Subgroups — C₇₉×#25490 #34137179

Order 20224.

664 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₉×#3165	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₉×#3077	C₂	1	1	yes	maximal, characteristic
3	C₂×#476×C₇₉	C₂	1	1	yes	maximal, characteristic
4	C₇₉×#2962	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₉×#2090	C₂	1	2	yes	maximal, complemented
6	C₇₉×#2063	C₂	1	2	yes	maximal
7	C₇₉×#1997	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₉×#1951	C₂	1	2	yes	maximal, complemented
9	C₇₉×#1950	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₉×#1931	C₂	1	2	yes	maximal
11	C₄×#100×C₇₉	C₂	1	1	yes	maximal, characteristic
12	#533×C₇₉	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
15	#501×C₇₉	—	2	2	no	—
16	#500×C₇₉	—	2	1	no	—
17	#498×C₇₉	—	2	1	no	—
18	#478×C₇₉	—	2	2	no	—
19	#476×C₇₉	—	2	1	no	—
20	#476×C₇₉	—	2	1	no	—
21	#476×C₇₉	—	2	2	no	—
22	#476×C₇₉	—	2	1	no	—
23	#474×C₇₉	—	2	1	no	—
24	#446×C₇₉	—	2	2	no	—
25	#446×C₇₉	—	2	1	no	—
26	C₈×Q₈×C₇₉	—	2	1	no	—
27	C₂×#108×C₇₉	C₂²	1	2	yes	—
28	#428×C₇₉	C₂²	1	2	yes	—
29	#428×C₇₉	C₂²	1	2	yes	—
30	#428×C₇₉	C₂²	1	2	yes	—
31	C₂×#106×C₇₉	C₂²	1	2	yes	—
32	#424×C₇₉	C₂²	1	2	yes	—
33	#423×C₇₉	C₂²	1	1	yes	characteristic
34	C₂×C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
35	#418×C₇₉	C₂²	1	2	yes	—
36	C₂×#102×C₇₉	C₂²	1	2	yes	—
37	C₂×#100×C₇₉	C₂²	1	1	yes	characteristic
38	C₂×#100×C₇₉	C₂²	1	1	yes	characteristic
39	#405×C₇₉	C₂²	1	2	yes	—
40	C₄×M₁₆×C₇₉	C₂²	1	1	yes	characteristic
41	C₄×M₁₆×C₇₉	C₂²	1	1	yes	characteristic
42	#343×C₇₉	C₂²	1	2	yes	—
43	#343×C₇₉	C₂²	1	2	yes	—
44	#343×C₇₉	C₂²	1	1	yes	characteristic
45	#343×C₇₉	C₂²	1	1	yes	characteristic
46	#341×C₇₉	C₂²	1	2	yes	—
47	C₂²×Q₈×C₇₉	—	2	1	no	—
48	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
49	C₂³×C₄×C₇₉	—	2	1	no	—
50	C₂×M₁₆×C₇₉	C₂³	1	2	yes	—
51	C₂×M₁₆×C₇₉	C₂³	1	1	yes	characteristic
52	C₂×M₁₆×C₇₉	C₂³	1	1	yes	characteristic
53	C₂×M₁₆×C₇₉	C₂³	1	1	yes	characteristic
54	C₂×M₁₆×C₇₉	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₇₉	C₂³	1	2	yes	—
56	C₄⋊Q₈×C₇₉	—	2	1	no	—
57	C₄⋊Q₈×C₇₉	—	2	1	no	—
58	C₄⋊Q₈×C₇₉	—	2	1	no	—
59	C₄⋊Q₈×C₇₉	—	2	1	no	—
60	C₄⋊Q₈×C₇₉	D₄	1	1	yes	characteristic
61	C₄⋊Q₈×C₇₉	D₄	1	1	yes	characteristic
62	#125×C₇₉	D₄	1	2	yes	—
63	C₂²⋊Q₈×C₇₉	—	2	1	no	—
64	C₂²⋊Q₈×C₇₉	—	2	1	no	—
65	C₄×Q₈×C₇₉	—	2	1	no	—
66	C₄×Q₈×C₇₉	—	2	1	no	—
67	C₄×D₄×C₇₉	—	2	1	no	—
68	C₄×D₄×C₇₉	—	2	1	no	—
69	C₄×D₄×C₇₉	—	2	1	no	—
70	C₄×D₄×C₇₉	—	2	1	no	—
71	#117×C₇₉	C₂³	1	2	yes	—
72	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
73	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
74	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
75	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
76	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
77	#108×C₇₉	—	2	4	no	—
78	#107×C₇₉	—	2	2	no	—
79	#107×C₇₉	—	2	2	no	—
80	#107×C₇₉	—	2	2	no	—
81	#106×C₇₉	—	2	2	no	—
82	#106×C₇₉	—	2	2	no	—
83	#106×C₇₉	—	2	2	no	—
84	#106×C₇₉	—	2	2	no	—
85	#106×C₇₉	—	2	2	no	—
86	C₄⋊C₈×C₇₉	—	2	2	no	—
87	C₄⋊C₈×C₇₉	—	2	2	no	—
88	C₄⋊C₈×C₇₉	—	2	1	no	—
89	C₄⋊C₈×C₇₉	—	2	1	no	—
90	C₄⋊C₈×C₇₉	D₄	1	1	yes	characteristic
91	C₄⋊C₈×C₇₉	D₄	1	1	yes	characteristic
92	C₄⋊C₈×C₇₉	D₄	1	2	yes	—
93	#102×C₇₉	—	2	2	no	—
94	#102×C₇₉	—	2	2	no	—
95	#102×C₇₉	—	2	2	no	—
96	#102×C₇₉	—	2	2	no	—
97	#100×C₇₉	—	2	2	no	—
98	#100×C₇₉	Q₈	1	4	yes	complemented
99	#97×C₇₉	—	2	2	no	—
100	#97×C₇₉	—	2	1	no	—
101	#97×C₇₉	—	2	1	no	—
102	C₄×C₈×C₇₉	—	2	2	no	—
103	C₄×C₈×C₇₉	—	2	1	no	—
104	C₄×C₈×C₇₉	—	2	1	no	—
105	C₂⁴×C₇₉	—	2	1	no	—
106	C₂×Q₈×C₇₉	—	2	1	no	—
107	C₂×Q₈×C₇₉	—	2	1	no	—
108	C₂×Q₈×C₇₉	—	4	1	no	—
109	C₂×Q₈×C₇₉	—	4	1	no	—
110	C₂×Q₈×C₇₉	—	8	2	no	—
111	C₂×D₄×C₇₉	—	2	1	no	—
112	C₂×D₄×C₇₉	—	2	1	no	—
113	C₂×D₄×C₇₉	—	2	1	no	—
114	C₂×D₄×C₇₉	—	2	1	no	—
115	C₂×D₄×C₇₉	—	2	1	no	—
116	C₂×D₄×C₇₉	C₂×Q₈	1	2	yes	—
117	C₂²×C₄×C₇₉	—	2	1	no	—
118	C₂²×C₄×C₇₉	—	2	2	no	—
119	C₂²×C₄×C₇₉	—	4	1	no	—
120	C₂²×C₄×C₇₉	—	4	1	no	—
121	C₂²×C₄×C₇₉	—	8	2	no	—
122	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
123	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
124	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
125	M₁₆×C₇₉	—	2	1	no	—
126	M₁₆×C₇₉	—	2	2	no	—
127	M₁₆×C₇₉	—	2	1	no	—
128	M₁₆×C₇₉	—	2	1	no	—
129	M₁₆×C₇₉	—	2	1	no	—
130	M₁₆×C₇₉	—	2	1	no	—
131	M₁₆×C₇₉	—	2	2	no	—
132	M₁₆×C₇₉	C₂×Q₈	1	2	yes	—
133	M₁₆×C₇₉	C₂×Q₈	1	2	yes	—
134	M₁₆×C₇₉	#41	1	2	yes	—
135	C₂×C₈×C₇₉	—	2	1	no	—
136	C₂×C₈×C₇₉	—	2	1	no	—
137	C₂×C₈×C₇₉	—	2	1	no	—
138	C₂×C₈×C₇₉	—	2	1	no	—
139	C₂×C₈×C₇₉	—	2	2	no	—
140	C₂×C₈×C₇₉	—	2	2	no	—
141	C₂×C₈×C₇₉	—	2	2	no	—
142	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
143	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
144	C₄⋊C₄×C₇₉	—	2	2	no	—
145	C₄⋊C₄×C₇₉	—	2	2	no	—
146	C₄⋊C₄×C₇₉	—	2	1	no	—
147	C₄⋊C₄×C₇₉	—	2	1	no	—
148	C₄⋊C₄×C₇₉	—	2	2	no	—
149	C₄⋊C₄×C₇₉	—	2	1	no	—
150	C₄⋊C₄×C₇₉	—	2	1	no	—
151	C₄⋊C₄×C₇₉	—	2	2	no	—
152	C₄⋊C₄×C₇₉	—	4	1	no	—
153	C₄⋊C₄×C₇₉	—	4	1	no	—
154	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
155	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
156	C₂²⋊C₄×C₇₉	—	2	2	no	—
157	C₂²⋊C₄×C₇₉	—	4	1	no	—
158	C₂²⋊C₄×C₇₉	—	4	1	no	—
159	C₄²×C₇₉	—	2	2	no	—
160	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
161	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
162	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
163	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
164	C₂³×C₇₉	—	2	2	no	—
165	C₂³×C₇₉	—	4	1	no	—
166	C₂³×C₇₉	—	4	1	no	—
167	C₂³×C₇₉	—	8	1	no	—
168	C₂³×C₇₉	—	8	1	no	—
169	C₂³×C₇₉	C₂×#41	1	1	yes	characteristic
170	Q₈×C₇₉	—	4	2	no	—
171	Q₈×C₇₉	—	8	1	no	—
172	Q₈×C₇₉	—	8	2	no	—
173	Q₈×C₇₉	—	8	2	no	—
174	D₄×C₇₉	—	2	2	no	—
175	D₄×C₇₉	—	2	2	no	—
176	D₄×C₇₉	—	4	1	no	—
177	D₄×C₇₉	—	4	1	no	—
178	C₂×C₄×C₇₉	—	2	2	no	—
179	C₂×C₄×C₇₉	—	2	2	no	—
180	C₂×C₄×C₇₉	—	2	2	no	—
181	C₂×C₄×C₇₉	—	4	1	no	—
182	C₂×C₄×C₇₉	—	4	1	no	—
183	C₂×C₄×C₇₉	—	4	2	no	—
184	C₂×C₄×C₇₉	—	8	2	no	—
185	C₂×C₄×C₇₉	—	8	2	no	—
186	C₂×C₄×C₇₉	—	8	1	no	—
187	C₂×C₄×C₇₉	—	8	2	no	—
188	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
189	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
190	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
191	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
192	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
193	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
194	C₂×C₄×C₇₉	C₂²×Q₈	1	1	yes	characteristic
195	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
196	C₂×C₄×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
197	C₂×C₄×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
198	C₈×C₇₉	—	2	2	no	—
199	C₈×C₇₉	—	2	2	no	—
200	C₈×C₇₉	—	2	2	no	—
201	C₈×C₇₉	—	2	2	no	—
202	C₈×C₇₉	—	2	2	no	—
203	C₈×C₇₉	—	4	1	no	—
204	C₈×C₇₉	—	4	2	no	—
205	C₂²×C₇₉	—	2	1	no	—
206	C₂²×C₇₉	—	2	1	no	—
207	C₂²×C₇₉	—	4	2	no	—
208	C₂²×C₇₉	—	8	2	no	—
209	C₂²×C₇₉	—	8	2	no	—
210	C₂²×C₇₉	—	8	1	no	—
211	C₂²×C₇₉	—	8	1	no	—
212	C₂²×C₇₉	C₂×#121	1	1	yes	characteristic
213	C₂²×C₇₉	#533	1	1	yes	characteristic
214	C₂²×C₇₉	#541	1	1	yes	characteristic
215	C₄×C₇₉	—	2	1	no	—
216	C₄×C₇₉	—	2	1	no	—
217	C₄×C₇₉	—	2	1	no	—
218	C₄×C₇₉	—	4	2	no	—
219	C₄×C₇₉	—	4	2	no	—
220	C₄×C₇₉	—	8	1	no	—
221	C₄×C₇₉	—	8	2	no	—
222	C₄×C₇₉	#471	1	2	yes	—
223	C₄×C₇₉	#547	1	1	yes	characteristic
224	C₄×C₇₉	#548	1	1	yes	characteristic
225	C₄×C₇₉	D₄×Q₈	1	1	yes	characteristic
226	C₄×C₇₉	D₄×Q₈	1	1	yes	characteristic
227	#25490	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
228	C₂×C₇₉	—	2	1	no	—
229	C₂×C₇₉	—	2	1	no	—
230	C₂×C₇₉	—	8	2	no	—
231	C₂×C₇₉	#2429	1	1	yes	characteristic
232	C₂×C₇₉	C₂×#471	1	1	yes	characteristic
233	C₂×C₇₉	#3068	1	1	yes	characteristic
234	#3165	C₂×C₇₉	1	1	yes	characteristic, complemented
235	#3077	C₂×C₇₉	1	1	yes	characteristic
236	C₂×#476	C₂×C₇₉	1	1	yes	characteristic
237	#2962	C₂×C₇₉	1	1	yes	characteristic, complemented
238	#2090	C₂×C₇₉	1	2	yes	complemented
239	#2063	C₂×C₇₉	1	2	yes	—
240	#1997	C₂×C₇₉	1	1	yes	characteristic, complemented
241	#1951	C₂×C₇₉	1	2	yes	complemented
242	#1950	C₂×C₇₉	1	1	yes	characteristic, complemented
243	#1931	C₂×C₇₉	1	2	yes	—
244	C₄×#100	C₂×C₇₉	1	1	yes	characteristic
245	C₇₉	#25490	1	1	yes	characteristic, direct product factor, Sylow
246	#533	C₂²×C₇₉	1	1	yes	characteristic
247	C₂×C₄⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic
248	C₂×C₄×D₄	C₂²×C₇₉	1	1	yes	characteristic
249	#501	—	2	2	no	—
250	#500	—	2	1	no	—
251	#498	—	2	1	no	—
252	#478	—	2	2	no	—
253	#476	—	2	1	no	—
254	#476	—	2	1	no	—
255	#476	—	2	2	no	—
256	#476	—	2	1	no	—
257	#474	—	2	1	no	—
258	#446	—	2	2	no	—
259	#446	—	2	1	no	—
260	C₈×Q₈	—	2	1	no	—
261	C₂×#108	C₂²×C₇₉	1	2	yes	—
262	#428	C₂²×C₇₉	1	2	yes	—
263	#428	C₂²×C₇₉	1	2	yes	—
264	#428	C₂²×C₇₉	1	2	yes	—
265	C₂×#106	C₂²×C₇₉	1	2	yes	—
266	#424	C₂²×C₇₉	1	2	yes	—
267	#423	C₂²×C₇₉	1	1	yes	characteristic
268	C₂×C₄⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
269	#418	C₂²×C₇₉	1	2	yes	—
270	C₂×#102	C₂²×C₇₉	1	2	yes	—
271	C₂×#100	C₂²×C₇₉	1	1	yes	characteristic
272	C₂×#100	C₂²×C₇₉	1	1	yes	characteristic
273	#405	C₂²×C₇₉	1	2	yes	—
274	C₄×M₁₆	C₂²×C₇₉	1	1	yes	characteristic
275	C₄×M₁₆	C₂²×C₇₉	1	1	yes	characteristic
276	#343	C₂²×C₇₉	1	2	yes	—
277	#343	C₂²×C₇₉	1	1	yes	characteristic
278	#343	C₂²×C₇₉	1	2	yes	—
279	#343	C₂²×C₇₉	1	1	yes	characteristic
280	#341	C₂²×C₇₉	1	2	yes	—
281	C₂²×Q₈	—	2	1	no	—
282	C₂²×D₄	C₂³×C₇₉	1	1	yes	characteristic
283	C₂³×C₄	—	2	1	no	—
284	C₂×M₁₆	C₂³×C₇₉	1	2	yes	—
285	C₂×M₁₆	C₂³×C₇₉	1	1	yes	characteristic
286	C₂×M₁₆	C₂³×C₇₉	1	1	yes	characteristic
287	C₂×M₁₆	C₂³×C₇₉	1	1	yes	characteristic
288	C₂×M₁₆	C₂³×C₇₉	1	1	yes	characteristic
289	C₂²×C₈	C₂³×C₇₉	1	2	yes	—
290	C₄⋊Q₈	—	2	1	no	—
291	C₄⋊Q₈	—	2	1	no	—
292	C₄⋊Q₈	—	2	1	no	—
293	C₄⋊Q₈	—	2	1	no	—
294	C₄⋊Q₈	D₄×C₇₉	1	1	yes	characteristic
295	C₄⋊Q₈	D₄×C₇₉	1	1	yes	characteristic
296	#125	D₄×C₇₉	1	2	yes	—
297	C₂²⋊Q₈	—	2	1	no	—
298	C₂²⋊Q₈	—	2	1	no	—
299	C₄×Q₈	—	2	1	no	—
300	C₄×Q₈	—	2	1	no	—
301	C₄×D₄	—	2	1	no	—
302	C₄×D₄	—	2	1	no	—
303	C₄×D₄	—	2	1	no	—
304	C₄×D₄	—	2	1	no	—
305	#117	C₂³×C₇₉	1	2	yes	—
306	C₂×C₄⋊C₄	—	2	1	no	—
307	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
308	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
309	C₂×C₂²⋊C₄	—	2	1	no	—
310	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
311	#108	—	2	4	no	—
312	#107	—	2	2	no	—
313	#107	—	2	2	no	—
314	#107	—	2	2	no	—
315	#106	—	2	2	no	—
316	#106	—	2	2	no	—
317	#106	—	2	2	no	—
318	#106	—	2	2	no	—
319	#106	—	2	2	no	—
320	C₄⋊C₈	—	2	2	no	—
321	C₄⋊C₈	—	2	2	no	—
322	C₄⋊C₈	—	2	1	no	—
323	C₄⋊C₈	—	2	1	no	—
324	C₄⋊C₈	D₄×C₇₉	1	1	yes	characteristic
325	C₄⋊C₈	D₄×C₇₉	1	1	yes	characteristic
326	C₄⋊C₈	D₄×C₇₉	1	2	yes	—
327	#102	—	2	2	no	—
328	#102	—	2	2	no	—
329	#102	—	2	2	no	—
330	#102	—	2	2	no	—
331	#100	—	2	2	no	—
332	#100	Q₈×C₇₉	1	4	yes	complemented
333	#97	—	2	2	no	—
334	#97	—	2	1	no	—
335	#97	—	2	1	no	—
336	C₄×C₈	—	2	2	no	—
337	C₄×C₈	—	2	1	no	—
338	C₄×C₈	—	2	1	no	—
339	C₂⁴	—	2	1	no	—
340	C₂×Q₈	—	2	1	no	—
341	C₂×Q₈	—	2	1	no	—
342	C₂×Q₈	—	4	1	no	—
343	C₂×Q₈	—	4	1	no	—
344	C₂×Q₈	—	8	2	no	—
345	C₂×D₄	—	2	1	no	—
346	C₂×D₄	—	2	1	no	—
347	C₂×D₄	—	2	1	no	—
348	C₂×D₄	—	2	1	no	—
349	C₂×D₄	—	2	1	no	—
350	C₂×D₄	C₂×Q₈×C₇₉	1	2	yes	—
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	4	1	no	—
354	C₂²×C₄	—	4	1	no	—
355	C₂²×C₄	—	8	2	no	—
356	C₂²×C₄	#41×C₇₉	1	1	yes	characteristic
357	C₂²×C₄	#41×C₇₉	1	1	yes	characteristic
358	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
359	M₁₆	—	2	1	no	—
360	M₁₆	—	2	1	no	—
361	M₁₆	—	2	1	no	—
362	M₁₆	—	2	1	no	—
363	M₁₆	—	2	2	no	—
364	M₁₆	—	2	1	no	—
365	M₁₆	—	2	2	no	—
366	M₁₆	C₂×Q₈×C₇₉	1	2	yes	—
367	M₁₆	C₂×Q₈×C₇₉	1	2	yes	—
368	M₁₆	#41×C₇₉	1	2	yes	—
369	C₂×C₈	—	2	1	no	—
370	C₂×C₈	—	2	1	no	—
371	C₂×C₈	—	2	1	no	—
372	C₂×C₈	—	2	2	no	—
373	C₂×C₈	—	2	2	no	—
374	C₂×C₈	—	2	1	no	—
375	C₂×C₈	—	2	2	no	—
376	C₂×C₈	C₂×D₄×C₇₉	1	2	yes	—
377	C₂×C₈	C₂×D₄×C₇₉	1	2	yes	—
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	—	2	1	no	—
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	2	2	no	—
383	C₄⋊C₄	—	2	1	no	—
384	C₄⋊C₄	—	2	1	no	—
385	C₄⋊C₄	—	2	2	no	—
386	C₄⋊C₄	—	4	1	no	—
387	C₄⋊C₄	—	4	1	no	—
388	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
389	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
390	C₂²⋊C₄	—	2	2	no	—
391	C₂²⋊C₄	—	4	1	no	—
392	C₂²⋊C₄	—	4	1	no	—
393	C₄²	—	2	2	no	—
394	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
395	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
396	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
397	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
398	C₂³	—	2	2	no	—
399	C₂³	—	4	1	no	—
400	C₂³	—	4	1	no	—
401	C₂³	—	8	1	no	—
402	C₂³	—	8	1	no	—
403	C₂³	C₂×#41×C₇₉	1	1	yes	characteristic
404	Q₈	—	4	2	no	—
405	Q₈	—	8	1	no	—
406	Q₈	—	8	2	no	—
407	Q₈	—	8	2	no	—
408	D₄	—	2	2	no	—
409	D₄	—	2	2	no	—
410	D₄	—	4	1	no	—
411	D₄	—	4	1	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	8	2	no	—
419	C₂×C₄	—	8	2	no	—
420	C₂×C₄	—	8	1	no	—
421	C₂×C₄	—	8	2	no	—
422	C₂×C₄	#121×C₇₉	1	1	yes	characteristic
423	C₂×C₄	#121×C₇₉	1	1	yes	characteristic
424	C₂×C₄	#121×C₇₉	1	1	yes	characteristic
425	C₂×C₄	#121×C₇₉	1	1	yes	characteristic
426	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
427	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
428	C₂×C₄	C₂²×Q₈×C₇₉	1	1	yes	characteristic
429	C₂×C₄	C₂×#41×C₇₉	1	1	yes	characteristic
430	C₂×C₄	2₋¹⁺⁴×C₇₉	1	1	yes	characteristic
431	C₂×C₄	2₋¹⁺⁴×C₇₉	1	1	yes	characteristic
432	C₈	—	2	2	no	—
433	C₈	—	2	2	no	—
434	C₈	—	2	2	no	—
435	C₈	—	2	2	no	—
436	C₈	—	2	2	no	—
437	C₈	—	4	1	no	—
438	C₈	—	4	2	no	—
439	C₂²	—	2	1	no	—
440	C₂²	—	2	1	no	—
441	C₂²	—	4	2	no	—
442	C₂²	—	8	2	no	—
443	C₂²	—	8	2	no	—
444	C₂²	—	8	1	no	—
445	C₂²	—	8	1	no	—
446	C₂²	C₂×#121×C₇₉	1	1	yes	characteristic
447	C₂²	#533×C₇₉	1	1	yes	characteristic
448	C₂²	#541×C₇₉	1	1	yes	characteristic
449	C₄	—	2	1	no	—
450	C₄	—	2	1	no	—
451	C₄	—	2	1	no	—
452	C₄	—	4	2	no	—
453	C₄	—	4	2	no	—
454	C₄	—	8	1	no	—
455	C₄	—	8	2	no	—
456	C₄	#471×C₇₉	1	2	yes	—
457	C₄	#547×C₇₉	1	1	yes	characteristic
458	C₄	#548×C₇₉	1	1	yes	characteristic
459	C₄	D₄×Q₈×C₇₉	1	1	yes	characteristic
460	C₄	D₄×Q₈×C₇₉	1	1	yes	characteristic
461	C₂	—	2	1	no	—
462	C₂	—	2	1	no	—
463	C₂	—	8	2	no	—
464	C₂	C₇₉×#2429	1	1	yes	characteristic
465	C₂	C₂×#471×C₇₉	1	1	yes	characteristic
466	C₂	C₇₉×#3068	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇₉	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₉
prime radical	C₂²×D₄×C₇₉	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ 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
1. C₇₉×#3165	C₂	semidirect
4. C₇₉×#2962	C₂	semidirect
5. C₇₉×#2090	C₂	semidirect
7. C₇₉×#1997	C₂	semidirect
8. C₇₉×#1951	C₂	semidirect
9. C₇₉×#1950	C₂	semidirect
98. #100×C₇₉	Q₈	semidirect
227. #25490	C₇₉	direct (N × H)
234. #3165	C₂×C₇₉	semidirect
237. #2962	C₂×C₇₉	semidirect
238. #2090	C₂×C₇₉	semidirect
240. #1997	C₂×C₇₉	semidirect
241. #1951	C₂×C₇₉	semidirect
242. #1950	C₂×C₇₉	semidirect
245. C₇₉	#25490	direct (N × H)
332. #100	Q₈×C₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₇₉×#3165	2
C₇₉×#3077	2
C₂×#476×C₇₉	2
C₇₉×#2962	2
C₇₉×#2090	2
C₇₉×#2063	2
C₇₉×#1997	2
C₇₉×#1951	2
C₇₉×#1950	2
C₇₉×#1931	2
C₄×#100×C₇₉	2
#25490	79

Subgroups — C79×#25490 #34137179

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#25490 #34137179