Subgroups — #34307071

Order 20224.

760 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×C₇₉⋊C₈	C₂	1	1	yes	maximal, characteristic
2	#23765878	C₂	1	1	yes	maximal, characteristic
3	#23764123	C₂	1	2	yes	maximal
4	#23764118	C₂	1	1	yes	maximal, characteristic
5	#23764116	C₂	1	1	yes	maximal, characteristic
6	#23764116	C₂	1	2	yes	maximal
7	#23763553	C₂	1	2	yes	maximal
8	#23763551	C₂	1	1	yes	maximal, characteristic
9	#23763260	C₂	1	2	yes	maximal
10	C₄×Dic₇₉⋊C₈	C₂	1	1	yes	maximal, characteristic
11	C₂×#446×C₇₉	C₂	1	1	yes	maximal, characteristic
12	Q₈×C₇₉⋊C₈	—	2	4	no	—
13	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
15	C₂×Dic₇₉⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×Dic₇₉⋊C₈	C₂²	1	2	yes	—
17	C₂×Dic₇₉⋊C₈	C₂²	1	2	yes	—
18	C₂×Dic₇₉⋊C₈	C₂²	1	2	yes	—
19	C₂×Dic₇₉⋊C₈	C₂²	1	2	yes	—
20	C₂×Dic₇₉⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₇₉⋊C₈	C₂²	1	2	yes	—
23	#19098470	C₄	1	1	yes	characteristic
24	#19098470	C₄	1	1	yes	characteristic
25	#19098462	C₄	1	1	yes	characteristic
26	#19098462	C₄	1	1	yes	characteristic
27	#19098449	C₄	1	2	yes	—
28	#19098449	C₄	1	2	yes	—
29	C₄×C₄⋊Dic₇₉	C₂²	1	1	yes	characteristic
30	C₄×C₄⋊Dic₇₉	C₂²	1	2	yes	—
31	#19098409	C₂²	1	2	yes	—
32	C₄²×Dic₇₉	C₂²	1	1	yes	characteristic
33	#19098317	C₂²	1	1	yes	characteristic
34	#19098317	C₂²	1	1	yes	characteristic
35	#19098317	C₂²	1	2	yes	—
36	#19098317	C₂²	1	2	yes	—
37	C₂×C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic
38	#446×C₇₉	—	2	4	no	—
39	C₂×C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
40	C₂×C₄⋊C₈×C₇₉	C₂²	1	2	yes	—
41	C₂×#97×C₇₉	C₂²	1	2	yes	—
42	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
43	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
44	C₂²×C₇₉⋊C₈	C₂³	1	2	yes	—
45	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
46	C₂×C₄⋊Dic₇₉	C₂×C₄	1	2	yes	—
47	C₂×C₄⋊Dic₇₉	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄⋊Dic₇₉	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄⋊Dic₇₉	C₂×C₄	1	2	yes	—
50	C₂×C₄×Dic₇₉	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄×Dic₇₉	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄×Dic₇₉	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄×Dic₇₉	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
55	C₂×C₄×Dic₇₉	C₂³	1	2	yes	—
56	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
57	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
58	C₄⋊(C₇₉⋊C₈)	—	2	4	no	—
59	Dic₇₉⋊C₈	—	2	2	no	—
60	Dic₇₉⋊C₈	—	2	4	no	—
61	Dic₇₉⋊C₈	—	4	2	no	—
62	Dic₇₉⋊C₈	—	4	2	no	—
63	Dic₇₉⋊C₈	—	4	2	no	—
64	Dic₇₉⋊C₈	Q₈	1	4	yes	complemented
65	C₄×C₇₉⋊C₈	—	2	2	no	—
66	C₄×C₇₉⋊C₈	—	2	4	no	—
67	C₇₉⋊#95	C₂×C₄	1	2	yes	—
68	C₇₉⋊#95	C₂×C₄	1	2	yes	—
69	C₇₉⋊#95	C₂×C₄	1	2	yes	—
70	C₇₉⋊#95	C₂×C₄	1	2	yes	—
71	C₇₉⋊#95	C₂×C₄	1	2	yes	—
72	C₇₉⋊#95	C₂×C₄	1	2	yes	—
73	C₇₉⋊#95	C₂×C₄	1	2	yes	—
74	C₂²×Q₈×C₇₉	C₂×C₄	1	1	yes	characteristic
75	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
76	C₂²×C₈×C₇₉	C₂³	1	2	yes	—
77	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
78	C₄×Q₈×C₇₉	D₄	1	4	yes	—
79	C₄×Q₈×C₇₉	Q₈	1	4	yes	—
80	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	2	yes	—
81	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
82	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
83	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
84	C₄⋊C₈×C₇₉	—	2	2	no	—
85	C₄⋊C₈×C₇₉	—	2	4	no	—
86	#97×C₇₉	—	2	4	no	—
87	C₄×C₈×C₇₉	—	2	2	no	—
88	C₂²×Dic₇₉	C₂²×C₄	1	2	yes	—
89	C₂²×Dic₇₉	C₂²×C₄	1	2	yes	—
90	C₂²×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
91	C₂²×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
92	C₂²×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
93	C₂²×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
94	C₂×C₇₉⋊C₈	—	2	1	no	—
95	C₂×C₇₉⋊C₈	—	2	1	no	—
96	C₂×C₇₉⋊C₈	—	2	2	no	—
97	C₂×C₇₉⋊C₈	—	2	1	no	—
98	C₂×C₇₉⋊C₈	—	2	2	no	—
99	C₂×C₇₉⋊C₈	—	2	2	no	—
100	C₂×C₇₉⋊C₈	—	2	1	no	—
101	C₂×C₇₉⋊C₈	—	2	1	no	—
102	C₂×C₇₉⋊C₈	C₂×Q₈	1	2	yes	—
103	C₄⋊Dic₇₉	—	2	4	no	—
104	C₄⋊Dic₇₉	—	2	2	no	—
105	C₄⋊Dic₇₉	—	2	2	no	—
106	C₄⋊Dic₇₉	—	4	2	no	—
107	C₄×Dic₇₉	—	2	2	no	—
108	C₄×Dic₇₉	—	2	2	no	—
109	C₄×Dic₇₉	—	2	2	no	—
110	C₄×Dic₇₉	—	2	1	no	—
111	C₄×Dic₇₉	—	2	2	no	—
112	C₄×Dic₇₉	—	2	1	no	—
113	C₄×Dic₇₉	—	2	2	no	—
114	C₄×Dic₇₉	—	4	1	no	—
115	C₄×Dic₇₉	C₂×Q₈	1	2	yes	—
116	C₄×Dic₇₉	#41	1	2	yes	—
117	C₂×Q₈×C₇₉	—	2	2	no	—
118	C₂×Q₈×C₇₉	—	2	2	no	—
119	C₂×Q₈×C₇₉	C₄⋊C₄	1	4	yes	—
120	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
121	C₂²×C₄×C₇₉	C₂²×C₄	1	2	yes	—
122	C₂²×C₄×C₇₉	C₂²×C₄	1	2	yes	—
123	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
124	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
125	C₂×C₈×C₇₉	—	2	1	no	—
126	C₂×C₈×C₇₉	—	2	1	no	—
127	C₂×C₈×C₇₉	—	2	2	no	—
128	C₂×C₈×C₇₉	—	2	1	no	—
129	C₂×C₈×C₇₉	—	2	2	no	—
130	C₂×C₈×C₇₉	—	2	1	no	—
131	C₂×C₈×C₇₉	—	2	2	no	—
132	C₂×C₈×C₇₉	—	2	1	no	—
133	C₂×C₈×C₇₉	C₂×Q₈	1	2	yes	—
134	C₄⋊C₄×C₇₉	C₄⋊C₄	1	8	yes	—
135	C₄⋊C₄×C₇₉	C₄⋊C₄	1	4	yes	—
136	C₄²×C₇₉	C₂×D₄	1	2	yes	—
137	C₄²×C₇₉	C₂×D₄	1	4	yes	—
138	C₄²×C₇₉	C₂×Q₈	1	4	yes	—
139	C₄²×C₇₉	C₂×Q₈	1	2	yes	—
140	C₂³×C₇₉	C₂³×C₄	1	1	yes	characteristic
141	Q₈×C₇₉	—	2	8	no	—
142	C₂×C₄×C₇₉	—	2	1	no	—
143	C₂×C₄×C₇₉	—	2	2	no	—
144	C₂×C₄×C₇₉	—	2	2	no	—
145	C₂×C₄×C₇₉	—	2	2	no	—
146	C₂×C₄×C₇₉	—	2	1	no	—
147	C₂×C₄×C₇₉	—	2	2	no	—
148	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	2	yes	—
149	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	4	yes	—
150	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	4	yes	—
151	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	2	yes	—
152	C₂×C₄×C₇₉	#131	1	2	yes	—
153	C₂×C₄×C₇₉	#131	1	2	yes	—
154	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
155	C₂×C₄×C₇₉	C₂²×Q₈	1	1	yes	characteristic
156	C₂×C₄×C₇₉	C₂²×Q₈	1	1	yes	characteristic
157	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
158	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
159	C₂×C₄×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
160	C₂×Dic₇₉	—	2	1	no	—
161	C₂×Dic₇₉	—	2	1	no	—
162	C₂×Dic₇₉	—	2	1	no	—
163	C₂×Dic₇₉	—	2	1	no	—
164	C₂×Dic₇₉	—	2	1	no	—
165	C₂×Dic₇₉	—	2	1	no	—
166	C₂×Dic₇₉	—	2	2	no	—
167	C₂×Dic₇₉	—	2	1	no	—
168	C₂×Dic₇₉	—	2	2	no	—
169	C₂×Dic₇₉	—	2	1	no	—
170	C₂×Dic₇₉	—	2	2	no	—
171	C₂×Dic₇₉	—	2	2	no	—
172	C₂×Dic₇₉	—	2	2	no	—
173	C₂×Dic₇₉	—	2	1	no	—
174	C₂×Dic₇₉	—	2	2	no	—
175	C₂×Dic₇₉	C₄×Q₈	1	2	yes	—
176	C₂×Dic₇₉	C₄×Q₈	1	2	yes	—
177	C₂×Dic₇₉	#131	1	2	yes	—
178	C₈×C₇₉	—	2	2	no	—
179	C₈×C₇₉	—	4	1	no	—
180	C₈×C₇₉	—	4	2	no	—
181	C₇₉⋊C₈	—	2	2	no	—
182	C₇₉⋊C₈	—	4	1	no	—
183	C₇₉⋊C₈	—	4	2	no	—
184	C₂²×C₇₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
185	C₂²×C₇₉	C₂×C₄×Q₈	1	1	yes	characteristic
186	C₂²×C₇₉	#520	1	1	yes	characteristic
187	C₂²×C₇₉	C₂×#131	1	1	yes	characteristic
188	C₂²×C₇₉	C₂×#131	1	1	yes	characteristic
189	C₂²×C₇₉	C₂×#131	1	1	yes	characteristic
190	C₂²×C₇₉	#568	1	1	yes	characteristic
191	C₄×C₇₉	—	2	4	no	—
192	C₄×C₇₉	—	2	2	no	—
193	C₄×C₇₉	—	2	4	no	—
194	C₄×C₇₉	#424	1	4	yes	—
195	C₄×C₇₉	D₄×Q₈	1	1	yes	characteristic
196	C₄×C₇₉	#550	1	1	yes	characteristic
197	C₄×C₇₉	#557	1	1	yes	characteristic
198	C₄×C₇₉	Q₈²	1	1	yes	characteristic
199	Dic₇₉	—	2	2	no	—
200	Dic₇₉	—	2	2	no	—
201	Dic₇₉	—	2	2	no	—
202	Dic₇₉	—	4	1	no	—
203	Dic₇₉	—	4	2	no	—
204	Dic₇₉	—	4	2	no	—
205	#22721	—	79	1	no	maximal, Sylow
206	C₂×C₇₉	Q₈×C₄⋊C₄	1	1	yes	characteristic
207	C₂×C₇₉	C₂×#424	1	1	yes	characteristic
208	C₂×C₇₉	#2906	1	1	yes	characteristic
209	C₂×C₇₉	#2960	1	1	yes	characteristic
210	C₂×C₇₉	#2962	1	1	yes	characteristic
211	C₂×C₇₉	#2993	1	1	yes	characteristic
212	C₂×C₇₉	#2994	1	1	yes	characteristic
213	C₂×#446	D₇₉	1	1	yes	characteristic
214	C₂×C₈×Q₈	—	79	1	no	—
215	#2295	—	79	1	no	—
216	#1940	—	79	2	no	—
217	#1939	—	79	2	no	—
218	#1939	—	79	1	no	—
219	#1939	—	79	1	no	—
220	#1843	—	79	2	no	—
221	#1842	—	79	1	no	—
222	#1768	—	79	2	no	—
223	C₄×C₄⋊C₈	—	79	1	no	—
224	C₇₉	#22721	1	1	yes	characteristic, complemented, Sylow
225	C₂×C₄×Q₈	C₂×D₇₉	1	1	yes	characteristic
226	#446	—	2	4	no	—
227	C₈×Q₈	—	158	4	no	—
228	C₂×C₄⋊C₈	—	79	2	no	—
229	C₂×C₄⋊C₈	—	79	2	no	—
230	C₂×C₄⋊C₈	—	79	2	no	—
231	C₂×C₄⋊C₈	—	79	1	no	—
232	C₂×C₄⋊C₈	—	79	2	no	—
233	C₂×C₄⋊C₈	—	79	1	no	—
234	C₂×C₄⋊C₈	—	79	1	no	—
235	C₂×C₄⋊C₈	—	79	2	no	—
236	C₂×C₄⋊C₈	C₂×D₇₉	1	1	yes	characteristic
237	C₂×C₄⋊C₈	C₂×D₇₉	1	2	yes	—
238	C₂×#97	C₂×D₇₉	1	2	yes	—
239	C₂×C₄×C₈	—	79	1	no	—
240	C₂×C₄×C₈	—	79	2	no	—
241	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
242	#391	—	79	1	no	—
243	#391	—	79	1	no	—
244	#389	—	79	1	no	—
245	#389	—	79	1	no	—
246	#387	—	79	2	no	—
247	#387	—	79	2	no	—
248	C₄×C₄⋊C₄	—	79	1	no	—
249	C₄×C₄⋊C₄	—	79	2	no	—
250	#376	—	79	2	no	—
251	C₄³	—	79	1	no	—
252	#336	—	79	1	no	—
253	#336	—	79	2	no	—
254	#336	—	79	2	no	—
255	#336	—	79	1	no	—
256	C₂²×Q₈	C₄×D₇₉	1	1	yes	characteristic
257	C₂²×C₈	—	79	1	no	—
258	C₂²×C₈	—	79	2	no	—
259	C₂²×C₈	—	79	1	no	—
260	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
261	C₂²×C₈	C₂²×D₇₉	1	2	yes	—
262	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
263	C₄×Q₈	Dic₁₅₈	1	4	yes	—
264	C₄×Q₈	C₂²⋊D₇₉	1	4	yes	—
265	C₂×C₄⋊C₄	—	79	2	no	—
266	C₂×C₄⋊C₄	—	79	2	no	—
267	C₂×C₄⋊C₄	—	79	1	no	—
268	C₂×C₄⋊C₄	—	79	1	no	—
269	C₂×C₄⋊C₄	C₄×D₇₉	1	2	yes	—
270	C₂×C₄⋊C₄	C₄×D₇₉	1	1	yes	characteristic
271	C₂×C₄²	—	79	1	no	—
272	C₂×C₄²	—	79	1	no	—
273	C₂×C₄²	—	79	1	no	—
274	C₂×C₄²	—	79	1	no	—
275	C₂×C₄²	—	79	1	no	—
276	C₂×C₄²	—	79	1	no	—
277	C₂×C₄²	—	79	2	no	—
278	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
279	C₂×C₄²	C₂²×D₇₉	1	2	yes	—
280	C₄⋊C₈	—	2	2	no	—
281	C₄⋊C₈	—	2	4	no	—
282	C₄⋊C₈	—	316	2	no	—
283	C₄⋊C₈	—	316	2	no	—
284	C₄⋊C₈	—	316	2	no	—
285	C₄⋊C₈	—	79	4	no	—
286	C₄⋊C₈	—	158	4	no	—
287	C₄⋊C₈	—	158	2	no	—
288	C₄⋊C₈	—	158	2	no	—
289	C₄⋊C₈	—	158	4	no	—
290	#97	—	2	4	no	—
291	C₄×C₈	—	2	2	no	—
292	C₄×C₈	—	158	2	no	—
293	C₄×C₈	—	158	4	no	—
294	#95	—	79	2	no	—
295	#95	—	79	2	no	—
296	#95	—	79	2	no	—
297	#95	—	79	2	no	—
298	#95	—	79	2	no	—
299	#95	—	79	2	no	—
300	#95	—	79	2	no	—
301	C₂×Q₈	—	2	2	no	—
302	C₂×Q₈	—	2	2	no	—
303	C₂×Q₈	Dic₇₉⋊C₄	1	4	yes	—
304	C₂²×C₄	—	79	1	no	—
305	C₂²×C₄	—	79	1	no	—
306	C₂²×C₄	—	79	1	no	—
307	C₂²×C₄	—	79	2	no	—
308	C₂²×C₄	—	79	2	no	—
309	C₂²×C₄	—	79	1	no	—
310	C₂²×C₄	C₂×C₄×D₇₉	1	2	yes	—
311	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
312	C₂²×C₄	C₂×C₄×D₇₉	1	2	yes	—
313	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
314	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
315	C₂×C₈	—	2	1	no	—
316	C₂×C₈	—	2	1	no	—
317	C₂×C₈	—	2	1	no	—
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	—	2	1	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	1	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	79	2	no	—
324	C₂×C₈	—	158	2	no	—
325	C₂×C₈	—	158	1	no	—
326	C₂×C₈	—	158	2	no	—
327	C₂×C₈	—	158	1	no	—
328	C₂×C₈	—	158	1	no	—
329	C₂×C₈	—	158	2	no	—
330	C₂×C₈	—	158	1	no	—
331	C₂×C₈	—	158	1	no	—
332	C₂×C₈	Q₈×D₇₉	1	2	yes	—
333	C₄⋊C₄	—	316	2	no	—
334	C₄⋊C₄	—	158	4	no	—
335	C₄⋊C₄	—	158	2	no	—
336	C₄⋊C₄	—	158	2	no	—
337	C₄⋊C₄	Dic₇₉⋊C₄	1	8	yes	—
338	C₄⋊C₄	Dic₇₉⋊C₄	1	4	yes	—
339	C₄²	—	316	1	no	—
340	C₄²	—	79	2	no	—
341	C₄²	—	79	2	no	—
342	C₄²	—	158	2	no	—
343	C₄²	—	158	2	no	—
344	C₄²	—	158	1	no	—
345	C₄²	—	158	2	no	—
346	C₄²	—	158	1	no	—
347	C₄²	—	158	2	no	—
348	C₄²	—	158	2	no	—
349	C₄²	C₂×C₂²⋊D₇₉	1	2	yes	—
350	C₄²	C₂×C₂²⋊D₇₉	1	4	yes	—
351	C₄²	C₂×Dic₁₅₈	1	4	yes	—
352	C₄²	C₂×Dic₁₅₈	1	2	yes	—
353	C₂³	C₂²×C₄×D₇₉	1	1	yes	characteristic
354	Q₈	—	2	8	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	79	2	no	—
362	C₂×C₄	—	79	2	no	—
363	C₂×C₄	—	79	2	no	—
364	C₂×C₄	—	158	2	no	—
365	C₂×C₄	—	158	1	no	—
366	C₂×C₄	—	158	2	no	—
367	C₂×C₄	—	158	2	no	—
368	C₂×C₄	—	158	1	no	—
369	C₂×C₄	—	158	2	no	—
370	C₂×C₄	—	158	2	no	—
371	C₂×C₄	—	158	1	no	—
372	C₂×C₄	—	158	2	no	—
373	C₂×C₄	—	158	1	no	—
374	C₂×C₄	—	158	1	no	—
375	C₂×C₄	—	158	1	no	—
376	C₂×C₄	—	158	1	no	—
377	C₂×C₄	—	158	1	no	—
378	C₂×C₄	—	158	1	no	—
379	C₂×C₄	C₂×Dic₇₉⋊C₄	1	2	yes	—
380	C₂×C₄	C₂×Dic₇₉⋊C₄	1	4	yes	—
381	C₂×C₄	C₂×Dic₇₉⋊C₄	1	4	yes	—
382	C₂×C₄	C₂×Dic₇₉⋊C₄	1	2	yes	—
383	C₂×C₄	#14579169	1	2	yes	—
384	C₂×C₄	#14579169	1	2	yes	—
385	C₂×C₄	C₂²×C₂²⋊D₇₉	1	1	yes	characteristic
386	C₂×C₄	C₂×Q₈×D₇₉	1	1	yes	characteristic
387	C₂×C₄	C₂²×Dic₁₅₈	1	1	yes	characteristic
388	C₂×C₄	#41×D₇₉	1	1	yes	characteristic
389	C₂×C₄	#14579207	1	1	yes	characteristic
390	C₂×C₄	#14579209	1	1	yes	characteristic
391	C₈	—	2	2	no	—
392	C₈	—	4	1	no	—
393	C₈	—	4	2	no	—
394	C₈	—	316	2	no	—
395	C₈	—	316	1	no	—
396	C₈	—	158	2	no	—
397	C₂²	C₂²×Dic₇₉⋊C₄	1	1	yes	characteristic
398	C₂²	C₄×Q₈×D₇₉	1	1	yes	characteristic
399	C₂²	#19099045	1	1	yes	characteristic
400	C₂²	#131×D₇₉	1	1	yes	characteristic
401	C₂²	C₂×#14579169	1	1	yes	characteristic
402	C₂²	C₂×#14579169	1	1	yes	characteristic
403	C₂²	#19099328	1	1	yes	characteristic
404	C₄	—	2	4	no	—
405	C₄	—	2	2	no	—
406	C₄	—	2	4	no	—
407	C₄	—	316	1	no	—
408	C₄	—	316	2	no	—
409	C₄	—	316	2	no	—
410	C₄	—	158	2	no	—
411	C₄	—	158	2	no	—
412	C₄	—	158	2	no	—
413	C₄	#19098591	1	4	yes	—
414	C₄	Q₈×C₂²⋊D₇₉	1	1	yes	characteristic
415	C₄	#19099232	1	1	yes	characteristic
416	C₄	#19099289	1	1	yes	characteristic
417	C₄	Q₈×Dic₁₅₈	1	1	yes	characteristic
418	C₂	Q₈×Dic₇₉⋊C₄	1	1	yes	characteristic
419	C₂	C₂×#19098591	1	1	yes	characteristic
420	C₂	#23771966	1	1	yes	characteristic
421	C₂	#23772331	1	1	yes	characteristic
422	C₂	#23772348	1	1	yes	characteristic
423	C₂	#23772552	1	1	yes	characteristic
424	C₂	#23772563	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₇₉
commutator, socle, prime radical	C₂³×C₇₉	C₂³×C₄
Fitting	C₂×#446×C₇₉	C₂
cosocle	C₂²×C₄×C₇₉	C₂⁴
hypercenter	C₂×#446	D₇₉
hypocenter	C₇₉	#22721
LCS	G ▷ C₂³×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#446

Complements

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

N	H ≅ G/N	type
64. Dic₇₉⋊C₈	Q₈	semidirect
224. C₇₉	#22721	semidirect

Maximal subgroups

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

subgroup	index
C₂×Q₈×C₇₉⋊C₈	2
#23765878	2
#23764123	2
#23764118	2
#23764116	2
#23763553	2
#23763551	2
#23763260	2
C₄×Dic₇₉⋊C₈	2
C₂×#446×C₇₉	2
#22721	79