Subgroups — #34197186

Order 20224.

1254 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#14579160	C₂	1	1	yes	maximal, characteristic
2	C₂×#19098326	C₂	1	1	yes	maximal, characteristic
3	C₂×#19098325	C₂	1	1	yes	maximal, characteristic
4	C₂×#19098325	C₂	1	1	yes	maximal, characteristic
5	C₂×#19098317	C₂	1	1	yes	maximal, characteristic
6	#23761629	C₂	1	1	yes	maximal, characteristic
7	C₂×#340×C₇₉	C₂	1	1	yes	maximal, characteristic
8	C₂³×Dic₁₅₈	—	2	1	no	—
9	C₂³×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
10	C₂×#14579160	—	2	2	no	—
11	C₂×#14579160	—	2	2	no	—
12	C₂×#14579160	—	2	2	no	—
13	C₂×#14579160	—	2	2	no	—
14	C₂×#14579160	—	2	2	no	—
15	C₂×#14579160	C₄	1	4	yes	complemented
16	C₂²×C₄⋊Dic₇₉	C₂²	1	1	yes	characteristic
17	C₂²×C₄⋊Dic₇₉	C₂²	1	1	yes	characteristic
18	C₂²×Dic₇₉⋊C₄	—	2	1	no	—
19	C₂²×C₄×Dic₇₉	C₂²	1	1	yes	characteristic
20	C₂×C₇₉⋊#95	—	2	1	no	—
21	C₂×C₇₉⋊#95	—	2	1	no	—
22	#19098326	—	2	2	no	—
23	#19098325	—	2	2	no	—
24	#19098325	—	2	2	no	—
25	#19098317	—	2	2	no	—
26	C₂³×C₈×C₇₉	C₂²	1	1	yes	characteristic
27	C₂²×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
28	C₂²×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
29	#340×C₇₉	—	2	2	no	—
30	C₂²×Dic₁₅₈	—	2	4	no	—
31	C₂²×Dic₁₅₈	—	2	4	no	—
32	C₂²×Dic₁₅₈	—	2	4	no	—
33	C₂²×Dic₁₅₈	—	4	2	no	—
34	C₂²×Dic₁₅₈	—	4	2	no	—
35	C₂²×Dic₁₅₈	—	4	2	no	—
36	C₂²×Dic₁₅₈	—	4	2	no	—
37	C₂³×Dic₇₉	—	2	1	no	—
38	C₂³×Dic₇₉	—	2	1	no	—
39	C₂³×Dic₇₉	D₄	1	1	yes	characteristic
40	C₂³×Dic₇₉	D₄	1	1	yes	characteristic
41	C₂²×C₇₉⋊C₈	—	2	1	no	—
42	C₂²×C₇₉⋊C₈	—	2	1	no	—
43	C₂²×C₇₉⋊C₈	—	2	1	no	—
44	C₂²×C₇₉⋊C₈	—	2	1	no	—
45	C₂²×C₇₉⋊C₈	—	2	1	no	—
46	C₂²×C₇₉⋊C₈	—	2	1	no	—
47	C₂²×C₇₉⋊C₈	Q₈	1	2	yes	complemented
48	#14579160	—	2	8	no	—
49	#14579160	—	2	8	no	—
50	#14579160	—	2	8	no	—
51	#14579160	—	2	8	no	—
52	C₂×C₄⋊Dic₇₉	—	2	1	no	—
53	C₂×C₄⋊Dic₇₉	—	2	1	no	—
54	C₂×C₄⋊Dic₇₉	—	2	1	no	—
55	C₂×C₄⋊Dic₇₉	—	2	1	no	—
56	C₂×C₄⋊Dic₇₉	—	2	1	no	—
57	C₂×C₄⋊Dic₇₉	—	2	1	no	—
58	C₂×C₄⋊Dic₇₉	—	2	1	no	—
59	C₂×C₄⋊Dic₇₉	—	2	1	no	—
60	C₂×C₄⋊Dic₇₉	C₂×C₄	1	2	yes	—
61	C₂×C₄⋊Dic₇₉	D₄	1	2	yes	—
62	C₂×C₄⋊Dic₇₉	D₄	1	2	yes	—
63	C₂×C₄⋊Dic₇₉	Q₈	1	2	yes	complemented
64	C₂×Dic₇₉⋊C₄	—	2	4	no	—
65	C₂×Dic₇₉⋊C₄	—	2	4	no	—
66	C₂×Dic₇₉⋊C₄	—	2	4	no	—
67	C₂×C₄×Dic₇₉	—	2	1	no	—
68	C₂×C₄×Dic₇₉	—	2	1	no	—
69	C₂×C₄×Dic₇₉	—	2	1	no	—
70	C₂×C₄×Dic₇₉	—	2	1	no	—
71	C₂×C₄×Dic₇₉	C₂×C₄	1	2	yes	—
72	C₂×C₄×Dic₇₉	D₄	1	2	yes	—
73	C₇₉⋊#95	—	4	2	no	—
74	C₇₉⋊#95	—	4	2	no	—
75	C₂³×C₄×C₇₉	—	2	1	no	—
76	C₂³×C₄×C₇₉	—	2	1	no	—
77	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
78	C₂²×C₈×C₇₉	—	2	1	no	—
79	C₂²×C₈×C₇₉	—	2	1	no	—
80	C₂²×C₈×C₇₉	—	2	1	no	—
81	C₂²×C₈×C₇₉	—	2	1	no	—
82	C₂²×C₈×C₇₉	—	2	1	no	—
83	C₂²×C₈×C₇₉	—	2	1	no	—
84	C₂²×C₈×C₇₉	Q₈	1	2	yes	complemented
85	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
86	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
87	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
88	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
89	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
90	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
91	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
92	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
93	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
94	C₂×C₄⋊C₄×C₇₉	D₄	1	2	yes	—
95	C₂×C₄⋊C₄×C₇₉	D₄	1	2	yes	—
96	C₂×C₄⋊C₄×C₇₉	Q₈	1	2	yes	complemented
97	C₂×Dic₁₅₈	—	2	16	no	—
98	C₂×Dic₁₅₈	—	4	8	no	—
99	C₂×Dic₁₅₈	—	4	8	no	—
100	C₂×Dic₁₅₈	—	4	8	no	—
101	C₂×Dic₁₅₈	—	4	8	no	—
102	C₂×Dic₁₅₈	—	4	8	no	—
103	C₂×Dic₁₅₈	—	4	8	no	—
104	C₂²×Dic₇₉	—	2	2	no	—
105	C₂²×Dic₇₉	—	2	1	no	—
106	C₂²×Dic₇₉	—	2	1	no	—
107	C₂²×Dic₇₉	—	2	1	no	—
108	C₂²×Dic₇₉	—	2	1	no	—
109	C₂²×Dic₇₉	—	2	2	no	—
110	C₂²×Dic₇₉	—	2	2	no	—
111	C₂²×Dic₇₉	—	2	2	no	—
112	C₂²×Dic₇₉	—	2	1	no	—
113	C₂²×Dic₇₉	—	2	1	no	—
114	C₂²×Dic₇₉	—	2	1	no	—
115	C₂²×Dic₇₉	—	2	1	no	—
116	C₂²×Dic₇₉	—	4	1	no	—
117	C₂²×Dic₇₉	—	4	1	no	—
118	C₂²×Dic₇₉	—	4	1	no	—
119	C₂²×Dic₇₉	—	4	1	no	—
120	C₂²×Dic₇₉	—	4	1	no	—
121	C₂²×Dic₇₉	—	4	1	no	—
122	C₂²×Dic₇₉	—	4	1	no	—
123	C₂²×Dic₇₉	—	4	1	no	—
124	C₂²×Dic₇₉	—	4	1	no	—
125	C₂²×Dic₇₉	—	4	1	no	—
126	C₂²×Dic₇₉	C₂²⋊C₄	1	2	yes	—
127	C₂²×Dic₇₉	C₂²⋊C₄	1	2	yes	—
128	C₂²×Dic₇₉	D₈	1	2	yes	—
129	C₂²×Dic₇₉	SD₁₆	1	2	yes	—
130	C₂²×Dic₇₉	SD₁₆	1	2	yes	—
131	C₂²×Dic₇₉	Q₁₆	1	2	yes	—
132	C₂×C₇₉⋊C₈	—	2	2	no	—
133	C₂×C₇₉⋊C₈	—	2	2	no	—
134	C₂×C₇₉⋊C₈	—	2	2	no	—
135	C₂×C₇₉⋊C₈	—	4	1	no	—
136	C₂×C₇₉⋊C₈	—	4	1	no	—
137	C₂×C₇₉⋊C₈	—	4	1	no	—
138	C₂×C₇₉⋊C₈	—	4	1	no	—
139	C₄⋊Dic₇₉	—	2	2	no	—
140	C₄⋊Dic₇₉	—	2	2	no	—
141	C₄⋊Dic₇₉	—	2	2	no	—
142	C₄⋊Dic₇₉	—	2	2	no	—
143	C₄⋊Dic₇₉	—	2	2	no	—
144	C₄⋊Dic₇₉	—	4	1	no	—
145	C₄⋊Dic₇₉	—	4	1	no	—
146	C₄⋊Dic₇₉	C₂²⋊C₄	1	4	yes	—
147	Dic₇₉⋊C₄	—	2	16	no	—
148	C₄×Dic₇₉	—	2	2	no	—
149	C₄×Dic₇₉	—	2	2	no	—
150	C₄×Dic₇₉	—	2	2	no	—
151	C₄×Dic₇₉	—	2	2	no	—
152	C₂⁴×C₇₉	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₇₉	—	2	2	no	—
154	C₂²×C₄×C₇₉	—	2	2	no	—
155	C₂²×C₄×C₇₉	—	2	2	no	—
156	C₂²×C₄×C₇₉	—	2	2	no	—
157	C₂²×C₄×C₇₉	—	4	1	no	—
158	C₂²×C₄×C₇₉	—	4	1	no	—
159	C₂²×C₄×C₇₉	—	4	1	no	—
160	C₂²×C₄×C₇₉	—	4	1	no	—
161	C₂²×C₄×C₇₉	—	4	1	no	—
162	C₂²×C₄×C₇₉	—	4	1	no	—
163	C₂²×C₄×C₇₉	—	4	1	no	—
164	C₂²×C₄×C₇₉	—	4	1	no	—
165	C₂²×C₄×C₇₉	—	4	1	no	—
166	C₂²×C₄×C₇₉	—	4	1	no	—
167	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
168	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₇₉	C₂×Q₈	1	1	yes	characteristic
174	C₂²×C₄×C₇₉	C₂×Q₈	1	1	yes	characteristic
175	C₂²×C₄×C₇₉	C₂×Q₈	1	1	yes	characteristic
176	C₂²×C₄×C₇₉	C₂×Q₈	1	1	yes	characteristic
177	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
178	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
179	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
180	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
181	C₂×C₈×C₇₉	—	2	2	no	—
182	C₂×C₈×C₇₉	—	2	2	no	—
183	C₂×C₈×C₇₉	—	2	2	no	—
184	C₂×C₈×C₇₉	—	4	1	no	—
185	C₂×C₈×C₇₉	—	4	1	no	—
186	C₂×C₈×C₇₉	—	4	1	no	—
187	C₂×C₈×C₇₉	—	4	1	no	—
188	C₄⋊C₄×C₇₉	—	2	2	no	—
189	C₄⋊C₄×C₇₉	—	2	2	no	—
190	C₄⋊C₄×C₇₉	—	2	2	no	—
191	C₄⋊C₄×C₇₉	—	2	2	no	—
192	C₄⋊C₄×C₇₉	—	2	2	no	—
193	C₄⋊C₄×C₇₉	—	4	1	no	—
194	C₄⋊C₄×C₇₉	—	4	1	no	—
195	C₄⋊C₄×C₇₉	C₂²⋊C₄	1	4	yes	—
196	C₂³×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
197	C₂³×C₇₉	#120	1	1	yes	characteristic
198	C₂³×C₇₉	#120	1	1	yes	characteristic
199	C₂³×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
200	C₂³×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
201	C₂³×C₇₉	#124	1	1	yes	characteristic
202	C₂³×C₇₉	C₄⋊Q₈	1	1	yes	characteristic
203	C₂³×C₇₉	C₂×D₈	1	1	yes	characteristic
204	C₂³×C₇₉	C₂×SD₁₆	1	1	yes	characteristic
205	C₂³×C₇₉	C₂×SD₁₆	1	1	yes	characteristic
206	C₂³×C₇₉	C₂×Q₁₆	1	1	yes	characteristic
207	C₂³×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
208	C₂³×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
209	C₂³×C₇₉	#137	1	1	yes	characteristic
210	C₂³×C₇₉	#137	1	1	yes	characteristic
211	C₂×C₄×C₇₉	—	2	4	no	—
212	C₂×C₄×C₇₉	—	4	2	no	—
213	C₂×C₄×C₇₉	—	4	2	no	—
214	C₂×C₄×C₇₉	—	4	2	no	—
215	C₂×C₄×C₇₉	—	4	2	no	—
216	C₂×C₄×C₇₉	—	4	2	no	—
217	C₂×C₄×C₇₉	—	4	2	no	—
218	C₂×C₄×C₇₉	—	4	2	no	—
219	C₂×C₄×C₇₉	—	4	2	no	—
220	C₂×C₄×C₇₉	—	4	2	no	—
221	C₂×C₄×C₇₉	—	8	1	no	—
222	C₂×C₄×C₇₉	—	8	1	no	—
223	C₂×C₄×C₇₉	—	8	1	no	—
224	C₂×C₄×C₇₉	—	8	1	no	—
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	C₄×Q₈	1	1	yes	characteristic
228	C₂×C₄×C₇₉	C₄×Q₈	1	1	yes	characteristic
229	C₂×C₄×C₇₉	C₄×Q₈	1	1	yes	characteristic
230	C₂×C₄×C₇₉	C₄×Q₈	1	1	yes	characteristic
231	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
232	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
233	C₂×C₄×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
234	C₂×C₄×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
235	C₂×C₄×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
236	C₂×C₄×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
237	C₂×C₄×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
238	C₂×C₄×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
239	C₂×C₄×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
240	C₂×C₄×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
241	C₂×C₄×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
242	C₂×C₄×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
243	C₂×C₄×C₇₉	#124	1	1	yes	characteristic
244	C₂×C₄×C₇₉	#124	1	1	yes	characteristic
245	C₂×C₄×C₇₉	#124	1	1	yes	characteristic
246	C₂×C₄×C₇₉	#124	1	1	yes	characteristic
247	C₂×C₄×C₇₉	#124	1	1	yes	characteristic
248	C₂×C₄×C₇₉	C₄⋊Q₈	1	1	yes	characteristic
249	C₂×C₄×C₇₉	C₄⋊Q₈	1	1	yes	characteristic
250	C₂×C₄×C₇₉	C₄⋊Q₈	1	1	yes	characteristic
251	C₂×C₄×C₇₉	C₄⋊Q₈	1	1	yes	characteristic
252	C₂×C₄×C₇₉	C₄⋊Q₈	1	1	yes	characteristic
253	C₂×Dic₇₉	—	2	2	no	—
254	C₂×Dic₇₉	—	2	2	no	—
255	C₂×Dic₇₉	—	2	2	no	—
256	C₂×Dic₇₉	—	2	2	no	—
257	C₂×Dic₇₉	—	2	2	no	—
258	C₂×Dic₇₉	—	2	2	no	—
259	C₂×Dic₇₉	—	2	2	no	—
260	C₂×Dic₇₉	—	2	2	no	—
261	C₂×Dic₇₉	—	2	2	no	—
262	C₂×Dic₇₉	—	2	2	no	—
263	C₂×Dic₇₉	—	2	2	no	—
264	C₂×Dic₇₉	—	2	2	no	—
265	C₂×Dic₇₉	—	2	4	no	—
266	C₂×Dic₇₉	—	4	2	no	—
267	C₂×Dic₇₉	—	4	2	no	—
268	C₂×Dic₇₉	—	4	2	no	—
269	C₂×Dic₇₉	—	4	2	no	—
270	C₂×Dic₇₉	—	4	2	no	—
271	C₂×Dic₇₉	—	4	2	no	—
272	C₂×Dic₇₉	—	4	2	no	—
273	C₂×Dic₇₉	—	4	2	no	—
274	C₂×Dic₇₉	—	4	2	no	—
275	C₂×Dic₇₉	—	8	1	no	—
276	C₂×Dic₇₉	—	8	1	no	—
277	C₂×Dic₇₉	—	8	1	no	—
278	C₂×Dic₇₉	—	8	1	no	—
279	C₂×Dic₇₉	#102	1	4	yes	—
280	C₂×Dic₇₉	#103	1	4	yes	—
281	Dic₁₅₈	—	4	32	no	—
282	C₈×C₇₉	—	4	2	no	—
283	C₇₉⋊C₈	—	4	2	no	—
284	C₂²×C₇₉	#379	1	1	yes	characteristic
285	C₂²×C₇₉	#391	1	1	yes	characteristic
286	C₂²×C₇₉	#391	1	1	yes	characteristic
287	C₂²×C₇₉	#393	1	1	yes	characteristic
288	C₂²×C₇₉	#393	1	1	yes	characteristic
289	C₂²×C₇₉	#395	1	1	yes	characteristic
290	C₂²×C₇₉	#395	1	1	yes	characteristic
291	C₂²×C₇₉	C₂×#102	1	1	yes	characteristic
292	C₂²×C₇₉	C₂×#103	1	1	yes	characteristic
293	C₂²×C₇₉	#418	1	1	yes	characteristic
294	C₂²×C₇₉	#419	1	1	yes	characteristic
295	C₂²×C₇₉	#447	1	1	yes	characteristic
296	C₂²×C₇₉	#447	1	1	yes	characteristic
297	C₂²×C₇₉	#448	1	1	yes	characteristic
298	C₂²×C₇₉	#448	1	1	yes	characteristic
299	C₂²×C₇₉	#450	1	1	yes	characteristic
300	C₂²×C₇₉	#450	1	1	yes	characteristic
301	C₂²×C₇₉	#451	1	1	yes	characteristic
302	C₂²×C₇₉	#451	1	1	yes	characteristic
303	C₂²×C₇₉	#474	1	1	yes	characteristic
304	C₂²×C₇₉	#474	1	1	yes	characteristic
305	C₂²×C₇₉	#475	1	1	yes	characteristic
306	C₂²×C₇₉	#475	1	1	yes	characteristic
307	C₂²×C₇₉	#476	1	1	yes	characteristic
308	C₂²×C₇₉	#476	1	1	yes	characteristic
309	C₂²×C₇₉	#477	1	1	yes	characteristic
310	C₂²×C₇₉	#477	1	1	yes	characteristic
311	C₂²×C₇₉	#486	1	1	yes	characteristic
312	C₂²×C₇₉	#487	1	1	yes	characteristic
313	C₂²×C₇₉	#489	1	1	yes	characteristic
314	C₂²×C₇₉	#489	1	1	yes	characteristic
315	C₂²×C₇₉	#498	1	1	yes	characteristic
316	C₂²×C₇₉	#500	1	1	yes	characteristic
317	C₂²×C₇₉	#501	1	1	yes	characteristic
318	C₂²×C₇₉	#501	1	1	yes	characteristic
319	C₄×C₇₉	—	4	4	no	—
320	C₄×C₇₉	—	8	2	no	—
321	C₄×C₇₉	#391	1	1	yes	characteristic
322	C₄×C₇₉	#391	1	1	yes	characteristic
323	C₄×C₇₉	#391	1	1	yes	characteristic
324	C₄×C₇₉	#391	1	1	yes	characteristic
325	C₄×C₇₉	#393	1	1	yes	characteristic
326	C₄×C₇₉	#393	1	1	yes	characteristic
327	C₄×C₇₉	#395	1	1	yes	characteristic
328	C₄×C₇₉	#395	1	1	yes	characteristic
329	Dic₇₉	—	2	4	no	—
330	Dic₇₉	—	2	4	no	—
331	Dic₇₉	—	4	4	no	—
332	Dic₇₉	—	8	2	no	—
333	#11384	—	79	1	no	maximal, Sylow
334	C₂×C₇₉	#1446	1	1	yes	characteristic
335	C₂×C₇₉	#1786	1	1	yes	characteristic
336	C₂×C₇₉	#1787	1	1	yes	characteristic
337	C₂×C₇₉	#1987	1	1	yes	characteristic
338	C₂×C₇₉	#1988	1	1	yes	characteristic
339	C₂×C₇₉	#1990	1	1	yes	characteristic
340	C₂×C₇₉	#1993	1	1	yes	characteristic
341	C₂×C₇₉	#2023	1	1	yes	characteristic
342	C₂×C₇₉	#2023	1	1	yes	characteristic
343	C₂×C₇₉	#2024	1	1	yes	characteristic
344	C₂×C₇₉	#2024	1	1	yes	characteristic
345	C₂×C₇₉	#2057	1	1	yes	characteristic
346	C₂×C₇₉	#2057	1	1	yes	characteristic
347	C₂×C₇₉	#2058	1	1	yes	characteristic
348	C₂×C₇₉	#2058	1	1	yes	characteristic
349	C₂²×C₄⋊Q₈	—	79	1	no	—
350	C₂×#340	—	79	1	no	—
351	C₂×#340	—	79	1	no	—
352	C₂×#340	—	79	1	no	—
353	C₂×#340	D₇₉	1	1	yes	characteristic
354	C₂×#336	—	79	1	no	—
355	C₄⋊#95	—	79	1	no	—
356	C₇₉	#11384	1	1	yes	characteristic, complemented, Sylow
357	C₂³×Q₈	—	158	1	no	—
358	C₂³×C₈	—	79	1	no	—
359	C₂³×C₈	C₂×D₇₉	1	1	yes	characteristic
360	C₂×C₄⋊Q₈	—	79	4	no	—
361	C₂×C₄⋊Q₈	—	158	2	no	—
362	C₂×C₄⋊Q₈	—	158	2	no	—
363	C₂×C₄⋊Q₈	—	158	2	no	—
364	C₂×C₄⋊Q₈	—	158	2	no	—
365	C₂×C₄⋊Q₈	—	158	2	no	—
366	C₂²×C₄⋊C₄	—	79	1	no	—
367	C₂²×C₄⋊C₄	—	79	1	no	—
368	C₂²×C₄⋊C₄	—	158	1	no	—
369	C₂²×C₄⋊C₄	C₂×D₇₉	1	1	yes	characteristic
370	C₂²×C₄⋊C₄	C₂×D₇₉	1	1	yes	characteristic
371	C₂²×C₄²	—	79	1	no	—
372	C₂×#95	—	158	1	no	—
373	C₂×#95	—	158	1	no	—
374	#340	—	2	2	no	—
375	#340	—	158	2	no	—
376	#340	—	158	2	no	—
377	#340	—	158	2	no	—
378	#336	—	158	2	no	—
379	C₂²×Q₈	—	316	2	no	—
380	C₂²×Q₈	—	316	2	no	—
381	C₂²×Q₈	—	316	2	no	—
382	C₂²×Q₈	—	316	2	no	—
383	C₂²×Q₈	—	158	4	no	—
384	C₂²×Q₈	—	158	4	no	—
385	C₂²×Q₈	—	158	4	no	—
386	C₂³×C₄	—	2	1	no	—
387	C₂³×C₄	—	2	1	no	—
388	C₂³×C₄	—	79	1	no	—
389	C₂³×C₄	—	79	1	no	—
390	C₂³×C₄	—	158	1	no	—
391	C₂³×C₄	—	158	1	no	—
392	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
393	C₂²×C₈	—	2	1	no	—
394	C₂²×C₈	—	2	1	no	—
395	C₂²×C₈	—	2	1	no	—
396	C₂²×C₈	—	2	1	no	—
397	C₂²×C₈	—	2	1	no	—
398	C₂²×C₈	—	2	1	no	—
399	C₂²×C₈	—	79	2	no	—
400	C₂²×C₈	—	158	1	no	—
401	C₂²×C₈	—	158	1	no	—
402	C₂²×C₈	—	158	1	no	—
403	C₂²×C₈	—	158	1	no	—
404	C₂²×C₈	—	158	1	no	—
405	C₂²×C₈	—	158	1	no	—
406	C₂²×C₈	Dic₁₅₈	1	2	yes	complemented
407	C₄⋊Q₈	—	158	8	no	—
408	C₄⋊Q₈	—	158	8	no	—
409	C₄⋊Q₈	—	158	8	no	—
410	C₄⋊Q₈	—	158	8	no	—
411	C₂×C₄⋊C₄	—	2	1	no	—
412	C₂×C₄⋊C₄	—	2	1	no	—
413	C₂×C₄⋊C₄	—	2	1	no	—
414	C₂×C₄⋊C₄	—	2	1	no	—
415	C₂×C₄⋊C₄	—	2	1	no	—
416	C₂×C₄⋊C₄	—	2	1	no	—
417	C₂×C₄⋊C₄	—	2	1	no	—
418	C₂×C₄⋊C₄	—	2	1	no	—
419	C₂×C₄⋊C₄	—	79	2	no	—
420	C₂×C₄⋊C₄	—	79	2	no	—
421	C₂×C₄⋊C₄	—	79	2	no	—
422	C₂×C₄⋊C₄	—	79	2	no	—
423	C₂×C₄⋊C₄	—	158	1	no	—
424	C₂×C₄⋊C₄	—	158	1	no	—
425	C₂×C₄⋊C₄	—	158	1	no	—
426	C₂×C₄⋊C₄	—	158	1	no	—
427	C₂×C₄⋊C₄	—	158	1	no	—
428	C₂×C₄⋊C₄	—	158	4	no	—
429	C₂×C₄⋊C₄	—	158	4	no	—
430	C₂×C₄⋊C₄	—	158	4	no	—
431	C₂×C₄⋊C₄	—	158	1	no	—
432	C₂×C₄⋊C₄	—	158	1	no	—
433	C₂×C₄⋊C₄	—	158	1	no	—
434	C₂×C₄⋊C₄	Dic₁₅₈	1	2	yes	complemented
435	C₂×C₄⋊C₄	C₄×D₇₉	1	2	yes	—
436	C₂×C₄⋊C₄	D₃₁₆	1	2	yes	—
437	C₂×C₄⋊C₄	C₂²⋊D₇₉	1	2	yes	—
438	C₂×C₄²	—	79	2	no	—
439	C₂×C₄²	—	79	2	no	—
440	C₂×C₄²	—	158	1	no	—
441	C₂×C₄²	—	158	1	no	—
442	C₂×C₄²	—	158	1	no	—
443	C₂×C₄²	—	158	1	no	—
444	#95	—	316	2	no	—
445	#95	—	316	2	no	—
446	C₂⁴	D₄×D₇₉	1	1	yes	characteristic
447	C₂×Q₈	—	316	8	no	—
448	C₂×Q₈	—	316	8	no	—
449	C₂×Q₈	—	316	8	no	—
450	C₂×Q₈	—	316	8	no	—
451	C₂×Q₈	—	316	8	no	—
452	C₂×Q₈	—	316	8	no	—
453	C₂×Q₈	—	158	16	no	—
454	C₂²×C₄	—	2	2	no	—
455	C₂²×C₄	—	2	2	no	—
456	C₂²×C₄	—	2	2	no	—
457	C₂²×C₄	—	2	2	no	—
458	C₂²×C₄	—	4	1	no	—
459	C₂²×C₄	—	4	1	no	—
460	C₂²×C₄	—	4	1	no	—
461	C₂²×C₄	—	4	1	no	—
462	C₂²×C₄	—	4	1	no	—
463	C₂²×C₄	—	4	1	no	—
464	C₂²×C₄	—	4	1	no	—
465	C₂²×C₄	—	4	1	no	—
466	C₂²×C₄	—	4	1	no	—
467	C₂²×C₄	—	4	1	no	—
468	C₂²×C₄	—	316	1	no	—
469	C₂²×C₄	—	316	1	no	—
470	C₂²×C₄	—	316	1	no	—
471	C₂²×C₄	—	316	1	no	—
472	C₂²×C₄	—	316	1	no	—
473	C₂²×C₄	—	316	1	no	—
474	C₂²×C₄	—	316	1	no	—
475	C₂²×C₄	—	316	1	no	—
476	C₂²×C₄	—	316	1	no	—
477	C₂²×C₄	—	316	1	no	—
478	C₂²×C₄	—	79	2	no	—
479	C₂²×C₄	—	79	2	no	—
480	C₂²×C₄	—	79	2	no	—
481	C₂²×C₄	—	79	2	no	—
482	C₂²×C₄	—	79	2	no	—
483	C₂²×C₄	—	79	2	no	—
484	C₂²×C₄	—	158	2	no	—
485	C₂²×C₄	—	158	2	no	—
486	C₂²×C₄	—	158	2	no	—
487	C₂²×C₄	—	158	2	no	—
488	C₂²×C₄	—	158	1	no	—
489	C₂²×C₄	—	158	1	no	—
490	C₂²×C₄	—	158	1	no	—
491	C₂²×C₄	—	158	1	no	—
492	C₂²×C₄	—	158	1	no	—
493	C₂²×C₄	—	158	1	no	—
494	C₂²×C₄	—	158	1	no	—
495	C₂²×C₄	—	158	1	no	—
496	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
497	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
498	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
499	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
500	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
501	C₂²×C₄	C₂×D₃₁₆	1	1	yes	characteristic
502	C₂²×C₄	Q₈×D₇₉	1	1	yes	characteristic
503	C₂²×C₄	Q₈×D₇₉	1	1	yes	characteristic
504	C₂²×C₄	C₂×Dic₁₅₈	1	1	yes	characteristic
505	C₂²×C₄	C₂×Dic₁₅₈	1	1	yes	characteristic
506	C₂²×C₄	#11929623	1	1	yes	characteristic
507	C₂²×C₄	#11929623	1	1	yes	characteristic
508	C₂²×C₄	#11929624	1	1	yes	characteristic
509	C₂²×C₄	#11929624	1	1	yes	characteristic
510	C₂×C₈	—	2	2	no	—
511	C₂×C₈	—	2	2	no	—
512	C₂×C₈	—	2	2	no	—
513	C₂×C₈	—	4	1	no	—
514	C₂×C₈	—	4	1	no	—
515	C₂×C₈	—	4	1	no	—
516	C₂×C₈	—	4	1	no	—
517	C₂×C₈	—	316	1	no	—
518	C₂×C₈	—	316	1	no	—
519	C₂×C₈	—	316	1	no	—
520	C₂×C₈	—	316	1	no	—
521	C₂×C₈	—	158	2	no	—
522	C₂×C₈	—	158	2	no	—
523	C₂×C₈	—	158	2	no	—
524	C₄⋊C₄	—	2	2	no	—
525	C₄⋊C₄	—	2	2	no	—
526	C₄⋊C₄	—	2	2	no	—
527	C₄⋊C₄	—	2	2	no	—
528	C₄⋊C₄	—	2	2	no	—
529	C₄⋊C₄	—	4	1	no	—
530	C₄⋊C₄	—	4	1	no	—
531	C₄⋊C₄	—	316	1	no	—
532	C₄⋊C₄	—	316	1	no	—
533	C₄⋊C₄	—	79	4	no	—
534	C₄⋊C₄	—	158	16	no	—
535	C₄⋊C₄	—	158	2	no	—
536	C₄⋊C₄	—	158	2	no	—
537	C₄⋊C₄	—	158	2	no	—
538	C₄⋊C₄	—	158	2	no	—
539	C₄⋊C₄	—	158	2	no	—
540	C₄⋊C₄	(C₂×D₇₉)⋊C₄	1	4	yes	—
541	C₄²	—	158	2	no	—
542	C₄²	—	158	2	no	—
543	C₄²	—	158	2	no	—
544	C₄²	—	158	2	no	—
545	C₂³	C₂²⋊C₄×D₇₉	1	1	yes	characteristic
546	C₂³	#14579129	1	1	yes	characteristic
547	C₂³	#14579131	1	1	yes	characteristic
548	C₂³	#14579138	1	1	yes	characteristic
549	C₂³	#14579139	1	1	yes	characteristic
550	C₂³	#14579147	1	1	yes	characteristic
551	C₂³	#14579160	1	1	yes	characteristic
552	C₂³	D₈×D₇₉	1	1	yes	characteristic
553	C₂³	SD₁₆×D₇₉	1	1	yes	characteristic
554	C₂³	SD₁₆×D₇₉	1	1	yes	characteristic
555	C₂³	Q₁₆×D₇₉	1	1	yes	characteristic
556	C₂³	#14579185	1	1	yes	characteristic
557	C₂³	#14579188	1	1	yes	characteristic
558	C₂³	#14579190	1	1	yes	characteristic
559	C₂³	#14579193	1	1	yes	characteristic
560	Q₈	—	316	32	no	—
561	C₂×C₄	—	2	4	no	—
562	C₂×C₄	—	4	2	no	—
563	C₂×C₄	—	4	2	no	—
564	C₂×C₄	—	4	2	no	—
565	C₂×C₄	—	4	2	no	—
566	C₂×C₄	—	4	2	no	—
567	C₂×C₄	—	4	2	no	—
568	C₂×C₄	—	4	2	no	—
569	C₂×C₄	—	4	2	no	—
570	C₂×C₄	—	4	2	no	—
571	C₂×C₄	—	8	1	no	—
572	C₂×C₄	—	8	1	no	—
573	C₂×C₄	—	8	1	no	—
574	C₂×C₄	—	8	1	no	—
575	C₂×C₄	—	316	2	no	—
576	C₂×C₄	—	316	2	no	—
577	C₂×C₄	—	316	2	no	—
578	C₂×C₄	—	316	2	no	—
579	C₂×C₄	—	316	2	no	—
580	C₂×C₄	—	316	2	no	—
581	C₂×C₄	—	316	2	no	—
582	C₂×C₄	—	316	2	no	—
583	C₂×C₄	—	316	2	no	—
584	C₂×C₄	—	79	4	no	—
585	C₂×C₄	—	79	4	no	—
586	C₂×C₄	—	632	1	no	—
587	C₂×C₄	—	632	1	no	—
588	C₂×C₄	—	632	1	no	—
589	C₂×C₄	—	632	1	no	—
590	C₂×C₄	—	158	4	no	—
591	C₂×C₄	—	158	2	no	—
592	C₂×C₄	—	158	2	no	—
593	C₂×C₄	—	158	2	no	—
594	C₂×C₄	—	158	2	no	—
595	C₂×C₄	—	158	2	no	—
596	C₂×C₄	—	158	2	no	—
597	C₂×C₄	—	158	2	no	—
598	C₂×C₄	—	158	2	no	—
599	C₂×C₄	—	158	2	no	—
600	C₂×C₄	—	158	2	no	—
601	C₂×C₄	—	158	2	no	—
602	C₂×C₄	—	158	2	no	—
603	C₂×C₄	C₂²⋊C₄×D₇₉	1	1	yes	characteristic
604	C₂×C₄	C₂×(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
605	C₂×C₄	#14579126	1	1	yes	characteristic
606	C₂×C₄	#14579126	1	1	yes	characteristic
607	C₂×C₄	C₄×Dic₁₅₈	1	1	yes	characteristic
608	C₂×C₄	C₄×Dic₁₅₈	1	1	yes	characteristic
609	C₂×C₄	#14579129	1	1	yes	characteristic
610	C₂×C₄	#14579131	1	1	yes	characteristic
611	C₂×C₄	#14579138	1	1	yes	characteristic
612	C₂×C₄	#14579138	1	1	yes	characteristic
613	C₂×C₄	#14579138	1	1	yes	characteristic
614	C₂×C₄	#14579139	1	1	yes	characteristic
615	C₂×C₄	#14579139	1	1	yes	characteristic
616	C₂×C₄	#14579139	1	1	yes	characteristic
617	C₂×C₄	#14579140	1	1	yes	characteristic
618	C₂×C₄	#14579140	1	1	yes	characteristic
619	C₂×C₄	#14579141	1	1	yes	characteristic
620	C₂×C₄	#14579141	1	1	yes	characteristic
621	C₂×C₄	#14579147	1	1	yes	characteristic
622	C₂×C₄	#14579147	1	1	yes	characteristic
623	C₂×C₄	#14579147	1	1	yes	characteristic
624	C₂×C₄	#14579148	1	1	yes	characteristic
625	C₂×C₄	#14579149	1	1	yes	characteristic
626	C₂×C₄	#14579159	1	1	yes	characteristic
627	C₂×C₄	#14579160	1	1	yes	characteristic
628	C₂×C₄	#14579160	1	1	yes	characteristic
629	C₂×C₄	#14579160	1	1	yes	characteristic
630	C₂×C₄	#14579161	1	1	yes	characteristic
631	C₈	—	4	2	no	—
632	C₈	—	316	2	no	—
633	C₂²	#19098418	1	1	yes	characteristic
634	C₂²	#19098467	1	1	yes	characteristic
635	C₂²	#19098467	1	1	yes	characteristic
636	C₂²	#19098475	1	1	yes	characteristic
637	C₂²	#19098476	1	1	yes	characteristic
638	C₂²	#19098483	1	1	yes	characteristic
639	C₂²	#19098484	1	1	yes	characteristic
640	C₂²	#102×D₇₉	1	1	yes	characteristic
641	C₂²	#103×D₇₉	1	1	yes	characteristic
642	C₂²	#19098566	1	1	yes	characteristic
643	C₂²	#19098570	1	1	yes	characteristic
644	C₂²	#19098695	1	1	yes	characteristic
645	C₂²	#19098698	1	1	yes	characteristic
646	C₂²	#19098700	1	1	yes	characteristic
647	C₂²	#19098703	1	1	yes	characteristic
648	C₂²	#19098712	1	1	yes	characteristic
649	C₂²	#19098715	1	1	yes	characteristic
650	C₂²	#19098717	1	1	yes	characteristic
651	C₂²	#19098720	1	1	yes	characteristic
652	C₂²	#19098841	1	1	yes	characteristic
653	C₂²	#19098842	1	1	yes	characteristic
654	C₂²	#19098846	1	1	yes	characteristic
655	C₂²	#19098847	1	1	yes	characteristic
656	C₂²	#19098851	1	1	yes	characteristic
657	C₂²	#19098852	1	1	yes	characteristic
658	C₂²	#19098856	1	1	yes	characteristic
659	C₂²	#19098857	1	1	yes	characteristic
660	C₂²	#19098908	1	1	yes	characteristic
661	C₂²	#19098912	1	1	yes	characteristic
662	C₂²	#19098921	1	1	yes	characteristic
663	C₂²	#19098924	1	1	yes	characteristic
664	C₂²	#19098960	1	1	yes	characteristic
665	C₂²	#19098967	1	1	yes	characteristic
666	C₂²	#19098970	1	1	yes	characteristic
667	C₂²	#19098971	1	1	yes	characteristic
668	C₄	—	4	4	no	—
669	C₄	—	8	2	no	—
670	C₄	—	316	4	no	—
671	C₄	—	632	2	no	—
672	C₄	—	158	4	no	—
673	C₄	—	158	4	no	—
674	C₄	#19098467	1	1	yes	characteristic
675	C₄	#19098467	1	1	yes	characteristic
676	C₄	#19098468	1	1	yes	characteristic
677	C₄	#19098469	1	1	yes	characteristic
678	C₄	#19098475	1	1	yes	characteristic
679	C₄	#19098476	1	1	yes	characteristic
680	C₄	#19098483	1	1	yes	characteristic
681	C₄	#19098484	1	1	yes	characteristic
682	C₂	#23761670	1	1	yes	characteristic
683	C₂	#23763329	1	1	yes	characteristic
684	C₂	#23763333	1	1	yes	characteristic
685	C₂	#23764346	1	1	yes	characteristic
686	C₂	#23764350	1	1	yes	characteristic
687	C₂	#23764359	1	1	yes	characteristic
688	C₂	#23764371	1	1	yes	characteristic
689	C₂	#23764534	1	1	yes	characteristic
690	C₂	#23764535	1	1	yes	characteristic
691	C₂	#23764539	1	1	yes	characteristic
692	C₂	#23764540	1	1	yes	characteristic
693	C₂	#23764726	1	1	yes	characteristic
694	C₂	#23764727	1	1	yes	characteristic
695	C₂	#23764731	1	1	yes	characteristic
696	C₂	#23764732	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	D₄×D₇₉
commutator	C₂²×C₄×C₇₉	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₇₉
Fitting	C₂×#340×C₇₉	C₂
socle, prime radical	C₂⁴×C₇₉	C₂×D₄
cosocle	C₂³×C₄×C₇₉	C₂³
hypercenter	C₂×#340	D₇₉
hypocenter	C₇₉	#11384
LCS	G ▷ C₂²×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₄ ◁ C₂×#340

Complements

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

N	H ≅ G/N	type
15. C₂×#14579160	C₄	semidirect
47. C₂²×C₇₉⋊C₈	Q₈	semidirect
63. C₂×C₄⋊Dic₇₉	Q₈	semidirect
84. C₂²×C₈×C₇₉	Q₈	semidirect
96. C₂×C₄⋊C₄×C₇₉	Q₈	semidirect
356. C₇₉	#11384	semidirect
406. C₂²×C₈	Dic₁₅₈	semidirect
434. C₂×C₄⋊C₄	Dic₁₅₈	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#14579160	2
C₂×#19098326	2
C₂×#19098325	2
C₂×#19098317	2
#23761629	2
C₂×#340×C₇₉	2
#11384	79