Subgroups — C₇₉×#25713 #34137402

Order 20224.

1102 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#553×C₇₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#501×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#474×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₉×#2563	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₉×#2034	C₂	1	2	yes	maximal, complemented
6	C₇₉×#2033	C₂	1	2	yes	maximal, complemented
7	C₇₉×#1989	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₉×#1955	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₉×#1854	C₂	1	2	yes	maximal, complemented
10	C₇₉×#1852	C₂	1	2	yes	maximal, complemented
11	C₇₉×#1762	C₂	1	1	yes	maximal, characteristic, complemented
12	#553×C₇₉	—	2	4	no	—
13	#553×C₇₉	—	2	4	no	—
14	C₂×C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
15	C₂×#126×C₇₉	—	2	1	no	—
16	C₂×#125×C₇₉	C₂²	1	1	yes	characteristic
17	C₂×#123×C₇₉	—	2	1	no	—
18	C₂×#121×C₇₉	—	2	1	no	—
19	C₂×#121×C₇₉	C₂²	1	1	yes	characteristic
20	C₂×#121×C₇₉	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₇₉	—	2	1	no	—
22	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
24	C₂×#117×C₇₉	C₂²	1	1	yes	characteristic
25	C₂²×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
26	#501×C₇₉	—	2	4	no	—
27	#474×C₇₉	—	2	4	no	—
28	C₂×#107×C₇₉	C₂²	1	2	yes	—
29	C₂×#107×C₇₉	C₂²	1	2	yes	—
30	C₂×#106×C₇₉	C₂²	1	2	yes	—
31	C₂×C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
32	C₂×#102×C₇₉	C₂²	1	2	yes	—
33	C₂×#102×C₇₉	C₂²	1	2	yes	—
34	C₂×C₂²⋊C₈×C₇₉	C₂²	1	2	yes	—
35	C₂×C₂²⋊C₈×C₇₉	C₂²	1	2	yes	—
36	C₂×#97×C₇₉	C₂²	1	1	yes	characteristic
37	#393×C₇₉	—	2	1	no	—
38	#393×C₇₉	—	2	1	no	—
39	#390×C₇₉	—	2	1	no	—
40	#382×C₇₉	—	2	1	no	—
41	#380×C₇₉	C₂²	1	2	yes	—
42	#380×C₇₉	C₂²	1	2	yes	—
43	C₄×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
44	#340×C₇₉	C₂²	1	2	yes	—
45	#340×C₇₉	C₂²	1	2	yes	—
46	#340×C₇₉	C₂²	1	2	yes	—
47	C₂²×Q₈×C₇₉	—	2	1	no	—
48	C₂²×D₄×C₇₉	—	2	1	no	—
49	C₂²×D₄×C₇₉	—	2	1	no	—
50	C₂²×D₄×C₇₉	D₄	1	1	yes	characteristic
51	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
52	C₂³×C₄×C₇₉	—	2	1	no	—
53	C₂³×C₄×C₇₉	—	2	1	no	—
54	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
55	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₇₉	C₂³	1	2	yes	—
57	C₂²×C₈×C₇₉	C₂³	1	2	yes	—
58	C₄⋊Q₈×C₇₉	—	2	2	no	—
59	C₄⋊Q₈×C₇₉	—	2	2	no	—
60	#126×C₇₉	—	2	8	no	—
61	#125×C₇₉	—	2	2	no	—
62	#125×C₇₉	D₄	1	4	yes	—
63	#123×C₇₉	—	2	8	no	—
64	#121×C₇₉	—	2	8	no	—
65	#121×C₇₉	—	2	2	no	—
66	#121×C₇₉	—	2	2	no	—
67	#121×C₇₉	—	2	2	no	—
68	#121×C₇₉	—	2	2	no	—
69	C₄×D₄×C₇₉	—	2	8	no	—
70	C₄×D₄×C₇₉	—	2	2	no	—
71	C₄×D₄×C₇₉	—	2	2	no	—
72	C₄×D₄×C₇₉	—	2	2	no	—
73	C₄×D₄×C₇₉	D₄	1	4	yes	—
74	#117×C₇₉	—	2	2	no	—
75	#117×C₇₉	—	2	2	no	—
76	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
77	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
78	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
79	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
80	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
81	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
82	C₂×C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
83	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
84	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
85	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
86	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
87	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
88	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
89	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
90	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
91	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
92	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
93	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
94	C₂×C₂²⋊C₄×C₇₉	D₄	1	1	yes	characteristic
95	C₂×C₂²⋊C₄×C₇₉	D₄	1	1	yes	characteristic
96	C₂×C₄²×C₇₉	—	2	1	no	—
97	C₂×C₄²×C₇₉	—	2	1	no	—
98	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
99	#107×C₇₉	—	2	4	no	—
100	#107×C₇₉	—	2	4	no	—
101	#106×C₇₉	—	2	4	no	—
102	C₄⋊C₈×C₇₉	—	2	2	no	—
103	#102×C₇₉	—	2	4	no	—
104	#102×C₇₉	—	2	4	no	—
105	C₂²⋊C₈×C₇₉	—	2	4	no	—
106	C₂²⋊C₈×C₇₉	—	2	4	no	—
107	#97×C₇₉	—	2	2	no	—
108	#95×C₇₉	—	2	1	no	—
109	#95×C₇₉	—	2	2	no	—
110	#95×C₇₉	—	2	2	no	—
111	C₂⁴×C₇₉	—	2	1	no	—
112	C₂⁴×C₇₉	C₂×D₄	1	1	yes	characteristic
113	C₂⁴×C₇₉	C₂×D₄	1	1	yes	characteristic
114	C₂×Q₈×C₇₉	—	4	2	no	—
115	C₂×Q₈×C₇₉	—	8	2	no	—
116	C₂×D₄×C₇₉	—	2	4	no	—
117	C₂×D₄×C₇₉	—	2	2	no	—
118	C₂×D₄×C₇₉	—	2	4	no	—
119	C₂×D₄×C₇₉	—	2	2	no	—
120	C₂×D₄×C₇₉	—	2	1	no	—
121	C₂×D₄×C₇₉	—	2	2	no	—
122	C₂×D₄×C₇₉	—	2	2	no	—
123	C₂×D₄×C₇₉	—	4	1	no	—
124	C₂×D₄×C₇₉	—	4	2	no	—
125	C₂×D₄×C₇₉	—	4	2	no	—
126	C₂×D₄×C₇₉	—	8	2	no	—
127	C₂×D₄×C₇₉	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₇₉	—	2	1	no	—
129	C₂²×C₄×C₇₉	—	2	1	no	—
130	C₂²×C₄×C₇₉	—	2	1	no	—
131	C₂²×C₄×C₇₉	—	2	4	no	—
132	C₂²×C₄×C₇₉	—	2	1	no	—
133	C₂²×C₄×C₇₉	—	2	1	no	—
134	C₂²×C₄×C₇₉	—	2	1	no	—
135	C₂²×C₄×C₇₉	—	2	1	no	—
136	C₂²×C₄×C₇₉	—	2	2	no	—
137	C₂²×C₄×C₇₉	—	2	2	no	—
138	C₂²×C₄×C₇₉	—	2	2	no	—
139	C₂²×C₄×C₇₉	—	2	2	no	—
140	C₂²×C₄×C₇₉	—	2	4	no	—
141	C₂²×C₄×C₇₉	—	2	2	no	—
142	C₂²×C₄×C₇₉	—	2	2	no	—
143	C₂²×C₄×C₇₉	—	8	2	no	—
144	C₂²×C₄×C₇₉	—	8	2	no	—
145	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
150	C₂×C₈×C₇₉	—	2	2	no	—
151	C₂×C₈×C₇₉	—	2	2	no	—
152	C₂×C₈×C₇₉	—	2	2	no	—
153	C₂×C₈×C₇₉	—	2	2	no	—
154	C₂×C₈×C₇₉	—	2	2	no	—
155	C₂×C₈×C₇₉	#41	1	4	yes	—
156	C₄⋊C₄×C₇₉	—	2	4	no	—
157	C₄⋊C₄×C₇₉	—	2	4	no	—
158	C₄⋊C₄×C₇₉	—	2	4	no	—
159	C₄⋊C₄×C₇₉	—	2	2	no	—
160	C₄⋊C₄×C₇₉	—	2	1	no	—
161	C₄⋊C₄×C₇₉	—	2	1	no	—
162	C₄⋊C₄×C₇₉	—	2	1	no	—
163	C₄⋊C₄×C₇₉	—	2	2	no	—
164	C₄⋊C₄×C₇₉	—	2	2	no	—
165	C₄⋊C₄×C₇₉	—	2	2	no	—
166	C₄⋊C₄×C₇₉	—	2	2	no	—
167	C₄⋊C₄×C₇₉	—	4	2	no	—
168	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
169	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
170	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
171	C₂²⋊C₄×C₇₉	—	2	4	no	—
172	C₂²⋊C₄×C₇₉	—	2	4	no	—
173	C₂²⋊C₄×C₇₉	—	2	4	no	—
174	C₂²⋊C₄×C₇₉	—	2	4	no	—
175	C₂²⋊C₄×C₇₉	—	2	2	no	—
176	C₂²⋊C₄×C₇₉	—	2	2	no	—
177	C₂²⋊C₄×C₇₉	—	8	2	no	—
178	C₂²⋊C₄×C₇₉	—	8	2	no	—
179	C₄²×C₇₉	—	2	4	no	—
180	C₄²×C₇₉	—	4	2	no	—
181	C₄²×C₇₉	C₂×D₄	1	2	yes	—
182	C₄²×C₇₉	C₂×D₄	1	2	yes	—
183	C₂³×C₇₉	—	2	1	no	—
184	C₂³×C₇₉	—	2	2	no	—
185	C₂³×C₇₉	—	2	1	no	—
186	C₂³×C₇₉	—	2	2	no	—
187	C₂³×C₇₉	—	2	1	no	—
188	C₂³×C₇₉	—	2	2	no	—
189	C₂³×C₇₉	—	2	2	no	—
190	C₂³×C₇₉	—	2	1	no	—
191	C₂³×C₇₉	—	2	1	no	—
192	C₂³×C₇₉	—	2	2	no	—
193	C₂³×C₇₉	—	4	2	no	—
194	C₂³×C₇₉	—	4	1	no	—
195	C₂³×C₇₉	—	4	1	no	—
196	C₂³×C₇₉	—	4	2	no	—
197	C₂³×C₇₉	#137	1	2	yes	—
198	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
199	Q₈×C₇₉	—	8	4	no	—
200	D₄×C₇₉	—	2	2	no	—
201	D₄×C₇₉	—	2	2	no	—
202	D₄×C₇₉	—	4	4	no	—
203	D₄×C₇₉	—	4	8	no	—
204	D₄×C₇₉	—	4	2	no	—
205	D₄×C₇₉	—	8	4	no	—
206	C₂×C₄×C₇₉	—	2	1	no	—
207	C₂×C₄×C₇₉	—	2	1	no	—
208	C₂×C₄×C₇₉	—	2	2	no	—
209	C₂×C₄×C₇₉	—	2	1	no	—
210	C₂×C₄×C₇₉	—	2	2	no	—
211	C₂×C₄×C₇₉	—	2	2	no	—
212	C₂×C₄×C₇₉	—	2	1	no	—
213	C₂×C₄×C₇₉	—	2	2	no	—
214	C₂×C₄×C₇₉	—	2	2	no	—
215	C₂×C₄×C₇₉	—	2	2	no	—
216	C₂×C₄×C₇₉	—	4	1	no	—
217	C₂×C₄×C₇₉	—	4	1	no	—
218	C₂×C₄×C₇₉	—	4	2	no	—
219	C₂×C₄×C₇₉	—	4	2	no	—
220	C₂×C₄×C₇₉	—	4	1	no	—
221	C₂×C₄×C₇₉	—	4	1	no	—
222	C₂×C₄×C₇₉	—	4	1	no	—
223	C₂×C₄×C₇₉	—	4	1	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	—	4	2	no	—
230	C₂×C₄×C₇₉	—	4	2	no	—
231	C₂×C₄×C₇₉	—	4	2	no	—
232	C₂×C₄×C₇₉	—	8	4	no	—
233	C₂×C₄×C₇₉	—	8	4	no	—
234	C₂×C₄×C₇₉	#120	1	2	yes	—
235	C₂×C₄×C₇₉	#120	1	2	yes	—
236	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
237	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
238	C₂×C₄×C₇₉	C₂×#41	1	2	yes	—
239	C₂×C₄×C₇₉	2₋¹⁺⁴	1	2	yes	—
240	C₈×C₇₉	—	2	4	no	—
241	C₈×C₇₉	—	4	2	no	—
242	C₂²×C₇₉	—	2	4	no	—
243	C₂²×C₇₉	—	2	2	no	—
244	C₂²×C₇₉	—	4	2	no	—
245	C₂²×C₇₉	—	4	1	no	—
246	C₂²×C₇₉	—	4	1	no	—
247	C₂²×C₇₉	—	4	2	no	—
248	C₂²×C₇₉	—	4	2	no	—
249	C₂²×C₇₉	—	4	1	no	—
250	C₂²×C₇₉	—	4	2	no	—
251	C₂²×C₇₉	—	4	1	no	—
252	C₂²×C₇₉	—	4	2	no	—
253	C₂²×C₇₉	—	4	2	no	—
254	C₂²×C₇₉	—	4	1	no	—
255	C₂²×C₇₉	—	8	2	no	—
256	C₂²×C₇₉	—	8	2	no	—
257	C₂²×C₇₉	C₂×#120	1	1	yes	characteristic
258	C₂²×C₇₉	#547	1	2	yes	—
259	C₂²×C₇₉	C₂×#137	1	1	yes	characteristic
260	C₂²×C₇₉	#575	1	1	yes	characteristic
261	C₂²×C₇₉	#576	1	2	yes	—
262	C₄×C₇₉	—	2	2	no	—
263	C₄×C₇₉	—	2	2	no	—
264	C₄×C₇₉	—	4	1	no	—
265	C₄×C₇₉	—	4	1	no	—
266	C₄×C₇₉	—	4	2	no	—
267	C₄×C₇₉	—	4	2	no	—
268	C₄×C₇₉	—	4	2	no	—
269	C₄×C₇₉	—	8	2	no	—
270	C₄×C₇₉	—	8	2	no	—
271	C₄×C₇₉	#532	1	1	yes	characteristic
272	C₄×C₇₉	#536	1	1	yes	characteristic
273	C₄×C₇₉	#548	1	2	yes	—
274	#25713	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
275	C₂×C₇₉	—	4	2	no	—
276	C₂×C₇₉	—	8	1	no	—
277	C₂×C₇₉	—	8	2	no	—
278	C₂×C₇₉	#2432	1	1	yes	characteristic
279	C₂×C₇₉	#3007	1	1	yes	characteristic
280	C₂×C₇₉	#3008	1	1	yes	characteristic
281	C₂×C₇₉	#3346	1	2	yes	—
282	C₂×C₇₉	#3347	1	2	yes	—
283	C₂×#553	C₂×C₇₉	1	1	yes	characteristic
284	C₂×#501	C₂×C₇₉	1	1	yes	characteristic, complemented
285	C₂×#474	C₂×C₇₉	1	1	yes	characteristic, complemented
286	#2563	C₂×C₇₉	1	1	yes	characteristic, complemented
287	#2034	C₂×C₇₉	1	2	yes	complemented
288	#2033	C₂×C₇₉	1	2	yes	complemented
289	#1989	C₂×C₇₉	1	1	yes	characteristic, complemented
290	#1955	C₂×C₇₉	1	1	yes	characteristic, complemented
291	#1854	C₂×C₇₉	1	2	yes	complemented
292	#1852	C₂×C₇₉	1	2	yes	complemented
293	#1762	C₂×C₇₉	1	1	yes	characteristic, complemented
294	C₇₉	#25713	1	1	yes	characteristic, direct product factor, Sylow
295	#553	—	2	4	no	—
296	#553	—	2	4	no	—
297	C₂×C₄⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic
298	C₂×#126	—	2	1	no	—
299	C₂×#125	C₂²×C₇₉	1	1	yes	characteristic
300	C₂×#123	—	2	1	no	—
301	C₂×#121	—	2	1	no	—
302	C₂×#121	C₂²×C₇₉	1	1	yes	characteristic
303	C₂×#121	C₂²×C₇₉	1	1	yes	characteristic
304	C₂×C₄×D₄	—	2	1	no	—
305	C₂×C₄×D₄	C₂²×C₇₉	1	1	yes	characteristic
306	C₂×C₄×D₄	C₂²×C₇₉	1	1	yes	characteristic
307	C₂×#117	C₂²×C₇₉	1	1	yes	characteristic
308	C₂²×C₄⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
309	#501	—	2	4	no	—
310	#474	—	2	4	no	—
311	C₂×#107	C₂²×C₇₉	1	2	yes	—
312	C₂×#107	C₂²×C₇₉	1	2	yes	—
313	C₂×#106	C₂²×C₇₉	1	2	yes	—
314	C₂×C₄⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
315	C₂×#102	C₂²×C₇₉	1	2	yes	—
316	C₂×#102	C₂²×C₇₉	1	2	yes	—
317	C₂×C₂²⋊C₈	C₂²×C₇₉	1	2	yes	—
318	C₂×C₂²⋊C₈	C₂²×C₇₉	1	2	yes	—
319	C₂×#97	C₂²×C₇₉	1	1	yes	characteristic
320	#393	—	2	1	no	—
321	#393	—	2	1	no	—
322	#390	—	2	1	no	—
323	#382	—	2	1	no	—
324	#380	C₂²×C₇₉	1	2	yes	—
325	#380	C₂²×C₇₉	1	2	yes	—
326	C₄×C₄⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
327	#340	C₂²×C₇₉	1	2	yes	—
328	#340	C₂²×C₇₉	1	2	yes	—
329	#340	C₂²×C₇₉	1	2	yes	—
330	C₂²×Q₈	—	2	1	no	—
331	C₂²×D₄	—	2	1	no	—
332	C₂²×D₄	—	2	1	no	—
333	C₂²×D₄	D₄×C₇₉	1	1	yes	characteristic
334	C₂²×D₄	C₂³×C₇₉	1	1	yes	characteristic
335	C₂³×C₄	—	2	1	no	—
336	C₂³×C₄	—	2	1	no	—
337	C₂³×C₄	C₂³×C₇₉	1	1	yes	characteristic
338	C₂³×C₄	C₂³×C₇₉	1	1	yes	characteristic
339	C₂²×C₈	C₂³×C₇₉	1	2	yes	—
340	C₂²×C₈	C₂³×C₇₉	1	2	yes	—
341	C₄⋊Q₈	—	2	2	no	—
342	C₄⋊Q₈	—	2	2	no	—
343	#126	—	2	8	no	—
344	#125	—	2	2	no	—
345	#125	D₄×C₇₉	1	4	yes	—
346	#123	—	2	8	no	—
347	#121	—	2	8	no	—
348	#121	—	2	2	no	—
349	#121	—	2	2	no	—
350	#121	—	2	2	no	—
351	#121	—	2	2	no	—
352	C₄×D₄	—	2	8	no	—
353	C₄×D₄	—	2	2	no	—
354	C₄×D₄	—	2	2	no	—
355	C₄×D₄	—	2	2	no	—
356	C₄×D₄	D₄×C₇₉	1	4	yes	—
357	#117	—	2	2	no	—
358	#117	—	2	2	no	—
359	C₂×C₄⋊C₄	—	2	1	no	—
360	C₂×C₄⋊C₄	—	2	1	no	—
361	C₂×C₄⋊C₄	—	2	1	no	—
362	C₂×C₄⋊C₄	—	2	2	no	—
363	C₂×C₄⋊C₄	—	2	2	no	—
364	C₂×C₄⋊C₄	—	2	1	no	—
365	C₂×C₄⋊C₄	D₄×C₇₉	1	1	yes	characteristic
366	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
367	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
368	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
369	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
370	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
371	C₂×C₂²⋊C₄	—	2	1	no	—
372	C₂×C₂²⋊C₄	—	2	1	no	—
373	C₂×C₂²⋊C₄	—	2	1	no	—
374	C₂×C₂²⋊C₄	—	2	1	no	—
375	C₂×C₂²⋊C₄	—	2	2	no	—
376	C₂×C₂²⋊C₄	—	2	2	no	—
377	C₂×C₂²⋊C₄	D₄×C₇₉	1	1	yes	characteristic
378	C₂×C₂²⋊C₄	D₄×C₇₉	1	1	yes	characteristic
379	C₂×C₄²	—	2	1	no	—
380	C₂×C₄²	—	2	1	no	—
381	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
382	#107	—	2	4	no	—
383	#107	—	2	4	no	—
384	#106	—	2	4	no	—
385	C₄⋊C₈	—	2	2	no	—
386	#102	—	2	4	no	—
387	#102	—	2	4	no	—
388	C₂²⋊C₈	—	2	4	no	—
389	C₂²⋊C₈	—	2	4	no	—
390	#97	—	2	2	no	—
391	#95	—	2	1	no	—
392	#95	—	2	2	no	—
393	#95	—	2	2	no	—
394	C₂⁴	—	2	1	no	—
395	C₂⁴	C₂×D₄×C₇₉	1	1	yes	characteristic
396	C₂⁴	C₂×D₄×C₇₉	1	1	yes	characteristic
397	C₂×Q₈	—	4	2	no	—
398	C₂×Q₈	—	8	2	no	—
399	C₂×D₄	—	2	4	no	—
400	C₂×D₄	—	2	2	no	—
401	C₂×D₄	—	2	4	no	—
402	C₂×D₄	—	2	2	no	—
403	C₂×D₄	—	2	1	no	—
404	C₂×D₄	—	2	2	no	—
405	C₂×D₄	—	2	2	no	—
406	C₂×D₄	—	4	1	no	—
407	C₂×D₄	—	4	2	no	—
408	C₂×D₄	—	4	2	no	—
409	C₂×D₄	—	8	2	no	—
410	C₂×D₄	C₂×D₄×C₇₉	1	2	yes	—
411	C₂²×C₄	—	2	1	no	—
412	C₂²×C₄	—	2	1	no	—
413	C₂²×C₄	—	2	1	no	—
414	C₂²×C₄	—	2	4	no	—
415	C₂²×C₄	—	2	1	no	—
416	C₂²×C₄	—	2	1	no	—
417	C₂²×C₄	—	2	1	no	—
418	C₂²×C₄	—	2	1	no	—
419	C₂²×C₄	—	2	2	no	—
420	C₂²×C₄	—	2	2	no	—
421	C₂²×C₄	—	2	2	no	—
422	C₂²×C₄	—	2	2	no	—
423	C₂²×C₄	—	2	4	no	—
424	C₂²×C₄	—	2	2	no	—
425	C₂²×C₄	—	2	2	no	—
426	C₂²×C₄	—	8	2	no	—
427	C₂²×C₄	—	8	2	no	—
428	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
429	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
430	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
431	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
432	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
433	C₂×C₈	—	2	2	no	—
434	C₂×C₈	—	2	2	no	—
435	C₂×C₈	—	2	2	no	—
436	C₂×C₈	—	2	2	no	—
437	C₂×C₈	—	2	2	no	—
438	C₂×C₈	#41×C₇₉	1	4	yes	—
439	C₄⋊C₄	—	2	4	no	—
440	C₄⋊C₄	—	2	4	no	—
441	C₄⋊C₄	—	2	4	no	—
442	C₄⋊C₄	—	2	2	no	—
443	C₄⋊C₄	—	2	1	no	—
444	C₄⋊C₄	—	2	1	no	—
445	C₄⋊C₄	—	2	1	no	—
446	C₄⋊C₄	—	2	2	no	—
447	C₄⋊C₄	—	2	2	no	—
448	C₄⋊C₄	—	2	2	no	—
449	C₄⋊C₄	—	2	2	no	—
450	C₄⋊C₄	—	4	2	no	—
451	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
452	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
453	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
454	C₂²⋊C₄	—	2	4	no	—
455	C₂²⋊C₄	—	2	4	no	—
456	C₂²⋊C₄	—	2	4	no	—
457	C₂²⋊C₄	—	2	4	no	—
458	C₂²⋊C₄	—	2	2	no	—
459	C₂²⋊C₄	—	2	2	no	—
460	C₂²⋊C₄	—	8	2	no	—
461	C₂²⋊C₄	—	8	2	no	—
462	C₄²	—	2	4	no	—
463	C₄²	—	4	2	no	—
464	C₄²	C₂×D₄×C₇₉	1	2	yes	—
465	C₄²	C₂×D₄×C₇₉	1	2	yes	—
466	C₂³	—	2	1	no	—
467	C₂³	—	2	2	no	—
468	C₂³	—	2	1	no	—
469	C₂³	—	2	2	no	—
470	C₂³	—	2	1	no	—
471	C₂³	—	2	2	no	—
472	C₂³	—	2	2	no	—
473	C₂³	—	2	1	no	—
474	C₂³	—	2	1	no	—
475	C₂³	—	2	2	no	—
476	C₂³	—	4	2	no	—
477	C₂³	—	4	1	no	—
478	C₂³	—	4	1	no	—
479	C₂³	—	4	2	no	—
480	C₂³	#137×C₇₉	1	2	yes	—
481	C₂³	C₂²×D₄×C₇₉	1	1	yes	characteristic
482	Q₈	—	8	4	no	—
483	D₄	—	2	2	no	—
484	D₄	—	2	2	no	—
485	D₄	—	4	4	no	—
486	D₄	—	4	8	no	—
487	D₄	—	4	2	no	—
488	D₄	—	8	4	no	—
489	C₂×C₄	—	2	1	no	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	1	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	4	1	no	—
500	C₂×C₄	—	4	1	no	—
501	C₂×C₄	—	4	2	no	—
502	C₂×C₄	—	4	2	no	—
503	C₂×C₄	—	4	1	no	—
504	C₂×C₄	—	4	1	no	—
505	C₂×C₄	—	4	1	no	—
506	C₂×C₄	—	4	1	no	—
507	C₂×C₄	—	4	2	no	—
508	C₂×C₄	—	4	2	no	—
509	C₂×C₄	—	4	2	no	—
510	C₂×C₄	—	4	2	no	—
511	C₂×C₄	—	4	2	no	—
512	C₂×C₄	—	4	2	no	—
513	C₂×C₄	—	4	2	no	—
514	C₂×C₄	—	4	2	no	—
515	C₂×C₄	—	8	4	no	—
516	C₂×C₄	—	8	4	no	—
517	C₂×C₄	#120×C₇₉	1	2	yes	—
518	C₂×C₄	#120×C₇₉	1	2	yes	—
519	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
520	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
521	C₂×C₄	C₂×#41×C₇₉	1	2	yes	—
522	C₂×C₄	2₋¹⁺⁴×C₇₉	1	2	yes	—
523	C₈	—	2	4	no	—
524	C₈	—	4	2	no	—
525	C₂²	—	2	4	no	—
526	C₂²	—	2	2	no	—
527	C₂²	—	4	2	no	—
528	C₂²	—	4	1	no	—
529	C₂²	—	4	1	no	—
530	C₂²	—	4	2	no	—
531	C₂²	—	4	2	no	—
532	C₂²	—	4	1	no	—
533	C₂²	—	4	2	no	—
534	C₂²	—	4	1	no	—
535	C₂²	—	4	2	no	—
536	C₂²	—	4	2	no	—
537	C₂²	—	4	1	no	—
538	C₂²	—	8	2	no	—
539	C₂²	—	8	2	no	—
540	C₂²	C₂×#120×C₇₉	1	1	yes	characteristic
541	C₂²	#547×C₇₉	1	2	yes	—
542	C₂²	C₂×#137×C₇₉	1	1	yes	characteristic
543	C₂²	#575×C₇₉	1	1	yes	characteristic
544	C₂²	#576×C₇₉	1	2	yes	—
545	C₄	—	2	2	no	—
546	C₄	—	2	2	no	—
547	C₄	—	4	1	no	—
548	C₄	—	4	1	no	—
549	C₄	—	4	2	no	—
550	C₄	—	4	2	no	—
551	C₄	—	4	2	no	—
552	C₄	—	8	2	no	—
553	C₄	—	8	2	no	—
554	C₄	#532×C₇₉	1	1	yes	characteristic
555	C₄	#536×C₇₉	1	1	yes	characteristic
556	C₄	#548×C₇₉	1	2	yes	—
557	C₂	—	4	2	no	—
558	C₂	—	8	1	no	—
559	C₂	—	8	2	no	—
560	C₂	C₇₉×#2432	1	1	yes	characteristic
561	C₂	C₇₉×#3007	1	1	yes	characteristic
562	C₂	C₇₉×#3008	1	1	yes	characteristic
563	C₂	C₇₉×#3346	1	2	yes	—
564	C₂	C₇₉×#3347	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₉
prime radical	C₂×#553×C₇₉	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₉ ◁ C₂×C₄×D₄×C₇₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#501×C₇₉	C₂	semidirect
3. C₂×#474×C₇₉	C₂	semidirect
4. C₇₉×#2563	C₂	semidirect
5. C₇₉×#2034	C₂	semidirect
6. C₇₉×#2033	C₂	semidirect
7. C₇₉×#1989	C₂	semidirect
8. C₇₉×#1955	C₂	semidirect
9. C₇₉×#1854	C₂	semidirect
10. C₇₉×#1852	C₂	semidirect
11. C₇₉×#1762	C₂	semidirect
274. #25713	C₇₉	direct (N × H)
284. C₂×#501	C₂×C₇₉	semidirect
285. C₂×#474	C₂×C₇₉	semidirect
286. #2563	C₂×C₇₉	semidirect
287. #2034	C₂×C₇₉	semidirect
288. #2033	C₂×C₇₉	semidirect
289. #1989	C₂×C₇₉	semidirect
290. #1955	C₂×C₇₉	semidirect
291. #1854	C₂×C₇₉	semidirect
292. #1852	C₂×C₇₉	semidirect
293. #1762	C₂×C₇₉	semidirect
294. C₇₉	#25713	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#553×C₇₉	2
C₂×#501×C₇₉	2
C₂×#474×C₇₉	2
C₇₉×#2563	2
C₇₉×#2034	2
C₇₉×#2033	2
C₇₉×#1989	2
C₇₉×#1955	2
C₇₉×#1854	2
C₇₉×#1852	2
C₇₉×#1762	2
#25713	79

Subgroups — C79×#25713 #34137402

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#25713 #34137402