Subgroups — #28481377

Order 15104.

588 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21424248	C₂	1	1	yes	maximal, characteristic
2	C₄×C₄⋊(C₅₉⋊C₈)	C₂	1	1	yes	maximal, characteristic
3	C₂×Q₈⋊(C₅₉⋊C₈)	C₂	1	2	yes	maximal
4	#21421937	C₂	1	2	yes	maximal
5	C₄²×Q₈×C₅₉	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
7	C₂×C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
8	C₂×C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
9	C₂×C₄⋊(C₅₉⋊C₈)	C₂²	1	2	yes	—
10	C₂×C₄×C₅₉⋊C₈	C₂²	1	2	yes	—
11	#16837157	—	2	1	no	—
12	Q₈⋊(C₅₉⋊C₈)	—	2	4	no	—
13	C₂×C₄×Q₈×C₅₉	C₄	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₅₉	C₄	1	1	yes	characteristic
15	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
16	C₄×C₄⋊C₄×C₅₉	—	2	1	no	—
17	C₄×C₄⋊C₄×C₅₉	—	2	1	no	—
18	C₄×C₄⋊C₄×C₅₉	—	2	1	no	—
19	C₄×C₄⋊C₄×C₅₉	C₄	1	1	yes	characteristic
20	C₄×C₄⋊C₄×C₅₉	C₄	1	1	yes	characteristic
21	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
22	C₄³×C₅₉	—	2	1	no	—
23	C₄³×C₅₉	C₂²	1	1	yes	characteristic
24	C₂²×C₅₉⋊C₈	—	2	2	no	—
25	C₂²×C₅₉⋊C₈	—	2	2	no	—
26	C₄⋊(C₅₉⋊C₈)	—	2	4	no	—
27	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
28	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
29	C₄⋊(C₅₉⋊C₈)	—	4	2	no	—
30	C₄⋊(C₅₉⋊C₈)	—	4	2	no	—
31	C₄×C₅₉⋊C₈	—	2	2	no	—
32	C₄×C₅₉⋊C₈	—	2	2	no	—
33	C₂²×Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
34	C₄×Q₈×C₅₉	—	2	2	no	—
35	C₄×Q₈×C₅₉	—	2	2	no	—
36	C₄×Q₈×C₅₉	—	2	2	no	—
37	C₄×Q₈×C₅₉	—	2	1	no	—
38	C₄×Q₈×C₅₉	—	2	1	no	—
39	C₄×Q₈×C₅₉	C₈	1	4	yes	complemented
40	C₄×Q₈×C₅₉	D₄	1	2	yes	—
41	C₄×Q₈×C₅₉	Q₈	1	2	yes	—
42	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
43	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
44	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
45	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄²×C₅₉	—	2	1	no	—
49	C₂×C₄²×C₅₉	—	2	1	no	—
50	C₂×C₄²×C₅₉	—	2	1	no	—
51	C₂×C₄²×C₅₉	—	2	1	no	—
52	C₂×C₄²×C₅₉	—	2	1	no	—
53	C₂×C₄²×C₅₉	—	2	1	no	—
54	C₂×C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄²×C₅₉	D₄	1	1	yes	characteristic
57	C₂×C₄²×C₅₉	D₄	1	1	yes	characteristic
58	C₂×C₄²×C₅₉	D₄	1	1	yes	characteristic
59	C₂×C₄²×C₅₉	D₄	1	1	yes	characteristic
60	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
61	#95×C₅₉	—	2	1	no	—
62	#95×C₅₉	—	2	1	no	—
63	#95×C₅₉	—	2	1	no	—
64	C₂×Q₈×C₅₉	—	2	1	no	—
65	C₂×Q₈×C₅₉	—	2	1	no	—
66	C₂×Q₈×C₅₉	—	2	1	no	—
67	C₂×Q₈×C₅₉	C₄⋊C₄	1	2	yes	—
68	C₂×Q₈×C₅₉	C₂×C₈	1	2	yes	—
69	C₂×Q₈×C₅₉	M₁₆	1	2	yes	—
70	C₂²×C₄×C₅₉	—	2	1	no	—
71	C₂²×C₄×C₅₉	—	2	1	no	—
72	C₂²×C₄×C₅₉	—	2	1	no	—
73	C₂²×C₄×C₅₉	—	2	1	no	—
74	C₂²×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
76	C₂²×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
77	C₂²×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
79	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
80	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
81	C₄⋊C₄×C₅₉	—	2	4	no	—
82	C₄⋊C₄×C₅₉	—	2	4	no	—
83	C₄⋊C₄×C₅₉	—	2	1	no	—
84	C₄⋊C₄×C₅₉	—	2	2	no	—
85	C₄⋊C₄×C₅₉	—	2	2	no	—
86	C₄⋊C₄×C₅₉	—	2	1	no	—
87	C₄⋊C₄×C₅₉	—	2	1	no	—
88	C₄⋊C₄×C₅₉	C₄⋊C₄	1	2	yes	—
89	C₄⋊C₄×C₅₉	C₂×C₈	1	2	yes	—
90	C₄⋊C₄×C₅₉	M₁₆	1	2	yes	—
91	C₄²×C₅₉	—	2	4	no	—
92	C₄²×C₅₉	—	2	4	no	—
93	C₄²×C₅₉	—	2	2	no	—
94	C₄²×C₅₉	—	2	2	no	—
95	C₄²×C₅₉	—	2	2	no	—
96	C₄²×C₅₉	—	2	1	no	—
97	C₄²×C₅₉	—	2	1	no	—
98	C₄²×C₅₉	—	2	1	no	—
99	C₄²×C₅₉	—	2	1	no	—
100	C₄²×C₅₉	—	4	1	no	—
101	C₄²×C₅₉	—	4	2	no	—
102	C₄²×C₅₉	—	4	2	no	—
103	C₄²×C₅₉	—	4	1	no	—
104	C₄²×C₅₉	—	4	1	no	—
105	C₄²×C₅₉	C₂×C₈	1	2	yes	—
106	C₄²×C₅₉	M₁₆	1	2	yes	—
107	C₄²×C₅₉	SD₁₆	1	2	yes	—
108	C₄²×C₅₉	Q₁₆	1	2	yes	—
109	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
110	C₄²×C₅₉	C₂×Q₈	1	1	yes	characteristic
111	C₄²×C₅₉	#41	1	1	yes	characteristic
112	C₄²×C₅₉	#41	1	1	yes	characteristic
113	C₂×C₅₉⋊C₈	—	2	4	no	—
114	C₂×C₅₉⋊C₈	—	4	2	no	—
115	C₂×C₅₉⋊C₈	—	4	2	no	—
116	C₂×C₅₉⋊C₈	—	4	2	no	—
117	C₂×C₅₉⋊C₈	—	4	2	no	—
118	C₂×C₅₉⋊C₈	—	4	2	no	—
119	C₂³×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
120	Q₈×C₅₉	—	2	2	no	—
121	Q₈×C₅₉	—	2	2	no	—
122	Q₈×C₅₉	—	2	2	no	—
123	Q₈×C₅₉	C₄⋊C₈	1	4	yes	complemented
124	C₂×C₄×C₅₉	—	2	2	no	—
125	C₂×C₄×C₅₉	—	2	2	no	—
126	C₂×C₄×C₅₉	—	2	1	no	—
127	C₂×C₄×C₅₉	—	2	2	no	—
128	C₂×C₄×C₅₉	—	2	1	no	—
129	C₂×C₄×C₅₉	—	2	1	no	—
130	C₂×C₄×C₅₉	—	2	1	no	—
131	C₂×C₄×C₅₉	—	2	1	no	—
132	C₂×C₄×C₅₉	—	2	1	no	—
133	C₂×C₄×C₅₉	—	2	2	no	—
134	C₂×C₄×C₅₉	—	2	2	no	—
135	C₂×C₄×C₅₉	—	2	1	no	—
136	C₂×C₄×C₅₉	—	2	2	no	—
137	C₂×C₄×C₅₉	—	2	1	no	—
138	C₂×C₄×C₅₉	—	2	1	no	—
139	C₂×C₄×C₅₉	—	4	1	no	—
140	C₂×C₄×C₅₉	—	4	1	no	—
141	C₂×C₄×C₅₉	—	4	1	no	—
142	C₂×C₄×C₅₉	—	4	1	no	—
143	C₂×C₄×C₅₉	—	4	1	no	—
144	C₂×C₄×C₅₉	—	4	1	no	—
145	C₂×C₄×C₅₉	C₂²⋊C₈	1	2	yes	—
146	C₂×C₄×C₅₉	C₂²⋊C₈	1	2	yes	—
147	C₂×C₄×C₅₉	#103	1	2	yes	—
148	C₂×C₄×C₅₉	#103	1	2	yes	—
149	C₂×C₄×C₅₉	#104	1	2	yes	—
150	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
151	C₂×C₄×C₅₉	#117	1	1	yes	characteristic
152	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
153	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
154	C₂×C₄×C₅₉	C₂²⋊Q₈	1	1	yes	characteristic
155	C₂×C₄×C₅₉	C₂²⋊Q₈	1	1	yes	characteristic
156	C₂×C₄×C₅₉	C₂²×C₈	1	1	yes	characteristic
157	C₂×C₄×C₅₉	C₂×M₁₆	1	1	yes	characteristic
158	C₂×C₄×C₅₉	C₂×M₁₆	1	1	yes	characteristic
159	C₂×C₄×C₅₉	C₂×M₁₆	1	1	yes	characteristic
160	C₂×C₄×C₅₉	C₂×SD₁₆	1	1	yes	characteristic
161	C₂×C₄×C₅₉	C₂×Q₁₆	1	1	yes	characteristic
162	C₂×C₄×C₅₉	AGL(1,ℤ/8)	1	1	yes	characteristic
163	C₂×C₄×C₅₉	#137	1	1	yes	characteristic
164	C₅₉⋊C₈	—	4	4	no	—
165	C₅₉⋊C₈	—	8	2	no	—
166	#8564	—	59	1	no	maximal, Sylow
167	C₂²×C₅₉	#380	1	1	yes	characteristic
168	C₂²×C₅₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
169	C₂²×C₅₉	#407	1	1	yes	characteristic
170	C₂²×C₅₉	C₂×#103	1	1	yes	characteristic
171	C₂²×C₅₉	#417	1	1	yes	characteristic
172	C₂²×C₅₉	C₂×#104	1	1	yes	characteristic
173	C₂²×C₅₉	#421	1	1	yes	characteristic
174	C₄×C₅₉	—	2	4	no	—
175	C₄×C₅₉	—	2	1	no	—
176	C₄×C₅₉	—	2	1	no	—
177	C₄×C₅₉	—	2	2	no	—
178	C₄×C₅₉	—	2	2	no	—
179	C₄×C₅₉	—	4	2	no	—
180	C₄×C₅₉	—	4	2	no	—
181	C₄×C₅₉	—	4	1	no	—
182	C₄×C₅₉	—	4	2	no	—
183	C₄×C₅₉	Q₈⋊C₈	1	4	yes	complemented
184	C₄×C₅₉	C₂×C₄⋊C₈	1	1	yes	characteristic
185	C₄×C₅₉	#423	1	1	yes	characteristic
186	C₄×C₅₉	#431	1	1	yes	characteristic
187	C₄×C₅₉	#432	1	1	yes	characteristic
188	C₄×C₅₉	#460	1	1	yes	characteristic
189	C₄×C₅₉	#462	1	1	yes	characteristic
190	C₄×C₅₉	#475	1	1	yes	characteristic
191	C₄×C₅₉	#477	1	1	yes	characteristic
192	C₄²×Q₈	D₅₉	1	1	yes	characteristic
193	#1842	—	59	1	no	—
194	C₄×C₄⋊C₈	—	59	1	no	—
195	C₂×Q₈⋊C₈	—	59	2	no	—
196	#1279	—	59	2	no	—
197	C₂×C₅₉	C₂×Q₈⋊C₈	1	1	yes	characteristic
198	C₂×C₅₉	#1477	1	1	yes	characteristic
199	C₂×C₅₉	#1487	1	1	yes	characteristic
200	C₂×C₅₉	#1489	1	1	yes	characteristic
201	C₂×C₅₉	#1797	1	1	yes	characteristic
202	C₂×C₅₉	#1803	1	1	yes	characteristic
203	C₂×C₅₉	#1806	1	1	yes	characteristic
204	C₂×C₄×Q₈	Dic₅₉	1	1	yes	characteristic
205	C₂×C₄×Q₈	Dic₅₉	1	1	yes	characteristic
206	C₂×C₄×Q₈	C₂×D₅₉	1	1	yes	characteristic
207	C₂×C₄⋊C₈	—	59	2	no	—
208	C₂×C₄⋊C₈	—	118	1	no	—
209	C₂×C₄⋊C₈	—	118	1	no	—
210	C₂×C₄⋊C₈	—	118	1	no	—
211	C₂×C₄×C₈	—	59	2	no	—
212	C₄×C₄⋊C₄	—	2	1	no	—
213	C₄×C₄⋊C₄	—	2	1	no	—
214	C₄×C₄⋊C₄	—	2	1	no	—
215	C₄×C₄⋊C₄	Dic₅₉	1	1	yes	characteristic
216	C₄×C₄⋊C₄	Dic₅₉	1	1	yes	characteristic
217	C₄×C₄⋊C₄	C₂×D₅₉	1	1	yes	characteristic
218	C₄³	—	2	1	no	—
219	C₄³	C₂×D₅₉	1	1	yes	characteristic
220	#336	—	118	1	no	—
221	Q₈⋊C₈	—	118	4	no	—
222	C₅₉	#8564	1	1	yes	characteristic, complemented, Sylow
223	C₂²×Q₈	C₂×Dic₅₉	1	1	yes	characteristic
224	C₂²×C₈	—	118	2	no	—
225	C₂²×C₈	—	118	2	no	—
226	C₄×Q₈	—	2	2	no	—
227	C₄×Q₈	—	2	2	no	—
228	C₄×Q₈	—	2	2	no	—
229	C₄×Q₈	—	2	1	no	—
230	C₄×Q₈	—	2	1	no	—
231	C₄×Q₈	C₅₉⋊C₈	1	4	yes	complemented
232	C₄×Q₈	Dic₁₁₈	1	2	yes	—
233	C₄×Q₈	D₂₃₆	1	2	yes	—
234	C₂×C₄⋊C₄	—	2	1	no	—
235	C₂×C₄⋊C₄	—	2	1	no	—
236	C₂×C₄⋊C₄	—	2	1	no	—
237	C₂×C₄⋊C₄	C₂×Dic₅₉	1	1	yes	characteristic
238	C₂×C₄⋊C₄	C₂×Dic₅₉	1	1	yes	characteristic
239	C₂×C₄⋊C₄	C₂×Dic₅₉	1	1	yes	characteristic
240	C₂×C₄²	—	2	1	no	—
241	C₂×C₄²	—	2	1	no	—
242	C₂×C₄²	—	2	1	no	—
243	C₂×C₄²	—	2	1	no	—
244	C₂×C₄²	—	2	1	no	—
245	C₂×C₄²	—	2	1	no	—
246	C₂×C₄²	C₂×Dic₅₉	1	1	yes	characteristic
247	C₂×C₄²	C₂×Dic₅₉	1	1	yes	characteristic
248	C₂×C₄²	C₂²⋊D₅₉	1	1	yes	characteristic
249	C₂×C₄²	C₂²⋊D₅₉	1	1	yes	characteristic
250	C₂×C₄²	C₂²⋊D₅₉	1	1	yes	characteristic
251	C₂×C₄²	C₂²⋊D₅₉	1	1	yes	characteristic
252	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
253	C₄⋊C₈	—	118	4	no	—
254	C₄⋊C₈	—	118	2	no	—
255	C₄⋊C₈	—	118	2	no	—
256	C₄⋊C₈	—	236	2	no	—
257	C₄⋊C₈	—	236	2	no	—
258	C₄×C₈	—	118	2	no	—
259	C₄×C₈	—	118	2	no	—
260	#95	—	2	1	no	—
261	#95	—	2	1	no	—
262	#95	—	2	1	no	—
263	C₂×Q₈	—	2	1	no	—
264	C₂×Q₈	—	2	1	no	—
265	C₂×Q₈	—	2	1	no	—
266	C₂×Q₈	C₂×C₅₉⋊C₈	1	2	yes	—
267	C₂×Q₈	#11745664	1	2	yes	—
268	C₂×Q₈	C₄⋊Dic₅₉	1	2	yes	—
269	C₂²×C₄	—	2	1	no	—
270	C₂²×C₄	—	2	1	no	—
271	C₂²×C₄	—	2	1	no	—
272	C₂²×C₄	—	2	1	no	—
273	C₂²×C₄	C₂²⋊Dic₅₉	1	1	yes	characteristic
274	C₂²×C₄	C₂²⋊Dic₅₉	1	1	yes	characteristic
275	C₂²×C₄	C₂²⋊Dic₅₉	1	1	yes	characteristic
276	C₂²×C₄	C₂²⋊Dic₅₉	1	1	yes	characteristic
277	C₂²×C₄	C₂²×Dic₅₉	1	1	yes	characteristic
278	C₂²×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
279	C₂²×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
280	C₂×C₈	—	118	4	no	—
281	C₂×C₈	—	236	2	no	—
282	C₂×C₈	—	236	2	no	—
283	C₂×C₈	—	236	2	no	—
284	C₂×C₈	—	236	2	no	—
285	C₂×C₈	—	236	2	no	—
286	C₄⋊C₄	—	2	4	no	—
287	C₄⋊C₄	—	2	4	no	—
288	C₄⋊C₄	—	2	1	no	—
289	C₄⋊C₄	—	2	2	no	—
290	C₄⋊C₄	—	2	2	no	—
291	C₄⋊C₄	—	2	1	no	—
292	C₄⋊C₄	—	2	1	no	—
293	C₄⋊C₄	C₂×C₅₉⋊C₈	1	2	yes	—
294	C₄⋊C₄	#11745664	1	2	yes	—
295	C₄⋊C₄	C₄⋊Dic₅₉	1	2	yes	—
296	C₄²	—	2	4	no	—
297	C₄²	—	2	4	no	—
298	C₄²	—	2	2	no	—
299	C₄²	—	2	2	no	—
300	C₄²	—	2	2	no	—
301	C₄²	—	2	1	no	—
302	C₄²	—	2	1	no	—
303	C₄²	—	2	1	no	—
304	C₄²	—	2	1	no	—
305	C₄²	—	4	1	no	—
306	C₄²	—	4	2	no	—
307	C₄²	—	4	2	no	—
308	C₄²	—	4	1	no	—
309	C₄²	—	4	1	no	—
310	C₄²	C₂×C₅₉⋊C₈	1	2	yes	—
311	C₄²	#11745664	1	2	yes	—
312	C₄²	#11745671	1	2	yes	—
313	C₄²	#11745672	1	2	yes	—
314	C₄²	C₂×Dic₁₁₈	1	1	yes	characteristic
315	C₄²	C₂×D₂₃₆	1	1	yes	characteristic
316	C₄²	#11745685	1	1	yes	characteristic
317	C₄²	#11745685	1	1	yes	characteristic
318	C₂³	C₂×C₂²⋊Dic₅₉	1	1	yes	characteristic
319	Q₈	—	2	2	no	—
320	Q₈	—	2	2	no	—
321	Q₈	—	2	2	no	—
322	Q₈	C₄⋊(C₅₉⋊C₈)	1	4	yes	complemented
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	4	1	no	—
339	C₂×C₄	—	4	1	no	—
340	C₂×C₄	—	4	1	no	—
341	C₂×C₄	—	4	1	no	—
342	C₂×C₄	—	4	1	no	—
343	C₂×C₄	—	4	1	no	—
344	C₂×C₄	C₂²⋊(C₅₉⋊C₈)	1	2	yes	—
345	C₂×C₄	C₂²⋊(C₅₉⋊C₈)	1	2	yes	—
346	C₂×C₄	#14273651	1	2	yes	—
347	C₂×C₄	#14273651	1	2	yes	—
348	C₂×C₄	#14273654	1	2	yes	—
349	C₂×C₄	C₂×C₄⋊Dic₅₉	1	1	yes	characteristic
350	C₂×C₄	#14273686	1	1	yes	characteristic
351	C₂×C₄	#14273701	1	1	yes	characteristic
352	C₂×C₄	#14273701	1	1	yes	characteristic
353	C₂×C₄	#14273706	1	1	yes	characteristic
354	C₂×C₄	#14273706	1	1	yes	characteristic
355	C₂×C₄	C₂²×C₅₉⋊C₈	1	1	yes	characteristic
356	C₂×C₄	C₂×#11745664	1	1	yes	characteristic
357	C₂×C₄	C₂×#11745664	1	1	yes	characteristic
358	C₂×C₄	C₂×#11745664	1	1	yes	characteristic
359	C₂×C₄	C₂×#11745671	1	1	yes	characteristic
360	C₂×C₄	C₂×#11745672	1	1	yes	characteristic
361	C₂×C₄	#14273752	1	1	yes	characteristic
362	C₂×C₄	#14273757	1	1	yes	characteristic
363	C₈	—	472	2	no	—
364	C₈	—	236	4	no	—
365	C₂²	#16837262	1	1	yes	characteristic
366	C₂²	C₂×C₂²⋊(C₅₉⋊C₈)	1	1	yes	characteristic
367	C₂²	#16837366	1	1	yes	characteristic
368	C₂²	C₂×#14273651	1	1	yes	characteristic
369	C₂²	#16837403	1	1	yes	characteristic
370	C₂²	C₂×#14273654	1	1	yes	characteristic
371	C₂²	#16837419	1	1	yes	characteristic
372	C₄	—	2	2	no	—
373	C₄	—	2	2	no	—
374	C₄	—	2	4	no	—
375	C₄	—	2	1	no	—
376	C₄	—	2	1	no	—
377	C₄	—	4	2	no	—
378	C₄	—	4	1	no	—
379	C₄	—	4	2	no	—
380	C₄	—	4	2	no	—
381	C₄	Q₈⋊(C₅₉⋊C₈)	1	4	yes	complemented
382	C₄	C₂×C₄⋊(C₅₉⋊C₈)	1	1	yes	characteristic
383	C₄	#16837426	1	1	yes	characteristic
384	C₄	#16837455	1	1	yes	characteristic
385	C₄	#16837459	1	1	yes	characteristic
386	C₄	#16837602	1	1	yes	characteristic
387	C₄	#16837612	1	1	yes	characteristic
388	C₄	#16837687	1	1	yes	characteristic
389	C₄	#16837697	1	1	yes	characteristic
390	C₂	C₂×Q₈⋊(C₅₉⋊C₈)	1	1	yes	characteristic
391	C₂	#21422483	1	1	yes	characteristic
392	C₂	#21422525	1	1	yes	characteristic
393	C₂	#21422535	1	1	yes	characteristic
394	C₂	#21424076	1	1	yes	characteristic
395	C₂	#21424101	1	1	yes	characteristic
396	C₂	#21424116	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₅₉
commutator	C₂×C₄×C₅₉	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₅₉
Fitting	C₄²×Q₈×C₅₉	C₂
socle, prime radical	C₂³×C₅₉	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₅₉	C₂³
hypercenter	C₄²×Q₈	D₅₉
hypocenter	C₅₉	#8564
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ C₄²×Q₈

Complements

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

N	H ≅ G/N	type
39. C₄×Q₈×C₅₉	C₈	semidirect
123. Q₈×C₅₉	C₄⋊C₈	semidirect
183. C₄×C₅₉	Q₈⋊C₈	semidirect
222. C₅₉	#8564	semidirect
231. C₄×Q₈	C₅₉⋊C₈	semidirect
322. Q₈	C₄⋊(C₅₉⋊C₈)	semidirect
381. C₄	Q₈⋊(C₅₉⋊C₈)	semidirect

Maximal subgroups

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

subgroup	index
#21424248	2
C₄×C₄⋊(C₅₉⋊C₈)	2
C₂×Q₈⋊(C₅₉⋊C₈)	2
#21421937	2
C₄²×Q₈×C₅₉	2
#8564	59