Subgroups — #34308196

Order 20224.

736 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	C₄×#14579126	C₂	1	1	yes	maximal, characteristic
2	#23764336	C₂	1	1	yes	maximal, characteristic
3	#23764335	C₂	1	1	yes	maximal, characteristic
4	#23763964	C₂	1	2	yes	maximal
5	#23763962	C₂	1	2	yes	maximal
6	#23763551	C₂	1	1	yes	maximal, characteristic
7	#23763515	C₂	1	2	yes	maximal
8	#23763269	C₂	1	1	yes	maximal, characteristic
9	#23763254	C₂	1	2	yes	maximal
10	C₄×Dic₇₉⋊C₈	C₂	1	1	yes	maximal, characteristic
11	C₇₉×#1770	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄×Dic₁₅₈	C₂²	1	1	yes	characteristic
13	C₂×#14579126	C₄	1	1	yes	characteristic
14	C₂×#14579126	C₄	1	1	yes	characteristic
15	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
16	C₂×Dic₇₉⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×Dic₇₉⋊C₈	C₂²	1	2	yes	—
18	C₂×Dic₇₉⋊C₈	C₂²	1	2	yes	—
19	C₂×Dic₇₉⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×#14579072	C₂²	1	2	yes	—
21	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
22	C₄⋊C₄×Dic₇₉	C₄	1	1	yes	characteristic
23	C₄⋊C₄×Dic₇₉	C₄	1	1	yes	characteristic
24	C₄×Dic₇₉⋊C₄	C₂²	1	2	yes	—
25	#19098414	C₄	1	2	yes	—
26	#19098414	C₄	1	2	yes	—
27	C₄²×Dic₇₉	C₂²	1	1	yes	characteristic
28	C₄²×Dic₇₉	C₂²	1	2	yes	—
29	#19098318	C₂²	1	2	yes	—
30	#19098317	C₂²	1	1	yes	characteristic
31	#19098317	C₂²	1	1	yes	characteristic
32	#19098317	C₂²	1	2	yes	—
33	#19098317	C₂²	1	2	yes	—
34	#19098317	C₂²	1	2	yes	—
35	#19098317	C₂²	1	2	yes	—
36	C₂×C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
37	C₂×#97×C₇₉	C₂²	1	2	yes	—
38	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
39	C₄×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
40	#336×C₇₉	C₂²	1	2	yes	—
41	C₂²×Dic₁₅₈	C₂×C₄	1	1	yes	characteristic
42	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
43	C₂²×C₇₉⋊C₈	C₂³	1	2	yes	—
44	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
45	C₄×Dic₁₅₈	—	2	2	no	—
46	C₄×Dic₁₅₈	—	2	2	no	—
47	#14579126	—	2	4	no	—
48	#14579126	—	2	4	no	—
49	C₂×C₄⋊Dic₇₉	C₂×C₄	1	1	yes	characteristic
50	C₂×Dic₇₉⋊C₄	C₂×C₄	1	2	yes	—
51	C₂×Dic₇₉⋊C₄	C₂×C₄	1	2	yes	—
52	C₂×Dic₇₉⋊C₄	C₂×C₄	1	2	yes	—
53	C₂×C₄×Dic₇₉	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄×Dic₇₉	C₂×C₄	1	2	yes	—
55	C₂×C₄×Dic₇₉	C₂×C₄	1	2	yes	—
56	C₂×C₄×Dic₇₉	C₂×C₄	1	2	yes	—
57	C₂×C₄×Dic₇₉	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄×Dic₇₉	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄×Dic₇₉	C₂×C₄	1	2	yes	—
60	C₂×C₄×Dic₇₉	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
62	C₂×C₄×Dic₇₉	C₂³	1	2	yes	—
63	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
64	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
65	Dic₇₉⋊C₈	—	2	2	no	—
66	Dic₇₉⋊C₈	—	2	4	no	—
67	Dic₇₉⋊C₈	—	4	2	no	—
68	Dic₇₉⋊C₈	Q₈	1	4	yes	complemented
69	#14579072	—	4	2	no	—
70	C₄×C₇₉⋊C₈	—	2	2	no	—
71	C₇₉⋊#95	C₂×C₄	1	2	yes	—
72	C₇₉⋊#95	C₂×C₄	1	2	yes	—
73	C₂²×C₈×C₇₉	C₂³	1	2	yes	—
74	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
75	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
76	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
78	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
79	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
80	C₄⋊C₈×C₇₉	—	2	2	no	—
81	#97×C₇₉	—	4	2	no	—
82	C₄×C₈×C₇₉	—	2	2	no	—
83	#95×C₇₉	C₂×C₄	1	2	yes	—
84	C₂×Dic₁₅₈	—	2	2	no	—
85	C₂×Dic₁₅₈	—	2	2	no	—
86	C₂×Dic₁₅₈	M₁₆	1	4	yes	—
87	C₂²×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
88	C₂²×Dic₇₉	C₂²×C₄	1	2	yes	—
89	C₂²×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
90	C₂²×Dic₇₉	C₂²×C₄	1	2	yes	—
91	C₂²×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
92	C₂²×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
93	C₂×C₇₉⋊C₈	—	2	1	no	—
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	2	no	—
98	C₂×C₇₉⋊C₈	—	2	1	no	—
99	C₂×C₇₉⋊C₈	—	2	2	no	—
100	C₂×C₇₉⋊C₈	—	2	1	no	—
101	C₂×C₇₉⋊C₈	C₂×Q₈	1	2	yes	—
102	C₄⋊Dic₇₉	—	2	2	no	—
103	Dic₇₉⋊C₄	—	2	4	no	—
104	Dic₇₉⋊C₄	—	2	4	no	—
105	Dic₇₉⋊C₄	—	2	4	no	—
106	C₄×Dic₇₉	—	2	4	no	—
107	C₄×Dic₇₉	—	2	4	no	—
108	C₄×Dic₇₉	—	2	2	no	—
109	C₄×Dic₇₉	—	2	4	no	—
110	C₄×Dic₇₉	—	2	2	no	—
111	C₄×Dic₇₉	—	2	2	no	—
112	C₄×Dic₇₉	—	2	2	no	—
113	C₄×Dic₇₉	—	2	1	no	—
114	C₄×Dic₇₉	—	2	1	no	—
115	C₄×Dic₇₉	—	4	1	no	—
116	C₄×Dic₇₉	—	4	2	no	—
117	C₄×Dic₇₉	M₁₆	1	4	yes	—
118	C₄×Dic₇₉	C₂×Q₈	1	2	yes	—
119	C₄×Dic₇₉	#41	1	2	yes	—
120	C₂²×C₄×C₇₉	C₂²×C₄	1	2	yes	—
121	C₂²×C₄×C₇₉	C₂²×C₄	1	2	yes	—
122	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
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	—	2	2	no	—
135	C₄⋊C₄×C₇₉	—	2	2	no	—
136	C₄²×C₇₉	—	2	2	no	—
137	C₄²×C₇₉	—	2	2	no	—
138	C₄²×C₇₉	#41	1	2	yes	—
139	C₄²×C₇₉	#41	1	2	yes	—
140	C₂³×C₇₉	C₂³×C₄	1	1	yes	characteristic
141	C₂×C₄×C₇₉	—	2	1	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	2	no	—
147	C₂×C₄×C₇₉	—	2	2	no	—
148	C₂×C₄×C₇₉	—	2	2	no	—
149	C₂×C₄×C₇₉	#117	1	2	yes	—
150	C₂×C₄×C₇₉	#117	1	2	yes	—
151	C₂×C₄×C₇₉	C₂×M₁₆	1	2	yes	—
152	C₂×C₄×C₇₉	C₂×M₁₆	1	2	yes	—
153	C₂×C₄×C₇₉	C₂²×Q₈	1	1	yes	characteristic
154	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
155	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
156	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
157	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
158	C₂×C₄×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
159	C₂×Dic₇₉	—	2	2	no	—
160	C₂×Dic₇₉	—	2	1	no	—
161	C₂×Dic₇₉	—	2	1	no	—
162	C₂×Dic₇₉	—	2	2	no	—
163	C₂×Dic₇₉	—	2	1	no	—
164	C₂×Dic₇₉	—	2	1	no	—
165	C₂×Dic₇₉	—	2	2	no	—
166	C₂×Dic₇₉	—	2	1	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	C₄×Q₈	1	2	yes	—
172	C₂×Dic₇₉	C₄×Q₈	1	2	yes	—
173	C₂×Dic₇₉	C₂×M₁₆	1	4	yes	—
174	C₂×Dic₇₉	C₂×M₁₆	1	2	yes	—
175	C₂×Dic₇₉	C₂×M₁₆	1	2	yes	—
176	C₂×Dic₇₉	#131	1	2	yes	—
177	Dic₁₅₈	—	2	8	no	—
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	C₂×#117	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	C₂²×M₁₆	1	1	yes	characteristic
188	C₂²×C₇₉	C₂²×M₁₆	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	2	no	—
192	C₄×C₇₉	—	4	2	no	—
193	C₄×C₇₉	—	4	2	no	—
194	C₄×C₇₉	#432	1	4	yes	—
195	C₄×C₇₉	#554	1	1	yes	characteristic
196	C₄×C₇₉	#556	1	1	yes	characteristic
197	C₄×C₇₉	#557	1	1	yes	characteristic
198	C₄×C₇₉	#559	1	1	yes	characteristic
199	Dic₇₉	—	2	4	no	—
200	Dic₇₉	—	2	2	no	—
201	Dic₇₉	—	2	2	no	—
202	Dic₇₉	—	4	2	no	—
203	Dic₇₉	—	4	1	no	—
204	Dic₇₉	#446	1	4	yes	—
205	#22825	—	79	1	no	maximal, Sylow
206	C₂×C₇₉	#2355	1	1	yes	characteristic
207	C₂×C₇₉	C₂×#432	1	1	yes	characteristic
208	C₂×C₇₉	#2925	1	1	yes	characteristic
209	C₂×C₇₉	C₂×#446	1	1	yes	characteristic
210	C₂×C₇₉	Q₈×M₁₆	1	1	yes	characteristic
211	C₂×C₇₉	#2989	1	1	yes	characteristic
212	C₂×C₇₉	#2991	1	1	yes	characteristic
213	C₄²×Q₈	—	79	1	no	—
214	#1984	—	79	1	no	—
215	#1984	—	79	1	no	—
216	#1917	—	79	2	no	—
217	#1917	—	79	2	no	—
218	#1842	—	79	1	no	—
219	#1831	—	79	2	no	—
220	#1770	—	79	1	no	—
221	#1770	D₇₉	1	1	yes	characteristic
222	#1767	—	79	2	no	—
223	C₄×C₄⋊C₈	—	79	1	no	—
224	C₇₉	#22825	1	1	yes	characteristic, complemented, Sylow
225	C₂×C₄×Q₈	—	79	1	no	—
226	C₂×C₄×Q₈	—	79	1	no	—
227	C₂×C₄×Q₈	—	79	1	no	—
228	C₂×C₄⋊C₈	—	79	2	no	—
229	C₂×C₄⋊C₈	—	79	1	no	—
230	C₂×C₄⋊C₈	—	79	1	no	—
231	C₂×C₄⋊C₈	—	79	2	no	—
232	C₂×C₄⋊C₈	—	79	1	no	—
233	C₂×C₄⋊C₈	C₂×D₇₉	1	1	yes	characteristic
234	C₂×#97	—	79	2	no	—
235	C₂×#97	C₂×D₇₉	1	2	yes	—
236	C₂×C₄×C₈	—	79	1	no	—
237	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
238	C₄×C₄⋊C₄	—	79	1	no	—
239	C₄×C₄⋊C₄	—	79	1	no	—
240	C₄×C₄⋊C₄	—	79	2	no	—
241	C₄×C₄⋊C₄	—	79	2	no	—
242	C₄×C₄⋊C₄	—	79	2	no	—
243	C₄×C₄⋊C₄	C₂×D₇₉	1	1	yes	characteristic
244	C₄³	—	79	2	no	—
245	C₄³	—	79	1	no	—
246	#336	—	79	2	no	—
247	#336	—	79	2	no	—
248	#336	—	79	1	no	—
249	#336	—	79	1	no	—
250	#336	—	79	2	no	—
251	#336	—	79	2	no	—
252	#336	—	79	2	no	—
253	#336	C₂×D₇₉	1	2	yes	—
254	C₂²×Q₈	—	79	1	no	—
255	C₂²×C₈	—	79	1	no	—
256	C₂²×C₈	—	79	1	no	—
257	C₂²×C₈	—	79	2	no	—
258	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
259	C₂²×C₈	C₂²×D₇₉	1	2	yes	—
260	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
261	C₄×Q₈	—	158	4	no	—
262	C₄×Q₈	—	158	4	no	—
263	C₄×Q₈	—	158	2	no	—
264	C₄×Q₈	—	158	2	no	—
265	C₂×C₄⋊C₄	—	79	2	no	—
266	C₂×C₄⋊C₄	—	79	2	no	—
267	C₂×C₄⋊C₄	—	79	2	no	—
268	C₂×C₄⋊C₄	—	79	1	no	—
269	C₂×C₄⋊C₄	C₄×D₇₉	1	1	yes	characteristic
270	C₂×C₄⋊C₄	C₄×D₇₉	1	1	yes	characteristic
271	C₂×C₄²	—	79	1	no	—
272	C₂×C₄²	—	79	2	no	—
273	C₂×C₄²	—	79	1	no	—
274	C₂×C₄²	—	79	1	no	—
275	C₂×C₄²	—	79	2	no	—
276	C₂×C₄²	—	79	2	no	—
277	C₂×C₄²	—	79	1	no	—
278	C₂×C₄²	—	79	2	no	—
279	C₂×C₄²	—	79	1	no	—
280	C₂×C₄²	—	79	2	no	—
281	C₂×C₄²	—	79	1	no	—
282	C₂×C₄²	C₂²×D₇₉	1	2	yes	—
283	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
284	C₄⋊C₈	—	2	2	no	—
285	C₄⋊C₈	—	316	2	no	—
286	C₄⋊C₈	—	79	4	no	—
287	C₄⋊C₈	—	158	2	no	—
288	C₄⋊C₈	—	158	4	no	—
289	C₄⋊C₈	—	158	2	no	—
290	#97	—	4	2	no	—
291	#97	—	316	2	no	—
292	C₄×C₈	—	2	2	no	—
293	C₄×C₈	—	158	2	no	—
294	#95	—	79	2	no	—
295	#95	—	79	2	no	—
296	#95	C₄×D₇₉	1	2	yes	—
297	C₂×Q₈	—	79	4	no	—
298	C₂×Q₈	—	158	2	no	—
299	C₂×Q₈	—	158	2	no	—
300	C₂²×C₄	—	79	1	no	—
301	C₂²×C₄	—	79	1	no	—
302	C₂²×C₄	—	79	1	no	—
303	C₂²×C₄	—	79	2	no	—
304	C₂²×C₄	—	79	2	no	—
305	C₂²×C₄	—	79	1	no	—
306	C₂²×C₄	C₂×C₄×D₇₉	1	2	yes	—
307	C₂²×C₄	C₂×C₄×D₇₉	1	2	yes	—
308	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
309	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
310	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
311	C₂×C₈	—	2	1	no	—
312	C₂×C₈	—	2	1	no	—
313	C₂×C₈	—	2	1	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	2	1	no	—
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	—	2	1	no	—
319	C₂×C₈	—	79	2	no	—
320	C₂×C₈	—	158	1	no	—
321	C₂×C₈	—	158	2	no	—
322	C₂×C₈	—	158	1	no	—
323	C₂×C₈	—	158	2	no	—
324	C₂×C₈	—	158	2	no	—
325	C₂×C₈	—	158	1	no	—
326	C₂×C₈	—	158	1	no	—
327	C₂×C₈	—	158	1	no	—
328	C₂×C₈	Q₈×D₇₉	1	2	yes	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	—	158	4	no	—
332	C₄⋊C₄	—	158	4	no	—
333	C₄⋊C₄	—	158	4	no	—
334	C₄⋊C₄	—	158	2	no	—
335	C₄²	—	2	2	no	—
336	C₄²	—	2	2	no	—
337	C₄²	—	316	1	no	—
338	C₄²	—	316	2	no	—
339	C₄²	—	79	2	no	—
340	C₄²	—	79	2	no	—
341	C₄²	—	79	4	no	—
342	C₄²	—	158	2	no	—
343	C₄²	—	158	4	no	—
344	C₄²	—	158	4	no	—
345	C₄²	—	158	4	no	—
346	C₄²	—	158	2	no	—
347	C₄²	—	158	2	no	—
348	C₄²	—	158	1	no	—
349	C₄²	—	158	1	no	—
350	C₄²	—	158	2	no	—
351	C₄²	#11929624	1	2	yes	—
352	C₄²	#11929624	1	2	yes	—
353	C₂³	C₂²×C₄×D₇₉	1	1	yes	characteristic
354	Q₈	—	158	8	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	79	2	no	—
364	C₂×C₄	—	79	2	no	—
365	C₂×C₄	—	79	2	no	—
366	C₂×C₄	—	79	2	no	—
367	C₂×C₄	—	79	2	no	—
368	C₂×C₄	—	79	4	no	—
369	C₂×C₄	—	158	2	no	—
370	C₂×C₄	—	158	1	no	—
371	C₂×C₄	—	158	1	no	—
372	C₂×C₄	—	158	1	no	—
373	C₂×C₄	—	158	2	no	—
374	C₂×C₄	—	158	2	no	—
375	C₂×C₄	—	158	2	no	—
376	C₂×C₄	—	158	1	no	—
377	C₂×C₄	—	158	1	no	—
378	C₂×C₄	—	158	2	no	—
379	C₂×C₄	—	158	1	no	—
380	C₂×C₄	—	158	1	no	—
381	C₂×C₄	#14579118	1	2	yes	—
382	C₂×C₄	#14579118	1	2	yes	—
383	C₂×C₄	M₁₆×D₇₉	1	2	yes	—
384	C₂×C₄	M₁₆×D₇₉	1	2	yes	—
385	C₂×C₄	C₂×Q₈×D₇₉	1	1	yes	characteristic
386	C₂×C₄	#41×D₇₉	1	1	yes	characteristic
387	C₂×C₄	C₂×#11929624	1	1	yes	characteristic
388	C₂×C₄	C₂×#11929624	1	1	yes	characteristic
389	C₂×C₄	#14579206	1	1	yes	characteristic
390	C₂×C₄	#14579208	1	1	yes	characteristic
391	C₈	—	2	2	no	—
392	C₈	—	4	1	no	—
393	C₈	—	4	2	no	—
394	C₈	—	316	1	no	—
395	C₈	—	316	2	no	—
396	C₈	—	158	2	no	—
397	C₂²	C₂×#14579118	1	1	yes	characteristic
398	C₂²	C₄×Q₈×D₇₉	1	1	yes	characteristic
399	C₂²	#19099042	1	1	yes	characteristic
400	C₂²	C₂×M₁₆×D₇₉	1	1	yes	characteristic
401	C₂²	C₂×M₁₆×D₇₉	1	1	yes	characteristic
402	C₂²	#131×D₇₉	1	1	yes	characteristic
403	C₂²	#19099328	1	1	yes	characteristic
404	C₄	—	2	2	no	—
405	C₄	—	4	2	no	—
406	C₄	—	4	2	no	—
407	C₄	—	316	1	no	—
408	C₄	—	316	2	no	—
409	C₄	—	79	4	no	—
410	C₄	—	158	2	no	—
411	C₄	—	158	4	no	—
412	C₄	—	158	2	no	—
413	C₄	#19098618	1	4	yes	—
414	C₄	#19099268	1	1	yes	characteristic
415	C₄	#19099281	1	1	yes	characteristic
416	C₄	#19099291	1	1	yes	characteristic
417	C₄	#19099296	1	1	yes	characteristic
418	C₂	#23766353	1	1	yes	characteristic
419	C₂	C₂×#19098618	1	1	yes	characteristic
420	C₂	#23772064	1	1	yes	characteristic
421	C₂	#446×D₇₉	1	1	yes	characteristic
422	C₂	#23772352	1	1	yes	characteristic
423	C₂	#23772515	1	1	yes	characteristic
424	C₂	#23772528	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₇₉
commutator, socle, prime radical	C₂³×C₇₉	C₂³×C₄
Fitting	C₇₉×#1770	C₂
cosocle	C₂²×C₄×C₇₉	C₂⁴
hypercenter	#1770	D₇₉
hypocenter	C₇₉	#22825
LCS	G ▷ C₂³×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂²×C₄ ◁ #1770

Complements

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

N	H ≅ G/N	type
68. Dic₇₉⋊C₈	Q₈	semidirect
224. C₇₉	#22825	semidirect

Maximal subgroups

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

subgroup	index
C₄×#14579126	2
#23764336	2
#23764335	2
#23763964	2
#23763962	2
#23763551	2
#23763515	2
#23763269	2
#23763254	2
C₄×Dic₇₉⋊C₈	2
C₇₉×#1770	2
#22825	79