Subgroups — #34307173

Order 20224.

876 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×Dic₁₅₈	C₂	1	1	yes	maximal, characteristic
2	C₂×#19098687	C₂	1	1	yes	maximal, characteristic
3	C₄×#14579126	C₂	1	1	yes	maximal, characteristic
4	#23764119	C₂	1	1	yes	maximal, characteristic
5	#23764117	C₂	1	2	yes	maximal
6	#23764115	C₂	1	2	yes	maximal
7	#23763516	C₂	1	1	yes	maximal, characteristic
8	#23763515	C₂	1	2	yes	maximal
9	C₄⋊C₈×Dic₇₉	C₂	1	2	yes	maximal
10	C₄×Dic₇₉⋊C₈	C₂	1	1	yes	maximal, characteristic
11	C₇₉×#1939	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	C₈×Dic₁₅₈	—	2	4	no	—
16	#19098687	—	2	4	no	—
17	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
18	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
19	C₂×Dic₇₉⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×Dic₇₉⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×Dic₇₉⋊C₈	C₂²	1	2	yes	—
22	C₂×Dic₇₉⋊C₈	C₂²	1	2	yes	—
23	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₈×Dic₇₉	C₂²	1	2	yes	—
25	C₂×C₈×Dic₇₉	C₂²	1	2	yes	—
26	C₄⋊C₄×Dic₇₉	C₄	1	1	yes	characteristic
27	C₄⋊C₄×Dic₇₉	C₄	1	1	yes	characteristic
28	C₄×Dic₇₉⋊C₄	C₂²	1	2	yes	—
29	#19098414	C₄	1	2	yes	—
30	#19098414	C₄	1	2	yes	—
31	C₄²×Dic₇₉	C₂²	1	1	yes	characteristic
32	C₄²×Dic₇₉	C₂²	1	2	yes	—
33	#19098318	C₂²	1	2	yes	—
34	#19098317	C₂²	1	1	yes	characteristic
35	#19098317	C₂²	1	1	yes	characteristic
36	#19098317	C₂²	1	2	yes	—
37	#19098317	C₂²	1	2	yes	—
38	C₂×C₄⋊C₈×C₇₉	C₂²	1	2	yes	—
39	C₂×C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
41	C₄×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
42	#336×C₇₉	C₂²	1	2	yes	—
43	C₂²×Dic₁₅₈	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₇₉⋊C₈	C₂³	1	2	yes	—
45	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
46	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
47	C₄×Dic₁₅₈	D₄	1	4	yes	—
48	C₄×Dic₁₅₈	Q₈	1	4	yes	—
49	#14579126	—	2	4	no	—
50	#14579126	C₈	1	8	yes	complemented
51	C₂×C₄⋊Dic₇₉	C₂×C₄	1	1	yes	characteristic
52	C₂×Dic₇₉⋊C₄	C₂×C₄	1	2	yes	—
53	C₂×Dic₇₉⋊C₄	C₂×C₄	1	2	yes	—
54	C₂×Dic₇₉⋊C₄	C₂×C₄	1	2	yes	—
55	C₂×C₄×Dic₇₉	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄×Dic₇₉	C₂×C₄	1	2	yes	—
57	C₂×C₄×Dic₇₉	C₂×C₄	1	2	yes	—
58	C₂×C₄×Dic₇₉	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄×Dic₇₉	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄×Dic₇₉	C₂×C₄	1	2	yes	—
61	C₂×C₄×Dic₇₉	C₂×C₄	1	2	yes	—
62	C₂×C₄×Dic₇₉	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
64	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
65	C₂×C₄×Dic₇₉	C₂³	1	2	yes	—
66	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
67	C₄⋊(C₇₉⋊C₈)	—	2	4	no	—
68	Dic₇₉⋊C₈	—	2	2	no	—
69	Dic₇₉⋊C₈	—	2	2	no	—
70	Dic₇₉⋊C₈	—	2	4	no	—
71	Dic₇₉⋊C₈	—	2	4	no	—
72	C₄×C₇₉⋊C₈	—	2	2	no	—
73	C₈×Dic₇₉	—	2	4	no	—
74	C₈×Dic₇₉	—	2	4	no	—
75	C₇₉⋊#95	C₂×C₄	1	2	yes	—
76	C₇₉⋊#95	C₂×C₄	1	2	yes	—
77	C₂²×C₈×C₇₉	C₂³	1	2	yes	—
78	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
79	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
80	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
82	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
83	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
84	C₄⋊C₈×C₇₉	—	2	4	no	—
85	C₄⋊C₈×C₇₉	—	2	2	no	—
86	C₄×C₈×C₇₉	—	2	2	no	—
87	#95×C₇₉	C₂×C₄	1	2	yes	—
88	C₂×Dic₁₅₈	C₄⋊C₄	1	4	yes	—
89	C₂×Dic₁₅₈	C₂×C₈	1	4	yes	—
90	C₂×Dic₁₅₈	M₁₆	1	4	yes	—
91	C₂²×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
92	C₂²×Dic₇₉	C₂²×C₄	1	2	yes	—
93	C₂²×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
94	C₂²×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
95	C₂²×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
96	C₂²×Dic₇₉	C₂²×C₄	1	2	yes	—
97	C₂×C₇₉⋊C₈	—	2	1	no	—
98	C₂×C₇₉⋊C₈	—	2	2	no	—
99	C₂×C₇₉⋊C₈	—	2	1	no	—
100	C₂×C₇₉⋊C₈	—	2	1	no	—
101	C₂×C₇₉⋊C₈	—	2	2	no	—
102	C₂×C₇₉⋊C₈	—	2	1	no	—
103	C₂×C₇₉⋊C₈	—	2	1	no	—
104	C₂×C₇₉⋊C₈	—	2	2	no	—
105	C₂×C₇₉⋊C₈	#41	1	2	yes	—
106	C₄⋊Dic₇₉	C₄⋊C₄	1	4	yes	—
107	Dic₇₉⋊C₄	—	2	4	no	—
108	Dic₇₉⋊C₄	C₄⋊C₄	1	8	yes	—
109	Dic₇₉⋊C₄	C₂×C₈	1	8	yes	—
110	C₄×Dic₇₉	—	2	4	no	—
111	C₄×Dic₇₉	—	2	2	no	—
112	C₄×Dic₇₉	—	2	4	no	—
113	C₄×Dic₇₉	—	2	2	no	—
114	C₄×Dic₇₉	—	2	1	no	—
115	C₄×Dic₇₉	—	2	1	no	—
116	C₄×Dic₇₉	—	2	1	no	—
117	C₄×Dic₇₉	—	2	1	no	—
118	C₄×Dic₇₉	—	4	1	no	—
119	C₄×Dic₇₉	—	4	2	no	—
120	C₄×Dic₇₉	C₂×C₈	1	8	yes	—
121	C₄×Dic₇₉	C₂×C₈	1	4	yes	—
122	C₄×Dic₇₉	C₂×D₄	1	4	yes	—
123	C₄×Dic₇₉	C₂×Q₈	1	4	yes	—
124	C₂²×C₄×C₇₉	C₂²×C₄	1	2	yes	—
125	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
126	C₂²×C₄×C₇₉	C₂²×C₄	1	2	yes	—
127	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
128	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
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	1	no	—
134	C₂×C₈×C₇₉	—	2	1	no	—
135	C₂×C₈×C₇₉	—	2	2	no	—
136	C₂×C₈×C₇₉	—	2	1	no	—
137	C₂×C₈×C₇₉	#41	1	2	yes	—
138	C₄⋊C₄×C₇₉	—	2	2	no	—
139	C₄⋊C₄×C₇₉	C₂×C₈	1	4	yes	—
140	C₄²×C₇₉	—	2	2	no	—
141	C₄²×C₇₉	—	2	2	no	—
142	C₄²×C₇₉	C₂×D₄	1	2	yes	—
143	C₄²×C₇₉	C₂×Q₈	1	2	yes	—
144	C₂³×C₇₉	C₂³×C₄	1	1	yes	characteristic
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	—	2	1	no	—
149	C₂×C₄×C₇₉	—	2	2	no	—
150	C₂×C₄×C₇₉	—	2	2	no	—
151	C₂×C₄×C₇₉	—	2	2	no	—
152	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	2	yes	—
153	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	2	yes	—
154	C₂×C₄×C₇₉	C₂²×C₈	1	4	yes	—
155	C₂×C₄×C₇₉	C₂²×C₈	1	2	yes	—
156	C₂×C₄×C₇₉	C₂×M₁₆	1	2	yes	—
157	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
158	C₂×C₄×C₇₉	C₂²×Q₈	1	1	yes	characteristic
159	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
160	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
161	C₂×C₄×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
162	C₂×C₄×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
163	C₂×Dic₇₉	—	2	1	no	—
164	C₂×Dic₇₉	—	2	1	no	—
165	C₂×Dic₇₉	—	2	1	no	—
166	C₂×Dic₇₉	—	2	1	no	—
167	C₂×Dic₇₉	—	2	2	no	—
168	C₂×Dic₇₉	—	2	1	no	—
169	C₂×Dic₇₉	—	2	1	no	—
170	C₂×Dic₇₉	—	2	2	no	—
171	C₂×Dic₇₉	—	2	1	no	—
172	C₂×Dic₇₉	—	2	1	no	—
173	C₂×Dic₇₉	—	2	1	no	—
174	C₂×Dic₇₉	C₂×C₄⋊C₄	1	4	yes	—
175	C₂×Dic₇₉	C₂×C₄⋊C₄	1	4	yes	—
176	C₂×Dic₇₉	C₂²×C₈	1	2	yes	—
177	C₂×Dic₇₉	C₂²×C₈	1	2	yes	—
178	C₂×Dic₇₉	C₂²×C₈	1	4	yes	—
179	C₂×Dic₇₉	C₂×M₁₆	1	4	yes	—
180	C₂×Dic₇₉	#131	1	2	yes	—
181	Dic₁₅₈	C₄⋊C₈	1	16	yes	complemented
182	C₈×C₇₉	—	2	2	no	—
183	C₈×C₇₉	—	4	2	no	—
184	C₈×C₇₉	—	4	1	no	—
185	C₇₉⋊C₈	—	2	2	no	—
186	C₇₉⋊C₈	—	4	1	no	—
187	C₇₉⋊C₈	—	4	2	no	—
188	C₂²×C₇₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
189	C₂²×C₇₉	C₄×#41	1	1	yes	characteristic
190	C₂²×C₇₉	#519	1	1	yes	characteristic
191	C₂²×C₇₉	C₂³×C₈	1	1	yes	characteristic
192	C₂²×C₇₉	C₂²×M₁₆	1	1	yes	characteristic
193	C₂²×C₇₉	C₂×#131	1	1	yes	characteristic
194	C₂²×C₇₉	#568	1	1	yes	characteristic
195	C₄×C₇₉	—	2	2	no	—
196	C₄×C₇₉	—	2	4	no	—
197	C₄×C₇₉	—	4	2	no	—
198	C₄×C₇₉	C₂×C₄⋊C₈	1	4	yes	—
199	C₄×C₇₉	#548	1	1	yes	characteristic
200	C₄×C₇₉	#548	1	1	yes	characteristic
201	C₄×C₇₉	#557	1	1	yes	characteristic
202	C₄×C₇₉	#557	1	1	yes	characteristic
203	Dic₇₉	—	2	4	no	—
204	Dic₇₉	—	2	2	no	—
205	Dic₇₉	—	2	2	no	—
206	Dic₇₉	—	2	2	no	—
207	Dic₇₉	—	4	1	no	—
208	Dic₇₉	C₂×C₄⋊C₈	1	8	yes	—
209	#22734	—	79	1	no	maximal, Sylow
210	C₂×C₇₉	#2351	1	1	yes	characteristic
211	C₂×C₇₉	C₂²×C₄⋊C₈	1	1	yes	characteristic
212	C₂×C₇₉	#2906	1	1	yes	characteristic
213	C₂×C₇₉	C₈×#41	1	1	yes	characteristic
214	C₂×C₇₉	#2971	1	1	yes	characteristic
215	C₂×C₇₉	#2982	1	1	yes	characteristic
216	C₂×C₇₉	#2984	1	1	yes	characteristic
217	C₂×C₈×Q₈	—	79	1	no	—
218	C₂×C₈×Q₈	—	79	1	no	—
219	C₄²×Q₈	—	79	1	no	—
220	#1939	—	79	2	no	—
221	#1939	—	79	1	no	—
222	#1939	—	79	2	no	—
223	#1939	D₇₉	1	1	yes	characteristic
224	#1831	—	79	1	no	—
225	#1831	—	79	2	no	—
226	C₄×C₄⋊C₈	—	79	2	no	—
227	C₄×C₄⋊C₈	—	79	1	no	—
228	C₇₉	#22734	1	1	yes	characteristic, complemented, Sylow
229	C₂×C₄×Q₈	—	79	1	no	—
230	C₂×C₄×Q₈	—	79	1	no	—
231	C₂×C₄×Q₈	—	79	1	no	—
232	C₈×Q₈	—	158	4	no	—
233	C₈×Q₈	—	158	4	no	—
234	C₂×C₄⋊C₈	—	79	2	no	—
235	C₂×C₄⋊C₈	—	79	2	no	—
236	C₂×C₄⋊C₈	—	79	1	no	—
237	C₂×C₄⋊C₈	—	79	1	no	—
238	C₂×C₄⋊C₈	—	79	1	no	—
239	C₂×C₄⋊C₈	—	79	2	no	—
240	C₂×C₄⋊C₈	C₂×D₇₉	1	1	yes	characteristic
241	C₂×C₄⋊C₈	C₂×D₇₉	1	2	yes	—
242	C₂×C₄×C₈	—	79	2	no	—
243	C₂×C₄×C₈	—	79	2	no	—
244	C₂×C₄×C₈	—	79	1	no	—
245	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
246	C₄×C₄⋊C₄	—	79	1	no	—
247	C₄×C₄⋊C₄	—	79	1	no	—
248	C₄×C₄⋊C₄	—	79	2	no	—
249	C₄×C₄⋊C₄	—	79	2	no	—
250	C₄×C₄⋊C₄	—	79	2	no	—
251	C₄×C₄⋊C₄	C₂×D₇₉	1	1	yes	characteristic
252	C₄³	—	79	2	no	—
253	C₄³	—	79	1	no	—
254	#336	—	79	2	no	—
255	#336	—	79	1	no	—
256	#336	—	79	2	no	—
257	#336	—	79	1	no	—
258	#336	—	79	2	no	—
259	#336	C₂×D₇₉	1	2	yes	—
260	C₂²×Q₈	—	79	1	no	—
261	C₂²×C₈	—	79	1	no	—
262	C₂²×C₈	—	79	2	no	—
263	C₂²×C₈	—	79	1	no	—
264	C₂²×C₈	C₂²×D₇₉	1	2	yes	—
265	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
266	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
267	C₄×Q₈	—	79	8	no	—
268	C₄×Q₈	—	79	4	no	—
269	C₄×Q₈	—	79	4	no	—
270	C₄×Q₈	—	158	4	no	—
271	C₂×C₄⋊C₄	—	79	2	no	—
272	C₂×C₄⋊C₄	—	79	2	no	—
273	C₂×C₄⋊C₄	—	79	1	no	—
274	C₂×C₄⋊C₄	—	79	2	no	—
275	C₂×C₄⋊C₄	C₄×D₇₉	1	1	yes	characteristic
276	C₂×C₄⋊C₄	C₄×D₇₉	1	1	yes	characteristic
277	C₂×C₄²	—	79	2	no	—
278	C₂×C₄²	—	79	1	no	—
279	C₂×C₄²	—	79	2	no	—
280	C₂×C₄²	—	79	1	no	—
281	C₂×C₄²	—	79	2	no	—
282	C₂×C₄²	—	79	2	no	—
283	C₂×C₄²	—	79	1	no	—
284	C₂×C₄²	—	79	1	no	—
285	C₂×C₄²	—	79	2	no	—
286	C₂×C₄²	—	79	1	no	—
287	C₂×C₄²	—	79	1	no	—
288	C₂×C₄²	C₂²×D₇₉	1	2	yes	—
289	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
290	C₄⋊C₈	—	2	4	no	—
291	C₄⋊C₈	—	2	2	no	—
292	C₄⋊C₈	—	158	4	no	—
293	C₄⋊C₈	—	158	4	no	—
294	C₄⋊C₈	—	158	4	no	—
295	C₄⋊C₈	—	158	2	no	—
296	C₄⋊C₈	—	158	2	no	—
297	C₄⋊C₈	—	158	2	no	—
298	C₄×C₈	—	2	2	no	—
299	C₄×C₈	—	158	4	no	—
300	C₄×C₈	—	158	4	no	—
301	C₄×C₈	—	158	2	no	—
302	#95	—	79	2	no	—
303	#95	—	79	2	no	—
304	#95	C₄×D₇₉	1	2	yes	—
305	C₂×Q₈	—	79	4	no	—
306	C₂×Q₈	—	79	4	no	—
307	C₂×Q₈	—	79	4	no	—
308	C₂²×C₄	—	79	2	no	—
309	C₂²×C₄	—	79	2	no	—
310	C₂²×C₄	—	79	1	no	—
311	C₂²×C₄	—	79	1	no	—
312	C₂²×C₄	—	79	1	no	—
313	C₂²×C₄	—	79	1	no	—
314	C₂²×C₄	C₂×C₄×D₇₉	1	2	yes	—
315	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
316	C₂²×C₄	C₂×C₄×D₇₉	1	2	yes	—
317	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
318	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
319	C₂×C₈	—	2	1	no	—
320	C₂×C₈	—	2	1	no	—
321	C₂×C₈	—	2	1	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	2	1	no	—
325	C₂×C₈	—	2	1	no	—
326	C₂×C₈	—	2	2	no	—
327	C₂×C₈	—	79	2	no	—
328	C₂×C₈	—	158	2	no	—
329	C₂×C₈	—	158	1	no	—
330	C₂×C₈	—	158	1	no	—
331	C₂×C₈	—	158	2	no	—
332	C₂×C₈	—	158	1	no	—
333	C₂×C₈	—	158	2	no	—
334	C₂×C₈	—	158	1	no	—
335	C₂×C₈	—	158	1	no	—
336	C₂×C₈	#11929623	1	2	yes	—
337	C₄⋊C₄	—	2	2	no	—
338	C₄⋊C₄	—	79	8	no	—
339	C₄⋊C₄	—	79	4	no	—
340	C₄⋊C₄	—	79	8	no	—
341	C₄⋊C₄	—	158	4	no	—
342	C₄⋊C₄	C₈×D₇₉	1	4	yes	—
343	C₄²	—	2	2	no	—
344	C₄²	—	2	2	no	—
345	C₄²	—	316	1	no	—
346	C₄²	—	316	2	no	—
347	C₄²	—	79	4	no	—
348	C₄²	—	79	8	no	—
349	C₄²	—	79	4	no	—
350	C₄²	—	79	4	no	—
351	C₄²	—	158	2	no	—
352	C₄²	—	158	4	no	—
353	C₄²	—	158	4	no	—
354	C₄²	—	158	1	no	—
355	C₄²	—	158	1	no	—
356	C₄²	—	158	1	no	—
357	C₄²	—	158	1	no	—
358	C₄²	—	158	2	no	—
359	C₄²	D₄×D₇₉	1	2	yes	—
360	C₄²	Q₈×D₇₉	1	2	yes	—
361	C₂³	C₂²×C₄×D₇₉	1	1	yes	characteristic
362	Q₈	—	79	16	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	79	4	no	—
371	C₂×C₄	—	79	4	no	—
372	C₂×C₄	—	79	4	no	—
373	C₂×C₄	—	79	4	no	—
374	C₂×C₄	—	79	2	no	—
375	C₂×C₄	—	79	2	no	—
376	C₂×C₄	—	79	2	no	—
377	C₂×C₄	—	158	1	no	—
378	C₂×C₄	—	158	1	no	—
379	C₂×C₄	—	158	1	no	—
380	C₂×C₄	—	158	1	no	—
381	C₂×C₄	—	158	1	no	—
382	C₂×C₄	—	158	1	no	—
383	C₂×C₄	—	158	1	no	—
384	C₂×C₄	—	158	2	no	—
385	C₂×C₄	—	158	1	no	—
386	C₂×C₄	—	158	1	no	—
387	C₂×C₄	—	158	2	no	—
388	C₂×C₄	C₄⋊C₄×D₇₉	1	2	yes	—
389	C₂×C₄	C₄⋊C₄×D₇₉	1	2	yes	—
390	C₂×C₄	C₂×C₈×D₇₉	1	4	yes	—
391	C₂×C₄	C₂×C₈×D₇₉	1	2	yes	—
392	C₂×C₄	M₁₆×D₇₉	1	2	yes	—
393	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
394	C₂×C₄	C₂×Q₈×D₇₉	1	1	yes	characteristic
395	C₂×C₄	#41×D₇₉	1	1	yes	characteristic
396	C₂×C₄	C₂×#11929623	1	1	yes	characteristic
397	C₂×C₄	#14579208	1	1	yes	characteristic
398	C₂×C₄	#14579209	1	1	yes	characteristic
399	C₈	—	2	2	no	—
400	C₈	—	4	2	no	—
401	C₈	—	4	1	no	—
402	C₈	—	316	1	no	—
403	C₈	—	316	2	no	—
404	C₈	—	158	2	no	—
405	C₂²	C₂×C₄⋊C₄×D₇₉	1	1	yes	characteristic
406	C₂²	C₄×#11929623	1	1	yes	characteristic
407	C₂²	#19099039	1	1	yes	characteristic
408	C₂²	C₂²×C₈×D₇₉	1	1	yes	characteristic
409	C₂²	C₂×M₁₆×D₇₉	1	1	yes	characteristic
410	C₂²	#131×D₇₉	1	1	yes	characteristic
411	C₂²	#19099328	1	1	yes	characteristic
412	C₄	—	2	2	no	—
413	C₄	—	2	4	no	—
414	C₄	—	4	2	no	—
415	C₄	—	316	1	no	—
416	C₄	—	79	8	no	—
417	C₄	—	158	4	no	—
418	C₄	—	158	2	no	—
419	C₄	—	158	2	no	—
420	C₄	—	158	2	no	—
421	C₄	C₄⋊C₈×D₇₉	1	4	yes	—
422	C₄	#19099219	1	1	yes	characteristic
423	C₄	#19099223	1	1	yes	characteristic
424	C₄	#19099288	1	1	yes	characteristic
425	C₄	#19099290	1	1	yes	characteristic
426	C₂	#23766319	1	1	yes	characteristic
427	C₂	C₂×C₄⋊C₈×D₇₉	1	1	yes	characteristic
428	C₂	#23771967	1	1	yes	characteristic
429	C₂	C₈×#11929623	1	1	yes	characteristic
430	C₂	#23772416	1	1	yes	characteristic
431	C₂	#23772479	1	1	yes	characteristic
432	C₂	#23772486	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₇₉
commutator	C₂²×C₇₉	C₂³×C₈
Fitting	C₇₉×#1939	C₂
socle, prime radical	C₂³×C₇₉	C₂³×C₄
cosocle	C₂²×C₄×C₇₉	C₂⁴
hypercenter	#1939	D₇₉
hypocenter	C₇₉	#22734
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂²×C₄ ◁ #1939

Complements

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

N	H ≅ G/N	type
50. #14579126	C₈	semidirect
181. Dic₁₅₈	C₄⋊C₈	semidirect
228. C₇₉	#22734	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₈×Dic₁₅₈	2
C₂×#19098687	2
C₄×#14579126	2
#23764119	2
#23764117	2
#23764115	2
#23763516	2
#23763515	2
C₄⋊C₈×Dic₇₉	2
C₄×Dic₇₉⋊C₈	2
C₇₉×#1939	2
#22734	79