Subgroups — C₇₉×#24531 #34136220

Order 20224.

1224 conjugacy classes of subgroups.

The subgroup lattice has 562 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×#2504	C₂	1	1	yes	maximal, characteristic, complemented
4	D₄×C₂²⋊C₄×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₉×#2073	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×#1824	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₉×#1804	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×#121×C₇₉	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₄×C₇₉	C₂²	1	2	yes	—
18	C₂²×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
19	C₂²×C₂²⋊C₄×C₇₉	—	2	1	no	—
20	#447×C₇₉	—	2	4	no	—
21	C₂×C₄⋊C₈×C₇₉	C₂²	1	2	yes	complemented
22	C₂×#102×C₇₉	—	2	4	no	—
23	C₂×#102×C₇₉	C₂²	1	2	yes	—
24	C₂×#102×C₇₉	C₂²	1	1	yes	characteristic
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	complemented
28	C₂×C₂²⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
29	#397×C₇₉	—	2	2	no	—
30	#390×C₇₉	C₂²	1	2	yes	—
31	#390×C₇₉	C₂²	1	2	yes	complemented
32	#386×C₇₉	—	2	1	no	—
33	#386×C₇₉	—	2	1	no	—
34	#386×C₇₉	—	2	2	no	—
35	#382×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	#121×C₇₉	—	2	2	no	—
66	#121×C₇₉	—	2	2	no	—
67	C₄×D₄×C₇₉	—	2	4	no	—
68	C₄×D₄×C₇₉	—	4	2	no	—
69	C₂×C₄⋊C₄×C₇₉	—	2	2	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	2	no	—
77	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
78	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
79	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
80	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
81	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
82	C₂×C₂²⋊C₄×C₇₉	—	4	4	no	—
83	C₂×C₂²⋊C₄×C₇₉	D₄	1	1	yes	characteristic
84	C₂×C₂²⋊C₄×C₇₉	D₄	1	1	yes	characteristic
85	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
86	C₄⋊C₈×C₇₉	—	4	2	no	—
87	#102×C₇₉	—	2	2	no	—
88	#102×C₇₉	—	2	2	no	—
89	#102×C₇₉	—	2	4	no	—
90	#102×C₇₉	—	2	4	no	—
91	#102×C₇₉	—	4	2	no	—
92	C₂²⋊C₈×C₇₉	—	2	2	no	—
93	#95×C₇₉	—	2	1	no	—
94	#95×C₇₉	—	2	2	no	—
95	#95×C₇₉	—	2	2	no	—
96	#95×C₇₉	D₄	1	2	yes	—
97	C₂⁴×C₇₉	—	2	1	no	—
98	C₂⁴×C₇₉	—	2	1	no	—
99	C₂⁴×C₇₉	—	2	4	no	—
100	C₂⁴×C₇₉	—	2	1	no	—
101	C₂⁴×C₇₉	—	4	4	no	—
102	C₂⁴×C₇₉	—	4	2	no	—
103	C₂⁴×C₇₉	—	4	2	no	—
104	C₂⁴×C₇₉	—	8	2	no	—
105	C₂⁴×C₇₉	C₂×D₄	1	1	yes	characteristic
106	C₂×D₄×C₇₉	—	2	8	no	—
107	C₂×D₄×C₇₉	—	2	4	no	—
108	C₂×D₄×C₇₉	—	2	1	no	—
109	C₂×D₄×C₇₉	—	2	1	no	—
110	C₂×D₄×C₇₉	—	2	2	no	—
111	C₂×D₄×C₇₉	—	2	1	no	—
112	C₂×D₄×C₇₉	—	2	1	no	—
113	C₂×D₄×C₇₉	—	2	2	no	—
114	C₂×D₄×C₇₉	—	2	2	no	—
115	C₂×D₄×C₇₉	—	2	2	no	—
116	C₂×D₄×C₇₉	—	2	2	no	—
117	C₂×D₄×C₇₉	—	4	4	no	—
118	C₂×D₄×C₇₉	—	4	8	no	—
119	C₂×D₄×C₇₉	—	4	4	no	—
120	C₂×D₄×C₇₉	—	4	2	no	—
121	C₂×D₄×C₇₉	—	4	2	no	—
122	C₂×D₄×C₇₉	—	4	2	no	—
123	C₂×D₄×C₇₉	C₂×D₄	1	2	yes	—
124	C₂×D₄×C₇₉	C₂×D₄	1	2	yes	—
125	C₂×D₄×C₇₉	#41	1	4	yes	—
126	C₂²×C₄×C₇₉	—	2	2	no	—
127	C₂²×C₄×C₇₉	—	2	2	no	—
128	C₂²×C₄×C₇₉	—	2	1	no	—
129	C₂²×C₄×C₇₉	—	2	2	no	—
130	C₂²×C₄×C₇₉	—	2	2	no	—
131	C₂²×C₄×C₇₉	—	4	4	no	—
132	C₂²×C₄×C₇₉	—	4	4	no	—
133	C₂²×C₄×C₇₉	—	4	2	no	—
134	C₂²×C₄×C₇₉	—	8	2	no	—
135	C₂²×C₄×C₇₉	—	8	2	no	—
136	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
137	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
138	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
140	C₂²×C₄×C₇₉	#41	1	2	yes	—
141	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
142	D₈×C₇₉	—	4	4	no	—
143	D₈×C₇₉	—	4	4	no	—
144	C₂×C₈×C₇₉	—	2	1	no	—
145	C₂×C₈×C₇₉	—	2	1	no	—
146	C₂×C₈×C₇₉	—	2	2	no	—
147	C₂×C₈×C₇₉	—	2	2	no	—
148	C₂×C₈×C₇₉	—	2	2	no	—
149	C₂×C₈×C₇₉	—	2	2	no	—
150	C₂×C₈×C₇₉	—	2	2	no	—
151	C₂×C₈×C₇₉	—	4	4	no	—
152	C₄⋊C₄×C₇₉	—	2	2	no	—
153	C₄⋊C₄×C₇₉	—	2	1	no	—
154	C₄⋊C₄×C₇₉	—	2	2	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	—	4	2	no	—
159	C₂²⋊C₄×C₇₉	—	2	2	no	—
160	C₂²⋊C₄×C₇₉	—	2	2	no	—
161	C₂²⋊C₄×C₇₉	—	4	4	no	—
162	C₂²⋊C₄×C₇₉	—	4	4	no	—
163	C₂²⋊C₄×C₇₉	—	4	2	no	—
164	C₂²⋊C₄×C₇₉	—	4	2	no	—
165	C₂²⋊C₄×C₇₉	—	8	2	no	—
166	C₂²⋊C₄×C₇₉	—	8	2	no	—
167	C₂²⋊C₄×C₇₉	—	8	2	no	—
168	C₄²×C₇₉	—	2	2	no	—
169	C₄²×C₇₉	—	2	2	no	—
170	C₂³×C₇₉	—	2	2	no	—
171	C₂³×C₇₉	—	2	2	no	—
172	C₂³×C₇₉	—	2	2	no	—
173	C₂³×C₇₉	—	2	4	no	—
174	C₂³×C₇₉	—	2	2	no	—
175	C₂³×C₇₉	—	4	8	no	—
176	C₂³×C₇₉	—	4	1	no	—
177	C₂³×C₇₉	—	4	1	no	—
178	C₂³×C₇₉	—	4	2	no	—
179	C₂³×C₇₉	—	4	2	no	—
180	C₂³×C₇₉	—	4	1	no	—
181	C₂³×C₇₉	—	4	1	no	—
182	C₂³×C₇₉	—	4	2	no	—
183	C₂³×C₇₉	—	4	8	no	—
184	C₂³×C₇₉	—	4	1	no	—
185	C₂³×C₇₉	—	4	2	no	—
186	C₂³×C₇₉	—	4	1	no	—
187	C₂³×C₇₉	—	4	1	no	—
188	C₂³×C₇₉	—	4	2	no	—
189	C₂³×C₇₉	—	8	4	no	—
190	C₂³×C₇₉	—	8	8	no	—
191	C₂³×C₇₉	—	8	8	no	—
192	C₂³×C₇₉	#121	1	2	yes	—
193	C₂³×C₇₉	#135	1	2	yes	—
194	C₂³×C₇₉	AGL(1,ℤ/8)	1	2	yes	—
195	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
196	D₄×C₇₉	—	2	2	no	—
197	D₄×C₇₉	—	2	2	no	—
198	D₄×C₇₉	—	2	2	no	—
199	D₄×C₇₉	—	2	4	no	—
200	D₄×C₇₉	—	4	8	no	—
201	D₄×C₇₉	—	4	1	no	—
202	D₄×C₇₉	—	4	1	no	—
203	D₄×C₇₉	—	4	2	no	—
204	D₄×C₇₉	—	4	2	no	—
205	D₄×C₇₉	—	8	4	no	—
206	D₄×C₇₉	#123	1	4	yes	—
207	C₂×C₄×C₇₉	—	2	2	no	—
208	C₂×C₄×C₇₉	—	2	2	no	—
209	C₂×C₄×C₇₉	—	2	2	no	—
210	C₂×C₄×C₇₉	—	2	4	no	—
211	C₂×C₄×C₇₉	—	2	2	no	—
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	—	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	2	no	—
222	C₂×C₄×C₇₉	—	4	1	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	—	8	8	no	—
227	C₂×C₄×C₇₉	—	8	4	no	—
228	C₂×C₄×C₇₉	#121	1	2	yes	—
229	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
230	C₂×C₄×C₇₉	C₂×#41	1	2	yes	—
231	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
232	C₂×C₄×C₇₉	H(5,𝔽₂)	1	2	yes	—
233	C₈×C₇₉	—	4	1	no	—
234	C₈×C₇₉	—	4	2	no	—
235	C₈×C₇₉	—	4	1	no	—
236	C₂²×C₇₉	—	2	2	no	—
237	C₂²×C₇₉	—	2	2	no	—
238	C₂²×C₇₉	—	2	4	no	—
239	C₂²×C₇₉	—	2	4	no	—
240	C₂²×C₇₉	—	2	4	no	—
241	C₂²×C₇₉	—	4	2	no	—
242	C₂²×C₇₉	—	4	2	no	—
243	C₂²×C₇₉	—	4	4	no	—
244	C₂²×C₇₉	—	4	4	no	—
245	C₂²×C₇₉	—	4	2	no	—
246	C₂²×C₇₉	—	4	2	no	—
247	C₂²×C₇₉	—	4	2	no	—
248	C₂²×C₇₉	—	8	16	no	—
249	C₂²×C₇₉	—	8	2	no	—
250	C₂²×C₇₉	—	8	2	no	—
251	C₂²×C₇₉	—	8	1	no	—
252	C₂²×C₇₉	—	8	1	no	—
253	C₂²×C₇₉	—	8	1	no	—
254	C₂²×C₇₉	—	8	2	no	—
255	C₂²×C₇₉	—	8	2	no	—
256	C₂²×C₇₉	#463	1	4	yes	—
257	C₂²×C₇₉	C₂×#121	1	1	yes	characteristic
258	C₂²×C₇₉	#546	1	2	yes	—
259	C₂²×C₇₉	C₂×#135	1	1	yes	characteristic
260	C₂²×C₇₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
261	C₂²×C₇₉	#576	1	2	yes	—
262	C₄×C₇₉	—	2	2	no	—
263	C₄×C₇₉	—	4	2	no	—
264	C₄×C₇₉	—	4	2	no	—
265	C₄×C₇₉	—	8	1	no	—
266	C₄×C₇₉	—	8	2	no	—
267	C₄×C₇₉	—	8	2	no	—
268	C₄×C₇₉	C₂×#123	1	1	yes	characteristic
269	C₄×C₇₉	#534	1	1	yes	characteristic
270	C₄×C₇₉	#551	1	2	yes	—
271	#24531	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
272	C₂×C₇₉	—	2	4	no	—
273	C₂×C₇₉	—	4	4	no	—
274	C₂×C₇₉	—	8	2	no	—
275	C₂×C₇₉	—	16	1	no	—
276	C₂×C₇₉	#2412	1	1	yes	characteristic
277	C₂×C₇₉	C₂×#463	1	1	yes	characteristic
278	C₂×C₇₉	#3041	1	1	yes	characteristic
279	C₂×C₇₉	#3297	1	2	yes	—
280	C₂×C₇₉	#3318	1	2	yes	—
281	C₂×#447	C₂×C₇₉	1	1	yes	characteristic
282	C₂²×#102	C₂×C₇₉	1	1	yes	characteristic, complemented
283	#2504	C₂×C₇₉	1	1	yes	characteristic, complemented
284	D₄×C₂²⋊C₄	C₂×C₇₉	1	1	yes	characteristic, complemented
285	#2073	C₂×C₇₉	1	2	yes	complemented
286	#2054	C₂×C₇₉	1	2	yes	complemented
287	#1893	C₂×C₇₉	1	1	yes	characteristic, complemented
288	#1879	C₂×C₇₉	1	2	yes	complemented
289	#1850	C₂×C₇₉	1	1	yes	characteristic, complemented
290	#1824	C₂×C₇₉	1	1	yes	characteristic, complemented
291	#1804	C₂×C₇₉	1	2	yes	complemented
292	C₇₉	#24531	1	1	yes	characteristic, direct product factor, Sylow
293	C₂³×D₄	C₂²×C₇₉	1	1	yes	characteristic
294	C₂²×D₈	C₂²×C₇₉	1	1	yes	characteristic
295	C₂²×D₈	C₂²×C₇₉	1	1	yes	characteristic
296	C₂³×C₈	C₂²×C₇₉	1	1	yes	characteristic
297	C₂×#121	C₂²×C₇₉	1	1	yes	characteristic
298	C₂×C₄×D₄	C₂²×C₇₉	1	2	yes	—
299	C₂²×C₄⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
300	C₂²×C₂²⋊C₄	—	2	1	no	—
301	#447	—	2	4	no	—
302	C₂×C₄⋊C₈	C₂²×C₇₉	1	2	yes	complemented
303	C₂×#102	—	2	4	no	—
304	C₂×#102	C₂²×C₇₉	1	2	yes	—
305	C₂×#102	C₂²×C₇₉	1	1	yes	characteristic
306	C₂×#102	C₂²×C₇₉	1	2	yes	—
307	C₂×#102	C₂²×C₇₉	1	1	yes	characteristic
308	C₂×#102	C₂²×C₇₉	1	2	yes	complemented
309	C₂×C₂²⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
310	#397	—	2	2	no	—
311	#390	C₂²×C₇₉	1	2	yes	—
312	#390	C₂²×C₇₉	1	2	yes	complemented
313	#386	—	2	1	no	—
314	#386	—	2	1	no	—
315	#386	—	2	2	no	—
316	#382	C₂²×C₇₉	1	2	yes	complemented
317	#380	C₂²×C₇₉	1	1	yes	characteristic
318	#379	—	2	1	no	—
319	C₄×C₂²⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
320	#340	C₂²×C₇₉	1	2	yes	complemented
321	#340	C₂²×C₇₉	1	2	yes	complemented
322	#340	C₂²×C₇₉	1	2	yes	complemented
323	#336	C₂²×C₇₉	1	2	yes	complemented
324	C₂⁵	—	2	1	no	—
325	C₂²×D₄	—	2	4	no	—
326	C₂²×D₄	—	2	1	no	—
327	C₂²×D₄	—	2	1	no	—
328	C₂²×D₄	—	2	2	no	—
329	C₂²×D₄	—	4	2	no	—
330	C₂²×D₄	D₄×C₇₉	1	4	yes	—
331	C₂²×D₄	C₂³×C₇₉	1	1	yes	characteristic
332	C₂²×D₄	C₂³×C₇₉	1	1	yes	characteristic
333	C₂²×D₄	C₂³×C₇₉	1	1	yes	characteristic
334	C₂³×C₄	—	2	1	no	—
335	C₂³×C₄	—	2	2	no	—
336	C₂³×C₄	C₂³×C₇₉	1	1	yes	characteristic
337	C₂×D₈	—	2	2	no	—
338	C₂×D₈	—	2	2	no	—
339	C₂×D₈	—	2	4	no	—
340	C₂×D₈	—	4	2	no	—
341	C₂²×C₈	—	2	2	no	—
342	C₂²×C₈	—	4	2	no	—
343	C₂²×C₈	C₂³×C₇₉	1	2	yes	—
344	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
345	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
346	#121	—	2	2	no	—
347	#121	—	2	2	no	—
348	C₄×D₄	—	2	4	no	—
349	C₄×D₄	—	4	2	no	—
350	C₂×C₄⋊C₄	—	2	2	no	—
351	C₂×C₄⋊C₄	—	2	2	no	—
352	C₂×C₄⋊C₄	—	2	1	no	—
353	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
354	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
355	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
356	C₂×C₂²⋊C₄	—	2	1	no	—
357	C₂×C₂²⋊C₄	—	2	2	no	—
358	C₂×C₂²⋊C₄	—	2	2	no	—
359	C₂×C₂²⋊C₄	—	2	1	no	—
360	C₂×C₂²⋊C₄	—	2	2	no	—
361	C₂×C₂²⋊C₄	—	2	2	no	—
362	C₂×C₂²⋊C₄	—	2	2	no	—
363	C₂×C₂²⋊C₄	—	4	4	no	—
364	C₂×C₂²⋊C₄	D₄×C₇₉	1	1	yes	characteristic
365	C₂×C₂²⋊C₄	D₄×C₇₉	1	1	yes	characteristic
366	C₂×C₄²	C₂³×C₇₉	1	2	yes	—
367	C₄⋊C₈	—	4	2	no	—
368	#102	—	2	4	no	—
369	#102	—	2	4	no	—
370	#102	—	2	2	no	—
371	#102	—	2	2	no	—
372	#102	—	4	2	no	—
373	C₂²⋊C₈	—	2	2	no	—
374	#95	—	2	1	no	—
375	#95	—	2	2	no	—
376	#95	—	2	2	no	—
377	#95	D₄×C₇₉	1	2	yes	—
378	C₂⁴	—	2	1	no	—
379	C₂⁴	—	2	1	no	—
380	C₂⁴	—	2	4	no	—
381	C₂⁴	—	2	1	no	—
382	C₂⁴	—	4	4	no	—
383	C₂⁴	—	4	2	no	—
384	C₂⁴	—	4	2	no	—
385	C₂⁴	—	8	2	no	—
386	C₂⁴	C₂×D₄×C₇₉	1	1	yes	characteristic
387	C₂×D₄	—	2	8	no	—
388	C₂×D₄	—	2	4	no	—
389	C₂×D₄	—	2	1	no	—
390	C₂×D₄	—	2	1	no	—
391	C₂×D₄	—	2	2	no	—
392	C₂×D₄	—	2	1	no	—
393	C₂×D₄	—	2	1	no	—
394	C₂×D₄	—	2	2	no	—
395	C₂×D₄	—	2	2	no	—
396	C₂×D₄	—	2	2	no	—
397	C₂×D₄	—	2	2	no	—
398	C₂×D₄	—	4	4	no	—
399	C₂×D₄	—	4	8	no	—
400	C₂×D₄	—	4	4	no	—
401	C₂×D₄	—	4	2	no	—
402	C₂×D₄	—	4	2	no	—
403	C₂×D₄	—	4	2	no	—
404	C₂×D₄	C₂×D₄×C₇₉	1	2	yes	—
405	C₂×D₄	C₂×D₄×C₇₉	1	2	yes	—
406	C₂×D₄	#41×C₇₉	1	4	yes	—
407	C₂²×C₄	—	2	2	no	—
408	C₂²×C₄	—	2	2	no	—
409	C₂²×C₄	—	2	1	no	—
410	C₂²×C₄	—	2	2	no	—
411	C₂²×C₄	—	2	2	no	—
412	C₂²×C₄	—	4	4	no	—
413	C₂²×C₄	—	4	4	no	—
414	C₂²×C₄	—	4	2	no	—
415	C₂²×C₄	—	8	2	no	—
416	C₂²×C₄	—	8	2	no	—
417	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
418	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
419	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
420	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
421	C₂²×C₄	#41×C₇₉	1	2	yes	—
422	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
423	D₈	—	4	4	no	—
424	D₈	—	4	4	no	—
425	C₂×C₈	—	2	1	no	—
426	C₂×C₈	—	2	1	no	—
427	C₂×C₈	—	2	2	no	—
428	C₂×C₈	—	2	2	no	—
429	C₂×C₈	—	2	2	no	—
430	C₂×C₈	—	2	2	no	—
431	C₂×C₈	—	2	2	no	—
432	C₂×C₈	—	4	4	no	—
433	C₄⋊C₄	—	2	2	no	—
434	C₄⋊C₄	—	2	1	no	—
435	C₄⋊C₄	—	2	2	no	—
436	C₄⋊C₄	—	2	2	no	—
437	C₄⋊C₄	—	2	1	no	—
438	C₄⋊C₄	—	2	2	no	—
439	C₄⋊C₄	—	4	2	no	—
440	C₂²⋊C₄	—	2	2	no	—
441	C₂²⋊C₄	—	2	2	no	—
442	C₂²⋊C₄	—	4	4	no	—
443	C₂²⋊C₄	—	4	4	no	—
444	C₂²⋊C₄	—	4	2	no	—
445	C₂²⋊C₄	—	4	2	no	—
446	C₂²⋊C₄	—	8	2	no	—
447	C₂²⋊C₄	—	8	2	no	—
448	C₂²⋊C₄	—	8	2	no	—
449	C₄²	—	2	2	no	—
450	C₄²	—	2	2	no	—
451	C₂³	—	2	2	no	—
452	C₂³	—	2	2	no	—
453	C₂³	—	2	2	no	—
454	C₂³	—	2	4	no	—
455	C₂³	—	2	2	no	—
456	C₂³	—	4	8	no	—
457	C₂³	—	4	1	no	—
458	C₂³	—	4	1	no	—
459	C₂³	—	4	2	no	—
460	C₂³	—	4	8	no	—
461	C₂³	—	4	2	no	—
462	C₂³	—	4	1	no	—
463	C₂³	—	4	1	no	—
464	C₂³	—	4	2	no	—
465	C₂³	—	4	1	no	—
466	C₂³	—	4	2	no	—
467	C₂³	—	4	1	no	—
468	C₂³	—	4	1	no	—
469	C₂³	—	4	2	no	—
470	C₂³	—	8	4	no	—
471	C₂³	—	8	8	no	—
472	C₂³	—	8	8	no	—
473	C₂³	#121×C₇₉	1	2	yes	—
474	C₂³	#135×C₇₉	1	2	yes	—
475	C₂³	AGL(1,ℤ/8)×C₇₉	1	2	yes	—
476	C₂³	C₂²×D₄×C₇₉	1	1	yes	characteristic
477	D₄	—	2	2	no	—
478	D₄	—	2	2	no	—
479	D₄	—	2	2	no	—
480	D₄	—	2	4	no	—
481	D₄	—	4	8	no	—
482	D₄	—	4	1	no	—
483	D₄	—	4	1	no	—
484	D₄	—	4	2	no	—
485	D₄	—	4	2	no	—
486	D₄	—	8	4	no	—
487	D₄	#123×C₇₉	1	4	yes	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	4	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	4	1	no	—
499	C₂×C₄	—	4	2	no	—
500	C₂×C₄	—	4	2	no	—
501	C₂×C₄	—	4	1	no	—
502	C₂×C₄	—	4	2	no	—
503	C₂×C₄	—	4	1	no	—
504	C₂×C₄	—	4	2	no	—
505	C₂×C₄	—	4	2	no	—
506	C₂×C₄	—	4	2	no	—
507	C₂×C₄	—	8	8	no	—
508	C₂×C₄	—	8	4	no	—
509	C₂×C₄	#121×C₇₉	1	2	yes	—
510	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
511	C₂×C₄	C₂×#41×C₇₉	1	2	yes	—
512	C₂×C₄	C₂×#41×C₇₉	1	1	yes	characteristic
513	C₂×C₄	H(5,𝔽₂)×C₇₉	1	2	yes	—
514	C₈	—	4	1	no	—
515	C₈	—	4	2	no	—
516	C₈	—	4	1	no	—
517	C₂²	—	2	2	no	—
518	C₂²	—	2	4	no	—
519	C₂²	—	2	4	no	—
520	C₂²	—	2	2	no	—
521	C₂²	—	2	4	no	—
522	C₂²	—	4	2	no	—
523	C₂²	—	4	2	no	—
524	C₂²	—	4	4	no	—
525	C₂²	—	4	4	no	—
526	C₂²	—	4	2	no	—
527	C₂²	—	4	2	no	—
528	C₂²	—	4	2	no	—
529	C₂²	—	8	16	no	—
530	C₂²	—	8	2	no	—
531	C₂²	—	8	2	no	—
532	C₂²	—	8	1	no	—
533	C₂²	—	8	1	no	—
534	C₂²	—	8	2	no	—
535	C₂²	—	8	2	no	—
536	C₂²	—	8	1	no	—
537	C₂²	#463×C₇₉	1	4	yes	—
538	C₂²	C₂×#121×C₇₉	1	1	yes	characteristic
539	C₂²	#546×C₇₉	1	2	yes	—
540	C₂²	C₂×#135×C₇₉	1	1	yes	characteristic
541	C₂²	C₂×AGL(1,ℤ/8)×C₇₉	1	1	yes	characteristic
542	C₂²	#576×C₇₉	1	2	yes	—
543	C₄	—	2	2	no	—
544	C₄	—	4	2	no	—
545	C₄	—	4	2	no	—
546	C₄	—	8	1	no	—
547	C₄	—	8	2	no	—
548	C₄	—	8	2	no	—
549	C₄	C₂×#123×C₇₉	1	1	yes	characteristic
550	C₄	#534×C₇₉	1	1	yes	characteristic
551	C₄	#551×C₇₉	1	2	yes	—
552	C₂	—	2	4	no	—
553	C₂	—	4	4	no	—
554	C₂	—	8	2	no	—
555	C₂	—	16	1	no	—
556	C₂	C₇₉×#2412	1	1	yes	characteristic
557	C₂	C₂×#463×C₇₉	1	1	yes	characteristic
558	C₂	C₇₉×#3041	1	1	yes	characteristic
559	C₂	C₇₉×#3297	1	2	yes	—
560	C₂	C₇₉×#3318	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×#2504	C₂	semidirect
4. D₄×C₂²⋊C₄×C₇₉	C₂	semidirect
5. C₇₉×#2073	C₂	semidirect
6. C₇₉×#2054	C₂	semidirect
7. C₇₉×#1893	C₂	semidirect
8. C₇₉×#1879	C₂	semidirect
9. C₇₉×#1850	C₂	semidirect
10. C₇₉×#1824	C₂	semidirect
11. C₇₉×#1804	C₂	semidirect
21. C₂×C₄⋊C₈×C₇₉	C₂²	semidirect
27. C₂×#102×C₇₉	C₂²	semidirect
31. #390×C₇₉	C₂²	semidirect
35. #382×C₇₉	C₂²	semidirect
39. #340×C₇₉	C₂²	semidirect
40. #340×C₇₉	C₂²	semidirect
41. #340×C₇₉	C₂²	semidirect
42. #336×C₇₉	C₂²	semidirect
271. #24531	C₇₉	direct (N × H)
282. C₂²×#102	C₂×C₇₉	semidirect
283. #2504	C₂×C₇₉	semidirect
284. D₄×C₂²⋊C₄	C₂×C₇₉	semidirect
285. #2073	C₂×C₇₉	semidirect
286. #2054	C₂×C₇₉	semidirect
287. #1893	C₂×C₇₉	semidirect
288. #1879	C₂×C₇₉	semidirect
289. #1850	C₂×C₇₉	semidirect
290. #1824	C₂×C₇₉	semidirect
291. #1804	C₂×C₇₉	semidirect
292. C₇₉	#24531	direct (N × H)
302. C₂×C₄⋊C₈	C₂²×C₇₉	semidirect
308. C₂×#102	C₂²×C₇₉	semidirect
312. #390	C₂²×C₇₉	semidirect
316. #382	C₂²×C₇₉	semidirect
320. #340	C₂²×C₇₉	semidirect
321. #340	C₂²×C₇₉	semidirect
322. #340	C₂²×C₇₉	semidirect
323. #336	C₂²×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×#2504	2
D₄×C₂²⋊C₄×C₇₉	2
C₇₉×#2073	2
C₇₉×#2054	2
C₇₉×#1893	2
C₇₉×#1879	2
C₇₉×#1850	2
C₇₉×#1824	2
C₇₉×#1804	2
#24531	79

Subgroups — C79×#24531 #34136220

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#24531 #34136220