Subgroups — C₇₉×#25837 #34137526

Order 20224.

1038 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈²×C₇₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#498×C₇₉	C₂	1	1	yes	maximal, characteristic
3	C₂×#475×C₇₉	C₂	1	1	yes	maximal, characteristic
4	C₇₉×#2546	C₂	1	1	yes	maximal, characteristic
5	C₇₉×#2058	C₂	1	4	yes	maximal
6	C₇₉×#1987	C₂	1	1	yes	maximal, characteristic
7	C₇₉×#1984	C₂	1	1	yes	maximal, characteristic
8	C₇₉×#1865	C₂	1	4	yes	maximal
9	C₄×#103×C₇₉	C₂	1	1	yes	maximal, characteristic
10	Q₈²×C₇₉	—	2	4	no	—
11	Q₈²×C₇₉	—	2	4	no	—
12	C₂×C₄⋊Q₈×C₇₉	—	2	1	no	—
13	C₂×C₄⋊Q₈×C₇₉	—	2	1	no	—
14	C₂×C₄⋊Q₈×C₇₉	—	2	2	no	—
15	C₂×C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊Q₈×C₇₉	C₂²	1	2	yes	—
17	C₂×C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
18	C₂×C₄×Q₈×C₇₉	—	2	1	no	—
19	C₂×C₄×Q₈×C₇₉	C₂²	1	2	yes	—
20	C₂×C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic
21	C₂×C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic
22	#498×C₇₉	—	2	4	no	—
23	#475×C₇₉	—	2	4	no	—
24	C₂×#106×C₇₉	C₂²	1	2	yes	—
25	C₂×#106×C₇₉	C₂²	1	4	yes	—
26	C₂×C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
27	C₂×#103×C₇₉	C₂²	1	2	yes	—
28	C₂×#103×C₇₉	C₂²	1	2	yes	—
29	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
30	#398×C₇₉	—	2	2	no	—
31	#391×C₇₉	—	2	1	no	—
32	#389×C₇₉	C₂²	1	4	yes	—
33	C₄×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
34	#340×C₇₉	C₂²	1	2	yes	—
35	#340×C₇₉	C₂²	1	4	yes	—
36	#336×C₇₉	C₂²	1	4	yes	—
37	C₂²×Q₈×C₇₉	—	2	2	no	—
38	C₂²×Q₈×C₇₉	—	2	1	no	—
39	C₂²×Q₈×C₇₉	—	2	1	no	—
40	C₂²×Q₈×C₇₉	D₄	1	1	yes	characteristic
41	C₂²×Q₈×C₇₉	C₂³	1	1	yes	characteristic
42	C₂²×C₈×C₇₉	C₂³	1	2	yes	—
43	C₂²×C₈×C₇₉	C₂³	1	2	yes	—
44	C₄⋊Q₈×C₇₉	—	2	16	no	—
45	C₄⋊Q₈×C₇₉	—	2	8	no	—
46	C₄⋊Q₈×C₇₉	—	2	4	no	—
47	C₄⋊Q₈×C₇₉	—	2	4	no	—
48	C₄⋊Q₈×C₇₉	—	2	2	no	—
49	C₄⋊Q₈×C₇₉	—	2	2	no	—
50	C₄⋊Q₈×C₇₉	—	2	2	no	—
51	C₄⋊Q₈×C₇₉	—	4	4	no	—
52	C₄⋊Q₈×C₇₉	D₄	1	4	yes	—
53	C₄×Q₈×C₇₉	—	2	8	no	—
54	C₄×Q₈×C₇₉	—	2	4	no	—
55	C₄×Q₈×C₇₉	—	2	4	no	—
56	C₄×Q₈×C₇₉	—	2	2	no	—
57	C₄×Q₈×C₇₉	—	2	2	no	—
58	C₄×Q₈×C₇₉	—	2	2	no	—
59	C₄×Q₈×C₇₉	D₄	1	4	yes	—
60	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
61	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
62	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
63	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
64	C₂×C₄⋊C₄×C₇₉	—	2	4	no	—
65	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
66	C₂×C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₇₉	D₄	1	2	yes	—
68	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
69	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
70	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
71	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
72	C₂×C₄²×C₇₉	—	2	2	no	—
73	C₂×C₄²×C₇₉	—	2	1	no	—
74	C₂×C₄²×C₇₉	—	2	1	no	—
75	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
76	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
77	#106×C₇₉	—	2	4	no	—
78	#106×C₇₉	—	2	8	no	—
79	C₄⋊C₈×C₇₉	—	2	2	no	—
80	#103×C₇₉	—	2	4	no	—
81	#103×C₇₉	Q₈	1	8	yes	complemented
82	C₄×C₈×C₇₉	—	2	2	no	—
83	#95×C₇₉	—	2	1	no	—
84	#95×C₇₉	—	2	4	no	—
85	C₂×Q₈×C₇₉	—	2	8	no	—
86	C₂×Q₈×C₇₉	—	2	2	no	—
87	C₂×Q₈×C₇₉	—	2	4	no	—
88	C₂×Q₈×C₇₉	—	2	2	no	—
89	C₂×Q₈×C₇₉	—	2	1	no	—
90	C₂×Q₈×C₇₉	—	2	2	no	—
91	C₂×Q₈×C₇₉	—	4	2	no	—
92	C₂×Q₈×C₇₉	—	4	2	no	—
93	C₂×Q₈×C₇₉	—	4	2	no	—
94	C₂×Q₈×C₇₉	—	8	2	no	—
95	C₂×Q₈×C₇₉	—	8	4	no	—
96	C₂×Q₈×C₇₉	SD₁₆	1	4	yes	—
97	C₂×Q₈×C₇₉	C₂×D₄	1	2	yes	—
98	C₂×Q₈×C₇₉	C₂×Q₈	1	4	yes	—
99	C₂²×C₄×C₇₉	—	2	1	no	—
100	C₂²×C₄×C₇₉	—	2	2	no	—
101	C₂²×C₄×C₇₉	—	2	2	no	—
102	C₂²×C₄×C₇₉	—	2	1	no	—
103	C₂²×C₄×C₇₉	—	2	2	no	—
104	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
109	C₂×C₈×C₇₉	—	2	2	no	—
110	C₂×C₈×C₇₉	—	2	2	no	—
111	C₂×C₈×C₇₉	—	2	2	no	—
112	C₂×C₈×C₇₉	—	2	4	no	—
113	C₂×C₈×C₇₉	C₂×Q₈	1	4	yes	—
114	C₄⋊C₄×C₇₉	—	2	8	no	—
115	C₄⋊C₄×C₇₉	—	2	8	no	—
116	C₄⋊C₄×C₇₉	—	2	4	no	—
117	C₄⋊C₄×C₇₉	—	2	4	no	—
118	C₄⋊C₄×C₇₉	—	2	4	no	—
119	C₄⋊C₄×C₇₉	—	2	2	no	—
120	C₄⋊C₄×C₇₉	—	2	2	no	—
121	C₄⋊C₄×C₇₉	—	2	1	no	—
122	C₄⋊C₄×C₇₉	—	2	2	no	—
123	C₄⋊C₄×C₇₉	—	2	2	no	—
124	C₄⋊C₄×C₇₉	—	2	2	no	—
125	C₄⋊C₄×C₇₉	—	4	2	no	—
126	C₄⋊C₄×C₇₉	—	4	8	no	—
127	C₄⋊C₄×C₇₉	C₂×D₄	1	4	yes	—
128	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
129	C₄⋊C₄×C₇₉	C₂×Q₈	1	4	yes	—
130	C₄²×C₇₉	—	2	8	no	—
131	C₄²×C₇₉	—	2	4	no	—
132	C₄²×C₇₉	—	2	2	no	—
133	C₄²×C₇₉	—	2	2	no	—
134	C₄²×C₇₉	—	4	2	no	—
135	C₄²×C₇₉	C₂×D₄	1	2	yes	—
136	C₄²×C₇₉	C₂×D₄	1	2	yes	—
137	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
138	Q₈×C₇₉	—	2	2	no	—
139	Q₈×C₇₉	—	2	4	no	—
140	Q₈×C₇₉	—	2	8	no	—
141	Q₈×C₇₉	—	8	4	no	—
142	Q₈×C₇₉	—	8	8	no	—
143	Q₈×C₇₉	—	8	4	no	—
144	Q₈×C₇₉	C₄⋊Q₈	1	4	yes	complemented
145	C₂×C₄×C₇₉	—	2	2	no	—
146	C₂×C₄×C₇₉	—	2	2	no	—
147	C₂×C₄×C₇₉	—	2	4	no	—
148	C₂×C₄×C₇₉	—	2	2	no	—
149	C₂×C₄×C₇₉	—	2	2	no	—
150	C₂×C₄×C₇₉	—	2	2	no	—
151	C₂×C₄×C₇₉	—	2	4	no	—
152	C₂×C₄×C₇₉	—	2	2	no	—
153	C₂×C₄×C₇₉	—	2	4	no	—
154	C₂×C₄×C₇₉	—	2	4	no	—
155	C₂×C₄×C₇₉	—	4	2	no	—
156	C₂×C₄×C₇₉	—	4	2	no	—
157	C₂×C₄×C₇₉	—	4	4	no	—
158	C₂×C₄×C₇₉	—	4	2	no	—
159	C₂×C₄×C₇₉	—	4	2	no	—
160	C₂×C₄×C₇₉	—	4	2	no	—
161	C₂×C₄×C₇₉	—	4	2	no	—
162	C₂×C₄×C₇₉	#120	1	2	yes	—
163	C₂×C₄×C₇₉	#120	1	2	yes	—
164	C₂×C₄×C₇₉	C₂×SD₁₆	1	4	yes	—
165	C₂×C₄×C₇₉	C₂×SD₁₆	1	2	yes	—
166	C₂×C₄×C₇₉	#137	1	2	yes	—
167	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
168	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₄×C₇₉	C₂²×Q₈	1	2	yes	—
170	C₂×C₄×C₇₉	2₋¹⁺⁴	1	2	yes	—
171	C₈×C₇₉	—	2	4	no	—
172	C₈×C₇₉	—	4	2	no	—
173	C₂²×C₇₉	C₂×#120	1	1	yes	characteristic
174	C₂²×C₇₉	D₄×Q₈	1	2	yes	—
175	C₂²×C₇₉	C₂²×SD₁₆	1	1	yes	characteristic
176	C₂²×C₇₉	C₂×#137	1	1	yes	characteristic
177	C₂²×C₇₉	#577	1	2	yes	—
178	C₄×C₇₉	—	2	4	no	—
179	C₄×C₇₉	—	2	4	no	—
180	C₄×C₇₉	—	2	2	no	—
181	C₄×C₇₉	—	4	4	no	—
182	C₄×C₇₉	—	4	2	no	—
183	C₄×C₇₉	—	4	4	no	—
184	C₄×C₇₉	—	4	2	no	—
185	C₄×C₇₉	—	8	2	no	—
186	C₄×C₇₉	#448	1	4	yes	—
187	C₄×C₇₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
188	C₄×C₇₉	#536	1	1	yes	characteristic
189	C₄×C₇₉	D₄×Q₈	1	2	yes	—
190	#25837	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
191	C₂×C₇₉	#2434	1	1	yes	characteristic
192	C₂×C₇₉	C₂×#448	1	1	yes	characteristic
193	C₂×C₇₉	#3009	1	1	yes	characteristic
194	C₂×C₇₉	Q₈×SD₁₆	1	2	yes	—
195	C₂×C₇₉	#3387	1	2	yes	—
196	C₂×Q₈²	C₂×C₇₉	1	1	yes	characteristic
197	C₂×#498	C₂×C₇₉	1	1	yes	characteristic
198	C₂×#475	C₂×C₇₉	1	1	yes	characteristic
199	#2546	C₂×C₇₉	1	1	yes	characteristic
200	#2058	C₂×C₇₉	1	4	yes	—
201	#1987	C₂×C₇₉	1	1	yes	characteristic
202	#1984	C₂×C₇₉	1	1	yes	characteristic
203	#1865	C₂×C₇₉	1	4	yes	—
204	C₄×#103	C₂×C₇₉	1	1	yes	characteristic
205	C₇₉	#25837	1	1	yes	characteristic, direct product factor, Sylow
206	Q₈²	—	2	4	no	—
207	Q₈²	—	2	4	no	—
208	C₂×C₄⋊Q₈	—	2	1	no	—
209	C₂×C₄⋊Q₈	—	2	1	no	—
210	C₂×C₄⋊Q₈	—	2	2	no	—
211	C₂×C₄⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic
212	C₂×C₄⋊Q₈	C₂²×C₇₉	1	2	yes	—
213	C₂×C₄⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic
214	C₂×C₄×Q₈	—	2	1	no	—
215	C₂×C₄×Q₈	C₂²×C₇₉	1	2	yes	—
216	C₂×C₄×Q₈	C₂²×C₇₉	1	1	yes	characteristic
217	C₂×C₄×Q₈	C₂²×C₇₉	1	1	yes	characteristic
218	#498	—	2	4	no	—
219	#475	—	2	4	no	—
220	C₂×#106	C₂²×C₇₉	1	2	yes	—
221	C₂×#106	C₂²×C₇₉	1	4	yes	—
222	C₂×C₄⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
223	C₂×#103	C₂²×C₇₉	1	2	yes	—
224	C₂×#103	C₂²×C₇₉	1	2	yes	—
225	C₂×C₄×C₈	C₂²×C₇₉	1	1	yes	characteristic
226	#398	—	2	2	no	—
227	#391	—	2	1	no	—
228	#389	C₂²×C₇₉	1	4	yes	—
229	C₄×C₄⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
230	#340	C₂²×C₇₉	1	2	yes	—
231	#340	C₂²×C₇₉	1	4	yes	—
232	#336	C₂²×C₇₉	1	4	yes	—
233	C₂²×Q₈	—	2	2	no	—
234	C₂²×Q₈	—	2	1	no	—
235	C₂²×Q₈	—	2	1	no	—
236	C₂²×Q₈	D₄×C₇₉	1	1	yes	characteristic
237	C₂²×Q₈	C₂³×C₇₉	1	1	yes	characteristic
238	C₂²×C₈	C₂³×C₇₉	1	2	yes	—
239	C₂²×C₈	C₂³×C₇₉	1	2	yes	—
240	C₄⋊Q₈	—	2	16	no	—
241	C₄⋊Q₈	—	2	8	no	—
242	C₄⋊Q₈	—	2	4	no	—
243	C₄⋊Q₈	—	2	4	no	—
244	C₄⋊Q₈	—	2	2	no	—
245	C₄⋊Q₈	—	2	2	no	—
246	C₄⋊Q₈	—	2	2	no	—
247	C₄⋊Q₈	—	4	4	no	—
248	C₄⋊Q₈	D₄×C₇₉	1	4	yes	—
249	C₄×Q₈	—	2	8	no	—
250	C₄×Q₈	—	2	4	no	—
251	C₄×Q₈	—	2	4	no	—
252	C₄×Q₈	—	2	2	no	—
253	C₄×Q₈	—	2	2	no	—
254	C₄×Q₈	—	2	2	no	—
255	C₄×Q₈	D₄×C₇₉	1	4	yes	—
256	C₂×C₄⋊C₄	—	2	2	no	—
257	C₂×C₄⋊C₄	—	2	1	no	—
258	C₂×C₄⋊C₄	—	2	2	no	—
259	C₂×C₄⋊C₄	—	2	1	no	—
260	C₂×C₄⋊C₄	—	2	4	no	—
261	C₂×C₄⋊C₄	—	2	1	no	—
262	C₂×C₄⋊C₄	D₄×C₇₉	1	1	yes	characteristic
263	C₂×C₄⋊C₄	D₄×C₇₉	1	2	yes	—
264	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
265	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
266	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
267	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
268	C₂×C₄²	—	2	2	no	—
269	C₂×C₄²	—	2	1	no	—
270	C₂×C₄²	—	2	1	no	—
271	C₂×C₄²	C₂³×C₇₉	1	2	yes	—
272	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
273	#106	—	2	4	no	—
274	#106	—	2	8	no	—
275	C₄⋊C₈	—	2	2	no	—
276	#103	—	2	4	no	—
277	#103	Q₈×C₇₉	1	8	yes	complemented
278	C₄×C₈	—	2	2	no	—
279	#95	—	2	1	no	—
280	#95	—	2	4	no	—
281	C₂×Q₈	—	2	8	no	—
282	C₂×Q₈	—	2	2	no	—
283	C₂×Q₈	—	2	4	no	—
284	C₂×Q₈	—	2	2	no	—
285	C₂×Q₈	—	2	1	no	—
286	C₂×Q₈	—	2	2	no	—
287	C₂×Q₈	—	4	2	no	—
288	C₂×Q₈	—	4	2	no	—
289	C₂×Q₈	—	4	2	no	—
290	C₂×Q₈	—	8	2	no	—
291	C₂×Q₈	—	8	4	no	—
292	C₂×Q₈	SD₁₆×C₇₉	1	4	yes	—
293	C₂×Q₈	C₂×D₄×C₇₉	1	2	yes	—
294	C₂×Q₈	C₂×Q₈×C₇₉	1	4	yes	—
295	C₂²×C₄	—	2	1	no	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	1	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
301	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
302	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
303	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
304	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
305	C₂×C₈	—	2	2	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	—	2	2	no	—
308	C₂×C₈	—	2	4	no	—
309	C₂×C₈	C₂×Q₈×C₇₉	1	4	yes	—
310	C₄⋊C₄	—	2	8	no	—
311	C₄⋊C₄	—	2	8	no	—
312	C₄⋊C₄	—	2	4	no	—
313	C₄⋊C₄	—	2	4	no	—
314	C₄⋊C₄	—	2	4	no	—
315	C₄⋊C₄	—	2	2	no	—
316	C₄⋊C₄	—	2	2	no	—
317	C₄⋊C₄	—	2	1	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	—	4	2	no	—
322	C₄⋊C₄	—	4	8	no	—
323	C₄⋊C₄	C₂×D₄×C₇₉	1	4	yes	—
324	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
325	C₄⋊C₄	C₂×Q₈×C₇₉	1	4	yes	—
326	C₄²	—	2	8	no	—
327	C₄²	—	2	4	no	—
328	C₄²	—	2	2	no	—
329	C₄²	—	2	2	no	—
330	C₄²	—	4	2	no	—
331	C₄²	C₂×D₄×C₇₉	1	2	yes	—
332	C₄²	C₂×D₄×C₇₉	1	2	yes	—
333	C₂³	C₂²×D₄×C₇₉	1	1	yes	characteristic
334	Q₈	—	2	8	no	—
335	Q₈	—	2	2	no	—
336	Q₈	—	2	4	no	—
337	Q₈	—	8	4	no	—
338	Q₈	—	8	8	no	—
339	Q₈	—	8	4	no	—
340	Q₈	C₄⋊Q₈×C₇₉	1	4	yes	complemented
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	4	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	4	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	4	no	—
350	C₂×C₄	—	2	4	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	4	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	#120×C₇₉	1	2	yes	—
359	C₂×C₄	#120×C₇₉	1	2	yes	—
360	C₂×C₄	C₂×SD₁₆×C₇₉	1	4	yes	—
361	C₂×C₄	C₂×SD₁₆×C₇₉	1	2	yes	—
362	C₂×C₄	#137×C₇₉	1	2	yes	—
363	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
364	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
365	C₂×C₄	C₂²×Q₈×C₇₉	1	2	yes	—
366	C₂×C₄	2₋¹⁺⁴×C₇₉	1	2	yes	—
367	C₈	—	2	4	no	—
368	C₈	—	4	2	no	—
369	C₂²	C₂×#120×C₇₉	1	1	yes	characteristic
370	C₂²	D₄×Q₈×C₇₉	1	2	yes	—
371	C₂²	C₂²×SD₁₆×C₇₉	1	1	yes	characteristic
372	C₂²	C₂×#137×C₇₉	1	1	yes	characteristic
373	C₂²	#577×C₇₉	1	2	yes	—
374	C₄	—	2	4	no	—
375	C₄	—	2	4	no	—
376	C₄	—	2	2	no	—
377	C₄	—	4	4	no	—
378	C₄	—	4	2	no	—
379	C₄	—	4	4	no	—
380	C₄	—	4	2	no	—
381	C₄	—	8	2	no	—
382	C₄	#448×C₇₉	1	4	yes	—
383	C₄	C₂×C₄⋊Q₈×C₇₉	1	1	yes	characteristic
384	C₄	#536×C₇₉	1	1	yes	characteristic
385	C₄	D₄×Q₈×C₇₉	1	2	yes	—
386	C₂	C₇₉×#2434	1	1	yes	characteristic
387	C₂	C₂×#448×C₇₉	1	1	yes	characteristic
388	C₂	C₇₉×#3009	1	1	yes	characteristic
389	C₂	Q₈×SD₁₆×C₇₉	1	2	yes	—
390	C₂	C₇₉×#3387	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂³×C₇₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₉
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₉ ◁ C₂×C₄×Q₈×C₇₉ ◁ G

Complements

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

N	H ≅ G/N	type
81. #103×C₇₉	Q₈	semidirect
144. Q₈×C₇₉	C₄⋊Q₈	semidirect
190. #25837	C₇₉	direct (N × H)
205. C₇₉	#25837	direct (N × H)
277. #103	Q₈×C₇₉	semidirect
340. Q₈	C₄⋊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×Q₈²×C₇₉	2
C₂×#498×C₇₉	2
C₂×#475×C₇₉	2
C₇₉×#2546	2
C₇₉×#2058	2
C₇₉×#1987	2
C₇₉×#1984	2
C₇₉×#1865	2
C₄×#103×C₇₉	2
#25837	79

Subgroups — C79×#25837 #34137526

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#25837 #34137526