Subgroups — C₇₉×#25570 #34137259

Order 20224.

1126 conjugacy classes of subgroups.

The subgroup lattice has 428 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
2	C₂×#487×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#462×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₉×#2542	C₂	1	1	yes	maximal, characteristic
5	C₇₉×#2001	C₂	1	4	yes	maximal, complemented
6	C₇₉×#1988	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₉×#1954	C₂	1	1	yes	maximal, characteristic
8	C₇₉×#1873	C₂	1	4	yes	maximal, complemented
9	C₄×#103×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×Q₁₆×C₇₉	C₂²	1	2	yes	—
11	#556×C₇₉	—	2	4	no	—
12	#556×C₇₉	—	2	4	no	—
13	C₂×C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
15	C₂×#126×C₇₉	—	2	2	no	—
16	C₂×#124×C₇₉	—	2	1	no	—
17	C₂×C₂²⋊Q₈×C₇₉	C₂²	1	2	yes	—
18	C₂×C₂²⋊Q₈×C₇₉	C₂²	1	4	yes	—
19	C₂×C₄×Q₈×C₇₉	—	2	1	no	—
20	C₂×C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
22	C₂×#117×C₇₉	C₂²	1	2	yes	—
23	#487×C₇₉	—	2	4	no	—
24	#462×C₇₉	—	2	4	no	—
25	C₂×C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
26	C₂×#103×C₇₉	C₂²	1	2	yes	—
27	C₂×#103×C₇₉	C₂²	1	4	yes	—
28	C₂×#103×C₇₉	C₂²	1	2	yes	—
29	C₂×C₂²⋊C₈×C₇₉	C₂²	1	4	yes	—
30	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
31	#399×C₇₉	—	2	2	no	—
32	#390×C₇₉	—	2	1	no	—
33	#384×C₇₉	—	2	1	no	—
34	C₄×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
35	#340×C₇₉	C₂²	1	4	yes	—
36	#340×C₇₉	C₂²	1	2	yes	—
37	C₂²×Q₈×C₇₉	—	2	1	no	—
38	C₂²×Q₈×C₇₉	C₂³	1	2	yes	—
39	C₂²×Q₈×C₇₉	C₂³	1	1	yes	characteristic
40	C₂²×D₄×C₇₉	D₄	1	1	yes	characteristic
41	C₂³×C₄×C₇₉	C₂³	1	2	yes	—
42	C₂×Q₁₆×C₇₉	—	2	4	no	—
43	C₂×Q₁₆×C₇₉	—	4	4	no	—
44	C₂²×C₈×C₇₉	C₂³	1	2	yes	—
45	C₂²×C₈×C₇₉	C₂³	1	2	yes	—
46	C₄⋊Q₈×C₇₉	—	2	2	no	—
47	C₄⋊Q₈×C₇₉	—	2	2	no	—
48	C₄⋊Q₈×C₇₉	—	2	2	no	—
49	C₄⋊Q₈×C₇₉	D₄	1	4	yes	—
50	#126×C₇₉	—	2	16	no	—
51	#124×C₇₉	—	2	8	no	—
52	C₂²⋊Q₈×C₇₉	—	2	4	no	—
53	C₂²⋊Q₈×C₇₉	—	2	4	no	—
54	C₂²⋊Q₈×C₇₉	—	2	8	no	—
55	C₂²⋊Q₈×C₇₉	—	4	4	no	—
56	C₄×Q₈×C₇₉	—	2	8	no	—
57	C₄×Q₈×C₇₉	—	2	2	no	—
58	C₄×Q₈×C₇₉	D₄	1	4	yes	—
59	C₄×D₄×C₇₉	—	2	2	no	—
60	C₄×D₄×C₇₉	—	2	2	no	—
61	#117×C₇₉	—	2	4	no	—
62	#117×C₇₉	—	2	4	no	—
63	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
64	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
65	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
66	C₂×C₄⋊C₄×C₇₉	—	2	4	no	—
67	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
68	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
69	C₂×C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
70	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
71	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
72	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
73	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
74	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
75	C₂×C₂²⋊C₄×C₇₉	—	2	4	no	—
76	C₂×C₂²⋊C₄×C₇₉	D₄	1	2	yes	—
77	C₂×C₄²×C₇₉	—	2	2	no	—
78	C₂×C₄²×C₇₉	—	2	1	no	—
79	C₂×C₄²×C₇₉	—	2	1	no	—
80	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
81	C₄⋊C₈×C₇₉	—	2	2	no	—
82	#103×C₇₉	—	2	4	no	—
83	#103×C₇₉	—	2	8	no	—
84	#103×C₇₉	—	2	4	no	—
85	C₂²⋊C₈×C₇₉	—	4	4	no	—
86	C₄×C₈×C₇₉	—	2	2	no	—
87	#95×C₇₉	—	2	1	no	—
88	C₂⁴×C₇₉	C₂×D₄	1	2	yes	—
89	C₂×Q₈×C₇₉	—	2	4	no	—
90	C₂×Q₈×C₇₉	—	2	1	no	—
91	C₂×Q₈×C₇₉	—	2	2	no	—
92	C₂×Q₈×C₇₉	—	2	2	no	—
93	C₂×Q₈×C₇₉	—	2	2	no	—
94	C₂×Q₈×C₇₉	—	2	4	no	—
95	C₂×Q₈×C₇₉	—	2	2	no	—
96	C₂×Q₈×C₇₉	—	2	4	no	—
97	C₂×Q₈×C₇₉	—	4	2	no	—
98	C₂×Q₈×C₇₉	—	4	2	no	—
99	C₂×Q₈×C₇₉	C₂×D₄	1	2	yes	—
100	C₂×D₄×C₇₉	—	2	2	no	—
101	C₂×D₄×C₇₉	—	2	2	no	—
102	C₂×D₄×C₇₉	—	2	2	no	—
103	C₂²×C₄×C₇₉	—	2	2	no	—
104	C₂²×C₄×C₇₉	—	2	1	no	—
105	C₂²×C₄×C₇₉	—	2	1	no	—
106	C₂²×C₄×C₇₉	—	2	2	no	—
107	C₂²×C₄×C₇₉	—	2	2	no	—
108	C₂²×C₄×C₇₉	—	2	2	no	—
109	C₂²×C₄×C₇₉	—	2	4	no	—
110	C₂²×C₄×C₇₉	—	2	4	no	—
111	C₂²×C₄×C₇₉	—	2	2	no	—
112	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
116	Q₁₆×C₇₉	—	4	8	no	—
117	C₂×C₈×C₇₉	—	2	2	no	—
118	C₂×C₈×C₇₉	—	2	2	no	—
119	C₂×C₈×C₇₉	—	2	2	no	—
120	C₂×C₈×C₇₉	—	2	2	no	—
121	C₂×C₈×C₇₉	—	2	4	no	—
122	C₄⋊C₄×C₇₉	—	2	8	no	—
123	C₄⋊C₄×C₇₉	—	2	4	no	—
124	C₄⋊C₄×C₇₉	—	2	4	no	—
125	C₄⋊C₄×C₇₉	—	2	2	no	—
126	C₄⋊C₄×C₇₉	—	2	1	no	—
127	C₄⋊C₄×C₇₉	—	2	2	no	—
128	C₄⋊C₄×C₇₉	—	2	2	no	—
129	C₄⋊C₄×C₇₉	—	4	8	no	—
130	C₄⋊C₄×C₇₉	—	4	2	no	—
131	C₄⋊C₄×C₇₉	—	4	2	no	—
132	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
133	C₄⋊C₄×C₇₉	C₂×D₄	1	4	yes	—
134	C₄⋊C₄×C₇₉	#41	1	4	yes	—
135	C₂²⋊C₄×C₇₉	—	2	8	no	—
136	C₂²⋊C₄×C₇₉	—	2	8	no	—
137	C₂²⋊C₄×C₇₉	—	2	4	no	—
138	C₂²⋊C₄×C₇₉	—	4	8	no	—
139	C₄²×C₇₉	—	2	8	no	—
140	C₄²×C₇₉	—	2	4	no	—
141	C₄²×C₇₉	—	4	2	no	—
142	C₄²×C₇₉	C₂×D₄	1	2	yes	—
143	C₄²×C₇₉	C₂×D₄	1	2	yes	—
144	C₂³×C₇₉	—	2	2	no	—
145	C₂³×C₇₉	—	2	4	no	—
146	C₂³×C₇₉	—	2	2	no	—
147	C₂³×C₇₉	—	2	2	no	—
148	C₂³×C₇₉	—	2	4	no	—
149	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
150	Q₈×C₇₉	—	2	2	no	—
151	Q₈×C₇₉	—	2	2	no	—
152	Q₈×C₇₉	—	4	2	no	—
153	Q₈×C₇₉	—	4	8	no	—
154	Q₈×C₇₉	—	4	2	no	—
155	Q₈×C₇₉	—	4	2	no	—
156	Q₈×C₇₉	—	4	4	no	—
157	D₄×C₇₉	—	4	4	no	—
158	C₂×C₄×C₇₉	—	2	2	no	—
159	C₂×C₄×C₇₉	—	2	2	no	—
160	C₂×C₄×C₇₉	—	2	2	no	—
161	C₂×C₄×C₇₉	—	2	2	no	—
162	C₂×C₄×C₇₉	—	2	4	no	—
163	C₂×C₄×C₇₉	—	2	4	no	—
164	C₂×C₄×C₇₉	—	2	4	no	—
165	C₂×C₄×C₇₉	—	4	2	no	—
166	C₂×C₄×C₇₉	—	4	2	no	—
167	C₂×C₄×C₇₉	—	4	2	no	—
168	C₂×C₄×C₇₉	—	4	2	no	—
169	C₂×C₄×C₇₉	—	4	2	no	—
170	C₂×C₄×C₇₉	—	4	2	no	—
171	C₂×C₄×C₇₉	—	4	2	no	—
172	C₂×C₄×C₇₉	—	4	2	no	—
173	C₂×C₄×C₇₉	—	4	4	no	—
174	C₂×C₄×C₇₉	—	4	2	no	—
175	C₂×C₄×C₇₉	—	4	4	no	—
176	C₂×C₄×C₇₉	#120	1	2	yes	—
177	C₂×C₄×C₇₉	#120	1	2	yes	—
178	C₂×C₄×C₇₉	#135	1	2	yes	—
179	C₂×C₄×C₇₉	#137	1	2	yes	—
180	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
181	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
182	C₂×C₄×C₇₉	C₂×#41	1	2	yes	—
183	C₂×C₄×C₇₉	H(5,𝔽₂)	1	2	yes	—
184	C₈×C₇₉	—	4	2	no	—
185	C₈×C₇₉	—	4	2	no	—
186	C₂²×C₇₉	—	4	4	no	—
187	C₂²×C₇₉	—	4	2	no	—
188	C₂²×C₇₉	—	4	2	no	—
189	C₂²×C₇₉	—	4	2	no	—
190	C₂²×C₇₉	—	4	4	no	—
191	C₂²×C₇₉	C₂×#120	1	1	yes	characteristic
192	C₂²×C₇₉	#546	1	2	yes	—
193	C₂²×C₇₉	C₂×#135	1	1	yes	characteristic
194	C₂²×C₇₉	C₂×#137	1	1	yes	characteristic
195	C₂²×C₇₉	#578	1	2	yes	—
196	C₄×C₇₉	—	2	2	no	—
197	C₄×C₇₉	—	4	2	no	—
198	C₄×C₇₉	—	4	2	no	—
199	C₄×C₇₉	—	4	4	no	—
200	C₄×C₇₉	—	4	2	no	—
201	C₄×C₇₉	—	4	4	no	—
202	C₄×C₇₉	—	8	2	no	—
203	C₄×C₇₉	#452	1	4	yes	—
204	C₄×C₇₉	#532	1	1	yes	characteristic
205	C₄×C₇₉	#535	1	1	yes	characteristic
206	C₄×C₇₉	#550	1	2	yes	—
207	#25570	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
208	C₂×C₇₉	—	8	2	no	—
209	C₂×C₇₉	#2431	1	1	yes	characteristic
210	C₂×C₇₉	C₂×#452	1	1	yes	characteristic
211	C₂×C₇₉	#3011	1	1	yes	characteristic
212	C₂×C₇₉	#3302	1	2	yes	—
213	C₂×C₇₉	#3328	1	2	yes	—
214	C₂×#556	C₂×C₇₉	1	1	yes	characteristic
215	C₂×#487	C₂×C₇₉	1	1	yes	characteristic, complemented
216	C₂×#462	C₂×C₇₉	1	1	yes	characteristic, complemented
217	#2542	C₂×C₇₉	1	1	yes	characteristic
218	#2001	C₂×C₇₉	1	4	yes	complemented
219	#1988	C₂×C₇₉	1	1	yes	characteristic, complemented
220	#1954	C₂×C₇₉	1	1	yes	characteristic
221	#1873	C₂×C₇₉	1	4	yes	complemented
222	C₄×#103	C₂×C₇₉	1	1	yes	characteristic, complemented
223	C₇₉	#25570	1	1	yes	characteristic, direct product factor, Sylow
224	C₂²×Q₁₆	C₂²×C₇₉	1	2	yes	—
225	#556	—	2	4	no	—
226	#556	—	2	4	no	—
227	C₂×C₄⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic
228	C₂×C₄⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic
229	C₂×#126	—	2	2	no	—
230	C₂×#124	—	2	1	no	—
231	C₂×C₂²⋊Q₈	C₂²×C₇₉	1	2	yes	—
232	C₂×C₂²⋊Q₈	C₂²×C₇₉	1	4	yes	—
233	C₂×C₄×Q₈	—	2	1	no	—
234	C₂×C₄×Q₈	C₂²×C₇₉	1	1	yes	characteristic
235	C₂×C₄×D₄	C₂²×C₇₉	1	1	yes	characteristic
236	C₂×#117	C₂²×C₇₉	1	2	yes	—
237	#487	—	2	4	no	—
238	#462	—	2	4	no	—
239	C₂×C₄⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
240	C₂×#103	C₂²×C₇₉	1	4	yes	—
241	C₂×#103	C₂²×C₇₉	1	2	yes	—
242	C₂×#103	C₂²×C₇₉	1	2	yes	—
243	C₂×C₂²⋊C₈	C₂²×C₇₉	1	4	yes	—
244	C₂×C₄×C₈	C₂²×C₇₉	1	1	yes	characteristic
245	#399	—	2	2	no	—
246	#390	—	2	1	no	—
247	#384	—	2	1	no	—
248	C₄×C₄⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
249	#340	C₂²×C₇₉	1	2	yes	—
250	#340	C₂²×C₇₉	1	4	yes	—
251	C₂²×Q₈	—	2	1	no	—
252	C₂²×Q₈	C₂³×C₇₉	1	2	yes	—
253	C₂²×Q₈	C₂³×C₇₉	1	1	yes	characteristic
254	C₂²×D₄	D₄×C₇₉	1	1	yes	characteristic
255	C₂³×C₄	C₂³×C₇₉	1	2	yes	—
256	C₂×Q₁₆	—	2	4	no	—
257	C₂×Q₁₆	—	4	4	no	—
258	C₂²×C₈	C₂³×C₇₉	1	2	yes	—
259	C₂²×C₈	C₂³×C₇₉	1	2	yes	—
260	C₄⋊Q₈	—	2	2	no	—
261	C₄⋊Q₈	—	2	2	no	—
262	C₄⋊Q₈	—	2	2	no	—
263	C₄⋊Q₈	D₄×C₇₉	1	4	yes	—
264	#126	—	2	16	no	—
265	#124	—	2	8	no	—
266	C₂²⋊Q₈	—	2	4	no	—
267	C₂²⋊Q₈	—	2	4	no	—
268	C₂²⋊Q₈	—	2	8	no	—
269	C₂²⋊Q₈	—	4	4	no	—
270	C₄×Q₈	—	2	8	no	—
271	C₄×Q₈	—	2	2	no	—
272	C₄×Q₈	D₄×C₇₉	1	4	yes	—
273	C₄×D₄	—	2	2	no	—
274	C₄×D₄	—	2	2	no	—
275	#117	—	2	4	no	—
276	#117	—	2	4	no	—
277	C₂×C₄⋊C₄	—	2	2	no	—
278	C₂×C₄⋊C₄	—	2	1	no	—
279	C₂×C₄⋊C₄	—	2	1	no	—
280	C₂×C₄⋊C₄	—	2	4	no	—
281	C₂×C₄⋊C₄	—	2	1	no	—
282	C₂×C₄⋊C₄	—	2	1	no	—
283	C₂×C₄⋊C₄	D₄×C₇₉	1	1	yes	characteristic
284	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
285	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
286	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
287	C₂×C₂²⋊C₄	—	2	2	no	—
288	C₂×C₂²⋊C₄	—	2	2	no	—
289	C₂×C₂²⋊C₄	—	2	4	no	—
290	C₂×C₂²⋊C₄	D₄×C₇₉	1	2	yes	—
291	C₂×C₄²	—	2	2	no	—
292	C₂×C₄²	—	2	1	no	—
293	C₂×C₄²	—	2	1	no	—
294	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
295	C₄⋊C₈	—	2	2	no	—
296	#103	—	2	4	no	—
297	#103	—	2	8	no	—
298	#103	—	2	4	no	—
299	C₂²⋊C₈	—	4	4	no	—
300	C₄×C₈	—	2	2	no	—
301	#95	—	2	1	no	—
302	C₂⁴	C₂×D₄×C₇₉	1	2	yes	—
303	C₂×Q₈	—	2	4	no	—
304	C₂×Q₈	—	2	1	no	—
305	C₂×Q₈	—	2	2	no	—
306	C₂×Q₈	—	2	2	no	—
307	C₂×Q₈	—	2	2	no	—
308	C₂×Q₈	—	2	4	no	—
309	C₂×Q₈	—	2	2	no	—
310	C₂×Q₈	—	2	4	no	—
311	C₂×Q₈	—	4	2	no	—
312	C₂×Q₈	—	4	2	no	—
313	C₂×Q₈	C₂×D₄×C₇₉	1	2	yes	—
314	C₂×D₄	—	2	2	no	—
315	C₂×D₄	—	2	2	no	—
316	C₂×D₄	—	2	2	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	2	1	no	—
319	C₂²×C₄	—	2	1	no	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	2	4	no	—
324	C₂²×C₄	—	2	4	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
327	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
328	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
329	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
330	Q₁₆	—	4	8	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	2	4	no	—
336	C₄⋊C₄	—	2	8	no	—
337	C₄⋊C₄	—	2	4	no	—
338	C₄⋊C₄	—	2	4	no	—
339	C₄⋊C₄	—	2	2	no	—
340	C₄⋊C₄	—	2	1	no	—
341	C₄⋊C₄	—	2	2	no	—
342	C₄⋊C₄	—	2	2	no	—
343	C₄⋊C₄	—	4	8	no	—
344	C₄⋊C₄	—	4	2	no	—
345	C₄⋊C₄	—	4	2	no	—
346	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
347	C₄⋊C₄	C₂×D₄×C₇₉	1	4	yes	—
348	C₄⋊C₄	#41×C₇₉	1	4	yes	—
349	C₂²⋊C₄	—	2	8	no	—
350	C₂²⋊C₄	—	2	8	no	—
351	C₂²⋊C₄	—	2	4	no	—
352	C₂²⋊C₄	—	4	8	no	—
353	C₄²	—	2	8	no	—
354	C₄²	—	2	4	no	—
355	C₄²	—	4	2	no	—
356	C₄²	C₂×D₄×C₇₉	1	2	yes	—
357	C₄²	C₂×D₄×C₇₉	1	2	yes	—
358	C₂³	—	2	2	no	—
359	C₂³	—	2	4	no	—
360	C₂³	—	2	2	no	—
361	C₂³	—	2	2	no	—
362	C₂³	—	2	4	no	—
363	C₂³	C₂²×D₄×C₇₉	1	1	yes	characteristic
364	Q₈	—	2	2	no	—
365	Q₈	—	2	2	no	—
366	Q₈	—	4	8	no	—
367	Q₈	—	4	2	no	—
368	Q₈	—	4	2	no	—
369	Q₈	—	4	2	no	—
370	Q₈	—	4	4	no	—
371	D₄	—	4	4	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	4	no	—
377	C₂×C₄	—	2	4	no	—
378	C₂×C₄	—	2	4	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	4	4	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	4	no	—
390	C₂×C₄	#120×C₇₉	1	2	yes	—
391	C₂×C₄	#120×C₇₉	1	2	yes	—
392	C₂×C₄	#135×C₇₉	1	2	yes	—
393	C₂×C₄	#137×C₇₉	1	2	yes	—
394	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
395	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
396	C₂×C₄	C₂×#41×C₇₉	1	2	yes	—
397	C₂×C₄	H(5,𝔽₂)×C₇₉	1	2	yes	—
398	C₈	—	4	2	no	—
399	C₈	—	4	2	no	—
400	C₂²	—	4	4	no	—
401	C₂²	—	4	4	no	—
402	C₂²	—	4	2	no	—
403	C₂²	—	4	2	no	—
404	C₂²	—	4	2	no	—
405	C₂²	C₂×#120×C₇₉	1	1	yes	characteristic
406	C₂²	#546×C₇₉	1	2	yes	—
407	C₂²	C₂×#135×C₇₉	1	1	yes	characteristic
408	C₂²	C₂×#137×C₇₉	1	1	yes	characteristic
409	C₂²	#578×C₇₉	1	2	yes	—
410	C₄	—	2	2	no	—
411	C₄	—	4	4	no	—
412	C₄	—	4	2	no	—
413	C₄	—	4	2	no	—
414	C₄	—	4	4	no	—
415	C₄	—	4	2	no	—
416	C₄	—	8	2	no	—
417	C₄	#452×C₇₉	1	4	yes	—
418	C₄	#532×C₇₉	1	1	yes	characteristic
419	C₄	#535×C₇₉	1	1	yes	characteristic
420	C₄	#550×C₇₉	1	2	yes	—
421	C₂	—	8	2	no	—
422	C₂	C₇₉×#2431	1	1	yes	characteristic
423	C₂	C₂×#452×C₇₉	1	1	yes	characteristic
424	C₂	C₇₉×#3011	1	1	yes	characteristic
425	C₂	C₇₉×#3302	1	2	yes	—
426	C₂	C₇₉×#3328	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₂×#487×C₇₉	C₂	semidirect
3. C₂×#462×C₇₉	C₂	semidirect
5. C₇₉×#2001	C₂	semidirect
6. C₇₉×#1988	C₂	semidirect
8. C₇₉×#1873	C₂	semidirect
9. C₄×#103×C₇₉	C₂	semidirect
207. #25570	C₇₉	direct (N × H)
215. C₂×#487	C₂×C₇₉	semidirect
216. C₂×#462	C₂×C₇₉	semidirect
218. #2001	C₂×C₇₉	semidirect
219. #1988	C₂×C₇₉	semidirect
221. #1873	C₂×C₇₉	semidirect
222. C₄×#103	C₂×C₇₉	semidirect
223. C₇₉	#25570	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×#487×C₇₉	2
C₂×#462×C₇₉	2
C₇₉×#2542	2
C₇₉×#2001	2
C₇₉×#1988	2
C₇₉×#1954	2
C₇₉×#1873	2
C₄×#103×C₇₉	2
#25570	79

Subgroups — C79×#25570 #34137259

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#25570 #34137259