Subgroups — C₇₉×#36696 #34148385

Order 20224.

1908 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₉×#2843	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₉×#2830	C₂	1	3	yes	maximal, complemented
3	C₇₉×#2829	C₂	1	6	yes	maximal, complemented
4	C₇₉×#2828	C₂	1	3	yes	maximal, complemented
5	C₇₉×#2823	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₉×#2818	C₂	1	2	yes	maximal, complemented
7	C₇₉×#2395	C₂	1	3	yes	maximal, complemented
8	C₇₉×#2392	C₂	1	6	yes	maximal, complemented
9	C₇₉×#2388	C₂	1	3	yes	maximal, complemented
10	C₄×#127×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×#126×C₇₉	C₂	1	2	yes	maximal, complemented
12	C₂²×#41×C₇₉	C₂²	1	1	yes	characteristic
13	C₂×#127×C₇₉	C₂²	1	1	yes	characteristic
14	C₂×#126×C₇₉	C₂²	1	2	yes	—
15	C₂×C₄×D₄×C₇₉	C₂²	1	3	yes	—
16	C₂×C₄×D₄×C₇₉	C₂²	1	3	yes	—
17	C₂×C₄×D₄×C₇₉	C₂²	1	6	yes	—
18	C₂×#117×C₇₉	C₂²	1	3	yes	—
19	#400×C₇₉	C₂²	1	3	yes	—
20	#399×C₇₉	C₂²	1	3	yes	—
21	#398×C₇₉	C₂²	1	3	yes	—
22	#398×C₇₉	C₂²	1	6	yes	—
23	#397×C₇₉	C₂²	1	6	yes	—
24	#397×C₇₉	C₂²	1	3	yes	—
25	#397×C₇₉	C₂²	1	6	yes	—
26	#396×C₇₉	C₂²	1	6	yes	—
27	#396×C₇₉	C₂²	1	6	yes	—
28	#395×C₇₉	C₂²	1	3	yes	—
29	#394×C₇₉	C₂²	1	6	yes	—
30	#394×C₇₉	C₂²	1	6	yes	—
31	#394×C₇₉	C₂²	1	3	yes	—
32	#394×C₇₉	C₂²	1	6	yes	—
33	#394×C₇₉	C₂²	1	6	yes	—
34	#394×C₇₉	C₂²	1	6	yes	—
35	#393×C₇₉	C₂²	1	3	yes	—
36	#392×C₇₉	C₂²	1	6	yes	—
37	#392×C₇₉	C₂²	1	6	yes	—
38	#392×C₇₉	C₂²	1	3	yes	—
39	#390×C₇₉	C₂²	1	3	yes	—
40	#390×C₇₉	C₂²	1	3	yes	—
41	#388×C₇₉	C₂²	1	6	yes	—
42	#387×C₇₉	C₂²	1	6	yes	—
43	#384×C₇₉	C₂²	1	1	yes	characteristic
44	#383×C₇₉	C₂²	1	2	yes	—
45	C₄×C₄⋊C₄×C₇₉	C₂²	1	6	yes	—
46	C₄×C₂²⋊C₄×C₇₉	C₂²	1	6	yes	—
47	C₄×C₂²⋊C₄×C₇₉	C₂²	1	3	yes	—
48	C₄×C₂²⋊C₄×C₇₉	C₂²	1	3	yes	—
49	C₄³×C₇₉	C₂²	1	1	yes	characteristic
50	C₂×#41×C₇₉	—	4	6	no	—
51	C₂²×Q₈×C₇₉	C₂³	1	1	yes	characteristic
52	C₂²×D₄×C₇₉	C₂³	1	3	yes	—
53	C₂²×D₄×C₇₉	C₂³	1	3	yes	—
54	C₂²×D₄×C₇₉	C₂³	1	6	yes	—
55	C₂²×D₄×C₇₉	C₂³	1	2	yes	—
56	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
57	C₂³×C₄×C₇₉	C₂³	1	3	yes	—
58	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
59	C₂³×C₄×C₇₉	C₂³	1	2	yes	—
60	#127×C₇₉	—	2	4	no	—
61	#126×C₇₉	—	2	8	no	—
62	C₄×D₄×C₇₉	—	4	12	no	—
63	C₄×D₄×C₇₉	—	4	6	no	—
64	C₄×D₄×C₇₉	—	4	6	no	—
65	#117×C₇₉	—	4	6	no	—
66	C₂×C₄⋊C₄×C₇₉	C₂³	1	6	yes	—
67	C₂×C₄⋊C₄×C₇₉	C₂³	1	3	yes	—
68	C₂×C₄⋊C₄×C₇₉	C₂³	1	3	yes	—
69	C₂×C₄⋊C₄×C₇₉	C₂³	1	3	yes	—
70	C₂×C₄⋊C₄×C₇₉	C₂³	1	3	yes	—
71	C₂×C₄⋊C₄×C₇₉	C₂³	1	6	yes	—
72	C₂×C₄⋊C₄×C₇₉	C₂³	1	6	yes	—
73	C₂×C₂²⋊C₄×C₇₉	C₂³	1	6	yes	—
74	C₂×C₂²⋊C₄×C₇₉	C₂³	1	6	yes	—
75	C₂×C₂²⋊C₄×C₇₉	C₂³	1	3	yes	—
76	C₂×C₂²⋊C₄×C₇₉	C₂³	1	6	yes	—
77	C₂×C₂²⋊C₄×C₇₉	C₂³	1	3	yes	—
78	C₂×C₂²⋊C₄×C₇₉	C₂³	1	6	yes	—
79	C₂×C₂²⋊C₄×C₇₉	C₂³	1	6	yes	—
80	C₂×C₂²⋊C₄×C₇₉	C₂³	1	6	yes	—
81	C₂×C₂²⋊C₄×C₇₉	C₂³	1	6	yes	—
82	C₂×C₂²⋊C₄×C₇₉	C₂³	1	6	yes	—
83	C₂×C₄²×C₇₉	C₂³	1	6	yes	—
84	C₂×C₄²×C₇₉	C₂³	1	3	yes	—
85	C₂×C₄²×C₇₉	C₂³	1	3	yes	—
86	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
87	#95×C₇₉	C₂³	1	6	yes	—
88	#95×C₇₉	C₂³	1	6	yes	—
89	#95×C₇₉	C₂³	1	3	yes	—
90	#95×C₇₉	C₂³	1	3	yes	—
91	#95×C₇₉	C₂³	1	3	yes	—
92	#95×C₇₉	C₂³	1	3	yes	—
93	#95×C₇₉	C₂³	1	6	yes	—
94	#95×C₇₉	C₂³	1	6	yes	—
95	C₂⁴×C₇₉	C₂⁴	1	2	yes	—
96	C₂⁴×C₇₉	C₂⁴	1	3	yes	—
97	C₂⁴×C₇₉	C₂⁴	1	1	yes	characteristic
98	#41×C₇₉	—	4	16	no	—
99	C₂×Q₈×C₇₉	—	4	3	no	—
100	C₂×D₄×C₇₉	—	2	6	no	—
101	C₂×D₄×C₇₉	—	2	6	no	—
102	C₂×D₄×C₇₉	—	4	3	no	—
103	C₂×D₄×C₇₉	—	4	3	no	—
104	C₂×D₄×C₇₉	—	4	6	no	—
105	C₂×D₄×C₇₉	—	4	3	no	—
106	C₂×D₄×C₇₉	—	4	3	no	—
107	C₂×D₄×C₇₉	—	4	6	no	—
108	C₂×D₄×C₇₉	—	4	6	no	—
109	C₂×D₄×C₇₉	—	4	6	no	—
110	C₂×D₄×C₇₉	—	4	3	no	—
111	C₂²×C₄×C₇₉	—	2	6	no	—
112	C₂²×C₄×C₇₉	—	2	12	no	—
113	C₂²×C₄×C₇₉	—	2	6	no	—
114	C₂²×C₄×C₇₉	—	2	12	no	—
115	C₂²×C₄×C₇₉	C₂⁴	1	6	yes	—
116	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
117	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
118	C₂²×C₄×C₇₉	C₂⁴	1	3	yes	—
119	C₂²×C₄×C₇₉	C₂⁴	1	6	yes	—
120	C₂²×C₄×C₇₉	C₂⁴	1	3	yes	—
121	C₂²×C₄×C₇₉	C₂⁴	1	3	yes	—
122	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
123	C₄⋊C₄×C₇₉	—	2	12	no	—
124	C₄⋊C₄×C₇₉	—	4	6	no	—
125	C₄⋊C₄×C₇₉	—	4	3	no	—
126	C₄⋊C₄×C₇₉	—	4	3	no	—
127	C₄⋊C₄×C₇₉	—	4	3	no	—
128	C₄⋊C₄×C₇₉	—	4	3	no	—
129	C₄⋊C₄×C₇₉	—	4	6	no	—
130	C₂²⋊C₄×C₇₉	—	2	12	no	—
131	C₂²⋊C₄×C₇₉	—	4	6	no	—
132	C₂²⋊C₄×C₇₉	—	4	6	no	—
133	C₂²⋊C₄×C₇₉	—	4	6	no	—
134	C₂²⋊C₄×C₇₉	—	4	6	no	—
135	C₂²⋊C₄×C₇₉	—	4	6	no	—
136	C₂²⋊C₄×C₇₉	—	4	3	no	—
137	C₂²⋊C₄×C₇₉	—	4	3	no	—
138	C₂²⋊C₄×C₇₉	—	4	6	no	—
139	C₂²⋊C₄×C₇₉	—	4	6	no	—
140	C₄²×C₇₉	—	2	12	no	—
141	C₄²×C₇₉	—	2	6	no	—
142	C₄²×C₇₉	—	4	3	no	—
143	C₄²×C₇₉	#41	1	4	yes	complemented
144	C₂³×C₇₉	—	2	2	no	—
145	C₂³×C₇₉	—	2	3	no	—
146	C₂³×C₇₉	—	2	1	no	—
147	C₂³×C₇₉	—	2	3	no	—
148	C₂³×C₇₉	—	2	6	no	—
149	C₂³×C₇₉	—	2	3	no	—
150	C₂³×C₇₉	—	2	6	no	—
151	C₂³×C₇₉	—	2	3	no	—
152	C₂³×C₇₉	—	2	6	no	—
153	C₂³×C₇₉	—	2	6	no	—
154	C₂³×C₇₉	—	2	3	no	—
155	C₂³×C₇₉	C₂⁵	1	1	yes	characteristic
156	Q₈×C₇₉	—	4	4	no	—
157	D₄×C₇₉	—	4	12	no	—
158	D₄×C₇₉	—	4	12	no	—
159	D₄×C₇₉	—	4	24	no	—
160	D₄×C₇₉	—	4	8	no	—
161	D₄×C₇₉	—	4	4	no	—
162	C₂×C₄×C₇₉	—	2	3	no	—
163	C₂×C₄×C₇₉	—	2	3	no	—
164	C₂×C₄×C₇₉	—	2	6	no	—
165	C₂×C₄×C₇₉	—	2	3	no	—
166	C₂×C₄×C₇₉	—	2	6	no	—
167	C₂×C₄×C₇₉	—	2	6	no	—
168	C₂×C₄×C₇₉	—	2	6	no	—
169	C₂×C₄×C₇₉	—	2	3	no	—
170	C₂×C₄×C₇₉	—	2	3	no	—
171	C₂×C₄×C₇₉	—	2	6	no	—
172	C₂×C₄×C₇₉	—	2	6	no	—
173	C₂×C₄×C₇₉	—	2	6	no	—
174	C₂×C₄×C₇₉	—	2	6	no	—
175	C₂×C₄×C₇₉	—	2	6	no	—
176	C₂×C₄×C₇₉	—	4	12	no	—
177	C₂×C₄×C₇₉	—	4	4	no	—
178	C₂×C₄×C₇₉	—	4	8	no	—
179	C₂×C₄×C₇₉	C₂×#41	1	6	yes	—
180	C₂×C₄×C₇₉	H(5,𝔽₂)	1	6	yes	—
181	C₂²×C₇₉	—	4	3	no	—
182	C₂²×C₇₉	—	4	6	no	—
183	C₂²×C₇₉	—	4	3	no	—
184	C₂²×C₇₉	—	4	6	no	—
185	C₂²×C₇₉	—	4	1	no	—
186	C₂²×C₇₉	—	4	2	no	—
187	C₂²×C₇₉	—	4	3	no	—
188	C₂²×C₇₉	—	4	6	no	—
189	C₂²×C₇₉	—	4	6	no	—
190	C₂²×C₇₉	—	4	3	no	—
191	C₂²×C₇₉	—	4	3	no	—
192	C₂²×C₇₉	C₂²×#41	1	1	yes	characteristic
193	C₂²×C₇₉	C₂×H(5,𝔽₂)	1	3	yes	—
194	C₂²×C₇₉	#585	1	3	yes	—
195	C₄×C₇₉	—	2	6	no	—
196	C₄×C₇₉	—	4	6	no	—
197	C₄×C₇₉	—	4	3	no	—
198	C₄×C₇₉	—	4	1	no	—
199	C₄×C₇₉	—	4	2	no	—
200	C₄×C₇₉	—	4	3	no	—
201	C₄×C₇₉	—	4	6	no	—
202	C₄×C₇₉	#560	1	4	yes	—
203	#36696	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
204	C₂×C₇₉	—	8	1	no	—
205	C₂×C₇₉	—	8	3	no	—
206	C₂×C₇₉	—	8	2	no	—
207	C₂×C₇₉	#3460	1	3	yes	—
208	C₂×C₇₉	C₂×#560	1	1	yes	characteristic
209	C₂×C₇₉	#3529	1	3	yes	—
210	#2843	C₂×C₇₉	1	1	yes	characteristic, complemented
211	#2830	C₂×C₇₉	1	3	yes	complemented
212	#2829	C₂×C₇₉	1	6	yes	complemented
213	#2828	C₂×C₇₉	1	3	yes	complemented
214	#2823	C₂×C₇₉	1	1	yes	characteristic, complemented
215	#2818	C₂×C₇₉	1	2	yes	complemented
216	#2395	C₂×C₇₉	1	3	yes	complemented
217	#2392	C₂×C₇₉	1	6	yes	complemented
218	#2388	C₂×C₇₉	1	3	yes	complemented
219	C₄×#127	C₂×C₇₉	1	1	yes	characteristic, complemented
220	C₄×#126	C₂×C₇₉	1	2	yes	complemented
221	C₇₉	#36696	1	1	yes	characteristic, direct product factor, Sylow
222	C₂²×#41	C₂²×C₇₉	1	1	yes	characteristic
223	C₂×#127	C₂²×C₇₉	1	1	yes	characteristic
224	C₂×#126	C₂²×C₇₉	1	2	yes	—
225	C₂×C₄×D₄	C₂²×C₇₉	1	3	yes	—
226	C₂×C₄×D₄	C₂²×C₇₉	1	3	yes	—
227	C₂×C₄×D₄	C₂²×C₇₉	1	6	yes	—
228	C₂×#117	C₂²×C₇₉	1	3	yes	—
229	#400	C₂²×C₇₉	1	3	yes	—
230	#399	C₂²×C₇₉	1	3	yes	—
231	#398	C₂²×C₇₉	1	3	yes	—
232	#398	C₂²×C₇₉	1	6	yes	—
233	#397	C₂²×C₇₉	1	6	yes	—
234	#397	C₂²×C₇₉	1	3	yes	—
235	#397	C₂²×C₇₉	1	6	yes	—
236	#396	C₂²×C₇₉	1	6	yes	—
237	#396	C₂²×C₇₉	1	6	yes	—
238	#395	C₂²×C₇₉	1	3	yes	—
239	#394	C₂²×C₇₉	1	6	yes	—
240	#394	C₂²×C₇₉	1	6	yes	—
241	#394	C₂²×C₇₉	1	3	yes	—
242	#394	C₂²×C₇₉	1	6	yes	—
243	#394	C₂²×C₇₉	1	6	yes	—
244	#394	C₂²×C₇₉	1	6	yes	—
245	#393	C₂²×C₇₉	1	3	yes	—
246	#392	C₂²×C₇₉	1	6	yes	—
247	#392	C₂²×C₇₉	1	6	yes	—
248	#392	C₂²×C₇₉	1	3	yes	—
249	#390	C₂²×C₇₉	1	3	yes	—
250	#390	C₂²×C₇₉	1	3	yes	—
251	#388	C₂²×C₇₉	1	6	yes	—
252	#387	C₂²×C₇₉	1	6	yes	—
253	#384	C₂²×C₇₉	1	1	yes	characteristic
254	#383	C₂²×C₇₉	1	2	yes	—
255	C₄×C₄⋊C₄	C₂²×C₇₉	1	6	yes	—
256	C₄×C₂²⋊C₄	C₂²×C₇₉	1	6	yes	—
257	C₄×C₂²⋊C₄	C₂²×C₇₉	1	3	yes	—
258	C₄×C₂²⋊C₄	C₂²×C₇₉	1	3	yes	—
259	C₄³	C₂²×C₇₉	1	1	yes	characteristic
260	C₂×#41	—	4	6	no	—
261	C₂²×Q₈	C₂³×C₇₉	1	1	yes	characteristic
262	C₂²×D₄	C₂³×C₇₉	1	3	yes	—
263	C₂²×D₄	C₂³×C₇₉	1	3	yes	—
264	C₂²×D₄	C₂³×C₇₉	1	6	yes	—
265	C₂²×D₄	C₂³×C₇₉	1	2	yes	—
266	C₂²×D₄	C₂³×C₇₉	1	1	yes	characteristic
267	C₂³×C₄	C₂³×C₇₉	1	3	yes	—
268	C₂³×C₄	C₂³×C₇₉	1	1	yes	characteristic
269	C₂³×C₄	C₂³×C₇₉	1	2	yes	—
270	#127	—	2	4	no	—
271	#126	—	2	8	no	—
272	C₄×D₄	—	4	12	no	—
273	C₄×D₄	—	4	6	no	—
274	C₄×D₄	—	4	6	no	—
275	#117	—	4	6	no	—
276	C₂×C₄⋊C₄	C₂³×C₇₉	1	6	yes	—
277	C₂×C₄⋊C₄	C₂³×C₇₉	1	3	yes	—
278	C₂×C₄⋊C₄	C₂³×C₇₉	1	3	yes	—
279	C₂×C₄⋊C₄	C₂³×C₇₉	1	3	yes	—
280	C₂×C₄⋊C₄	C₂³×C₇₉	1	3	yes	—
281	C₂×C₄⋊C₄	C₂³×C₇₉	1	6	yes	—
282	C₂×C₄⋊C₄	C₂³×C₇₉	1	6	yes	—
283	C₂×C₂²⋊C₄	C₂³×C₇₉	1	6	yes	—
284	C₂×C₂²⋊C₄	C₂³×C₇₉	1	6	yes	—
285	C₂×C₂²⋊C₄	C₂³×C₇₉	1	3	yes	—
286	C₂×C₂²⋊C₄	C₂³×C₇₉	1	6	yes	—
287	C₂×C₂²⋊C₄	C₂³×C₇₉	1	3	yes	—
288	C₂×C₂²⋊C₄	C₂³×C₇₉	1	6	yes	—
289	C₂×C₂²⋊C₄	C₂³×C₇₉	1	6	yes	—
290	C₂×C₂²⋊C₄	C₂³×C₇₉	1	6	yes	—
291	C₂×C₂²⋊C₄	C₂³×C₇₉	1	6	yes	—
292	C₂×C₂²⋊C₄	C₂³×C₇₉	1	6	yes	—
293	C₂×C₄²	C₂³×C₇₉	1	6	yes	—
294	C₂×C₄²	C₂³×C₇₉	1	3	yes	—
295	C₂×C₄²	C₂³×C₇₉	1	3	yes	—
296	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
297	#95	C₂³×C₇₉	1	6	yes	—
298	#95	C₂³×C₇₉	1	6	yes	—
299	#95	C₂³×C₇₉	1	3	yes	—
300	#95	C₂³×C₇₉	1	3	yes	—
301	#95	C₂³×C₇₉	1	3	yes	—
302	#95	C₂³×C₇₉	1	3	yes	—
303	#95	C₂³×C₇₉	1	6	yes	—
304	#95	C₂³×C₇₉	1	6	yes	—
305	C₂⁴	C₂⁴×C₇₉	1	2	yes	—
306	C₂⁴	C₂⁴×C₇₉	1	3	yes	—
307	C₂⁴	C₂⁴×C₇₉	1	1	yes	characteristic
308	#41	—	4	16	no	—
309	C₂×Q₈	—	4	3	no	—
310	C₂×D₄	—	2	6	no	—
311	C₂×D₄	—	2	6	no	—
312	C₂×D₄	—	4	3	no	—
313	C₂×D₄	—	4	3	no	—
314	C₂×D₄	—	4	6	no	—
315	C₂×D₄	—	4	6	no	—
316	C₂×D₄	—	4	3	no	—
317	C₂×D₄	—	4	3	no	—
318	C₂×D₄	—	4	3	no	—
319	C₂×D₄	—	4	6	no	—
320	C₂×D₄	—	4	6	no	—
321	C₂²×C₄	—	2	6	no	—
322	C₂²×C₄	—	2	12	no	—
323	C₂²×C₄	—	2	6	no	—
324	C₂²×C₄	—	2	12	no	—
325	C₂²×C₄	C₂⁴×C₇₉	1	6	yes	—
326	C₂²×C₄	C₂⁴×C₇₉	1	2	yes	—
327	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
328	C₂²×C₄	C₂⁴×C₇₉	1	3	yes	—
329	C₂²×C₄	C₂⁴×C₇₉	1	6	yes	—
330	C₂²×C₄	C₂⁴×C₇₉	1	3	yes	—
331	C₂²×C₄	C₂⁴×C₇₉	1	3	yes	—
332	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
333	C₄⋊C₄	—	2	12	no	—
334	C₄⋊C₄	—	4	3	no	—
335	C₄⋊C₄	—	4	3	no	—
336	C₄⋊C₄	—	4	3	no	—
337	C₄⋊C₄	—	4	3	no	—
338	C₄⋊C₄	—	4	6	no	—
339	C₄⋊C₄	—	4	6	no	—
340	C₂²⋊C₄	—	2	12	no	—
341	C₂²⋊C₄	—	4	6	no	—
342	C₂²⋊C₄	—	4	6	no	—
343	C₂²⋊C₄	—	4	3	no	—
344	C₂²⋊C₄	—	4	3	no	—
345	C₂²⋊C₄	—	4	6	no	—
346	C₂²⋊C₄	—	4	6	no	—
347	C₂²⋊C₄	—	4	6	no	—
348	C₂²⋊C₄	—	4	6	no	—
349	C₂²⋊C₄	—	4	6	no	—
350	C₄²	—	2	12	no	—
351	C₄²	—	2	6	no	—
352	C₄²	—	4	3	no	—
353	C₄²	#41×C₇₉	1	4	yes	complemented
354	C₂³	—	2	2	no	—
355	C₂³	—	2	3	no	—
356	C₂³	—	2	1	no	—
357	C₂³	—	2	3	no	—
358	C₂³	—	2	6	no	—
359	C₂³	—	2	3	no	—
360	C₂³	—	2	6	no	—
361	C₂³	—	2	3	no	—
362	C₂³	—	2	6	no	—
363	C₂³	—	2	6	no	—
364	C₂³	—	2	3	no	—
365	C₂³	C₂⁵×C₇₉	1	1	yes	characteristic
366	Q₈	—	4	4	no	—
367	D₄	—	4	12	no	—
368	D₄	—	4	12	no	—
369	D₄	—	4	24	no	—
370	D₄	—	4	8	no	—
371	D₄	—	4	4	no	—
372	C₂×C₄	—	2	3	no	—
373	C₂×C₄	—	2	3	no	—
374	C₂×C₄	—	2	6	no	—
375	C₂×C₄	—	2	3	no	—
376	C₂×C₄	—	2	6	no	—
377	C₂×C₄	—	2	6	no	—
378	C₂×C₄	—	2	6	no	—
379	C₂×C₄	—	2	3	no	—
380	C₂×C₄	—	2	3	no	—
381	C₂×C₄	—	2	6	no	—
382	C₂×C₄	—	2	6	no	—
383	C₂×C₄	—	2	6	no	—
384	C₂×C₄	—	2	6	no	—
385	C₂×C₄	—	2	6	no	—
386	C₂×C₄	—	4	12	no	—
387	C₂×C₄	—	4	4	no	—
388	C₂×C₄	—	4	8	no	—
389	C₂×C₄	C₂×#41×C₇₉	1	6	yes	—
390	C₂×C₄	H(5,𝔽₂)×C₇₉	1	6	yes	—
391	C₂²	—	4	3	no	—
392	C₂²	—	4	6	no	—
393	C₂²	—	4	3	no	—
394	C₂²	—	4	6	no	—
395	C₂²	—	4	1	no	—
396	C₂²	—	4	2	no	—
397	C₂²	—	4	3	no	—
398	C₂²	—	4	6	no	—
399	C₂²	—	4	6	no	—
400	C₂²	—	4	3	no	—
401	C₂²	—	4	3	no	—
402	C₂²	C₂²×#41×C₇₉	1	1	yes	characteristic
403	C₂²	C₂×H(5,𝔽₂)×C₇₉	1	3	yes	—
404	C₂²	#585×C₇₉	1	3	yes	—
405	C₄	—	2	6	no	—
406	C₄	—	4	6	no	—
407	C₄	—	4	1	no	—
408	C₄	—	4	2	no	—
409	C₄	—	4	3	no	—
410	C₄	—	4	6	no	—
411	C₄	—	4	3	no	—
412	C₄	#560×C₇₉	1	4	yes	—
413	C₂	—	8	1	no	—
414	C₂	—	8	3	no	—
415	C₂	—	8	2	no	—
416	C₂	C₇₉×#3460	1	3	yes	—
417	C₂	C₂×#560×C₇₉	1	1	yes	characteristic
418	C₂	C₇₉×#3529	1	3	yes	—

	subgroup	G/H
center	C₂²×C₄×C₇₉	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇₉
socle	C₂³×C₇₉	C₂⁵
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₇₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇₉×#2843	C₂	semidirect
2. C₇₉×#2830	C₂	semidirect
3. C₇₉×#2829	C₂	semidirect
4. C₇₉×#2828	C₂	semidirect
5. C₇₉×#2823	C₂	semidirect
6. C₇₉×#2818	C₂	semidirect
7. C₇₉×#2395	C₂	semidirect
8. C₇₉×#2392	C₂	semidirect
9. C₇₉×#2388	C₂	semidirect
10. C₄×#127×C₇₉	C₂	semidirect
11. C₄×#126×C₇₉	C₂	semidirect
143. C₄²×C₇₉	#41	semidirect
203. #36696	C₇₉	direct (N × H)
210. #2843	C₂×C₇₉	semidirect
211. #2830	C₂×C₇₉	semidirect
212. #2829	C₂×C₇₉	semidirect
213. #2828	C₂×C₇₉	semidirect
214. #2823	C₂×C₇₉	semidirect
215. #2818	C₂×C₇₉	semidirect
216. #2395	C₂×C₇₉	semidirect
217. #2392	C₂×C₇₉	semidirect
218. #2388	C₂×C₇₉	semidirect
219. C₄×#127	C₂×C₇₉	semidirect
220. C₄×#126	C₂×C₇₉	semidirect
221. C₇₉	#36696	direct (N × H)
353. C₄²	#41×C₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₇₉×#2843	2
C₇₉×#2830	2
C₇₉×#2829	2
C₇₉×#2828	2
C₇₉×#2823	2
C₇₉×#2818	2
C₇₉×#2395	2
C₇₉×#2392	2
C₇₉×#2388	2
C₄×#127×C₇₉	2
C₄×#126×C₇₉	2
#36696	79

Subgroups — C79×#36696 #34148385

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#36696 #34148385