Subgroups — C₇₉×#61892 #34173581

Order 20224.

1770 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₉×#3502	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#559×C₇₉	C₂	1	1	yes	maximal, characteristic
3	C₇₉×#3400	C₂	1	8	yes	maximal, complemented
4	C₇₉×#3375	C₂	1	8	yes	maximal, complemented
5	C₇₉×#3215	C₂	1	4	yes	maximal, complemented
6	C₇₉×#3208	C₂	1	2	yes	maximal
7	C₇₉×#3110	C₂	1	4	yes	maximal, complemented
8	C₇₉×#3104	C₂	1	2	yes	maximal, complemented
9	C₇₉×#2983	C₂	1	1	yes	maximal, characteristic, complemented
10	#559×C₇₉	—	2	4	no	—
11	#559×C₇₉	C₂²	1	8	yes	—
12	Q₈²×C₇₉	C₂²	1	4	yes	complemented
13	#557×C₇₉	—	2	4	no	—
14	#557×C₇₉	C₂²	1	4	yes	complemented
15	#544×C₇₉	—	2	1	no	—
16	#544×C₇₉	—	2	2	no	—
17	#533×C₇₉	C₂²	1	2	yes	—
18	#533×C₇₉	C₂²	1	4	yes	—
19	C₂×#127×C₇₉	C₂²	1	1	yes	characteristic
20	C₂×#124×C₇₉	—	2	1	no	—
21	C₂×#124×C₇₉	C₂²	1	2	yes	—
22	C₂×#123×C₇₉	—	2	2	no	—
23	#519×C₇₉	—	2	1	no	—
24	C₂×C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic
25	C₂×C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic
26	C₂×C₄×D₄×C₇₉	—	2	1	no	—
27	C₂×C₄×D₄×C₇₉	C₂²	1	2	yes	—
28	#497×C₇₉	C₂²	1	8	yes	complemented
29	#492×C₇₉	C₂²	1	4	yes	—
30	#489×C₇₉	C₂²	1	8	yes	complemented
31	#486×C₇₉	C₂²	1	4	yes	—
32	#484×C₇₉	C₂²	1	4	yes	—
33	#477×C₇₉	C₂²	1	4	yes	complemented
34	#474×C₇₉	C₂²	1	8	yes	complemented
35	#464×C₇₉	C₂²	1	16	yes	complemented
36	#462×C₇₉	C₂²	1	4	yes	complemented
37	#461×C₇₉	C₂²	1	8	yes	complemented
38	#460×C₇₉	C₂²	1	8	yes	—
39	#451×C₇₉	C₂²	1	4	yes	—
40	#450×C₇₉	C₂²	1	8	yes	—
41	#446×C₇₉	C₂²	1	8	yes	complemented
42	#440×C₇₉	C₂²	1	16	yes	complemented
43	C₄×Q₁₆×C₇₉	C₂²	1	8	yes	complemented
44	#432×C₇₉	C₂²	1	4	yes	—
45	#431×C₇₉	C₂²	1	2	yes	—
46	C₂²×Q₈×C₇₉	D₄	1	1	yes	characteristic
47	C₂²×Q₈×C₇₉	C₂³	1	1	yes	characteristic
48	C₂²×D₄×C₇₉	—	2	1	no	—
49	C₂²×D₄×C₇₉	—	2	1	no	—
50	C₂²×D₄×C₇₉	C₂³	1	2	yes	—
51	C₂³×C₄×C₇₉	—	2	2	no	—
52	C₂×Q₁₆×C₇₉	C₂³	1	8	yes	—
53	C₂×SD₁₆×C₇₉	C₂³	1	16	yes	—
54	C₄⋊Q₈×C₇₉	—	2	4	no	—
55	C₄⋊Q₈×C₇₉	—	2	8	no	—
56	C₄⋊Q₈×C₇₉	C₂³	1	4	yes	—
57	C₄⋊Q₈×C₇₉	C₂³	1	2	yes	—
58	C₄⋊Q₈×C₇₉	C₂³	1	4	yes	—
59	C₄⋊Q₈×C₇₉	C₂³	1	2	yes	—
60	#127×C₇₉	—	2	2	no	—
61	#127×C₇₉	C₂³	1	4	yes	—
62	#125×C₇₉	—	2	4	no	—
63	#125×C₇₉	—	2	8	no	—
64	#125×C₇₉	—	2	4	no	—
65	#125×C₇₉	—	2	2	no	—
66	#124×C₇₉	—	2	8	no	—
67	#124×C₇₉	—	2	4	no	—
68	#124×C₇₉	C₂³	1	8	yes	—
69	#123×C₇₉	—	2	16	no	—
70	C₂²⋊Q₈×C₇₉	—	2	4	no	—
71	C₂²⋊Q₈×C₇₉	—	2	2	no	—
72	C₂²⋊Q₈×C₇₉	C₂³	1	4	yes	—
73	C₄×Q₈×C₇₉	—	2	4	no	—
74	C₄×Q₈×C₇₉	—	2	4	no	—
75	C₄×Q₈×C₇₉	—	2	2	no	—
76	C₄×Q₈×C₇₉	—	2	4	no	—
77	C₄×Q₈×C₇₉	—	2	2	no	—
78	C₄×Q₈×C₇₉	D₄	1	4	yes	—
79	C₄×Q₈×C₇₉	C₂³	1	4	yes	—
80	C₄×Q₈×C₇₉	C₂³	1	4	yes	—
81	C₄×Q₈×C₇₉	C₂³	1	8	yes	—
82	C₄×Q₈×C₇₉	C₂³	1	4	yes	—
83	C₄×D₄×C₇₉	—	2	8	no	—
84	C₄×D₄×C₇₉	—	2	4	no	—
85	C₄×D₄×C₇₉	C₂³	1	8	yes	—
86	#117×C₇₉	—	2	4	no	—
87	#117×C₇₉	—	2	2	no	—
88	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
89	C₂×C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₇₉	D₄	1	2	yes	—
91	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
92	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
93	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
94	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
95	C₂×C₄²×C₇₉	—	2	1	no	—
96	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
97	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
98	#107×C₇₉	C₂³	1	8	yes	—
99	C₄⋊C₈×C₇₉	C₂³	1	4	yes	—
100	C₄⋊C₈×C₇₉	C₂³	1	8	yes	—
101	#103×C₇₉	C₂³	1	8	yes	—
102	#103×C₇₉	C₂³	1	8	yes	—
103	#102×C₇₉	C₂³	1	16	yes	—
104	C₂²⋊C₈×C₇₉	C₂³	1	4	yes	—
105	#97×C₇₉	C₂³	1	8	yes	—
106	C₄×C₈×C₇₉	C₂³	1	4	yes	—
107	C₂⁴×C₇₉	—	2	2	no	—
108	C₂×Q₈×C₇₉	—	2	4	no	—
109	C₂×Q₈×C₇₉	—	2	1	no	—
110	C₂×Q₈×C₇₉	—	2	4	no	—
111	C₂×Q₈×C₇₉	—	2	2	no	—
112	C₂×Q₈×C₇₉	—	4	2	no	—
113	C₂×Q₈×C₇₉	C₂×D₄	1	4	yes	—
114	C₂×Q₈×C₇₉	C₂⁴	1	2	yes	—
115	C₂×Q₈×C₇₉	C₂⁴	1	4	yes	—
116	C₂×D₄×C₇₉	—	2	2	no	—
117	C₂×D₄×C₇₉	—	2	4	no	—
118	C₂×D₄×C₇₉	—	2	4	no	—
119	C₂×D₄×C₇₉	—	4	4	no	—
120	C₂×D₄×C₇₉	—	4	4	no	—
121	C₂×D₄×C₇₉	—	8	2	no	—
122	C₂×D₄×C₇₉	C₂⁴	1	4	yes	—
123	C₂²×C₄×C₇₉	—	2	1	no	—
124	C₂²×C₄×C₇₉	—	2	1	no	—
125	C₂²×C₄×C₇₉	—	2	8	no	—
126	C₂²×C₄×C₇₉	—	8	4	no	—
127	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
129	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
132	Q₁₆×C₇₉	—	4	8	no	—
133	SD₁₆×C₇₉	—	4	16	no	—
134	C₂×C₈×C₇₉	C₂⁴	1	8	yes	—
135	C₄⋊C₄×C₇₉	—	2	4	no	—
136	C₄⋊C₄×C₇₉	—	2	1	no	—
137	C₄⋊C₄×C₇₉	—	2	4	no	—
138	C₄⋊C₄×C₇₉	—	2	2	no	—
139	C₄⋊C₄×C₇₉	—	2	4	no	—
140	C₄⋊C₄×C₇₉	—	2	2	no	—
141	C₄⋊C₄×C₇₉	—	2	4	no	—
142	C₄⋊C₄×C₇₉	—	2	4	no	—
143	C₄⋊C₄×C₇₉	—	2	2	no	—
144	C₄⋊C₄×C₇₉	—	2	8	no	—
145	C₄⋊C₄×C₇₉	—	2	4	no	—
146	C₄⋊C₄×C₇₉	C₂×D₄	1	4	yes	—
147	C₄⋊C₄×C₇₉	C₂×D₄	1	8	yes	—
148	C₄⋊C₄×C₇₉	C₂⁴	1	4	yes	—
149	C₄⋊C₄×C₇₉	C₂⁴	1	2	yes	—
150	C₂²⋊C₄×C₇₉	—	2	4	no	—
151	C₂²⋊C₄×C₇₉	—	2	8	no	—
152	C₂²⋊C₄×C₇₉	—	2	8	no	—
153	C₂²⋊C₄×C₇₉	—	2	8	no	—
154	C₄²×C₇₉	—	2	4	no	—
155	C₄²×C₇₉	—	2	8	no	—
156	C₄²×C₇₉	—	2	4	no	—
157	C₄²×C₇₉	C₂×D₄	1	4	yes	—
158	C₄²×C₇₉	C₂×D₄	1	2	yes	—
159	C₄²×C₇₉	C₂⁴	1	2	yes	—
160	C₄²×C₇₉	C₂⁴	1	4	yes	—
161	C₂³×C₇₉	—	2	4	no	—
162	C₂³×C₇₉	—	4	4	no	—
163	C₂³×C₇₉	—	4	4	no	—
164	C₂³×C₇₉	—	4	4	no	—
165	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
166	Q₈×C₇₉	—	2	8	no	—
167	Q₈×C₇₉	—	2	8	no	—
168	Q₈×C₇₉	—	2	4	no	—
169	Q₈×C₇₉	—	4	2	no	—
170	Q₈×C₇₉	—	8	4	no	—
171	Q₈×C₇₉	—	8	2	no	—
172	D₄×C₇₉	—	2	8	no	—
173	D₄×C₇₉	—	4	4	no	—
174	D₄×C₇₉	—	4	8	no	—
175	D₄×C₇₉	—	8	4	no	—
176	C₂×C₄×C₇₉	—	2	4	no	—
177	C₂×C₄×C₇₉	—	2	2	no	—
178	C₂×C₄×C₇₉	—	2	4	no	—
179	C₂×C₄×C₇₉	—	2	4	no	—
180	C₂×C₄×C₇₉	—	2	2	no	—
181	C₂×C₄×C₇₉	—	2	2	no	—
182	C₂×C₄×C₇₉	—	4	2	no	—
183	C₂×C₄×C₇₉	—	4	1	no	—
184	C₂×C₄×C₇₉	—	4	2	no	—
185	C₂×C₄×C₇₉	—	4	2	no	—
186	C₂×C₄×C₇₉	—	8	8	no	—
187	C₂×C₄×C₇₉	#137	1	4	yes	—
188	C₂×C₄×C₇₉	C₂²×D₄	1	4	yes	—
189	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
190	C₂×C₄×C₇₉	C₂²×D₄	1	4	yes	—
191	C₂×C₄×C₇₉	C₂²×D₄	1	2	yes	—
192	C₂×C₄×C₇₉	C₂²×D₄	1	2	yes	—
193	C₂×C₄×C₇₉	C₂⁵	1	1	yes	characteristic
194	C₈×C₇₉	—	2	8	no	—
195	C₂²×C₇₉	—	2	1	no	—
196	C₂²×C₇₉	—	2	1	no	—
197	C₂²×C₇₉	—	4	4	no	—
198	C₂²×C₇₉	—	4	4	no	—
199	C₂²×C₇₉	—	4	4	no	—
200	C₂²×C₇₉	—	8	8	no	—
201	C₂²×C₇₉	C₂×#137	1	2	yes	—
202	C₂²×C₇₉	C₂³×D₄	1	1	yes	characteristic
203	C₄×C₇₉	—	2	4	no	—
204	C₄×C₇₉	—	2	2	no	—
205	C₄×C₇₉	—	2	1	no	—
206	C₄×C₇₉	—	2	4	no	—
207	C₄×C₇₉	—	4	2	no	—
208	C₄×C₇₉	—	4	4	no	—
209	C₄×C₇₉	—	4	2	no	—
210	C₄×C₇₉	—	4	4	no	—
211	C₄×C₇₉	C₂×#137	1	4	yes	—
212	C₄×C₇₉	#585	1	2	yes	—
213	#61892	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
214	C₂×C₇₉	—	2	2	no	—
215	C₂×C₇₉	—	8	4	no	—
216	C₂×C₇₉	#3487	1	1	yes	characteristic
217	C₂×C₇₉	C₂²×#137	1	1	yes	characteristic
218	C₂×C₇₉	#3585	1	1	yes	characteristic
219	#3502	C₂×C₇₉	1	1	yes	characteristic, complemented
220	C₂×#559	C₂×C₇₉	1	1	yes	characteristic
221	#3400	C₂×C₇₉	1	8	yes	complemented
222	#3375	C₂×C₇₉	1	8	yes	complemented
223	#3215	C₂×C₇₉	1	4	yes	complemented
224	#3208	C₂×C₇₉	1	2	yes	—
225	#3110	C₂×C₇₉	1	4	yes	complemented
226	#3104	C₂×C₇₉	1	2	yes	complemented
227	#2983	C₂×C₇₉	1	1	yes	characteristic, complemented
228	C₇₉	#61892	1	1	yes	characteristic, direct product factor, Sylow
229	#559	—	2	4	no	—
230	#559	C₂²×C₇₉	1	8	yes	—
231	Q₈²	C₂²×C₇₉	1	4	yes	complemented
232	#557	—	2	4	no	—
233	#557	C₂²×C₇₉	1	4	yes	complemented
234	#544	—	2	1	no	—
235	#544	—	2	2	no	—
236	#533	C₂²×C₇₉	1	2	yes	—
237	#533	C₂²×C₇₉	1	4	yes	—
238	C₂×#127	C₂²×C₇₉	1	1	yes	characteristic
239	C₂×#124	—	2	1	no	—
240	C₂×#124	C₂²×C₇₉	1	2	yes	—
241	C₂×#123	—	2	2	no	—
242	#519	—	2	1	no	—
243	C₂×C₄×Q₈	C₂²×C₇₉	1	1	yes	characteristic
244	C₂×C₄×Q₈	C₂²×C₇₉	1	1	yes	characteristic
245	C₂×C₄×D₄	—	2	1	no	—
246	C₂×C₄×D₄	C₂²×C₇₉	1	2	yes	—
247	#497	C₂²×C₇₉	1	8	yes	complemented
248	#492	C₂²×C₇₉	1	4	yes	—
249	#489	C₂²×C₇₉	1	8	yes	complemented
250	#486	C₂²×C₇₉	1	4	yes	—
251	#484	C₂²×C₇₉	1	4	yes	—
252	#477	C₂²×C₇₉	1	4	yes	complemented
253	#474	C₂²×C₇₉	1	8	yes	complemented
254	#464	C₂²×C₇₉	1	16	yes	complemented
255	#462	C₂²×C₇₉	1	4	yes	complemented
256	#461	C₂²×C₇₉	1	8	yes	complemented
257	#460	C₂²×C₇₉	1	8	yes	—
258	#451	C₂²×C₇₉	1	4	yes	—
259	#450	C₂²×C₇₉	1	8	yes	—
260	#446	C₂²×C₇₉	1	8	yes	complemented
261	#440	C₂²×C₇₉	1	16	yes	complemented
262	C₄×Q₁₆	C₂²×C₇₉	1	8	yes	complemented
263	#432	C₂²×C₇₉	1	4	yes	—
264	#431	C₂²×C₇₉	1	2	yes	—
265	C₂²×Q₈	D₄×C₇₉	1	1	yes	characteristic
266	C₂²×Q₈	C₂³×C₇₉	1	1	yes	characteristic
267	C₂²×D₄	—	2	1	no	—
268	C₂²×D₄	—	2	1	no	—
269	C₂²×D₄	C₂³×C₇₉	1	2	yes	—
270	C₂³×C₄	—	2	2	no	—
271	C₂×Q₁₆	C₂³×C₇₉	1	8	yes	—
272	C₂×SD₁₆	C₂³×C₇₉	1	16	yes	—
273	C₄⋊Q₈	—	2	4	no	—
274	C₄⋊Q₈	—	2	8	no	—
275	C₄⋊Q₈	C₂³×C₇₉	1	4	yes	—
276	C₄⋊Q₈	C₂³×C₇₉	1	2	yes	—
277	C₄⋊Q₈	C₂³×C₇₉	1	4	yes	—
278	C₄⋊Q₈	C₂³×C₇₉	1	2	yes	—
279	#127	—	2	2	no	—
280	#127	C₂³×C₇₉	1	4	yes	—
281	#125	—	2	4	no	—
282	#125	—	2	8	no	—
283	#125	—	2	4	no	—
284	#125	—	2	2	no	—
285	#124	—	2	8	no	—
286	#124	—	2	4	no	—
287	#124	C₂³×C₇₉	1	8	yes	—
288	#123	—	2	16	no	—
289	C₂²⋊Q₈	—	2	4	no	—
290	C₂²⋊Q₈	—	2	2	no	—
291	C₂²⋊Q₈	C₂³×C₇₉	1	4	yes	—
292	C₄×Q₈	—	2	4	no	—
293	C₄×Q₈	—	2	4	no	—
294	C₄×Q₈	—	2	2	no	—
295	C₄×Q₈	—	2	4	no	—
296	C₄×Q₈	—	2	2	no	—
297	C₄×Q₈	D₄×C₇₉	1	4	yes	—
298	C₄×Q₈	C₂³×C₇₉	1	4	yes	—
299	C₄×Q₈	C₂³×C₇₉	1	4	yes	—
300	C₄×Q₈	C₂³×C₇₉	1	8	yes	—
301	C₄×Q₈	C₂³×C₇₉	1	4	yes	—
302	C₄×D₄	—	2	8	no	—
303	C₄×D₄	—	2	4	no	—
304	C₄×D₄	C₂³×C₇₉	1	8	yes	—
305	#117	—	2	4	no	—
306	#117	—	2	2	no	—
307	C₂×C₄⋊C₄	—	2	1	no	—
308	C₂×C₄⋊C₄	D₄×C₇₉	1	1	yes	characteristic
309	C₂×C₄⋊C₄	D₄×C₇₉	1	2	yes	—
310	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
311	C₂×C₂²⋊C₄	—	2	2	no	—
312	C₂×C₂²⋊C₄	—	2	2	no	—
313	C₂×C₂²⋊C₄	—	2	2	no	—
314	C₂×C₄²	—	2	1	no	—
315	C₂×C₄²	C₂³×C₇₉	1	2	yes	—
316	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
317	#107	C₂³×C₇₉	1	8	yes	—
318	C₄⋊C₈	C₂³×C₇₉	1	4	yes	—
319	C₄⋊C₈	C₂³×C₇₉	1	8	yes	—
320	#103	C₂³×C₇₉	1	8	yes	—
321	#103	C₂³×C₇₉	1	8	yes	—
322	#102	C₂³×C₇₉	1	16	yes	—
323	C₂²⋊C₈	C₂³×C₇₉	1	4	yes	—
324	#97	C₂³×C₇₉	1	8	yes	—
325	C₄×C₈	C₂³×C₇₉	1	4	yes	—
326	C₂⁴	—	2	2	no	—
327	C₂×Q₈	—	2	4	no	—
328	C₂×Q₈	—	2	1	no	—
329	C₂×Q₈	—	2	4	no	—
330	C₂×Q₈	—	2	2	no	—
331	C₂×Q₈	—	4	2	no	—
332	C₂×Q₈	C₂×D₄×C₇₉	1	4	yes	—
333	C₂×Q₈	C₂⁴×C₇₉	1	2	yes	—
334	C₂×Q₈	C₂⁴×C₇₉	1	4	yes	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	—	2	4	no	—
337	C₂×D₄	—	2	4	no	—
338	C₂×D₄	—	4	4	no	—
339	C₂×D₄	—	4	4	no	—
340	C₂×D₄	—	8	2	no	—
341	C₂×D₄	C₂⁴×C₇₉	1	4	yes	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	8	no	—
345	C₂²×C₄	—	8	4	no	—
346	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
347	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
348	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
349	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
350	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
351	Q₁₆	—	4	8	no	—
352	SD₁₆	—	4	16	no	—
353	C₂×C₈	C₂⁴×C₇₉	1	8	yes	—
354	C₄⋊C₄	—	2	4	no	—
355	C₄⋊C₄	—	2	1	no	—
356	C₄⋊C₄	—	2	4	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	2	4	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	2	4	no	—
361	C₄⋊C₄	—	2	4	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	8	no	—
364	C₄⋊C₄	—	2	4	no	—
365	C₄⋊C₄	C₂×D₄×C₇₉	1	4	yes	—
366	C₄⋊C₄	C₂×D₄×C₇₉	1	8	yes	—
367	C₄⋊C₄	C₂⁴×C₇₉	1	4	yes	—
368	C₄⋊C₄	C₂⁴×C₇₉	1	2	yes	—
369	C₂²⋊C₄	—	2	4	no	—
370	C₂²⋊C₄	—	2	8	no	—
371	C₂²⋊C₄	—	2	8	no	—
372	C₂²⋊C₄	—	2	8	no	—
373	C₄²	—	2	4	no	—
374	C₄²	—	2	8	no	—
375	C₄²	—	2	4	no	—
376	C₄²	C₂×D₄×C₇₉	1	4	yes	—
377	C₄²	C₂×D₄×C₇₉	1	2	yes	—
378	C₄²	C₂⁴×C₇₉	1	2	yes	—
379	C₄²	C₂⁴×C₇₉	1	4	yes	—
380	C₂³	—	2	4	no	—
381	C₂³	—	4	4	no	—
382	C₂³	—	4	4	no	—
383	C₂³	—	4	4	no	—
384	C₂³	C₂²×D₄×C₇₉	1	1	yes	characteristic
385	Q₈	—	2	8	no	—
386	Q₈	—	2	8	no	—
387	Q₈	—	2	4	no	—
388	Q₈	—	4	2	no	—
389	Q₈	—	8	4	no	—
390	Q₈	—	8	2	no	—
391	D₄	—	2	8	no	—
392	D₄	—	4	4	no	—
393	D₄	—	4	8	no	—
394	D₄	—	8	4	no	—
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	4	no	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	8	8	no	—
406	C₂×C₄	#137×C₇₉	1	4	yes	—
407	C₂×C₄	C₂²×D₄×C₇₉	1	4	yes	—
408	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
409	C₂×C₄	C₂²×D₄×C₇₉	1	4	yes	—
410	C₂×C₄	C₂²×D₄×C₇₉	1	2	yes	—
411	C₂×C₄	C₂²×D₄×C₇₉	1	2	yes	—
412	C₂×C₄	C₂⁵×C₇₉	1	1	yes	characteristic
413	C₈	—	2	8	no	—
414	C₂²	—	2	1	no	—
415	C₂²	—	2	1	no	—
416	C₂²	—	4	4	no	—
417	C₂²	—	4	4	no	—
418	C₂²	—	4	4	no	—
419	C₂²	—	8	8	no	—
420	C₂²	C₂×#137×C₇₉	1	2	yes	—
421	C₂²	C₂³×D₄×C₇₉	1	1	yes	characteristic
422	C₄	—	2	4	no	—
423	C₄	—	2	4	no	—
424	C₄	—	2	2	no	—
425	C₄	—	2	1	no	—
426	C₄	—	4	2	no	—
427	C₄	—	4	4	no	—
428	C₄	—	4	2	no	—
429	C₄	—	4	4	no	—
430	C₄	C₂×#137×C₇₉	1	4	yes	—
431	C₄	#585×C₇₉	1	2	yes	—
432	C₂	—	2	2	no	—
433	C₂	—	8	4	no	—
434	C₂	C₇₉×#3487	1	1	yes	characteristic
435	C₂	C₂²×#137×C₇₉	1	1	yes	characteristic
436	C₂	C₇₉×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇₉
prime radical	C₂×#127×C₇₉	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇₉ ◁ C₂×C₄×Q₈×C₇₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇₉×#3502	C₂	semidirect
3. C₇₉×#3400	C₂	semidirect
4. C₇₉×#3375	C₂	semidirect
5. C₇₉×#3215	C₂	semidirect
7. C₇₉×#3110	C₂	semidirect
8. C₇₉×#3104	C₂	semidirect
9. C₇₉×#2983	C₂	semidirect
12. Q₈²×C₇₉	C₂²	semidirect
14. #557×C₇₉	C₂²	semidirect
28. #497×C₇₉	C₂²	semidirect
30. #489×C₇₉	C₂²	semidirect
33. #477×C₇₉	C₂²	semidirect
34. #474×C₇₉	C₂²	semidirect
35. #464×C₇₉	C₂²	semidirect
36. #462×C₇₉	C₂²	semidirect
37. #461×C₇₉	C₂²	semidirect
41. #446×C₇₉	C₂²	semidirect
42. #440×C₇₉	C₂²	semidirect
43. C₄×Q₁₆×C₇₉	C₂²	semidirect
213. #61892	C₇₉	direct (N × H)
219. #3502	C₂×C₇₉	semidirect
221. #3400	C₂×C₇₉	semidirect
222. #3375	C₂×C₇₉	semidirect
223. #3215	C₂×C₇₉	semidirect
225. #3110	C₂×C₇₉	semidirect
226. #3104	C₂×C₇₉	semidirect
227. #2983	C₂×C₇₉	semidirect
228. C₇₉	#61892	direct (N × H)
231. Q₈²	C₂²×C₇₉	semidirect
233. #557	C₂²×C₇₉	semidirect
247. #497	C₂²×C₇₉	semidirect
249. #489	C₂²×C₇₉	semidirect
252. #477	C₂²×C₇₉	semidirect
253. #474	C₂²×C₇₉	semidirect
254. #464	C₂²×C₇₉	semidirect
255. #462	C₂²×C₇₉	semidirect
256. #461	C₂²×C₇₉	semidirect
260. #446	C₂²×C₇₉	semidirect
261. #440	C₂²×C₇₉	semidirect
262. C₄×Q₁₆	C₂²×C₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₇₉×#3502	2
C₂×#559×C₇₉	2
C₇₉×#3400	2
C₇₉×#3375	2
C₇₉×#3215	2
C₇₉×#3208	2
C₇₉×#3110	2
C₇₉×#3104	2
C₇₉×#2983	2
#61892	79

Subgroups — C79×#61892 #34173581

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#61892 #34173581