Subgroups — C₇₉×#25710 #34137399

Order 20224.

1080 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#555×C₇₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#501×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#478×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₉×#2562	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×#1988	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×#1854	C₂	1	2	yes	maximal, complemented
11	C₇₉×#1762	C₂	1	1	yes	maximal, characteristic, complemented
12	#555×C₇₉	—	2	4	no	—
13	#555×C₇₉	—	2	4	no	—
14	C₂×C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
15	C₂×#125×C₇₉	C₂²	1	1	yes	characteristic
16	C₂×#124×C₇₉	—	2	2	no	—
17	C₂×#121×C₇₉	—	2	1	no	—
18	C₂×#121×C₇₉	C₂²	1	2	yes	—
19	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
21	C₂×#117×C₇₉	—	2	1	no	—
22	C₂×#117×C₇₉	C₂²	1	2	yes	—
23	#501×C₇₉	—	2	4	no	—
24	#478×C₇₉	—	2	4	no	—
25	C₂×#107×C₇₉	C₂²	1	2	yes	—
26	C₂×#107×C₇₉	C₂²	1	1	yes	characteristic
27	C₂×#106×C₇₉	C₂²	1	2	yes	—
28	C₂×#106×C₇₉	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
30	C₂×#102×C₇₉	C₂²	1	2	yes	—
31	C₂×#102×C₇₉	C₂²	1	1	yes	characteristic
32	C₂×#102×C₇₉	C₂²	1	1	yes	characteristic
33	C₂×C₂²⋊C₈×C₇₉	C₂²	1	2	yes	—
34	C₂×C₂²⋊C₈×C₇₉	C₂²	1	2	yes	—
35	C₂×#97×C₇₉	C₂²	1	1	yes	characteristic
36	#400×C₇₉	—	2	1	no	—
37	#394×C₇₉	—	2	1	no	—
38	#388×C₇₉	—	2	2	no	—
39	#380×C₇₉	C₂²	1	2	yes	—
40	#380×C₇₉	C₂²	1	2	yes	—
41	C₄×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
42	#340×C₇₉	C₂²	1	2	yes	—
43	#340×C₇₉	C₂²	1	2	yes	—
44	#340×C₇₉	C₂²	1	2	yes	—
45	C₂²×Q₈×C₇₉	—	2	1	no	—
46	C₂²×D₄×C₇₉	—	2	2	no	—
47	C₂²×D₄×C₇₉	D₄	1	1	yes	characteristic
48	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
49	C₂³×C₄×C₇₉	—	2	1	no	—
50	C₂³×C₄×C₇₉	C₂³	1	2	yes	—
51	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₇₉	C₂³	1	2	yes	—
54	C₄⋊Q₈×C₇₉	—	2	2	no	—
55	C₄⋊Q₈×C₇₉	D₄	1	4	yes	—
56	#125×C₇₉	—	2	2	no	—
57	#125×C₇₉	—	2	2	no	—
58	#124×C₇₉	—	2	16	no	—
59	#121×C₇₉	—	2	8	no	—
60	#121×C₇₉	—	2	4	no	—
61	#121×C₇₉	—	2	4	no	—
62	C₄×D₄×C₇₉	—	2	2	no	—
63	C₄×D₄×C₇₉	—	2	2	no	—
64	C₄×D₄×C₇₉	—	2	2	no	—
65	C₄×D₄×C₇₉	D₄	1	4	yes	—
66	#117×C₇₉	—	2	8	no	—
67	#117×C₇₉	—	2	4	no	—
68	#117×C₇₉	—	2	4	no	—
69	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
70	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
71	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
72	C₂×C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
73	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
74	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
75	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
76	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
77	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
78	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
79	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
80	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
81	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
82	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
83	C₂×C₂²⋊C₄×C₇₉	D₄	1	2	yes	—
84	C₂×C₄²×C₇₉	—	2	2	no	—
85	C₂×C₄²×C₇₉	—	2	1	no	—
86	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
87	#107×C₇₉	—	2	2	no	—
88	#107×C₇₉	—	2	4	no	—
89	#106×C₇₉	—	2	2	no	—
90	#106×C₇₉	—	2	4	no	—
91	C₄⋊C₈×C₇₉	—	2	2	no	—
92	#102×C₇₉	—	2	2	no	—
93	#102×C₇₉	—	2	2	no	—
94	#102×C₇₉	—	2	4	no	—
95	C₂²⋊C₈×C₇₉	—	2	4	no	—
96	C₂²⋊C₈×C₇₉	—	2	4	no	—
97	#97×C₇₉	—	2	2	no	—
98	#95×C₇₉	—	2	1	no	—
99	#95×C₇₉	—	2	2	no	—
100	#95×C₇₉	—	2	2	no	—
101	C₂⁴×C₇₉	—	2	1	no	—
102	C₂⁴×C₇₉	C₂×D₄	1	2	yes	—
103	C₂×Q₈×C₇₉	—	2	4	no	—
104	C₂×Q₈×C₇₉	—	8	1	no	—
105	C₂×Q₈×C₇₉	—	8	1	no	—
106	C₂×D₄×C₇₉	—	2	8	no	—
107	C₂×D₄×C₇₉	—	2	2	no	—
108	C₂×D₄×C₇₉	—	2	1	no	—
109	C₂×D₄×C₇₉	—	2	2	no	—
110	C₂×D₄×C₇₉	—	2	2	no	—
111	C₂×D₄×C₇₉	—	4	2	no	—
112	C₂×D₄×C₇₉	—	8	2	no	—
113	C₂×D₄×C₇₉	—	8	2	no	—
114	C₂×D₄×C₇₉	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₇₉	—	2	1	no	—
116	C₂²×C₄×C₇₉	—	2	2	no	—
117	C₂²×C₄×C₇₉	—	2	4	no	—
118	C₂²×C₄×C₇₉	—	2	2	no	—
119	C₂²×C₄×C₇₉	—	2	2	no	—
120	C₂²×C₄×C₇₉	—	2	2	no	—
121	C₂²×C₄×C₇₉	—	2	2	no	—
122	C₂²×C₄×C₇₉	—	2	2	no	—
123	C₂²×C₄×C₇₉	—	2	2	no	—
124	C₂²×C₄×C₇₉	—	2	2	no	—
125	C₂²×C₄×C₇₉	—	2	1	no	—
126	C₂²×C₄×C₇₉	—	2	1	no	—
127	C₂²×C₄×C₇₉	—	4	4	no	—
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	C₂×C₈×C₇₉	—	2	2	no	—
133	C₂×C₈×C₇₉	—	2	1	no	—
134	C₂×C₈×C₇₉	—	2	1	no	—
135	C₂×C₈×C₇₉	—	2	2	no	—
136	C₂×C₈×C₇₉	—	2	2	no	—
137	C₂×C₈×C₇₉	—	2	2	no	—
138	C₂×C₈×C₇₉	#41	1	4	yes	—
139	C₄⋊C₄×C₇₉	—	2	4	no	—
140	C₄⋊C₄×C₇₉	—	2	2	no	—
141	C₄⋊C₄×C₇₉	—	2	1	no	—
142	C₄⋊C₄×C₇₉	—	2	2	no	—
143	C₄⋊C₄×C₇₉	—	2	1	no	—
144	C₄⋊C₄×C₇₉	—	2	1	no	—
145	C₄⋊C₄×C₇₉	—	2	1	no	—
146	C₄⋊C₄×C₇₉	—	2	1	no	—
147	C₄⋊C₄×C₇₉	—	2	2	no	—
148	C₄⋊C₄×C₇₉	—	2	2	no	—
149	C₄⋊C₄×C₇₉	—	4	2	no	—
150	C₄⋊C₄×C₇₉	—	4	2	no	—
151	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
152	C₄⋊C₄×C₇₉	C₂×D₄	1	4	yes	—
153	C₂²⋊C₄×C₇₉	—	2	8	no	—
154	C₂²⋊C₄×C₇₉	—	2	8	no	—
155	C₂²⋊C₄×C₇₉	—	2	4	no	—
156	C₂²⋊C₄×C₇₉	—	2	4	no	—
157	C₂²⋊C₄×C₇₉	—	4	4	no	—
158	C₂²⋊C₄×C₇₉	—	8	2	no	—
159	C₄²×C₇₉	—	2	8	no	—
160	C₄²×C₇₉	—	8	1	no	—
161	C₄²×C₇₉	C₂×D₄	1	2	yes	—
162	C₄²×C₇₉	C₂×D₄	1	2	yes	—
163	C₂³×C₇₉	—	2	2	no	—
164	C₂³×C₇₉	—	2	2	no	—
165	C₂³×C₇₉	—	2	2	no	—
166	C₂³×C₇₉	—	2	2	no	—
167	C₂³×C₇₉	—	2	2	no	—
168	C₂³×C₇₉	—	2	2	no	—
169	C₂³×C₇₉	—	2	2	no	—
170	C₂³×C₇₉	—	2	2	no	—
171	C₂³×C₇₉	—	4	2	no	—
172	C₂³×C₇₉	—	4	2	no	—
173	C₂³×C₇₉	—	4	1	no	—
174	C₂³×C₇₉	—	4	1	no	—
175	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
176	Q₈×C₇₉	—	8	4	no	—
177	D₄×C₇₉	—	2	2	no	—
178	D₄×C₇₉	—	2	2	no	—
179	D₄×C₇₉	—	4	4	no	—
180	D₄×C₇₉	—	4	2	no	—
181	D₄×C₇₉	—	8	8	no	—
182	C₂×C₄×C₇₉	—	2	2	no	—
183	C₂×C₄×C₇₉	—	2	1	no	—
184	C₂×C₄×C₇₉	—	2	1	no	—
185	C₂×C₄×C₇₉	—	2	2	no	—
186	C₂×C₄×C₇₉	—	2	2	no	—
187	C₂×C₄×C₇₉	—	2	4	no	—
188	C₂×C₄×C₇₉	—	2	2	no	—
189	C₂×C₄×C₇₉	—	2	2	no	—
190	C₂×C₄×C₇₉	—	4	8	no	—
191	C₂×C₄×C₇₉	—	4	2	no	—
192	C₂×C₄×C₇₉	—	4	2	no	—
193	C₂×C₄×C₇₉	—	4	2	no	—
194	C₂×C₄×C₇₉	—	4	2	no	—
195	C₂×C₄×C₇₉	—	4	2	no	—
196	C₂×C₄×C₇₉	—	4	2	no	—
197	C₂×C₄×C₇₉	—	4	2	no	—
198	C₂×C₄×C₇₉	—	4	1	no	—
199	C₂×C₄×C₇₉	—	4	1	no	—
200	C₂×C₄×C₇₉	—	4	2	no	—
201	C₂×C₄×C₇₉	—	4	2	no	—
202	C₂×C₄×C₇₉	—	4	2	no	—
203	C₂×C₄×C₇₉	—	4	2	no	—
204	C₂×C₄×C₇₉	—	4	1	no	—
205	C₂×C₄×C₇₉	—	4	1	no	—
206	C₂×C₄×C₇₉	#120	1	2	yes	—
207	C₂×C₄×C₇₉	#120	1	2	yes	—
208	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
209	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
210	C₂×C₄×C₇₉	C₂×#41	1	2	yes	—
211	C₂×C₄×C₇₉	2₋¹⁺⁴	1	2	yes	—
212	C₈×C₇₉	—	2	4	no	—
213	C₈×C₇₉	—	4	1	no	—
214	C₈×C₇₉	—	4	1	no	—
215	C₂²×C₇₉	—	4	2	no	—
216	C₂²×C₇₉	—	4	2	no	—
217	C₂²×C₇₉	—	4	2	no	—
218	C₂²×C₇₉	—	4	2	no	—
219	C₂²×C₇₉	—	4	2	no	—
220	C₂²×C₇₉	—	4	2	no	—
221	C₂²×C₇₉	—	4	2	no	—
222	C₂²×C₇₉	—	4	2	no	—
223	C₂²×C₇₉	—	4	2	no	—
224	C₂²×C₇₉	—	4	2	no	—
225	C₂²×C₇₉	—	8	2	no	—
226	C₂²×C₇₉	—	8	2	no	—
227	C₂²×C₇₉	C₂×#120	1	1	yes	characteristic
228	C₂²×C₇₉	#547	1	2	yes	—
229	C₂²×C₇₉	#575	1	2	yes	—
230	C₂²×C₇₉	#576	1	1	yes	characteristic
231	C₂²×C₇₉	#577	1	1	yes	characteristic
232	C₄×C₇₉	—	2	2	no	—
233	C₄×C₇₉	—	2	2	no	—
234	C₄×C₇₉	—	4	2	no	—
235	C₄×C₇₉	—	4	2	no	—
236	C₄×C₇₉	—	4	4	no	—
237	C₄×C₇₉	—	8	2	no	—
238	C₄×C₇₉	—	8	1	no	—
239	C₄×C₇₉	—	8	1	no	—
240	C₄×C₇₉	#532	1	1	yes	characteristic
241	C₄×C₇₉	#536	1	1	yes	characteristic
242	C₄×C₇₉	#548	1	2	yes	—
243	#25710	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
244	C₂×C₇₉	—	8	2	no	—
245	C₂×C₇₉	—	8	2	no	—
246	C₂×C₇₉	#2432	1	1	yes	characteristic
247	C₂×C₇₉	#3005	1	1	yes	characteristic
248	C₂×C₇₉	#3012	1	1	yes	characteristic
249	C₂×C₇₉	#3347	1	2	yes	—
250	C₂×C₇₉	#3348	1	2	yes	—
251	C₂×#555	C₂×C₇₉	1	1	yes	characteristic
252	C₂×#501	C₂×C₇₉	1	1	yes	characteristic, complemented
253	C₂×#478	C₂×C₇₉	1	1	yes	characteristic, complemented
254	#2562	C₂×C₇₉	1	1	yes	characteristic, complemented
255	#2034	C₂×C₇₉	1	2	yes	complemented
256	#2033	C₂×C₇₉	1	2	yes	complemented
257	#1988	C₂×C₇₉	1	1	yes	characteristic, complemented
258	#1955	C₂×C₇₉	1	1	yes	characteristic, complemented
259	#1854	C₂×C₇₉	1	2	yes	complemented
260	#1854	C₂×C₇₉	1	2	yes	complemented
261	#1762	C₂×C₇₉	1	1	yes	characteristic, complemented
262	C₇₉	#25710	1	1	yes	characteristic, direct product factor, Sylow
263	#555	—	2	4	no	—
264	#555	—	2	4	no	—
265	C₂×C₄⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic
266	C₂×#125	C₂²×C₇₉	1	1	yes	characteristic
267	C₂×#124	—	2	2	no	—
268	C₂×#121	—	2	1	no	—
269	C₂×#121	C₂²×C₇₉	1	2	yes	—
270	C₂×C₄×D₄	C₂²×C₇₉	1	1	yes	characteristic
271	C₂×C₄×D₄	C₂²×C₇₉	1	1	yes	characteristic
272	C₂×#117	—	2	1	no	—
273	C₂×#117	C₂²×C₇₉	1	2	yes	—
274	#501	—	2	4	no	—
275	#478	—	2	4	no	—
276	C₂×#107	C₂²×C₇₉	1	1	yes	characteristic
277	C₂×#107	C₂²×C₇₉	1	2	yes	—
278	C₂×#106	C₂²×C₇₉	1	1	yes	characteristic
279	C₂×#106	C₂²×C₇₉	1	2	yes	—
280	C₂×C₄⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
281	C₂×#102	C₂²×C₇₉	1	1	yes	characteristic
282	C₂×#102	C₂²×C₇₉	1	1	yes	characteristic
283	C₂×#102	C₂²×C₇₉	1	2	yes	—
284	C₂×C₂²⋊C₈	C₂²×C₇₉	1	2	yes	—
285	C₂×C₂²⋊C₈	C₂²×C₇₉	1	2	yes	—
286	C₂×#97	C₂²×C₇₉	1	1	yes	characteristic
287	#400	—	2	1	no	—
288	#394	—	2	1	no	—
289	#388	—	2	2	no	—
290	#380	C₂²×C₇₉	1	2	yes	—
291	#380	C₂²×C₇₉	1	2	yes	—
292	C₄×C₄⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
293	#340	C₂²×C₇₉	1	2	yes	—
294	#340	C₂²×C₇₉	1	2	yes	—
295	#340	C₂²×C₇₉	1	2	yes	—
296	C₂²×Q₈	—	2	1	no	—
297	C₂²×D₄	—	2	2	no	—
298	C₂²×D₄	D₄×C₇₉	1	1	yes	characteristic
299	C₂²×D₄	C₂³×C₇₉	1	1	yes	characteristic
300	C₂³×C₄	—	2	1	no	—
301	C₂³×C₄	C₂³×C₇₉	1	2	yes	—
302	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
303	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
304	C₂²×C₈	C₂³×C₇₉	1	2	yes	—
305	C₄⋊Q₈	—	2	2	no	—
306	C₄⋊Q₈	D₄×C₇₉	1	4	yes	—
307	#125	—	2	2	no	—
308	#125	—	2	2	no	—
309	#124	—	2	16	no	—
310	#121	—	2	8	no	—
311	#121	—	2	4	no	—
312	#121	—	2	4	no	—
313	C₄×D₄	—	2	2	no	—
314	C₄×D₄	—	2	2	no	—
315	C₄×D₄	—	2	2	no	—
316	C₄×D₄	D₄×C₇₉	1	4	yes	—
317	#117	—	2	8	no	—
318	#117	—	2	4	no	—
319	#117	—	2	4	no	—
320	C₂×C₄⋊C₄	—	2	1	no	—
321	C₂×C₄⋊C₄	—	2	1	no	—
322	C₂×C₄⋊C₄	—	2	1	no	—
323	C₂×C₄⋊C₄	D₄×C₇₉	1	1	yes	characteristic
324	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
325	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
326	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
327	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
328	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
329	C₂×C₂²⋊C₄	—	2	2	no	—
330	C₂×C₂²⋊C₄	—	2	2	no	—
331	C₂×C₂²⋊C₄	—	2	1	no	—
332	C₂×C₂²⋊C₄	—	2	2	no	—
333	C₂×C₂²⋊C₄	—	2	2	no	—
334	C₂×C₂²⋊C₄	D₄×C₇₉	1	2	yes	—
335	C₂×C₄²	—	2	2	no	—
336	C₂×C₄²	—	2	1	no	—
337	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
338	#107	—	2	2	no	—
339	#107	—	2	4	no	—
340	#106	—	2	2	no	—
341	#106	—	2	4	no	—
342	C₄⋊C₈	—	2	2	no	—
343	#102	—	2	2	no	—
344	#102	—	2	2	no	—
345	#102	—	2	4	no	—
346	C₂²⋊C₈	—	2	4	no	—
347	C₂²⋊C₈	—	2	4	no	—
348	#97	—	2	2	no	—
349	#95	—	2	1	no	—
350	#95	—	2	2	no	—
351	#95	—	2	2	no	—
352	C₂⁴	—	2	1	no	—
353	C₂⁴	C₂×D₄×C₇₉	1	2	yes	—
354	C₂×Q₈	—	2	4	no	—
355	C₂×Q₈	—	8	1	no	—
356	C₂×Q₈	—	8	1	no	—
357	C₂×D₄	—	2	8	no	—
358	C₂×D₄	—	2	2	no	—
359	C₂×D₄	—	2	1	no	—
360	C₂×D₄	—	2	2	no	—
361	C₂×D₄	—	2	2	no	—
362	C₂×D₄	—	4	2	no	—
363	C₂×D₄	—	8	2	no	—
364	C₂×D₄	—	8	2	no	—
365	C₂×D₄	C₂×D₄×C₇₉	1	2	yes	—
366	C₂²×C₄	—	2	1	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	2	4	no	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	2	1	no	—
377	C₂²×C₄	—	2	1	no	—
378	C₂²×C₄	—	4	4	no	—
379	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
380	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
381	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
382	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
383	C₂×C₈	—	2	2	no	—
384	C₂×C₈	—	2	2	no	—
385	C₂×C₈	—	2	1	no	—
386	C₂×C₈	—	2	1	no	—
387	C₂×C₈	—	2	2	no	—
388	C₂×C₈	—	2	2	no	—
389	C₂×C₈	#41×C₇₉	1	4	yes	—
390	C₄⋊C₄	—	2	4	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	2	1	no	—
393	C₄⋊C₄	—	2	2	no	—
394	C₄⋊C₄	—	2	1	no	—
395	C₄⋊C₄	—	2	1	no	—
396	C₄⋊C₄	—	2	1	no	—
397	C₄⋊C₄	—	2	1	no	—
398	C₄⋊C₄	—	2	2	no	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	4	2	no	—
401	C₄⋊C₄	—	4	2	no	—
402	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
403	C₄⋊C₄	C₂×D₄×C₇₉	1	4	yes	—
404	C₂²⋊C₄	—	2	8	no	—
405	C₂²⋊C₄	—	2	8	no	—
406	C₂²⋊C₄	—	2	4	no	—
407	C₂²⋊C₄	—	2	4	no	—
408	C₂²⋊C₄	—	4	4	no	—
409	C₂²⋊C₄	—	8	2	no	—
410	C₄²	—	2	8	no	—
411	C₄²	—	8	1	no	—
412	C₄²	C₂×D₄×C₇₉	1	2	yes	—
413	C₄²	C₂×D₄×C₇₉	1	2	yes	—
414	C₂³	—	2	2	no	—
415	C₂³	—	2	2	no	—
416	C₂³	—	2	2	no	—
417	C₂³	—	2	2	no	—
418	C₂³	—	2	2	no	—
419	C₂³	—	2	2	no	—
420	C₂³	—	2	2	no	—
421	C₂³	—	2	2	no	—
422	C₂³	—	4	2	no	—
423	C₂³	—	4	2	no	—
424	C₂³	—	4	1	no	—
425	C₂³	—	4	1	no	—
426	C₂³	C₂²×D₄×C₇₉	1	1	yes	characteristic
427	Q₈	—	8	4	no	—
428	D₄	—	2	2	no	—
429	D₄	—	2	2	no	—
430	D₄	—	4	4	no	—
431	D₄	—	4	2	no	—
432	D₄	—	8	8	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	4	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	4	8	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	1	no	—
450	C₂×C₄	—	4	1	no	—
451	C₂×C₄	—	4	2	no	—
452	C₂×C₄	—	4	2	no	—
453	C₂×C₄	—	4	2	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	—	4	1	no	—
456	C₂×C₄	—	4	1	no	—
457	C₂×C₄	#120×C₇₉	1	2	yes	—
458	C₂×C₄	#120×C₇₉	1	2	yes	—
459	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
460	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
461	C₂×C₄	C₂×#41×C₇₉	1	2	yes	—
462	C₂×C₄	2₋¹⁺⁴×C₇₉	1	2	yes	—
463	C₈	—	2	4	no	—
464	C₈	—	4	1	no	—
465	C₈	—	4	1	no	—
466	C₂²	—	4	2	no	—
467	C₂²	—	4	2	no	—
468	C₂²	—	4	2	no	—
469	C₂²	—	4	2	no	—
470	C₂²	—	4	2	no	—
471	C₂²	—	4	2	no	—
472	C₂²	—	4	2	no	—
473	C₂²	—	4	2	no	—
474	C₂²	—	4	2	no	—
475	C₂²	—	4	2	no	—
476	C₂²	—	8	2	no	—
477	C₂²	—	8	2	no	—
478	C₂²	C₂×#120×C₇₉	1	1	yes	characteristic
479	C₂²	#547×C₇₉	1	2	yes	—
480	C₂²	#575×C₇₉	1	2	yes	—
481	C₂²	#576×C₇₉	1	1	yes	characteristic
482	C₂²	#577×C₇₉	1	1	yes	characteristic
483	C₄	—	2	2	no	—
484	C₄	—	2	2	no	—
485	C₄	—	4	2	no	—
486	C₄	—	4	2	no	—
487	C₄	—	4	4	no	—
488	C₄	—	8	2	no	—
489	C₄	—	8	1	no	—
490	C₄	—	8	1	no	—
491	C₄	#532×C₇₉	1	1	yes	characteristic
492	C₄	#536×C₇₉	1	1	yes	characteristic
493	C₄	#548×C₇₉	1	2	yes	—
494	C₂	—	8	2	no	—
495	C₂	—	8	2	no	—
496	C₂	C₇₉×#2432	1	1	yes	characteristic
497	C₂	C₇₉×#3005	1	1	yes	characteristic
498	C₂	C₇₉×#3012	1	1	yes	characteristic
499	C₂	C₇₉×#3347	1	2	yes	—
500	C₂	C₇₉×#3348	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₉
prime radical	C₂×#555×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×#478×C₇₉	C₂	semidirect
4. C₇₉×#2562	C₂	semidirect
5. C₇₉×#2034	C₂	semidirect
6. C₇₉×#2033	C₂	semidirect
7. C₇₉×#1988	C₂	semidirect
8. C₇₉×#1955	C₂	semidirect
9. C₇₉×#1854	C₂	semidirect
10. C₇₉×#1854	C₂	semidirect
11. C₇₉×#1762	C₂	semidirect
243. #25710	C₇₉	direct (N × H)
252. C₂×#501	C₂×C₇₉	semidirect
253. C₂×#478	C₂×C₇₉	semidirect
254. #2562	C₂×C₇₉	semidirect
255. #2034	C₂×C₇₉	semidirect
256. #2033	C₂×C₇₉	semidirect
257. #1988	C₂×C₇₉	semidirect
258. #1955	C₂×C₇₉	semidirect
259. #1854	C₂×C₇₉	semidirect
260. #1854	C₂×C₇₉	semidirect
261. #1762	C₂×C₇₉	semidirect
262. C₇₉	#25710	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×#555×C₇₉	2
C₂×#501×C₇₉	2
C₂×#478×C₇₉	2
C₇₉×#2562	2
C₇₉×#2034	2
C₇₉×#2033	2
C₇₉×#1988	2
C₇₉×#1955	2
C₇₉×#1854	2
C₇₉×#1762	2
#25710	79

Subgroups — C79×#25710 #34137399

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#25710 #34137399