Subgroups — C₂×C₇₉×#3393 #34173078

Order 20224.

1958 conjugacy classes of subgroups.

The subgroup lattice has 370 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	2	yes	maximal, complemented
2	C₇₉×#3393	C₂	1	16	yes	maximal, direct product factor
3	C₂×#495×C₇₉	C₂	1	2	yes	maximal
4	C₂×#494×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#464×C₇₉	C₂	1	4	yes	maximal, complemented
6	C₂×#461×C₇₉	C₂	1	2	yes	maximal, complemented
7	C₂×C₈×Q₈×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×Q₁₆×C₇₉	C₂	1	2	yes	maximal, complemented
9	C₂×C₄×D₈×C₇₉	C₂	1	1	yes	maximal, characteristic
10	C₂²×Q₁₆×C₇₉	C₂²	1	2	yes	—
11	C₂²×Q₁₆×C₇₉	C₂²	1	2	yes	—
12	C₂²×SD₁₆×C₇₉	C₂²	1	4	yes	—
13	C₂²×D₈×C₇₉	C₂²	1	1	yes	characteristic
14	#556×C₇₉	—	2	8	no	—
15	#556×C₇₉	C₂²	1	16	yes	complemented
16	C₂×C₄⋊Q₈×C₇₉	C₂²	1	2	yes	—
17	C₂×#126×C₇₉	—	2	4	no	—
18	C₂×#124×C₇₉	C₂²	1	4	yes	—
19	C₂×C₂²⋊Q₈×C₇₉	—	2	2	no	—
20	C₂×C₄×Q₈×C₇₉	C₂²	1	4	yes	—
21	C₂×C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₇₉	C₂²	1	2	yes	—
23	C₂×#117×C₇₉	—	2	2	no	—
24	#495×C₇₉	C₂²	1	16	yes	—
25	#494×C₇₉	C₂²	1	8	yes	complemented
26	#464×C₇₉	C₂²	1	32	yes	complemented
27	#461×C₇₉	C₂²	1	16	yes	complemented
28	C₈×Q₈×C₇₉	C₂²	1	8	yes	complemented
29	C₄×Q₁₆×C₇₉	C₂²	1	16	yes	complemented
30	C₄×D₈×C₇₉	C₂²	1	8	yes	—
31	C₂×#107×C₇₉	C₂²	1	1	yes	characteristic
32	C₂×C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
33	C₂×C₄⋊C₈×C₇₉	C₂²	1	2	yes	—
34	C₂×#103×C₇₉	C₂²	1	4	yes	—
35	C₂×#102×C₇₉	C₂²	1	2	yes	—
36	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₈×C₇₉	C₂²	1	2	yes	—
38	C₂²×Q₈×C₇₉	D₄	1	1	yes	characteristic
39	C₂²×Q₈×C₇₉	C₂³	1	4	yes	—
40	C₂²×D₄×C₇₉	C₂³	1	2	yes	—
41	C₂³×C₄×C₇₉	—	2	2	no	—
42	C₂×Q₁₆×C₇₉	—	2	8	no	—
43	C₂×Q₁₆×C₇₉	—	4	4	no	—
44	C₂×Q₁₆×C₇₉	C₂³	1	8	yes	—
45	C₂×Q₁₆×C₇₉	C₂³	1	8	yes	—
46	C₂×SD₁₆×C₇₉	—	4	8	no	—
47	C₂×SD₁₆×C₇₉	C₂³	1	16	yes	—
48	C₂×D₈×C₇₉	—	2	4	no	—
49	C₂×D₈×C₇₉	C₂³	1	4	yes	—
50	C₂²×C₈×C₇₉	C₂³	1	2	yes	—
51	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
53	C₄⋊Q₈×C₇₉	—	2	4	no	—
54	C₄⋊Q₈×C₇₉	C₂³	1	8	yes	—
55	#126×C₇₉	—	2	32	no	—
56	#124×C₇₉	—	2	8	no	—
57	#124×C₇₉	C₂³	1	16	yes	—
58	C₂²⋊Q₈×C₇₉	—	2	16	no	—
59	C₄×Q₈×C₇₉	—	2	8	no	—
60	C₄×Q₈×C₇₉	D₄	1	4	yes	—
61	C₄×Q₈×C₇₉	C₂³	1	16	yes	—
62	C₄×Q₈×C₇₉	C₂³	1	4	yes	—
63	C₄×D₄×C₇₉	—	2	4	no	—
64	C₄×D₄×C₇₉	C₂³	1	8	yes	—
65	#117×C₇₉	—	2	16	no	—
66	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
67	C₂×C₄⋊C₄×C₇₉	—	2	4	no	—
68	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
69	C₂×C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
70	C₂×C₄⋊C₄×C₇₉	D₄	1	2	yes	—
71	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
72	C₂×C₂²⋊C₄×C₇₉	—	2	4	no	—
73	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
74	C₂×C₂²⋊C₄×C₇₉	—	2	4	no	—
75	C₂×C₄²×C₇₉	—	2	4	no	—
76	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
78	#107×C₇₉	C₂³	1	4	yes	—
79	C₄⋊C₈×C₇₉	C₂³	1	4	yes	—
80	C₄⋊C₈×C₇₉	C₂³	1	8	yes	—
81	#103×C₇₉	C₂³	1	16	yes	—
82	#102×C₇₉	C₂³	1	8	yes	—
83	C₄×C₈×C₇₉	C₂³	1	4	yes	—
84	C₄×C₈×C₇₉	C₂³	1	8	yes	—
85	C₂⁴×C₇₉	—	2	2	no	—
86	C₂×Q₈×C₇₉	—	2	4	no	—
87	C₂×Q₈×C₇₉	—	2	4	no	—
88	C₂×Q₈×C₇₉	—	2	8	no	—
89	C₂×Q₈×C₇₉	—	2	8	no	—
90	C₂×Q₈×C₇₉	C₂×D₄	1	4	yes	—
91	C₂×Q₈×C₇₉	C₂⁴	1	8	yes	—
92	C₂×D₄×C₇₉	—	2	2	no	—
93	C₂×D₄×C₇₉	—	2	4	no	—
94	C₂×D₄×C₇₉	—	2	4	no	—
95	C₂×D₄×C₇₉	C₂⁴	1	4	yes	—
96	C₂²×C₄×C₇₉	—	2	2	no	—
97	C₂²×C₄×C₇₉	—	2	4	no	—
98	C₂²×C₄×C₇₉	—	2	8	no	—
99	C₂²×C₄×C₇₉	—	4	8	no	—
100	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
101	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
105	Q₁₆×C₇₉	—	2	16	no	—
106	Q₁₆×C₇₉	—	4	8	no	—
107	SD₁₆×C₇₉	—	4	16	no	—
108	D₈×C₇₉	—	2	8	no	—
109	C₂×C₈×C₇₉	—	2	4	no	—
110	C₂×C₈×C₇₉	—	2	2	no	—
111	C₂×C₈×C₇₉	#41	1	4	yes	—
112	C₂×C₈×C₇₉	C₂⁴	1	2	yes	—
113	C₂×C₈×C₇₉	C₂⁴	1	4	yes	—
114	C₂×C₈×C₇₉	C₂⁴	1	2	yes	—
115	C₄⋊C₄×C₇₉	—	2	8	no	—
116	C₄⋊C₄×C₇₉	—	2	16	no	—
117	C₄⋊C₄×C₇₉	—	2	8	no	—
118	C₄⋊C₄×C₇₉	—	2	2	no	—
119	C₄⋊C₄×C₇₉	C₂×D₄	1	4	yes	—
120	C₄⋊C₄×C₇₉	C₂×D₄	1	8	yes	—
121	C₄⋊C₄×C₇₉	C₂⁴	1	4	yes	—
122	C₂²⋊C₄×C₇₉	—	2	16	no	—
123	C₂²⋊C₄×C₇₉	—	2	8	no	—
124	C₂²⋊C₄×C₇₉	—	2	16	no	—
125	C₄²×C₇₉	—	2	16	no	—
126	C₄²×C₇₉	C₂×D₄	1	2	yes	—
127	C₄²×C₇₉	C₂×D₄	1	4	yes	—
128	C₄²×C₇₉	C₂⁴	1	2	yes	—
129	C₄²×C₇₉	C₂⁴	1	4	yes	—
130	C₂³×C₇₉	—	2	4	no	—
131	C₂³×C₇₉	—	4	4	no	—
132	C₂³×C₇₉	—	4	4	no	—
133	C₂³×C₇₉	—	4	4	no	—
134	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
135	Q₈×C₇₉	—	2	8	no	—
136	Q₈×C₇₉	—	2	8	no	—
137	Q₈×C₇₉	—	2	8	no	—
138	Q₈×C₇₉	—	4	8	no	—
139	D₄×C₇₉	—	2	4	no	—
140	D₄×C₇₉	—	2	4	no	—
141	D₄×C₇₉	—	4	4	no	—
142	C₂×C₄×C₇₉	—	2	4	no	—
143	C₂×C₄×C₇₉	—	2	4	no	—
144	C₂×C₄×C₇₉	—	2	2	no	—
145	C₂×C₄×C₇₉	—	2	4	no	—
146	C₂×C₄×C₇₉	—	2	8	no	—
147	C₂×C₄×C₇₉	—	4	8	no	—
148	C₂×C₄×C₇₉	—	4	4	no	—
149	C₂×C₄×C₇₉	—	4	16	no	—
150	C₂×C₄×C₇₉	#135	1	4	yes	—
151	C₂×C₄×C₇₉	C₂²×D₄	1	4	yes	—
152	C₂×C₄×C₇₉	C₂²×D₄	1	2	yes	—
153	C₂×C₄×C₇₉	C₂²×D₄	1	4	yes	—
154	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
155	C₂×C₄×C₇₉	C₂²×D₄	1	2	yes	—
156	C₂×C₄×C₇₉	C₂×#41	1	2	yes	—
157	C₂×C₄×C₇₉	H(5,𝔽₂)	1	2	yes	—
158	C₂×C₄×C₇₉	C₂⁵	1	1	yes	characteristic
159	C₈×C₇₉	—	2	4	no	—
160	C₈×C₇₉	—	2	2	no	—
161	C₈×C₇₉	C₂×#41	1	4	yes	—
162	C₂²×C₇₉	—	4	4	no	—
163	C₂²×C₇₉	—	4	4	no	—
164	C₂²×C₇₉	—	4	4	no	—
165	C₂²×C₇₉	—	8	8	no	—
166	C₂²×C₇₉	#550	1	2	yes	—
167	C₂²×C₇₉	C₂×#135	1	2	yes	—
168	C₂²×C₇₉	#578	1	2	yes	—
169	C₂²×C₇₉	C₂³×D₄	1	1	yes	characteristic
170	C₄×C₇₉	—	2	4	no	—
171	C₄×C₇₉	—	2	4	no	—
172	C₄×C₇₉	—	2	2	no	—
173	C₄×C₇₉	—	4	8	no	—
174	C₄×C₇₉	—	4	4	no	—
175	C₄×C₇₉	#550	1	2	yes	—
176	C₄×C₇₉	C₂×#135	1	4	yes	—
177	C₄×C₇₉	C₂²×#41	1	1	yes	characteristic
178	C₄×C₇₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
179	C₂×#3393	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
180	C₂×C₇₉	—	8	4	no	—
181	C₂×C₇₉	#3393	1	4	yes	direct product factor
182	C₂×C₇₉	C₂×#550	1	1	yes	characteristic
183	C₂×C₇₉	C₂²×#135	1	1	yes	characteristic
184	C₂×C₇₉	C₂×#578	1	1	yes	characteristic
185	C₂×#556	C₂×C₇₉	1	2	yes	complemented
186	#3393	C₂×C₇₉	1	16	yes	direct product factor
187	C₂×#495	C₂×C₇₉	1	2	yes	—
188	C₂×#494	C₂×C₇₉	1	1	yes	characteristic, complemented
189	C₂×#464	C₂×C₇₉	1	4	yes	complemented
190	C₂×#461	C₂×C₇₉	1	2	yes	complemented
191	C₂×C₈×Q₈	C₂×C₇₉	1	1	yes	characteristic, complemented
192	C₂×C₄×Q₁₆	C₂×C₇₉	1	2	yes	complemented
193	C₂×C₄×D₈	C₂×C₇₉	1	1	yes	characteristic
194	C₇₉	C₂×#3393	1	1	yes	characteristic, direct product factor, Sylow
195	C₂²×Q₁₆	C₂²×C₇₉	1	2	yes	—
196	C₂²×Q₁₆	C₂²×C₇₉	1	2	yes	—
197	C₂²×SD₁₆	C₂²×C₇₉	1	4	yes	—
198	C₂²×D₈	C₂²×C₇₉	1	1	yes	characteristic
199	#556	—	2	8	no	—
200	#556	C₂²×C₇₉	1	16	yes	complemented
201	C₂×C₄⋊Q₈	C₂²×C₇₉	1	2	yes	—
202	C₂×#126	—	2	4	no	—
203	C₂×#124	C₂²×C₇₉	1	4	yes	—
204	C₂×C₂²⋊Q₈	—	2	2	no	—
205	C₂×C₄×Q₈	C₂²×C₇₉	1	4	yes	—
206	C₂×C₄×Q₈	C₂²×C₇₉	1	1	yes	characteristic
207	C₂×C₄×D₄	C₂²×C₇₉	1	2	yes	—
208	C₂×#117	—	2	2	no	—
209	#495	C₂²×C₇₉	1	16	yes	—
210	#494	C₂²×C₇₉	1	8	yes	complemented
211	#464	C₂²×C₇₉	1	32	yes	complemented
212	#461	C₂²×C₇₉	1	16	yes	complemented
213	C₈×Q₈	C₂²×C₇₉	1	8	yes	complemented
214	C₄×Q₁₆	C₂²×C₇₉	1	16	yes	complemented
215	C₄×D₈	C₂²×C₇₉	1	8	yes	—
216	C₂×#107	C₂²×C₇₉	1	1	yes	characteristic
217	C₂×C₄⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
218	C₂×C₄⋊C₈	C₂²×C₇₉	1	2	yes	—
219	C₂×#103	C₂²×C₇₉	1	4	yes	—
220	C₂×#102	C₂²×C₇₉	1	2	yes	—
221	C₂×C₄×C₈	C₂²×C₇₉	1	1	yes	characteristic
222	C₂×C₄×C₈	C₂²×C₇₉	1	2	yes	—
223	C₂²×Q₈	D₄×C₇₉	1	1	yes	characteristic
224	C₂²×Q₈	C₂³×C₇₉	1	4	yes	—
225	C₂²×D₄	C₂³×C₇₉	1	2	yes	—
226	C₂³×C₄	—	2	2	no	—
227	C₂×Q₁₆	—	2	8	no	—
228	C₂×Q₁₆	—	4	4	no	—
229	C₂×Q₁₆	C₂³×C₇₉	1	8	yes	—
230	C₂×Q₁₆	C₂³×C₇₉	1	8	yes	—
231	C₂×SD₁₆	—	4	8	no	—
232	C₂×SD₁₆	C₂³×C₇₉	1	16	yes	—
233	C₂×D₈	—	2	4	no	—
234	C₂×D₈	C₂³×C₇₉	1	4	yes	—
235	C₂²×C₈	C₂³×C₇₉	1	2	yes	—
236	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
237	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
238	C₄⋊Q₈	—	2	4	no	—
239	C₄⋊Q₈	C₂³×C₇₉	1	8	yes	—
240	#126	—	2	32	no	—
241	#124	—	2	8	no	—
242	#124	C₂³×C₇₉	1	16	yes	—
243	C₂²⋊Q₈	—	2	16	no	—
244	C₄×Q₈	—	2	8	no	—
245	C₄×Q₈	D₄×C₇₉	1	4	yes	—
246	C₄×Q₈	C₂³×C₇₉	1	16	yes	—
247	C₄×Q₈	C₂³×C₇₉	1	4	yes	—
248	C₄×D₄	—	2	4	no	—
249	C₄×D₄	C₂³×C₇₉	1	8	yes	—
250	#117	—	2	16	no	—
251	C₂×C₄⋊C₄	—	2	2	no	—
252	C₂×C₄⋊C₄	—	2	4	no	—
253	C₂×C₄⋊C₄	—	2	2	no	—
254	C₂×C₄⋊C₄	D₄×C₇₉	1	1	yes	characteristic
255	C₂×C₄⋊C₄	D₄×C₇₉	1	2	yes	—
256	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
257	C₂×C₂²⋊C₄	—	2	4	no	—
258	C₂×C₂²⋊C₄	—	2	2	no	—
259	C₂×C₂²⋊C₄	—	2	4	no	—
260	C₂×C₄²	—	2	4	no	—
261	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
262	C₂×C₄²	C₂³×C₇₉	1	2	yes	—
263	#107	C₂³×C₇₉	1	4	yes	—
264	C₄⋊C₈	C₂³×C₇₉	1	4	yes	—
265	C₄⋊C₈	C₂³×C₇₉	1	8	yes	—
266	#103	C₂³×C₇₉	1	16	yes	—
267	#102	C₂³×C₇₉	1	8	yes	—
268	C₄×C₈	C₂³×C₇₉	1	4	yes	—
269	C₄×C₈	C₂³×C₇₉	1	8	yes	—
270	C₂⁴	—	2	2	no	—
271	C₂×Q₈	—	2	4	no	—
272	C₂×Q₈	—	2	4	no	—
273	C₂×Q₈	—	2	8	no	—
274	C₂×Q₈	—	2	8	no	—
275	C₂×Q₈	C₂×D₄×C₇₉	1	4	yes	—
276	C₂×Q₈	C₂⁴×C₇₉	1	8	yes	—
277	C₂×D₄	—	2	2	no	—
278	C₂×D₄	—	2	4	no	—
279	C₂×D₄	—	2	4	no	—
280	C₂×D₄	C₂⁴×C₇₉	1	4	yes	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	4	no	—
283	C₂²×C₄	—	2	8	no	—
284	C₂²×C₄	—	4	8	no	—
285	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
286	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
287	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
288	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
289	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
290	Q₁₆	—	2	16	no	—
291	Q₁₆	—	4	8	no	—
292	SD₁₆	—	4	16	no	—
293	D₈	—	2	8	no	—
294	C₂×C₈	—	2	4	no	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	#41×C₇₉	1	4	yes	—
297	C₂×C₈	C₂⁴×C₇₉	1	2	yes	—
298	C₂×C₈	C₂⁴×C₇₉	1	4	yes	—
299	C₂×C₈	C₂⁴×C₇₉	1	2	yes	—
300	C₄⋊C₄	—	2	8	no	—
301	C₄⋊C₄	—	2	16	no	—
302	C₄⋊C₄	—	2	8	no	—
303	C₄⋊C₄	—	2	2	no	—
304	C₄⋊C₄	C₂×D₄×C₇₉	1	4	yes	—
305	C₄⋊C₄	C₂×D₄×C₇₉	1	8	yes	—
306	C₄⋊C₄	C₂⁴×C₇₉	1	4	yes	—
307	C₂²⋊C₄	—	2	16	no	—
308	C₂²⋊C₄	—	2	8	no	—
309	C₂²⋊C₄	—	2	16	no	—
310	C₄²	—	2	16	no	—
311	C₄²	C₂×D₄×C₇₉	1	2	yes	—
312	C₄²	C₂×D₄×C₇₉	1	4	yes	—
313	C₄²	C₂⁴×C₇₉	1	2	yes	—
314	C₄²	C₂⁴×C₇₉	1	4	yes	—
315	C₂³	—	2	4	no	—
316	C₂³	—	4	4	no	—
317	C₂³	—	4	4	no	—
318	C₂³	—	4	4	no	—
319	C₂³	C₂²×D₄×C₇₉	1	1	yes	characteristic
320	Q₈	—	2	8	no	—
321	Q₈	—	2	8	no	—
322	Q₈	—	2	8	no	—
323	Q₈	—	4	8	no	—
324	D₄	—	2	4	no	—
325	D₄	—	2	4	no	—
326	D₄	—	4	4	no	—
327	C₂×C₄	—	2	4	no	—
328	C₂×C₄	—	2	4	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	4	no	—
331	C₂×C₄	—	2	8	no	—
332	C₂×C₄	—	4	8	no	—
333	C₂×C₄	—	4	4	no	—
334	C₂×C₄	—	4	16	no	—
335	C₂×C₄	#135×C₇₉	1	4	yes	—
336	C₂×C₄	C₂²×D₄×C₇₉	1	4	yes	—
337	C₂×C₄	C₂²×D₄×C₇₉	1	2	yes	—
338	C₂×C₄	C₂²×D₄×C₇₉	1	4	yes	—
339	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
340	C₂×C₄	C₂²×D₄×C₇₉	1	2	yes	—
341	C₂×C₄	C₂×#41×C₇₉	1	2	yes	—
342	C₂×C₄	H(5,𝔽₂)×C₇₉	1	2	yes	—
343	C₂×C₄	C₂⁵×C₇₉	1	1	yes	characteristic
344	C₈	—	2	4	no	—
345	C₈	—	2	2	no	—
346	C₈	C₂×#41×C₇₉	1	4	yes	—
347	C₂²	—	4	4	no	—
348	C₂²	—	4	4	no	—
349	C₂²	—	4	4	no	—
350	C₂²	—	8	8	no	—
351	C₂²	#550×C₇₉	1	2	yes	—
352	C₂²	C₂×#135×C₇₉	1	2	yes	—
353	C₂²	#578×C₇₉	1	2	yes	—
354	C₂²	C₂³×D₄×C₇₉	1	1	yes	characteristic
355	C₄	—	2	4	no	—
356	C₄	—	2	4	no	—
357	C₄	—	2	2	no	—
358	C₄	—	4	4	no	—
359	C₄	—	4	8	no	—
360	C₄	#550×C₇₉	1	2	yes	—
361	C₄	C₂×#135×C₇₉	1	4	yes	—
362	C₄	C₂²×#41×C₇₉	1	1	yes	characteristic
363	C₄	C₂×H(5,𝔽₂)×C₇₉	1	1	yes	characteristic
364	C₂	—	8	4	no	—
365	C₂	C₇₉×#3393	1	4	yes	direct product factor
366	C₂	C₂×#550×C₇₉	1	1	yes	characteristic
367	C₂	C₂²×#135×C₇₉	1	1	yes	characteristic
368	C₂	C₂×#578×C₇₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₉	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇₉
prime radical	C₂²×D₈×C₇₉	C₂²
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. C₇₉×#3393	C₂	direct (N × H)
4. C₂×#494×C₇₉	C₂	semidirect
5. C₂×#464×C₇₉	C₂	semidirect
6. C₂×#461×C₇₉	C₂	semidirect
7. C₂×C₈×Q₈×C₇₉	C₂	semidirect
8. C₂×C₄×Q₁₆×C₇₉	C₂	semidirect
15. #556×C₇₉	C₂²	semidirect
25. #494×C₇₉	C₂²	semidirect
26. #464×C₇₉	C₂²	semidirect
27. #461×C₇₉	C₂²	semidirect
28. C₈×Q₈×C₇₉	C₂²	semidirect
29. C₄×Q₁₆×C₇₉	C₂²	semidirect
179. C₂×#3393	C₇₉	direct (N × H)
181. C₂×C₇₉	#3393	direct (N × H)
185. C₂×#556	C₂×C₇₉	semidirect
186. #3393	C₂×C₇₉	direct (N × H)
188. C₂×#494	C₂×C₇₉	semidirect
189. C₂×#464	C₂×C₇₉	semidirect
190. C₂×#461	C₂×C₇₉	semidirect
191. C₂×C₈×Q₈	C₂×C₇₉	semidirect
192. C₂×C₄×Q₁₆	C₂×C₇₉	semidirect
194. C₇₉	C₂×#3393	direct (N × H)
200. #556	C₂²×C₇₉	semidirect
210. #494	C₂²×C₇₉	semidirect
211. #464	C₂²×C₇₉	semidirect
212. #461	C₂²×C₇₉	semidirect
213. C₈×Q₈	C₂²×C₇₉	semidirect
214. C₄×Q₁₆	C₂²×C₇₉	semidirect
365. C₂	C₇₉×#3393	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
C₇₉×#3393	2
C₂×#495×C₇₉	2
C₂×#494×C₇₉	2
C₂×#464×C₇₉	2
C₂×#461×C₇₉	2
C₂×C₈×Q₈×C₇₉	2
C₂×C₄×Q₁₆×C₇₉	2
C₂×C₄×D₈×C₇₉	2
C₂×#3393	79

Subgroups — C2×C79×#3393 #34173078

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇₉×#3393 #34173078