Subgroups — C₇₉×#24529 #34136218

Order 20224.

966 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#451×C₇₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×#103×C₇₉	C₂	1	1	yes	maximal, characteristic
3	C₇₉×#2503	C₂	1	1	yes	maximal, characteristic
4	Q₈×C₂²⋊C₄×C₇₉	C₂	1	1	yes	maximal, characteristic
5	C₇₉×#2074	C₂	1	2	yes	maximal, complemented
6	C₇₉×#2056	C₂	1	2	yes	maximal, complemented
7	C₇₉×#1892	C₂	1	1	yes	maximal, characteristic
8	C₇₉×#1878	C₂	1	2	yes	maximal, complemented
9	C₇₉×#1850	C₂	1	1	yes	maximal, characteristic
10	C₇₉×#1823	C₂	1	1	yes	maximal, characteristic
11	C₇₉×#1805	C₂	1	2	yes	maximal, complemented
12	C₂³×Q₈×C₇₉	C₂²	1	1	yes	characteristic
13	C₂²×Q₁₆×C₇₉	C₂²	1	1	yes	characteristic
14	C₂²×Q₁₆×C₇₉	C₂²	1	1	yes	characteristic
15	C₂³×C₈×C₇₉	C₂²	1	1	yes	characteristic
16	C₂×C₂²⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
17	C₂×C₄×Q₈×C₇₉	C₂²	1	2	yes	—
18	C₂²×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
19	#451×C₇₉	—	2	4	no	—
20	C₂×C₄⋊C₈×C₇₉	C₂²	1	2	yes	—
21	C₂×#103×C₇₉	—	2	4	no	—
22	C₂×#103×C₇₉	C₂²	1	2	yes	—
23	C₂×#103×C₇₉	C₂²	1	1	yes	characteristic
24	C₂×#103×C₇₉	C₂²	1	2	yes	—
25	C₂×#103×C₇₉	C₂²	1	1	yes	characteristic
26	C₂×#103×C₇₉	C₂²	1	2	yes	—
27	C₂×C₂²⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
28	#400×C₇₉	—	2	2	no	—
29	#391×C₇₉	—	2	2	no	—
30	#391×C₇₉	C₂²	1	2	yes	—
31	#391×C₇₉	C₂²	1	2	yes	—
32	#382×C₇₉	C₂²	1	2	yes	—
33	#381×C₇₉	—	2	1	no	—
34	#381×C₇₉	—	2	1	no	—
35	#380×C₇₉	—	2	1	no	—
36	#380×C₇₉	C₂²	1	1	yes	characteristic
37	C₄×C₂²⋊C₄×C₇₉	—	2	1	no	—
38	C₄×C₂²⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
39	#340×C₇₉	C₂²	1	2	yes	—
40	#340×C₇₉	C₂²	1	2	yes	—
41	#340×C₇₉	C₂²	1	2	yes	—
42	#336×C₇₉	C₂²	1	2	yes	—
43	C₂²×Q₈×C₇₉	—	2	1	no	—
44	C₂²×Q₈×C₇₉	—	2	2	no	—
45	C₂²×Q₈×C₇₉	—	2	4	no	—
46	C₂²×Q₈×C₇₉	—	4	2	no	—
47	C₂²×Q₈×C₇₉	D₄	1	4	yes	—
48	C₂²×Q₈×C₇₉	C₂³	1	1	yes	characteristic
49	C₂²×Q₈×C₇₉	C₂³	1	1	yes	characteristic
50	C₂²×Q₈×C₇₉	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₇₉	—	2	1	no	—
52	C₂³×C₄×C₇₉	—	2	1	no	—
53	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
54	C₂×Q₁₆×C₇₉	—	2	2	no	—
55	C₂×Q₁₆×C₇₉	—	2	2	no	—
56	C₂×Q₁₆×C₇₉	—	2	4	no	—
57	C₂×Q₁₆×C₇₉	—	4	2	no	—
58	C₂²×C₈×C₇₉	—	2	2	no	—
59	C₂²×C₈×C₇₉	—	4	2	no	—
60	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
61	C₂²×C₈×C₇₉	C₂³	1	2	yes	—
62	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
63	C₂²⋊Q₈×C₇₉	—	2	2	no	—
64	C₂²⋊Q₈×C₇₉	—	2	2	no	—
65	C₄×Q₈×C₇₉	—	2	4	no	—
66	C₄×Q₈×C₇₉	—	4	2	no	—
67	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
68	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
69	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
70	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
71	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
72	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
73	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
74	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
75	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
76	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
77	C₂×C₂²⋊C₄×C₇₉	D₄	1	1	yes	characteristic
78	C₂×C₂²⋊C₄×C₇₉	D₄	1	1	yes	characteristic
79	C₂×C₄²×C₇₉	—	2	2	no	—
80	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
81	C₄⋊C₈×C₇₉	—	4	2	no	—
82	#103×C₇₉	—	2	2	no	—
83	#103×C₇₉	—	2	2	no	—
84	#103×C₇₉	—	2	4	no	—
85	#103×C₇₉	—	2	4	no	—
86	#103×C₇₉	—	4	2	no	—
87	C₂²⋊C₈×C₇₉	—	2	2	no	—
88	#95×C₇₉	—	2	2	no	—
89	#95×C₇₉	—	2	2	no	—
90	#95×C₇₉	—	2	1	no	—
91	#95×C₇₉	—	2	2	no	—
92	#95×C₇₉	—	2	2	no	—
93	#95×C₇₉	—	2	2	no	—
94	#95×C₇₉	—	2	2	no	—
95	#95×C₇₉	D₄	1	2	yes	—
96	C₂⁴×C₇₉	C₂×D₄	1	1	yes	characteristic
97	C₂×Q₈×C₇₉	—	2	4	no	—
98	C₂×Q₈×C₇₉	—	2	1	no	—
99	C₂×Q₈×C₇₉	—	2	1	no	—
100	C₂×Q₈×C₇₉	—	2	2	no	—
101	C₂×Q₈×C₇₉	—	2	8	no	—
102	C₂×Q₈×C₇₉	—	2	1	no	—
103	C₂×Q₈×C₇₉	—	2	2	no	—
104	C₂×Q₈×C₇₉	—	2	1	no	—
105	C₂×Q₈×C₇₉	—	2	2	no	—
106	C₂×Q₈×C₇₉	—	2	2	no	—
107	C₂×Q₈×C₇₉	—	2	2	no	—
108	C₂×Q₈×C₇₉	—	4	4	no	—
109	C₂×Q₈×C₇₉	—	4	4	no	—
110	C₂×Q₈×C₇₉	—	4	8	no	—
111	C₂×Q₈×C₇₉	C₂×D₄	1	2	yes	—
112	C₂×Q₈×C₇₉	C₂×D₄	1	2	yes	—
113	C₂×Q₈×C₇₉	#41	1	4	yes	—
114	C₂²×C₄×C₇₉	—	2	1	no	—
115	C₂²×C₄×C₇₉	—	2	2	no	—
116	C₂²×C₄×C₇₉	—	2	2	no	—
117	C₂²×C₄×C₇₉	—	2	4	no	—
118	C₂²×C₄×C₇₉	—	2	1	no	—
119	C₂²×C₄×C₇₉	—	2	1	no	—
120	C₂²×C₄×C₇₉	—	2	1	no	—
121	C₂²×C₄×C₇₉	—	2	2	no	—
122	C₂²×C₄×C₇₉	—	2	2	no	—
123	C₂²×C₄×C₇₉	—	4	4	no	—
124	C₂²×C₄×C₇₉	—	4	2	no	—
125	C₂²×C₄×C₇₉	—	4	2	no	—
126	C₂²×C₄×C₇₉	—	4	2	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	2	yes	—
131	C₂²×C₄×C₇₉	#41	1	2	yes	—
132	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
133	Q₁₆×C₇₉	—	4	4	no	—
134	Q₁₆×C₇₉	—	4	4	no	—
135	C₂×C₈×C₇₉	—	2	1	no	—
136	C₂×C₈×C₇₉	—	2	1	no	—
137	C₂×C₈×C₇₉	—	2	2	no	—
138	C₂×C₈×C₇₉	—	2	2	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	—	4	4	no	—
143	C₄⋊C₄×C₇₉	—	2	2	no	—
144	C₄⋊C₄×C₇₉	—	2	1	no	—
145	C₄⋊C₄×C₇₉	—	2	2	no	—
146	C₄⋊C₄×C₇₉	—	2	2	no	—
147	C₄⋊C₄×C₇₉	—	2	1	no	—
148	C₄⋊C₄×C₇₉	—	2	2	no	—
149	C₄⋊C₄×C₇₉	—	4	4	no	—
150	C₄⋊C₄×C₇₉	—	4	2	no	—
151	C₄⋊C₄×C₇₉	—	4	2	no	—
152	C₂²⋊C₄×C₇₉	—	2	2	no	—
153	C₂²⋊C₄×C₇₉	—	2	2	no	—
154	C₂²⋊C₄×C₇₉	—	4	2	no	—
155	C₂²⋊C₄×C₇₉	—	4	2	no	—
156	C₄²×C₇₉	—	2	2	no	—
157	C₄²×C₇₉	—	2	2	no	—
158	C₄²×C₇₉	—	4	4	no	—
159	C₂³×C₇₉	—	2	2	no	—
160	C₂³×C₇₉	—	2	2	no	—
161	C₂³×C₇₉	#121	1	2	yes	—
162	C₂³×C₇₉	#135	1	2	yes	—
163	C₂³×C₇₉	#137	1	2	yes	—
164	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
165	Q₈×C₇₉	—	2	2	no	—
166	Q₈×C₇₉	—	2	4	no	—
167	Q₈×C₇₉	—	2	2	no	—
168	Q₈×C₇₉	—	2	2	no	—
169	Q₈×C₇₉	—	4	8	no	—
170	Q₈×C₇₉	—	4	2	no	—
171	Q₈×C₇₉	—	4	1	no	—
172	Q₈×C₇₉	—	4	1	no	—
173	Q₈×C₇₉	—	4	2	no	—
174	Q₈×C₇₉	#123	1	4	yes	—
175	C₂×C₄×C₇₉	—	2	2	no	—
176	C₂×C₄×C₇₉	—	2	4	no	—
177	C₂×C₄×C₇₉	—	2	2	no	—
178	C₂×C₄×C₇₉	—	2	2	no	—
179	C₂×C₄×C₇₉	—	2	2	no	—
180	C₂×C₄×C₇₉	—	2	4	no	—
181	C₂×C₄×C₇₉	—	2	2	no	—
182	C₂×C₄×C₇₉	—	2	2	no	—
183	C₂×C₄×C₇₉	—	2	2	no	—
184	C₂×C₄×C₇₉	—	2	2	no	—
185	C₂×C₄×C₇₉	—	2	2	no	—
186	C₂×C₄×C₇₉	—	2	2	no	—
187	C₂×C₄×C₇₉	—	2	2	no	—
188	C₂×C₄×C₇₉	—	4	8	no	—
189	C₂×C₄×C₇₉	—	4	2	no	—
190	C₂×C₄×C₇₉	—	4	1	no	—
191	C₂×C₄×C₇₉	—	4	1	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	2	no	—
199	C₂×C₄×C₇₉	—	4	2	no	—
200	C₂×C₄×C₇₉	—	8	4	no	—
201	C₂×C₄×C₇₉	#121	1	2	yes	—
202	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
203	C₂×C₄×C₇₉	C₂×#41	1	2	yes	—
204	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
205	C₂×C₄×C₇₉	H(5,𝔽₂)	1	2	yes	—
206	C₈×C₇₉	—	4	1	no	—
207	C₈×C₇₉	—	4	2	no	—
208	C₈×C₇₉	—	4	1	no	—
209	C₂²×C₇₉	—	2	2	no	—
210	C₂²×C₇₉	—	2	2	no	—
211	C₂²×C₇₉	—	2	4	no	—
212	C₂²×C₇₉	—	2	4	no	—
213	C₂²×C₇₉	#464	1	4	yes	—
214	C₂²×C₇₉	C₂×#121	1	1	yes	characteristic
215	C₂²×C₇₉	#546	1	2	yes	—
216	C₂²×C₇₉	C₂×#135	1	1	yes	characteristic
217	C₂²×C₇₉	C₂×#137	1	1	yes	characteristic
218	C₂²×C₇₉	#578	1	2	yes	—
219	C₄×C₇₉	—	2	2	no	—
220	C₄×C₇₉	—	2	4	no	—
221	C₄×C₇₉	—	4	2	no	—
222	C₄×C₇₉	—	4	2	no	—
223	C₄×C₇₉	—	4	2	no	—
224	C₄×C₇₉	—	8	1	no	—
225	C₄×C₇₉	—	8	2	no	—
226	C₄×C₇₉	—	8	1	no	—
227	C₄×C₇₉	—	8	2	no	—
228	C₄×C₇₉	C₂×#123	1	1	yes	characteristic
229	C₄×C₇₉	#534	1	1	yes	characteristic
230	C₄×C₇₉	#551	1	2	yes	—
231	#24529	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
232	C₂×C₇₉	—	2	4	no	—
233	C₂×C₇₉	#2412	1	1	yes	characteristic
234	C₂×C₇₉	C₂×#464	1	1	yes	characteristic
235	C₂×C₇₉	#3044	1	1	yes	characteristic
236	C₂×C₇₉	#3300	1	2	yes	—
237	C₂×C₇₉	#3312	1	2	yes	—
238	C₂×#451	C₂×C₇₉	1	1	yes	characteristic
239	C₂²×#103	C₂×C₇₉	1	1	yes	characteristic
240	#2503	C₂×C₇₉	1	1	yes	characteristic
241	Q₈×C₂²⋊C₄	C₂×C₇₉	1	1	yes	characteristic
242	#2074	C₂×C₇₉	1	2	yes	complemented
243	#2056	C₂×C₇₉	1	2	yes	complemented
244	#1892	C₂×C₇₉	1	1	yes	characteristic
245	#1878	C₂×C₇₉	1	2	yes	complemented
246	#1850	C₂×C₇₉	1	1	yes	characteristic
247	#1823	C₂×C₇₉	1	1	yes	characteristic
248	#1805	C₂×C₇₉	1	2	yes	complemented
249	C₇₉	#24529	1	1	yes	characteristic, direct product factor, Sylow
250	C₂³×Q₈	C₂²×C₇₉	1	1	yes	characteristic
251	C₂²×Q₁₆	C₂²×C₇₉	1	1	yes	characteristic
252	C₂²×Q₁₆	C₂²×C₇₉	1	1	yes	characteristic
253	C₂³×C₈	C₂²×C₇₉	1	1	yes	characteristic
254	C₂×C₂²⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic
255	C₂×C₄×Q₈	C₂²×C₇₉	1	2	yes	—
256	C₂²×C₄⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
257	#451	—	2	4	no	—
258	C₂×C₄⋊C₈	C₂²×C₇₉	1	2	yes	—
259	C₂×#103	—	2	4	no	—
260	C₂×#103	C₂²×C₇₉	1	2	yes	—
261	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic
262	C₂×#103	C₂²×C₇₉	1	2	yes	—
263	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic
264	C₂×#103	C₂²×C₇₉	1	2	yes	—
265	C₂×C₂²⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
266	#400	—	2	2	no	—
267	#391	—	2	2	no	—
268	#391	C₂²×C₇₉	1	2	yes	—
269	#391	C₂²×C₇₉	1	2	yes	—
270	#382	C₂²×C₇₉	1	2	yes	—
271	#381	—	2	1	no	—
272	#381	—	2	1	no	—
273	#380	—	2	1	no	—
274	#380	C₂²×C₇₉	1	1	yes	characteristic
275	C₄×C₂²⋊C₄	—	2	1	no	—
276	C₄×C₂²⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
277	#340	C₂²×C₇₉	1	2	yes	—
278	#340	C₂²×C₇₉	1	2	yes	—
279	#340	C₂²×C₇₉	1	2	yes	—
280	#336	C₂²×C₇₉	1	2	yes	—
281	C₂²×Q₈	—	2	1	no	—
282	C₂²×Q₈	—	2	2	no	—
283	C₂²×Q₈	—	2	4	no	—
284	C₂²×Q₈	—	4	2	no	—
285	C₂²×Q₈	D₄×C₇₉	1	4	yes	—
286	C₂²×Q₈	C₂³×C₇₉	1	1	yes	characteristic
287	C₂²×Q₈	C₂³×C₇₉	1	1	yes	characteristic
288	C₂²×Q₈	C₂³×C₇₉	1	1	yes	characteristic
289	C₂³×C₄	—	2	1	no	—
290	C₂³×C₄	—	2	1	no	—
291	C₂³×C₄	C₂³×C₇₉	1	1	yes	characteristic
292	C₂×Q₁₆	—	2	2	no	—
293	C₂×Q₁₆	—	2	2	no	—
294	C₂×Q₁₆	—	2	4	no	—
295	C₂×Q₁₆	—	4	2	no	—
296	C₂²×C₈	—	2	2	no	—
297	C₂²×C₈	—	4	2	no	—
298	C₂²×C₈	C₂³×C₇₉	1	2	yes	—
299	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
300	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
301	C₂²⋊Q₈	—	2	2	no	—
302	C₂²⋊Q₈	—	2	2	no	—
303	C₄×Q₈	—	2	4	no	—
304	C₄×Q₈	—	4	2	no	—
305	C₂×C₄⋊C₄	—	2	2	no	—
306	C₂×C₄⋊C₄	—	2	2	no	—
307	C₂×C₄⋊C₄	—	2	1	no	—
308	C₂×C₄⋊C₄	—	2	2	no	—
309	C₂×C₄⋊C₄	—	2	1	no	—
310	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
311	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
312	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
313	C₂×C₂²⋊C₄	—	2	1	no	—
314	C₂×C₂²⋊C₄	—	2	1	no	—
315	C₂×C₂²⋊C₄	D₄×C₇₉	1	1	yes	characteristic
316	C₂×C₂²⋊C₄	D₄×C₇₉	1	1	yes	characteristic
317	C₂×C₄²	—	2	2	no	—
318	C₂×C₄²	C₂³×C₇₉	1	2	yes	—
319	C₄⋊C₈	—	4	2	no	—
320	#103	—	2	4	no	—
321	#103	—	2	4	no	—
322	#103	—	2	2	no	—
323	#103	—	2	2	no	—
324	#103	—	4	2	no	—
325	C₂²⋊C₈	—	2	2	no	—
326	#95	—	2	2	no	—
327	#95	—	2	2	no	—
328	#95	—	2	1	no	—
329	#95	—	2	2	no	—
330	#95	—	2	2	no	—
331	#95	—	2	2	no	—
332	#95	—	2	2	no	—
333	#95	D₄×C₇₉	1	2	yes	—
334	C₂⁴	C₂×D₄×C₇₉	1	1	yes	characteristic
335	C₂×Q₈	—	2	4	no	—
336	C₂×Q₈	—	2	1	no	—
337	C₂×Q₈	—	2	1	no	—
338	C₂×Q₈	—	2	2	no	—
339	C₂×Q₈	—	2	8	no	—
340	C₂×Q₈	—	2	1	no	—
341	C₂×Q₈	—	2	2	no	—
342	C₂×Q₈	—	2	1	no	—
343	C₂×Q₈	—	2	2	no	—
344	C₂×Q₈	—	2	2	no	—
345	C₂×Q₈	—	2	2	no	—
346	C₂×Q₈	—	4	4	no	—
347	C₂×Q₈	—	4	4	no	—
348	C₂×Q₈	—	4	8	no	—
349	C₂×Q₈	C₂×D₄×C₇₉	1	2	yes	—
350	C₂×Q₈	C₂×D₄×C₇₉	1	2	yes	—
351	C₂×Q₈	#41×C₇₉	1	4	yes	—
352	C₂²×C₄	—	2	1	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	4	no	—
356	C₂²×C₄	—	2	1	no	—
357	C₂²×C₄	—	2	1	no	—
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	4	4	no	—
362	C₂²×C₄	—	4	2	no	—
363	C₂²×C₄	—	4	2	no	—
364	C₂²×C₄	—	4	2	no	—
365	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
366	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
367	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
368	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
369	C₂²×C₄	#41×C₇₉	1	2	yes	—
370	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
371	Q₁₆	—	4	4	no	—
372	Q₁₆	—	4	4	no	—
373	C₂×C₈	—	2	1	no	—
374	C₂×C₈	—	2	1	no	—
375	C₂×C₈	—	2	2	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	2	2	no	—
379	C₂×C₈	—	2	2	no	—
380	C₂×C₈	—	4	4	no	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	2	1	no	—
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	—	2	1	no	—
386	C₄⋊C₄	—	2	2	no	—
387	C₄⋊C₄	—	4	4	no	—
388	C₄⋊C₄	—	4	2	no	—
389	C₄⋊C₄	—	4	2	no	—
390	C₂²⋊C₄	—	2	2	no	—
391	C₂²⋊C₄	—	2	2	no	—
392	C₂²⋊C₄	—	4	2	no	—
393	C₂²⋊C₄	—	4	2	no	—
394	C₄²	—	2	2	no	—
395	C₄²	—	2	2	no	—
396	C₄²	—	4	4	no	—
397	C₂³	—	2	2	no	—
398	C₂³	—	2	2	no	—
399	C₂³	#121×C₇₉	1	2	yes	—
400	C₂³	#135×C₇₉	1	2	yes	—
401	C₂³	#137×C₇₉	1	2	yes	—
402	C₂³	C₂²×D₄×C₇₉	1	1	yes	characteristic
403	Q₈	—	2	2	no	—
404	Q₈	—	2	4	no	—
405	Q₈	—	2	2	no	—
406	Q₈	—	2	2	no	—
407	Q₈	—	4	8	no	—
408	Q₈	—	4	2	no	—
409	Q₈	—	4	1	no	—
410	Q₈	—	4	1	no	—
411	Q₈	—	4	2	no	—
412	Q₈	#123×C₇₉	1	4	yes	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	4	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	4	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	4	8	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	1	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	—	4	2	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	8	4	no	—
439	C₂×C₄	#121×C₇₉	1	2	yes	—
440	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
441	C₂×C₄	C₂×#41×C₇₉	1	2	yes	—
442	C₂×C₄	C₂×#41×C₇₉	1	1	yes	characteristic
443	C₂×C₄	H(5,𝔽₂)×C₇₉	1	2	yes	—
444	C₈	—	4	1	no	—
445	C₈	—	4	2	no	—
446	C₈	—	4	1	no	—
447	C₂²	—	2	2	no	—
448	C₂²	—	2	4	no	—
449	C₂²	—	2	4	no	—
450	C₂²	—	2	2	no	—
451	C₂²	#464×C₇₉	1	4	yes	—
452	C₂²	C₂×#121×C₇₉	1	1	yes	characteristic
453	C₂²	#546×C₇₉	1	2	yes	—
454	C₂²	C₂×#135×C₇₉	1	1	yes	characteristic
455	C₂²	C₂×#137×C₇₉	1	1	yes	characteristic
456	C₂²	#578×C₇₉	1	2	yes	—
457	C₄	—	2	2	no	—
458	C₄	—	2	4	no	—
459	C₄	—	4	2	no	—
460	C₄	—	4	2	no	—
461	C₄	—	4	2	no	—
462	C₄	—	8	2	no	—
463	C₄	—	8	1	no	—
464	C₄	—	8	2	no	—
465	C₄	—	8	1	no	—
466	C₄	C₂×#123×C₇₉	1	1	yes	characteristic
467	C₄	#534×C₇₉	1	1	yes	characteristic
468	C₄	#551×C₇₉	1	2	yes	—
469	C₂	—	2	4	no	—
470	C₂	C₇₉×#2412	1	1	yes	characteristic
471	C₂	C₂×#464×C₇₉	1	1	yes	characteristic
472	C₂	C₇₉×#3044	1	1	yes	characteristic
473	C₂	C₇₉×#3300	1	2	yes	—
474	C₂	C₇₉×#3312	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₉
prime radical	C₂⁴×C₇₉	C₂×D₄
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
5. C₇₉×#2074	C₂	semidirect
6. C₇₉×#2056	C₂	semidirect
8. C₇₉×#1878	C₂	semidirect
11. C₇₉×#1805	C₂	semidirect
231. #24529	C₇₉	direct (N × H)
242. #2074	C₂×C₇₉	semidirect
243. #2056	C₂×C₇₉	semidirect
245. #1878	C₂×C₇₉	semidirect
248. #1805	C₂×C₇₉	semidirect
249. C₇₉	#24529	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×#451×C₇₉	2
C₂²×#103×C₇₉	2
C₇₉×#2503	2
Q₈×C₂²⋊C₄×C₇₉	2
C₇₉×#2074	2
C₇₉×#2056	2
C₇₉×#1892	2
C₇₉×#1878	2
C₇₉×#1850	2
C₇₉×#1823	2
C₇₉×#1805	2
#24529	79

Subgroups — C79×#24529 #34136218

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#24529 #34136218