Subgroups — C₇₉×#24498 #34136187

Order 20224.

924 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#485×C₇₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#419×C₇₉	C₂	1	1	yes	maximal, characteristic
3	C₇₉×#2434	C₂	1	1	yes	maximal, characteristic
4	C₇₉×#2346	C₂	1	1	yes	maximal, characteristic
5	C₇₉×#2068	C₂	1	2	yes	maximal, complemented
6	C₇₉×#2043	C₂	1	2	yes	maximal, complemented
7	C₇₉×#1981	C₂	1	2	yes	maximal, complemented
8	C₇₉×#1927	C₂	1	2	yes	maximal, complemented
9	C₇₉×#1894	C₂	1	1	yes	maximal, characteristic
10	C₇₉×#1851	C₂	1	1	yes	maximal, characteristic
11	C₇₉×#1787	C₂	1	1	yes	maximal, characteristic
12	C₂³×Q₈×C₇₉	C₂²	1	1	yes	characteristic
13	C₂²×M₁₆×C₇₉	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊Q₈×C₇₉	C₂²	1	2	yes	—
15	C₂×C₂²⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
16	C₂×#117×C₇₉	C₂²	1	1	yes	characteristic
17	#485×C₇₉	—	2	4	no	—
18	C₂×#107×C₇₉	C₂²	1	1	yes	characteristic
19	C₂×#106×C₇₉	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊C₈×C₇₉	C₂²	1	2	yes	—
21	#419×C₇₉	—	2	4	no	—
22	C₂×#103×C₇₉	C₂²	1	2	yes	—
23	C₂×#103×C₇₉	C₂²	1	1	yes	characteristic
24	C₂×#103×C₇₉	C₂²	1	2	yes	—
25	C₂×#103×C₇₉	C₂²	1	1	yes	characteristic
26	C₂×#103×C₇₉	C₂²	1	2	yes	—
27	C₂×#103×C₇₉	C₂²	1	2	yes	—
28	C₂×#103×C₇₉	C₂²	1	2	yes	—
29	C₂×C₂²⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
30	#395×C₇₉	—	2	1	no	—
31	#395×C₇₉	—	2	1	no	—
32	#391×C₇₉	C₂²	1	2	yes	—
33	#389×C₇₉	C₂²	1	2	yes	—
34	#388×C₇₉	—	2	2	no	—
35	#385×C₇₉	—	2	2	no	—
36	#382×C₇₉	—	2	1	no	—
37	#380×C₇₉	C₂²	1	1	yes	characteristic
38	C₄×C₄⋊C₄×C₇₉	C₂²	1	2	yes	—
39	C₄×C₂²⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
40	#376×C₇₉	—	2	1	no	—
41	#340×C₇₉	C₂²	1	2	yes	—
42	#336×C₇₉	C₂²	1	2	yes	—
43	C₂²×Q₈×C₇₉	—	2	1	no	—
44	C₂²×Q₈×C₇₉	—	2	4	no	—
45	C₂²×Q₈×C₇₉	—	2	2	no	—
46	C₂²×Q₈×C₇₉	—	2	2	no	—
47	C₂²×Q₈×C₇₉	—	4	2	no	—
48	C₂²×Q₈×C₇₉	C₂³	1	1	yes	characteristic
49	C₂²×Q₈×C₇₉	C₂³	1	2	yes	—
50	C₂³×C₄×C₇₉	—	2	1	no	—
51	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
52	C₂×M₁₆×C₇₉	—	2	2	no	—
53	C₂×M₁₆×C₇₉	—	4	2	no	—
54	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₇₉	C₂³	1	2	yes	—
56	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
57	C₄⋊Q₈×C₇₉	—	2	4	no	—
58	C₄⋊Q₈×C₇₉	—	4	2	no	—
59	C₂²⋊Q₈×C₇₉	—	2	2	no	—
60	C₂²⋊Q₈×C₇₉	—	2	2	no	—
61	#117×C₇₉	—	2	2	no	—
62	#117×C₇₉	D₄	1	4	yes	—
63	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
64	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
65	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
66	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
67	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
69	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
70	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
71	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
72	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
73	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
74	C₂×C₂²⋊C₄×C₇₉	D₄	1	2	yes	—
75	C₂×C₄²×C₇₉	—	2	1	no	—
76	C₂×C₄²×C₇₉	—	2	2	no	—
77	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
78	#107×C₇₉	—	2	2	no	—
79	#106×C₇₉	—	2	2	no	—
80	C₄⋊C₈×C₇₉	—	4	2	no	—
81	#103×C₇₉	—	2	4	no	—
82	#103×C₇₉	—	2	4	no	—
83	#103×C₇₉	—	2	4	no	—
84	#103×C₇₉	—	2	2	no	—
85	#103×C₇₉	—	2	2	no	—
86	#103×C₇₉	—	4	2	no	—
87	#103×C₇₉	—	4	2	no	—
88	C₂²⋊C₈×C₇₉	—	2	2	no	—
89	#95×C₇₉	—	2	1	no	—
90	#95×C₇₉	—	2	2	no	—
91	#95×C₇₉	—	2	2	no	—
92	#95×C₇₉	—	2	2	no	—
93	#95×C₇₉	—	2	2	no	—
94	#95×C₇₉	D₄	1	1	yes	characteristic
95	#95×C₇₉	D₄	1	1	yes	characteristic
96	C₂⁴×C₇₉	C₂×D₄	1	1	yes	characteristic
97	C₂×Q₈×C₇₉	—	2	2	no	—
98	C₂×Q₈×C₇₉	—	2	8	no	—
99	C₂×Q₈×C₇₉	—	2	2	no	—
100	C₂×Q₈×C₇₉	—	2	1	no	—
101	C₂×Q₈×C₇₉	—	2	2	no	—
102	C₂×Q₈×C₇₉	—	2	2	no	—
103	C₂×Q₈×C₇₉	—	2	1	no	—
104	C₂×Q₈×C₇₉	—	2	2	no	—
105	C₂×Q₈×C₇₉	—	2	2	no	—
106	C₂×Q₈×C₇₉	—	2	2	no	—
107	C₂×Q₈×C₇₉	—	4	4	no	—
108	C₂×Q₈×C₇₉	—	4	8	no	—
109	C₂×Q₈×C₇₉	—	4	4	no	—
110	C₂×Q₈×C₇₉	—	4	2	no	—
111	C₂×Q₈×C₇₉	#41	1	4	yes	—
112	C₂²×C₄×C₇₉	—	2	2	no	—
113	C₂²×C₄×C₇₉	—	2	2	no	—
114	C₂²×C₄×C₇₉	—	2	1	no	—
115	C₂²×C₄×C₇₉	—	2	1	no	—
116	C₂²×C₄×C₇₉	—	2	2	no	—
117	C₂²×C₄×C₇₉	—	2	1	no	—
118	C₂²×C₄×C₇₉	—	2	2	no	—
119	C₂²×C₄×C₇₉	—	2	1	no	—
120	C₂²×C₄×C₇₉	—	4	4	no	—
121	C₂²×C₄×C₇₉	—	4	2	no	—
122	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
123	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
126	C₂²×C₄×C₇₉	#41	1	2	yes	—
127	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
128	M₁₆×C₇₉	—	4	4	no	—
129	C₂×C₈×C₇₉	—	2	1	no	—
130	C₂×C₈×C₇₉	—	2	1	no	—
131	C₂×C₈×C₇₉	—	2	2	no	—
132	C₂×C₈×C₇₉	—	2	2	no	—
133	C₂×C₈×C₇₉	—	2	2	no	—
134	C₂×C₈×C₇₉	—	2	2	no	—
135	C₂×C₈×C₇₉	—	2	2	no	—
136	C₄⋊C₄×C₇₉	—	2	1	no	—
137	C₄⋊C₄×C₇₉	—	2	1	no	—
138	C₄⋊C₄×C₇₉	—	2	1	no	—
139	C₄⋊C₄×C₇₉	—	2	2	no	—
140	C₄⋊C₄×C₇₉	—	2	1	no	—
141	C₄⋊C₄×C₇₉	—	2	2	no	—
142	C₄⋊C₄×C₇₉	—	4	4	no	—
143	C₄⋊C₄×C₇₉	—	4	4	no	—
144	C₄⋊C₄×C₇₉	—	4	2	no	—
145	C₄⋊C₄×C₇₉	—	8	2	no	—
146	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
147	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
148	C₂²⋊C₄×C₇₉	—	2	4	no	—
149	C₂²⋊C₄×C₇₉	—	2	4	no	—
150	C₂²⋊C₄×C₇₉	—	4	2	no	—
151	C₂²⋊C₄×C₇₉	—	8	1	no	—
152	C₄²×C₇₉	—	2	4	no	—
153	C₄²×C₇₉	—	2	2	no	—
154	C₄²×C₇₉	—	2	2	no	—
155	C₄²×C₇₉	—	4	4	no	—
156	C₂³×C₇₉	—	2	2	no	—
157	C₂³×C₇₉	—	2	2	no	—
158	C₂³×C₇₉	—	2	1	no	—
159	C₂³×C₇₉	—	2	1	no	—
160	C₂³×C₇₉	#121	1	2	yes	—
161	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
162	Q₈×C₇₉	—	2	4	no	—
163	Q₈×C₇₉	—	2	4	no	—
164	Q₈×C₇₉	—	4	8	no	—
165	Q₈×C₇₉	—	4	2	no	—
166	Q₈×C₇₉	—	4	2	no	—
167	Q₈×C₇₉	—	4	1	no	—
168	Q₈×C₇₉	—	4	1	no	—
169	Q₈×C₇₉	—	4	2	no	—
170	C₂×C₄×C₇₉	—	2	2	no	—
171	C₂×C₄×C₇₉	—	2	2	no	—
172	C₂×C₄×C₇₉	—	2	2	no	—
173	C₂×C₄×C₇₉	—	2	2	no	—
174	C₂×C₄×C₇₉	—	2	2	no	—
175	C₂×C₄×C₇₉	—	2	4	no	—
176	C₂×C₄×C₇₉	—	2	2	no	—
177	C₂×C₄×C₇₉	—	2	2	no	—
178	C₂×C₄×C₇₉	—	2	2	no	—
179	C₂×C₄×C₇₉	—	2	4	no	—
180	C₂×C₄×C₇₉	—	2	2	no	—
181	C₂×C₄×C₇₉	—	2	2	no	—
182	C₂×C₄×C₇₉	—	4	8	no	—
183	C₂×C₄×C₇₉	—	4	2	no	—
184	C₂×C₄×C₇₉	—	4	2	no	—
185	C₂×C₄×C₇₉	—	4	2	no	—
186	C₂×C₄×C₇₉	—	4	1	no	—
187	C₂×C₄×C₇₉	—	4	1	no	—
188	C₂×C₄×C₇₉	—	4	1	no	—
189	C₂×C₄×C₇₉	—	4	1	no	—
190	C₂×C₄×C₇₉	—	4	2	no	—
191	C₂×C₄×C₇₉	—	4	2	no	—
192	C₂×C₄×C₇₉	—	4	2	no	—
193	C₂×C₄×C₇₉	—	4	2	no	—
194	C₂×C₄×C₇₉	—	4	1	no	—
195	C₂×C₄×C₇₉	—	4	1	no	—
196	C₂×C₄×C₇₉	#121	1	2	yes	—
197	C₂×C₄×C₇₉	#137	1	4	yes	—
198	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
199	C₂×C₄×C₇₉	C₂×#41	1	2	yes	—
200	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
201	C₂×C₄×C₇₉	H(5,𝔽₂)	1	2	yes	—
202	C₈×C₇₉	—	4	1	no	—
203	C₈×C₇₉	—	4	1	no	—
204	C₈×C₇₉	—	4	2	no	—
205	C₂²×C₇₉	—	2	2	no	—
206	C₂²×C₇₉	—	2	2	no	—
207	C₂²×C₇₉	—	2	2	no	—
208	C₂²×C₇₉	—	4	2	no	—
209	C₂²×C₇₉	—	4	2	no	—
210	C₂²×C₇₉	C₂×#121	1	1	yes	characteristic
211	C₂²×C₇₉	#546	1	2	yes	—
212	C₂²×C₇₉	C₂×#137	1	2	yes	—
213	C₂²×C₇₉	#577	1	1	yes	characteristic
214	C₂²×C₇₉	#578	1	1	yes	characteristic
215	C₄×C₇₉	—	2	2	no	—
216	C₄×C₇₉	—	2	4	no	—
217	C₄×C₇₉	—	4	2	no	—
218	C₄×C₇₉	—	4	4	no	—
219	C₄×C₇₉	—	4	2	no	—
220	C₄×C₇₉	—	4	2	no	—
221	C₄×C₇₉	—	8	2	no	—
222	C₄×C₇₉	—	8	1	no	—
223	C₄×C₇₉	—	8	1	no	—
224	C₄×C₇₉	#525	1	1	yes	characteristic
225	C₄×C₇₉	#535	1	1	yes	characteristic
226	C₄×C₇₉	#551	1	2	yes	—
227	#24498	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
228	C₂×C₇₉	—	4	2	no	—
229	C₂×C₇₉	#2411	1	1	yes	characteristic
230	C₂×C₇₉	#3039	1	1	yes	characteristic
231	C₂×C₇₉	#3046	1	1	yes	characteristic
232	C₂×C₇₉	#3312	1	2	yes	—
233	C₂×C₇₉	#3329	1	2	yes	—
234	C₂×#485	C₂×C₇₉	1	1	yes	characteristic
235	C₂×#419	C₂×C₇₉	1	1	yes	characteristic
236	#2434	C₂×C₇₉	1	1	yes	characteristic
237	#2346	C₂×C₇₉	1	1	yes	characteristic
238	#2068	C₂×C₇₉	1	2	yes	complemented
239	#2043	C₂×C₇₉	1	2	yes	complemented
240	#1981	C₂×C₇₉	1	2	yes	complemented
241	#1927	C₂×C₇₉	1	2	yes	complemented
242	#1894	C₂×C₇₉	1	1	yes	characteristic
243	#1851	C₂×C₇₉	1	1	yes	characteristic
244	#1787	C₂×C₇₉	1	1	yes	characteristic
245	C₇₉	#24498	1	1	yes	characteristic, direct product factor, Sylow
246	C₂³×Q₈	C₂²×C₇₉	1	1	yes	characteristic
247	C₂²×M₁₆	C₂²×C₇₉	1	1	yes	characteristic
248	C₂×C₄⋊Q₈	C₂²×C₇₉	1	2	yes	—
249	C₂×C₂²⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic
250	C₂×#117	C₂²×C₇₉	1	1	yes	characteristic
251	#485	—	2	4	no	—
252	C₂×#107	C₂²×C₇₉	1	1	yes	characteristic
253	C₂×#106	C₂²×C₇₉	1	1	yes	characteristic
254	C₂×C₄⋊C₈	C₂²×C₇₉	1	2	yes	—
255	#419	—	2	4	no	—
256	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic
257	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic
258	C₂×#103	C₂²×C₇₉	1	2	yes	—
259	C₂×#103	C₂²×C₇₉	1	2	yes	—
260	C₂×#103	C₂²×C₇₉	1	2	yes	—
261	C₂×#103	C₂²×C₇₉	1	2	yes	—
262	C₂×#103	C₂²×C₇₉	1	2	yes	—
263	C₂×C₂²⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
264	#395	—	2	1	no	—
265	#395	—	2	1	no	—
266	#391	C₂²×C₇₉	1	2	yes	—
267	#389	C₂²×C₇₉	1	2	yes	—
268	#388	—	2	2	no	—
269	#385	—	2	2	no	—
270	#382	—	2	1	no	—
271	#380	C₂²×C₇₉	1	1	yes	characteristic
272	C₄×C₄⋊C₄	C₂²×C₇₉	1	2	yes	—
273	C₄×C₂²⋊C₄	C₂²×C₇₉	1	1	yes	characteristic
274	#376	—	2	1	no	—
275	#340	C₂²×C₇₉	1	2	yes	—
276	#336	C₂²×C₇₉	1	2	yes	—
277	C₂²×Q₈	—	2	1	no	—
278	C₂²×Q₈	—	2	4	no	—
279	C₂²×Q₈	—	2	2	no	—
280	C₂²×Q₈	—	2	2	no	—
281	C₂²×Q₈	—	4	2	no	—
282	C₂²×Q₈	C₂³×C₇₉	1	1	yes	characteristic
283	C₂²×Q₈	C₂³×C₇₉	1	2	yes	—
284	C₂³×C₄	—	2	1	no	—
285	C₂³×C₄	C₂³×C₇₉	1	1	yes	characteristic
286	C₂×M₁₆	—	2	2	no	—
287	C₂×M₁₆	—	4	2	no	—
288	C₂²×C₈	C₂³×C₇₉	1	2	yes	—
289	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
290	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
291	C₄⋊Q₈	—	2	4	no	—
292	C₄⋊Q₈	—	4	2	no	—
293	C₂²⋊Q₈	—	2	2	no	—
294	C₂²⋊Q₈	—	2	2	no	—
295	#117	—	2	2	no	—
296	#117	D₄×C₇₉	1	4	yes	—
297	C₂×C₄⋊C₄	—	2	1	no	—
298	C₂×C₄⋊C₄	—	2	2	no	—
299	C₂×C₄⋊C₄	—	2	2	no	—
300	C₂×C₄⋊C₄	—	2	2	no	—
301	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
302	C₂×C₄⋊C₄	C₂³×C₇₉	1	2	yes	—
303	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
304	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
305	C₂×C₂²⋊C₄	—	2	1	no	—
306	C₂×C₂²⋊C₄	—	2	1	no	—
307	C₂×C₂²⋊C₄	—	2	1	no	—
308	C₂×C₂²⋊C₄	D₄×C₇₉	1	2	yes	—
309	C₂×C₄²	—	2	1	no	—
310	C₂×C₄²	—	2	2	no	—
311	C₂×C₄²	C₂³×C₇₉	1	2	yes	—
312	#107	—	2	2	no	—
313	#106	—	2	2	no	—
314	C₄⋊C₈	—	4	2	no	—
315	#103	—	2	4	no	—
316	#103	—	2	4	no	—
317	#103	—	2	4	no	—
318	#103	—	2	2	no	—
319	#103	—	2	2	no	—
320	#103	—	4	2	no	—
321	#103	—	4	2	no	—
322	C₂²⋊C₈	—	2	2	no	—
323	#95	—	2	1	no	—
324	#95	—	2	2	no	—
325	#95	—	2	2	no	—
326	#95	—	2	2	no	—
327	#95	—	2	2	no	—
328	#95	D₄×C₇₉	1	1	yes	characteristic
329	#95	D₄×C₇₉	1	1	yes	characteristic
330	C₂⁴	C₂×D₄×C₇₉	1	1	yes	characteristic
331	C₂×Q₈	—	2	2	no	—
332	C₂×Q₈	—	2	8	no	—
333	C₂×Q₈	—	2	2	no	—
334	C₂×Q₈	—	2	1	no	—
335	C₂×Q₈	—	2	2	no	—
336	C₂×Q₈	—	2	2	no	—
337	C₂×Q₈	—	2	1	no	—
338	C₂×Q₈	—	2	2	no	—
339	C₂×Q₈	—	2	2	no	—
340	C₂×Q₈	—	2	2	no	—
341	C₂×Q₈	—	4	4	no	—
342	C₂×Q₈	—	4	8	no	—
343	C₂×Q₈	—	4	4	no	—
344	C₂×Q₈	—	4	2	no	—
345	C₂×Q₈	#41×C₇₉	1	4	yes	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	2	1	no	—
349	C₂²×C₄	—	2	1	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	1	no	—
354	C₂²×C₄	—	4	4	no	—
355	C₂²×C₄	—	4	2	no	—
356	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
357	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
358	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
359	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
360	C₂²×C₄	#41×C₇₉	1	2	yes	—
361	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
362	M₁₆	—	4	4	no	—
363	C₂×C₈	—	2	1	no	—
364	C₂×C₈	—	2	1	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	2	2	no	—
368	C₂×C₈	—	2	2	no	—
369	C₂×C₈	—	2	2	no	—
370	C₄⋊C₄	—	2	1	no	—
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	2	1	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	1	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	4	4	no	—
377	C₄⋊C₄	—	4	4	no	—
378	C₄⋊C₄	—	4	2	no	—
379	C₄⋊C₄	—	8	2	no	—
380	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
381	C₄⋊C₄	C₂×D₄×C₇₉	1	2	yes	—
382	C₂²⋊C₄	—	2	4	no	—
383	C₂²⋊C₄	—	2	4	no	—
384	C₂²⋊C₄	—	4	2	no	—
385	C₂²⋊C₄	—	8	1	no	—
386	C₄²	—	2	4	no	—
387	C₄²	—	2	2	no	—
388	C₄²	—	2	2	no	—
389	C₄²	—	4	4	no	—
390	C₂³	—	2	2	no	—
391	C₂³	—	2	2	no	—
392	C₂³	—	2	1	no	—
393	C₂³	—	2	1	no	—
394	C₂³	#121×C₇₉	1	2	yes	—
395	C₂³	C₂²×D₄×C₇₉	1	1	yes	characteristic
396	Q₈	—	2	4	no	—
397	Q₈	—	2	4	no	—
398	Q₈	—	4	8	no	—
399	Q₈	—	4	2	no	—
400	Q₈	—	4	2	no	—
401	Q₈	—	4	1	no	—
402	Q₈	—	4	1	no	—
403	Q₈	—	4	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	4	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	4	8	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	4	1	no	—
423	C₂×C₄	—	4	1	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	1	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	#121×C₇₉	1	2	yes	—
431	C₂×C₄	#137×C₇₉	1	4	yes	—
432	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
433	C₂×C₄	C₂×#41×C₇₉	1	2	yes	—
434	C₂×C₄	C₂×#41×C₇₉	1	1	yes	characteristic
435	C₂×C₄	H(5,𝔽₂)×C₇₉	1	2	yes	—
436	C₈	—	4	1	no	—
437	C₈	—	4	2	no	—
438	C₈	—	4	1	no	—
439	C₂²	—	2	2	no	—
440	C₂²	—	2	2	no	—
441	C₂²	—	2	2	no	—
442	C₂²	—	4	2	no	—
443	C₂²	—	4	2	no	—
444	C₂²	C₂×#121×C₇₉	1	1	yes	characteristic
445	C₂²	#546×C₇₉	1	2	yes	—
446	C₂²	C₂×#137×C₇₉	1	2	yes	—
447	C₂²	#577×C₇₉	1	1	yes	characteristic
448	C₂²	#578×C₇₉	1	1	yes	characteristic
449	C₄	—	2	4	no	—
450	C₄	—	2	2	no	—
451	C₄	—	4	2	no	—
452	C₄	—	4	2	no	—
453	C₄	—	4	2	no	—
454	C₄	—	4	4	no	—
455	C₄	—	8	1	no	—
456	C₄	—	8	2	no	—
457	C₄	—	8	1	no	—
458	C₄	#525×C₇₉	1	1	yes	characteristic
459	C₄	#535×C₇₉	1	1	yes	characteristic
460	C₄	#551×C₇₉	1	2	yes	—
461	C₂	—	4	2	no	—
462	C₂	C₇₉×#2411	1	1	yes	characteristic
463	C₂	C₇₉×#3039	1	1	yes	characteristic
464	C₂	C₇₉×#3046	1	1	yes	characteristic
465	C₂	C₇₉×#3312	1	2	yes	—
466	C₂	C₇₉×#3329	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
5. C₇₉×#2068	C₂	semidirect
6. C₇₉×#2043	C₂	semidirect
7. C₇₉×#1981	C₂	semidirect
8. C₇₉×#1927	C₂	semidirect
227. #24498	C₇₉	direct (N × H)
238. #2068	C₂×C₇₉	semidirect
239. #2043	C₂×C₇₉	semidirect
240. #1981	C₂×C₇₉	semidirect
241. #1927	C₂×C₇₉	semidirect
245. C₇₉	#24498	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×#485×C₇₉	2
C₂×#419×C₇₉	2
C₇₉×#2434	2
C₇₉×#2346	2
C₇₉×#2068	2
C₇₉×#2043	2
C₇₉×#1981	2
C₇₉×#1927	2
C₇₉×#1894	2
C₇₉×#1851	2
C₇₉×#1787	2
#24498	79

Subgroups — C79×#24498 #34136187

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#24498 #34136187