Subgroups — C₂×C₇₉×#1486 #34129129

Order 20224.

1714 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×D₄×C₇₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#431×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#423×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₉×#1486	C₂	1	8	yes	maximal, direct product factor
5	C₂×D₄⋊C₈×C₇₉	C₂	1	4	yes	maximal, complemented
6	C₂³×D₄×C₇₉	C₄	1	1	yes	characteristic
7	C₂⁴×C₄×C₇₉	—	2	1	no	—
8	C₂²×M₁₆×C₇₉	—	2	1	no	—
9	C₂×C₄×D₄×C₇₉	—	2	1	no	—
10	C₂×C₄×D₄×C₇₉	—	2	2	no	—
11	C₂×C₄×D₄×C₇₉	—	2	2	no	—
12	C₂×C₄×D₄×C₇₉	—	2	1	no	—
13	C₂×C₄×D₄×C₇₉	C₄	1	4	yes	—
14	C₂×C₄×D₄×C₇₉	C₄	1	2	yes	—
15	C₂×C₄×D₄×C₇₉	C₂²	1	4	yes	—
16	C₂×C₄×D₄×C₇₉	C₂²	1	2	yes	—
17	C₂²×C₄⋊C₄×C₇₉	C₄	1	1	yes	characteristic
18	C₂²×C₂²⋊C₄×C₇₉	—	2	1	no	—
19	C₂²×C₄²×C₇₉	C₂²	1	1	yes	characteristic
20	#431×C₇₉	—	2	2	no	—
21	#431×C₇₉	C₂²	1	4	yes	complemented
22	#423×C₇₉	—	2	2	no	—
23	#423×C₇₉	C₂²	1	4	yes	complemented
24	C₂×C₄⋊C₈×C₇₉	—	2	1	no	—
25	C₂×C₄⋊C₈×C₇₉	—	2	1	no	—
26	C₂×C₄⋊C₈×C₇₉	C₂²	1	2	yes	complemented
27	C₂×C₂²⋊C₈×C₇₉	—	2	1	no	—
28	C₂×C₄×C₈×C₇₉	C₂²	1	2	yes	complemented
29	D₄⋊C₈×C₇₉	C₂²	1	16	yes	complemented
30	C₂⁵×C₇₉	—	2	1	no	—
31	C₂²×D₄×C₇₉	—	2	8	no	—
32	C₂²×D₄×C₇₉	—	2	1	no	—
33	C₂²×D₄×C₇₉	—	2	2	no	—
34	C₂²×D₄×C₇₉	C₂×C₄	1	4	yes	—
35	C₂²×D₄×C₇₉	C₂×C₄	1	2	yes	—
36	C₂³×C₄×C₇₉	—	2	1	no	—
37	C₂³×C₄×C₇₉	—	2	4	no	—
38	C₂³×C₄×C₇₉	—	2	2	no	—
39	C₂³×C₄×C₇₉	—	2	4	no	—
40	C₂³×C₄×C₇₉	—	2	2	no	—
41	C₂³×C₄×C₇₉	—	4	4	no	—
42	C₂³×C₄×C₇₉	—	4	4	no	—
43	C₂³×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
44	C₂³×C₄×C₇₉	D₄	1	1	yes	characteristic
45	C₂³×C₄×C₇₉	D₄	1	1	yes	characteristic
46	C₂×M₁₆×C₇₉	—	2	4	no	—
47	C₂×M₁₆×C₇₉	—	4	4	no	—
48	C₂²×C₈×C₇₉	—	2	2	no	—
49	C₂²×C₈×C₇₉	—	2	2	no	—
50	C₄×D₄×C₇₉	—	2	4	no	—
51	C₄×D₄×C₇₉	—	2	4	no	—
52	C₄×D₄×C₇₉	—	2	4	no	—
53	C₄×D₄×C₇₉	—	2	2	no	—
54	C₄×D₄×C₇₉	—	2	4	no	—
55	C₄×D₄×C₇₉	—	2	2	no	—
56	C₄×D₄×C₇₉	—	2	4	no	—
57	C₄×D₄×C₇₉	C₂×C₄	1	8	yes	—
58	C₄×D₄×C₇₉	C₂×C₄	1	4	yes	—
59	C₄×D₄×C₇₉	C₂³	1	4	yes	—
60	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
61	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
62	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	4	yes	—
63	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
64	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
65	C₂×C₂²⋊C₄×C₇₉	—	2	4	no	—
66	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
67	C₂×C₂²⋊C₄×C₇₉	—	2	4	no	—
68	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄²×C₇₉	C₂×C₄	1	2	yes	—
70	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
71	C₂×C₄²×C₇₉	D₄	1	2	yes	—
72	C₂×C₄²×C₇₉	D₄	1	2	yes	—
73	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
74	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
75	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
76	C₄⋊C₈×C₇₉	—	2	4	no	—
77	C₄⋊C₈×C₇₉	—	2	4	no	—
78	C₄⋊C₈×C₇₉	—	2	2	no	—
79	C₄⋊C₈×C₇₉	C₂³	1	4	yes	complemented
80	C₂²⋊C₈×C₇₉	—	2	4	no	—
81	C₄×C₈×C₇₉	—	2	2	no	—
82	C₄×C₈×C₇₉	C₂³	1	4	yes	complemented
83	C₂⁴×C₇₉	—	2	8	no	—
84	C₂⁴×C₇₉	—	2	4	no	—
85	C₂⁴×C₇₉	—	2	2	no	—
86	C₂⁴×C₇₉	—	4	4	no	—
87	C₂⁴×C₇₉	—	4	4	no	—
88	C₂⁴×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
89	C₂×D₄×C₇₉	—	2	8	no	—
90	C₂×D₄×C₇₉	—	2	16	no	—
91	C₂×D₄×C₇₉	—	2	16	no	—
92	C₂×D₄×C₇₉	—	2	4	no	—
93	C₂×D₄×C₇₉	—	2	2	no	—
94	C₂×D₄×C₇₉	—	2	4	no	—
95	C₂×D₄×C₇₉	M₁₆	1	8	yes	complemented
96	C₂×D₄×C₇₉	C₂²×C₄	1	4	yes	—
97	C₂²×C₄×C₇₉	—	2	4	no	—
98	C₂²×C₄×C₇₉	—	2	4	no	—
99	C₂²×C₄×C₇₉	—	2	2	no	—
100	C₂²×C₄×C₇₉	—	2	8	no	—
101	C₂²×C₄×C₇₉	—	2	4	no	—
102	C₂²×C₄×C₇₉	—	2	4	no	—
103	C₂²×C₄×C₇₉	—	4	2	no	—
104	C₂²×C₄×C₇₉	—	4	4	no	—
105	C₂²×C₄×C₇₉	—	4	16	no	—
106	C₂²×C₄×C₇₉	—	4	8	no	—
107	C₂²×C₄×C₇₉	—	4	4	no	—
108	C₂²×C₄×C₇₉	—	4	8	no	—
109	C₂²×C₄×C₇₉	—	4	8	no	—
110	C₂²×C₄×C₇₉	—	4	4	no	—
111	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
112	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
113	C₂²×C₄×C₇₉	C₂²⋊C₄	1	2	yes	—
114	C₂²×C₄×C₇₉	C₂²⋊C₄	1	2	yes	—
115	C₂²×C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
116	C₂²×C₄×C₇₉	C₂²⋊C₄	1	2	yes	—
117	C₂²×C₄×C₇₉	D₈	1	4	yes	—
118	C₂²×C₄×C₇₉	SD₁₆	1	4	yes	—
119	C₂²×C₄×C₇₉	C₂²×C₄	1	2	yes	—
120	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
121	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
123	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
124	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
125	M₁₆×C₇₉	—	4	8	no	—
126	C₂×C₈×C₇₉	—	2	4	no	—
127	C₂×C₈×C₇₉	—	2	4	no	—
128	C₂×C₈×C₇₉	—	4	4	no	—
129	C₂×C₈×C₇₉	—	4	4	no	—
130	C₄⋊C₄×C₇₉	—	2	4	no	—
131	C₄⋊C₄×C₇₉	—	2	2	no	—
132	C₄⋊C₄×C₇₉	C₂²×C₄	1	4	yes	—
133	C₂²⋊C₄×C₇₉	—	2	8	no	—
134	C₂²⋊C₄×C₇₉	—	2	4	no	—
135	C₂²⋊C₄×C₇₉	—	2	4	no	—
136	C₄²×C₇₉	C₂²⋊C₄	1	2	yes	—
137	C₄²×C₇₉	C₂²⋊C₄	1	2	yes	—
138	C₄²×C₇₉	C₂²⋊C₄	1	2	yes	—
139	C₄²×C₇₉	C₂²×C₄	1	2	yes	—
140	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
141	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
142	C₄²×C₇₉	C₂×D₄	1	2	yes	—
143	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
144	C₄²×C₇₉	C₂×D₄	1	2	yes	—
145	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
146	C₂³×C₇₉	—	2	2	no	—
147	C₂³×C₇₉	—	2	2	no	—
148	C₂³×C₇₉	—	2	16	no	—
149	C₂³×C₇₉	—	2	4	no	—
150	C₂³×C₇₉	—	2	8	no	—
151	C₂³×C₇₉	—	4	8	no	—
152	C₂³×C₇₉	—	4	32	no	—
153	C₂³×C₇₉	—	4	8	no	—
154	C₂³×C₇₉	—	4	4	no	—
155	C₂³×C₇₉	—	4	4	no	—
156	C₂³×C₇₉	#102	1	4	yes	—
157	C₂³×C₇₉	C₂×C₂²⋊C₄	1	2	yes	—
158	C₂³×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
159	D₄×C₇₉	—	2	16	no	—
160	D₄×C₇₉	—	2	4	no	—
161	D₄×C₇₉	—	2	8	no	—
162	D₄×C₇₉	C₂×M₁₆	1	8	yes	complemented
163	C₂×C₄×C₇₉	—	2	2	no	—
164	C₂×C₄×C₇₉	—	2	2	no	—
165	C₂×C₄×C₇₉	—	2	2	no	—
166	C₂×C₄×C₇₉	—	2	4	no	—
167	C₂×C₄×C₇₉	—	2	4	no	—
168	C₂×C₄×C₇₉	—	2	4	no	—
169	C₂×C₄×C₇₉	—	4	2	no	—
170	C₂×C₄×C₇₉	—	4	2	no	—
171	C₂×C₄×C₇₉	—	4	8	no	—
172	C₂×C₄×C₇₉	—	4	4	no	—
173	C₂×C₄×C₇₉	—	4	4	no	—
174	C₂×C₄×C₇₉	—	4	4	no	—
175	C₂×C₄×C₇₉	—	4	16	no	—
176	C₂×C₄×C₇₉	—	4	8	no	—
177	C₂×C₄×C₇₉	#102	1	8	yes	—
178	C₂×C₄×C₇₉	#102	1	4	yes	—
179	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	2	yes	—
180	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
181	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	2	yes	—
182	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
183	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	2	yes	—
184	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
185	C₂×C₄×C₇₉	C₂×M₁₆	1	4	yes	—
186	C₂×C₄×C₇₉	C₂×D₈	1	2	yes	—
187	C₂×C₄×C₇₉	C₂×D₈	1	4	yes	—
188	C₂×C₄×C₇₉	C₂×SD₁₆	1	4	yes	—
189	C₂×C₄×C₇₉	C₂×SD₁₆	1	2	yes	—
190	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
191	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
192	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
193	C₈×C₇₉	—	4	4	no	—
194	C₈×C₇₉	—	4	4	no	—
195	C₂²×C₇₉	—	2	2	no	—
196	C₂²×C₇₉	—	2	2	no	—
197	C₂²×C₇₉	—	2	8	no	—
198	C₂²×C₇₉	—	2	8	no	—
199	C₂²×C₇₉	—	4	32	no	—
200	C₂²×C₇₉	—	4	4	no	—
201	C₂²×C₇₉	—	4	4	no	—
202	C₂²×C₇₉	—	4	16	no	—
203	C₂²×C₇₉	#407	1	2	yes	—
204	C₂²×C₇₉	C₂×#102	1	4	yes	—
205	C₂²×C₇₉	C₂×#102	1	2	yes	—
206	C₂²×C₇₉	#421	1	2	yes	—
207	C₂²×C₇₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
208	C₄×C₇₉	—	2	2	no	—
209	C₄×C₇₉	—	2	1	no	—
210	C₄×C₇₉	—	2	2	no	—
211	C₄×C₇₉	—	2	1	no	—
212	C₄×C₇₉	—	4	4	no	—
213	C₄×C₇₉	#407	1	2	yes	—
214	C₄×C₇₉	C₂×#102	1	4	yes	—
215	C₄×C₇₉	C₂×#102	1	2	yes	—
216	C₄×C₇₉	C₂²×M₁₆	1	2	yes	—
217	C₄×C₇₉	C₂²×D₈	1	1	yes	characteristic
218	C₄×C₇₉	C₂²×SD₁₆	1	1	yes	characteristic
219	C₂×#1486	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
220	C₂×C₇₉	—	2	4	no	—
221	C₂×C₇₉	—	4	8	no	—
222	C₂×C₇₉	#1486	1	4	yes	direct product factor
223	C₂×C₇₉	C₂×#407	1	1	yes	characteristic
224	C₂×C₇₉	C₂²×#102	1	1	yes	characteristic
225	C₂×C₇₉	C₂×#421	1	1	yes	characteristic
226	C₂²×C₄×D₄	C₂×C₇₉	1	1	yes	characteristic
227	C₂×#431	C₂×C₇₉	1	1	yes	characteristic, complemented
228	C₂×#423	C₂×C₇₉	1	1	yes	characteristic, complemented
229	#1486	C₂×C₇₉	1	8	yes	direct product factor
230	C₂×D₄⋊C₈	C₂×C₇₉	1	4	yes	complemented
231	C₇₉	C₂×#1486	1	1	yes	characteristic, direct product factor, Sylow
232	C₂³×D₄	C₄×C₇₉	1	1	yes	characteristic
233	C₂⁴×C₄	—	2	1	no	—
234	C₂²×M₁₆	—	2	1	no	—
235	C₂×C₄×D₄	—	2	1	no	—
236	C₂×C₄×D₄	—	2	1	no	—
237	C₂×C₄×D₄	—	2	2	no	—
238	C₂×C₄×D₄	—	2	2	no	—
239	C₂×C₄×D₄	C₄×C₇₉	1	4	yes	—
240	C₂×C₄×D₄	C₄×C₇₉	1	2	yes	—
241	C₂×C₄×D₄	C₂²×C₇₉	1	2	yes	—
242	C₂×C₄×D₄	C₂²×C₇₉	1	4	yes	—
243	C₂²×C₄⋊C₄	C₄×C₇₉	1	1	yes	characteristic
244	C₂²×C₂²⋊C₄	—	2	1	no	—
245	C₂²×C₄²	C₂²×C₇₉	1	1	yes	characteristic
246	#431	—	2	2	no	—
247	#431	C₂²×C₇₉	1	4	yes	complemented
248	#423	—	2	2	no	—
249	#423	C₂²×C₇₉	1	4	yes	complemented
250	C₂×C₄⋊C₈	—	2	1	no	—
251	C₂×C₄⋊C₈	—	2	1	no	—
252	C₂×C₄⋊C₈	C₂²×C₇₉	1	2	yes	complemented
253	C₂×C₂²⋊C₈	—	2	1	no	—
254	C₂×C₄×C₈	C₂²×C₇₉	1	2	yes	complemented
255	D₄⋊C₈	C₂²×C₇₉	1	16	yes	complemented
256	C₂⁵	—	2	1	no	—
257	C₂²×D₄	—	2	8	no	—
258	C₂²×D₄	—	2	1	no	—
259	C₂²×D₄	—	2	2	no	—
260	C₂²×D₄	C₂×C₄×C₇₉	1	4	yes	—
261	C₂²×D₄	C₂×C₄×C₇₉	1	2	yes	—
262	C₂³×C₄	—	2	1	no	—
263	C₂³×C₄	—	2	4	no	—
264	C₂³×C₄	—	2	2	no	—
265	C₂³×C₄	—	2	2	no	—
266	C₂³×C₄	—	2	4	no	—
267	C₂³×C₄	—	4	4	no	—
268	C₂³×C₄	—	4	4	no	—
269	C₂³×C₄	C₂×C₄×C₇₉	1	1	yes	characteristic
270	C₂³×C₄	D₄×C₇₉	1	1	yes	characteristic
271	C₂³×C₄	D₄×C₇₉	1	1	yes	characteristic
272	C₂×M₁₆	—	2	4	no	—
273	C₂×M₁₆	—	4	4	no	—
274	C₂²×C₈	—	2	2	no	—
275	C₂²×C₈	—	2	2	no	—
276	C₄×D₄	—	2	4	no	—
277	C₄×D₄	—	2	4	no	—
278	C₄×D₄	—	2	4	no	—
279	C₄×D₄	—	2	2	no	—
280	C₄×D₄	—	2	2	no	—
281	C₄×D₄	—	2	4	no	—
282	C₄×D₄	—	2	4	no	—
283	C₄×D₄	C₂×C₄×C₇₉	1	4	yes	—
284	C₄×D₄	C₂×C₄×C₇₉	1	8	yes	—
285	C₄×D₄	C₂³×C₇₉	1	4	yes	—
286	C₂×C₄⋊C₄	—	2	1	no	—
287	C₂×C₄⋊C₄	—	2	2	no	—
288	C₂×C₄⋊C₄	C₂×C₄×C₇₉	1	4	yes	—
289	C₂×C₄⋊C₄	C₂×C₄×C₇₉	1	2	yes	—
290	C₂×C₂²⋊C₄	—	2	2	no	—
291	C₂×C₂²⋊C₄	—	2	4	no	—
292	C₂×C₂²⋊C₄	—	2	2	no	—
293	C₂×C₂²⋊C₄	—	2	4	no	—
294	C₂×C₄²	C₂×C₄×C₇₉	1	1	yes	characteristic
295	C₂×C₄²	C₂×C₄×C₇₉	1	2	yes	—
296	C₂×C₄²	D₄×C₇₉	1	1	yes	characteristic
297	C₂×C₄²	D₄×C₇₉	1	1	yes	characteristic
298	C₂×C₄²	D₄×C₇₉	1	2	yes	—
299	C₂×C₄²	D₄×C₇₉	1	2	yes	—
300	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
301	C₂×C₄²	C₂³×C₇₉	1	2	yes	—
302	C₄⋊C₈	—	2	4	no	—
303	C₄⋊C₈	—	2	4	no	—
304	C₄⋊C₈	—	2	2	no	—
305	C₄⋊C₈	C₂³×C₇₉	1	4	yes	complemented
306	C₂²⋊C₈	—	2	4	no	—
307	C₄×C₈	—	2	2	no	—
308	C₄×C₈	C₂³×C₇₉	1	4	yes	complemented
309	C₂⁴	—	2	8	no	—
310	C₂⁴	—	2	4	no	—
311	C₂⁴	—	2	2	no	—
312	C₂⁴	—	4	4	no	—
313	C₂⁴	—	4	4	no	—
314	C₂⁴	C₂²⋊C₄×C₇₉	1	1	yes	characteristic
315	C₂×D₄	—	2	8	no	—
316	C₂×D₄	—	2	16	no	—
317	C₂×D₄	—	2	16	no	—
318	C₂×D₄	—	2	4	no	—
319	C₂×D₄	—	2	2	no	—
320	C₂×D₄	—	2	4	no	—
321	C₂×D₄	M₁₆×C₇₉	1	8	yes	complemented
322	C₂×D₄	C₂²×C₄×C₇₉	1	4	yes	—
323	C₂²×C₄	—	2	4	no	—
324	C₂²×C₄	—	2	4	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	8	no	—
327	C₂²×C₄	—	2	4	no	—
328	C₂²×C₄	—	2	4	no	—
329	C₂²×C₄	—	4	2	no	—
330	C₂²×C₄	—	4	4	no	—
331	C₂²×C₄	—	4	16	no	—
332	C₂²×C₄	—	4	8	no	—
333	C₂²×C₄	—	4	4	no	—
334	C₂²×C₄	—	4	8	no	—
335	C₂²×C₄	—	4	8	no	—
336	C₂²×C₄	—	4	4	no	—
337	C₂²×C₄	C₂²⋊C₄×C₇₉	1	1	yes	characteristic
338	C₂²×C₄	C₂²⋊C₄×C₇₉	1	1	yes	characteristic
339	C₂²×C₄	C₂²⋊C₄×C₇₉	1	2	yes	—
340	C₂²×C₄	C₂²⋊C₄×C₇₉	1	2	yes	—
341	C₂²×C₄	C₂²⋊C₄×C₇₉	1	2	yes	—
342	C₂²×C₄	C₂²⋊C₄×C₇₉	1	1	yes	characteristic
343	C₂²×C₄	D₈×C₇₉	1	4	yes	—
344	C₂²×C₄	SD₁₆×C₇₉	1	4	yes	—
345	C₂²×C₄	C₂²×C₄×C₇₉	1	2	yes	—
346	C₂²×C₄	C₂²×C₄×C₇₉	1	1	yes	characteristic
347	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
348	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
349	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
350	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
351	M₁₆	—	4	8	no	—
352	C₂×C₈	—	2	4	no	—
353	C₂×C₈	—	2	4	no	—
354	C₂×C₈	—	4	4	no	—
355	C₂×C₈	—	4	4	no	—
356	C₄⋊C₄	—	2	4	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	C₂²×C₄×C₇₉	1	4	yes	—
359	C₂²⋊C₄	—	2	8	no	—
360	C₂²⋊C₄	—	2	4	no	—
361	C₂²⋊C₄	—	2	4	no	—
362	C₄²	C₂²⋊C₄×C₇₉	1	2	yes	—
363	C₄²	C₂²⋊C₄×C₇₉	1	2	yes	—
364	C₄²	C₂²⋊C₄×C₇₉	1	2	yes	—
365	C₄²	C₂²×C₄×C₇₉	1	1	yes	characteristic
366	C₄²	C₂²×C₄×C₇₉	1	2	yes	—
367	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
368	C₄²	C₂×D₄×C₇₉	1	2	yes	—
369	C₄²	C₂×D₄×C₇₉	1	1	yes	characteristic
370	C₄²	C₂×D₄×C₇₉	1	2	yes	—
371	C₄²	C₂⁴×C₇₉	1	1	yes	characteristic
372	C₂³	—	2	2	no	—
373	C₂³	—	2	2	no	—
374	C₂³	—	2	16	no	—
375	C₂³	—	2	4	no	—
376	C₂³	—	2	8	no	—
377	C₂³	—	4	32	no	—
378	C₂³	—	4	8	no	—
379	C₂³	—	4	4	no	—
380	C₂³	—	4	8	no	—
381	C₂³	—	4	4	no	—
382	C₂³	#102×C₇₉	1	4	yes	—
383	C₂³	C₂×C₂²⋊C₄×C₇₉	1	2	yes	—
384	C₂³	C₂×C₂²⋊C₄×C₇₉	1	1	yes	characteristic
385	D₄	—	2	16	no	—
386	D₄	—	2	4	no	—
387	D₄	—	2	8	no	—
388	D₄	C₂×M₁₆×C₇₉	1	8	yes	complemented
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	4	no	—
393	C₂×C₄	—	2	4	no	—
394	C₂×C₄	—	2	4	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	8	no	—
398	C₂×C₄	—	4	4	no	—
399	C₂×C₄	—	4	4	no	—
400	C₂×C₄	—	4	4	no	—
401	C₂×C₄	—	4	8	no	—
402	C₂×C₄	—	4	16	no	—
403	C₂×C₄	#102×C₇₉	1	8	yes	—
404	C₂×C₄	#102×C₇₉	1	4	yes	—
405	C₂×C₄	C₂×C₂²⋊C₄×C₇₉	1	2	yes	—
406	C₂×C₄	C₂×C₂²⋊C₄×C₇₉	1	1	yes	characteristic
407	C₂×C₄	C₂×C₂²⋊C₄×C₇₉	1	2	yes	—
408	C₂×C₄	C₂×C₂²⋊C₄×C₇₉	1	1	yes	characteristic
409	C₂×C₄	C₂×C₂²⋊C₄×C₇₉	1	2	yes	—
410	C₂×C₄	C₂×C₂²⋊C₄×C₇₉	1	1	yes	characteristic
411	C₂×C₄	C₂×M₁₆×C₇₉	1	4	yes	—
412	C₂×C₄	C₂×D₈×C₇₉	1	2	yes	—
413	C₂×C₄	C₂×D₈×C₇₉	1	4	yes	—
414	C₂×C₄	C₂×SD₁₆×C₇₉	1	4	yes	—
415	C₂×C₄	C₂×SD₁₆×C₇₉	1	2	yes	—
416	C₂×C₄	C₂³×C₄×C₇₉	1	1	yes	characteristic
417	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
418	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
419	C₈	—	4	4	no	—
420	C₈	—	4	4	no	—
421	C₂²	—	2	8	no	—
422	C₂²	—	2	2	no	—
423	C₂²	—	2	2	no	—
424	C₂²	—	2	8	no	—
425	C₂²	—	4	32	no	—
426	C₂²	—	4	16	no	—
427	C₂²	—	4	4	no	—
428	C₂²	—	4	4	no	—
429	C₂²	#407×C₇₉	1	2	yes	—
430	C₂²	C₂×#102×C₇₉	1	4	yes	—
431	C₂²	C₂×#102×C₇₉	1	2	yes	—
432	C₂²	#421×C₇₉	1	2	yes	—
433	C₂²	C₂²×C₂²⋊C₄×C₇₉	1	1	yes	characteristic
434	C₄	—	2	2	no	—
435	C₄	—	2	1	no	—
436	C₄	—	2	1	no	—
437	C₄	—	2	2	no	—
438	C₄	—	4	4	no	—
439	C₄	#407×C₇₉	1	2	yes	—
440	C₄	C₂×#102×C₇₉	1	2	yes	—
441	C₄	C₂×#102×C₇₉	1	4	yes	—
442	C₄	C₂²×M₁₆×C₇₉	1	2	yes	—
443	C₄	C₂²×D₈×C₇₉	1	1	yes	characteristic
444	C₄	C₂²×SD₁₆×C₇₉	1	1	yes	characteristic
445	C₂	—	2	4	no	—
446	C₂	—	4	8	no	—
447	C₂	C₇₉×#1486	1	4	yes	direct product factor
448	C₂	C₂×#407×C₇₉	1	1	yes	characteristic
449	C₂	C₂²×#102×C₇₉	1	1	yes	characteristic
450	C₂	C₂×#421×C₇₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₇₉	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₇₉
Frattini, cosocle	C₄²	C₂⁴×C₇₉
socle	C₂³×C₇₉	C₂×C₂²⋊C₄
prime radical	C₂³×D₄×C₇₉	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₇₉ ◁ C₂²×C₄²×C₇₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#431×C₇₉	C₂	semidirect
3. C₂×#423×C₇₉	C₂	semidirect
4. C₇₉×#1486	C₂	direct (N × H)
5. C₂×D₄⋊C₈×C₇₉	C₂	semidirect
21. #431×C₇₉	C₂²	semidirect
23. #423×C₇₉	C₂²	semidirect
26. C₂×C₄⋊C₈×C₇₉	C₂²	semidirect
28. C₂×C₄×C₈×C₇₉	C₂²	semidirect
29. D₄⋊C₈×C₇₉	C₂²	semidirect
79. C₄⋊C₈×C₇₉	C₂³	semidirect
82. C₄×C₈×C₇₉	C₂³	semidirect
95. C₂×D₄×C₇₉	M₁₆	semidirect
162. D₄×C₇₉	C₂×M₁₆	semidirect
219. C₂×#1486	C₇₉	direct (N × H)
222. C₂×C₇₉	#1486	direct (N × H)
227. C₂×#431	C₂×C₇₉	semidirect
228. C₂×#423	C₂×C₇₉	semidirect
229. #1486	C₂×C₇₉	direct (N × H)
230. C₂×D₄⋊C₈	C₂×C₇₉	semidirect
231. C₇₉	C₂×#1486	direct (N × H)
247. #431	C₂²×C₇₉	semidirect
249. #423	C₂²×C₇₉	semidirect
252. C₂×C₄⋊C₈	C₂²×C₇₉	semidirect
254. C₂×C₄×C₈	C₂²×C₇₉	semidirect
255. D₄⋊C₈	C₂²×C₇₉	semidirect
305. C₄⋊C₈	C₂³×C₇₉	semidirect
308. C₄×C₈	C₂³×C₇₉	semidirect
321. C₂×D₄	M₁₆×C₇₉	semidirect
388. D₄	C₂×M₁₆×C₇₉	semidirect
447. C₂	C₇₉×#1486	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₄×D₄×C₇₉	2
C₂×#431×C₇₉	2
C₂×#423×C₇₉	2
C₇₉×#1486	2
C₂×D₄⋊C₈×C₇₉	2
C₂×#1486	79

Subgroups — C2×C79×#1486 #34129129

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇₉×#1486 #34129129