×C₇₉	D₄×Q₈	1	1	yes	characteristic
209	C₄×C₇₉	#554	1	1	yes	characteristic
210	#22650	—	79	1	no	maximal, Sylow
211	C₂×C₇₉	—	4	4	no	—
212	C₂×C₇₉	D₄×C₄⋊C₄	1	1	yes	characteristic
213	C₂×C₇₉	C₂×#423	1	1	yes	characteristic
214	C₂×C₇₉	#2906	1	1	yes	characteristic
215	C₂×C₇₉	C₂×#436	1	1	yes	characteristic
216	C₂×C₇₉	D₄×M₁₆	1	1	yes	characteristic
217	C₂×C₇₉	#2989	1	1	yes	characteristic
218	C₂×C₇₉	#2991	1	1	yes	characteristic
219	C₂×#436	—	79	2	no	—
220	C₂×#423	—	79	2	no	—
221	C₄²×D₄	D₇₉	1	1	yes	characteristic
222	#1939	—	79	2	no	—
223	#1851	—	79	4	no	—
224	#1842	—	79	1	no	—
225	#1797	—	79	2	no	—
226	C₄×C₄⋊C₈	—	79	1	no	—
227	C₇₉	#22650	1	1	yes	characteristic, complemented, Sylow
228	C₂²×M₁₆	—	79	4	no	—
229	C₂×C₄×D₄	Dic₇₉	1	1	yes	characteristic
230	C₂×C₄×D₄	Dic₇₉	1	1	yes	characteristic
231	C₂×C₄×D₄	C₂×D₇₉	1	1	yes	characteristic
232	C₂²×C₄²	C₂×D₇₉	1	2	yes	—
233	#436	—	158	8	no	—
234	#423	—	158	8	no	—
235	C₂×C₄⋊C₈	—	79	2	no	—
236	C₂×C₄⋊C₈	—	79	1	no	—
237	C₂×C₄⋊C₈	—	79	1	no	—
238	C₂×C₄⋊C₈	—	79	2	no	—
239	C₂×C₄⋊C₈	—	79	2	no	—
240	C₂×C₄⋊C₈	—	79	4	no	—
241	C₂×C₂²⋊C₈	—	79	4	no	—
242	C₂×C₄×C₈	—	79	2	no	—
243	C₄×C₄⋊C₄	Dic₇₉	1	1	yes	characteristic
244	C₄×C₄⋊C₄	Dic₇₉	1	1	yes	characteristic
245	C₄×C₄⋊C₄	C₂×D₇₉	1	1	yes	characteristic
246	C₄×C₂²⋊C₄	Dic₇₉	1	2	yes	—
247	C₄×C₂²⋊C₄	Dic₇₉	1	2	yes	—
248	C₄×C₂²⋊C₄	C₂×D₇₉	1	2	yes	—
249	C₄³	C₂×D₇₉	1	1	yes	characteristic
250	#336	—	79	4	no	—
251	#336	—	79	2	no	—
252	C₂²×D₄	C₂×Dic₇₉	1	1	yes	characteristic
253	C₂³×C₄	C₂×Dic₇₉	1	2	yes	—
254	C₂³×C₄	C₂×Dic₇₉	1	2	yes	—
255	C₂³×C₄	C₂²×D₇₉	1	2	yes	—
256	C₂×M₁₆	—	316	4	no	—
257	C₂×M₁₆	—	158	8	no	—
258	C₂×M₁₆	—	158	8	no	—
259	C₂²×C₈	—	79	2	no	—
260	C₂²×C₈	—	79	4	no	—
261	C₂²×C₈	—	79	2	no	—
262	C₄×D₄	—	2	4	no	—
263	C₄×D₄	—	2	4	no	—
264	C₄×D₄	Dic₁₅₈	1	4	yes	—
265	C₄×D₄	D₃₁₆	1	4	yes	—
266	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
267	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
268	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
269	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	2	yes	—
270	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	2	yes	—
271	C₂×C₂²⋊C₄	C₂×Dic₇₉	1	2	yes	—
272	C₂×C₄²	—	2	4	no	—
273	C₂×C₄²	—	2	4	no	—
274	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
275	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
276	C₂×C₄²	C₂×Dic₇₉	1	2	yes	—
277	C₂×C₄²	C₂×Dic₇₉	1	2	yes	—
278	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
279	C₂×C₄²	C₂×Dic₇₉	1	1	yes	characteristic
280	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
281	C₂×C₄²	C₂²×D₇₉	1	2	yes	—
282	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
283	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
284	C₄⋊C₈	—	316	2	no	—
285	C₄⋊C₈	—	79	4	no	—
286	C₄⋊C₈	—	158	8	no	—
287	C₄⋊C₈	—	158	4	no	—
288	C₄⋊C₈	—	158	4	no	—
289	C₄⋊C₈	—	158	2	no	—
290	C₂²⋊C₈	—	158	8	no	—
291	C₄×C₈	—	158	4	no	—
292	#95	C₂×Dic₇₉	1	2	yes	—
293	#95	C₂×Dic₇₉	1	2	yes	—
294	#95	C₂×Dic₇₉	1	2	yes	—
295	C₂⁴	C₂²×Dic₇₉	1	2	yes	—
296	C₂×D₄	—	2	2	no	—
297	C₂×D₄	—	2	2	no	—
298	C₂×D₄	C₄⋊Dic₇₉	1	4	yes	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	4	no	—
304	C₂²×C₄	—	2	4	no	—
305	C₂²×C₄	—	2	4	no	—
306	C₂²×C₄	—	2	4	no	—
307	C₂²×C₄	—	2	4	no	—
308	C₂²×C₄	—	4	2	no	—
309	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
310	C₂²×C₄	C₂²×Dic₇₉	1	2	yes	—
311	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
312	C₂²×C₄	C₂²×Dic₇₉	1	2	yes	—
313	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
314	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
315	C₂²×C₄	C₂²×Dic₇₉	1	2	yes	—
316	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
317	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
318	C₂²×C₄	C₂×D₃₁₆	1	4	yes	—
319	C₂²×C₄	C₂×Dic₁₅₈	1	4	yes	—
320	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
321	M₁₆	—	316	16	no	—
322	C₂×C₈	—	79	4	no	—
323	C₂×C₈	—	158	2	no	—
324	C₂×C₈	—	158	4	no	—
325	C₂×C₈	—	158	2	no	—
326	C₂×C₈	—	158	4	no	—
327	C₂×C₈	—	158	2	no	—
328	C₂×C₈	—	158	4	no	—
329	C₂×C₈	—	158	2	no	—
330	C₂×C₈	—	158	2	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	C₄⋊Dic₇₉	1	4	yes	—
333	C₄⋊C₄	#11929608	1	4	yes	complemented
334	C₂²⋊C₄	—	2	4	no	—
335	C₂²⋊C₄	—	2	4	no	—
336	C₂²⋊C₄	C₄⋊Dic₇₉	1	8	yes	—
337	C₄²	—	2	2	no	—
338	C₄²	—	2	1	no	—
339	C₄²	—	2	1	no	—
340	C₄²	—	2	4	no	—
341	C₄²	—	2	4	no	—
342	C₄²	—	2	2	no	—
343	C₄²	—	2	2	no	—
344	C₄²	—	2	2	no	—
345	C₄²	—	4	1	no	—
346	C₄²	#11929608	1	4	yes	complemented
347	C₄²	D₄×D₇₉	1	2	yes	—
348	C₄²	C₂×D₃₁₆	1	2	yes	—
349	C₄²	C₂×Dic₁₅₈	1	2	yes	—
350	C₄²	#11929623	1	2	yes	—
351	C₂³	—	2	2	no	—
352	C₂³	—	2	2	no	—
353	C₂³	—	2	2	no	—
354	C₂³	—	2	2	no	—
355	C₂³	—	2	2	no	—
356	C₂³	—	2	2	no	—
357	C₂³	C₂×C₄⋊Dic₇₉	1	4	yes	—
358	C₂³	C₂³×Dic₇₉	1	1	yes	characteristic
359	D₄	—	2	8	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	4	no	—
371	C₂×C₄	—	2	4	no	—
372	C₂×C₄	—	2	4	no	—
373	C₂×C₄	—	2	4	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	4	8	no	—
381	C₂×C₄	—	4	8	no	—
382	C₂×C₄	C₂×C₄⋊Dic₇₉	1	2	yes	—
383	C₂×C₄	C₂×C₄⋊Dic₇₉	1	4	yes	—
384	C₂×C₄	C₂×C₄⋊Dic₇₉	1	2	yes	—
385	C₂×C₄	D₄×Dic₇₉	1	2	yes	—
386	C₂×C₄	D₄×Dic₇₉	1	2	yes	—
387	C₂×C₄	C₂×#11929608	1	2	yes	—
388	C₂×C₄	C₂×#11929608	1	4	yes	—
389	C₂×C₄	C₂×#11929608	1	2	yes	—
390	C₂×C₄	C₂×#11929608	1	2	yes	—
391	C₂×C₄	C₂×#11929608	1	2	yes	—
392	C₂×C₄	#14579168	1	2	yes	—
393	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
394	C₂×C₄	C₂²×D₃₁₆	1	1	yes	characteristic
395	C₂×C₄	C₂²×Dic₁₅₈	1	1	yes	characteristic
396	C₂×C₄	C₂×#11929623	1	1	yes	characteristic
397	C₂×C₄	#14579207	1	1	yes	characteristic
398	C₂×C₄	#14579208	1	1	yes	characteristic
399	C₈	—	316	4	no	—
400	C₈	—	316	2	no	—
401	C₈	—	158	4	no	—
402	C₂²	—	2	4	no	—
403	C₂²	—	2	4	no	—
404	C₂²	—	2	4	no	—
405	C₂²	—	4	2	no	—
406	C₂²	—	4	2	no	—
407	C₂²	—	4	2	no	—
408	C₂²	—	4	2	no	—
409	C₂²	C₂²×C₄⋊Dic₇₉	1	1	yes	characteristic
410	C₂²	C₂×D₄×Dic₇₉	1	1	yes	characteristic
411	C₂²	#19099046	1	1	yes	characteristic
412	C₂²	C₂²×#11929608	1	1	yes	characteristic
413	C₂²	C₂²×#11929608	1	1	yes	characteristic
414	C₂²	C₂×#14579168	1	1	yes	characteristic
415	C₂²	#19099330	1	1	yes	characteristic
416	C₄	—	2	4	no	—
417	C₄	—	2	2	no	—
418	C₄	—	2	2	no	—
419	C₄	—	2	2	no	—
420	C₄	—	2	4	no	—
421	C₄	—	4	1	no	—
422	C₄	—	4	2	no	—
423	C₄	#19098587	1	4	yes	complemented
424	C₄	#19098641	1	4	yes	complemented
425	C₄	D₄×D₃₁₆	1	1	yes	characteristic
426	C₄	#19099217	1	1	yes	characteristic
427	C₄	D₄×Dic₁₅₈	1	1	yes	characteristic
428	C₄	#19099270	1	1	yes	characteristic
429	C₂	—	4	4	no	—
430	C₂	D₄×C₄⋊Dic₇₉	1	1	yes	characteristic
431	C₂	C₂×#19098587	1	1	yes	characteristic
432	C₂	#23771968	1	1	yes	characteristic
433	C₂	C₂×#19098641	1	1	yes	characteristic
434	C₂	D₄×#11929608	1	1	yes	characteristic
435	C₂	#23772517	1	1	yes	characteristic
436	C₂	#23772532	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₇₉
commutator, socle	C₂³×C₇₉	C₂³×C₄
Fitting	C₄²×D₄×C₇₉	C₂
prime radical	C₂²×D₄×C₇₉	C₂×C₄
cosocle	C₂²×C₄×C₇₉	C₂⁴
hypercenter	C₄²×D₄	D₇₉
hypocenter	C₇₉	#22650
LCS	G ▷ C₂³×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₄²×D₄

Complements

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

N	H ≅ G/N	type
2. C₂×#19098587	C₂	semidirect
3. #23764119	C₂	semidirect
4. #23763585	C₂	semidirect
5. #23763552	C₂	semidirect
6. #23763380	C₂	semidirect
7. C₄×C₄⋊(C₇₉⋊C₈)	C₂	semidirect
44. C₄⋊(C₇₉⋊C₈)	D₄	semidirect
114. C₄⋊C₄×C₇₉	M₁₆	semidirect
127. C₄²×C₇₉	M₁₆	semidirect
204. C₄×C₇₉	#423	semidirect
205. C₄×C₇₉	#436	semidirect
227. C₇₉	#22650	semidirect
333. C₄⋊C₄	#11929608	semidirect
346. C₄²	#11929608	semidirect
423. C₄	#19098587	semidirect
424. C₄	#19098641	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×#19098587	2
#23764119	2
#23763585	2
#23763552	2
#23763380	2
C₄×C₄⋊(C₇₉⋊C₈)	2
C₄²×D₄×C₇₉	2
#22650	79