Subgroups — C₇₉×#24526 #34136215

Order 20224.

1280 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#447×C₇₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×#102×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₉×#2501	C₂	1	1	yes	maximal, characteristic, complemented
4	D₄×C₂²⋊C₄×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₉×#2071	C₂	1	2	yes	maximal, complemented
6	C₇₉×#2054	C₂	1	2	yes	maximal, complemented
7	C₇₉×#1893	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₉×#1879	C₂	1	2	yes	maximal, complemented
9	C₇₉×#1850	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₉×#1823	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₉×#1802	C₂	1	2	yes	maximal, complemented
12	C₂³×D₄×C₇₉	C₂²	1	1	yes	characteristic
13	C₂²×D₈×C₇₉	C₂²	1	1	yes	characteristic
14	C₂²×D₈×C₇₉	C₂²	1	1	yes	characteristic
15	C₂³×C₈×C₇₉	C₂²	1	1	yes	characteristic
16	C₂×#123×C₇₉	—	2	1	no	—
17	C₂×#123×C₇₉	—	2	1	no	—
18	C₂×#121×C₇₉	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₄×C₇₉	C₂²	1	2	yes	—
20	C₂²×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
21	C₂²×C₂²⋊C₄×C₇₉	—	2	1	no	—
22	#447×C₇₉	—	2	4	no	—
23	C₂×C₄⋊C₈×C₇₉	C₂²	1	2	yes	complemented
24	C₂×#102×C₇₉	—	2	4	no	—
25	C₂×#102×C₇₉	C₂²	1	2	yes	—
26	C₂×#102×C₇₉	C₂²	1	1	yes	characteristic
27	C₂×#102×C₇₉	C₂²	1	2	yes	—
28	C₂×#102×C₇₉	C₂²	1	1	yes	characteristic
29	C₂×#102×C₇₉	C₂²	1	2	yes	complemented
30	C₂×C₂²⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
31	#399×C₇₉	—	2	2	no	—
32	#390×C₇₉	C₂²	1	2	yes	—
33	#390×C₇₉	C₂²	1	2	yes	complemented
34	#386×C₇₉	—	2	2	no	—
35	#384×C₇₉	C₂²	1	2	yes	complemented
36	#380×C₇₉	C₂²	1	1	yes	characteristic
37	#379×C₇₉	—	2	1	no	—
38	C₄×C₂²⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
39	#340×C₇₉	C₂²	1	2	yes	complemented
40	#340×C₇₉	C₂²	1	2	yes	complemented
41	#340×C₇₉	C₂²	1	2	yes	complemented
42	#336×C₇₉	C₂²	1	2	yes	complemented
43	C₂⁵×C₇₉	—	2	1	no	—
44	C₂²×D₄×C₇₉	—	2	4	no	—
45	C₂²×D₄×C₇₉	—	2	1	no	—
46	C₂²×D₄×C₇₉	—	2	1	no	—
47	C₂²×D₄×C₇₉	—	2	2	no	—
48	C₂²×D₄×C₇₉	—	4	2	no	—
49	C₂²×D₄×C₇₉	D₄	1	4	yes	—
50	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
51	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
52	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
53	C₂³×C₄×C₇₉	—	2	1	no	—
54	C₂³×C₄×C₇₉	—	2	2	no	—
55	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
56	C₂×D₈×C₇₉	—	2	2	no	—
57	C₂×D₈×C₇₉	—	2	2	no	—
58	C₂×D₈×C₇₉	—	2	4	no	—
59	C₂×D₈×C₇₉	—	4	2	no	—
60	C₂²×C₈×C₇₉	—	2	2	no	—
61	C₂²×C₈×C₇₉	—	4	2	no	—
62	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₇₉	C₂³	1	2	yes	—
64	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
65	#123×C₇₉	—	4	4	no	—
66	#123×C₇₉	—	4	4	no	—
67	#121×C₇₉	—	2	2	no	—
68	#121×C₇₉	—	2	2	no	—
69	C₄×D₄×C₇₉	—	2	4	no	—
70	C₄×D₄×C₇₉	—	4	2	no	—
71	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
72	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
73	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
74	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
75	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
76	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
77	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
78	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
79	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
80	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
81	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
82	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
83	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
84	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
85	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
86	C₂×C₂²⋊C₄×C₇₉	—	4	4	no	—
87	C₂×C₂²⋊C₄×C₇₉	D₄	1	1	yes	characteristic
88	C₂×C₂²⋊C₄×C₇₉	D₄	1	1	yes	characteristic
89	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
90	C₄⋊C₈×C₇₉	—	4	2	no	—
91	#102×C₇₉	—	2	2	no	—
92	#102×C₇₉	—	2	2	no	—
93	#102×C₇₉	—	2	4	no	—
94	#102×C₇₉	—	2	4	no	—
95	#102×C₇₉	—	4	2	no	—
96	C₂²⋊C₈×C₇₉	—	2	2	no	—
97	#95×C₇₉	—	2	1	no	—
98	#95×C₇₉	D₄	1	2	yes	—
99	C₂⁴×C₇₉	—	2	1	no	—
100	C₂⁴×C₇₉	—	2	1	no	—
101	C₂⁴×C₇₉	—	2	4	no	—
102	C₂⁴×C₇₉	—	2	1	no	—
103	C₂⁴×C₇₉	—	4	4	no	—
104	C₂⁴×C₇₉	—	4	2	no	—
105	C₂⁴×C₇₉	—	4	2	no	—
106	C₂⁴×C₇₉	—	8	2	no	—
107	C₂⁴×C₇₉	C₂×D₄	1	1	yes	characteristic
108	C₂×D₄×C₇₉	—	2	8	no	—
109	C₂×D₄×C₇₉	—	2	4	no	—
110	C₂×D₄×C₇₉	—	2	1	no	—
111	C₂×D₄×C₇₉	—	2	1	no	—
112	C₂×D₄×C₇₉	—	2	2	no	—
113	C₂×D₄×C₇₉	—	2	1	no	—
114	C₂×D₄×C₇₉	—	2	1	no	—
115	C₂×D₄×C₇₉	—	2	2	no	—
116	C₂×D₄×C₇₉	—	2	2	no	—
117	C₂×D₄×C₇₉	—	2	2	no	—
118	C₂×D₄×C₇₉	—	2	2	no	—
119	C₂×D₄×C₇₉	—	4	4	no	—
120	C₂×D₄×C₇₉	—	4	8	no	—
121	C₂×D₄×C₇₉	—	4	4	no	—
122	C₂×D₄×C₇₉	—	4	2	no	—
123	C₂×D₄×C₇₉	—	4	2	no	—
124	C₂×D₄×C₇₉	—	4	2	no	—
125	C₂×D₄×C₇₉	C₂×D₄	1	2	yes	—
126	C₂×D₄×C₇₉	C₂×D₄	1	2	yes	—
127	C₂×D₄×C₇₉	#41	1	4	yes	—
128	C₂²×C₄×C₇₉	—	2	2	no	—
129	C₂²×C₄×C₇₉	—	2	2	no	—
130	C₂²×C₄×C₇₉	—	2	2	no	—
131	C₂²×C₄×C₇₉	—	2	2	no	—
132	C₂²×C₄×C₇₉	—	2	1	no	—
133	C₂²×C₄×C₇₉	—	4	4	no	—
134	C₂²×C₄×C₇₉	—	4	2	no	—
135	C₂²×C₄×C₇₉	—	4	2	no	—
136	C₂²×C₄×C₇₉	—	4	2	no	—
137	C₂²×C₄×C₇₉	—	4	4	no	—
138	C₂²×C₄×C₇₉	—	8	2	no	—
139	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
140	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
142	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
143	C₂²×C₄×C₇₉	#41	1	2	yes	—
144	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
145	D₈×C₇₉	—	4	4	no	—
146	D₈×C₇₉	—	4	4	no	—
147	C₂×C₈×C₇₉	—	2	1	no	—
148	C₂×C₈×C₇₉	—	2	1	no	—
149	C₂×C₈×C₇₉	—	2	2	no	—
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	—	4	4	no	—
155	C₄⋊C₄×C₇₉	—	2	2	no	—
156	C₄⋊C₄×C₇₉	—	2	1	no	—
157	C₄⋊C₄×C₇₉	—	2	2	no	—
158	C₄⋊C₄×C₇₉	—	2	2	no	—
159	C₄⋊C₄×C₇₉	—	2	1	no	—
160	C₄⋊C₄×C₇₉	—	2	2	no	—
161	C₄⋊C₄×C₇₉	—	4	4	no	—
162	C₄⋊C₄×C₇₉	—	4	2	no	—
163	C₄⋊C₄×C₇₉	—	4	4	no	—
164	C₂²⋊C₄×C₇₉	—	2	2	no	—
165	C₂²⋊C₄×C₇₉	—	4	4	no	—
166	C₂²⋊C₄×C₇₉	—	4	4	no	—
167	C₂²⋊C₄×C₇₉	—	4	2	no	—
168	C₂²⋊C₄×C₇₉	—	4	2	no	—
169	C₂²⋊C₄×C₇₉	—	4	4	no	—
170	C₂²⋊C₄×C₇₉	—	4	4	no	—
171	C₂²⋊C₄×C₇₉	—	8	2	no	—
172	C₂²⋊C₄×C₇₉	D₈	1	4	yes	complemented
173	C₄²×C₇₉	—	2	2	no	—
174	C₄²×C₇₉	—	2	2	no	—
175	C₂³×C₇₉	—	2	2	no	—
176	C₂³×C₇₉	—	2	2	no	—
177	C₂³×C₇₉	—	2	2	no	—
178	C₂³×C₇₉	—	2	4	no	—
179	C₂³×C₇₉	—	2	2	no	—
180	C₂³×C₇₉	—	4	8	no	—
181	C₂³×C₇₉	—	4	1	no	—
182	C₂³×C₇₉	—	4	1	no	—
183	C₂³×C₇₉	—	4	2	no	—
184	C₂³×C₇₉	—	4	2	no	—
185	C₂³×C₇₉	—	4	1	no	—
186	C₂³×C₇₉	—	4	1	no	—
187	C₂³×C₇₉	—	4	2	no	—
188	C₂³×C₇₉	—	4	8	no	—
189	C₂³×C₇₉	—	4	1	no	—
190	C₂³×C₇₉	—	4	2	no	—
191	C₂³×C₇₉	—	4	1	no	—
192	C₂³×C₇₉	—	4	1	no	—
193	C₂³×C₇₉	—	4	2	no	—
194	C₂³×C₇₉	—	8	4	no	—
195	C₂³×C₇₉	—	8	8	no	—
196	C₂³×C₇₉	—	8	8	no	—
197	C₂³×C₇₉	#121	1	2	yes	—
198	C₂³×C₇₉	C₂×D₈	1	2	yes	—
199	C₂³×C₇₉	AGL(1,ℤ/8)	1	2	yes	—
200	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
201	D₄×C₇₉	—	2	2	no	—
202	D₄×C₇₉	—	2	2	no	—
203	D₄×C₇₉	—	2	2	no	—
204	D₄×C₇₉	—	2	4	no	—
205	D₄×C₇₉	—	4	8	no	—
206	D₄×C₇₉	—	4	1	no	—
207	D₄×C₇₉	—	4	1	no	—
208	D₄×C₇₉	—	4	2	no	—
209	D₄×C₇₉	—	4	2	no	—
210	D₄×C₇₉	—	8	4	no	—
211	D₄×C₇₉	#123	1	4	yes	complemented
212	C₂×C₄×C₇₉	—	2	2	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	—	2	2	no	—
217	C₂×C₄×C₇₉	—	2	4	no	—
218	C₂×C₄×C₇₉	—	2	2	no	—
219	C₂×C₄×C₇₉	—	2	2	no	—
220	C₂×C₄×C₇₉	—	2	2	no	—
221	C₂×C₄×C₇₉	—	4	1	no	—
222	C₂×C₄×C₇₉	—	4	2	no	—
223	C₂×C₄×C₇₉	—	4	2	no	—
224	C₂×C₄×C₇₉	—	4	2	no	—
225	C₂×C₄×C₇₉	—	4	2	no	—
226	C₂×C₄×C₇₉	—	4	1	no	—
227	C₂×C₄×C₇₉	—	4	2	no	—
228	C₂×C₄×C₇₉	—	4	1	no	—
229	C₂×C₄×C₇₉	—	4	2	no	—
230	C₂×C₄×C₇₉	—	8	8	no	—
231	C₂×C₄×C₇₉	—	8	4	no	—
232	C₂×C₄×C₇₉	#121	1	2	yes	—
233	C₂×C₄×C₇₉	C₂×D₈	1	4	yes	—
234	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
235	C₂×C₄×C₇₉	C₂×#41	1	2	yes	—
236	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
237	C₂×C₄×C₇₉	H(5,𝔽₂)	1	2	yes	—
238	C₈×C₇₉	—	4	1	no	—
239	C₈×C₇₉	—	4	2	no	—
240	C₈×C₇₉	—	4	1	no	—
241	C₂²×C₇₉	—	2	2	no	—
242	C₂²×C₇₉	—	2	4	no	—
243	C₂²×C₇₉	—	2	2	no	—
244	C₂²×C₇₉	—	2	4	no	—
245	C₂²×C₇₉	—	2	4	no	—
246	C₂²×C₇₉	—	4	2	no	—
247	C₂²×C₇₉	—	4	4	no	—
248	C₂²×C₇₉	—	4	2	no	—
249	C₂²×C₇₉	—	4	4	no	—
250	C₂²×C₇₉	—	4	2	no	—
251	C₂²×C₇₉	—	4	2	no	—
252	C₂²×C₇₉	—	4	2	no	—
253	C₂²×C₇₉	—	8	16	no	—
254	C₂²×C₇₉	—	8	2	no	—
255	C₂²×C₇₉	—	8	2	no	—
256	C₂²×C₇₉	—	8	1	no	—
257	C₂²×C₇₉	—	8	1	no	—
258	C₂²×C₇₉	—	8	2	no	—
259	C₂²×C₇₉	—	8	1	no	—
260	C₂²×C₇₉	—	8	2	no	—
261	C₂²×C₇₉	#459	1	4	yes	—
262	C₂²×C₇₉	C₂×#121	1	1	yes	characteristic
263	C₂²×C₇₉	#546	1	2	yes	—
264	C₂²×C₇₉	C₂²×D₈	1	1	yes	characteristic
265	C₂²×C₇₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
266	C₂²×C₇₉	#577	1	2	yes	—
267	C₄×C₇₉	—	2	2	no	—
268	C₄×C₇₉	—	2	4	no	—
269	C₄×C₇₉	—	4	2	no	—
270	C₄×C₇₉	—	8	2	no	—
271	C₄×C₇₉	—	8	1	no	—
272	C₄×C₇₉	—	8	2	no	—
273	C₄×C₇₉	C₂×#123	1	1	yes	characteristic
274	C₄×C₇₉	#534	1	1	yes	characteristic
275	C₄×C₇₉	#551	1	2	yes	—
276	#24526	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
277	C₂×C₇₉	—	2	4	no	—
278	C₂×C₇₉	—	4	4	no	—
279	C₂×C₇₉	—	8	2	no	—
280	C₂×C₇₉	—	16	1	no	—
281	C₂×C₇₉	#2412	1	1	yes	characteristic
282	C₂×C₇₉	C₂×#459	1	1	yes	characteristic
283	C₂×C₇₉	#3042	1	1	yes	characteristic
284	C₂×C₇₉	#3294	1	2	yes	—
285	C₂×C₇₉	#3306	1	2	yes	—
286	C₂×#447	C₂×C₇₉	1	1	yes	characteristic
287	C₂²×#102	C₂×C₇₉	1	1	yes	characteristic, complemented
288	#2501	C₂×C₇₉	1	1	yes	characteristic, complemented
289	D₄×C₂²⋊C₄	C₂×C₇₉	1	1	yes	characteristic, complemented
290	#2071	C₂×C₇₉	1	2	yes	complemented
291	#2054	C₂×C₇₉	1	2	yes	complemented
292	#1893	C₂×C₇₉	1	1	yes	characteristic, complemented
293	#1879	C₂×C₇₉	1	2	yes	complemented
294	#1850	C₂×C₇₉	1	1	yes	characteristic, complemented
295	#1823	C₂×C₇₉	1	1	yes	characteristic, complemented
296	#1802	C₂×C₇₉	1	2	yes	complemented
297	C₇₉	#24526	1	1	yes	characteristic, direct product factor, Sylow
298	C₂³×D₄	C₂²×C₇₉	1	1	yes	characteristic
299	C₂²×D₈	C₂²×C₇₉	1	1	yes	characteristic
300	C₂²×D₈	C₂²×C₇₉	1	1	yes	characteristic
301	C₂³×C₈	C₂²×C₇₉	1	1	yes	characteristic
302	C₂×#123	—	2	1	no	—
303	C₂×#123	—	2	1	no	—
304	C₂×#121	C₂²×C₇₉	1	1	yes	characteristic
305	C₂×C₄×D₄	C₂²×C₇₉	1	2	yes	—
306	C₂²×C₄⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
307	C₂²×C₂²⋊C₄	—	2	1	no	—
308	#447	—	2	4	no	—
309	C₂×C₄⋊C₈	C₂²×C₇₉	1	2	yes	complemented
310	C₂×#102	—	2	4	no	—
311	C₂×#102	C₂²×C₇₉	1	2	yes	—
312	C₂×#102	C₂²×C₇₉	1	1	yes	characteristic
313	C₂×#102	C₂²×C₇₉	1	2	yes	—
314	C₂×#102	C₂²×C₇₉	1	1	yes	characteristic
315	C₂×#102	C₂²×C₇₉	1	2	yes	complemented
316	C₂×C₂²⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
317	#399	—	2	2	no	—
318	#390	C₂²×C₇₉	1	2	yes	—
319	#390	C₂²×C₇₉	1	2	yes	complemented
320	#386	—	2	2	no	—
321	#384	C₂²×C₇₉	1	2	yes	complemented
322	#380	C₂²×C₇₉	1	1	yes	characteristic
323	#379	—	2	1	no	—
324	C₄×C₂²⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
325	#340	C₂²×C₇₉	1	2	yes	complemented
326	#340	C₂²×C₇₉	1	2	yes	complemented
327	#340	C₂²×C₇₉	1	2	yes	complemented
328	#336	C₂²×C₇₉	1	2	yes	complemented
329	C₂⁵	—	2	1	no	—
330	C₂²×D₄	—	2	4	no	—
331	C₂²×D₄	—	2	1	no	—
332	C₂²×D₄	—	2	1	no	—
333	C₂²×D₄	—	2	2	no	—
334	C₂²×D₄	—	4	2	no	—
335	C₂²×D₄	D₄×C₇₉	1	4	yes	—
336	C₂²×D₄	C₂³×C₇₉	1	1	yes	characteristic
337	C₂²×D₄	C₂³×C₇₉	1	1	yes	characteristic
338	C₂²×D₄	C₂³×C₇₉	1	1	yes	characteristic
339	C₂³×C₄	—	2	1	no	—
340	C₂³×C₄	—	2	2	no	—
341	C₂³×C₄	C₂³×C₇₉	1	1	yes	characteristic
342	C₂×D₈	—	2	2	no	—
343	C₂×D₈	—	2	2	no	—
344	C₂×D₈	—	2	4	no	—
345	C₂×D₈	—	4	2	no	—
346	C₂²×C₈	—	2	2	no	—
347	C₂²×C₈	—	4	2	no	—
348	C₂²×C₈	C₂³×C₇₉	1	2	yes	—
349	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
350	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
351	#123	—	4	4	no	—
352	#123	—	4	4	no	—
353	#121	—	2	2	no	—
354	#121	—	2	2	no	—
355	C₄×D₄	—	2	4	no	—
356	C₄×D₄	—	4	2	no	—
357	C₂×C₄⋊C₄	—	2	2	no	—
358	C₂×C₄⋊C₄	—	2	2	no	—
359	C₂×C₄⋊C₄	—	2	1	no	—
360	C₂×C₄⋊C₄	—	2	2	no	—
361	C₂×C₄⋊C₄	—	2	2	no	—
362	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
363	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
364	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
365	C₂×C₂²⋊C₄	—	2	1	no	—
366	C₂×C₂²⋊C₄	—	2	2	no	—
367	C₂×C₂²⋊C₄	—	2	2	no	—
368	C₂×C₂²⋊C₄	—	2	1	no	—
369	C₂×C₂²⋊C₄	—	2	2	no	—
370	C₂×C₂²⋊C₄	—	2	2	no	—
371	C₂×C₂²⋊C₄	—	2	2	no	—
372	C₂×C₂²⋊C₄	—	4	4	no	—
373	C₂×C₂²⋊C₄	D₄×C₇₉	1	1	yes	characteristic
374	C₂×C₂²⋊C₄	D₄×C₇₉	1	1	yes	characteristic
375	C₂×C₄²	C₂³×C₇₉	1	2	yes	—
376	C₄⋊C₈	—	4	2	no	—
377	#102	—	2	4	no	—
378	#102	—	2	4	no	—
379	#102	—	2	2	no	—
380	#102	—	2	2	no	—
381	#102	—	4	2	no	—
382	C₂²⋊C₈	—	2	2	no	—
383	#95	—	2	1	no	—
384	#95	D₄×C₇₉	1	2	yes	—
385	C₂⁴	—	2	1	no	—
386	C₂⁴	—	2	1	no	—
387	C₂⁴	—	2	4	no	—
388	C₂⁴	—	2	1	no	—
389	C₂⁴	—	4	4	no	—
390	C₂⁴	—	4	2	no	—
391	C₂⁴	—	4	2	no	—
392	C₂⁴	—	8	2	no	—
393	C₂⁴	C₂×D₄×C₇₉	1	1	yes	characteristic
394	C₂×D₄	—	2	8	no	—
395	C₂×D₄	—	2	4	no	—
396	C₂×D₄	—	2	1	no	—
397	C₂×D₄	—	2	1	no	—
398	C₂×D₄	—	2	2	no	—
399	C₂×D₄	—	2	1	no	—
400	C₂×D₄	—	2	1	no	—
401	C₂×D₄	—	2	2	no	—
402	C₂×D₄	—	2	2	no	—
403	C₂×D₄	—	2	2	no	—
404	C₂×D₄	—	2	2	no	—
405	C₂×D₄	—	4	4	no	—
406	C₂×D₄	—	4	8	no	—
407	C₂×D₄	—	4	4	no	—
408	C₂×D₄	—	4	2	no	—
409	C₂×D₄	—	4	2	no	—
410	C₂×D₄	—	4	2	no	—
411	C₂×D₄	C₂×D₄×C₇₉	1	2	yes	—
412	C₂×D₄	C₂×D₄×C₇₉	1	2	yes	—
413	C₂×D₄	#41×C₇₉	1	4	yes	—
414	C₂²×C₄	—	2	2	no	—
415	C₂²×C₄	—	2	2	no	—
416	C₂²×C₄	—	2	2	no	—
417	C₂²×C₄	—	2	2	no	—
418	C₂²×C₄	—	2	1	no	—
419	C₂²×C₄	—	4	4	no	—
420	C₂²×C₄	—	4	2	no	—
421	C₂²×C₄	—	4	2	no	—
422	C₂²×C₄	—	4	2	no	—
423	C₂²×C₄	—	4	4	no	—
424	C₂²×C₄	—	8	2	no	—
425	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
426	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
427	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
428	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
429	C₂²×C₄	#41×C₇₉	1	2	yes	—
430	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
431	D₈	—	4	4	no	—
432	D₈	—	4	4	no	—
433	C₂×C₈	—	2	1	no	—
434	C₂×C₈	—	2	1	no	—
435	C₂×C₈	—	2	2	no	—
436	C₂×C₈	—	2	2	no	—
437	C₂×C₈	—	2	2	no	—
438	C₂×C₈	—	2	2	no	—
439	C₂×C₈	—	2	2	no	—
440	C₂×C₈	—	4	4	no	—
441	C₄⋊C₄	—	2	2	no	—
442	C₄⋊C₄	—	2	1	no	—
443	C₄⋊C₄	—	2	2	no	—
444	C₄⋊C₄	—	2	2	no	—
445	C₄⋊C₄	—	2	1	no	—
446	C₄⋊C₄	—	2	2	no	—
447	C₄⋊C₄	—	4	4	no	—
448	C₄⋊C₄	—	4	2	no	—
449	C₄⋊C₄	—	4	4	no	—
450	C₂²⋊C₄	—	2	2	no	—
451	C₂²⋊C₄	—	4	4	no	—
452	C₂²⋊C₄	—	4	4	no	—
453	C₂²⋊C₄	—	4	2	no	—
454	C₂²⋊C₄	—	4	2	no	—
455	C₂²⋊C₄	—	4	4	no	—
456	C₂²⋊C₄	—	4	4	no	—
457	C₂²⋊C₄	—	8	2	no	—
458	C₂²⋊C₄	D₈×C₇₉	1	4	yes	complemented
459	C₄²	—	2	2	no	—
460	C₄²	—	2	2	no	—
461	C₂³	—	2	2	no	—
462	C₂³	—	2	2	no	—
463	C₂³	—	2	2	no	—
464	C₂³	—	2	4	no	—
465	C₂³	—	2	2	no	—
466	C₂³	—	4	8	no	—
467	C₂³	—	4	1	no	—
468	C₂³	—	4	1	no	—
469	C₂³	—	4	2	no	—
470	C₂³	—	4	8	no	—
471	C₂³	—	4	2	no	—
472	C₂³	—	4	1	no	—
473	C₂³	—	4	1	no	—
474	C₂³	—	4	2	no	—
475	C₂³	—	4	1	no	—
476	C₂³	—	4	2	no	—
477	C₂³	—	4	1	no	—
478	C₂³	—	4	1	no	—
479	C₂³	—	4	2	no	—
480	C₂³	—	8	4	no	—
481	C₂³	—	8	8	no	—
482	C₂³	—	8	8	no	—
483	C₂³	#121×C₇₉	1	2	yes	—
484	C₂³	C₂×D₈×C₇₉	1	2	yes	—
485	C₂³	AGL(1,ℤ/8)×C₇₉	1	2	yes	—
486	C₂³	C₂²×D₄×C₇₉	1	1	yes	characteristic
487	D₄	—	2	2	no	—
488	D₄	—	2	2	no	—
489	D₄	—	2	2	no	—
490	D₄	—	2	4	no	—
491	D₄	—	4	8	no	—
492	D₄	—	4	1	no	—
493	D₄	—	4	1	no	—
494	D₄	—	4	2	no	—
495	D₄	—	4	2	no	—
496	D₄	—	8	4	no	—
497	D₄	#123×C₇₉	1	4	yes	complemented
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	2	4	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	2	2	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	4	1	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	1	no	—
513	C₂×C₄	—	4	2	no	—
514	C₂×C₄	—	4	1	no	—
515	C₂×C₄	—	4	2	no	—
516	C₂×C₄	—	8	8	no	—
517	C₂×C₄	—	8	4	no	—
518	C₂×C₄	#121×C₇₉	1	2	yes	—
519	C₂×C₄	C₂×D₈×C₇₉	1	4	yes	—
520	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
521	C₂×C₄	C₂×#41×C₇₉	1	2	yes	—
522	C₂×C₄	C₂×#41×C₇₉	1	1	yes	characteristic
523	C₂×C₄	H(5,𝔽₂)×C₇₉	1	2	yes	—
524	C₈	—	4	1	no	—
525	C₈	—	4	2	no	—
526	C₈	—	4	1	no	—
527	C₂²	—	2	4	no	—
528	C₂²	—	2	2	no	—
529	C₂²	—	2	4	no	—
530	C₂²	—	2	2	no	—
531	C₂²	—	2	4	no	—
532	C₂²	—	4	2	no	—
533	C₂²	—	4	4	no	—
534	C₂²	—	4	2	no	—
535	C₂²	—	4	4	no	—
536	C₂²	—	4	2	no	—
537	C₂²	—	4	2	no	—
538	C₂²	—	4	2	no	—
539	C₂²	—	8	16	no	—
540	C₂²	—	8	2	no	—
541	C₂²	—	8	2	no	—
542	C₂²	—	8	1	no	—
543	C₂²	—	8	2	no	—
544	C₂²	—	8	1	no	—
545	C₂²	—	8	2	no	—
546	C₂²	—	8	1	no	—
547	C₂²	#459×C₇₉	1	4	yes	—
548	C₂²	C₂×#121×C₇₉	1	1	yes	characteristic
549	C₂²	#546×C₇₉	1	2	yes	—
550	C₂²	C₂²×D₈×C₇₉	1	1	yes	characteristic
551	C₂²	C₂×AGL(1,ℤ/8)×C₇₉	1	1	yes	characteristic
552	C₂²	#577×C₇₉	1	2	yes	—
553	C₄	—	2	4	no	—
554	C₄	—	2	2	no	—
555	C₄	—	4	2	no	—
556	C₄	—	8	2	no	—
557	C₄	—	8	1	no	—
558	C₄	—	8	2	no	—
559	C₄	C₂×#123×C₇₉	1	1	yes	characteristic
560	C₄	#534×C₇₉	1	1	yes	characteristic
561	C₄	#551×C₇₉	1	2	yes	—
562	C₂	—	2	4	no	—
563	C₂	—	4	4	no	—
564	C₂	—	8	2	no	—
565	C₂	—	16	1	no	—
566	C₂	C₇₉×#2412	1	1	yes	characteristic
567	C₂	C₂×#459×C₇₉	1	1	yes	characteristic
568	C₂	C₇₉×#3042	1	1	yes	characteristic
569	C₂	C₇₉×#3294	1	2	yes	—
570	C₂	C₇₉×#3306	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₉
prime radical	C₂×#447×C₇₉	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₉ ◁ C₄×C₂²⋊C₄×C₇₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×#102×C₇₉	C₂	semidirect
3. C₇₉×#2501	C₂	semidirect
4. D₄×C₂²⋊C₄×C₇₉	C₂	semidirect
5. C₇₉×#2071	C₂	semidirect
6. C₇₉×#2054	C₂	semidirect
7. C₇₉×#1893	C₂	semidirect
8. C₇₉×#1879	C₂	semidirect
9. C₇₉×#1850	C₂	semidirect
10. C₇₉×#1823	C₂	semidirect
11. C₇₉×#1802	C₂	semidirect
23. C₂×C₄⋊C₈×C₇₉	C₂²	semidirect
29. C₂×#102×C₇₉	C₂²	semidirect
33. #390×C₇₉	C₂²	semidirect
35. #384×C₇₉	C₂²	semidirect
39. #340×C₇₉	C₂²	semidirect
40. #340×C₇₉	C₂²	semidirect
41. #340×C₇₉	C₂²	semidirect
42. #336×C₇₉	C₂²	semidirect
172. C₂²⋊C₄×C₇₉	D₈	semidirect
211. D₄×C₇₉	#123	semidirect
276. #24526	C₇₉	direct (N × H)
287. C₂²×#102	C₂×C₇₉	semidirect
288. #2501	C₂×C₇₉	semidirect
289. D₄×C₂²⋊C₄	C₂×C₇₉	semidirect
290. #2071	C₂×C₇₉	semidirect
291. #2054	C₂×C₇₉	semidirect
292. #1893	C₂×C₇₉	semidirect
293. #1879	C₂×C₇₉	semidirect
294. #1850	C₂×C₇₉	semidirect
295. #1823	C₂×C₇₉	semidirect
296. #1802	C₂×C₇₉	semidirect
297. C₇₉	#24526	direct (N × H)
309. C₂×C₄⋊C₈	C₂²×C₇₉	semidirect
315. C₂×#102	C₂²×C₇₉	semidirect
319. #390	C₂²×C₇₉	semidirect
321. #384	C₂²×C₇₉	semidirect
325. #340	C₂²×C₇₉	semidirect
326. #340	C₂²×C₇₉	semidirect
327. #340	C₂²×C₇₉	semidirect
328. #336	C₂²×C₇₉	semidirect
458. C₂²⋊C₄	D₈×C₇₉	semidirect
497. D₄	#123×C₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#447×C₇₉	2
C₂²×#102×C₇₉	2
C₇₉×#2501	2
D₄×C₂²⋊C₄×C₇₉	2
C₇₉×#2071	2
C₇₉×#2054	2
C₇₉×#1893	2
C₇₉×#1879	2
C₇₉×#1850	2
C₇₉×#1823	2
C₇₉×#1802	2
#24526	79

Subgroups — C79×#24526 #34136215

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#24526 #34136215