Subgroups — C₇₉×#18651 #34130340

Order 20224.

1126 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₉×#3499	C₂	1	1	yes	maximal, characteristic
2	C₇₉×#3206	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#498×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₉×#3079	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₉×#1654	C₂	1	4	yes	maximal, complemented
6	C₇₉×#1651	C₂	1	4	yes	maximal, complemented
7	C₇₉×#1546	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₉×#1492	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₉×#1476	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×2₋¹⁺⁴×C₇₉	—	2	1	no	—
11	D₄×Q₈×C₇₉	—	2	1	no	—
12	D₄×Q₈×C₇₉	C₂²	1	2	yes	—
13	#547×C₇₉	—	2	2	no	—
14	#547×C₇₉	—	2	1	no	—
15	#547×C₇₉	—	2	2	no	—
16	#547×C₇₉	C₂²	1	2	yes	—
17	#536×C₇₉	—	2	2	no	—
18	#536×C₇₉	—	2	1	no	—
19	#532×C₇₉	—	2	1	no	—
20	#532×C₇₉	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊Q₈×C₇₉	—	2	1	no	—
22	C₂×C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
24	C₄×#41×C₇₉	C₂²	1	1	yes	characteristic
25	#498×C₇₉	—	2	2	no	—
26	#498×C₇₉	C₂²	1	4	yes	—
27	#492×C₇₉	—	2	1	no	—
28	#487×C₇₉	—	2	1	no	—
29	#477×C₇₉	—	2	1	no	—
30	#476×C₇₉	—	2	1	no	—
31	#475×C₇₉	C₂²	1	2	yes	—
32	#474×C₇₉	C₂²	1	2	yes	—
33	#461×C₇₉	C₂²	1	4	yes	—
34	#448×C₇₉	—	2	2	no	—
35	#431×C₇₉	C₂²	1	1	yes	characteristic
36	#428×C₇₉	—	2	1	no	—
37	C₂×#106×C₇₉	—	2	2	no	—
38	#423×C₇₉	C₂²	1	1	yes	characteristic
39	#417×C₇₉	—	2	1	no	—
40	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
41	#332×C₇₉	C₂²	1	4	yes	—
42	Q₈⋊C₈×C₇₉	C₂²	1	2	yes	—
43	D₄⋊C₈×C₇₉	C₂²	1	4	yes	—
44	D₄⋊C₈×C₇₉	C₂²	1	2	yes	—
45	2₋¹⁺⁴×C₇₉	—	4	4	no	—
46	2₋¹⁺⁴×C₇₉	—	4	4	no	—
47	C₂×#41×C₇₉	—	2	2	no	—
48	C₂×#41×C₇₉	—	2	4	no	—
49	C₂×#41×C₇₉	—	2	2	no	—
50	C₂×#41×C₇₉	—	2	1	no	—
51	C₂×#41×C₇₉	D₄	1	1	yes	characteristic
52	C₂²×Q₈×C₇₉	—	2	2	no	—
53	C₂²×Q₈×C₇₉	—	2	2	no	—
54	C₂²×Q₈×C₇₉	—	2	1	no	—
55	C₂²×Q₈×C₇₉	—	2	1	no	—
56	C₂×SD₁₆×C₇₉	—	2	4	no	—
57	C₂×M₁₆×C₇₉	—	2	1	no	—
58	C₂²×C₈×C₇₉	—	2	1	no	—
59	C₄⋊Q₈×C₇₉	—	2	2	no	—
60	C₄⋊Q₈×C₇₉	—	2	2	no	—
61	C₄⋊Q₈×C₇₉	—	2	2	no	—
62	C₄⋊Q₈×C₇₉	—	2	1	no	—
63	C₄⋊Q₈×C₇₉	—	2	1	no	—
64	C₄⋊Q₈×C₇₉	—	2	1	no	—
65	C₄⋊Q₈×C₇₉	—	2	1	no	—
66	C₄⋊Q₈×C₇₉	—	2	1	no	—
67	C₄⋊Q₈×C₇₉	D₄	1	1	yes	characteristic
68	C₄⋊Q₈×C₇₉	D₄	1	2	yes	—
69	C₄⋊Q₈×C₇₉	C₂³	1	2	yes	—
70	C₄⋊Q₈×C₇₉	C₂³	1	2	yes	—
71	#127×C₇₉	D₄	1	1	yes	characteristic
72	#124×C₇₉	—	2	2	no	—
73	#124×C₇₉	—	2	1	no	—
74	#123×C₇₉	—	2	4	no	—
75	#123×C₇₉	—	2	4	no	—
76	#123×C₇₉	—	2	4	no	—
77	C₂²⋊Q₈×C₇₉	—	2	4	no	—
78	C₂²⋊Q₈×C₇₉	—	2	2	no	—
79	C₂²⋊Q₈×C₇₉	—	2	4	no	—
80	C₂²⋊Q₈×C₇₉	—	2	2	no	—
81	#121×C₇₉	—	2	2	no	—
82	#121×C₇₉	—	2	2	no	—
83	#121×C₇₉	—	2	1	no	—
84	#121×C₇₉	D₄	1	2	yes	—
85	C₄×Q₈×C₇₉	D₄	1	1	yes	characteristic
86	C₄×Q₈×C₇₉	C₂³	1	1	yes	characteristic
87	C₄×D₄×C₇₉	—	2	2	no	—
88	C₄×D₄×C₇₉	—	2	2	no	—
89	C₄×D₄×C₇₉	—	2	1	no	—
90	C₄×D₄×C₇₉	—	2	1	no	—
91	C₄×D₄×C₇₉	—	2	1	no	—
92	C₄×D₄×C₇₉	D₄	1	1	yes	characteristic
93	C₄×D₄×C₇₉	C₂³	1	2	yes	—
94	C₄×D₄×C₇₉	C₂³	1	1	yes	characteristic
95	#117×C₇₉	—	2	1	no	—
96	#117×C₇₉	D₄	1	1	yes	characteristic
97	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
98	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
99	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
100	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
101	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
102	C₂×C₄⋊C₄×C₇₉	D₄	1	2	yes	—
103	C₂×C₄²×C₇₉	—	2	1	no	—
104	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
105	#107×C₇₉	—	2	2	no	—
106	#106×C₇₉	—	2	8	no	—
107	#106×C₇₉	—	2	2	no	—
108	C₄⋊C₈×C₇₉	—	2	1	no	—
109	C₄⋊C₈×C₇₉	C₂³	1	2	yes	—
110	C₄⋊C₈×C₇₉	C₂³	1	2	yes	—
111	#103×C₇₉	—	2	2	no	—
112	#103×C₇₉	—	2	4	no	—
113	#102×C₇₉	—	2	2	no	—
114	C₂²⋊C₈×C₇₉	—	2	1	no	—
115	C₄×C₈×C₇₉	—	2	1	no	—
116	C₄×C₈×C₇₉	—	2	1	no	—
117	C₄×C₈×C₇₉	C₂³	1	2	yes	—
118	#41×C₇₉	—	2	2	no	—
119	#41×C₇₉	—	4	8	no	—
120	#41×C₇₉	—	4	16	no	—
121	#41×C₇₉	—	4	4	no	—
122	#41×C₇₉	—	4	4	no	—
123	#41×C₇₉	—	4	2	no	—
124	#41×C₇₉	—	4	2	no	—
125	#41×C₇₉	SD₁₆	1	4	yes	complemented
126	C₂×Q₈×C₇₉	—	2	4	no	—
127	C₂×Q₈×C₇₉	—	2	2	no	—
128	C₂×Q₈×C₇₉	—	2	1	no	—
129	C₂×Q₈×C₇₉	—	2	2	no	—
130	C₂×Q₈×C₇₉	—	2	2	no	—
131	C₂×Q₈×C₇₉	—	4	8	no	—
132	C₂×Q₈×C₇₉	—	4	4	no	—
133	C₂×Q₈×C₇₉	—	4	4	no	—
134	C₂×Q₈×C₇₉	—	4	1	no	—
135	C₂×Q₈×C₇₉	—	4	2	no	—
136	C₂×Q₈×C₇₉	—	4	2	no	—
137	C₂×Q₈×C₇₉	—	8	2	no	—
138	C₂×Q₈×C₇₉	C₂×D₄	1	1	yes	characteristic
139	C₂×D₄×C₇₉	—	2	1	no	—
140	C₂×D₄×C₇₉	—	2	4	no	—
141	C₂×D₄×C₇₉	—	2	2	no	—
142	C₂×D₄×C₇₉	—	2	1	no	—
143	C₂×D₄×C₇₉	—	2	1	no	—
144	C₂×D₄×C₇₉	C₂×D₄	1	2	yes	—
145	C₂×D₄×C₇₉	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₇₉	—	2	1	no	—
147	C₂²×C₄×C₇₉	—	2	4	no	—
148	C₂²×C₄×C₇₉	—	2	4	no	—
149	C₂²×C₄×C₇₉	—	2	2	no	—
150	C₂²×C₄×C₇₉	—	2	1	no	—
151	C₂²×C₄×C₇₉	—	2	1	no	—
152	C₂²×C₄×C₇₉	—	2	2	no	—
153	C₂²×C₄×C₇₉	—	4	1	no	—
154	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
157	SD₁₆×C₇₉	—	8	4	no	—
158	M₁₆×C₇₉	—	4	2	no	—
159	C₂×C₈×C₇₉	—	2	4	no	—
160	C₂×C₈×C₇₉	—	2	2	no	—
161	C₂×C₈×C₇₉	—	2	2	no	—
162	C₂×C₈×C₇₉	—	2	2	no	—
163	C₄⋊C₄×C₇₉	—	2	4	no	—
164	C₄⋊C₄×C₇₉	—	2	4	no	—
165	C₄⋊C₄×C₇₉	—	2	1	no	—
166	C₄⋊C₄×C₇₉	—	2	2	no	—
167	C₄⋊C₄×C₇₉	—	2	2	no	—
168	C₄⋊C₄×C₇₉	—	2	1	no	—
169	C₄⋊C₄×C₇₉	—	2	2	no	—
170	C₄⋊C₄×C₇₉	—	2	1	no	—
171	C₄⋊C₄×C₇₉	—	2	2	no	—
172	C₄⋊C₄×C₇₉	—	2	2	no	—
173	C₄⋊C₄×C₇₉	—	4	1	no	—
174	C₄⋊C₄×C₇₉	—	4	1	no	—
175	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
176	C₄⋊C₄×C₇₉	C₂×D₄	1	4	yes	—
177	C₄⋊C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
178	C₄⋊C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
179	C₂²⋊C₄×C₇₉	—	2	4	no	—
180	C₂²⋊C₄×C₇₉	—	2	4	no	—
181	C₂²⋊C₄×C₇₉	—	2	1	no	—
182	C₂²⋊C₄×C₇₉	—	2	1	no	—
183	C₂²⋊C₄×C₇₉	—	2	2	no	—
184	C₂²⋊C₄×C₇₉	—	2	1	no	—
185	C₂²⋊C₄×C₇₉	—	2	2	no	—
186	C₄²×C₇₉	—	2	1	no	—
187	C₄²×C₇₉	—	2	1	no	—
188	C₄²×C₇₉	—	2	1	no	—
189	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
190	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
191	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
192	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
193	C₂³×C₇₉	—	2	1	no	—
194	C₂³×C₇₉	—	2	2	no	—
195	C₂³×C₇₉	#120	1	1	yes	characteristic
196	Q₈×C₇₉	—	2	1	no	—
197	Q₈×C₇₉	—	4	8	no	—
198	Q₈×C₇₉	—	4	2	no	—
199	Q₈×C₇₉	—	4	2	no	—
200	Q₈×C₇₉	—	4	2	no	—
201	Q₈×C₇₉	—	4	4	no	—
202	Q₈×C₇₉	—	4	4	no	—
203	Q₈×C₇₉	—	8	2	no	—
204	Q₈×C₇₉	C₂×SD₁₆	1	2	yes	—
205	D₄×C₇₉	—	2	4	no	—
206	D₄×C₇₉	—	2	1	no	—
207	D₄×C₇₉	—	2	4	no	—
208	D₄×C₇₉	—	4	8	no	—
209	D₄×C₇₉	—	4	4	no	—
210	D₄×C₇₉	—	4	2	no	—
211	D₄×C₇₉	—	4	2	no	—
212	D₄×C₇₉	C₂×SD₁₆	1	2	yes	—
213	C₂×C₄×C₇₉	—	2	1	no	—
214	C₂×C₄×C₇₉	—	2	2	no	—
215	C₂×C₄×C₇₉	—	2	4	no	—
216	C₂×C₄×C₇₉	—	2	2	no	—
217	C₂×C₄×C₇₉	—	2	1	no	—
218	C₂×C₄×C₇₉	—	2	1	no	—
219	C₂×C₄×C₇₉	—	2	4	no	—
220	C₂×C₄×C₇₉	—	2	2	no	—
221	C₂×C₄×C₇₉	—	4	8	no	—
222	C₂×C₄×C₇₉	—	4	8	no	—
223	C₂×C₄×C₇₉	—	4	4	no	—
224	C₂×C₄×C₇₉	—	4	2	no	—
225	C₂×C₄×C₇₉	—	4	2	no	—
226	C₂×C₄×C₇₉	—	4	2	no	—
227	C₂×C₄×C₇₉	—	4	2	no	—
228	C₂×C₄×C₇₉	—	4	2	no	—
229	C₂×C₄×C₇₉	—	8	2	no	—
230	C₂×C₄×C₇₉	#120	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	C₂×SD₁₆	1	2	yes	—
234	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	2	yes	—
235	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
236	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
237	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
238	C₈×C₇₉	—	2	4	no	—
239	C₈×C₇₉	—	4	2	no	—
240	C₈×C₇₉	—	4	2	no	—
241	C₂²×C₇₉	—	2	1	no	—
242	C₂²×C₇₉	—	2	1	no	—
243	C₂²×C₇₉	—	2	2	no	—
244	C₂²×C₇₉	—	4	1	no	—
245	C₂²×C₇₉	—	4	1	no	—
246	C₂²×C₇₉	—	4	2	no	—
247	C₂²×C₇₉	—	4	2	no	—
248	C₂²×C₇₉	—	4	2	no	—
249	C₂²×C₇₉	#450	1	2	yes	—
250	C₂²×C₇₉	C₂×#120	1	1	yes	characteristic
251	C₄×C₇₉	—	2	2	no	—
252	C₄×C₇₉	—	2	1	no	—
253	C₄×C₇₉	—	2	1	no	—
254	C₄×C₇₉	—	4	4	no	—
255	C₄×C₇₉	—	4	2	no	—
256	C₄×C₇₉	—	4	1	no	—
257	C₄×C₇₉	—	4	1	no	—
258	C₄×C₇₉	—	8	2	no	—
259	C₄×C₇₉	#450	1	2	yes	—
260	C₄×C₇₉	#456	1	2	yes	—
261	C₄×C₇₉	C₂²×SD₁₆	1	1	yes	characteristic
262	C₄×C₇₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
263	C₄×C₇₉	#577	1	2	yes	—
264	#18651	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
265	C₂×C₇₉	—	2	2	no	—
266	C₂×C₇₉	—	4	2	no	—
267	C₂×C₇₉	—	8	2	no	—
268	C₂×C₇₉	C₂×#450	1	1	yes	characteristic
269	C₂×C₇₉	#3010	1	1	yes	characteristic
270	C₂×C₇₉	C₂×#456	1	1	yes	characteristic
271	#3499	C₂×C₇₉	1	1	yes	characteristic
272	#3206	C₂×C₇₉	1	1	yes	characteristic, complemented
273	C₂×#498	C₂×C₇₉	1	1	yes	characteristic, complemented
274	#3079	C₂×C₇₉	1	1	yes	characteristic, complemented
275	#1654	C₂×C₇₉	1	4	yes	complemented
276	#1651	C₂×C₇₉	1	4	yes	complemented
277	#1546	C₂×C₇₉	1	1	yes	characteristic, complemented
278	#1492	C₂×C₇₉	1	1	yes	characteristic, complemented
279	#1476	C₂×C₇₉	1	1	yes	characteristic, complemented
280	C₇₉	#18651	1	1	yes	characteristic, direct product factor, Sylow
281	C₂×2₋¹⁺⁴	—	2	1	no	—
282	D₄×Q₈	—	2	1	no	—
283	D₄×Q₈	C₂²×C₇₉	1	2	yes	—
284	#547	—	2	2	no	—
285	#547	—	2	1	no	—
286	#547	—	2	2	no	—
287	#547	C₂²×C₇₉	1	2	yes	—
288	#536	—	2	2	no	—
289	#536	—	2	1	no	—
290	#532	—	2	1	no	—
291	#532	C₂²×C₇₉	1	1	yes	characteristic
292	C₂×C₄⋊Q₈	—	2	1	no	—
293	C₂×C₄⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic
294	C₂×C₄⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic
295	C₄×#41	C₂²×C₇₉	1	1	yes	characteristic
296	#498	—	2	2	no	—
297	#498	C₂²×C₇₉	1	4	yes	—
298	#492	—	2	1	no	—
299	#487	—	2	1	no	—
300	#477	—	2	1	no	—
301	#476	—	2	1	no	—
302	#475	C₂²×C₇₉	1	2	yes	—
303	#474	C₂²×C₇₉	1	2	yes	—
304	#461	C₂²×C₇₉	1	4	yes	—
305	#448	—	2	2	no	—
306	#431	C₂²×C₇₉	1	1	yes	characteristic
307	#428	—	2	1	no	—
308	C₂×#106	—	2	2	no	—
309	#423	C₂²×C₇₉	1	1	yes	characteristic
310	#417	—	2	1	no	—
311	C₂×C₄×C₈	C₂²×C₇₉	1	1	yes	characteristic
312	#332	C₂²×C₇₉	1	4	yes	—
313	Q₈⋊C₈	C₂²×C₇₉	1	2	yes	—
314	D₄⋊C₈	C₂²×C₇₉	1	4	yes	—
315	D₄⋊C₈	C₂²×C₇₉	1	2	yes	—
316	2₋¹⁺⁴	—	4	4	no	—
317	2₋¹⁺⁴	—	4	4	no	—
318	C₂×#41	—	2	2	no	—
319	C₂×#41	—	2	4	no	—
320	C₂×#41	—	2	2	no	—
321	C₂×#41	—	2	1	no	—
322	C₂×#41	D₄×C₇₉	1	1	yes	characteristic
323	C₂²×Q₈	—	2	2	no	—
324	C₂²×Q₈	—	2	2	no	—
325	C₂²×Q₈	—	2	1	no	—
326	C₂²×Q₈	—	2	1	no	—
327	C₂×SD₁₆	—	2	4	no	—
328	C₂×M₁₆	—	2	1	no	—
329	C₂²×C₈	—	2	1	no	—
330	C₄⋊Q₈	—	2	2	no	—
331	C₄⋊Q₈	—	2	2	no	—
332	C₄⋊Q₈	—	2	2	no	—
333	C₄⋊Q₈	—	2	1	no	—
334	C₄⋊Q₈	—	2	1	no	—
335	C₄⋊Q₈	—	2	1	no	—
336	C₄⋊Q₈	—	2	1	no	—
337	C₄⋊Q₈	—	2	1	no	—
338	C₄⋊Q₈	D₄×C₇₉	1	1	yes	characteristic
339	C₄⋊Q₈	D₄×C₇₉	1	2	yes	—
340	C₄⋊Q₈	C₂³×C₇₉	1	2	yes	—
341	C₄⋊Q₈	C₂³×C₇₉	1	2	yes	—
342	#127	D₄×C₇₉	1	1	yes	characteristic
343	#124	—	2	2	no	—
344	#124	—	2	1	no	—
345	#123	—	2	4	no	—
346	#123	—	2	4	no	—
347	#123	—	2	4	no	—
348	C₂²⋊Q₈	—	2	4	no	—
349	C₂²⋊Q₈	—	2	2	no	—
350	C₂²⋊Q₈	—	2	4	no	—
351	C₂²⋊Q₈	—	2	2	no	—
352	#121	—	2	2	no	—
353	#121	—	2	2	no	—
354	#121	—	2	1	no	—
355	#121	D₄×C₇₉	1	2	yes	—
356	C₄×Q₈	D₄×C₇₉	1	1	yes	characteristic
357	C₄×Q₈	C₂³×C₇₉	1	1	yes	characteristic
358	C₄×D₄	—	2	2	no	—
359	C₄×D₄	—	2	2	no	—
360	C₄×D₄	—	2	1	no	—
361	C₄×D₄	—	2	1	no	—
362	C₄×D₄	—	2	1	no	—
363	C₄×D₄	D₄×C₇₉	1	1	yes	characteristic
364	C₄×D₄	C₂³×C₇₉	1	1	yes	characteristic
365	C₄×D₄	C₂³×C₇₉	1	2	yes	—
366	#117	—	2	1	no	—
367	#117	D₄×C₇₉	1	1	yes	characteristic
368	C₂×C₄⋊C₄	—	2	2	no	—
369	C₂×C₄⋊C₄	—	2	1	no	—
370	C₂×C₄⋊C₄	—	2	2	no	—
371	C₂×C₄⋊C₄	—	2	1	no	—
372	C₂×C₄⋊C₄	—	2	1	no	—
373	C₂×C₄⋊C₄	D₄×C₇₉	1	2	yes	—
374	C₂×C₄²	—	2	1	no	—
375	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
376	#107	—	2	2	no	—
377	#106	—	2	8	no	—
378	#106	—	2	2	no	—
379	C₄⋊C₈	—	2	1	no	—
380	C₄⋊C₈	C₂³×C₇₉	1	2	yes	—
381	C₄⋊C₈	C₂³×C₇₉	1	2	yes	—
382	#103	—	2	2	no	—
383	#103	—	2	4	no	—
384	#102	—	2	2	no	—
385	C₂²⋊C₈	—	2	1	no	—
386	C₄×C₈	—	2	1	no	—
387	C₄×C₈	—	2	1	no	—
388	C₄×C₈	C₂³×C₇₉	1	2	yes	—
389	#41	—	2	2	no	—
390	#41	—	4	8	no	—
391	#41	—	4	16	no	—
392	#41	—	4	4	no	—
393	#41	—	4	4	no	—
394	#41	—	4	2	no	—
395	#41	—	4	2	no	—
396	#41	SD₁₆×C₇₉	1	4	yes	complemented
397	C₂×Q₈	—	2	4	no	—
398	C₂×Q₈	—	2	2	no	—
399	C₂×Q₈	—	2	1	no	—
400	C₂×Q₈	—	2	2	no	—
401	C₂×Q₈	—	2	2	no	—
402	C₂×Q₈	—	4	8	no	—
403	C₂×Q₈	—	4	4	no	—
404	C₂×Q₈	—	4	4	no	—
405	C₂×Q₈	—	4	1	no	—
406	C₂×Q₈	—	4	2	no	—
407	C₂×Q₈	—	4	2	no	—
408	C₂×Q₈	—	8	2	no	—
409	C₂×Q₈	C₂×D₄×C₇₉	1	1	yes	characteristic
410	C₂×D₄	—	2	1	no	—
411	C₂×D₄	—	2	4	no	—
412	C₂×D₄	—	2	2	no	—
413	C₂×D₄	—	2	1	no	—
414	C₂×D₄	—	2	1	no	—
415	C₂×D₄	C₂×D₄×C₇₉	1	2	yes	—
416	C₂×D₄	C₂×D₄×C₇₉	1	1	yes	characteristic
417	C₂²×C₄	—	2	1	no	—
418	C₂²×C₄	—	2	4	no	—
419	C₂²×C₄	—	2	4	no	—
420	C₂²×C₄	—	2	2	no	—
421	C₂²×C₄	—	2	1	no	—
422	C₂²×C₄	—	2	1	no	—
423	C₂²×C₄	—	2	2	no	—
424	C₂²×C₄	—	4	1	no	—
425	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
426	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
427	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
428	SD₁₆	—	8	4	no	—
429	M₁₆	—	4	2	no	—
430	C₂×C₈	—	2	4	no	—
431	C₂×C₈	—	2	2	no	—
432	C₂×C₈	—	2	2	no	—
433	C₂×C₈	—	2	2	no	—
434	C₄⋊C₄	—	2	4	no	—
435	C₄⋊C₄	—	2	4	no	—
436	C₄⋊C₄	—	2	1	no	—
437	C₄⋊C₄	—	2	2	no	—
438	C₄⋊C₄	—	2	2	no	—
439	C₄⋊C₄	—	2	1	no	—
440	C₄⋊C₄	—	2	2	no	—
441	C₄⋊C₄	—	2	1	no	—
442	C₄⋊C₄	—	2	2	no	—
443	C₄⋊C₄	—	2	2	no	—
444	C₄⋊C₄	—	4	1	no	—
445	C₄⋊C₄	—	4	1	no	—
446	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
447	C₄⋊C₄	C₂×D₄×C₇₉	1	4	yes	—
448	C₄⋊C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
449	C₄⋊C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
450	C₂²⋊C₄	—	2	4	no	—
451	C₂²⋊C₄	—	2	4	no	—
452	C₂²⋊C₄	—	2	1	no	—
453	C₂²⋊C₄	—	2	1	no	—
454	C₂²⋊C₄	—	2	2	no	—
455	C₂²⋊C₄	—	2	1	no	—
456	C₂²⋊C₄	—	2	2	no	—
457	C₄²	—	2	1	no	—
458	C₄²	—	2	1	no	—
459	C₄²	—	2	1	no	—
460	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
461	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
462	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
463	C₄²	C₂⁴×C₇₉	1	1	yes	characteristic
464	C₂³	—	2	1	no	—
465	C₂³	—	2	2	no	—
466	C₂³	#120×C₇₉	1	1	yes	characteristic
467	Q₈	—	2	1	no	—
468	Q₈	—	4	8	no	—
469	Q₈	—	4	2	no	—
470	Q₈	—	4	4	no	—
471	Q₈	—	4	2	no	—
472	Q₈	—	4	2	no	—
473	Q₈	—	4	4	no	—
474	Q₈	—	8	2	no	—
475	Q₈	C₂×SD₁₆×C₇₉	1	2	yes	—
476	D₄	—	2	4	no	—
477	D₄	—	2	1	no	—
478	D₄	—	2	4	no	—
479	D₄	—	4	8	no	—
480	D₄	—	4	4	no	—
481	D₄	—	4	2	no	—
482	D₄	—	4	2	no	—
483	D₄	C₂×SD₁₆×C₇₉	1	2	yes	—
484	C₂×C₄	—	2	1	no	—
485	C₂×C₄	—	2	4	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	1	no	—
489	C₂×C₄	—	2	1	no	—
490	C₂×C₄	—	2	4	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	4	8	no	—
493	C₂×C₄	—	4	8	no	—
494	C₂×C₄	—	4	4	no	—
495	C₂×C₄	—	4	2	no	—
496	C₂×C₄	—	4	2	no	—
497	C₂×C₄	—	4	2	no	—
498	C₂×C₄	—	4	2	no	—
499	C₂×C₄	—	4	2	no	—
500	C₂×C₄	—	8	2	no	—
501	C₂×C₄	#120×C₇₉	1	1	yes	characteristic
502	C₂×C₄	#120×C₇₉	1	1	yes	characteristic
503	C₂×C₄	#120×C₇₉	1	1	yes	characteristic
504	C₂×C₄	C₂×SD₁₆×C₇₉	1	2	yes	—
505	C₂×C₄	AGL(1,ℤ/8)×C₇₉	1	2	yes	—
506	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
507	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
508	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
509	C₈	—	2	4	no	—
510	C₈	—	4	2	no	—
511	C₈	—	4	2	no	—
512	C₂²	—	2	1	no	—
513	C₂²	—	2	1	no	—
514	C₂²	—	2	2	no	—
515	C₂²	—	4	1	no	—
516	C₂²	—	4	1	no	—
517	C₂²	—	4	2	no	—
518	C₂²	—	4	2	no	—
519	C₂²	—	4	2	no	—
520	C₂²	#450×C₇₉	1	2	yes	—
521	C₂²	C₂×#120×C₇₉	1	1	yes	characteristic
522	C₄	—	2	2	no	—
523	C₄	—	2	1	no	—
524	C₄	—	2	1	no	—
525	C₄	—	4	4	no	—
526	C₄	—	4	2	no	—
527	C₄	—	4	1	no	—
528	C₄	—	4	1	no	—
529	C₄	—	8	2	no	—
530	C₄	#450×C₇₉	1	2	yes	—
531	C₄	#456×C₇₉	1	2	yes	—
532	C₄	C₂²×SD₁₆×C₇₉	1	1	yes	characteristic
533	C₄	C₂×AGL(1,ℤ/8)×C₇₉	1	1	yes	characteristic
534	C₄	#577×C₇₉	1	2	yes	—
535	C₂	—	2	2	no	—
536	C₂	—	4	2	no	—
537	C₂	—	8	2	no	—
538	C₂	C₂×#450×C₇₉	1	1	yes	characteristic
539	C₂	C₇₉×#3010	1	1	yes	characteristic
540	C₂	C₂×#456×C₇₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₇₉
prime radical	C₇₉×#3499	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₇₉ ◁ C₂×C₄²×C₇₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇₉×#3206	C₂	semidirect
3. C₂×#498×C₇₉	C₂	semidirect
4. C₇₉×#3079	C₂	semidirect
5. C₇₉×#1654	C₂	semidirect
6. C₇₉×#1651	C₂	semidirect
7. C₇₉×#1546	C₂	semidirect
8. C₇₉×#1492	C₂	semidirect
9. C₇₉×#1476	C₂	semidirect
125. #41×C₇₉	SD₁₆	semidirect
264. #18651	C₇₉	direct (N × H)
272. #3206	C₂×C₇₉	semidirect
273. C₂×#498	C₂×C₇₉	semidirect
274. #3079	C₂×C₇₉	semidirect
275. #1654	C₂×C₇₉	semidirect
276. #1651	C₂×C₇₉	semidirect
277. #1546	C₂×C₇₉	semidirect
278. #1492	C₂×C₇₉	semidirect
279. #1476	C₂×C₇₉	semidirect
280. C₇₉	#18651	direct (N × H)
396. #41	SD₁₆×C₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₇₉×#3499	2
C₇₉×#3206	2
C₂×#498×C₇₉	2
C₇₉×#3079	2
C₇₉×#1654	2
C₇₉×#1651	2
C₇₉×#1546	2
C₇₉×#1492	2
C₇₉×#1476	2
#18651	79

Subgroups — C79×#18651 #34130340

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#18651 #34130340