Subgroups — C₂×C₇₉×#3397 #34173083

Order 20224.

2250 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#556×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#550×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₉×#3397	C₂	1	16	yes	maximal, direct product factor
4	C₂×#496×C₇₉	C₂	1	2	yes	maximal, complemented
5	C₂×#492×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#460×C₇₉	C₂	1	2	yes	maximal, complemented
7	C₂×#463×C₇₉	C₂	1	2	yes	maximal, complemented
8	C₂×#461×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#459×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#446×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#440×C₇₉	C₂	1	2	yes	maximal, complemented
12	C₂×C₄×D₈×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×#41×C₇₉	—	2	1	no	—
14	C₂²×SD₁₆×C₇₉	C₂²	1	2	yes	—
15	C₂²×SD₁₆×C₇₉	C₂²	1	2	yes	—
16	C₂²×SD₁₆×C₇₉	C₂²	1	2	yes	—
17	C₂²×D₈×C₇₉	C₂²	1	1	yes	characteristic
18	C₂²×D₈×C₇₉	C₂²	1	2	yes	—
19	#556×C₇₉	—	2	4	no	—
20	#556×C₇₉	C₂²	1	8	yes	complemented
21	#550×C₇₉	—	2	4	no	—
22	#550×C₇₉	C₂²	1	8	yes	complemented
23	C₂×C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
24	C₂×#127×C₇₉	C₂²	1	1	yes	characteristic
25	C₂×#127×C₇₉	C₂²	1	2	yes	—
26	C₂×#126×C₇₉	—	2	2	no	—
27	C₂×#124×C₇₉	C₂²	1	2	yes	—
28	C₂×C₂²⋊Q₈×C₇₉	—	2	1	no	—
29	C₂×#121×C₇₉	—	2	1	no	—
30	C₂×#121×C₇₉	—	2	2	no	—
31	C₂×C₄×Q₈×C₇₉	C₂²	1	2	yes	—
32	C₂×C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
34	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₇₉	C₂²	1	2	yes	—
36	C₂×#117×C₇₉	—	2	1	no	—
37	#496×C₇₉	C₂²	1	16	yes	complemented
38	#492×C₇₉	C₂²	1	8	yes	complemented
39	#463×C₇₉	C₂²	1	16	yes	complemented
40	#461×C₇₉	C₂²	1	8	yes	complemented
41	#460×C₇₉	C₂²	1	16	yes	complemented
42	#459×C₇₉	C₂²	1	8	yes	complemented
43	#446×C₇₉	C₂²	1	8	yes	complemented
44	#440×C₇₉	C₂²	1	16	yes	complemented
45	C₄×D₈×C₇₉	C₂²	1	8	yes	complemented
46	C₂×#107×C₇₉	C₂²	1	1	yes	characteristic
47	C₂×C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
48	C₂×C₄⋊C₈×C₇₉	C₂²	1	2	yes	—
49	C₂×#103×C₇₉	C₂²	1	2	yes	—
50	C₂×#102×C₇₉	C₂²	1	2	yes	—
51	C₂×#102×C₇₉	C₂²	1	1	yes	characteristic
52	C₂×#102×C₇₉	C₂²	1	1	yes	characteristic
53	C₂×#97×C₇₉	C₂²	1	2	yes	—
54	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
55	C₂×#41×C₇₉	—	2	8	no	—
56	C₂×#41×C₇₉	—	4	8	no	—
57	C₂²×Q₈×C₇₉	D₄	1	1	yes	characteristic
58	C₂²×Q₈×C₇₉	C₂³	1	2	yes	—
59	C₂²×D₄×C₇₉	—	2	2	no	—
60	C₂²×D₄×C₇₉	—	2	1	no	—
61	C₂²×D₄×C₇₉	—	2	2	no	—
62	C₂²×D₄×C₇₉	—	2	1	no	—
63	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
64	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
65	C₂²×D₄×C₇₉	C₂³	1	2	yes	—
66	C₂³×C₄×C₇₉	—	2	1	no	—
67	C₂³×C₄×C₇₉	—	2	2	no	—
68	C₂³×C₄×C₇₉	—	2	1	no	—
69	C₂×SD₁₆×C₇₉	—	2	8	no	—
70	C₂×SD₁₆×C₇₉	—	4	4	no	—
71	C₂×SD₁₆×C₇₉	—	4	4	no	—
72	C₂×SD₁₆×C₇₉	C₂³	1	8	yes	—
73	C₂×SD₁₆×C₇₉	C₂³	1	8	yes	—
74	C₂×SD₁₆×C₇₉	C₂³	1	8	yes	—
75	C₂×D₈×C₇₉	—	2	4	no	—
76	C₂×D₈×C₇₉	—	4	4	no	—
77	C₂×D₈×C₇₉	C₂³	1	4	yes	—
78	C₂×D₈×C₇₉	C₂³	1	8	yes	—
79	C₂²×C₈×C₇₉	C₂³	1	2	yes	—
80	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
81	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
82	C₄⋊Q₈×C₇₉	—	2	2	no	—
83	C₄⋊Q₈×C₇₉	C₂³	1	4	yes	—
84	#127×C₇₉	—	2	2	no	—
85	#127×C₇₉	—	2	4	no	—
86	#127×C₇₉	C₂³	1	4	yes	—
87	#127×C₇₉	C₂³	1	8	yes	—
88	#126×C₇₉	—	2	16	no	—
89	#124×C₇₉	—	2	4	no	—
90	#124×C₇₉	C₂³	1	8	yes	—
91	C₂²⋊Q₈×C₇₉	—	2	8	no	—
92	#121×C₇₉	—	2	8	no	—
93	#121×C₇₉	—	2	16	no	—
94	C₄×Q₈×C₇₉	—	2	4	no	—
95	C₄×Q₈×C₇₉	D₄	1	4	yes	—
96	C₄×Q₈×C₇₉	C₂³	1	8	yes	—
97	C₄×Q₈×C₇₉	C₂³	1	4	yes	—
98	C₄×D₄×C₇₉	—	2	2	no	—
99	C₄×D₄×C₇₉	—	2	4	no	—
100	C₄×D₄×C₇₉	—	2	2	no	—
101	C₄×D₄×C₇₉	C₂³	1	4	yes	—
102	C₄×D₄×C₇₉	C₂³	1	4	yes	—
103	C₄×D₄×C₇₉	C₂³	1	8	yes	—
104	#117×C₇₉	—	2	8	no	—
105	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
106	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
107	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
108	C₂×C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
109	C₂×C₄⋊C₄×C₇₉	D₄	1	2	yes	—
110	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
111	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
112	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
113	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
114	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
115	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
116	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
117	C₂×C₄²×C₇₉	—	2	2	no	—
118	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
119	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
120	#107×C₇₉	C₂³	1	4	yes	—
121	C₄⋊C₈×C₇₉	C₂³	1	4	yes	—
122	C₄⋊C₈×C₇₉	C₂³	1	8	yes	—
123	#103×C₇₉	C₂³	1	8	yes	—
124	#102×C₇₉	C₂³	1	4	yes	—
125	#102×C₇₉	C₂³	1	4	yes	—
126	#102×C₇₉	C₂³	1	8	yes	—
127	#97×C₇₉	C₂³	1	8	yes	—
128	C₄×C₈×C₇₉	C₂³	1	4	yes	—
129	C₂⁴×C₇₉	—	2	1	no	—
130	C₂⁴×C₇₉	—	2	1	no	—
131	C₂⁴×C₇₉	—	2	2	no	—
132	#41×C₇₉	—	4	32	no	—
133	C₂×Q₈×C₇₉	—	2	4	no	—
134	C₂×Q₈×C₇₉	—	2	2	no	—
135	C₂×Q₈×C₇₉	—	2	4	no	—
136	C₂×Q₈×C₇₉	—	2	4	no	—
137	C₂×Q₈×C₇₉	C₂×D₄	1	4	yes	—
138	C₂×Q₈×C₇₉	C₂⁴	1	4	yes	—
139	C₂×D₄×C₇₉	—	2	1	no	—
140	C₂×D₄×C₇₉	—	2	1	no	—
141	C₂×D₄×C₇₉	—	2	2	no	—
142	C₂×D₄×C₇₉	—	2	8	no	—
143	C₂×D₄×C₇₉	—	2	4	no	—
144	C₂×D₄×C₇₉	—	2	8	no	—
145	C₂×D₄×C₇₉	—	2	4	no	—
146	C₂×D₄×C₇₉	—	2	2	no	—
147	C₂×D₄×C₇₉	—	2	2	no	—
148	C₂×D₄×C₇₉	—	2	4	no	—
149	C₂×D₄×C₇₉	—	2	2	no	—
150	C₂×D₄×C₇₉	—	2	4	no	—
151	C₂×D₄×C₇₉	—	2	2	no	—
152	C₂×D₄×C₇₉	—	4	8	no	—
153	C₂×D₄×C₇₉	—	4	4	no	—
154	C₂×D₄×C₇₉	—	8	4	no	—
155	C₂×D₄×C₇₉	—	8	2	no	—
156	C₂×D₄×C₇₉	C₂⁴	1	2	yes	—
157	C₂×D₄×C₇₉	C₂⁴	1	2	yes	—
158	C₂×D₄×C₇₉	C₂⁴	1	4	yes	—
159	C₂²×C₄×C₇₉	—	2	1	no	—
160	C₂²×C₄×C₇₉	—	2	2	no	—
161	C₂²×C₄×C₇₉	—	2	1	no	—
162	C₂²×C₄×C₇₉	—	2	4	no	—
163	C₂²×C₄×C₇₉	—	2	8	no	—
164	C₂²×C₄×C₇₉	—	2	4	no	—
165	C₂²×C₄×C₇₉	—	4	8	no	—
166	C₂²×C₄×C₇₉	—	4	4	no	—
167	C₂²×C₄×C₇₉	—	4	4	no	—
168	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
169	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
171	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
173	SD₁₆×C₇₉	—	2	16	no	—
174	SD₁₆×C₇₉	—	4	8	no	—
175	SD₁₆×C₇₉	—	4	8	no	—
176	D₈×C₇₉	—	2	8	no	—
177	D₈×C₇₉	—	4	8	no	—
178	C₂×C₈×C₇₉	—	2	4	no	—
179	C₂×C₈×C₇₉	—	2	2	no	—
180	C₂×C₈×C₇₉	#41	1	4	yes	complemented
181	C₂×C₈×C₇₉	C₂⁴	1	2	yes	—
182	C₂×C₈×C₇₉	C₂⁴	1	4	yes	—
183	C₂×C₈×C₇₉	C₂⁴	1	2	yes	—
184	C₄⋊C₄×C₇₉	—	2	4	no	—
185	C₄⋊C₄×C₇₉	—	2	8	no	—
186	C₄⋊C₄×C₇₉	—	2	4	no	—
187	C₄⋊C₄×C₇₉	—	2	1	no	—
188	C₄⋊C₄×C₇₉	—	2	1	no	—
189	C₄⋊C₄×C₇₉	C₂×D₄	1	4	yes	—
190	C₄⋊C₄×C₇₉	C₂×D₄	1	8	yes	—
191	C₄⋊C₄×C₇₉	C₂⁴	1	2	yes	—
192	C₄⋊C₄×C₇₉	C₂⁴	1	2	yes	—
193	C₂²⋊C₄×C₇₉	—	2	8	no	—
194	C₂²⋊C₄×C₇₉	—	2	8	no	—
195	C₂²⋊C₄×C₇₉	—	2	4	no	—
196	C₂²⋊C₄×C₇₉	—	2	4	no	—
197	C₂²⋊C₄×C₇₉	—	2	8	no	—
198	C₄²×C₇₉	—	2	8	no	—
199	C₄²×C₇₉	C₂×D₄	1	2	yes	—
200	C₄²×C₇₉	C₂×D₄	1	4	yes	—
201	C₄²×C₇₉	C₂⁴	1	2	yes	—
202	C₄²×C₇₉	C₂⁴	1	4	yes	—
203	C₂³×C₇₉	—	2	2	no	—
204	C₂³×C₇₉	—	2	2	no	—
205	C₂³×C₇₉	—	2	4	no	—
206	C₂³×C₇₉	—	4	2	no	—
207	C₂³×C₇₉	—	4	2	no	—
208	C₂³×C₇₉	—	4	4	no	—
209	C₂³×C₇₉	—	4	4	no	—
210	C₂³×C₇₉	—	4	2	no	—
211	C₂³×C₇₉	—	4	2	no	—
212	C₂³×C₇₉	—	4	2	no	—
213	C₂³×C₇₉	—	4	4	no	—
214	C₂³×C₇₉	—	4	2	no	—
215	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
216	Q₈×C₇₉	—	2	8	no	—
217	Q₈×C₇₉	—	2	4	no	—
218	Q₈×C₇₉	—	2	4	no	—
219	Q₈×C₇₉	—	4	4	no	—
220	D₄×C₇₉	—	2	2	no	—
221	D₄×C₇₉	—	2	2	no	—
222	D₄×C₇₉	—	2	4	no	—
223	D₄×C₇₉	—	2	2	no	—
224	D₄×C₇₉	—	2	4	no	—
225	D₄×C₇₉	—	2	2	no	—
226	D₄×C₇₉	—	4	16	no	—
227	D₄×C₇₉	—	4	2	no	—
228	D₄×C₇₉	—	4	2	no	—
229	D₄×C₇₉	—	4	4	no	—
230	D₄×C₇₉	—	4	8	no	—
231	D₄×C₇₉	—	8	8	no	—
232	D₄×C₇₉	—	8	4	no	—
233	C₂×C₄×C₇₉	—	2	4	no	—
234	C₂×C₄×C₇₉	—	2	4	no	—
235	C₂×C₄×C₇₉	—	2	2	no	—
236	C₂×C₄×C₇₉	—	2	2	no	—
237	C₂×C₄×C₇₉	—	2	4	no	—
238	C₂×C₄×C₇₉	—	2	2	no	—
239	C₂×C₄×C₇₉	—	4	16	no	—
240	C₂×C₄×C₇₉	—	4	4	no	—
241	C₂×C₄×C₇₉	—	4	2	no	—
242	C₂×C₄×C₇₉	—	4	2	no	—
243	C₂×C₄×C₇₉	—	4	8	no	—
244	C₂×C₄×C₇₉	—	4	8	no	—
245	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	4	yes	—
246	C₂×C₄×C₇₉	C₂²×D₄	1	4	yes	—
247	C₂×C₄×C₇₉	C₂²×D₄	1	2	yes	—
248	C₂×C₄×C₇₉	C₂²×D₄	1	4	yes	—
249	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
250	C₂×C₄×C₇₉	C₂²×D₄	1	2	yes	—
251	C₂×C₄×C₇₉	C₂×#41	1	2	yes	—
252	C₂×C₄×C₇₉	H(5,𝔽₂)	1	2	yes	—
253	C₂×C₄×C₇₉	C₂⁵	1	1	yes	characteristic
254	C₈×C₇₉	—	2	4	no	—
255	C₈×C₇₉	—	2	2	no	—
256	C₈×C₇₉	C₂×#41	1	4	yes	complemented
257	C₂²×C₇₉	—	4	2	no	—
258	C₂²×C₇₉	—	4	2	no	—
259	C₂²×C₇₉	—	4	4	no	—
260	C₂²×C₇₉	—	4	4	no	—
261	C₂²×C₇₉	—	4	2	no	—
262	C₂²×C₇₉	—	4	2	no	—
263	C₂²×C₇₉	—	4	2	no	—
264	C₂²×C₇₉	—	4	4	no	—
265	C₂²×C₇₉	—	4	2	no	—
266	C₂²×C₇₉	—	8	4	no	—
267	C₂²×C₇₉	—	8	8	no	—
268	C₂²×C₇₉	—	8	4	no	—
269	C₂²×C₇₉	#550	1	2	yes	—
270	C₂²×C₇₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
271	C₂²×C₇₉	#577	1	2	yes	—
272	C₂²×C₇₉	C₂³×D₄	1	1	yes	characteristic
273	C₄×C₇₉	—	2	4	no	—
274	C₄×C₇₉	—	2	4	no	—
275	C₄×C₇₉	—	2	2	no	—
276	C₄×C₇₉	—	4	4	no	—
277	C₄×C₇₉	—	4	2	no	—
278	C₄×C₇₉	—	4	2	no	—
279	C₄×C₇₉	#550	1	2	yes	—
280	C₄×C₇₉	C₂×AGL(1,ℤ/8)	1	4	yes	—
281	C₄×C₇₉	C₂²×#41	1	1	yes	characteristic
282	C₄×C₇₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
283	C₂×#3397	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
284	C₂×C₇₉	—	8	2	no	—
285	C₂×C₇₉	—	8	4	no	—
286	C₂×C₇₉	—	8	2	no	—
287	C₂×C₇₉	#3397	1	4	yes	direct product factor
288	C₂×C₇₉	C₂×#550	1	1	yes	characteristic
289	C₂×C₇₉	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
290	C₂×C₇₉	C₂×#577	1	1	yes	characteristic
291	C₂×#556	C₂×C₇₉	1	1	yes	characteristic, complemented
292	C₂×#550	C₂×C₇₉	1	1	yes	characteristic, complemented
293	#3397	C₂×C₇₉	1	16	yes	direct product factor
294	C₂×#496	C₂×C₇₉	1	2	yes	complemented
295	C₂×#492	C₂×C₇₉	1	1	yes	characteristic, complemented
296	C₂×#460	C₂×C₇₉	1	2	yes	complemented
297	C₂×#463	C₂×C₇₉	1	2	yes	complemented
298	C₂×#461	C₂×C₇₉	1	1	yes	characteristic, complemented
299	C₂×#459	C₂×C₇₉	1	1	yes	characteristic, complemented
300	C₂×#446	C₂×C₇₉	1	1	yes	characteristic, complemented
301	C₂×#440	C₂×C₇₉	1	2	yes	complemented
302	C₂×C₄×D₈	C₂×C₇₉	1	1	yes	characteristic, complemented
303	C₇₉	C₂×#3397	1	1	yes	characteristic, direct product factor, Sylow
304	C₂²×#41	—	2	1	no	—
305	C₂²×SD₁₆	C₂²×C₇₉	1	2	yes	—
306	C₂²×SD₁₆	C₂²×C₇₉	1	2	yes	—
307	C₂²×SD₁₆	C₂²×C₇₉	1	2	yes	—
308	C₂²×D₈	C₂²×C₇₉	1	1	yes	characteristic
309	C₂²×D₈	C₂²×C₇₉	1	2	yes	—
310	#556	—	2	4	no	—
311	#556	C₂²×C₇₉	1	8	yes	complemented
312	#550	—	2	4	no	—
313	#550	C₂²×C₇₉	1	8	yes	complemented
314	C₂×C₄⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic
315	C₂×#127	C₂²×C₇₉	1	1	yes	characteristic
316	C₂×#127	C₂²×C₇₉	1	2	yes	—
317	C₂×#126	—	2	2	no	—
318	C₂×#124	C₂²×C₇₉	1	2	yes	—
319	C₂×C₂²⋊Q₈	—	2	1	no	—
320	C₂×#121	—	2	1	no	—
321	C₂×#121	—	2	2	no	—
322	C₂×C₄×Q₈	C₂²×C₇₉	1	2	yes	—
323	C₂×C₄×Q₈	C₂²×C₇₉	1	1	yes	characteristic
324	C₂×C₄×D₄	C₂²×C₇₉	1	1	yes	characteristic
325	C₂×C₄×D₄	C₂²×C₇₉	1	1	yes	characteristic
326	C₂×C₄×D₄	C₂²×C₇₉	1	2	yes	—
327	C₂×#117	—	2	1	no	—
328	#496	C₂²×C₇₉	1	16	yes	complemented
329	#492	C₂²×C₇₉	1	8	yes	complemented
330	#463	C₂²×C₇₉	1	16	yes	complemented
331	#461	C₂²×C₇₉	1	8	yes	complemented
332	#460	C₂²×C₇₉	1	16	yes	complemented
333	#459	C₂²×C₇₉	1	8	yes	complemented
334	#446	C₂²×C₇₉	1	8	yes	complemented
335	#440	C₂²×C₇₉	1	16	yes	complemented
336	C₄×D₈	C₂²×C₇₉	1	8	yes	complemented
337	C₂×#107	C₂²×C₇₉	1	1	yes	characteristic
338	C₂×C₄⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
339	C₂×C₄⋊C₈	C₂²×C₇₉	1	2	yes	—
340	C₂×#103	C₂²×C₇₉	1	2	yes	—
341	C₂×#102	C₂²×C₇₉	1	1	yes	characteristic
342	C₂×#102	C₂²×C₇₉	1	1	yes	characteristic
343	C₂×#102	C₂²×C₇₉	1	2	yes	—
344	C₂×#97	C₂²×C₇₉	1	2	yes	—
345	C₂×C₄×C₈	C₂²×C₇₉	1	1	yes	characteristic
346	C₂×#41	—	2	8	no	—
347	C₂×#41	—	4	8	no	—
348	C₂²×Q₈	D₄×C₇₉	1	1	yes	characteristic
349	C₂²×Q₈	C₂³×C₇₉	1	2	yes	—
350	C₂²×D₄	—	2	2	no	—
351	C₂²×D₄	—	2	1	no	—
352	C₂²×D₄	—	2	2	no	—
353	C₂²×D₄	—	2	1	no	—
354	C₂²×D₄	C₂³×C₇₉	1	1	yes	characteristic
355	C₂²×D₄	C₂³×C₇₉	1	1	yes	characteristic
356	C₂²×D₄	C₂³×C₇₉	1	2	yes	—
357	C₂³×C₄	—	2	1	no	—
358	C₂³×C₄	—	2	2	no	—
359	C₂³×C₄	—	2	1	no	—
360	C₂×SD₁₆	—	2	8	no	—
361	C₂×SD₁₆	—	4	4	no	—
362	C₂×SD₁₆	—	4	4	no	—
363	C₂×SD₁₆	C₂³×C₇₉	1	8	yes	—
364	C₂×SD₁₆	C₂³×C₇₉	1	8	yes	—
365	C₂×SD₁₆	C₂³×C₇₉	1	8	yes	—
366	C₂×D₈	—	2	4	no	—
367	C₂×D₈	—	4	4	no	—
368	C₂×D₈	C₂³×C₇₉	1	4	yes	—
369	C₂×D₈	C₂³×C₇₉	1	8	yes	—
370	C₂²×C₈	C₂³×C₇₉	1	2	yes	—
371	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
372	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
373	C₄⋊Q₈	—	2	2	no	—
374	C₄⋊Q₈	C₂³×C₇₉	1	4	yes	—
375	#127	—	2	2	no	—
376	#127	—	2	4	no	—
377	#127	C₂³×C₇₉	1	4	yes	—
378	#127	C₂³×C₇₉	1	8	yes	—
379	#126	—	2	16	no	—
380	#124	—	2	4	no	—
381	#124	C₂³×C₇₉	1	8	yes	—
382	C₂²⋊Q₈	—	2	8	no	—
383	#121	—	2	8	no	—
384	#121	—	2	16	no	—
385	C₄×Q₈	—	2	4	no	—
386	C₄×Q₈	D₄×C₇₉	1	4	yes	—
387	C₄×Q₈	C₂³×C₇₉	1	8	yes	—
388	C₄×Q₈	C₂³×C₇₉	1	4	yes	—
389	C₄×D₄	—	2	2	no	—
390	C₄×D₄	—	2	4	no	—
391	C₄×D₄	—	2	2	no	—
392	C₄×D₄	C₂³×C₇₉	1	4	yes	—
393	C₄×D₄	C₂³×C₇₉	1	8	yes	—
394	C₄×D₄	C₂³×C₇₉	1	4	yes	—
395	#117	—	2	8	no	—
396	C₂×C₄⋊C₄	—	2	1	no	—
397	C₂×C₄⋊C₄	—	2	2	no	—
398	C₂×C₄⋊C₄	—	2	1	no	—
399	C₂×C₄⋊C₄	D₄×C₇₉	1	1	yes	characteristic
400	C₂×C₄⋊C₄	D₄×C₇₉	1	2	yes	—
401	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
402	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
403	C₂×C₂²⋊C₄	—	2	2	no	—
404	C₂×C₂²⋊C₄	—	2	2	no	—
405	C₂×C₂²⋊C₄	—	2	1	no	—
406	C₂×C₂²⋊C₄	—	2	1	no	—
407	C₂×C₂²⋊C₄	—	2	2	no	—
408	C₂×C₄²	—	2	2	no	—
409	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
410	C₂×C₄²	C₂³×C₇₉	1	2	yes	—
411	#107	C₂³×C₇₉	1	4	yes	—
412	C₄⋊C₈	C₂³×C₇₉	1	4	yes	—
413	C₄⋊C₈	C₂³×C₇₉	1	8	yes	—
414	#103	C₂³×C₇₉	1	8	yes	—
415	#102	C₂³×C₇₉	1	4	yes	—
416	#102	C₂³×C₇₉	1	4	yes	—
417	#102	C₂³×C₇₉	1	8	yes	—
418	#97	C₂³×C₇₉	1	8	yes	—
419	C₄×C₈	C₂³×C₇₉	1	4	yes	—
420	C₂⁴	—	2	1	no	—
421	C₂⁴	—	2	1	no	—
422	C₂⁴	—	2	2	no	—
423	#41	—	4	32	no	—
424	C₂×Q₈	—	2	4	no	—
425	C₂×Q₈	—	2	2	no	—
426	C₂×Q₈	—	2	4	no	—
427	C₂×Q₈	—	2	4	no	—
428	C₂×Q₈	C₂×D₄×C₇₉	1	4	yes	—
429	C₂×Q₈	C₂⁴×C₇₉	1	4	yes	—
430	C₂×D₄	—	2	1	no	—
431	C₂×D₄	—	2	1	no	—
432	C₂×D₄	—	2	2	no	—
433	C₂×D₄	—	2	8	no	—
434	C₂×D₄	—	2	4	no	—
435	C₂×D₄	—	2	8	no	—
436	C₂×D₄	—	2	4	no	—
437	C₂×D₄	—	2	2	no	—
438	C₂×D₄	—	2	2	no	—
439	C₂×D₄	—	2	4	no	—
440	C₂×D₄	—	2	2	no	—
441	C₂×D₄	—	2	4	no	—
442	C₂×D₄	—	2	2	no	—
443	C₂×D₄	—	4	8	no	—
444	C₂×D₄	—	4	4	no	—
445	C₂×D₄	—	8	4	no	—
446	C₂×D₄	—	8	2	no	—
447	C₂×D₄	C₂⁴×C₇₉	1	2	yes	—
448	C₂×D₄	C₂⁴×C₇₉	1	2	yes	—
449	C₂×D₄	C₂⁴×C₇₉	1	4	yes	—
450	C₂²×C₄	—	2	1	no	—
451	C₂²×C₄	—	2	2	no	—
452	C₂²×C₄	—	2	1	no	—
453	C₂²×C₄	—	2	4	no	—
454	C₂²×C₄	—	2	8	no	—
455	C₂²×C₄	—	2	4	no	—
456	C₂²×C₄	—	4	8	no	—
457	C₂²×C₄	—	4	4	no	—
458	C₂²×C₄	—	4	4	no	—
459	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
460	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
461	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
462	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
463	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
464	SD₁₆	—	2	16	no	—
465	SD₁₆	—	4	8	no	—
466	SD₁₆	—	4	8	no	—
467	D₈	—	2	8	no	—
468	D₈	—	4	8	no	—
469	C₂×C₈	—	2	4	no	—
470	C₂×C₈	—	2	2	no	—
471	C₂×C₈	#41×C₇₉	1	4	yes	complemented
472	C₂×C₈	C₂⁴×C₇₉	1	2	yes	—
473	C₂×C₈	C₂⁴×C₇₉	1	4	yes	—
474	C₂×C₈	C₂⁴×C₇₉	1	2	yes	—
475	C₄⋊C₄	—	2	4	no	—
476	C₄⋊C₄	—	2	8	no	—
477	C₄⋊C₄	—	2	4	no	—
478	C₄⋊C₄	—	2	1	no	—
479	C₄⋊C₄	—	2	1	no	—
480	C₄⋊C₄	C₂×D₄×C₇₉	1	4	yes	—
481	C₄⋊C₄	C₂×D₄×C₇₉	1	8	yes	—
482	C₄⋊C₄	C₂⁴×C₇₉	1	2	yes	—
483	C₄⋊C₄	C₂⁴×C₇₉	1	2	yes	—
484	C₂²⋊C₄	—	2	8	no	—
485	C₂²⋊C₄	—	2	8	no	—
486	C₂²⋊C₄	—	2	4	no	—
487	C₂²⋊C₄	—	2	4	no	—
488	C₂²⋊C₄	—	2	8	no	—
489	C₄²	—	2	8	no	—
490	C₄²	C₂×D₄×C₇₉	1	2	yes	—
491	C₄²	C₂×D₄×C₇₉	1	4	yes	—
492	C₄²	C₂⁴×C₇₉	1	2	yes	—
493	C₄²	C₂⁴×C₇₉	1	4	yes	—
494	C₂³	—	2	2	no	—
495	C₂³	—	2	4	no	—
496	C₂³	—	2	2	no	—
497	C₂³	—	4	2	no	—
498	C₂³	—	4	2	no	—
499	C₂³	—	4	4	no	—
500	C₂³	—	4	4	no	—
501	C₂³	—	4	2	no	—
502	C₂³	—	4	2	no	—
503	C₂³	—	4	2	no	—
504	C₂³	—	4	4	no	—
505	C₂³	—	4	2	no	—
506	C₂³	C₂²×D₄×C₇₉	1	1	yes	characteristic
507	Q₈	—	2	8	no	—
508	Q₈	—	2	4	no	—
509	Q₈	—	2	4	no	—
510	Q₈	—	4	4	no	—
511	D₄	—	2	2	no	—
512	D₄	—	2	2	no	—
513	D₄	—	2	4	no	—
514	D₄	—	2	2	no	—
515	D₄	—	2	4	no	—
516	D₄	—	2	2	no	—
517	D₄	—	4	16	no	—
518	D₄	—	4	2	no	—
519	D₄	—	4	2	no	—
520	D₄	—	4	4	no	—
521	D₄	—	4	8	no	—
522	D₄	—	8	8	no	—
523	D₄	—	8	4	no	—
524	C₂×C₄	—	2	4	no	—
525	C₂×C₄	—	2	4	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	2	2	no	—
528	C₂×C₄	—	2	4	no	—
529	C₂×C₄	—	2	2	no	—
530	C₂×C₄	—	4	16	no	—
531	C₂×C₄	—	4	4	no	—
532	C₂×C₄	—	4	2	no	—
533	C₂×C₄	—	4	2	no	—
534	C₂×C₄	—	4	8	no	—
535	C₂×C₄	—	4	8	no	—
536	C₂×C₄	AGL(1,ℤ/8)×C₇₉	1	4	yes	—
537	C₂×C₄	C₂²×D₄×C₇₉	1	4	yes	—
538	C₂×C₄	C₂²×D₄×C₇₉	1	2	yes	—
539	C₂×C₄	C₂²×D₄×C₇₉	1	4	yes	—
540	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
541	C₂×C₄	C₂²×D₄×C₇₉	1	2	yes	—
542	C₂×C₄	C₂×#41×C₇₉	1	2	yes	—
543	C₂×C₄	H(5,𝔽₂)×C₇₉	1	2	yes	—
544	C₂×C₄	C₂⁵×C₇₉	1	1	yes	characteristic
545	C₈	—	2	4	no	—
546	C₈	—	2	2	no	—
547	C₈	C₂×#41×C₇₉	1	4	yes	complemented
548	C₂²	—	4	4	no	—
549	C₂²	—	4	2	no	—
550	C₂²	—	4	2	no	—
551	C₂²	—	4	4	no	—
552	C₂²	—	4	2	no	—
553	C₂²	—	4	2	no	—
554	C₂²	—	4	2	no	—
555	C₂²	—	4	2	no	—
556	C₂²	—	4	4	no	—
557	C₂²	—	8	4	no	—
558	C₂²	—	8	8	no	—
559	C₂²	—	8	4	no	—
560	C₂²	#550×C₇₉	1	2	yes	—
561	C₂²	C₂×AGL(1,ℤ/8)×C₇₉	1	2	yes	—
562	C₂²	#577×C₇₉	1	2	yes	—
563	C₂²	C₂³×D₄×C₇₉	1	1	yes	characteristic
564	C₄	—	2	4	no	—
565	C₄	—	2	4	no	—
566	C₄	—	2	2	no	—
567	C₄	—	4	2	no	—
568	C₄	—	4	2	no	—
569	C₄	—	4	4	no	—
570	C₄	#550×C₇₉	1	2	yes	—
571	C₄	C₂×AGL(1,ℤ/8)×C₇₉	1	4	yes	—
572	C₄	C₂²×#41×C₇₉	1	1	yes	characteristic
573	C₄	C₂×H(5,𝔽₂)×C₇₉	1	1	yes	characteristic
574	C₂	—	8	4	no	—
575	C₂	—	8	2	no	—
576	C₂	—	8	2	no	—
577	C₂	C₇₉×#3397	1	4	yes	direct product factor
578	C₂	C₂×#550×C₇₉	1	1	yes	characteristic
579	C₂	C₂²×AGL(1,ℤ/8)×C₇₉	1	1	yes	characteristic
580	C₂	C₂×#577×C₇₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₉	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇₉
LCS	G ▷ C₂×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
1. C₂×#556×C₇₉	C₂	semidirect
2. C₂×#550×C₇₉	C₂	semidirect
3. C₇₉×#3397	C₂	direct (N × H)
4. C₂×#496×C₇₉	C₂	semidirect
5. C₂×#492×C₇₉	C₂	semidirect
6. C₂×#460×C₇₉	C₂	semidirect
7. C₂×#463×C₇₉	C₂	semidirect
8. C₂×#461×C₇₉	C₂	semidirect
9. C₂×#459×C₇₉	C₂	semidirect
10. C₂×#446×C₇₉	C₂	semidirect
11. C₂×#440×C₇₉	C₂	semidirect
12. C₂×C₄×D₈×C₇₉	C₂	semidirect
20. #556×C₇₉	C₂²	semidirect
22. #550×C₇₉	C₂²	semidirect
37. #496×C₇₉	C₂²	semidirect
38. #492×C₇₉	C₂²	semidirect
39. #463×C₇₉	C₂²	semidirect
40. #461×C₇₉	C₂²	semidirect
41. #460×C₇₉	C₂²	semidirect
42. #459×C₇₉	C₂²	semidirect
43. #446×C₇₉	C₂²	semidirect
44. #440×C₇₉	C₂²	semidirect
45. C₄×D₈×C₇₉	C₂²	semidirect
180. C₂×C₈×C₇₉	#41	semidirect
256. C₈×C₇₉	C₂×#41	semidirect
283. C₂×#3397	C₇₉	direct (N × H)
287. C₂×C₇₉	#3397	direct (N × H)
291. C₂×#556	C₂×C₇₉	semidirect
292. C₂×#550	C₂×C₇₉	semidirect
293. #3397	C₂×C₇₉	direct (N × H)
294. C₂×#496	C₂×C₇₉	semidirect
295. C₂×#492	C₂×C₇₉	semidirect
296. C₂×#460	C₂×C₇₉	semidirect
297. C₂×#463	C₂×C₇₉	semidirect
298. C₂×#461	C₂×C₇₉	semidirect
299. C₂×#459	C₂×C₇₉	semidirect
300. C₂×#446	C₂×C₇₉	semidirect
301. C₂×#440	C₂×C₇₉	semidirect
302. C₂×C₄×D₈	C₂×C₇₉	semidirect
303. C₇₉	C₂×#3397	direct (N × H)
311. #556	C₂²×C₇₉	semidirect
313. #550	C₂²×C₇₉	semidirect
328. #496	C₂²×C₇₉	semidirect
329. #492	C₂²×C₇₉	semidirect
330. #463	C₂²×C₇₉	semidirect
331. #461	C₂²×C₇₉	semidirect
332. #460	C₂²×C₇₉	semidirect
333. #459	C₂²×C₇₉	semidirect
334. #446	C₂²×C₇₉	semidirect
335. #440	C₂²×C₇₉	semidirect
336. C₄×D₈	C₂²×C₇₉	semidirect
471. C₂×C₈	#41×C₇₉	semidirect
547. C₈	C₂×#41×C₇₉	semidirect
577. C₂	C₇₉×#3397	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×#556×C₇₉	2
C₂×#550×C₇₉	2
C₇₉×#3397	2
C₂×#496×C₇₉	2
C₂×#492×C₇₉	2
C₂×#460×C₇₉	2
C₂×#463×C₇₉	2
C₂×#461×C₇₉	2
C₂×#459×C₇₉	2
C₂×#446×C₇₉	2
C₂×#440×C₇₉	2
C₂×C₄×D₈×C₇₉	2
C₂×#3397	79

Subgroups — C2×C79×#3397 #34173083

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇₉×#3397 #34173083