Subgroups — C₇₉×#21329 #34133018

Order 20224.

1162 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#533×C₇₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#423×C₇₉	C₂	1	1	yes	maximal, characteristic
3	C₄×#117×C₇₉	C₂	1	1	yes	maximal, characteristic
4	C₇₉×#1995	C₂	1	4	yes	maximal, complemented
5	C₇₉×#1994	C₂	1	4	yes	maximal, complemented
6	C₇₉×#1733	C₂	1	4	yes	maximal
7	C₂²×M₁₆×C₇₉	C₂²	1	2	yes	—
8	#533×C₇₉	—	2	2	no	—
9	#533×C₇₉	—	2	2	no	—
10	#533×C₇₉	C₄	1	2	yes	complemented
11	#533×C₇₉	C₄	1	2	yes	complemented
12	#533×C₇₉	C₂²	1	2	yes	—
13	#533×C₇₉	C₂²	1	2	yes	—
14	C₂×C₄⋊Q₈×C₇₉	C₄	1	2	yes	complemented
15	C₂×#125×C₇₉	C₄	1	2	yes	complemented
16	C₂×C₂²⋊Q₈×C₇₉	—	2	2	no	—
17	C₂×C₄×Q₈×C₇₉	—	2	2	no	—
18	C₂×#117×C₇₉	C₂²	1	2	yes	—
19	C₂×#117×C₇₉	C₂²	1	2	yes	—
20	C₂²×C₄²×C₇₉	C₂²	1	1	yes	characteristic
21	#423×C₇₉	—	2	2	no	—
22	#423×C₇₉	C₂²	1	2	yes	—
23	#423×C₇₉	C₂²	1	2	yes	—
24	C₂×C₄⋊C₈×C₇₉	—	2	2	no	—
25	C₄×C₄⋊C₄×C₇₉	—	2	2	no	—
26	C₄×C₂²⋊C₄×C₇₉	—	2	2	no	—
27	#376×C₇₉	C₂²	1	2	yes	—
28	C₄³×C₇₉	C₂²	1	2	yes	—
29	#339×C₇₉	C₂²	1	16	yes	—
30	C₂²×Q₈×C₇₉	—	2	2	no	—
31	C₂³×C₄×C₇₉	D₄	1	2	yes	—
32	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
33	C₂×M₁₆×C₇₉	—	2	2	no	—
34	C₂×M₁₆×C₇₉	—	2	8	no	—
35	C₂×M₁₆×C₇₉	C₂³	1	4	yes	—
36	C₂²×C₈×C₇₉	—	2	2	no	—
37	C₄⋊Q₈×C₇₉	—	2	2	no	—
38	C₄⋊Q₈×C₇₉	—	2	2	no	—
39	C₄⋊Q₈×C₇₉	C₂×C₄	1	4	yes	—
40	C₄⋊Q₈×C₇₉	C₂×C₄	1	4	yes	—
41	#125×C₇₉	—	2	4	no	—
42	#125×C₇₉	C₂×C₄	1	4	yes	—
43	#125×C₇₉	C₂×C₄	1	4	yes	—
44	C₂²⋊Q₈×C₇₉	—	2	4	no	—
45	C₂²⋊Q₈×C₇₉	—	2	4	no	—
46	C₂²⋊Q₈×C₇₉	—	2	4	no	—
47	C₂²⋊Q₈×C₇₉	—	2	4	no	—
48	C₄×Q₈×C₇₉	—	2	4	no	—
49	C₄×Q₈×C₇₉	—	2	4	no	—
50	C₄×Q₈×C₇₉	—	2	4	no	—
51	C₄×Q₈×C₇₉	—	2	4	no	—
52	#117×C₇₉	—	2	2	no	—
53	#117×C₇₉	—	2	2	no	—
54	#117×C₇₉	—	2	4	no	—
55	#117×C₇₉	C₂×C₄	1	4	yes	—
56	#117×C₇₉	Q₈	1	8	yes	complemented
57	#117×C₇₉	C₂³	1	4	yes	—
58	C₂×C₄⋊C₄×C₇₉	—	2	4	no	—
59	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
60	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
61	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	4	yes	—
62	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
63	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
64	C₂×C₄²×C₇₉	—	2	2	no	—
65	C₂×C₄²×C₇₉	—	2	4	no	—
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	C₂×C₄	1	1	yes	characteristic
70	C₂×C₄²×C₇₉	D₄	1	2	yes	—
71	C₂×C₄²×C₇₉	D₄	1	2	yes	—
72	C₂×C₄²×C₇₉	D₄	1	2	yes	—
73	C₂×C₄²×C₇₉	C₂³	1	4	yes	—
74	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
75	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
76	C₄⋊C₈×C₇₉	—	2	4	no	—
77	C₄⋊C₈×C₇₉	—	2	4	no	—
78	#95×C₇₉	—	2	4	no	—
79	C₂⁴×C₇₉	C₂×D₄	1	1	yes	characteristic
80	C₂×Q₈×C₇₉	—	2	4	no	—
81	C₂×Q₈×C₇₉	—	2	4	no	—
82	C₂×Q₈×C₇₉	—	4	8	no	—
83	C₂²×C₄×C₇₉	—	2	4	no	—
84	C₂²×C₄×C₇₉	—	2	4	no	—
85	C₂²×C₄×C₇₉	—	4	4	no	—
86	C₂²×C₄×C₇₉	C₂²⋊C₄	1	2	yes	—
87	C₂²×C₄×C₇₉	C₂²⋊C₄	1	2	yes	—
88	C₂²×C₄×C₇₉	C₂²⋊C₄	1	2	yes	—
89	C₂²×C₄×C₇₉	C₂²⋊C₄	1	2	yes	—
90	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
92	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
93	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
94	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₇₉	C₂×Q₈	1	4	yes	—
98	C₂²×C₄×C₇₉	#41	1	4	yes	—
99	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
100	M₁₆×C₇₉	—	2	8	no	—
101	M₁₆×C₇₉	—	4	4	no	—
102	C₂×C₈×C₇₉	—	2	4	no	—
103	C₂×C₈×C₇₉	—	4	4	no	—
104	C₄⋊C₄×C₇₉	—	2	8	no	—
105	C₄⋊C₄×C₇₉	—	2	8	no	—
106	C₄⋊C₄×C₇₉	—	2	4	no	—
107	C₄⋊C₄×C₇₉	—	2	4	no	—
108	C₄⋊C₄×C₇₉	—	2	4	no	—
109	C₄⋊C₄×C₇₉	—	2	8	no	—
110	C₄⋊C₄×C₇₉	C₂²×C₄	1	8	yes	—
111	C₂²⋊C₄×C₇₉	—	2	4	no	—
112	C₂²⋊C₄×C₇₉	—	2	8	no	—
113	C₂²⋊C₄×C₇₉	—	2	4	no	—
114	C₄²×C₇₉	—	2	4	no	—
115	C₄²×C₇₉	—	2	4	no	—
116	C₄²×C₇₉	—	2	4	no	—
117	C₄²×C₇₉	—	4	8	no	—
118	C₄²×C₇₉	C₂²⋊C₄	1	2	yes	—
119	C₄²×C₇₉	C₂²⋊C₄	1	2	yes	—
120	C₄²×C₇₉	C₂²⋊C₄	1	2	yes	—
121	C₄²×C₇₉	C₂²⋊C₄	1	2	yes	—
122	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
123	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
124	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
125	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
126	C₄²×C₇₉	C₂×D₄	1	2	yes	—
127	C₄²×C₇₉	C₂×D₄	1	2	yes	—
128	C₄²×C₇₉	C₂×Q₈	1	8	yes	complemented
129	C₂³×C₇₉	—	4	2	no	—
130	C₂³×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
131	C₂³×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
132	C₂³×C₇₉	C₂²⋊Q₈	1	4	yes	—
133	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
134	Q₈×C₇₉	—	4	8	no	—
135	Q₈×C₇₉	—	4	8	no	—
136	C₂×C₄×C₇₉	—	2	4	no	—
137	C₂×C₄×C₇₉	—	2	4	no	—
138	C₂×C₄×C₇₉	—	2	4	no	—
139	C₂×C₄×C₇₉	—	2	8	no	—
140	C₂×C₄×C₇₉	—	2	8	no	—
141	C₂×C₄×C₇₉	—	4	2	no	—
142	C₂×C₄×C₇₉	—	4	2	no	—
143	C₂×C₄×C₇₉	—	4	2	no	—
144	C₂×C₄×C₇₉	—	4	8	no	—
145	C₂×C₄×C₇₉	—	4	8	no	—
146	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	2	yes	—
147	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	2	yes	—
148	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	2	yes	—
149	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
151	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	2	yes	—
152	C₂×C₄×C₇₉	C₄×Q₈	1	4	yes	—
153	C₂×C₄×C₇₉	C₄×Q₈	1	4	yes	—
154	C₂×C₄×C₇₉	C₂²⋊Q₈	1	4	yes	—
155	C₂×C₄×C₇₉	#124	1	2	yes	—
156	C₂×C₄×C₇₉	#124	1	2	yes	—
157	C₂×C₄×C₇₉	C₄⋊Q₈	1	2	yes	—
158	C₂×C₄×C₇₉	C₄⋊Q₈	1	2	yes	—
159	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
160	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
161	C₂×C₄×C₇₉	C₂²×Q₈	1	2	yes	—
162	C₂×C₄×C₇₉	C₂×#41	1	2	yes	—
163	C₈×C₇₉	—	4	4	no	—
164	C₂²×C₇₉	—	2	2	no	—
165	C₂²×C₇₉	—	2	2	no	—
166	C₂²×C₇₉	—	2	2	no	—
167	C₂²×C₇₉	—	4	4	no	—
168	C₂²×C₇₉	#391	1	2	yes	—
169	C₂²×C₇₉	#391	1	2	yes	—
170	C₂²×C₇₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
171	C₂²×C₇₉	C₂×C₂²⋊Q₈	1	2	yes	—
172	C₄×C₇₉	—	2	2	no	—
173	C₄×C₇₉	—	2	2	no	—
174	C₄×C₇₉	—	2	2	no	—
175	C₄×C₇₉	—	4	8	no	—
176	C₄×C₇₉	—	4	8	no	—
177	C₄×C₇₉	#391	1	2	yes	—
178	C₄×C₇₉	#391	1	2	yes	—
179	C₄×C₇₉	#421	1	4	yes	—
180	C₄×C₇₉	C₂×C₄×Q₈	1	2	yes	—
181	C₄×C₇₉	C₂×#124	1	1	yes	characteristic
182	C₄×C₇₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
183	#21329	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
184	C₂×C₇₉	—	2	2	no	—
185	C₂×C₇₉	—	2	2	no	—
186	C₂×C₇₉	—	2	2	no	—
187	C₂×C₇₉	C₂×#391	1	1	yes	characteristic
188	C₂×C₇₉	C₂×#421	1	2	yes	—
189	C₂×#533	C₂×C₇₉	1	1	yes	characteristic
190	C₂×#423	C₂×C₇₉	1	1	yes	characteristic
191	C₄×#117	C₂×C₇₉	1	1	yes	characteristic
192	#1995	C₂×C₇₉	1	4	yes	complemented
193	#1994	C₂×C₇₉	1	4	yes	complemented
194	#1733	C₂×C₇₉	1	4	yes	—
195	C₇₉	#21329	1	1	yes	characteristic, direct product factor, Sylow
196	C₂²×M₁₆	C₂²×C₇₉	1	2	yes	—
197	#533	—	2	2	no	—
198	#533	—	2	2	no	—
199	#533	C₄×C₇₉	1	2	yes	complemented
200	#533	C₄×C₇₉	1	2	yes	complemented
201	#533	C₂²×C₇₉	1	2	yes	—
202	#533	C₂²×C₇₉	1	2	yes	—
203	C₂×C₄⋊Q₈	C₄×C₇₉	1	2	yes	complemented
204	C₂×#125	C₄×C₇₉	1	2	yes	complemented
205	C₂×C₂²⋊Q₈	—	2	2	no	—
206	C₂×C₄×Q₈	—	2	2	no	—
207	C₂×#117	C₂²×C₇₉	1	2	yes	—
208	C₂×#117	C₂²×C₇₉	1	2	yes	—
209	C₂²×C₄²	C₂²×C₇₉	1	1	yes	characteristic
210	#423	—	2	2	no	—
211	#423	C₂²×C₇₉	1	2	yes	—
212	#423	C₂²×C₇₉	1	2	yes	—
213	C₂×C₄⋊C₈	—	2	2	no	—
214	C₄×C₄⋊C₄	—	2	2	no	—
215	C₄×C₂²⋊C₄	—	2	2	no	—
216	#376	C₂²×C₇₉	1	2	yes	—
217	C₄³	C₂²×C₇₉	1	2	yes	—
218	#339	C₂²×C₇₉	1	16	yes	—
219	C₂²×Q₈	—	2	2	no	—
220	C₂³×C₄	D₄×C₇₉	1	2	yes	—
221	C₂³×C₄	C₂³×C₇₉	1	1	yes	characteristic
222	C₂×M₁₆	—	2	2	no	—
223	C₂×M₁₆	—	2	8	no	—
224	C₂×M₁₆	C₂³×C₇₉	1	4	yes	—
225	C₂²×C₈	—	2	2	no	—
226	C₄⋊Q₈	—	2	2	no	—
227	C₄⋊Q₈	—	2	2	no	—
228	C₄⋊Q₈	C₂×C₄×C₇₉	1	4	yes	—
229	C₄⋊Q₈	C₂×C₄×C₇₉	1	4	yes	—
230	#125	—	2	4	no	—
231	#125	C₂×C₄×C₇₉	1	4	yes	—
232	#125	C₂×C₄×C₇₉	1	4	yes	—
233	C₂²⋊Q₈	—	2	4	no	—
234	C₂²⋊Q₈	—	2	4	no	—
235	C₂²⋊Q₈	—	2	4	no	—
236	C₂²⋊Q₈	—	2	4	no	—
237	C₄×Q₈	—	2	4	no	—
238	C₄×Q₈	—	2	4	no	—
239	C₄×Q₈	—	2	4	no	—
240	C₄×Q₈	—	2	4	no	—
241	#117	—	2	2	no	—
242	#117	—	2	2	no	—
243	#117	—	2	4	no	—
244	#117	C₂×C₄×C₇₉	1	4	yes	—
245	#117	Q₈×C₇₉	1	8	yes	complemented
246	#117	C₂³×C₇₉	1	4	yes	—
247	C₂×C₄⋊C₄	—	2	4	no	—
248	C₂×C₄⋊C₄	—	2	2	no	—
249	C₂×C₄⋊C₄	—	2	2	no	—
250	C₂×C₄⋊C₄	C₂×C₄×C₇₉	1	4	yes	—
251	C₂×C₂²⋊C₄	—	2	2	no	—
252	C₂×C₂²⋊C₄	—	2	2	no	—
253	C₂×C₄²	—	2	2	no	—
254	C₂×C₄²	—	2	4	no	—
255	C₂×C₄²	C₂×C₄×C₇₉	1	1	yes	characteristic
256	C₂×C₄²	C₂×C₄×C₇₉	1	1	yes	characteristic
257	C₂×C₄²	C₂×C₄×C₇₉	1	1	yes	characteristic
258	C₂×C₄²	C₂×C₄×C₇₉	1	1	yes	characteristic
259	C₂×C₄²	D₄×C₇₉	1	2	yes	—
260	C₂×C₄²	D₄×C₇₉	1	2	yes	—
261	C₂×C₄²	D₄×C₇₉	1	2	yes	—
262	C₂×C₄²	C₂³×C₇₉	1	4	yes	—
263	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
264	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
265	C₄⋊C₈	—	2	4	no	—
266	C₄⋊C₈	—	2	4	no	—
267	#95	—	2	4	no	—
268	C₂⁴	C₂×D₄×C₇₉	1	1	yes	characteristic
269	C₂×Q₈	—	2	4	no	—
270	C₂×Q₈	—	2	4	no	—
271	C₂×Q₈	—	4	8	no	—
272	C₂²×C₄	—	2	4	no	—
273	C₂²×C₄	—	2	4	no	—
274	C₂²×C₄	—	4	4	no	—
275	C₂²×C₄	C₂²⋊C₄×C₇₉	1	2	yes	—
276	C₂²×C₄	C₂²⋊C₄×C₇₉	1	2	yes	—
277	C₂²×C₄	C₂²⋊C₄×C₇₉	1	2	yes	—
278	C₂²×C₄	C₂²⋊C₄×C₇₉	1	2	yes	—
279	C₂²×C₄	C₂²×C₄×C₇₉	1	1	yes	characteristic
280	C₂²×C₄	C₂²×C₄×C₇₉	1	1	yes	characteristic
281	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
282	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
283	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
284	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
285	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
286	C₂²×C₄	C₂×Q₈×C₇₉	1	4	yes	—
287	C₂²×C₄	#41×C₇₉	1	4	yes	—
288	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
289	M₁₆	—	2	8	no	—
290	M₁₆	—	4	4	no	—
291	C₂×C₈	—	2	4	no	—
292	C₂×C₈	—	4	4	no	—
293	C₄⋊C₄	—	2	8	no	—
294	C₄⋊C₄	—	2	8	no	—
295	C₄⋊C₄	—	2	4	no	—
296	C₄⋊C₄	—	2	4	no	—
297	C₄⋊C₄	—	2	4	no	—
298	C₄⋊C₄	—	2	8	no	—
299	C₄⋊C₄	C₂²×C₄×C₇₉	1	8	yes	—
300	C₂²⋊C₄	—	2	4	no	—
301	C₂²⋊C₄	—	2	8	no	—
302	C₂²⋊C₄	—	2	4	no	—
303	C₄²	—	2	4	no	—
304	C₄²	—	2	4	no	—
305	C₄²	—	2	4	no	—
306	C₄²	—	4	8	no	—
307	C₄²	C₂²⋊C₄×C₇₉	1	2	yes	—
308	C₄²	C₂²⋊C₄×C₇₉	1	2	yes	—
309	C₄²	C₂²⋊C₄×C₇₉	1	2	yes	—
310	C₄²	C₂²⋊C₄×C₇₉	1	2	yes	—
311	C₄²	C₂²×C₄×C₇₉	1	1	yes	characteristic
312	C₄²	C₂²×C₄×C₇₉	1	1	yes	characteristic
313	C₄²	C₂²×C₄×C₇₉	1	1	yes	characteristic
314	C₄²	C₂²×C₄×C₇₉	1	1	yes	characteristic
315	C₄²	C₂×D₄×C₇₉	1	2	yes	—
316	C₄²	C₂×D₄×C₇₉	1	2	yes	—
317	C₄²	C₂×Q₈×C₇₉	1	8	yes	complemented
318	C₂³	—	4	2	no	—
319	C₂³	C₂×C₂²⋊C₄×C₇₉	1	1	yes	characteristic
320	C₂³	C₂×C₂²⋊C₄×C₇₉	1	1	yes	characteristic
321	C₂³	C₂²⋊Q₈×C₇₉	1	4	yes	—
322	C₂³	C₂²×D₄×C₇₉	1	1	yes	characteristic
323	Q₈	—	4	8	no	—
324	Q₈	—	4	8	no	—
325	C₂×C₄	—	2	4	no	—
326	C₂×C₄	—	2	4	no	—
327	C₂×C₄	—	2	4	no	—
328	C₂×C₄	—	2	8	no	—
329	C₂×C₄	—	2	8	no	—
330	C₂×C₄	—	4	2	no	—
331	C₂×C₄	—	4	2	no	—
332	C₂×C₄	—	4	2	no	—
333	C₂×C₄	—	4	8	no	—
334	C₂×C₄	—	4	8	no	—
335	C₂×C₄	C₂×C₂²⋊C₄×C₇₉	1	2	yes	—
336	C₂×C₄	C₂×C₂²⋊C₄×C₇₉	1	2	yes	—
337	C₂×C₄	C₂×C₂²⋊C₄×C₇₉	1	2	yes	—
338	C₂×C₄	C₂×C₂²⋊C₄×C₇₉	1	2	yes	—
339	C₂×C₄	C₂×C₂²⋊C₄×C₇₉	1	1	yes	characteristic
340	C₂×C₄	C₂×C₂²⋊C₄×C₇₉	1	1	yes	characteristic
341	C₂×C₄	C₄×Q₈×C₇₉	1	4	yes	—
342	C₂×C₄	C₄×Q₈×C₇₉	1	4	yes	—
343	C₂×C₄	C₂²⋊Q₈×C₇₉	1	4	yes	—
344	C₂×C₄	#124×C₇₉	1	2	yes	—
345	C₂×C₄	#124×C₇₉	1	2	yes	—
346	C₂×C₄	C₄⋊Q₈×C₇₉	1	2	yes	—
347	C₂×C₄	C₄⋊Q₈×C₇₉	1	2	yes	—
348	C₂×C₄	C₂³×C₄×C₇₉	1	1	yes	characteristic
349	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
350	C₂×C₄	C₂²×Q₈×C₇₉	1	2	yes	—
351	C₂×C₄	C₂×#41×C₇₉	1	2	yes	—
352	C₈	—	4	4	no	—
353	C₂²	—	2	2	no	—
354	C₂²	—	2	2	no	—
355	C₂²	—	2	2	no	—
356	C₂²	—	4	4	no	—
357	C₂²	#391×C₇₉	1	2	yes	—
358	C₂²	#391×C₇₉	1	2	yes	—
359	C₂²	C₂²×C₂²⋊C₄×C₇₉	1	1	yes	characteristic
360	C₂²	C₂×C₂²⋊Q₈×C₇₉	1	2	yes	—
361	C₄	—	2	2	no	—
362	C₄	—	2	2	no	—
363	C₄	—	2	2	no	—
364	C₄	—	4	8	no	—
365	C₄	—	4	8	no	—
366	C₄	#391×C₇₉	1	2	yes	—
367	C₄	#391×C₇₉	1	2	yes	—
368	C₄	#421×C₇₉	1	4	yes	—
369	C₄	C₂×C₄×Q₈×C₇₉	1	2	yes	—
370	C₄	C₂×#124×C₇₉	1	1	yes	characteristic
371	C₄	C₂×C₄⋊Q₈×C₇₉	1	1	yes	characteristic
372	C₂	—	2	2	no	—
373	C₂	—	2	2	no	—
374	C₂	—	2	2	no	—
375	C₂	C₂×#391×C₇₉	1	1	yes	characteristic
376	C₂	C₂×#421×C₇₉	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₇₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₇₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₉
socle	C₂²×C₇₉	C₂²×C₂²⋊C₄
prime radical	C₂⁴×C₇₉	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇₉ ◁ C₂²×C₄²×C₇₉ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₇₉×#1995	C₂	semidirect
5. C₇₉×#1994	C₂	semidirect
10. #533×C₇₉	C₄	semidirect
11. #533×C₇₉	C₄	semidirect
14. C₂×C₄⋊Q₈×C₇₉	C₄	semidirect
15. C₂×#125×C₇₉	C₄	semidirect
56. #117×C₇₉	Q₈	semidirect
128. C₄²×C₇₉	C₂×Q₈	semidirect
183. #21329	C₇₉	direct (N × H)
192. #1995	C₂×C₇₉	semidirect
193. #1994	C₂×C₇₉	semidirect
195. C₇₉	#21329	direct (N × H)
199. #533	C₄×C₇₉	semidirect
200. #533	C₄×C₇₉	semidirect
203. C₂×C₄⋊Q₈	C₄×C₇₉	semidirect
204. C₂×#125	C₄×C₇₉	semidirect
245. #117	Q₈×C₇₉	semidirect
317. C₄²	C₂×Q₈×C₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#533×C₇₉	2
C₂×#423×C₇₉	2
C₄×#117×C₇₉	2
C₇₉×#1995	2
C₇₉×#1994	2
C₇₉×#1733	2
#21329	79

Subgroups — C79×#21329 #34133018

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#21329 #34133018