Subgroups — C₇₉×#24542 #34136231

Order 20224.

1078 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#449×C₇₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#417×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₉×#2501	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₉×#2341	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×#1895	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₉×#1880	C₂	1	2	yes	maximal, complemented
9	C₇₉×#1851	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₉×#1824	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₉×#1803	C₂	1	2	yes	maximal, complemented
12	C₂²×#41×C₇₉	C₂²	1	1	yes	characteristic
13	C₂²×SD₁₆×C₇₉	C₂²	1	1	yes	characteristic
14	C₂²×D₈×C₇₉	C₂²	1	1	yes	characteristic
15	C₂²×M₁₆×C₇₉	C₂²	1	1	yes	characteristic
16	C₂×#123×C₇₉	—	2	2	no	—
17	C₂×#121×C₇₉	C₂²	1	1	yes	characteristic
18	C₂×C₄×Q₈×C₇₉	C₂²	1	2	yes	—
19	C₂²×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
20	#449×C₇₉	—	2	4	no	—
21	C₂×C₄⋊C₈×C₇₉	C₂²	1	2	yes	—
22	#417×C₇₉	—	2	4	no	—
23	C₂×#103×C₇₉	C₂²	1	1	yes	characteristic
24	C₂×#103×C₇₉	C₂²	1	2	yes	—
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×C₂²⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
29	#399×C₇₉	—	2	1	no	—
30	#399×C₇₉	—	2	1	no	—
31	#390×C₇₉	—	2	2	no	—
32	#390×C₇₉	C₂²	1	2	yes	—
33	#390×C₇₉	C₂²	1	2	yes	—
34	#384×C₇₉	C₂²	1	2	yes	—
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	C₂×#41×C₇₉	—	2	2	no	—
44	C₂×#41×C₇₉	—	2	4	no	—
45	C₂×#41×C₇₉	—	4	2	no	—
46	C₂×#41×C₇₉	D₄	1	4	yes	—
47	C₂²×Q₈×C₇₉	C₂³	1	1	yes	characteristic
48	C₂²×D₄×C₇₉	—	2	1	no	—
49	C₂²×D₄×C₇₉	—	2	1	no	—
50	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
51	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
52	C₂³×C₄×C₇₉	—	2	1	no	—
53	C₂³×C₄×C₇₉	—	2	1	no	—
54	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
55	C₂×SD₁₆×C₇₉	—	2	2	no	—
56	C₂×SD₁₆×C₇₉	—	2	4	no	—
57	C₂×D₈×C₇₉	—	2	2	no	—
58	C₂×D₈×C₇₉	—	4	2	no	—
59	C₂×M₁₆×C₇₉	—	2	2	no	—
60	C₂×M₁₆×C₇₉	—	4	2	no	—
61	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
62	C₂²×C₈×C₇₉	C₂³	1	2	yes	—
63	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
64	#123×C₇₉	—	4	8	no	—
65	#121×C₇₉	—	2	2	no	—
66	#121×C₇₉	—	2	2	no	—
67	C₄×Q₈×C₇₉	—	2	4	no	—
68	C₄×Q₈×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	—	2	2	no	—
73	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
74	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
75	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
76	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
77	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
83	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
84	C₂×C₂²⋊C₄×C₇₉	D₄	1	2	yes	—
85	C₂×C₄²×C₇₉	—	2	2	no	—
86	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
87	C₄⋊C₈×C₇₉	—	4	2	no	—
88	#103×C₇₉	—	2	4	no	—
89	#103×C₇₉	—	2	2	no	—
90	#102×C₇₉	—	2	4	no	—
91	#102×C₇₉	—	2	2	no	—
92	#102×C₇₉	—	4	2	no	—
93	C₂²⋊C₈×C₇₉	—	2	2	no	—
94	#95×C₇₉	—	2	1	no	—
95	#95×C₇₉	D₄	1	1	yes	characteristic
96	#95×C₇₉	D₄	1	1	yes	characteristic
97	C₂⁴×C₇₉	—	2	1	no	—
98	C₂⁴×C₇₉	—	2	1	no	—
99	C₂⁴×C₇₉	C₂×D₄	1	1	yes	characteristic
100	#41×C₇₉	—	2	8	no	—
101	#41×C₇₉	—	4	4	no	—
102	#41×C₇₉	—	4	8	no	—
103	C₂×Q₈×C₇₉	—	2	1	no	—
104	C₂×Q₈×C₇₉	—	2	2	no	—
105	C₂×Q₈×C₇₉	C₂×D₄	1	2	yes	—
106	C₂×Q₈×C₇₉	#41	1	4	yes	—
107	C₂×D₄×C₇₉	—	2	4	no	—
108	C₂×D₄×C₇₉	—	2	1	no	—
109	C₂×D₄×C₇₉	—	2	2	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	2	no	—
114	C₂×D₄×C₇₉	—	2	2	no	—
115	C₂×D₄×C₇₉	—	4	4	no	—
116	C₂×D₄×C₇₉	—	4	4	no	—
117	C₂×D₄×C₇₉	—	4	2	no	—
118	C₂×D₄×C₇₉	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₇₉	—	2	1	no	—
120	C₂²×C₄×C₇₉	—	2	2	no	—
121	C₂²×C₄×C₇₉	—	2	2	no	—
122	C₂²×C₄×C₇₉	—	2	4	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	—	4	4	no	—
127	C₂²×C₄×C₇₉	—	4	4	no	—
128	C₂²×C₄×C₇₉	—	4	2	no	—
129	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
130	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
132	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
133	C₂²×C₄×C₇₉	#41	1	2	yes	—
134	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
135	SD₁₆×C₇₉	—	4	4	no	—
136	D₈×C₇₉	—	4	4	no	—
137	M₁₆×C₇₉	—	4	4	no	—
138	C₂×C₈×C₇₉	—	2	1	no	—
139	C₂×C₈×C₇₉	—	2	1	no	—
140	C₂×C₈×C₇₉	—	2	2	no	—
141	C₂×C₈×C₇₉	—	2	2	no	—
142	C₂×C₈×C₇₉	—	2	2	no	—
143	C₂×C₈×C₇₉	—	2	2	no	—
144	C₂×C₈×C₇₉	—	2	2	no	—
145	C₄⋊C₄×C₇₉	—	2	2	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	—	2	1	no	—
150	C₄⋊C₄×C₇₉	—	2	2	no	—
151	C₄⋊C₄×C₇₉	—	4	4	no	—
152	C₄⋊C₄×C₇₉	—	4	4	no	—
153	C₄⋊C₄×C₇₉	—	4	2	no	—
154	C₄⋊C₄×C₇₉	—	4	4	no	—
155	C₂²⋊C₄×C₇₉	—	2	4	no	—
156	C₂²⋊C₄×C₇₉	—	4	4	no	—
157	C₂²⋊C₄×C₇₉	—	4	2	no	—
158	C₂²⋊C₄×C₇₉	—	4	4	no	—
159	C₂²⋊C₄×C₇₉	—	4	4	no	—
160	C₂²⋊C₄×C₇₉	—	8	2	no	—
161	C₂²⋊C₄×C₇₉	—	8	1	no	—
162	C₄²×C₇₉	—	2	2	no	—
163	C₄²×C₇₉	—	2	2	no	—
164	C₄²×C₇₉	—	4	4	no	—
165	C₂³×C₇₉	—	2	2	no	—
166	C₂³×C₇₉	—	2	2	no	—
167	C₂³×C₇₉	—	2	1	no	—
168	C₂³×C₇₉	—	2	1	no	—
169	C₂³×C₇₉	—	2	2	no	—
170	C₂³×C₇₉	—	4	2	no	—
171	C₂³×C₇₉	—	4	2	no	—
172	C₂³×C₇₉	—	4	1	no	—
173	C₂³×C₇₉	—	4	1	no	—
174	C₂³×C₇₉	—	4	1	no	—
175	C₂³×C₇₉	—	4	2	no	—
176	C₂³×C₇₉	—	4	2	no	—
177	C₂³×C₇₉	—	4	1	no	—
178	C₂³×C₇₉	—	4	1	no	—
179	C₂³×C₇₉	#121	1	2	yes	—
180	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
181	Q₈×C₇₉	—	2	2	no	—
182	Q₈×C₇₉	—	2	4	no	—
183	Q₈×C₇₉	#123	1	4	yes	complemented
184	D₄×C₇₉	—	2	2	no	—
185	D₄×C₇₉	—	2	2	no	—
186	D₄×C₇₉	—	4	8	no	—
187	D₄×C₇₉	—	4	1	no	—
188	D₄×C₇₉	—	4	1	no	—
189	D₄×C₇₉	—	4	2	no	—
190	D₄×C₇₉	—	4	2	no	—
191	D₄×C₇₉	—	8	4	no	—
192	C₂×C₄×C₇₉	—	2	2	no	—
193	C₂×C₄×C₇₉	—	2	2	no	—
194	C₂×C₄×C₇₉	—	2	4	no	—
195	C₂×C₄×C₇₉	—	2	2	no	—
196	C₂×C₄×C₇₉	—	2	2	no	—
197	C₂×C₄×C₇₉	—	2	2	no	—
198	C₂×C₄×C₇₉	—	2	2	no	—
199	C₂×C₄×C₇₉	—	2	4	no	—
200	C₂×C₄×C₇₉	—	2	2	no	—
201	C₂×C₄×C₇₉	—	2	2	no	—
202	C₂×C₄×C₇₉	—	2	2	no	—
203	C₂×C₄×C₇₉	—	4	8	no	—
204	C₂×C₄×C₇₉	—	4	1	no	—
205	C₂×C₄×C₇₉	—	4	2	no	—
206	C₂×C₄×C₇₉	—	4	2	no	—
207	C₂×C₄×C₇₉	—	4	2	no	—
208	C₂×C₄×C₇₉	—	4	2	no	—
209	C₂×C₄×C₇₉	—	4	2	no	—
210	C₂×C₄×C₇₉	—	4	2	no	—
211	C₂×C₄×C₇₉	—	4	2	no	—
212	C₂×C₄×C₇₉	—	8	4	no	—
213	C₂×C₄×C₇₉	#121	1	2	yes	—
214	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	4	yes	—
215	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
216	C₂×C₄×C₇₉	C₂×#41	1	2	yes	—
217	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
218	C₂×C₄×C₇₉	H(5,𝔽₂)	1	2	yes	—
219	C₈×C₇₉	—	4	1	no	—
220	C₈×C₇₉	—	4	2	no	—
221	C₈×C₇₉	—	4	1	no	—
222	C₂²×C₇₉	—	2	2	no	—
223	C₂²×C₇₉	—	2	2	no	—
224	C₂²×C₇₉	—	2	2	no	—
225	C₂²×C₇₉	—	4	2	no	—
226	C₂²×C₇₉	—	4	2	no	—
227	C₂²×C₇₉	—	4	2	no	—
228	C₂²×C₇₉	—	4	2	no	—
229	C₂²×C₇₉	—	4	2	no	—
230	C₂²×C₇₉	—	8	2	no	—
231	C₂²×C₇₉	—	8	2	no	—
232	C₂²×C₇₉	—	8	2	no	—
233	C₂²×C₇₉	—	8	1	no	—
234	C₂²×C₇₉	—	8	1	no	—
235	C₂²×C₇₉	—	8	1	no	—
236	C₂²×C₇₉	—	8	2	no	—
237	C₂²×C₇₉	C₂×#121	1	1	yes	characteristic
238	C₂²×C₇₉	#546	1	2	yes	—
239	C₂²×C₇₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
240	C₂²×C₇₉	#577	1	1	yes	characteristic
241	C₂²×C₇₉	#578	1	1	yes	characteristic
242	C₄×C₇₉	—	2	2	no	—
243	C₄×C₇₉	—	2	4	no	—
244	C₄×C₇₉	—	2	4	no	—
245	C₄×C₇₉	—	4	2	no	—
246	C₄×C₇₉	—	8	2	no	—
247	C₄×C₇₉	—	8	2	no	—
248	C₄×C₇₉	—	8	1	no	—
249	C₄×C₇₉	C₂×#123	1	1	yes	characteristic
250	C₄×C₇₉	#534	1	1	yes	characteristic
251	C₄×C₇₉	#551	1	2	yes	—
252	#24542	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
253	C₂×C₇₉	—	4	2	no	—
254	C₂×C₇₉	—	8	2	no	—
255	C₂×C₇₉	—	16	1	no	—
256	C₂×C₇₉	#2412	1	1	yes	characteristic
257	C₂×C₇₉	#3038	1	1	yes	characteristic
258	C₂×C₇₉	#3046	1	1	yes	characteristic
259	C₂×C₇₉	#3308	1	2	yes	—
260	C₂×C₇₉	#3332	1	2	yes	—
261	C₂×#449	C₂×C₇₉	1	1	yes	characteristic
262	C₂×#417	C₂×C₇₉	1	1	yes	characteristic, complemented
263	#2501	C₂×C₇₉	1	1	yes	characteristic, complemented
264	#2341	C₂×C₇₉	1	1	yes	characteristic, complemented
265	#2071	C₂×C₇₉	1	2	yes	complemented
266	#2054	C₂×C₇₉	1	2	yes	complemented
267	#1895	C₂×C₇₉	1	1	yes	characteristic, complemented
268	#1880	C₂×C₇₉	1	2	yes	complemented
269	#1851	C₂×C₇₉	1	1	yes	characteristic, complemented
270	#1824	C₂×C₇₉	1	1	yes	characteristic, complemented
271	#1803	C₂×C₇₉	1	2	yes	complemented
272	C₇₉	#24542	1	1	yes	characteristic, direct product factor, Sylow
273	C₂²×#41	C₂²×C₇₉	1	1	yes	characteristic
274	C₂²×SD₁₆	C₂²×C₇₉	1	1	yes	characteristic
275	C₂²×D₈	C₂²×C₇₉	1	1	yes	characteristic
276	C₂²×M₁₆	C₂²×C₇₉	1	1	yes	characteristic
277	C₂×#123	—	2	2	no	—
278	C₂×#121	C₂²×C₇₉	1	1	yes	characteristic
279	C₂×C₄×Q₈	C₂²×C₇₉	1	2	yes	—
280	C₂²×C₄⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
281	#449	—	2	4	no	—
282	C₂×C₄⋊C₈	C₂²×C₇₉	1	2	yes	—
283	#417	—	2	4	no	—
284	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic
285	C₂×#103	C₂²×C₇₉	1	2	yes	—
286	C₂×#102	C₂²×C₇₉	1	2	yes	—
287	C₂×#102	C₂²×C₇₉	1	1	yes	characteristic
288	C₂×#102	C₂²×C₇₉	1	2	yes	—
289	C₂×C₂²⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
290	#399	—	2	1	no	—
291	#399	—	2	1	no	—
292	#390	—	2	2	no	—
293	#390	C₂²×C₇₉	1	2	yes	—
294	#390	C₂²×C₇₉	1	2	yes	—
295	#384	C₂²×C₇₉	1	2	yes	—
296	#380	—	2	1	no	—
297	#380	C₂²×C₇₉	1	1	yes	characteristic
298	C₄×C₂²⋊C₄	—	2	1	no	—
299	C₄×C₂²⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
300	#340	C₂²×C₇₉	1	2	yes	—
301	#340	C₂²×C₇₉	1	2	yes	—
302	#340	C₂²×C₇₉	1	2	yes	—
303	#336	C₂²×C₇₉	1	2	yes	—
304	C₂×#41	—	2	2	no	—
305	C₂×#41	—	2	4	no	—
306	C₂×#41	—	4	2	no	—
307	C₂×#41	D₄×C₇₉	1	4	yes	—
308	C₂²×Q₈	C₂³×C₇₉	1	1	yes	characteristic
309	C₂²×D₄	—	2	1	no	—
310	C₂²×D₄	—	2	1	no	—
311	C₂²×D₄	C₂³×C₇₉	1	1	yes	characteristic
312	C₂²×D₄	C₂³×C₇₉	1	1	yes	characteristic
313	C₂³×C₄	—	2	1	no	—
314	C₂³×C₄	—	2	1	no	—
315	C₂³×C₄	C₂³×C₇₉	1	1	yes	characteristic
316	C₂×SD₁₆	—	2	2	no	—
317	C₂×SD₁₆	—	2	4	no	—
318	C₂×D₈	—	2	2	no	—
319	C₂×D₈	—	4	2	no	—
320	C₂×M₁₆	—	2	2	no	—
321	C₂×M₁₆	—	4	2	no	—
322	C₂²×C₈	C₂³×C₇₉	1	2	yes	—
323	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
324	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
325	#123	—	4	8	no	—
326	#121	—	2	2	no	—
327	#121	—	2	2	no	—
328	C₄×Q₈	—	2	4	no	—
329	C₄×Q₈	—	4	2	no	—
330	C₂×C₄⋊C₄	—	2	2	no	—
331	C₂×C₄⋊C₄	—	2	2	no	—
332	C₂×C₄⋊C₄	—	2	1	no	—
333	C₂×C₄⋊C₄	—	2	2	no	—
334	C₂×C₄⋊C₄	—	2	2	no	—
335	C₂×C₄⋊C₄	—	2	2	no	—
336	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
337	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
338	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
339	C₂×C₂²⋊C₄	—	2	1	no	—
340	C₂×C₂²⋊C₄	—	2	2	no	—
341	C₂×C₂²⋊C₄	—	2	2	no	—
342	C₂×C₂²⋊C₄	—	2	2	no	—
343	C₂×C₂²⋊C₄	—	2	1	no	—
344	C₂×C₂²⋊C₄	—	2	2	no	—
345	C₂×C₂²⋊C₄	D₄×C₇₉	1	2	yes	—
346	C₂×C₄²	—	2	2	no	—
347	C₂×C₄²	C₂³×C₇₉	1	2	yes	—
348	C₄⋊C₈	—	4	2	no	—
349	#103	—	2	4	no	—
350	#103	—	2	2	no	—
351	#102	—	2	4	no	—
352	#102	—	2	2	no	—
353	#102	—	4	2	no	—
354	C₂²⋊C₈	—	2	2	no	—
355	#95	—	2	1	no	—
356	#95	D₄×C₇₉	1	1	yes	characteristic
357	#95	D₄×C₇₉	1	1	yes	characteristic
358	C₂⁴	—	2	1	no	—
359	C₂⁴	—	2	1	no	—
360	C₂⁴	C₂×D₄×C₇₉	1	1	yes	characteristic
361	#41	—	2	8	no	—
362	#41	—	4	4	no	—
363	#41	—	4	8	no	—
364	C₂×Q₈	—	2	1	no	—
365	C₂×Q₈	—	2	2	no	—
366	C₂×Q₈	C₂×D₄×C₇₉	1	2	yes	—
367	C₂×Q₈	#41×C₇₉	1	4	yes	—
368	C₂×D₄	—	2	4	no	—
369	C₂×D₄	—	2	1	no	—
370	C₂×D₄	—	2	2	no	—
371	C₂×D₄	—	2	1	no	—
372	C₂×D₄	—	2	1	no	—
373	C₂×D₄	—	2	2	no	—
374	C₂×D₄	—	2	2	no	—
375	C₂×D₄	—	2	2	no	—
376	C₂×D₄	—	4	4	no	—
377	C₂×D₄	—	4	4	no	—
378	C₂×D₄	—	4	2	no	—
379	C₂×D₄	C₂×D₄×C₇₉	1	2	yes	—
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	—	2	2	no	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	2	4	no	—
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	2	1	no	—
387	C₂²×C₄	—	4	4	no	—
388	C₂²×C₄	—	4	4	no	—
389	C₂²×C₄	—	4	2	no	—
390	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
391	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
392	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
393	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
394	C₂²×C₄	#41×C₇₉	1	2	yes	—
395	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
396	SD₁₆	—	4	4	no	—
397	D₈	—	4	4	no	—
398	M₁₆	—	4	4	no	—
399	C₂×C₈	—	2	1	no	—
400	C₂×C₈	—	2	1	no	—
401	C₂×C₈	—	2	2	no	—
402	C₂×C₈	—	2	2	no	—
403	C₂×C₈	—	2	2	no	—
404	C₂×C₈	—	2	2	no	—
405	C₂×C₈	—	2	2	no	—
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	—	2	1	no	—
408	C₄⋊C₄	—	2	2	no	—
409	C₄⋊C₄	—	2	2	no	—
410	C₄⋊C₄	—	2	1	no	—
411	C₄⋊C₄	—	2	2	no	—
412	C₄⋊C₄	—	4	4	no	—
413	C₄⋊C₄	—	4	4	no	—
414	C₄⋊C₄	—	4	2	no	—
415	C₄⋊C₄	—	4	4	no	—
416	C₂²⋊C₄	—	2	4	no	—
417	C₂²⋊C₄	—	4	4	no	—
418	C₂²⋊C₄	—	4	2	no	—
419	C₂²⋊C₄	—	4	4	no	—
420	C₂²⋊C₄	—	4	4	no	—
421	C₂²⋊C₄	—	8	2	no	—
422	C₂²⋊C₄	—	8	1	no	—
423	C₄²	—	2	2	no	—
424	C₄²	—	2	2	no	—
425	C₄²	—	4	4	no	—
426	C₂³	—	2	2	no	—
427	C₂³	—	2	2	no	—
428	C₂³	—	2	1	no	—
429	C₂³	—	2	1	no	—
430	C₂³	—	2	2	no	—
431	C₂³	—	4	2	no	—
432	C₂³	—	4	2	no	—
433	C₂³	—	4	1	no	—
434	C₂³	—	4	1	no	—
435	C₂³	—	4	1	no	—
436	C₂³	—	4	2	no	—
437	C₂³	—	4	2	no	—
438	C₂³	—	4	1	no	—
439	C₂³	—	4	1	no	—
440	C₂³	#121×C₇₉	1	2	yes	—
441	C₂³	C₂²×D₄×C₇₉	1	1	yes	characteristic
442	Q₈	—	2	2	no	—
443	Q₈	—	2	4	no	—
444	Q₈	#123×C₇₉	1	4	yes	complemented
445	D₄	—	2	2	no	—
446	D₄	—	2	2	no	—
447	D₄	—	4	8	no	—
448	D₄	—	4	1	no	—
449	D₄	—	4	1	no	—
450	D₄	—	4	2	no	—
451	D₄	—	4	2	no	—
452	D₄	—	8	4	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	4	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	4	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	4	8	no	—
465	C₂×C₄	—	4	1	no	—
466	C₂×C₄	—	4	2	no	—
467	C₂×C₄	—	4	2	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	—	4	2	no	—
470	C₂×C₄	—	4	2	no	—
471	C₂×C₄	—	4	2	no	—
472	C₂×C₄	—	4	2	no	—
473	C₂×C₄	—	8	4	no	—
474	C₂×C₄	#121×C₇₉	1	2	yes	—
475	C₂×C₄	AGL(1,ℤ/8)×C₇₉	1	4	yes	—
476	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
477	C₂×C₄	C₂×#41×C₇₉	1	2	yes	—
478	C₂×C₄	C₂×#41×C₇₉	1	1	yes	characteristic
479	C₂×C₄	H(5,𝔽₂)×C₇₉	1	2	yes	—
480	C₈	—	4	1	no	—
481	C₈	—	4	2	no	—
482	C₈	—	4	1	no	—
483	C₂²	—	2	2	no	—
484	C₂²	—	2	2	no	—
485	C₂²	—	2	2	no	—
486	C₂²	—	4	2	no	—
487	C₂²	—	4	2	no	—
488	C₂²	—	4	2	no	—
489	C₂²	—	4	2	no	—
490	C₂²	—	4	2	no	—
491	C₂²	—	8	2	no	—
492	C₂²	—	8	2	no	—
493	C₂²	—	8	1	no	—
494	C₂²	—	8	1	no	—
495	C₂²	—	8	2	no	—
496	C₂²	—	8	2	no	—
497	C₂²	—	8	1	no	—
498	C₂²	C₂×#121×C₇₉	1	1	yes	characteristic
499	C₂²	#546×C₇₉	1	2	yes	—
500	C₂²	C₂×AGL(1,ℤ/8)×C₇₉	1	2	yes	—
501	C₂²	#577×C₇₉	1	1	yes	characteristic
502	C₂²	#578×C₇₉	1	1	yes	characteristic
503	C₄	—	2	4	no	—
504	C₄	—	2	2	no	—
505	C₄	—	2	4	no	—
506	C₄	—	4	2	no	—
507	C₄	—	8	2	no	—
508	C₄	—	8	1	no	—
509	C₄	—	8	2	no	—
510	C₄	C₂×#123×C₇₉	1	1	yes	characteristic
511	C₄	#534×C₇₉	1	1	yes	characteristic
512	C₄	#551×C₇₉	1	2	yes	—
513	C₂	—	4	2	no	—
514	C₂	—	8	2	no	—
515	C₂	—	16	1	no	—
516	C₂	C₇₉×#2412	1	1	yes	characteristic
517	C₂	C₇₉×#3038	1	1	yes	characteristic
518	C₂	C₇₉×#3046	1	1	yes	characteristic
519	C₂	C₇₉×#3308	1	2	yes	—
520	C₂	C₇₉×#3332	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₉
prime radical	C₂×#449×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. C₂×#417×C₇₉	C₂	semidirect
3. C₇₉×#2501	C₂	semidirect
4. C₇₉×#2341	C₂	semidirect
5. C₇₉×#2071	C₂	semidirect
6. C₇₉×#2054	C₂	semidirect
7. C₇₉×#1895	C₂	semidirect
8. C₇₉×#1880	C₂	semidirect
9. C₇₉×#1851	C₂	semidirect
10. C₇₉×#1824	C₂	semidirect
11. C₇₉×#1803	C₂	semidirect
183. Q₈×C₇₉	#123	semidirect
252. #24542	C₇₉	direct (N × H)
262. C₂×#417	C₂×C₇₉	semidirect
263. #2501	C₂×C₇₉	semidirect
264. #2341	C₂×C₇₉	semidirect
265. #2071	C₂×C₇₉	semidirect
266. #2054	C₂×C₇₉	semidirect
267. #1895	C₂×C₇₉	semidirect
268. #1880	C₂×C₇₉	semidirect
269. #1851	C₂×C₇₉	semidirect
270. #1824	C₂×C₇₉	semidirect
271. #1803	C₂×C₇₉	semidirect
272. C₇₉	#24542	direct (N × H)
444. Q₈	#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×#449×C₇₉	2
C₂×#417×C₇₉	2
C₇₉×#2501	2
C₇₉×#2341	2
C₇₉×#2071	2
C₇₉×#2054	2
C₇₉×#1895	2
C₇₉×#1880	2
C₇₉×#1851	2
C₇₉×#1824	2
C₇₉×#1803	2
#24542	79

Subgroups — C79×#24542 #34136231

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#24542 #34136231