Subgroups — C₇₉×#25469 #34137158

Order 20224.

838 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×#474×C₇₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×Q₈×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₉×#2546	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₉×#2538	C₂	1	1	yes	maximal, characteristic
5	C₇₉×#2086	C₂	1	2	yes	maximal, complemented
6	C₇₉×#2067	C₂	1	2	yes	maximal
7	C₇₉×#1990	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₉×#1947	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₉×#1942	C₂	1	2	yes	maximal, complemented
10	C₇₉×#1934	C₂	1	2	yes	maximal
11	C₄×#102×C₇₉	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄⋊Q₈×C₇₉	—	2	1	no	—
13	C₂×C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
14	C₂×C₂²⋊Q₈×C₇₉	—	2	1	no	—
15	C₂×C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic
16	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
17	#474×C₇₉	—	2	4	no	—
18	C₈×Q₈×C₇₉	—	2	4	no	—
19	C₂×#107×C₇₉	C₂²	1	2	yes	—
20	C₂×#107×C₇₉	C₂²	1	2	yes	—
21	C₂×C₄⋊C₈×C₇₉	C₂²	1	2	yes	—
22	C₂×C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
23	C₂×#102×C₇₉	C₂²	1	1	yes	characteristic
24	C₂×#102×C₇₉	C₂²	1	2	yes	—
25	C₂×#102×C₇₉	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₇₉	C₂²	1	2	yes	—
28	#398×C₇₉	—	2	2	no	—
29	#396×C₇₉	—	2	2	no	—
30	#391×C₇₉	—	2	1	no	—
31	#390×C₇₉	C₂²	1	2	yes	—
32	#389×C₇₉	C₂²	1	2	yes	—
33	#389×C₇₉	C₂²	1	2	yes	—
34	#389×C₇₉	C₂²	1	2	yes	—
35	#384×C₇₉	C₂²	1	1	yes	characteristic
36	#380×C₇₉	—	2	1	no	—
37	C₄×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
38	#340×C₇₉	C₂²	1	1	yes	characteristic
39	#340×C₇₉	C₂²	1	1	yes	characteristic
40	#340×C₇₉	C₂²	1	2	yes	—
41	#340×C₇₉	C₂²	1	2	yes	—
42	#340×C₇₉	C₂²	1	2	yes	—
43	C₂²×Q₈×C₇₉	—	2	1	no	—
44	C₂²×Q₈×C₇₉	D₄	1	1	yes	characteristic
45	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₇₉	—	2	1	no	—
47	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₇₉	C₂³	1	2	yes	—
49	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
50	C₄⋊Q₈×C₇₉	—	2	2	no	—
51	C₄⋊Q₈×C₇₉	—	2	2	no	—
52	C₄⋊Q₈×C₇₉	—	4	4	no	—
53	C₂²⋊Q₈×C₇₉	—	4	4	no	—
54	C₄×Q₈×C₇₉	—	2	2	no	—
55	C₄×Q₈×C₇₉	—	2	2	no	—
56	C₄×D₄×C₇₉	—	2	2	no	—
57	C₄×D₄×C₇₉	—	2	2	no	—
58	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
59	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
60	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
61	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
62	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
63	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
64	C₂×C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₇₉	D₄	1	2	yes	—
66	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
68	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
69	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
70	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
71	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
72	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
73	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
74	C₂×C₄²×C₇₉	—	2	1	no	—
75	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
76	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
77	#107×C₇₉	—	2	4	no	—
78	#107×C₇₉	—	2	4	no	—
79	C₄⋊C₈×C₇₉	—	2	4	no	—
80	C₄⋊C₈×C₇₉	D₄	1	4	yes	—
81	#102×C₇₉	—	2	4	no	—
82	#102×C₇₉	—	2	2	no	—
83	#102×C₇₉	Q₈	1	4	yes	complemented
84	C₄×C₈×C₇₉	—	2	4	no	—
85	C₄×C₈×C₇₉	—	2	2	no	—
86	#95×C₇₉	—	2	1	no	—
87	#95×C₇₉	—	2	2	no	—
88	#95×C₇₉	—	2	2	no	—
89	#95×C₇₉	—	2	2	no	—
90	C₂⁴×C₇₉	—	2	1	no	—
91	C₂×Q₈×C₇₉	—	2	2	no	—
92	C₂×Q₈×C₇₉	—	2	2	no	—
93	C₂×Q₈×C₇₉	—	4	2	no	—
94	C₂×Q₈×C₇₉	—	4	2	no	—
95	C₂×Q₈×C₇₉	—	4	2	no	—
96	C₂×Q₈×C₇₉	D₈	1	4	yes	—
97	C₂×D₄×C₇₉	—	2	1	no	—
98	C₂×D₄×C₇₉	—	2	1	no	—
99	C₂×D₄×C₇₉	—	2	1	no	—
100	C₂×D₄×C₇₉	—	2	1	no	—
101	C₂×D₄×C₇₉	—	2	1	no	—
102	C₂×D₄×C₇₉	C₂×Q₈	1	2	yes	—
103	C₂²×C₄×C₇₉	—	2	1	no	—
104	C₂²×C₄×C₇₉	—	2	1	no	—
105	C₂²×C₄×C₇₉	—	2	1	no	—
106	C₂²×C₄×C₇₉	—	2	2	no	—
107	C₂²×C₄×C₇₉	—	2	2	no	—
108	C₂²×C₄×C₇₉	—	4	2	no	—
109	C₂²×C₄×C₇₉	—	4	2	no	—
110	C₂²×C₄×C₇₉	—	4	2	no	—
111	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
116	C₂×C₈×C₇₉	—	2	1	no	—
117	C₂×C₈×C₇₉	—	2	1	no	—
118	C₂×C₈×C₇₉	—	2	2	no	—
119	C₂×C₈×C₇₉	—	2	1	no	—
120	C₂×C₈×C₇₉	—	2	2	no	—
121	C₂×C₈×C₇₉	—	2	1	no	—
122	C₂×C₈×C₇₉	—	2	1	no	—
123	C₂×C₈×C₇₉	C₂×D₄	1	4	yes	—
124	C₂×C₈×C₇₉	C₂×Q₈	1	2	yes	—
125	C₄⋊C₄×C₇₉	—	2	4	no	—
126	C₄⋊C₄×C₇₉	—	2	2	no	—
127	C₄⋊C₄×C₇₉	—	2	1	no	—
128	C₄⋊C₄×C₇₉	—	2	1	no	—
129	C₄⋊C₄×C₇₉	—	2	2	no	—
130	C₄⋊C₄×C₇₉	—	2	1	no	—
131	C₄⋊C₄×C₇₉	—	2	2	no	—
132	C₄⋊C₄×C₇₉	—	2	1	no	—
133	C₄⋊C₄×C₇₉	—	2	2	no	—
134	C₄⋊C₄×C₇₉	—	2	2	no	—
135	C₄⋊C₄×C₇₉	—	4	2	no	—
136	C₄⋊C₄×C₇₉	—	4	2	no	—
137	C₄⋊C₄×C₇₉	—	4	4	no	—
138	C₄⋊C₄×C₇₉	—	4	4	no	—
139	C₄⋊C₄×C₇₉	—	4	4	no	—
140	C₄⋊C₄×C₇₉	—	8	1	no	—
141	C₄⋊C₄×C₇₉	C₂×Q₈	1	2	yes	—
142	C₄⋊C₄×C₇₉	#41	1	2	yes	—
143	C₂²⋊C₄×C₇₉	—	4	2	no	—
144	C₂²⋊C₄×C₇₉	—	4	4	no	—
145	C₂²⋊C₄×C₇₉	—	8	2	no	—
146	C₄²×C₇₉	—	2	2	no	—
147	C₄²×C₇₉	—	2	2	no	—
148	C₄²×C₇₉	—	4	2	no	—
149	C₄²×C₇₉	C₂×D₄	1	2	yes	—
150	C₄²×C₇₉	#41	1	2	yes	—
151	C₂³×C₇₉	—	2	2	no	—
152	C₂³×C₇₉	—	4	1	no	—
153	C₂³×C₇₉	—	4	1	no	—
154	C₂³×C₇₉	—	4	1	no	—
155	C₂³×C₇₉	—	4	1	no	—
156	C₂³×C₇₉	—	4	1	no	—
157	C₂³×C₇₉	—	4	1	no	—
158	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
159	Q₈×C₇₉	—	2	8	no	—
160	Q₈×C₇₉	—	8	4	no	—
161	D₄×C₇₉	—	2	2	no	—
162	D₄×C₇₉	—	2	2	no	—
163	D₄×C₇₉	—	4	1	no	—
164	D₄×C₇₉	—	4	1	no	—
165	C₂×C₄×C₇₉	—	2	2	no	—
166	C₂×C₄×C₇₉	—	2	2	no	—
167	C₂×C₄×C₇₉	—	2	1	no	—
168	C₂×C₄×C₇₉	—	2	1	no	—
169	C₂×C₄×C₇₉	—	2	2	no	—
170	C₂×C₄×C₇₉	—	2	2	no	—
171	C₂×C₄×C₇₉	—	2	2	no	—
172	C₂×C₄×C₇₉	—	2	2	no	—
173	C₂×C₄×C₇₉	—	2	2	no	—
174	C₂×C₄×C₇₉	—	4	1	no	—
175	C₂×C₄×C₇₉	—	4	1	no	—
176	C₂×C₄×C₇₉	—	4	1	no	—
177	C₂×C₄×C₇₉	—	4	1	no	—
178	C₂×C₄×C₇₉	—	4	1	no	—
179	C₂×C₄×C₇₉	—	4	2	no	—
180	C₂×C₄×C₇₉	—	4	2	no	—
181	C₂×C₄×C₇₉	—	4	2	no	—
182	C₂×C₄×C₇₉	—	4	1	no	—
183	C₂×C₄×C₇₉	—	4	2	no	—
184	C₂×C₄×C₇₉	—	4	1	no	—
185	C₂×C₄×C₇₉	—	4	2	no	—
186	C₂×C₄×C₇₉	—	4	2	no	—
187	C₂×C₄×C₇₉	—	8	4	no	—
188	C₂×C₄×C₇₉	#121	1	2	yes	—
189	C₂×C₄×C₇₉	#121	1	2	yes	—
190	C₂×C₄×C₇₉	C₂×D₈	1	4	yes	—
191	C₂×C₄×C₇₉	C₂×D₈	1	2	yes	—
192	C₂×C₄×C₇₉	#135	1	2	yes	—
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	C₂×#41	1	1	yes	characteristic
197	C₂×C₄×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
198	C₂×C₄×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
199	C₈×C₇₉	—	2	4	no	—
200	C₈×C₇₉	—	2	2	no	—
201	C₈×C₇₉	—	4	1	no	—
202	C₂²×C₇₉	—	4	2	no	—
203	C₂²×C₇₉	—	4	2	no	—
204	C₂²×C₇₉	—	4	2	no	—
205	C₂²×C₇₉	—	8	1	no	—
206	C₂²×C₇₉	—	8	1	no	—
207	C₂²×C₇₉	—	8	1	no	—
208	C₂²×C₇₉	—	8	1	no	—
209	C₂²×C₇₉	C₂×#121	1	1	yes	characteristic
210	C₂²×C₇₉	#548	1	1	yes	characteristic
211	C₂²×C₇₉	D₄×Q₈	1	1	yes	characteristic
212	C₂²×C₇₉	C₂²×D₈	1	1	yes	characteristic
213	C₂²×C₇₉	C₂×#135	1	1	yes	characteristic
214	C₂²×C₇₉	#577	1	1	yes	characteristic
215	C₂²×C₇₉	#578	1	1	yes	characteristic
216	C₄×C₇₉	—	2	4	no	—
217	C₄×C₇₉	—	2	2	no	—
218	C₄×C₇₉	—	4	2	no	—
219	C₄×C₇₉	—	4	2	no	—
220	C₄×C₇₉	—	4	2	no	—
221	C₄×C₇₉	—	8	2	no	—
222	C₄×C₇₉	—	8	1	no	—
223	C₄×C₇₉	—	8	2	no	—
224	C₄×C₇₉	#466	1	4	yes	—
225	C₄×C₇₉	#533	1	1	yes	characteristic
226	C₄×C₇₉	#541	1	1	yes	characteristic
227	C₄×C₇₉	#547	1	1	yes	characteristic
228	C₄×C₇₉	D₄×Q₈	1	1	yes	characteristic
229	#25469	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
230	C₂×C₇₉	—	8	2	no	—
231	C₂×C₇₉	#2429	1	1	yes	characteristic
232	C₂×C₇₉	C₂×#466	1	1	yes	characteristic
233	C₂×C₇₉	#3063	1	1	yes	characteristic
234	C₂×C₇₉	#3358	1	1	yes	characteristic
235	C₂×C₇₉	#3364	1	1	yes	characteristic
236	C₂×C₇₉	Q₈×D₈	1	1	yes	characteristic
237	C₂×C₇₉	#3381	1	1	yes	characteristic
238	C₂×#474	C₂×C₇₉	1	1	yes	characteristic
239	C₂×C₈×Q₈	C₂×C₇₉	1	1	yes	characteristic, complemented
240	#2546	C₂×C₇₉	1	1	yes	characteristic, complemented
241	#2538	C₂×C₇₉	1	1	yes	characteristic
242	#2086	C₂×C₇₉	1	2	yes	complemented
243	#2067	C₂×C₇₉	1	2	yes	—
244	#1990	C₂×C₇₉	1	1	yes	characteristic, complemented
245	#1947	C₂×C₇₉	1	1	yes	characteristic, complemented
246	#1942	C₂×C₇₉	1	2	yes	complemented
247	#1934	C₂×C₇₉	1	2	yes	—
248	C₄×#102	C₂×C₇₉	1	1	yes	characteristic
249	C₇₉	#25469	1	1	yes	characteristic, direct product factor, Sylow
250	C₂×C₄⋊Q₈	—	2	1	no	—
251	C₂×C₄⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic
252	C₂×C₂²⋊Q₈	—	2	1	no	—
253	C₂×C₄×Q₈	C₂²×C₇₉	1	1	yes	characteristic
254	C₂×C₄×D₄	C₂²×C₇₉	1	1	yes	characteristic
255	#474	—	2	4	no	—
256	C₈×Q₈	—	2	4	no	—
257	C₂×#107	C₂²×C₇₉	1	2	yes	—
258	C₂×#107	C₂²×C₇₉	1	2	yes	—
259	C₂×C₄⋊C₈	C₂²×C₇₉	1	2	yes	—
260	C₂×C₄⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
261	C₂×#102	C₂²×C₇₉	1	1	yes	characteristic
262	C₂×#102	C₂²×C₇₉	1	2	yes	—
263	C₂×#102	C₂²×C₇₉	1	1	yes	characteristic
264	C₂×C₄×C₈	C₂²×C₇₉	1	2	yes	—
265	C₂×C₄×C₈	C₂²×C₇₉	1	1	yes	characteristic
266	#398	—	2	2	no	—
267	#396	—	2	2	no	—
268	#391	—	2	1	no	—
269	#390	C₂²×C₇₉	1	2	yes	—
270	#389	C₂²×C₇₉	1	2	yes	—
271	#389	C₂²×C₇₉	1	2	yes	—
272	#389	C₂²×C₇₉	1	2	yes	—
273	#384	C₂²×C₇₉	1	1	yes	characteristic
274	#380	—	2	1	no	—
275	C₄×C₄⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
276	#340	C₂²×C₇₉	1	2	yes	—
277	#340	C₂²×C₇₉	1	1	yes	characteristic
278	#340	C₂²×C₇₉	1	2	yes	—
279	#340	C₂²×C₇₉	1	2	yes	—
280	#340	C₂²×C₇₉	1	1	yes	characteristic
281	C₂²×Q₈	—	2	1	no	—
282	C₂²×Q₈	D₄×C₇₉	1	1	yes	characteristic
283	C₂²×D₄	C₂³×C₇₉	1	1	yes	characteristic
284	C₂³×C₄	—	2	1	no	—
285	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
286	C₂²×C₈	C₂³×C₇₉	1	2	yes	—
287	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
288	C₄⋊Q₈	—	2	2	no	—
289	C₄⋊Q₈	—	2	2	no	—
290	C₄⋊Q₈	—	4	4	no	—
291	C₂²⋊Q₈	—	4	4	no	—
292	C₄×Q₈	—	2	2	no	—
293	C₄×Q₈	—	2	2	no	—
294	C₄×D₄	—	2	2	no	—
295	C₄×D₄	—	2	2	no	—
296	C₂×C₄⋊C₄	—	2	1	no	—
297	C₂×C₄⋊C₄	—	2	2	no	—
298	C₂×C₄⋊C₄	—	2	2	no	—
299	C₂×C₄⋊C₄	—	2	2	no	—
300	C₂×C₄⋊C₄	—	2	1	no	—
301	C₂×C₄⋊C₄	—	2	1	no	—
302	C₂×C₄⋊C₄	D₄×C₇₉	1	1	yes	characteristic
303	C₂×C₄⋊C₄	D₄×C₇₉	1	2	yes	—
304	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
305	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
306	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
307	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
308	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
309	C₂×C₂²⋊C₄	—	2	1	no	—
310	C₂×C₂²⋊C₄	—	2	2	no	—
311	C₂×C₂²⋊C₄	—	2	2	no	—
312	C₂×C₄²	—	2	1	no	—
313	C₂×C₄²	C₂³×C₇₉	1	2	yes	—
314	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
315	#107	—	2	4	no	—
316	#107	—	2	4	no	—
317	C₄⋊C₈	—	2	4	no	—
318	C₄⋊C₈	D₄×C₇₉	1	4	yes	—
319	#102	—	2	4	no	—
320	#102	—	2	2	no	—
321	#102	Q₈×C₇₉	1	4	yes	complemented
322	C₄×C₈	—	2	4	no	—
323	C₄×C₈	—	2	2	no	—
324	#95	—	2	1	no	—
325	#95	—	2	2	no	—
326	#95	—	2	2	no	—
327	#95	—	2	2	no	—
328	C₂⁴	—	2	1	no	—
329	C₂×Q₈	—	2	2	no	—
330	C₂×Q₈	—	2	2	no	—
331	C₂×Q₈	—	4	2	no	—
332	C₂×Q₈	—	4	2	no	—
333	C₂×Q₈	—	4	2	no	—
334	C₂×Q₈	D₈×C₇₉	1	4	yes	—
335	C₂×D₄	—	2	1	no	—
336	C₂×D₄	—	2	1	no	—
337	C₂×D₄	—	2	1	no	—
338	C₂×D₄	—	2	1	no	—
339	C₂×D₄	—	2	1	no	—
340	C₂×D₄	C₂×Q₈×C₇₉	1	2	yes	—
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	4	2	no	—
347	C₂²×C₄	—	4	2	no	—
348	C₂²×C₄	—	4	2	no	—
349	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
350	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
351	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
352	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
353	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	2	1	no	—
358	C₂×C₈	—	2	1	no	—
359	C₂×C₈	—	2	1	no	—
360	C₂×C₈	—	2	1	no	—
361	C₂×C₈	C₂×D₄×C₇₉	1	4	yes	—
362	C₂×C₈	C₂×Q₈×C₇₉	1	2	yes	—
363	C₄⋊C₄	—	2	4	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	2	1	no	—
366	C₄⋊C₄	—	2	1	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	2	1	no	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	—	2	1	no	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	4	2	no	—
374	C₄⋊C₄	—	4	2	no	—
375	C₄⋊C₄	—	4	4	no	—
376	C₄⋊C₄	—	4	4	no	—
377	C₄⋊C₄	—	4	4	no	—
378	C₄⋊C₄	—	8	1	no	—
379	C₄⋊C₄	C₂×Q₈×C₇₉	1	2	yes	—
380	C₄⋊C₄	#41×C₇₉	1	2	yes	—
381	C₂²⋊C₄	—	4	2	no	—
382	C₂²⋊C₄	—	4	4	no	—
383	C₂²⋊C₄	—	8	2	no	—
384	C₄²	—	2	2	no	—
385	C₄²	—	2	2	no	—
386	C₄²	—	4	2	no	—
387	C₄²	C₂×D₄×C₇₉	1	2	yes	—
388	C₄²	#41×C₇₉	1	2	yes	—
389	C₂³	—	2	2	no	—
390	C₂³	—	4	1	no	—
391	C₂³	—	4	1	no	—
392	C₂³	—	4	1	no	—
393	C₂³	—	4	1	no	—
394	C₂³	—	4	1	no	—
395	C₂³	—	4	1	no	—
396	C₂³	C₂²×D₄×C₇₉	1	1	yes	characteristic
397	Q₈	—	2	8	no	—
398	Q₈	—	8	4	no	—
399	D₄	—	2	2	no	—
400	D₄	—	2	2	no	—
401	D₄	—	4	1	no	—
402	D₄	—	4	1	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	4	1	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	8	4	no	—
426	C₂×C₄	#121×C₇₉	1	2	yes	—
427	C₂×C₄	#121×C₇₉	1	2	yes	—
428	C₂×C₄	C₂×D₈×C₇₉	1	4	yes	—
429	C₂×C₄	C₂×D₈×C₇₉	1	2	yes	—
430	C₂×C₄	#135×C₇₉	1	2	yes	—
431	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
432	C₂×C₄	C₂²×Q₈×C₇₉	1	1	yes	characteristic
433	C₂×C₄	C₂×#41×C₇₉	1	1	yes	characteristic
434	C₂×C₄	C₂×#41×C₇₉	1	1	yes	characteristic
435	C₂×C₄	2₋¹⁺⁴×C₇₉	1	1	yes	characteristic
436	C₂×C₄	2₋¹⁺⁴×C₇₉	1	1	yes	characteristic
437	C₈	—	2	4	no	—
438	C₈	—	2	2	no	—
439	C₈	—	4	1	no	—
440	C₂²	—	4	2	no	—
441	C₂²	—	4	2	no	—
442	C₂²	—	4	2	no	—
443	C₂²	—	8	1	no	—
444	C₂²	—	8	1	no	—
445	C₂²	—	8	1	no	—
446	C₂²	—	8	1	no	—
447	C₂²	C₂×#121×C₇₉	1	1	yes	characteristic
448	C₂²	#548×C₇₉	1	1	yes	characteristic
449	C₂²	D₄×Q₈×C₇₉	1	1	yes	characteristic
450	C₂²	C₂²×D₈×C₇₉	1	1	yes	characteristic
451	C₂²	C₂×#135×C₇₉	1	1	yes	characteristic
452	C₂²	#577×C₇₉	1	1	yes	characteristic
453	C₂²	#578×C₇₉	1	1	yes	characteristic
454	C₄	—	2	4	no	—
455	C₄	—	2	2	no	—
456	C₄	—	4	2	no	—
457	C₄	—	4	2	no	—
458	C₄	—	4	2	no	—
459	C₄	—	8	1	no	—
460	C₄	—	8	2	no	—
461	C₄	—	8	2	no	—
462	C₄	#466×C₇₉	1	4	yes	—
463	C₄	#533×C₇₉	1	1	yes	characteristic
464	C₄	#541×C₇₉	1	1	yes	characteristic
465	C₄	#547×C₇₉	1	1	yes	characteristic
466	C₄	D₄×Q₈×C₇₉	1	1	yes	characteristic
467	C₂	—	8	2	no	—
468	C₂	C₇₉×#2429	1	1	yes	characteristic
469	C₂	C₂×#466×C₇₉	1	1	yes	characteristic
470	C₂	C₇₉×#3063	1	1	yes	characteristic
471	C₂	C₇₉×#3358	1	1	yes	characteristic
472	C₂	C₇₉×#3364	1	1	yes	characteristic
473	C₂	Q₈×D₈×C₇₉	1	1	yes	characteristic
474	C₂	C₇₉×#3381	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₉
prime radical	C₂²×D₄×C₇₉	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₉ ◁ C₂×C₄×Q₈×C₇₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₈×Q₈×C₇₉	C₂	semidirect
3. C₇₉×#2546	C₂	semidirect
5. C₇₉×#2086	C₂	semidirect
7. C₇₉×#1990	C₂	semidirect
8. C₇₉×#1947	C₂	semidirect
9. C₇₉×#1942	C₂	semidirect
83. #102×C₇₉	Q₈	semidirect
229. #25469	C₇₉	direct (N × H)
239. C₂×C₈×Q₈	C₂×C₇₉	semidirect
240. #2546	C₂×C₇₉	semidirect
242. #2086	C₂×C₇₉	semidirect
244. #1990	C₂×C₇₉	semidirect
245. #1947	C₂×C₇₉	semidirect
246. #1942	C₂×C₇₉	semidirect
249. C₇₉	#25469	direct (N × H)
321. #102	Q₈×C₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#474×C₇₉	2
C₂×C₈×Q₈×C₇₉	2
C₇₉×#2546	2
C₇₉×#2538	2
C₇₉×#2086	2
C₇₉×#2067	2
C₇₉×#1990	2
C₇₉×#1947	2
C₇₉×#1942	2
C₇₉×#1934	2
C₄×#102×C₇₉	2
#25469	79

Subgroups — C79×#25469 #34137158

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#25469 #34137158