Subgroups — C₇₉×#23642 #34135331

Order 20224.

1166 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#428×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#407×C₇₉	C₂	1	1	yes	maximal, characteristic
3	C₇₉×#2280	C₂	1	1	yes	maximal, characteristic
4	C₂×#380×C₇₉	C₂	1	1	yes	maximal, characteristic
5	C₇₉×#2077	C₂	1	2	yes	maximal, complemented
6	C₇₉×#2077	C₂	1	2	yes	maximal, complemented
7	C₇₉×#2076	C₂	1	2	yes	maximal, complemented
8	C₇₉×#2075	C₂	1	2	yes	maximal, complemented
9	C₇₉×#1736	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₉×#1736	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₉×#1736	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂⁴×C₄×C₇₉	C₂²	1	1	yes	characteristic
13	C₂²×M₁₆×C₇₉	C₂²	1	1	yes	characteristic
14	C₂²×M₁₆×C₇₉	C₂²	1	1	yes	characteristic
15	C₂×#117×C₇₉	C₂²	1	1	yes	characteristic
16	C₂×#117×C₇₉	C₂²	1	1	yes	characteristic
17	C₂²×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
18	C₂²×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
19	C₂²×C₂²⋊C₄×C₇₉	—	2	1	no	—
20	#428×C₇₉	—	2	4	no	—
21	C₂×#107×C₇₉	C₂²	1	2	yes	complemented
22	C₂×#106×C₇₉	C₂²	1	2	yes	complemented
23	#407×C₇₉	—	2	4	no	—
24	C₂×C₂²⋊C₈×C₇₉	C₂²	1	2	yes	—
25	C₂×C₂²⋊C₈×C₇₉	C₂²	1	2	yes	—
26	#381×C₇₉	—	2	1	no	—
27	#380×C₇₉	—	2	1	no	—
28	#380×C₇₉	—	2	1	no	—
29	#380×C₇₉	C₂²	1	2	yes	—
30	#380×C₇₉	C₂²	1	2	yes	—
31	#380×C₇₉	C₂²	1	1	yes	characteristic
32	#380×C₇₉	C₂²	1	1	yes	characteristic
33	#380×C₇₉	C₂²	1	1	yes	characteristic
34	#380×C₇₉	C₂²	1	1	yes	characteristic
35	#379×C₇₉	—	2	1	no	—
36	C₄×C₂²⋊C₄×C₇₉	—	2	1	no	—
37	C₄×C₂²⋊C₄×C₇₉	—	2	1	no	—
38	C₂×#95×C₇₉	—	2	1	no	—
39	#340×C₇₉	C₂²	1	2	yes	complemented
40	#340×C₇₉	C₂²	1	2	yes	complemented
41	#340×C₇₉	C₂²	1	2	yes	complemented
42	#340×C₇₉	C₂²	1	2	yes	complemented
43	#340×C₇₉	C₂²	1	2	yes	complemented
44	#340×C₇₉	C₂²	1	2	yes	complemented
45	C₂⁵×C₇₉	D₄	1	1	yes	characteristic
46	C₂³×C₄×C₇₉	—	2	2	no	—
47	C₂³×C₄×C₇₉	—	2	2	no	—
48	C₂³×C₄×C₇₉	—	2	2	no	—
49	C₂³×C₄×C₇₉	—	2	2	no	—
50	C₂³×C₄×C₇₉	—	2	2	no	—
51	C₂³×C₄×C₇₉	—	2	2	no	—
52	C₂³×C₄×C₇₉	—	2	1	no	—
53	C₂³×C₄×C₇₉	—	2	1	no	—
54	C₂³×C₄×C₇₉	D₄	1	1	yes	characteristic
55	C₂³×C₄×C₇₉	D₄	1	1	yes	characteristic
56	C₂³×C₄×C₇₉	D₄	1	1	yes	characteristic
57	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
58	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
59	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
60	C₂×M₁₆×C₇₉	—	2	2	no	—
61	C₂×M₁₆×C₇₉	—	2	2	no	—
62	C₂×M₁₆×C₇₉	—	2	2	no	—
63	C₂×M₁₆×C₇₉	—	2	2	no	—
64	C₂×M₁₆×C₇₉	—	2	2	no	—
65	C₂×M₁₆×C₇₉	D₄	1	4	yes	—
66	C₂²×C₈×C₇₉	C₂³	1	2	yes	—
67	C₂²×C₈×C₇₉	C₂³	1	2	yes	—
68	#117×C₇₉	—	2	2	no	—
69	#117×C₇₉	—	2	2	no	—
70	#117×C₇₉	—	2	2	no	—
71	#117×C₇₉	—	2	2	no	—
72	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
73	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
74	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
75	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
76	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
77	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
78	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
79	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
80	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
82	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
83	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
84	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
85	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
86	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
87	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
88	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
89	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
90	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
91	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
92	C₂×C₂²⋊C₄×C₇₉	—	4	4	no	—
93	C₂×C₄²×C₇₉	—	2	1	no	—
94	C₂×C₄²×C₇₉	—	2	1	no	—
95	#107×C₇₉	—	2	4	no	—
96	#106×C₇₉	—	2	4	no	—
97	C₂²⋊C₈×C₇₉	—	2	4	no	—
98	C₂²⋊C₈×C₇₉	—	2	4	no	—
99	#95×C₇₉	—	2	2	no	—
100	#95×C₇₉	—	2	2	no	—
101	#95×C₇₉	—	2	1	no	—
102	#95×C₇₉	—	2	1	no	—
103	#95×C₇₉	—	2	1	no	—
104	#95×C₇₉	—	2	1	no	—
105	C₂⁴×C₇₉	—	2	2	no	—
106	C₂⁴×C₇₉	—	2	2	no	—
107	C₂⁴×C₇₉	—	2	2	no	—
108	C₂⁴×C₇₉	—	2	2	no	—
109	C₂⁴×C₇₉	—	2	2	no	—
110	C₂⁴×C₇₉	—	4	1	no	—
111	C₂⁴×C₇₉	—	4	1	no	—
112	C₂⁴×C₇₉	C₂×D₄	1	1	yes	characteristic
113	C₂⁴×C₇₉	C₂×D₄	1	1	yes	characteristic
114	C₂⁴×C₇₉	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₇₉	—	2	2	no	—
116	C₂²×C₄×C₇₉	—	2	2	no	—
117	C₂²×C₄×C₇₉	—	2	2	no	—
118	C₂²×C₄×C₇₉	—	2	2	no	—
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	—	2	2	no	—
124	C₂²×C₄×C₇₉	—	2	1	no	—
125	C₂²×C₄×C₇₉	—	2	1	no	—
126	C₂²×C₄×C₇₉	—	2	1	no	—
127	C₂²×C₄×C₇₉	—	2	1	no	—
128	C₂²×C₄×C₇₉	—	2	1	no	—
129	C₂²×C₄×C₇₉	—	2	1	no	—
130	C₂²×C₄×C₇₉	—	2	1	no	—
131	C₂²×C₄×C₇₉	—	2	1	no	—
132	C₂²×C₄×C₇₉	—	2	1	no	—
133	C₂²×C₄×C₇₉	—	2	1	no	—
134	C₂²×C₄×C₇₉	—	2	1	no	—
135	C₂²×C₄×C₇₉	—	2	1	no	—
136	C₂²×C₄×C₇₉	—	2	1	no	—
137	C₂²×C₄×C₇₉	—	2	1	no	—
138	C₂²×C₄×C₇₉	—	2	1	no	—
139	C₂²×C₄×C₇₉	—	2	1	no	—
140	C₂²×C₄×C₇₉	—	2	2	no	—
141	C₂²×C₄×C₇₉	—	2	2	no	—
142	C₂²×C₄×C₇₉	—	4	4	no	—
143	C₂²×C₄×C₇₉	—	4	4	no	—
144	C₂²×C₄×C₇₉	—	4	4	no	—
145	C₂²×C₄×C₇₉	—	4	4	no	—
146	C₂²×C₄×C₇₉	—	4	2	no	—
147	C₂²×C₄×C₇₉	—	4	2	no	—
148	C₂²×C₄×C₇₉	—	4	2	no	—
149	C₂²×C₄×C₇₉	—	4	2	no	—
150	C₂²×C₄×C₇₉	—	4	2	no	—
151	C₂²×C₄×C₇₉	—	4	2	no	—
152	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
156	C₂²×C₄×C₇₉	#41	1	2	yes	—
157	C₂²×C₄×C₇₉	#41	1	2	yes	—
158	C₂²×C₄×C₇₉	#41	1	2	yes	—
159	C₂²×C₄×C₇₉	#41	1	2	yes	—
160	C₂²×C₄×C₇₉	#41	1	2	yes	—
161	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
162	M₁₆×C₇₉	—	2	8	no	—
163	M₁₆×C₇₉	—	4	4	no	—
164	C₂×C₈×C₇₉	—	2	2	no	—
165	C₂×C₈×C₇₉	—	2	2	no	—
166	C₂×C₈×C₇₉	—	2	2	no	—
167	C₂×C₈×C₇₉	—	2	2	no	—
168	C₂×C₈×C₇₉	—	2	2	no	—
169	C₂×C₈×C₇₉	C₂×D₄	1	4	yes	—
170	C₄⋊C₄×C₇₉	—	2	1	no	—
171	C₄⋊C₄×C₇₉	—	2	2	no	—
172	C₄⋊C₄×C₇₉	—	2	1	no	—
173	C₄⋊C₄×C₇₉	—	2	2	no	—
174	C₄⋊C₄×C₇₉	—	2	2	no	—
175	C₄⋊C₄×C₇₉	—	2	2	no	—
176	C₄⋊C₄×C₇₉	—	2	1	no	—
177	C₄⋊C₄×C₇₉	—	2	1	no	—
178	C₄⋊C₄×C₇₉	—	2	1	no	—
179	C₄⋊C₄×C₇₉	—	2	1	no	—
180	C₄⋊C₄×C₇₉	—	2	1	no	—
181	C₄⋊C₄×C₇₉	—	2	1	no	—
182	C₄⋊C₄×C₇₉	—	4	2	no	—
183	C₄⋊C₄×C₇₉	—	4	2	no	—
184	C₂²⋊C₄×C₇₉	—	4	2	no	—
185	C₂²⋊C₄×C₇₉	—	4	2	no	—
186	C₂²⋊C₄×C₇₉	—	4	4	no	—
187	C₂²⋊C₄×C₇₉	—	4	2	no	—
188	C₂²⋊C₄×C₇₉	—	4	2	no	—
189	C₂²⋊C₄×C₇₉	—	4	2	no	—
190	C₂²⋊C₄×C₇₉	—	4	4	no	—
191	C₂²⋊C₄×C₇₉	—	4	2	no	—
192	C₄²×C₇₉	—	4	2	no	—
193	C₄²×C₇₉	—	4	2	no	—
194	C₂³×C₇₉	—	2	1	no	—
195	C₂³×C₇₉	—	2	1	no	—
196	C₂³×C₇₉	—	2	1	no	—
197	C₂³×C₇₉	—	2	1	no	—
198	C₂³×C₇₉	—	2	8	no	—
199	C₂³×C₇₉	—	2	1	no	—
200	C₂³×C₇₉	—	2	1	no	—
201	C₂³×C₇₉	—	2	1	no	—
202	C₂³×C₇₉	—	2	1	no	—
203	C₂³×C₇₉	—	2	1	no	—
204	C₂³×C₇₉	—	2	1	no	—
205	C₂³×C₇₉	—	2	1	no	—
206	C₂³×C₇₉	—	2	1	no	—
207	C₂³×C₇₉	—	2	1	no	—
208	C₂³×C₇₉	—	2	1	no	—
209	C₂³×C₇₉	—	2	1	no	—
210	C₂³×C₇₉	—	2	1	no	—
211	C₂³×C₇₉	—	4	4	no	—
212	C₂³×C₇₉	—	4	4	no	—
213	C₂³×C₇₉	—	4	4	no	—
214	C₂³×C₇₉	—	4	4	no	—
215	C₂³×C₇₉	—	4	4	no	—
216	C₂³×C₇₉	—	4	4	no	—
217	C₂³×C₇₉	#121	1	2	yes	—
218	C₂³×C₇₉	#123	1	2	yes	—
219	C₂³×C₇₉	#123	1	2	yes	—
220	C₂³×C₇₉	AGL(1,ℤ/8)	1	2	yes	—
221	C₂³×C₇₉	#137	1	2	yes	—
222	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
223	C₂×C₄×C₇₉	—	2	1	no	—
224	C₂×C₄×C₇₉	—	2	1	no	—
225	C₂×C₄×C₇₉	—	2	1	no	—
226	C₂×C₄×C₇₉	—	2	1	no	—
227	C₂×C₄×C₇₉	—	2	1	no	—
228	C₂×C₄×C₇₉	—	2	1	no	—
229	C₂×C₄×C₇₉	—	4	4	no	—
230	C₂×C₄×C₇₉	—	4	1	no	—
231	C₂×C₄×C₇₉	—	4	1	no	—
232	C₂×C₄×C₇₉	—	4	1	no	—
233	C₂×C₄×C₇₉	—	4	1	no	—
234	C₂×C₄×C₇₉	—	4	1	no	—
235	C₂×C₄×C₇₉	—	4	1	no	—
236	C₂×C₄×C₇₉	—	4	1	no	—
237	C₂×C₄×C₇₉	—	4	1	no	—
238	C₂×C₄×C₇₉	—	4	4	no	—
239	C₂×C₄×C₇₉	—	4	4	no	—
240	C₂×C₄×C₇₉	—	4	1	no	—
241	C₂×C₄×C₇₉	—	4	1	no	—
242	C₂×C₄×C₇₉	—	4	2	no	—
243	C₂×C₄×C₇₉	—	4	1	no	—
244	C₂×C₄×C₇₉	—	4	1	no	—
245	C₂×C₄×C₇₉	—	4	2	no	—
246	C₂×C₄×C₇₉	—	4	2	no	—
247	C₂×C₄×C₇₉	—	4	2	no	—
248	C₂×C₄×C₇₉	—	4	1	no	—
249	C₂×C₄×C₇₉	—	4	1	no	—
250	C₂×C₄×C₇₉	—	4	1	no	—
251	C₂×C₄×C₇₉	—	4	1	no	—
252	C₂×C₄×C₇₉	—	4	1	no	—
253	C₂×C₄×C₇₉	—	4	1	no	—
254	C₂×C₄×C₇₉	—	4	1	no	—
255	C₂×C₄×C₇₉	—	4	1	no	—
256	C₂×C₄×C₇₉	—	4	2	no	—
257	C₂×C₄×C₇₉	—	4	2	no	—
258	C₂×C₄×C₇₉	—	8	4	no	—
259	C₂×C₄×C₇₉	—	8	4	no	—
260	C₂×C₄×C₇₉	#121	1	2	yes	—
261	C₂×C₄×C₇₉	#123	1	4	yes	—
262	C₂×C₄×C₇₉	#123	1	2	yes	—
263	C₂×C₄×C₇₉	#123	1	2	yes	—
264	C₂×C₄×C₇₉	#124	1	4	yes	—
265	C₂×C₄×C₇₉	#126	1	4	yes	—
266	C₂×C₄×C₇₉	#126	1	4	yes	—
267	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
268	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
269	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
270	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
271	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
272	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
273	C₈×C₇₉	—	2	4	no	—
274	C₈×C₇₉	—	4	2	no	—
275	C₂²×C₇₉	—	2	2	no	—
276	C₂²×C₇₉	—	2	2	no	—
277	C₂²×C₇₉	—	2	2	no	—
278	C₂²×C₇₉	—	2	2	no	—
279	C₂²×C₇₉	—	2	2	no	—
280	C₂²×C₇₉	—	2	2	no	—
281	C₂²×C₇₉	—	2	2	no	—
282	C₂²×C₇₉	—	2	2	no	—
283	C₂²×C₇₉	—	2	2	no	—
284	C₂²×C₇₉	—	2	2	no	—
285	C₂²×C₇₉	—	2	2	no	—
286	C₂²×C₇₉	—	2	2	no	—
287	C₂²×C₇₉	—	4	16	no	—
288	C₂²×C₇₉	—	4	1	no	—
289	C₂²×C₇₉	—	4	1	no	—
290	C₂²×C₇₉	—	4	1	no	—
291	C₂²×C₇₉	—	4	1	no	—
292	C₂²×C₇₉	—	4	1	no	—
293	C₂²×C₇₉	—	4	1	no	—
294	C₂²×C₇₉	—	4	1	no	—
295	C₂²×C₇₉	—	4	1	no	—
296	C₂²×C₇₉	#397	1	4	yes	—
297	C₂²×C₇₉	C₂×#121	1	1	yes	characteristic
298	C₂²×C₇₉	C₂×#123	1	1	yes	characteristic
299	C₂²×C₇₉	C₂×#123	1	1	yes	characteristic
300	C₂²×C₇₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
301	C₂²×C₇₉	C₂×#137	1	1	yes	characteristic
302	C₂²×C₇₉	#575	1	1	yes	characteristic
303	C₂²×C₇₉	#575	1	1	yes	characteristic
304	C₄×C₇₉	—	4	1	no	—
305	C₄×C₇₉	—	4	1	no	—
306	C₄×C₇₉	—	8	1	no	—
307	C₄×C₇₉	—	8	1	no	—
308	C₄×C₇₉	—	8	2	no	—
309	C₄×C₇₉	—	8	1	no	—
310	C₄×C₇₉	—	8	2	no	—
311	C₄×C₇₉	—	8	1	no	—
312	C₄×C₇₉	#397	1	4	yes	—
313	C₄×C₇₉	C₂×#123	1	1	yes	characteristic
314	C₄×C₇₉	C₂×#124	1	1	yes	characteristic
315	C₄×C₇₉	C₂×#126	1	1	yes	characteristic
316	C₄×C₇₉	C₂×#126	1	1	yes	characteristic
317	#23642	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
318	C₂×C₇₉	—	2	4	no	—
319	C₂×C₇₉	—	4	2	no	—
320	C₂×C₇₉	—	4	2	no	—
321	C₂×C₇₉	C₂×#397	1	1	yes	characteristic
322	C₂×C₇₉	#3055	1	1	yes	characteristic
323	C₂×C₇₉	#3056	1	1	yes	characteristic
324	C₂×C₇₉	#3092	1	1	yes	characteristic
325	C₂×C₇₉	#3093	1	1	yes	characteristic
326	C₂×C₇₉	#3094	1	1	yes	characteristic
327	C₂×C₇₉	#3095	1	1	yes	characteristic
328	C₂×#428	C₂×C₇₉	1	1	yes	characteristic, complemented
329	C₂×#407	C₂×C₇₉	1	1	yes	characteristic
330	#2280	C₂×C₇₉	1	1	yes	characteristic
331	C₂×#380	C₂×C₇₉	1	1	yes	characteristic
332	#2077	C₂×C₇₉	1	2	yes	complemented
333	#2077	C₂×C₇₉	1	2	yes	complemented
334	#2076	C₂×C₇₉	1	2	yes	complemented
335	#2075	C₂×C₇₉	1	2	yes	complemented
336	#1736	C₂×C₇₉	1	1	yes	characteristic, complemented
337	#1736	C₂×C₇₉	1	1	yes	characteristic, complemented
338	#1736	C₂×C₇₉	1	1	yes	characteristic, complemented
339	C₇₉	#23642	1	1	yes	characteristic, direct product factor, Sylow
340	C₂⁴×C₄	C₂²×C₇₉	1	1	yes	characteristic
341	C₂²×M₁₆	C₂²×C₇₉	1	1	yes	characteristic
342	C₂²×M₁₆	C₂²×C₇₉	1	1	yes	characteristic
343	C₂×#117	C₂²×C₇₉	1	1	yes	characteristic
344	C₂×#117	C₂²×C₇₉	1	1	yes	characteristic
345	C₂²×C₄⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
346	C₂²×C₄⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
347	C₂²×C₂²⋊C₄	—	2	1	no	—
348	#428	—	2	4	no	—
349	C₂×#107	C₂²×C₇₉	1	2	yes	complemented
350	C₂×#106	C₂²×C₇₉	1	2	yes	complemented
351	#407	—	2	4	no	—
352	C₂×C₂²⋊C₈	C₂²×C₇₉	1	2	yes	—
353	C₂×C₂²⋊C₈	C₂²×C₇₉	1	2	yes	—
354	#381	—	2	1	no	—
355	#380	—	2	1	no	—
356	#380	—	2	1	no	—
357	#380	C₂²×C₇₉	1	1	yes	characteristic
358	#380	C₂²×C₇₉	1	2	yes	—
359	#380	C₂²×C₇₉	1	1	yes	characteristic
360	#380	C₂²×C₇₉	1	2	yes	—
361	#380	C₂²×C₇₉	1	1	yes	characteristic
362	#380	C₂²×C₇₉	1	1	yes	characteristic
363	#379	—	2	1	no	—
364	C₄×C₂²⋊C₄	—	2	1	no	—
365	C₄×C₂²⋊C₄	—	2	1	no	—
366	C₂×#95	—	2	1	no	—
367	#340	C₂²×C₇₉	1	2	yes	complemented
368	#340	C₂²×C₇₉	1	2	yes	complemented
369	#340	C₂²×C₇₉	1	2	yes	complemented
370	#340	C₂²×C₇₉	1	2	yes	complemented
371	#340	C₂²×C₇₉	1	2	yes	complemented
372	#340	C₂²×C₇₉	1	2	yes	complemented
373	C₂⁵	D₄×C₇₉	1	1	yes	characteristic
374	C₂³×C₄	—	2	2	no	—
375	C₂³×C₄	—	2	2	no	—
376	C₂³×C₄	—	2	2	no	—
377	C₂³×C₄	—	2	2	no	—
378	C₂³×C₄	—	2	2	no	—
379	C₂³×C₄	—	2	2	no	—
380	C₂³×C₄	—	2	1	no	—
381	C₂³×C₄	—	2	1	no	—
382	C₂³×C₄	D₄×C₇₉	1	1	yes	characteristic
383	C₂³×C₄	D₄×C₇₉	1	1	yes	characteristic
384	C₂³×C₄	D₄×C₇₉	1	1	yes	characteristic
385	C₂³×C₄	C₂³×C₇₉	1	1	yes	characteristic
386	C₂³×C₄	C₂³×C₇₉	1	1	yes	characteristic
387	C₂³×C₄	C₂³×C₇₉	1	1	yes	characteristic
388	C₂×M₁₆	—	2	2	no	—
389	C₂×M₁₆	—	2	2	no	—
390	C₂×M₁₆	—	2	2	no	—
391	C₂×M₁₆	—	2	2	no	—
392	C₂×M₁₆	—	2	2	no	—
393	C₂×M₁₆	D₄×C₇₉	1	4	yes	—
394	C₂²×C₈	C₂³×C₇₉	1	2	yes	—
395	C₂²×C₈	C₂³×C₇₉	1	2	yes	—
396	#117	—	2	2	no	—
397	#117	—	2	2	no	—
398	#117	—	2	2	no	—
399	#117	—	2	2	no	—
400	C₂×C₄⋊C₄	—	2	2	no	—
401	C₂×C₄⋊C₄	—	2	2	no	—
402	C₂×C₄⋊C₄	—	2	2	no	—
403	C₂×C₄⋊C₄	—	2	2	no	—
404	C₂×C₄⋊C₄	—	2	1	no	—
405	C₂×C₄⋊C₄	—	2	1	no	—
406	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
407	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
408	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
409	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
410	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
411	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
412	C₂×C₂²⋊C₄	—	2	2	no	—
413	C₂×C₂²⋊C₄	—	2	2	no	—
414	C₂×C₂²⋊C₄	—	2	1	no	—
415	C₂×C₂²⋊C₄	—	2	1	no	—
416	C₂×C₂²⋊C₄	—	2	1	no	—
417	C₂×C₂²⋊C₄	—	2	1	no	—
418	C₂×C₂²⋊C₄	—	2	1	no	—
419	C₂×C₂²⋊C₄	—	2	1	no	—
420	C₂×C₂²⋊C₄	—	4	4	no	—
421	C₂×C₄²	—	2	1	no	—
422	C₂×C₄²	—	2	1	no	—
423	#107	—	2	4	no	—
424	#106	—	2	4	no	—
425	C₂²⋊C₈	—	2	4	no	—
426	C₂²⋊C₈	—	2	4	no	—
427	#95	—	2	2	no	—
428	#95	—	2	2	no	—
429	#95	—	2	1	no	—
430	#95	—	2	1	no	—
431	#95	—	2	1	no	—
432	#95	—	2	1	no	—
433	C₂⁴	—	2	2	no	—
434	C₂⁴	—	2	2	no	—
435	C₂⁴	—	2	2	no	—
436	C₂⁴	—	2	2	no	—
437	C₂⁴	—	2	2	no	—
438	C₂⁴	—	4	1	no	—
439	C₂⁴	—	4	1	no	—
440	C₂⁴	C₂×D₄×C₇₉	1	1	yes	characteristic
441	C₂⁴	C₂×D₄×C₇₉	1	1	yes	characteristic
442	C₂⁴	C₂×D₄×C₇₉	1	1	yes	characteristic
443	C₂²×C₄	—	2	2	no	—
444	C₂²×C₄	—	2	2	no	—
445	C₂²×C₄	—	2	2	no	—
446	C₂²×C₄	—	2	2	no	—
447	C₂²×C₄	—	2	2	no	—
448	C₂²×C₄	—	2	2	no	—
449	C₂²×C₄	—	2	2	no	—
450	C₂²×C₄	—	2	2	no	—
451	C₂²×C₄	—	2	2	no	—
452	C₂²×C₄	—	2	1	no	—
453	C₂²×C₄	—	2	1	no	—
454	C₂²×C₄	—	2	1	no	—
455	C₂²×C₄	—	2	1	no	—
456	C₂²×C₄	—	2	1	no	—
457	C₂²×C₄	—	2	1	no	—
458	C₂²×C₄	—	2	1	no	—
459	C₂²×C₄	—	2	1	no	—
460	C₂²×C₄	—	2	1	no	—
461	C₂²×C₄	—	2	1	no	—
462	C₂²×C₄	—	2	1	no	—
463	C₂²×C₄	—	2	1	no	—
464	C₂²×C₄	—	2	1	no	—
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	2	1	no	—
467	C₂²×C₄	—	2	1	no	—
468	C₂²×C₄	—	2	2	no	—
469	C₂²×C₄	—	2	2	no	—
470	C₂²×C₄	—	4	4	no	—
471	C₂²×C₄	—	4	4	no	—
472	C₂²×C₄	—	4	4	no	—
473	C₂²×C₄	—	4	4	no	—
474	C₂²×C₄	—	4	2	no	—
475	C₂²×C₄	—	4	2	no	—
476	C₂²×C₄	—	4	2	no	—
477	C₂²×C₄	—	4	2	no	—
478	C₂²×C₄	—	4	2	no	—
479	C₂²×C₄	—	4	2	no	—
480	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
481	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
482	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
483	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
484	C₂²×C₄	#41×C₇₉	1	2	yes	—
485	C₂²×C₄	#41×C₇₉	1	2	yes	—
486	C₂²×C₄	#41×C₇₉	1	2	yes	—
487	C₂²×C₄	#41×C₇₉	1	2	yes	—
488	C₂²×C₄	#41×C₇₉	1	2	yes	—
489	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
490	M₁₆	—	2	8	no	—
491	M₁₆	—	4	4	no	—
492	C₂×C₈	—	2	2	no	—
493	C₂×C₈	—	2	2	no	—
494	C₂×C₈	—	2	2	no	—
495	C₂×C₈	—	2	2	no	—
496	C₂×C₈	—	2	2	no	—
497	C₂×C₈	C₂×D₄×C₇₉	1	4	yes	—
498	C₄⋊C₄	—	2	1	no	—
499	C₄⋊C₄	—	2	2	no	—
500	C₄⋊C₄	—	2	1	no	—
501	C₄⋊C₄	—	2	2	no	—
502	C₄⋊C₄	—	2	2	no	—
503	C₄⋊C₄	—	2	2	no	—
504	C₄⋊C₄	—	2	1	no	—
505	C₄⋊C₄	—	2	1	no	—
506	C₄⋊C₄	—	2	1	no	—
507	C₄⋊C₄	—	2	1	no	—
508	C₄⋊C₄	—	2	1	no	—
509	C₄⋊C₄	—	2	1	no	—
510	C₄⋊C₄	—	4	2	no	—
511	C₄⋊C₄	—	4	2	no	—
512	C₂²⋊C₄	—	4	4	no	—
513	C₂²⋊C₄	—	4	2	no	—
514	C₂²⋊C₄	—	4	2	no	—
515	C₂²⋊C₄	—	4	2	no	—
516	C₂²⋊C₄	—	4	2	no	—
517	C₂²⋊C₄	—	4	4	no	—
518	C₂²⋊C₄	—	4	2	no	—
519	C₂²⋊C₄	—	4	2	no	—
520	C₄²	—	4	2	no	—
521	C₄²	—	4	2	no	—
522	C₂³	—	2	1	no	—
523	C₂³	—	2	1	no	—
524	C₂³	—	2	1	no	—
525	C₂³	—	2	1	no	—
526	C₂³	—	2	8	no	—
527	C₂³	—	2	1	no	—
528	C₂³	—	2	1	no	—
529	C₂³	—	2	1	no	—
530	C₂³	—	2	1	no	—
531	C₂³	—	2	1	no	—
532	C₂³	—	2	1	no	—
533	C₂³	—	2	1	no	—
534	C₂³	—	2	1	no	—
535	C₂³	—	2	1	no	—
536	C₂³	—	2	1	no	—
537	C₂³	—	2	1	no	—
538	C₂³	—	2	1	no	—
539	C₂³	—	4	4	no	—
540	C₂³	—	4	4	no	—
541	C₂³	—	4	4	no	—
542	C₂³	—	4	4	no	—
543	C₂³	—	4	4	no	—
544	C₂³	—	4	4	no	—
545	C₂³	#121×C₇₉	1	2	yes	—
546	C₂³	#123×C₇₉	1	2	yes	—
547	C₂³	#123×C₇₉	1	2	yes	—
548	C₂³	AGL(1,ℤ/8)×C₇₉	1	2	yes	—
549	C₂³	#137×C₇₉	1	2	yes	—
550	C₂³	C₂²×D₄×C₇₉	1	1	yes	characteristic
551	C₂×C₄	—	2	1	no	—
552	C₂×C₄	—	2	1	no	—
553	C₂×C₄	—	2	1	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	4	4	no	—
558	C₂×C₄	—	4	1	no	—
559	C₂×C₄	—	4	1	no	—
560	C₂×C₄	—	4	1	no	—
561	C₂×C₄	—	4	1	no	—
562	C₂×C₄	—	4	1	no	—
563	C₂×C₄	—	4	1	no	—
564	C₂×C₄	—	4	1	no	—
565	C₂×C₄	—	4	1	no	—
566	C₂×C₄	—	4	4	no	—
567	C₂×C₄	—	4	4	no	—
568	C₂×C₄	—	4	1	no	—
569	C₂×C₄	—	4	1	no	—
570	C₂×C₄	—	4	2	no	—
571	C₂×C₄	—	4	1	no	—
572	C₂×C₄	—	4	1	no	—
573	C₂×C₄	—	4	2	no	—
574	C₂×C₄	—	4	2	no	—
575	C₂×C₄	—	4	2	no	—
576	C₂×C₄	—	4	1	no	—
577	C₂×C₄	—	4	1	no	—
578	C₂×C₄	—	4	1	no	—
579	C₂×C₄	—	4	1	no	—
580	C₂×C₄	—	4	1	no	—
581	C₂×C₄	—	4	1	no	—
582	C₂×C₄	—	4	1	no	—
583	C₂×C₄	—	4	1	no	—
584	C₂×C₄	—	4	2	no	—
585	C₂×C₄	—	4	2	no	—
586	C₂×C₄	—	8	4	no	—
587	C₂×C₄	—	8	4	no	—
588	C₂×C₄	#121×C₇₉	1	2	yes	—
589	C₂×C₄	#123×C₇₉	1	4	yes	—
590	C₂×C₄	#123×C₇₉	1	2	yes	—
591	C₂×C₄	#123×C₇₉	1	2	yes	—
592	C₂×C₄	#124×C₇₉	1	4	yes	—
593	C₂×C₄	#126×C₇₉	1	4	yes	—
594	C₂×C₄	#126×C₇₉	1	4	yes	—
595	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
596	C₂×C₄	C₂×#41×C₇₉	1	1	yes	characteristic
597	C₂×C₄	C₂×#41×C₇₉	1	1	yes	characteristic
598	C₂×C₄	C₂×#41×C₇₉	1	1	yes	characteristic
599	C₂×C₄	C₂×#41×C₇₉	1	1	yes	characteristic
600	C₂×C₄	C₂×#41×C₇₉	1	1	yes	characteristic
601	C₈	—	2	4	no	—
602	C₈	—	4	2	no	—
603	C₂²	—	2	2	no	—
604	C₂²	—	2	2	no	—
605	C₂²	—	2	2	no	—
606	C₂²	—	2	2	no	—
607	C₂²	—	2	2	no	—
608	C₂²	—	2	2	no	—
609	C₂²	—	2	2	no	—
610	C₂²	—	2	2	no	—
611	C₂²	—	2	2	no	—
612	C₂²	—	2	2	no	—
613	C₂²	—	2	2	no	—
614	C₂²	—	2	2	no	—
615	C₂²	—	4	16	no	—
616	C₂²	—	4	1	no	—
617	C₂²	—	4	1	no	—
618	C₂²	—	4	1	no	—
619	C₂²	—	4	1	no	—
620	C₂²	—	4	1	no	—
621	C₂²	—	4	1	no	—
622	C₂²	—	4	1	no	—
623	C₂²	—	4	1	no	—
624	C₂²	#397×C₇₉	1	4	yes	—
625	C₂²	C₂×#121×C₇₉	1	1	yes	characteristic
626	C₂²	C₂×#123×C₇₉	1	1	yes	characteristic
627	C₂²	C₂×#123×C₇₉	1	1	yes	characteristic
628	C₂²	C₂×AGL(1,ℤ/8)×C₇₉	1	1	yes	characteristic
629	C₂²	C₂×#137×C₇₉	1	1	yes	characteristic
630	C₂²	#575×C₇₉	1	1	yes	characteristic
631	C₂²	#575×C₇₉	1	1	yes	characteristic
632	C₄	—	4	1	no	—
633	C₄	—	4	1	no	—
634	C₄	—	8	2	no	—
635	C₄	—	8	1	no	—
636	C₄	—	8	1	no	—
637	C₄	—	8	1	no	—
638	C₄	—	8	1	no	—
639	C₄	—	8	2	no	—
640	C₄	#397×C₇₉	1	4	yes	—
641	C₄	C₂×#123×C₇₉	1	1	yes	characteristic
642	C₄	C₂×#124×C₇₉	1	1	yes	characteristic
643	C₄	C₂×#126×C₇₉	1	1	yes	characteristic
644	C₄	C₂×#126×C₇₉	1	1	yes	characteristic
645	C₂	—	2	4	no	—
646	C₂	—	4	2	no	—
647	C₂	—	4	2	no	—
648	C₂	C₂×#397×C₇₉	1	1	yes	characteristic
649	C₂	C₇₉×#3055	1	1	yes	characteristic
650	C₂	C₇₉×#3056	1	1	yes	characteristic
651	C₂	C₇₉×#3092	1	1	yes	characteristic
652	C₂	C₇₉×#3093	1	1	yes	characteristic
653	C₂	C₇₉×#3094	1	1	yes	characteristic
654	C₂	C₇₉×#3095	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₉
prime radical	C₂⁵×C₇₉	D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₉ ◁ C₂⁴×C₄×C₇₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#428×C₇₉	C₂	semidirect
5. C₇₉×#2077	C₂	semidirect
6. C₇₉×#2077	C₂	semidirect
7. C₇₉×#2076	C₂	semidirect
8. C₇₉×#2075	C₂	semidirect
9. C₇₉×#1736	C₂	semidirect
10. C₇₉×#1736	C₂	semidirect
11. C₇₉×#1736	C₂	semidirect
21. C₂×#107×C₇₉	C₂²	semidirect
22. C₂×#106×C₇₉	C₂²	semidirect
39. #340×C₇₉	C₂²	semidirect
40. #340×C₇₉	C₂²	semidirect
41. #340×C₇₉	C₂²	semidirect
42. #340×C₇₉	C₂²	semidirect
43. #340×C₇₉	C₂²	semidirect
44. #340×C₇₉	C₂²	semidirect
317. #23642	C₇₉	direct (N × H)
328. C₂×#428	C₂×C₇₉	semidirect
332. #2077	C₂×C₇₉	semidirect
333. #2077	C₂×C₇₉	semidirect
334. #2076	C₂×C₇₉	semidirect
335. #2075	C₂×C₇₉	semidirect
336. #1736	C₂×C₇₉	semidirect
337. #1736	C₂×C₇₉	semidirect
338. #1736	C₂×C₇₉	semidirect
339. C₇₉	#23642	direct (N × H)
349. C₂×#107	C₂²×C₇₉	semidirect
350. C₂×#106	C₂²×C₇₉	semidirect
367. #340	C₂²×C₇₉	semidirect
368. #340	C₂²×C₇₉	semidirect
369. #340	C₂²×C₇₉	semidirect
370. #340	C₂²×C₇₉	semidirect
371. #340	C₂²×C₇₉	semidirect
372. #340	C₂²×C₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#428×C₇₉	2
C₂×#407×C₇₉	2
C₇₉×#2280	2
C₂×#380×C₇₉	2
C₇₉×#2077	2
C₇₉×#2076	2
C₇₉×#2075	2
C₇₉×#1736	2
#23642	79

Subgroups — C79×#23642 #34135331

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#23642 #34135331