Subgroups — C₇₉×#17613 #34129302

Order 20224.

1350 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₉×#3496	C₂	1	1	yes	maximal, characteristic
2	C₇₉×#2972	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₉×#2349	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₉×#1519	C₂	1	4	yes	maximal, complemented
5	C₇₉×#1517	C₂	1	2	yes	maximal, complemented
6	C₇₉×#1502	C₂	1	2	yes	maximal, complemented
7	C₂×#327×C₇₉	C₂	1	4	yes	maximal, complemented
8	C₂×H(5,𝔽₂)×C₇₉	—	2	1	no	—
9	#547×C₇₉	C₄	1	4	yes	complemented
10	#546×C₇₉	—	2	4	no	—
11	D₄²×C₇₉	C₄	1	4	yes	complemented
12	#537×C₇₉	—	2	1	no	—
13	#534×C₇₉	—	2	2	no	—
14	#532×C₇₉	C₂²	1	2	yes	—
15	C₂×#121×C₇₉	C₂²	1	4	yes	—
16	C₂×C₄×D₄×C₇₉	—	2	1	no	—
17	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
18	C₈×D₄×C₇₉	—	2	4	no	—
19	#431×C₇₉	C₂²	1	2	yes	complemented
20	C₂×C₂²⋊C₈×C₇₉	C₂²	1	4	yes	complemented
21	#389×C₇₉	—	2	1	no	—
22	#385×C₇₉	—	2	2	no	—
23	#382×C₇₉	C₂²	1	1	yes	characteristic, complemented
24	#380×C₇₉	C₂²	1	2	yes	complemented
25	C₄×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic, complemented
26	C₂×#95×C₇₉	C₂²	1	2	yes	complemented
27	#327×C₇₉	C₂²	1	4	yes	complemented
28	#327×C₇₉	C₂²	1	8	yes	complemented
29	#327×C₇₉	C₂²	1	4	yes	complemented
30	H(5,𝔽₂)×C₇₉	—	4	4	no	—
31	H(5,𝔽₂)×C₇₉	—	4	4	no	—
32	C₂×#41×C₇₉	—	2	4	no	—
33	C₂×#41×C₇₉	—	2	2	no	—
34	C₂²×D₄×C₇₉	—	2	4	no	—
35	C₂²×D₄×C₇₉	—	2	4	no	—
36	C₂²×D₄×C₇₉	C₂×C₄	1	4	yes	complemented
37	C₂²×D₄×C₇₉	D₄	1	1	yes	characteristic
38	C₂³×C₄×C₇₉	—	2	2	no	—
39	C₂³×C₄×C₇₉	C₂³	1	2	yes	—
40	C₂²×C₈×C₇₉	—	2	4	no	—
41	C₄⋊Q₈×C₇₉	C₂×C₄	1	2	yes	complemented
42	#127×C₇₉	C₂×C₄	1	2	yes	complemented
43	#124×C₇₉	—	2	2	no	—
44	#123×C₇₉	—	2	8	no	—
45	C₂²⋊Q₈×C₇₉	—	2	4	no	—
46	#121×C₇₉	—	2	4	no	—
47	#121×C₇₉	—	2	4	no	—
48	#121×C₇₉	—	2	2	no	—
49	#121×C₇₉	—	2	4	no	—
50	#121×C₇₉	C₂×C₄	1	8	yes	complemented
51	#121×C₇₉	C₂³	1	4	yes	—
52	#120×C₇₉	—	2	8	no	—
53	C₄×D₄×C₇₉	—	2	2	no	—
54	C₄×D₄×C₇₉	—	4	4	no	—
55	C₄×D₄×C₇₉	C₂×C₄	1	4	yes	—
56	C₄×D₄×C₇₉	C₂×C₄	1	4	yes	complemented
57	C₄×D₄×C₇₉	D₄	1	4	yes	—
58	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
59	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
60	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
61	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	4	yes	complemented
62	C₂×C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
63	C₂×C₂²⋊C₄×C₇₉	—	2	4	no	—
64	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
65	C₂×C₂²⋊C₄×C₇₉	D₄	1	2	yes	—
66	C₂×C₄²×C₇₉	—	2	1	no	—
67	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
68	C₄⋊C₈×C₇₉	—	2	2	no	—
69	C₂²⋊C₈×C₇₉	—	2	4	no	—
70	C₂²⋊C₈×C₇₉	C₂³	1	4	yes	—
71	C₄×C₈×C₇₉	—	2	2	no	—
72	#95×C₇₉	—	2	2	no	—
73	#95×C₇₉	—	2	1	no	—
74	#95×C₇₉	C₂³	1	1	yes	characteristic
75	#95×C₇₉	C₂³	1	2	yes	—
76	#95×C₇₉	C₂³	1	1	yes	characteristic
77	C₂⁴×C₇₉	—	2	4	no	—
78	C₂⁴×C₇₉	C₂×D₄	1	2	yes	—
79	#41×C₇₉	—	4	16	no	—
80	#41×C₇₉	—	4	4	no	—
81	#41×C₇₉	—	4	4	no	—
82	C₂×Q₈×C₇₉	—	2	2	no	—
83	C₂×D₄×C₇₉	—	2	8	no	—
84	C₂×D₄×C₇₉	—	2	4	no	—
85	C₂×D₄×C₇₉	—	2	2	no	—
86	C₂×D₄×C₇₉	—	2	2	no	—
87	C₂×D₄×C₇₉	—	2	4	no	—
88	C₂×D₄×C₇₉	—	4	8	no	—
89	C₂×D₄×C₇₉	—	4	8	no	—
90	C₂×D₄×C₇₉	—	4	16	no	—
91	C₂×D₄×C₇₉	—	8	4	no	—
92	C₂×D₄×C₇₉	C₂²⋊C₄	1	4	yes	—
93	C₂×D₄×C₇₉	D₈	1	4	yes	—
94	C₂×D₄×C₇₉	SD₁₆	1	4	yes	—
95	C₂×D₄×C₇₉	C₂²×C₄	1	4	yes	—
96	C₂²×C₄×C₇₉	—	2	4	no	—
97	C₂²×C₄×C₇₉	—	2	1	no	—
98	C₂²×C₄×C₇₉	—	2	4	no	—
99	C₂²×C₄×C₇₉	—	2	2	no	—
100	C₂²×C₄×C₇₉	—	2	1	no	—
101	C₂²×C₄×C₇₉	—	4	4	no	—
102	C₂²×C₄×C₇₉	—	4	4	no	—
103	C₂²×C₄×C₇₉	—	8	2	no	—
104	C₂²×C₄×C₇₉	—	8	2	no	—
105	C₂²×C₄×C₇₉	C₂²×C₄	1	4	yes	—
106	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₇₉	C₂×D₄	1	4	yes	—
109	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
111	C₂×C₈×C₇₉	—	2	4	no	—
112	C₂×C₈×C₇₉	—	8	4	no	—
113	C₄⋊C₄×C₇₉	—	2	4	no	—
114	C₄⋊C₄×C₇₉	—	2	2	no	—
115	C₄⋊C₄×C₇₉	—	4	2	no	—
116	C₄⋊C₄×C₇₉	—	4	2	no	—
117	C₄⋊C₄×C₇₉	—	8	2	no	—
118	C₄⋊C₄×C₇₉	C₂²⋊C₄	1	4	yes	—
119	C₄⋊C₄×C₇₉	C₂²×C₄	1	4	yes	—
120	C₂²⋊C₄×C₇₉	—	2	8	no	—
121	C₂²⋊C₄×C₇₉	—	2	4	no	—
122	C₂²⋊C₄×C₇₉	—	2	4	no	—
123	C₂²⋊C₄×C₇₉	—	4	4	no	—
124	C₂²⋊C₄×C₇₉	C₂²⋊C₄	1	8	yes	—
125	C₄²×C₇₉	—	4	2	no	—
126	C₄²×C₇₉	C₂²×C₄	1	2	yes	—
127	C₄²×C₇₉	C₂×D₄	1	2	yes	—
128	C₂³×C₇₉	—	2	4	no	—
129	C₂³×C₇₉	—	4	2	no	—
130	C₂³×C₇₉	—	4	2	no	—
131	C₂³×C₇₉	—	4	8	no	—
132	C₂³×C₇₉	—	8	4	no	—
133	C₂³×C₇₉	—	8	4	no	—
134	C₂³×C₇₉	C₂×C₂²⋊C₄	1	4	yes	—
135	C₂³×C₇₉	C₂×D₈	1	4	yes	—
136	C₂³×C₇₉	C₂×SD₁₆	1	4	yes	—
137	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
138	Q₈×C₇₉	—	4	4	no	—
139	D₄×C₇₉	—	4	4	no	—
140	D₄×C₇₉	—	4	4	no	—
141	D₄×C₇₉	—	4	4	no	—
142	D₄×C₇₉	—	4	16	no	—
143	D₄×C₇₉	—	4	4	no	—
144	D₄×C₇₉	—	8	2	no	—
145	D₄×C₇₉	—	8	4	no	—
146	D₄×C₇₉	#102	1	16	yes	—
147	C₂×C₄×C₇₉	—	2	2	no	—
148	C₂×C₄×C₇₉	—	2	4	no	—
149	C₂×C₄×C₇₉	—	4	1	no	—
150	C₂×C₄×C₇₉	—	4	2	no	—
151	C₂×C₄×C₇₉	—	4	4	no	—
152	C₂×C₄×C₇₉	—	4	1	no	—
153	C₂×C₄×C₇₉	—	4	4	no	—
154	C₂×C₄×C₇₉	—	4	1	no	—
155	C₂×C₄×C₇₉	—	4	1	no	—
156	C₂×C₄×C₇₉	—	4	8	no	—
157	C₂×C₄×C₇₉	—	4	8	no	—
158	C₂×C₄×C₇₉	—	4	1	no	—
159	C₂×C₄×C₇₉	—	4	1	no	—
160	C₂×C₄×C₇₉	—	4	2	no	—
161	C₂×C₄×C₇₉	—	4	2	no	—
162	C₂×C₄×C₇₉	—	4	1	no	—
163	C₂×C₄×C₇₉	—	4	2	no	—
164	C₂×C₄×C₇₉	—	8	8	no	—
165	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	2	yes	—
166	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	4	yes	—
167	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	2	yes	—
168	C₂×C₄×C₇₉	C₂×D₈	1	2	yes	—
169	C₂×C₄×C₇₉	C₂×SD₁₆	1	2	yes	—
170	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
171	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
172	C₈×C₇₉	—	4	4	no	—
173	C₂²×C₇₉	—	2	1	no	—
174	C₂²×C₇₉	—	2	4	no	—
175	C₂²×C₇₉	—	2	1	no	—
176	C₂²×C₇₉	—	2	4	no	—
177	C₂²×C₇₉	—	4	4	no	—
178	C₂²×C₇₉	—	4	4	no	—
179	C₂²×C₇₉	—	4	4	no	—
180	C₂²×C₇₉	—	4	4	no	—
181	C₂²×C₇₉	—	4	4	no	—
182	C₂²×C₇₉	—	16	8	no	—
183	C₂²×C₇₉	C₂×#102	1	8	yes	—
184	C₂²×C₇₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
185	C₂²×C₇₉	C₂²×D₈	1	1	yes	characteristic
186	C₂²×C₇₉	C₂²×SD₁₆	1	1	yes	characteristic
187	C₄×C₇₉	—	2	1	no	—
188	C₄×C₇₉	—	2	1	no	—
189	C₄×C₇₉	—	2	4	no	—
190	C₄×C₇₉	—	2	2	no	—
191	C₄×C₇₉	—	4	2	no	—
192	C₄×C₇₉	—	4	4	no	—
193	C₄×C₇₉	—	8	1	no	—
194	C₄×C₇₉	—	8	2	no	—
195	C₄×C₇₉	C₂×#102	1	4	yes	—
196	#17613	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
197	C₂×C₇₉	—	2	1	no	—
198	C₂×C₇₉	—	2	1	no	—
199	C₂×C₇₉	—	2	8	no	—
200	C₂×C₇₉	—	8	4	no	—
201	C₂×C₇₉	#2883	1	1	yes	characteristic
202	C₂×C₇₉	C₂²×#102	1	1	yes	characteristic
203	C₂×C₇₉	#2901	1	1	yes	characteristic
204	#3496	C₂×C₇₉	1	1	yes	characteristic
205	#2972	C₂×C₇₉	1	1	yes	characteristic, complemented
206	#2349	C₂×C₇₉	1	1	yes	characteristic, complemented
207	#1519	C₂×C₇₉	1	4	yes	complemented
208	#1517	C₂×C₇₉	1	2	yes	complemented
209	#1502	C₂×C₇₉	1	2	yes	complemented
210	C₂×#327	C₂×C₇₉	1	4	yes	complemented
211	C₇₉	#17613	1	1	yes	characteristic, direct product factor, Sylow
212	C₂×H(5,𝔽₂)	—	2	1	no	—
213	#547	C₄×C₇₉	1	4	yes	complemented
214	#546	—	2	4	no	—
215	D₄²	C₄×C₇₉	1	4	yes	complemented
216	#537	—	2	1	no	—
217	#534	—	2	2	no	—
218	#532	C₂²×C₇₉	1	2	yes	—
219	C₂×#121	C₂²×C₇₉	1	4	yes	—
220	C₂×C₄×D₄	—	2	1	no	—
221	C₂×C₄×D₄	C₂²×C₇₉	1	1	yes	characteristic
222	C₈×D₄	—	2	4	no	—
223	#431	C₂²×C₇₉	1	2	yes	complemented
224	C₂×C₂²⋊C₈	C₂²×C₇₉	1	4	yes	complemented
225	#389	—	2	1	no	—
226	#385	—	2	2	no	—
227	#382	C₂²×C₇₉	1	1	yes	characteristic, complemented
228	#380	C₂²×C₇₉	1	2	yes	complemented
229	C₄×C₄⋊C₄	C₂²×C₇₉	1	1	yes	characteristic, complemented
230	C₂×#95	C₂²×C₇₉	1	2	yes	complemented
231	#327	C₂²×C₇₉	1	4	yes	complemented
232	#327	C₂²×C₇₉	1	8	yes	complemented
233	#327	C₂²×C₇₉	1	4	yes	complemented
234	H(5,𝔽₂)	—	4	4	no	—
235	H(5,𝔽₂)	—	4	4	no	—
236	C₂×#41	—	2	4	no	—
237	C₂×#41	—	2	2	no	—
238	C₂²×D₄	—	2	4	no	—
239	C₂²×D₄	—	2	4	no	—
240	C₂²×D₄	C₂×C₄×C₇₉	1	4	yes	complemented
241	C₂²×D₄	D₄×C₇₉	1	1	yes	characteristic
242	C₂³×C₄	—	2	2	no	—
243	C₂³×C₄	C₂³×C₇₉	1	2	yes	—
244	C₂²×C₈	—	2	4	no	—
245	C₄⋊Q₈	C₂×C₄×C₇₉	1	2	yes	complemented
246	#127	C₂×C₄×C₇₉	1	2	yes	complemented
247	#124	—	2	2	no	—
248	#123	—	2	8	no	—
249	C₂²⋊Q₈	—	2	4	no	—
250	#121	—	2	4	no	—
251	#121	—	2	4	no	—
252	#121	—	2	2	no	—
253	#121	—	2	4	no	—
254	#121	C₂×C₄×C₇₉	1	8	yes	complemented
255	#121	C₂³×C₇₉	1	4	yes	—
256	#120	—	2	8	no	—
257	C₄×D₄	—	2	2	no	—
258	C₄×D₄	—	4	4	no	—
259	C₄×D₄	C₂×C₄×C₇₉	1	4	yes	—
260	C₄×D₄	C₂×C₄×C₇₉	1	4	yes	complemented
261	C₄×D₄	D₄×C₇₉	1	4	yes	—
262	C₂×C₄⋊C₄	—	2	1	no	—
263	C₂×C₄⋊C₄	—	2	1	no	—
264	C₂×C₄⋊C₄	—	2	2	no	—
265	C₂×C₄⋊C₄	C₂×C₄×C₇₉	1	4	yes	complemented
266	C₂×C₄⋊C₄	D₄×C₇₉	1	1	yes	characteristic
267	C₂×C₂²⋊C₄	—	2	4	no	—
268	C₂×C₂²⋊C₄	—	2	2	no	—
269	C₂×C₂²⋊C₄	D₄×C₇₉	1	2	yes	—
270	C₂×C₄²	—	2	1	no	—
271	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
272	C₄⋊C₈	—	2	2	no	—
273	C₂²⋊C₈	—	2	4	no	—
274	C₂²⋊C₈	C₂³×C₇₉	1	4	yes	—
275	C₄×C₈	—	2	2	no	—
276	#95	—	2	2	no	—
277	#95	—	2	1	no	—
278	#95	C₂³×C₇₉	1	1	yes	characteristic
279	#95	C₂³×C₇₉	1	2	yes	—
280	#95	C₂³×C₇₉	1	1	yes	characteristic
281	C₂⁴	—	2	4	no	—
282	C₂⁴	C₂×D₄×C₇₉	1	2	yes	—
283	#41	—	4	16	no	—
284	#41	—	4	4	no	—
285	#41	—	4	4	no	—
286	C₂×Q₈	—	2	2	no	—
287	C₂×D₄	—	2	8	no	—
288	C₂×D₄	—	2	4	no	—
289	C₂×D₄	—	2	2	no	—
290	C₂×D₄	—	2	2	no	—
291	C₂×D₄	—	2	4	no	—
292	C₂×D₄	—	4	8	no	—
293	C₂×D₄	—	4	8	no	—
294	C₂×D₄	—	4	16	no	—
295	C₂×D₄	—	8	4	no	—
296	C₂×D₄	C₂²⋊C₄×C₇₉	1	4	yes	—
297	C₂×D₄	D₈×C₇₉	1	4	yes	—
298	C₂×D₄	SD₁₆×C₇₉	1	4	yes	—
299	C₂×D₄	C₂²×C₄×C₇₉	1	4	yes	—
300	C₂²×C₄	—	2	4	no	—
301	C₂²×C₄	—	2	1	no	—
302	C₂²×C₄	—	2	4	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	1	no	—
305	C₂²×C₄	—	4	4	no	—
306	C₂²×C₄	—	4	4	no	—
307	C₂²×C₄	—	8	2	no	—
308	C₂²×C₄	—	8	2	no	—
309	C₂²×C₄	C₂²×C₄×C₇₉	1	4	yes	—
310	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
311	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
312	C₂²×C₄	C₂×D₄×C₇₉	1	4	yes	—
313	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
314	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
315	C₂×C₈	—	2	4	no	—
316	C₂×C₈	—	8	4	no	—
317	C₄⋊C₄	—	2	4	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	4	2	no	—
320	C₄⋊C₄	—	4	2	no	—
321	C₄⋊C₄	—	8	2	no	—
322	C₄⋊C₄	C₂²⋊C₄×C₇₉	1	4	yes	—
323	C₄⋊C₄	C₂²×C₄×C₇₉	1	4	yes	—
324	C₂²⋊C₄	—	2	8	no	—
325	C₂²⋊C₄	—	2	4	no	—
326	C₂²⋊C₄	—	2	4	no	—
327	C₂²⋊C₄	—	4	4	no	—
328	C₂²⋊C₄	C₂²⋊C₄×C₇₉	1	8	yes	—
329	C₄²	—	4	2	no	—
330	C₄²	C₂²×C₄×C₇₉	1	2	yes	—
331	C₄²	C₂×D₄×C₇₉	1	2	yes	—
332	C₂³	—	2	4	no	—
333	C₂³	—	4	2	no	—
334	C₂³	—	4	2	no	—
335	C₂³	—	4	8	no	—
336	C₂³	—	8	4	no	—
337	C₂³	—	8	4	no	—
338	C₂³	C₂×C₂²⋊C₄×C₇₉	1	4	yes	—
339	C₂³	C₂×D₈×C₇₉	1	4	yes	—
340	C₂³	C₂×SD₁₆×C₇₉	1	4	yes	—
341	C₂³	C₂²×D₄×C₇₉	1	1	yes	characteristic
342	Q₈	—	4	4	no	—
343	D₄	—	4	4	no	—
344	D₄	—	4	4	no	—
345	D₄	—	4	4	no	—
346	D₄	—	4	16	no	—
347	D₄	—	4	4	no	—
348	D₄	—	8	2	no	—
349	D₄	—	8	4	no	—
350	D₄	#102×C₇₉	1	16	yes	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	4	no	—
353	C₂×C₄	—	4	1	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	4	no	—
356	C₂×C₄	—	4	1	no	—
357	C₂×C₄	—	4	4	no	—
358	C₂×C₄	—	4	1	no	—
359	C₂×C₄	—	4	1	no	—
360	C₂×C₄	—	4	8	no	—
361	C₂×C₄	—	4	8	no	—
362	C₂×C₄	—	4	1	no	—
363	C₂×C₄	—	4	1	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	1	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	8	8	no	—
369	C₂×C₄	C₂×C₂²⋊C₄×C₇₉	1	2	yes	—
370	C₂×C₄	C₂×C₂²⋊C₄×C₇₉	1	4	yes	—
371	C₂×C₄	C₂×C₂²⋊C₄×C₇₉	1	2	yes	—
372	C₂×C₄	C₂×D₈×C₇₉	1	2	yes	—
373	C₂×C₄	C₂×SD₁₆×C₇₉	1	2	yes	—
374	C₂×C₄	C₂³×C₄×C₇₉	1	1	yes	characteristic
375	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
376	C₈	—	4	4	no	—
377	C₂²	—	2	1	no	—
378	C₂²	—	2	4	no	—
379	C₂²	—	2	1	no	—
380	C₂²	—	2	4	no	—
381	C₂²	—	4	4	no	—
382	C₂²	—	4	4	no	—
383	C₂²	—	4	4	no	—
384	C₂²	—	4	4	no	—
385	C₂²	—	4	4	no	—
386	C₂²	—	16	8	no	—
387	C₂²	C₂×#102×C₇₉	1	8	yes	—
388	C₂²	C₂²×C₂²⋊C₄×C₇₉	1	1	yes	characteristic
389	C₂²	C₂²×D₈×C₇₉	1	1	yes	characteristic
390	C₂²	C₂²×SD₁₆×C₇₉	1	1	yes	characteristic
391	C₄	—	2	1	no	—
392	C₄	—	2	1	no	—
393	C₄	—	2	4	no	—
394	C₄	—	2	2	no	—
395	C₄	—	4	2	no	—
396	C₄	—	4	4	no	—
397	C₄	—	8	2	no	—
398	C₄	—	8	1	no	—
399	C₄	C₂×#102×C₇₉	1	4	yes	—
400	C₂	—	2	1	no	—
401	C₂	—	2	1	no	—
402	C₂	—	2	8	no	—
403	C₂	—	8	4	no	—
404	C₂	C₇₉×#2883	1	1	yes	characteristic
405	C₂	C₂²×#102×C₇₉	1	1	yes	characteristic
406	C₂	C₇₉×#2901	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇₉	C₂²×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₇₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₉
prime radical	C₇₉×#3496	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₇₉ ◁ C₂×C₄×D₄×C₇₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇₉×#2972	C₂	semidirect
3. C₇₉×#2349	C₂	semidirect
4. C₇₉×#1519	C₂	semidirect
5. C₇₉×#1517	C₂	semidirect
6. C₇₉×#1502	C₂	semidirect
7. C₂×#327×C₇₉	C₂	semidirect
9. #547×C₇₉	C₄	semidirect
11. D₄²×C₇₉	C₄	semidirect
19. #431×C₇₉	C₂²	semidirect
20. C₂×C₂²⋊C₈×C₇₉	C₂²	semidirect
23. #382×C₇₉	C₂²	semidirect
24. #380×C₇₉	C₂²	semidirect
25. C₄×C₄⋊C₄×C₇₉	C₂²	semidirect
26. C₂×#95×C₇₉	C₂²	semidirect
27. #327×C₇₉	C₂²	semidirect
28. #327×C₇₉	C₂²	semidirect
29. #327×C₇₉	C₂²	semidirect
36. C₂²×D₄×C₇₉	C₂×C₄	semidirect
41. C₄⋊Q₈×C₇₉	C₂×C₄	semidirect
42. #127×C₇₉	C₂×C₄	semidirect
50. #121×C₇₉	C₂×C₄	semidirect
56. C₄×D₄×C₇₉	C₂×C₄	semidirect
61. C₂×C₄⋊C₄×C₇₉	C₂×C₄	semidirect
196. #17613	C₇₉	direct (N × H)
205. #2972	C₂×C₇₉	semidirect
206. #2349	C₂×C₇₉	semidirect
207. #1519	C₂×C₇₉	semidirect
208. #1517	C₂×C₇₉	semidirect
209. #1502	C₂×C₇₉	semidirect
210. C₂×#327	C₂×C₇₉	semidirect
211. C₇₉	#17613	direct (N × H)
213. #547	C₄×C₇₉	semidirect
215. D₄²	C₄×C₇₉	semidirect
223. #431	C₂²×C₇₉	semidirect
224. C₂×C₂²⋊C₈	C₂²×C₇₉	semidirect
227. #382	C₂²×C₇₉	semidirect
228. #380	C₂²×C₇₉	semidirect
229. C₄×C₄⋊C₄	C₂²×C₇₉	semidirect
230. C₂×#95	C₂²×C₇₉	semidirect
231. #327	C₂²×C₇₉	semidirect
232. #327	C₂²×C₇₉	semidirect
233. #327	C₂²×C₇₉	semidirect
240. C₂²×D₄	C₂×C₄×C₇₉	semidirect
245. C₄⋊Q₈	C₂×C₄×C₇₉	semidirect
246. #127	C₂×C₄×C₇₉	semidirect
254. #121	C₂×C₄×C₇₉	semidirect
260. C₄×D₄	C₂×C₄×C₇₉	semidirect
265. C₂×C₄⋊C₄	C₂×C₄×C₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₇₉×#3496	2
C₇₉×#2972	2
C₇₉×#2349	2
C₇₉×#1519	2
C₇₉×#1517	2
C₇₉×#1502	2
C₂×#327×C₇₉	2
#17613	79

Subgroups — C79×#17613 #34129302

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#17613 #34129302