Subgroups — C₇₉×#25472 #34137161

Order 20224.

770 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#475×C₇₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×Q₈×C₇₉	C₂	1	1	yes	maximal, characteristic
3	C₇₉×#2582	C₂	1	1	yes	maximal, characteristic
4	C₇₉×#2546	C₂	1	1	yes	maximal, characteristic
5	C₇₉×#2088	C₂	1	2	yes	maximal
6	C₇₉×#2066	C₂	1	2	yes	maximal
7	C₇₉×#1990	C₂	1	1	yes	maximal, characteristic
8	C₇₉×#1948	C₂	1	1	yes	maximal, characteristic
9	C₇₉×#1941	C₂	1	2	yes	maximal
10	C₇₉×#1933	C₂	1	2	yes	maximal
11	C₄×#103×C₇₉	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄⋊Q₈×C₇₉	—	2	1	no	—
13	C₂×C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic
15	C₂×C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic
16	#475×C₇₉	—	2	4	no	—
17	C₈×Q₈×C₇₉	—	2	4	no	—
18	C₂×#106×C₇₉	C₂²	1	2	yes	—
19	C₂×#106×C₇₉	C₂²	1	2	yes	—
20	C₂×C₄⋊C₈×C₇₉	C₂²	1	2	yes	—
21	C₂×C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
22	C₂×#103×C₇₉	C₂²	1	1	yes	characteristic
23	C₂×#103×C₇₉	C₂²	1	2	yes	—
24	C₂×#103×C₇₉	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₈×C₇₉	C₂²	1	2	yes	—
27	#398×C₇₉	—	2	2	no	—
28	#398×C₇₉	—	2	2	no	—
29	#391×C₇₉	—	2	1	no	—
30	#391×C₇₉	—	2	1	no	—
31	#391×C₇₉	C₂²	1	2	yes	—
32	#389×C₇₉	—	2	1	no	—
33	#389×C₇₉	C₂²	1	2	yes	—
34	#389×C₇₉	C₂²	1	2	yes	—
35	#389×C₇₉	C₂²	1	2	yes	—
36	#384×C₇₉	C₂²	1	1	yes	characteristic
37	C₄×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
38	#340×C₇₉	C₂²	1	1	yes	characteristic
39	#340×C₇₉	C₂²	1	1	yes	characteristic
40	#340×C₇₉	C₂²	1	2	yes	—
41	#340×C₇₉	C₂²	1	2	yes	—
42	#340×C₇₉	C₂²	1	2	yes	—
43	C₂²×Q₈×C₇₉	—	2	1	no	—
44	C₂²×Q₈×C₇₉	D₄	1	1	yes	characteristic
45	C₂²×Q₈×C₇₉	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₇₉	C₂³	1	2	yes	—
48	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
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	—	2	2	no	—
53	C₄×Q₈×C₇₉	—	2	2	no	—
54	C₄×Q₈×C₇₉	—	2	2	no	—
55	C₄×Q₈×C₇₉	—	2	2	no	—
56	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
57	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
58	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
59	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
60	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
61	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
62	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
63	C₂×C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₇₉	D₄	1	2	yes	—
65	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
67	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
68	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
69	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₇₉	—	2	1	no	—
71	C₂×C₄²×C₇₉	—	2	1	no	—
72	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
73	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
74	#106×C₇₉	—	2	4	no	—
75	#106×C₇₉	—	2	4	no	—
76	C₄⋊C₈×C₇₉	—	2	4	no	—
77	C₄⋊C₈×C₇₉	D₄	1	4	yes	—
78	#103×C₇₉	—	2	4	no	—
79	#103×C₇₉	—	2	2	no	—
80	#103×C₇₉	Q₈	1	4	yes	complemented
81	C₄×C₈×C₇₉	—	2	4	no	—
82	C₄×C₈×C₇₉	—	2	2	no	—
83	#95×C₇₉	—	2	1	no	—
84	#95×C₇₉	—	2	2	no	—
85	#95×C₇₉	—	2	2	no	—
86	#95×C₇₉	—	2	2	no	—
87	#95×C₇₉	—	2	2	no	—
88	#95×C₇₉	—	2	2	no	—
89	C₂×Q₈×C₇₉	—	2	2	no	—
90	C₂×Q₈×C₇₉	—	2	2	no	—
91	C₂×Q₈×C₇₉	—	2	1	no	—
92	C₂×Q₈×C₇₉	—	2	1	no	—
93	C₂×Q₈×C₇₉	—	2	1	no	—
94	C₂×Q₈×C₇₉	—	2	1	no	—
95	C₂×Q₈×C₇₉	—	2	1	no	—
96	C₂×Q₈×C₇₉	—	4	2	no	—
97	C₂×Q₈×C₇₉	—	4	2	no	—
98	C₂×Q₈×C₇₉	—	4	2	no	—
99	C₂×Q₈×C₇₉	SD₁₆	1	4	yes	—
100	C₂×Q₈×C₇₉	C₂×Q₈	1	2	yes	—
101	C₂²×C₄×C₇₉	—	2	1	no	—
102	C₂²×C₄×C₇₉	—	2	1	no	—
103	C₂²×C₄×C₇₉	—	2	1	no	—
104	C₂²×C₄×C₇₉	—	2	2	no	—
105	C₂²×C₄×C₇₉	—	2	1	no	—
106	C₂²×C₄×C₇₉	—	2	2	no	—
107	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
112	C₂×C₈×C₇₉	—	2	1	no	—
113	C₂×C₈×C₇₉	—	2	1	no	—
114	C₂×C₈×C₇₉	—	2	2	no	—
115	C₂×C₈×C₇₉	—	2	1	no	—
116	C₂×C₈×C₇₉	—	2	2	no	—
117	C₂×C₈×C₇₉	—	2	1	no	—
118	C₂×C₈×C₇₉	—	2	1	no	—
119	C₂×C₈×C₇₉	C₂×D₄	1	4	yes	—
120	C₂×C₈×C₇₉	C₂×Q₈	1	2	yes	—
121	C₄⋊C₄×C₇₉	—	2	4	no	—
122	C₄⋊C₄×C₇₉	—	2	2	no	—
123	C₄⋊C₄×C₇₉	—	2	1	no	—
124	C₄⋊C₄×C₇₉	—	2	1	no	—
125	C₄⋊C₄×C₇₉	—	2	2	no	—
126	C₄⋊C₄×C₇₉	—	2	1	no	—
127	C₄⋊C₄×C₇₉	—	2	2	no	—
128	C₄⋊C₄×C₇₉	—	2	1	no	—
129	C₄⋊C₄×C₇₉	—	2	2	no	—
130	C₄⋊C₄×C₇₉	—	2	2	no	—
131	C₄⋊C₄×C₇₉	—	4	2	no	—
132	C₄⋊C₄×C₇₉	—	4	2	no	—
133	C₄⋊C₄×C₇₉	—	4	4	no	—
134	C₄⋊C₄×C₇₉	—	4	4	no	—
135	C₄⋊C₄×C₇₉	—	4	2	no	—
136	C₄⋊C₄×C₇₉	—	8	1	no	—
137	C₄⋊C₄×C₇₉	—	8	2	no	—
138	C₄⋊C₄×C₇₉	C₂×Q₈	1	2	yes	—
139	C₄⋊C₄×C₇₉	#41	1	2	yes	—
140	C₄²×C₇₉	—	2	2	no	—
141	C₄²×C₇₉	—	2	2	no	—
142	C₄²×C₇₉	—	4	2	no	—
143	C₄²×C₇₉	—	4	2	no	—
144	C₄²×C₇₉	C₂×D₄	1	2	yes	—
145	C₄²×C₇₉	#41	1	2	yes	—
146	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
147	Q₈×C₇₉	—	2	8	no	—
148	Q₈×C₇₉	—	2	2	no	—
149	Q₈×C₇₉	—	2	2	no	—
150	Q₈×C₇₉	—	4	1	no	—
151	Q₈×C₇₉	—	4	1	no	—
152	Q₈×C₇₉	—	8	4	no	—
153	C₂×C₄×C₇₉	—	2	2	no	—
154	C₂×C₄×C₇₉	—	2	2	no	—
155	C₂×C₄×C₇₉	—	2	1	no	—
156	C₂×C₄×C₇₉	—	2	1	no	—
157	C₂×C₄×C₇₉	—	2	2	no	—
158	C₂×C₄×C₇₉	—	2	2	no	—
159	C₂×C₄×C₇₉	—	2	2	no	—
160	C₂×C₄×C₇₉	—	2	2	no	—
161	C₂×C₄×C₇₉	—	2	2	no	—
162	C₂×C₄×C₇₉	—	2	2	no	—
163	C₂×C₄×C₇₉	—	4	1	no	—
164	C₂×C₄×C₇₉	—	4	1	no	—
165	C₂×C₄×C₇₉	—	4	1	no	—
166	C₂×C₄×C₇₉	—	4	1	no	—
167	C₂×C₄×C₇₉	—	4	1	no	—
168	C₂×C₄×C₇₉	—	4	1	no	—
169	C₂×C₄×C₇₉	—	4	1	no	—
170	C₂×C₄×C₇₉	—	4	2	no	—
171	C₂×C₄×C₇₉	—	4	2	no	—
172	C₂×C₄×C₇₉	—	4	2	no	—
173	C₂×C₄×C₇₉	—	4	2	no	—
174	C₂×C₄×C₇₉	—	4	2	no	—
175	C₂×C₄×C₇₉	—	4	2	no	—
176	C₂×C₄×C₇₉	—	4	1	no	—
177	C₂×C₄×C₇₉	—	4	1	no	—
178	C₂×C₄×C₇₉	#121	1	2	yes	—
179	C₂×C₄×C₇₉	#121	1	2	yes	—
180	C₂×C₄×C₇₉	C₂×SD₁₆	1	4	yes	—
181	C₂×C₄×C₇₉	C₂×SD₁₆	1	2	yes	—
182	C₂×C₄×C₇₉	#135	1	2	yes	—
183	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
184	C₂×C₄×C₇₉	C₂²×Q₈	1	1	yes	characteristic
185	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
186	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
187	C₂×C₄×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
188	C₂×C₄×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
189	C₈×C₇₉	—	2	4	no	—
190	C₈×C₇₉	—	2	2	no	—
191	C₈×C₇₉	—	4	1	no	—
192	C₂²×C₇₉	C₂×#121	1	1	yes	characteristic
193	C₂²×C₇₉	#548	1	1	yes	characteristic
194	C₂²×C₇₉	D₄×Q₈	1	1	yes	characteristic
195	C₂²×C₇₉	C₂²×SD₁₆	1	1	yes	characteristic
196	C₂²×C₇₉	C₂×#135	1	1	yes	characteristic
197	C₂²×C₇₉	#577	1	1	yes	characteristic
198	C₂²×C₇₉	#578	1	1	yes	characteristic
199	C₄×C₇₉	—	2	4	no	—
200	C₄×C₇₉	—	2	2	no	—
201	C₄×C₇₉	—	4	2	no	—
202	C₄×C₇₉	—	4	2	no	—
203	C₄×C₇₉	—	4	2	no	—
204	C₄×C₇₉	—	4	2	no	—
205	C₄×C₇₉	—	8	2	no	—
206	C₄×C₇₉	—	8	2	no	—
207	C₄×C₇₉	—	8	1	no	—
208	C₄×C₇₉	#465	1	4	yes	—
209	C₄×C₇₉	#533	1	1	yes	characteristic
210	C₄×C₇₉	#541	1	1	yes	characteristic
211	C₄×C₇₉	#547	1	1	yes	characteristic
212	C₄×C₇₉	D₄×Q₈	1	1	yes	characteristic
213	#25472	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
214	C₂×C₇₉	#2429	1	1	yes	characteristic
215	C₂×C₇₉	C₂×#465	1	1	yes	characteristic
216	C₂×C₇₉	#3063	1	1	yes	characteristic
217	C₂×C₇₉	#3359	1	1	yes	characteristic
218	C₂×C₇₉	#3365	1	1	yes	characteristic
219	C₂×C₇₉	Q₈×SD₁₆	1	1	yes	characteristic
220	C₂×C₇₉	#3383	1	1	yes	characteristic
221	C₂×#475	C₂×C₇₉	1	1	yes	characteristic
222	C₂×C₈×Q₈	C₂×C₇₉	1	1	yes	characteristic
223	#2582	C₂×C₇₉	1	1	yes	characteristic
224	#2546	C₂×C₇₉	1	1	yes	characteristic
225	#2088	C₂×C₇₉	1	2	yes	—
226	#2066	C₂×C₇₉	1	2	yes	—
227	#1990	C₂×C₇₉	1	1	yes	characteristic
228	#1948	C₂×C₇₉	1	1	yes	characteristic
229	#1941	C₂×C₇₉	1	2	yes	—
230	#1933	C₂×C₇₉	1	2	yes	—
231	C₄×#103	C₂×C₇₉	1	1	yes	characteristic
232	C₇₉	#25472	1	1	yes	characteristic, direct product factor, Sylow
233	C₂×C₄⋊Q₈	—	2	1	no	—
234	C₂×C₄⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic
235	C₂×C₄×Q₈	C₂²×C₇₉	1	1	yes	characteristic
236	C₂×C₄×Q₈	C₂²×C₇₉	1	1	yes	characteristic
237	#475	—	2	4	no	—
238	C₈×Q₈	—	2	4	no	—
239	C₂×#106	C₂²×C₇₉	1	2	yes	—
240	C₂×#106	C₂²×C₇₉	1	2	yes	—
241	C₂×C₄⋊C₈	C₂²×C₇₉	1	2	yes	—
242	C₂×C₄⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
243	C₂×#103	C₂²×C₇₉	1	2	yes	—
244	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic
245	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic
246	C₂×C₄×C₈	C₂²×C₇₉	1	2	yes	—
247	C₂×C₄×C₈	C₂²×C₇₉	1	1	yes	characteristic
248	#398	—	2	2	no	—
249	#398	—	2	2	no	—
250	#391	—	2	1	no	—
251	#391	—	2	1	no	—
252	#391	C₂²×C₇₉	1	2	yes	—
253	#389	—	2	1	no	—
254	#389	C₂²×C₇₉	1	2	yes	—
255	#389	C₂²×C₇₉	1	2	yes	—
256	#389	C₂²×C₇₉	1	2	yes	—
257	#384	C₂²×C₇₉	1	1	yes	characteristic
258	C₄×C₄⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
259	#340	C₂²×C₇₉	1	2	yes	—
260	#340	C₂²×C₇₉	1	1	yes	characteristic
261	#340	C₂²×C₇₉	1	2	yes	—
262	#340	C₂²×C₇₉	1	2	yes	—
263	#340	C₂²×C₇₉	1	1	yes	characteristic
264	C₂²×Q₈	—	2	1	no	—
265	C₂²×Q₈	D₄×C₇₉	1	1	yes	characteristic
266	C₂²×Q₈	C₂³×C₇₉	1	1	yes	characteristic
267	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
268	C₂²×C₈	C₂³×C₇₉	1	2	yes	—
269	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
270	C₄⋊Q₈	—	2	2	no	—
271	C₄⋊Q₈	—	2	2	no	—
272	C₄⋊Q₈	—	4	4	no	—
273	C₄×Q₈	—	2	2	no	—
274	C₄×Q₈	—	2	2	no	—
275	C₄×Q₈	—	2	2	no	—
276	C₄×Q₈	—	2	2	no	—
277	C₂×C₄⋊C₄	—	2	1	no	—
278	C₂×C₄⋊C₄	—	2	2	no	—
279	C₂×C₄⋊C₄	—	2	2	no	—
280	C₂×C₄⋊C₄	—	2	1	no	—
281	C₂×C₄⋊C₄	—	2	1	no	—
282	C₂×C₄⋊C₄	—	2	1	no	—
283	C₂×C₄⋊C₄	—	2	2	no	—
284	C₂×C₄⋊C₄	D₄×C₇₉	1	1	yes	characteristic
285	C₂×C₄⋊C₄	D₄×C₇₉	1	2	yes	—
286	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
287	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
288	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
289	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
290	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
291	C₂×C₄²	—	2	1	no	—
292	C₂×C₄²	—	2	1	no	—
293	C₂×C₄²	C₂³×C₇₉	1	2	yes	—
294	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
295	#106	—	2	4	no	—
296	#106	—	2	4	no	—
297	C₄⋊C₈	—	2	4	no	—
298	C₄⋊C₈	D₄×C₇₉	1	4	yes	—
299	#103	—	2	4	no	—
300	#103	—	2	2	no	—
301	#103	Q₈×C₇₉	1	4	yes	complemented
302	C₄×C₈	—	2	4	no	—
303	C₄×C₈	—	2	2	no	—
304	#95	—	2	1	no	—
305	#95	—	2	2	no	—
306	#95	—	2	2	no	—
307	#95	—	2	2	no	—
308	#95	—	2	2	no	—
309	#95	—	2	2	no	—
310	C₂×Q₈	—	2	2	no	—
311	C₂×Q₈	—	2	2	no	—
312	C₂×Q₈	—	2	1	no	—
313	C₂×Q₈	—	2	1	no	—
314	C₂×Q₈	—	2	1	no	—
315	C₂×Q₈	—	2	1	no	—
316	C₂×Q₈	—	2	1	no	—
317	C₂×Q₈	—	4	2	no	—
318	C₂×Q₈	—	4	2	no	—
319	C₂×Q₈	—	4	2	no	—
320	C₂×Q₈	SD₁₆×C₇₉	1	4	yes	—
321	C₂×Q₈	C₂×Q₈×C₇₉	1	2	yes	—
322	C₂²×C₄	—	2	1	no	—
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
329	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
330	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
331	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
332	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
333	C₂×C₈	—	2	1	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	2	1	no	—
337	C₂×C₈	—	2	1	no	—
338	C₂×C₈	—	2	1	no	—
339	C₂×C₈	—	2	1	no	—
340	C₂×C₈	C₂×D₄×C₇₉	1	4	yes	—
341	C₂×C₈	C₂×Q₈×C₇₉	1	2	yes	—
342	C₄⋊C₄	—	2	4	no	—
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	2	1	no	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	2	1	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	2	1	no	—
350	C₄⋊C₄	—	2	2	no	—
351	C₄⋊C₄	—	2	2	no	—
352	C₄⋊C₄	—	4	2	no	—
353	C₄⋊C₄	—	4	2	no	—
354	C₄⋊C₄	—	4	4	no	—
355	C₄⋊C₄	—	4	4	no	—
356	C₄⋊C₄	—	4	2	no	—
357	C₄⋊C₄	—	8	1	no	—
358	C₄⋊C₄	—	8	2	no	—
359	C₄⋊C₄	C₂×Q₈×C₇₉	1	2	yes	—
360	C₄⋊C₄	#41×C₇₉	1	2	yes	—
361	C₄²	—	2	2	no	—
362	C₄²	—	2	2	no	—
363	C₄²	—	4	2	no	—
364	C₄²	—	4	2	no	—
365	C₄²	C₂×D₄×C₇₉	1	2	yes	—
366	C₄²	#41×C₇₉	1	2	yes	—
367	C₂³	C₂²×D₄×C₇₉	1	1	yes	characteristic
368	Q₈	—	2	8	no	—
369	Q₈	—	2	2	no	—
370	Q₈	—	2	2	no	—
371	Q₈	—	4	1	no	—
372	Q₈	—	4	1	no	—
373	Q₈	—	8	4	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	4	1	no	—
385	C₂×C₄	—	4	1	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	#121×C₇₉	1	2	yes	—
400	C₂×C₄	#121×C₇₉	1	2	yes	—
401	C₂×C₄	C₂×SD₁₆×C₇₉	1	4	yes	—
402	C₂×C₄	C₂×SD₁₆×C₇₉	1	2	yes	—
403	C₂×C₄	#135×C₇₉	1	2	yes	—
404	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
405	C₂×C₄	C₂²×Q₈×C₇₉	1	1	yes	characteristic
406	C₂×C₄	C₂×#41×C₇₉	1	1	yes	characteristic
407	C₂×C₄	C₂×#41×C₇₉	1	1	yes	characteristic
408	C₂×C₄	2₋¹⁺⁴×C₇₉	1	1	yes	characteristic
409	C₂×C₄	2₋¹⁺⁴×C₇₉	1	1	yes	characteristic
410	C₈	—	2	4	no	—
411	C₈	—	2	2	no	—
412	C₈	—	4	1	no	—
413	C₂²	C₂×#121×C₇₉	1	1	yes	characteristic
414	C₂²	#548×C₇₉	1	1	yes	characteristic
415	C₂²	D₄×Q₈×C₇₉	1	1	yes	characteristic
416	C₂²	C₂²×SD₁₆×C₇₉	1	1	yes	characteristic
417	C₂²	C₂×#135×C₇₉	1	1	yes	characteristic
418	C₂²	#577×C₇₉	1	1	yes	characteristic
419	C₂²	#578×C₇₉	1	1	yes	characteristic
420	C₄	—	2	4	no	—
421	C₄	—	2	2	no	—
422	C₄	—	4	2	no	—
423	C₄	—	4	2	no	—
424	C₄	—	4	2	no	—
425	C₄	—	4	2	no	—
426	C₄	—	8	2	no	—
427	C₄	—	8	1	no	—
428	C₄	—	8	2	no	—
429	C₄	#465×C₇₉	1	4	yes	—
430	C₄	#533×C₇₉	1	1	yes	characteristic
431	C₄	#541×C₇₉	1	1	yes	characteristic
432	C₄	#547×C₇₉	1	1	yes	characteristic
433	C₄	D₄×Q₈×C₇₉	1	1	yes	characteristic
434	C₂	C₇₉×#2429	1	1	yes	characteristic
435	C₂	C₂×#465×C₇₉	1	1	yes	characteristic
436	C₂	C₇₉×#3063	1	1	yes	characteristic
437	C₂	C₇₉×#3359	1	1	yes	characteristic
438	C₂	C₇₉×#3365	1	1	yes	characteristic
439	C₂	Q₈×SD₁₆×C₇₉	1	1	yes	characteristic
440	C₂	C₇₉×#3383	1	1	yes	characteristic

	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
80. #103×C₇₉	Q₈	semidirect
213. #25472	C₇₉	direct (N × H)
232. C₇₉	#25472	direct (N × H)
301. #103	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×#475×C₇₉	2
C₂×C₈×Q₈×C₇₉	2
C₇₉×#2582	2
C₇₉×#2546	2
C₇₉×#2088	2
C₇₉×#2066	2
C₇₉×#1990	2
C₇₉×#1948	2
C₇₉×#1941	2
C₇₉×#1933	2
C₄×#103×C₇₉	2
#25472	79

Subgroups — C79×#25472 #34137161

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#25472 #34137161