Subgroups — C₂×C₇₉×#2057 #34135237

Order 20224.

1454 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄⋊Q₈×C₇₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×#107×C₇₉	C₂	1	2	yes	maximal
3	C₂×#389×C₇₉	C₂	1	1	yes	maximal, characteristic
4	C₇₉×#2057	C₂	1	8	yes	maximal, direct product factor
5	C₂×#340×C₇₉	C₂	1	2	yes	maximal
6	C₂×#336×C₇₉	C₂	1	1	yes	maximal, characteristic
7	C₂³×Q₈×C₇₉	—	2	1	no	—
8	C₂³×C₈×C₇₉	C₂²	1	2	yes	—
9	C₂×C₄⋊Q₈×C₇₉	—	2	8	no	—
10	C₂×C₄⋊Q₈×C₇₉	—	2	2	no	—
11	C₂×C₄⋊Q₈×C₇₉	C₂²	1	4	yes	—
12	C₂²×C₄⋊C₄×C₇₉	—	2	1	no	—
13	C₂²×C₄⋊C₄×C₇₉	—	2	1	no	—
14	C₂²×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
15	C₂²×C₄⋊C₄×C₇₉	C₂²	1	2	yes	—
16	C₂²×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
17	C₂²×C₄²×C₇₉	C₂²	1	1	yes	characteristic
18	C₂×#107×C₇₉	—	2	8	no	—
19	C₂×#107×C₇₉	C₂²	1	8	yes	—
20	#389×C₇₉	—	2	2	no	—
21	#389×C₇₉	C₂²	1	4	yes	—
22	C₂×#95×C₇₉	—	2	1	no	—
23	#340×C₇₉	C₂²	1	8	yes	—
24	#336×C₇₉	C₂²	1	4	yes	—
25	C₂²×Q₈×C₇₉	—	2	8	no	—
26	C₂²×Q₈×C₇₉	—	2	4	no	—
27	C₂²×Q₈×C₇₉	—	4	4	no	—
28	C₂²×Q₈×C₇₉	—	4	4	no	—
29	C₂³×C₄×C₇₉	—	2	2	no	—
30	C₂³×C₄×C₇₉	—	2	1	no	—
31	C₂³×C₄×C₇₉	—	2	1	no	—
32	C₂³×C₄×C₇₉	D₄	1	1	yes	characteristic
33	C₂³×C₄×C₇₉	D₄	1	1	yes	characteristic
34	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
35	C₂²×C₈×C₇₉	—	2	4	no	—
36	C₂²×C₈×C₇₉	—	2	4	no	—
37	C₂²×C₈×C₇₉	Q₈	1	8	yes	complemented
38	C₂²×C₈×C₇₉	C₂³	1	4	yes	—
39	C₄⋊Q₈×C₇₉	—	2	16	no	—
40	C₄⋊Q₈×C₇₉	—	2	16	no	—
41	C₂×C₄⋊C₄×C₇₉	—	2	8	no	—
42	C₂×C₄⋊C₄×C₇₉	—	2	4	no	—
43	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
44	C₂×C₄⋊C₄×C₇₉	—	2	4	no	—
45	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
46	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
47	C₂×C₄⋊C₄×C₇₉	—	2	4	no	—
48	C₂×C₄⋊C₄×C₇₉	—	2	4	no	—
49	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
50	C₂×C₄⋊C₄×C₇₉	—	4	4	no	—
51	C₂×C₄⋊C₄×C₇₉	D₄	1	8	yes	—
52	C₂×C₄⋊C₄×C₇₉	Q₈	1	4	yes	complemented
53	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
54	C₂×C₄⋊C₄×C₇₉	C₂³	1	4	yes	—
55	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
56	C₂×C₄²×C₇₉	—	2	4	no	—
57	C₂×C₄²×C₇₉	D₄	1	2	yes	—
58	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
59	#107×C₇₉	—	2	16	no	—
60	#95×C₇₉	—	2	4	no	—
61	C₂⁴×C₇₉	C₂×D₄	1	1	yes	characteristic
62	C₂×Q₈×C₇₉	—	2	16	no	—
63	C₂×Q₈×C₇₉	—	4	8	no	—
64	C₂×Q₈×C₇₉	—	4	32	no	—
65	C₂×Q₈×C₇₉	—	4	8	no	—
66	C₂²×C₄×C₇₉	—	2	2	no	—
67	C₂²×C₄×C₇₉	—	2	2	no	—
68	C₂²×C₄×C₇₉	—	2	2	no	—
69	C₂²×C₄×C₇₉	—	2	2	no	—
70	C₂²×C₄×C₇₉	—	2	8	no	—
71	C₂²×C₄×C₇₉	—	2	4	no	—
72	C₂²×C₄×C₇₉	—	2	2	no	—
73	C₂²×C₄×C₇₉	—	2	4	no	—
74	C₂²×C₄×C₇₉	—	2	2	no	—
75	C₂²×C₄×C₇₉	—	4	2	no	—
76	C₂²×C₄×C₇₉	—	4	4	no	—
77	C₂²×C₄×C₇₉	—	4	4	no	—
78	C₂²×C₄×C₇₉	—	4	2	no	—
79	C₂²×C₄×C₇₉	—	4	2	no	—
80	C₂²×C₄×C₇₉	—	4	2	no	—
81	C₂²×C₄×C₇₉	—	4	2	no	—
82	C₂²×C₄×C₇₉	D₈	1	4	yes	—
83	C₂²×C₄×C₇₉	Q₁₆	1	4	yes	—
84	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
85	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
86	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₇₉	C₂×D₄	1	4	yes	—
88	C₂²×C₄×C₇₉	C₂×Q₈	1	4	yes	—
89	C₂²×C₄×C₇₉	C₂×Q₈	1	2	yes	—
90	C₂²×C₄×C₇₉	#41	1	2	yes	—
91	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
92	C₂×C₈×C₇₉	—	2	16	no	—
93	C₂×C₈×C₇₉	—	2	4	no	—
94	C₂×C₈×C₇₉	—	2	4	no	—
95	C₂×C₈×C₇₉	C₂×Q₈	1	8	yes	complemented
96	C₄⋊C₄×C₇₉	—	2	16	no	—
97	C₄⋊C₄×C₇₉	—	2	8	no	—
98	C₄⋊C₄×C₇₉	—	2	4	no	—
99	C₄⋊C₄×C₇₉	—	2	4	no	—
100	C₄⋊C₄×C₇₉	—	2	2	no	—
101	C₄⋊C₄×C₇₉	—	2	4	no	—
102	C₄⋊C₄×C₇₉	—	4	2	no	—
103	C₄⋊C₄×C₇₉	—	4	8	no	—
104	C₄⋊C₄×C₇₉	C₂×D₄	1	8	yes	—
105	C₄⋊C₄×C₇₉	C₂×Q₈	1	4	yes	complemented
106	C₄²×C₇₉	—	2	4	no	—
107	C₄²×C₇₉	—	2	4	no	—
108	C₂³×C₇₉	#120	1	2	yes	—
109	C₂³×C₇₉	C₂²⋊Q₈	1	2	yes	—
110	C₂³×C₇₉	C₄⋊Q₈	1	2	yes	—
111	C₂³×C₇₉	C₂×D₈	1	2	yes	—
112	C₂³×C₇₉	C₂×Q₁₆	1	2	yes	—
113	C₂³×C₇₉	AGL(1,ℤ/8)	1	2	yes	—
114	C₂³×C₇₉	#137	1	2	yes	—
115	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
116	Q₈×C₇₉	—	4	32	no	—
117	C₂×C₄×C₇₉	—	2	2	no	—
118	C₂×C₄×C₇₉	—	2	2	no	—
119	C₂×C₄×C₇₉	—	2	2	no	—
120	C₂×C₄×C₇₉	—	2	2	no	—
121	C₂×C₄×C₇₉	—	2	8	no	—
122	C₂×C₄×C₇₉	—	2	8	no	—
123	C₂×C₄×C₇₉	—	2	8	no	—
124	C₂×C₄×C₇₉	—	2	4	no	—
125	C₂×C₄×C₇₉	—	4	2	no	—
126	C₂×C₄×C₇₉	—	4	4	no	—
127	C₂×C₄×C₇₉	—	4	4	no	—
128	C₂×C₄×C₇₉	—	4	2	no	—
129	C₂×C₄×C₇₉	—	4	16	no	—
130	C₂×C₄×C₇₉	—	4	8	no	—
131	C₂×C₄×C₇₉	—	4	2	no	—
132	C₂×C₄×C₇₉	—	4	2	no	—
133	C₂×C₄×C₇₉	—	4	2	no	—
134	C₂×C₄×C₇₉	—	8	4	no	—
135	C₂×C₄×C₇₉	#120	1	2	yes	—
136	C₂×C₄×C₇₉	C₂²⋊Q₈	1	8	yes	—
137	C₂×C₄×C₇₉	C₂²⋊Q₈	1	2	yes	—
138	C₂×C₄×C₇₉	C₄⋊Q₈	1	8	yes	—
139	C₂×C₄×C₇₉	C₄⋊Q₈	1	2	yes	—
140	C₂×C₄×C₇₉	C₂×D₈	1	4	yes	—
141	C₂×C₄×C₇₉	C₂×Q₁₆	1	4	yes	—
142	C₂×C₄×C₇₉	C₂²×D₄	1	2	yes	—
143	C₂×C₄×C₇₉	C₂²×Q₈	1	2	yes	—
144	C₂×C₄×C₇₉	C₂²×Q₈	1	1	yes	characteristic
145	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
146	C₈×C₇₉	—	2	8	no	—
147	C₂²×C₇₉	#395	1	4	yes	—
148	C₂²×C₇₉	#447	1	4	yes	—
149	C₂²×C₇₉	#451	1	4	yes	—
150	C₂²×C₇₉	#474	1	4	yes	—
151	C₂²×C₇₉	#477	1	4	yes	—
152	C₂²×C₇₉	#500	1	4	yes	—
153	C₂²×C₇₉	#501	1	4	yes	—
154	C₂²×C₇₉	C₂×#120	1	1	yes	characteristic
155	C₂²×C₇₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
156	C₂²×C₇₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
157	C₂²×C₇₉	C₂²×D₈	1	1	yes	characteristic
158	C₂²×C₇₉	C₂²×Q₁₆	1	1	yes	characteristic
159	C₂²×C₇₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
160	C₂²×C₇₉	C₂×#137	1	1	yes	characteristic
161	C₄×C₇₉	—	2	4	no	—
162	C₄×C₇₉	—	2	4	no	—
163	C₄×C₇₉	—	4	8	no	—
164	C₄×C₇₉	—	4	4	no	—
165	C₄×C₇₉	—	8	2	no	—
166	C₄×C₇₉	#395	1	4	yes	—
167	C₄×C₇₉	C₂×C₂²⋊Q₈	1	2	yes	—
168	C₄×C₇₉	C₂×C₄⋊Q₈	1	2	yes	—
169	C₂×#2057	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
170	C₂×C₇₉	#2057	1	8	yes	direct product factor
171	C₂×C₇₉	C₂×#395	1	1	yes	characteristic
172	C₂×C₇₉	C₂×#447	1	1	yes	characteristic
173	C₂×C₇₉	C₂×#451	1	1	yes	characteristic
174	C₂×C₇₉	C₂×#474	1	1	yes	characteristic
175	C₂×C₇₉	C₂×#477	1	1	yes	characteristic
176	C₂×C₇₉	C₂×#500	1	1	yes	characteristic
177	C₂×C₇₉	C₂×#501	1	1	yes	characteristic
178	C₂²×C₄⋊Q₈	C₂×C₇₉	1	1	yes	characteristic
179	C₂²×#107	C₂×C₇₉	1	2	yes	—
180	C₂×#389	C₂×C₇₉	1	1	yes	characteristic
181	#2057	C₂×C₇₉	1	8	yes	direct product factor
182	C₂×#340	C₂×C₇₉	1	2	yes	—
183	C₂×#336	C₂×C₇₉	1	1	yes	characteristic
184	C₇₉	C₂×#2057	1	1	yes	characteristic, direct product factor, Sylow
185	C₂³×Q₈	—	2	1	no	—
186	C₂³×C₈	C₂²×C₇₉	1	2	yes	—
187	C₂×C₄⋊Q₈	—	2	8	no	—
188	C₂×C₄⋊Q₈	—	2	2	no	—
189	C₂×C₄⋊Q₈	C₂²×C₇₉	1	4	yes	—
190	C₂²×C₄⋊C₄	—	2	1	no	—
191	C₂²×C₄⋊C₄	—	2	1	no	—
192	C₂²×C₄⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
193	C₂²×C₄⋊C₄	C₂²×C₇₉	1	2	yes	—
194	C₂²×C₄⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
195	C₂²×C₄²	C₂²×C₇₉	1	1	yes	characteristic
196	C₂×#107	—	2	8	no	—
197	C₂×#107	C₂²×C₇₉	1	8	yes	—
198	#389	—	2	2	no	—
199	#389	C₂²×C₇₉	1	4	yes	—
200	C₂×#95	—	2	1	no	—
201	#340	C₂²×C₇₉	1	8	yes	—
202	#336	C₂²×C₇₉	1	4	yes	—
203	C₂²×Q₈	—	2	8	no	—
204	C₂²×Q₈	—	2	4	no	—
205	C₂²×Q₈	—	4	4	no	—
206	C₂²×Q₈	—	4	4	no	—
207	C₂³×C₄	—	2	2	no	—
208	C₂³×C₄	—	2	1	no	—
209	C₂³×C₄	—	2	1	no	—
210	C₂³×C₄	D₄×C₇₉	1	1	yes	characteristic
211	C₂³×C₄	D₄×C₇₉	1	1	yes	characteristic
212	C₂³×C₄	C₂³×C₇₉	1	1	yes	characteristic
213	C₂²×C₈	—	2	4	no	—
214	C₂²×C₈	—	2	4	no	—
215	C₂²×C₈	Q₈×C₇₉	1	8	yes	complemented
216	C₂²×C₈	C₂³×C₇₉	1	4	yes	—
217	C₄⋊Q₈	—	2	16	no	—
218	C₄⋊Q₈	—	2	16	no	—
219	C₂×C₄⋊C₄	—	2	8	no	—
220	C₂×C₄⋊C₄	—	2	4	no	—
221	C₂×C₄⋊C₄	—	2	2	no	—
222	C₂×C₄⋊C₄	—	2	4	no	—
223	C₂×C₄⋊C₄	—	2	1	no	—
224	C₂×C₄⋊C₄	—	2	2	no	—
225	C₂×C₄⋊C₄	—	2	4	no	—
226	C₂×C₄⋊C₄	—	2	4	no	—
227	C₂×C₄⋊C₄	—	2	1	no	—
228	C₂×C₄⋊C₄	—	4	4	no	—
229	C₂×C₄⋊C₄	D₄×C₇₉	1	8	yes	—
230	C₂×C₄⋊C₄	Q₈×C₇₉	1	4	yes	complemented
231	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
232	C₂×C₄⋊C₄	C₂³×C₇₉	1	4	yes	—
233	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
234	C₂×C₄²	—	2	4	no	—
235	C₂×C₄²	D₄×C₇₉	1	2	yes	—
236	C₂×C₄²	C₂³×C₇₉	1	2	yes	—
237	#107	—	2	16	no	—
238	#95	—	2	4	no	—
239	C₂⁴	C₂×D₄×C₇₉	1	1	yes	characteristic
240	C₂×Q₈	—	2	16	no	—
241	C₂×Q₈	—	4	32	no	—
242	C₂×Q₈	—	4	8	no	—
243	C₂×Q₈	—	4	8	no	—
244	C₂²×C₄	—	2	2	no	—
245	C₂²×C₄	—	2	2	no	—
246	C₂²×C₄	—	2	2	no	—
247	C₂²×C₄	—	2	2	no	—
248	C₂²×C₄	—	2	8	no	—
249	C₂²×C₄	—	2	4	no	—
250	C₂²×C₄	—	2	2	no	—
251	C₂²×C₄	—	2	4	no	—
252	C₂²×C₄	—	2	2	no	—
253	C₂²×C₄	—	4	2	no	—
254	C₂²×C₄	—	4	4	no	—
255	C₂²×C₄	—	4	4	no	—
256	C₂²×C₄	—	4	2	no	—
257	C₂²×C₄	—	4	2	no	—
258	C₂²×C₄	—	4	2	no	—
259	C₂²×C₄	—	4	2	no	—
260	C₂²×C₄	D₈×C₇₉	1	4	yes	—
261	C₂²×C₄	Q₁₆×C₇₉	1	4	yes	—
262	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
263	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
264	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
265	C₂²×C₄	C₂×D₄×C₇₉	1	4	yes	—
266	C₂²×C₄	C₂×Q₈×C₇₉	1	4	yes	—
267	C₂²×C₄	C₂×Q₈×C₇₉	1	2	yes	—
268	C₂²×C₄	#41×C₇₉	1	2	yes	—
269	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
270	C₂×C₈	—	2	16	no	—
271	C₂×C₈	—	2	4	no	—
272	C₂×C₈	—	2	4	no	—
273	C₂×C₈	C₂×Q₈×C₇₉	1	8	yes	complemented
274	C₄⋊C₄	—	2	16	no	—
275	C₄⋊C₄	—	2	8	no	—
276	C₄⋊C₄	—	2	4	no	—
277	C₄⋊C₄	—	2	4	no	—
278	C₄⋊C₄	—	2	2	no	—
279	C₄⋊C₄	—	2	4	no	—
280	C₄⋊C₄	—	4	2	no	—
281	C₄⋊C₄	—	4	8	no	—
282	C₄⋊C₄	C₂×D₄×C₇₉	1	8	yes	—
283	C₄⋊C₄	C₂×Q₈×C₇₉	1	4	yes	complemented
284	C₄²	—	2	4	no	—
285	C₄²	—	2	4	no	—
286	C₂³	#120×C₇₉	1	2	yes	—
287	C₂³	C₂²⋊Q₈×C₇₉	1	2	yes	—
288	C₂³	C₄⋊Q₈×C₇₉	1	2	yes	—
289	C₂³	C₂×D₈×C₇₉	1	2	yes	—
290	C₂³	C₂×Q₁₆×C₇₉	1	2	yes	—
291	C₂³	AGL(1,ℤ/8)×C₇₉	1	2	yes	—
292	C₂³	#137×C₇₉	1	2	yes	—
293	C₂³	C₂²×D₄×C₇₉	1	1	yes	characteristic
294	Q₈	—	4	32	no	—
295	C₂×C₄	—	2	8	no	—
296	C₂×C₄	—	2	8	no	—
297	C₂×C₄	—	2	2	no	—
298	C₂×C₄	—	2	2	no	—
299	C₂×C₄	—	2	2	no	—
300	C₂×C₄	—	2	2	no	—
301	C₂×C₄	—	2	8	no	—
302	C₂×C₄	—	2	4	no	—
303	C₂×C₄	—	4	16	no	—
304	C₂×C₄	—	4	8	no	—
305	C₂×C₄	—	4	2	no	—
306	C₂×C₄	—	4	4	no	—
307	C₂×C₄	—	4	4	no	—
308	C₂×C₄	—	4	2	no	—
309	C₂×C₄	—	4	2	no	—
310	C₂×C₄	—	4	2	no	—
311	C₂×C₄	—	4	2	no	—
312	C₂×C₄	—	8	4	no	—
313	C₂×C₄	#120×C₇₉	1	2	yes	—
314	C₂×C₄	C₂²⋊Q₈×C₇₉	1	8	yes	—
315	C₂×C₄	C₂²⋊Q₈×C₇₉	1	2	yes	—
316	C₂×C₄	C₄⋊Q₈×C₇₉	1	8	yes	—
317	C₂×C₄	C₄⋊Q₈×C₇₉	1	2	yes	—
318	C₂×C₄	C₂×D₈×C₇₉	1	4	yes	—
319	C₂×C₄	C₂×Q₁₆×C₇₉	1	4	yes	—
320	C₂×C₄	C₂²×D₄×C₇₉	1	2	yes	—
321	C₂×C₄	C₂²×Q₈×C₇₉	1	2	yes	—
322	C₂×C₄	C₂²×Q₈×C₇₉	1	1	yes	characteristic
323	C₂×C₄	C₂×#41×C₇₉	1	1	yes	characteristic
324	C₈	—	2	8	no	—
325	C₂²	#395×C₇₉	1	4	yes	—
326	C₂²	#447×C₇₉	1	4	yes	—
327	C₂²	#451×C₇₉	1	4	yes	—
328	C₂²	#474×C₇₉	1	4	yes	—
329	C₂²	#477×C₇₉	1	4	yes	—
330	C₂²	#500×C₇₉	1	4	yes	—
331	C₂²	#501×C₇₉	1	4	yes	—
332	C₂²	C₂×#120×C₇₉	1	1	yes	characteristic
333	C₂²	C₂×C₂²⋊Q₈×C₇₉	1	1	yes	characteristic
334	C₂²	C₂×C₄⋊Q₈×C₇₉	1	1	yes	characteristic
335	C₂²	C₂²×D₈×C₇₉	1	1	yes	characteristic
336	C₂²	C₂²×Q₁₆×C₇₉	1	1	yes	characteristic
337	C₂²	C₂×AGL(1,ℤ/8)×C₇₉	1	1	yes	characteristic
338	C₂²	C₂×#137×C₇₉	1	1	yes	characteristic
339	C₄	—	2	4	no	—
340	C₄	—	2	4	no	—
341	C₄	—	4	4	no	—
342	C₄	—	4	8	no	—
343	C₄	—	8	2	no	—
344	C₄	#395×C₇₉	1	4	yes	—
345	C₄	C₂×C₂²⋊Q₈×C₇₉	1	2	yes	—
346	C₄	C₂×C₄⋊Q₈×C₇₉	1	2	yes	—
347	C₂	C₇₉×#2057	1	8	yes	direct product factor
348	C₂	C₂×#395×C₇₉	1	1	yes	characteristic
349	C₂	C₂×#447×C₇₉	1	1	yes	characteristic
350	C₂	C₂×#451×C₇₉	1	1	yes	characteristic
351	C₂	C₂×#474×C₇₉	1	1	yes	characteristic
352	C₂	C₂×#477×C₇₉	1	1	yes	characteristic
353	C₂	C₂×#500×C₇₉	1	1	yes	characteristic
354	C₂	C₂×#501×C₇₉	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
4. C₇₉×#2057	C₂	direct (N × H)
37. C₂²×C₈×C₇₉	Q₈	semidirect
52. C₂×C₄⋊C₄×C₇₉	Q₈	semidirect
95. C₂×C₈×C₇₉	C₂×Q₈	semidirect
105. C₄⋊C₄×C₇₉	C₂×Q₈	semidirect
169. C₂×#2057	C₇₉	direct (N × H)
170. C₂×C₇₉	#2057	direct (N × H)
181. #2057	C₂×C₇₉	direct (N × H)
184. C₇₉	C₂×#2057	direct (N × H)
215. C₂²×C₈	Q₈×C₇₉	semidirect
230. C₂×C₄⋊C₄	Q₈×C₇₉	semidirect
273. C₂×C₈	C₂×Q₈×C₇₉	semidirect
283. C₄⋊C₄	C₂×Q₈×C₇₉	semidirect
347. C₂	C₇₉×#2057	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⋊Q₈×C₇₉	2
C₂²×#107×C₇₉	2
C₂×#389×C₇₉	2
C₇₉×#2057	2
C₂×#340×C₇₉	2
C₂×#336×C₇₉	2
C₂×#2057	79

Subgroups — C2×C79×#2057 #34135237

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇₉×#2057 #34135237