Subgroups — C₅₉×#35644 #28447753

Order 15104.

2354 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₉×#544	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₂²⋊Q₈×C₅₉	C₂	1	1	yes	maximal, characteristic
3	C₅₉×#2561	C₂	1	4	yes	maximal
4	C₅₉×#2503	C₂	1	4	yes	maximal, complemented
5	C₅₉×#2492	C₂	1	8	yes	maximal, complemented
6	C₅₉×#2489	C₂	1	8	yes	maximal, complemented
7	C₅₉×#2310	C₂	1	2	yes	maximal, complemented
8	C₅₉×#2280	C₂	1	2	yes	maximal
9	C₅₉×#2274	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×Q₈×C₅₉	C₂²	1	1	yes	characteristic
11	C₂⁴×C₄×C₅₉	C₂²	1	1	yes	characteristic
12	C₅₉×#544	—	2	8	no	—
13	C₂×C₄⋊Q₈×C₅₉	C₂²	1	4	yes	complemented
14	C₂×#125×C₅₉	C₂²	1	4	yes	complemented
15	C₂×C₂²⋊Q₈×C₅₉	—	2	8	no	—
16	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	8	yes	—
17	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	4	yes	—
18	C₂×#117×C₅₉	C₂²	1	2	yes	—
19	C₂×#117×C₅₉	C₂²	1	2	yes	—
20	C₂²×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
21	C₂²×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
22	C₂²×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
23	C₅₉×#400	C₂²	1	16	yes	complemented
24	C₅₉×#397	C₂²	1	8	yes	—
25	C₅₉×#393	C₂²	1	8	yes	—
26	C₅₉×#391	C₂²	1	4	yes	complemented
27	C₅₉×#391	C₂²	1	8	yes	complemented
28	C₅₉×#391	C₂²	1	8	yes	complemented
29	C₅₉×#391	C₂²	1	4	yes	complemented
30	C₅₉×#388	C₂²	1	16	yes	—
31	C₅₉×#382	C₂²	1	8	yes	complemented
32	C₅₉×#381	C₂²	1	4	yes	—
33	C₅₉×#381	C₂²	1	8	yes	—
34	C₅₉×#380	C₂²	1	4	yes	—
35	C₅₉×#380	C₂²	1	4	yes	—
36	C₅₉×#379	C₂²	1	4	yes	—
37	C₄×C₄⋊C₄×C₅₉	C₂²	1	8	yes	complemented
38	C₄×C₂²⋊C₄×C₅₉	C₂²	1	8	yes	—
39	C₄×C₂²⋊C₄×C₅₉	C₂²	1	4	yes	—
40	C₂⁵×C₅₉	C₂³	1	1	yes	characteristic
41	C₂²×Q₈×C₅₉	—	2	4	no	—
42	C₂²×Q₈×C₅₉	—	2	8	no	—
43	C₂²×Q₈×C₅₉	C₂³	1	4	yes	—
44	C₂²×Q₈×C₅₉	C₂³	1	4	yes	—
45	C₂³×C₄×C₅₉	—	2	4	no	—
46	C₂³×C₄×C₅₉	—	2	8	no	—
47	C₂³×C₄×C₅₉	C₂³	1	4	yes	—
48	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
49	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
50	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
51	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
52	C₄⋊Q₈×C₅₉	—	2	16	no	—
53	#125×C₅₉	—	2	16	no	—
54	C₂²⋊Q₈×C₅₉	—	2	16	no	—
55	C₂²⋊Q₈×C₅₉	—	2	32	no	—
56	#117×C₅₉	—	2	8	no	—
57	#117×C₅₉	—	2	8	no	—
58	C₂×C₄⋊C₄×C₅₉	—	2	8	no	—
59	C₂×C₄⋊C₄×C₅₉	D₄	1	8	yes	—
60	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
61	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
62	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
63	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
64	C₂×C₄⋊C₄×C₅₉	C₂³	1	8	yes	—
65	C₂×C₄⋊C₄×C₅₉	C₂³	1	8	yes	—
66	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
67	C₂×C₂²⋊C₄×C₅₉	—	2	8	no	—
68	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
69	C₂×C₂²⋊C₄×C₅₉	C₂³	1	8	yes	—
70	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
71	C₂×C₂²⋊C₄×C₅₉	C₂³	1	8	yes	—
72	C₂×C₂²⋊C₄×C₅₉	C₂³	1	8	yes	—
73	C₂×C₄²×C₅₉	C₂³	1	4	yes	—
74	C₂×C₄²×C₅₉	C₂³	1	4	yes	—
75	C₂×C₄²×C₅₉	C₂³	1	8	yes	—
76	#95×C₅₉	C₂³	1	8	yes	—
77	#95×C₅₉	C₂³	1	8	yes	—
78	#95×C₅₉	C₂³	1	8	yes	—
79	#95×C₅₉	C₂³	1	16	yes	—
80	#95×C₅₉	C₂³	1	16	yes	—
81	C₂⁴×C₅₉	—	2	2	no	—
82	C₂⁴×C₅₉	—	2	4	no	—
83	C₂⁴×C₅₉	—	2	4	no	—
84	C₂⁴×C₅₉	—	4	2	no	—
85	C₂⁴×C₅₉	C₂⁴	1	2	yes	—
86	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
87	C₂×Q₈×C₅₉	—	2	8	no	—
88	C₂×Q₈×C₅₉	—	2	8	no	—
89	C₂×Q₈×C₅₉	—	2	8	no	—
90	C₂×Q₈×C₅₉	—	2	8	no	—
91	C₂×Q₈×C₅₉	—	4	8	no	—
92	C₂×Q₈×C₅₉	—	4	16	no	—
93	C₂²×C₄×C₅₉	—	2	4	no	—
94	C₂²×C₄×C₅₉	—	2	2	no	—
95	C₂²×C₄×C₅₉	—	2	4	no	—
96	C₂²×C₄×C₅₉	—	2	8	no	—
97	C₂²×C₄×C₅₉	—	2	8	no	—
98	C₂²×C₄×C₅₉	—	2	8	no	—
99	C₂²×C₄×C₅₉	—	2	8	no	—
100	C₂²×C₄×C₅₉	—	4	4	no	—
101	C₂²×C₄×C₅₉	—	4	16	no	—
102	C₂²×C₄×C₅₉	C₂×D₄	1	8	yes	—
103	C₂²×C₄×C₅₉	C₂×D₄	1	4	yes	—
104	C₂²×C₄×C₅₉	#41	1	8	yes	—
105	C₂²×C₄×C₅₉	C₂⁴	1	8	yes	—
106	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
107	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
108	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
109	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
110	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
111	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
112	C₄⋊C₄×C₅₉	—	2	16	no	—
113	C₄⋊C₄×C₅₉	—	2	4	no	—
114	C₄⋊C₄×C₅₉	—	2	4	no	—
115	C₄⋊C₄×C₅₉	—	2	8	no	—
116	C₄⋊C₄×C₅₉	—	2	16	no	—
117	C₄⋊C₄×C₅₉	—	2	8	no	—
118	C₄⋊C₄×C₅₉	C₂×D₄	1	16	yes	—
119	C₂²⋊C₄×C₅₉	—	2	8	no	—
120	C₂²⋊C₄×C₅₉	—	2	8	no	—
121	C₂²⋊C₄×C₅₉	—	2	16	no	—
122	C₂²⋊C₄×C₅₉	—	2	16	no	—
123	C₂²⋊C₄×C₅₉	—	4	8	no	—
124	C₄²×C₅₉	—	2	8	no	—
125	C₄²×C₅₉	—	2	8	no	—
126	C₄²×C₅₉	—	4	8	no	—
127	C₂³×C₅₉	—	2	2	no	—
128	C₂³×C₅₉	—	2	2	no	—
129	C₂³×C₅₉	—	2	8	no	—
130	C₂³×C₅₉	—	2	2	no	—
131	C₂³×C₅₉	—	2	4	no	—
132	C₂³×C₅₉	—	2	2	no	—
133	C₂³×C₅₉	—	2	4	no	—
134	C₂³×C₅₉	—	4	16	no	—
135	C₂³×C₅₉	—	4	4	no	—
136	C₂³×C₅₉	—	4	4	no	—
137	C₂³×C₅₉	C₂²×D₄	1	2	yes	—
138	C₂³×C₅₉	C₂×#41	1	4	yes	—
139	C₂³×C₅₉	2₋¹⁺⁴	1	4	yes	—
140	C₂³×C₅₉	C₂⁵	1	1	yes	characteristic
141	Q₈×C₅₉	—	4	16	no	—
142	Q₈×C₅₉	—	8	8	no	—
143	C₂×C₄×C₅₉	—	2	8	no	—
144	C₂×C₄×C₅₉	—	2	4	no	—
145	C₂×C₄×C₅₉	—	2	4	no	—
146	C₂×C₄×C₅₉	—	2	4	no	—
147	C₂×C₄×C₅₉	—	2	2	no	—
148	C₂×C₄×C₅₉	—	2	8	no	—
149	C₂×C₄×C₅₉	—	2	4	no	—
150	C₂×C₄×C₅₉	—	2	8	no	—
151	C₂×C₄×C₅₉	—	2	8	no	—
152	C₂×C₄×C₅₉	—	2	8	no	—
153	C₂×C₄×C₅₉	—	2	8	no	—
154	C₂×C₄×C₅₉	—	2	8	no	—
155	C₂×C₄×C₅₉	—	4	8	no	—
156	C₂×C₄×C₅₉	—	4	4	no	—
157	C₂×C₄×C₅₉	—	4	8	no	—
158	C₂×C₄×C₅₉	—	4	16	no	—
159	C₂×C₄×C₅₉	#124	1	16	yes	—
160	C₂×C₄×C₅₉	C₂²×D₄	1	8	yes	—
161	C₂×C₄×C₅₉	C₂²×D₄	1	4	yes	—
162	C₂×C₄×C₅₉	C₂×#41	1	4	yes	—
163	C₂×C₄×C₅₉	C₂×#41	1	4	yes	—
164	#35644	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
165	C₂²×C₅₉	—	2	2	no	—
166	C₂²×C₅₉	—	2	2	no	—
167	C₂²×C₅₉	—	2	8	no	—
168	C₂²×C₅₉	—	2	4	no	—
169	C₂²×C₅₉	—	2	8	no	—
170	C₂²×C₅₉	—	4	16	no	—
171	C₂²×C₅₉	—	4	2	no	—
172	C₂²×C₅₉	—	4	2	no	—
173	C₂²×C₅₉	—	4	4	no	—
174	C₂²×C₅₉	C₂×#124	1	4	yes	—
175	C₂²×C₅₉	C₂³×D₄	1	1	yes	characteristic
176	C₂²×C₅₉	C₂²×#41	1	2	yes	—
177	C₂²×C₅₉	C₂×2₋¹⁺⁴	1	2	yes	—
178	C₂²×C₅₉	#585	1	2	yes	—
179	C₄×C₅₉	—	2	8	no	—
180	C₄×C₅₉	—	4	2	no	—
181	C₄×C₅₉	—	4	4	no	—
182	C₄×C₅₉	—	4	4	no	—
183	C₄×C₅₉	—	4	4	no	—
184	C₄×C₅₉	—	4	8	no	—
185	C₄×C₅₉	C₂×#124	1	8	yes	—
186	C₂×#544	C₂×C₅₉	1	1	yes	characteristic, complemented
187	C₂²×C₂²⋊Q₈	C₂×C₅₉	1	1	yes	characteristic
188	#2561	C₂×C₅₉	1	4	yes	—
189	#2503	C₂×C₅₉	1	4	yes	complemented
190	#2492	C₂×C₅₉	1	8	yes	complemented
191	#2489	C₂×C₅₉	1	8	yes	complemented
192	#2310	C₂×C₅₉	1	2	yes	complemented
193	#2280	C₂×C₅₉	1	2	yes	—
194	#2274	C₂×C₅₉	1	1	yes	characteristic, complemented
195	C₂×C₅₉	—	2	4	no	—
196	C₂×C₅₉	—	4	4	no	—
197	C₂×C₅₉	C₂²×#124	1	1	yes	characteristic
198	C₂×C₅₉	#3485	1	1	yes	characteristic
199	C₂×C₅₉	#3486	1	1	yes	characteristic
200	C₂×C₅₉	#3495	1	4	yes	—
201	C₂³×Q₈	C₂²×C₅₉	1	1	yes	characteristic
202	C₂⁴×C₄	C₂²×C₅₉	1	1	yes	characteristic
203	#544	—	2	8	no	—
204	C₂×C₄⋊Q₈	C₂²×C₅₉	1	4	yes	complemented
205	C₂×#125	C₂²×C₅₉	1	4	yes	complemented
206	C₂×C₂²⋊Q₈	—	2	8	no	—
207	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	4	yes	—
208	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	8	yes	—
209	C₂×#117	C₂²×C₅₉	1	2	yes	—
210	C₂×#117	C₂²×C₅₉	1	2	yes	—
211	C₂²×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
212	C₂²×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
213	C₂²×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
214	#400	C₂²×C₅₉	1	16	yes	complemented
215	#397	C₂²×C₅₉	1	8	yes	—
216	#393	C₂²×C₅₉	1	8	yes	—
217	#391	C₂²×C₅₉	1	4	yes	complemented
218	#391	C₂²×C₅₉	1	8	yes	complemented
219	#391	C₂²×C₅₉	1	4	yes	complemented
220	#391	C₂²×C₅₉	1	8	yes	complemented
221	#388	C₂²×C₅₉	1	16	yes	—
222	#382	C₂²×C₅₉	1	8	yes	complemented
223	#381	C₂²×C₅₉	1	8	yes	—
224	#381	C₂²×C₅₉	1	4	yes	—
225	#380	C₂²×C₅₉	1	4	yes	—
226	#380	C₂²×C₅₉	1	4	yes	—
227	#379	C₂²×C₅₉	1	4	yes	—
228	C₄×C₄⋊C₄	C₂²×C₅₉	1	8	yes	complemented
229	C₄×C₂²⋊C₄	C₂²×C₅₉	1	4	yes	—
230	C₄×C₂²⋊C₄	C₂²×C₅₉	1	8	yes	—
231	C₅₉	#35644	1	1	yes	characteristic, direct product factor, Sylow
232	C₂⁵	C₂³×C₅₉	1	1	yes	characteristic
233	C₂²×Q₈	—	2	4	no	—
234	C₂²×Q₈	—	2	8	no	—
235	C₂²×Q₈	C₂³×C₅₉	1	4	yes	—
236	C₂²×Q₈	C₂³×C₅₉	1	4	yes	—
237	C₂³×C₄	—	2	4	no	—
238	C₂³×C₄	—	2	8	no	—
239	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
240	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
241	C₂³×C₄	C₂³×C₅₉	1	4	yes	—
242	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
243	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
244	C₄⋊Q₈	—	2	16	no	—
245	#125	—	2	16	no	—
246	C₂²⋊Q₈	—	2	16	no	—
247	C₂²⋊Q₈	—	2	32	no	—
248	#117	—	2	8	no	—
249	#117	—	2	8	no	—
250	C₂×C₄⋊C₄	—	2	8	no	—
251	C₂×C₄⋊C₄	D₄×C₅₉	1	8	yes	—
252	C₂×C₄⋊C₄	C₂³×C₅₉	1	8	yes	—
253	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
254	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
255	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
256	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
257	C₂×C₄⋊C₄	C₂³×C₅₉	1	8	yes	—
258	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
259	C₂×C₂²⋊C₄	—	2	8	no	—
260	C₂×C₂²⋊C₄	C₂³×C₅₉	1	8	yes	—
261	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
262	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
263	C₂×C₂²⋊C₄	C₂³×C₅₉	1	8	yes	—
264	C₂×C₂²⋊C₄	C₂³×C₅₉	1	8	yes	—
265	C₂×C₄²	C₂³×C₅₉	1	4	yes	—
266	C₂×C₄²	C₂³×C₅₉	1	4	yes	—
267	C₂×C₄²	C₂³×C₅₉	1	8	yes	—
268	#95	C₂³×C₅₉	1	8	yes	—
269	#95	C₂³×C₅₉	1	8	yes	—
270	#95	C₂³×C₅₉	1	8	yes	—
271	#95	C₂³×C₅₉	1	16	yes	—
272	#95	C₂³×C₅₉	1	16	yes	—
273	C₂⁴	—	2	2	no	—
274	C₂⁴	—	2	4	no	—
275	C₂⁴	—	2	4	no	—
276	C₂⁴	—	4	2	no	—
277	C₂⁴	C₂⁴×C₅₉	1	2	yes	—
278	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
279	C₂×Q₈	—	2	8	no	—
280	C₂×Q₈	—	2	8	no	—
281	C₂×Q₈	—	2	8	no	—
282	C₂×Q₈	—	2	8	no	—
283	C₂×Q₈	—	4	8	no	—
284	C₂×Q₈	—	4	16	no	—
285	C₂²×C₄	—	2	4	no	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	2	4	no	—
288	C₂²×C₄	—	2	8	no	—
289	C₂²×C₄	—	2	8	no	—
290	C₂²×C₄	—	2	8	no	—
291	C₂²×C₄	—	2	8	no	—
292	C₂²×C₄	—	4	4	no	—
293	C₂²×C₄	—	4	16	no	—
294	C₂²×C₄	C₂×D₄×C₅₉	1	8	yes	—
295	C₂²×C₄	C₂×D₄×C₅₉	1	4	yes	—
296	C₂²×C₄	#41×C₅₉	1	8	yes	—
297	C₂²×C₄	C₂⁴×C₅₉	1	8	yes	—
298	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
299	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
300	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
301	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
302	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
303	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
304	C₄⋊C₄	—	2	16	no	—
305	C₄⋊C₄	—	2	4	no	—
306	C₄⋊C₄	—	2	4	no	—
307	C₄⋊C₄	—	2	8	no	—
308	C₄⋊C₄	—	2	16	no	—
309	C₄⋊C₄	—	2	8	no	—
310	C₄⋊C₄	C₂×D₄×C₅₉	1	16	yes	—
311	C₂²⋊C₄	—	2	8	no	—
312	C₂²⋊C₄	—	2	8	no	—
313	C₂²⋊C₄	—	2	16	no	—
314	C₂²⋊C₄	—	2	16	no	—
315	C₂²⋊C₄	—	4	8	no	—
316	C₄²	—	2	8	no	—
317	C₄²	—	2	8	no	—
318	C₄²	—	4	8	no	—
319	C₂³	—	2	2	no	—
320	C₂³	—	2	2	no	—
321	C₂³	—	2	8	no	—
322	C₂³	—	2	2	no	—
323	C₂³	—	2	4	no	—
324	C₂³	—	2	2	no	—
325	C₂³	—	2	4	no	—
326	C₂³	—	4	16	no	—
327	C₂³	—	4	4	no	—
328	C₂³	—	4	4	no	—
329	C₂³	C₂²×D₄×C₅₉	1	2	yes	—
330	C₂³	C₂×#41×C₅₉	1	4	yes	—
331	C₂³	2₋¹⁺⁴×C₅₉	1	4	yes	—
332	C₂³	C₂⁵×C₅₉	1	1	yes	characteristic
333	Q₈	—	4	16	no	—
334	Q₈	—	8	8	no	—
335	C₂×C₄	—	2	8	no	—
336	C₂×C₄	—	2	4	no	—
337	C₂×C₄	—	2	4	no	—
338	C₂×C₄	—	2	4	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	8	no	—
341	C₂×C₄	—	2	4	no	—
342	C₂×C₄	—	2	8	no	—
343	C₂×C₄	—	2	8	no	—
344	C₂×C₄	—	2	8	no	—
345	C₂×C₄	—	2	8	no	—
346	C₂×C₄	—	2	8	no	—
347	C₂×C₄	—	4	8	no	—
348	C₂×C₄	—	4	4	no	—
349	C₂×C₄	—	4	8	no	—
350	C₂×C₄	—	4	16	no	—
351	C₂×C₄	#124×C₅₉	1	16	yes	—
352	C₂×C₄	C₂²×D₄×C₅₉	1	8	yes	—
353	C₂×C₄	C₂²×D₄×C₅₉	1	4	yes	—
354	C₂×C₄	C₂×#41×C₅₉	1	4	yes	—
355	C₂×C₄	C₂×#41×C₅₉	1	4	yes	—
356	C₂²	—	2	2	no	—
357	C₂²	—	2	2	no	—
358	C₂²	—	2	8	no	—
359	C₂²	—	2	4	no	—
360	C₂²	—	2	8	no	—
361	C₂²	—	4	16	no	—
362	C₂²	—	4	2	no	—
363	C₂²	—	4	2	no	—
364	C₂²	—	4	4	no	—
365	C₂²	C₂×#124×C₅₉	1	4	yes	—
366	C₂²	C₂³×D₄×C₅₉	1	1	yes	characteristic
367	C₂²	C₂²×#41×C₅₉	1	2	yes	—
368	C₂²	C₂×2₋¹⁺⁴×C₅₉	1	2	yes	—
369	C₂²	C₅₉×#585	1	2	yes	—
370	C₄	—	2	8	no	—
371	C₄	—	4	2	no	—
372	C₄	—	4	4	no	—
373	C₄	—	4	4	no	—
374	C₄	—	4	4	no	—
375	C₄	—	4	8	no	—
376	C₄	C₂×#124×C₅₉	1	8	yes	—
377	C₂	—	2	4	no	—
378	C₂	—	4	4	no	—
379	C₂	C₂²×#124×C₅₉	1	1	yes	characteristic
380	C₂	C₅₉×#3485	1	1	yes	characteristic
381	C₂	C₅₉×#3486	1	1	yes	characteristic
382	C₂	C₅₉×#3495	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₅₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₉
prime radical	C₂⁵×C₅₉	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅₉×#544	C₂	semidirect
4. C₅₉×#2503	C₂	semidirect
5. C₅₉×#2492	C₂	semidirect
6. C₅₉×#2489	C₂	semidirect
7. C₅₉×#2310	C₂	semidirect
9. C₅₉×#2274	C₂	semidirect
13. C₂×C₄⋊Q₈×C₅₉	C₂²	semidirect
14. C₂×#125×C₅₉	C₂²	semidirect
23. C₅₉×#400	C₂²	semidirect
26. C₅₉×#391	C₂²	semidirect
27. C₅₉×#391	C₂²	semidirect
28. C₅₉×#391	C₂²	semidirect
29. C₅₉×#391	C₂²	semidirect
31. C₅₉×#382	C₂²	semidirect
37. C₄×C₄⋊C₄×C₅₉	C₂²	semidirect
164. #35644	C₅₉	direct (N × H)
186. C₂×#544	C₂×C₅₉	semidirect
189. #2503	C₂×C₅₉	semidirect
190. #2492	C₂×C₅₉	semidirect
191. #2489	C₂×C₅₉	semidirect
192. #2310	C₂×C₅₉	semidirect
194. #2274	C₂×C₅₉	semidirect
204. C₂×C₄⋊Q₈	C₂²×C₅₉	semidirect
205. C₂×#125	C₂²×C₅₉	semidirect
214. #400	C₂²×C₅₉	semidirect
217. #391	C₂²×C₅₉	semidirect
218. #391	C₂²×C₅₉	semidirect
219. #391	C₂²×C₅₉	semidirect
220. #391	C₂²×C₅₉	semidirect
222. #382	C₂²×C₅₉	semidirect
228. C₄×C₄⋊C₄	C₂²×C₅₉	semidirect
231. C₅₉	#35644	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×C₅₉×#544	2
C₂²×C₂²⋊Q₈×C₅₉	2
C₅₉×#2561	2
C₅₉×#2503	2
C₅₉×#2492	2
C₅₉×#2489	2
C₅₉×#2310	2
C₅₉×#2280	2
C₅₉×#2274	2
#35644	59

Subgroups — C59×#35644 #28447753

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#35644 #28447753