Subgroups — C₅₉×#17439 #28429548

Order 15104.

1206 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×2₋¹⁺⁴×C₅₉	C₂	1	1	yes	maximal, characteristic
2	C₅₉×#2988	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈×#41×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₉×#1479	C₂	1	3	yes	maximal, complemented
5	C₅₉×#1477	C₂	1	3	yes	maximal, complemented
6	C₅₉×#1476	C₂	1	3	yes	maximal, complemented
7	C₂×C₅₉×Q₈⋊C₈	C₂	1	3	yes	maximal, complemented
8	C₂×2₋¹⁺⁴×C₅₉	C₄	1	1	yes	characteristic
9	C₅₉×#520	—	2	3	no	—
10	C₅₉×#520	C₄	1	3	yes	—
11	C₅₉×#520	C₄	1	1	yes	characteristic
12	C₅₉×#519	—	2	1	no	—
13	C₅₉×#519	C₄	1	3	yes	—
14	C₄×#41×C₅₉	—	2	3	no	—
15	C₄×#41×C₅₉	C₂²	1	3	yes	—
16	C₄×#41×C₅₉	C₂²	1	1	yes	characteristic
17	C₂×C₄×Q₈×C₅₉	—	2	1	no	—
18	C₂×C₄×Q₈×C₅₉	C₂²	1	3	yes	—
19	C₈×Q₈×C₅₉	—	2	1	no	—
20	C₈×Q₈×C₅₉	—	2	1	no	—
21	C₈×D₄×C₅₉	—	2	3	no	—
22	C₈×D₄×C₅₉	—	2	3	no	—
23	C₅₉×#431	C₂²	1	3	yes	—
24	C₅₉×#431	C₂²	1	3	yes	—
25	C₂×C₄⋊C₈×C₅₉	C₂²	1	3	yes	—
26	C₂×C₄×C₈×C₅₉	C₂²	1	3	yes	—
27	C₅₉×Q₈⋊C₈	C₂²	1	3	yes	—
28	C₅₉×Q₈⋊C₈	C₂²	1	6	yes	—
29	C₅₉×Q₈⋊C₈	C₂²	1	3	yes	—
30	C₅₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
31	C₅₉×D₄⋊C₈	C₂²	1	3	yes	—
32	2₋¹⁺⁴×C₅₉	—	2	4	no	—
33	2₋¹⁺⁴×C₅₉	C₈	1	8	yes	complemented
34	C₂×#41×C₅₉	—	2	3	no	—
35	C₂×#41×C₅₉	C₂×C₄	1	3	yes	—
36	C₂×#41×C₅₉	C₂×C₄	1	1	yes	characteristic
37	C₂²×Q₈×C₅₉	—	2	1	no	—
38	C₂²×Q₈×C₅₉	C₂×C₄	1	3	yes	—
39	C₂²×C₈×C₅₉	—	2	3	no	—
40	C₂²×C₈×C₅₉	—	2	3	no	—
41	C₄×Q₈×C₅₉	—	2	1	no	—
42	C₄×Q₈×C₅₉	—	2	3	no	—
43	C₄×Q₈×C₅₉	—	2	3	no	—
44	C₄×Q₈×C₅₉	—	2	3	no	—
45	C₄×Q₈×C₅₉	—	2	3	no	—
46	C₄×Q₈×C₅₉	C₂×C₄	1	6	yes	—
47	C₄×Q₈×C₅₉	C₂×C₄	1	3	yes	—
48	C₄×Q₈×C₅₉	D₄	1	1	yes	characteristic
49	C₄×Q₈×C₅₉	D₄	1	1	yes	characteristic
50	C₄×Q₈×C₅₉	C₂³	1	3	yes	—
51	C₄×D₄×C₅₉	—	2	3	no	—
52	C₄×D₄×C₅₉	—	2	3	no	—
53	C₄×D₄×C₅₉	—	2	3	no	—
54	C₄×D₄×C₅₉	—	2	6	no	—
55	C₄×D₄×C₅₉	C₂×C₄	1	3	yes	—
56	C₄×D₄×C₅₉	D₄	1	3	yes	—
57	C₄×D₄×C₅₉	D₄	1	3	yes	—
58	C₄×D₄×C₅₉	C₂³	1	1	yes	characteristic
59	#117×C₅₉	—	2	3	no	—
60	#117×C₅₉	—	2	6	no	—
61	#117×C₅₉	—	2	3	no	—
62	#117×C₅₉	C₂×C₄	1	3	yes	—
63	#117×C₅₉	C₂×C₄	1	3	yes	—
64	C₂×C₄⋊C₄×C₅₉	—	2	3	no	—
65	C₂×C₄⋊C₄×C₅₉	—	2	3	no	—
66	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	3	yes	—
67	C₂×C₄²×C₅₉	—	2	3	no	—
68	C₂×C₄²×C₅₉	—	2	3	no	—
69	C₂×C₄²×C₅₉	C₂³	1	3	yes	—
70	C₄⋊C₈×C₅₉	—	2	3	no	—
71	C₄⋊C₈×C₅₉	—	2	3	no	—
72	C₄⋊C₈×C₅₉	C₂³	1	3	yes	—
73	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
74	C₂²⋊C₈×C₅₉	—	2	3	no	—
75	C₂²⋊C₈×C₅₉	—	2	3	no	—
76	C₄×C₈×C₅₉	—	2	3	no	—
77	C₄×C₈×C₅₉	—	2	3	no	—
78	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
79	C₄×C₈×C₅₉	C₂³	1	3	yes	—
80	#41×C₅₉	—	2	24	no	—
81	#41×C₅₉	—	2	6	no	—
82	#41×C₅₉	C₂×C₈	1	4	yes	—
83	#41×C₅₉	C₂×C₈	1	12	yes	complemented
84	#41×C₅₉	M₁₆	1	4	yes	—
85	C₂×Q₈×C₅₉	—	2	8	no	—
86	C₂×Q₈×C₅₉	—	2	3	no	—
87	C₂×Q₈×C₅₉	—	2	6	no	—
88	C₂×Q₈×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
89	C₂×Q₈×C₅₉	C₂×C₈	1	12	yes	complemented
90	C₂×Q₈×C₅₉	C₂²×C₄	1	3	yes	—
91	C₂×D₄×C₅₉	—	2	3	no	—
92	C₂×D₄×C₅₉	C₂²⋊C₄	1	3	yes	—
93	C₂×D₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₄×C₅₉	—	2	3	no	—
95	C₂²×C₄×C₅₉	—	2	3	no	—
96	C₂²×C₄×C₅₉	—	2	3	no	—
97	C₂²×C₄×C₅₉	—	2	1	no	—
98	C₂²×C₄×C₅₉	—	2	3	no	—
99	C₂²×C₄×C₅₉	C₂²×C₄	1	3	yes	—
100	C₂²×C₄×C₅₉	C₂×D₄	1	3	yes	—
101	C₂²×C₄×C₅₉	C₂×D₄	1	3	yes	—
102	C₂×C₈×C₅₉	—	2	1	no	—
103	C₂×C₈×C₅₉	—	2	3	no	—
104	C₂×C₈×C₅₉	—	2	1	no	—
105	C₂×C₈×C₅₉	—	2	3	no	—
106	C₂×C₈×C₅₉	—	4	6	no	—
107	C₂×C₈×C₅₉	—	8	3	no	—
108	C₄⋊C₄×C₅₉	—	2	6	no	—
109	C₄⋊C₄×C₅₉	—	2	3	no	—
110	C₄⋊C₄×C₅₉	—	2	3	no	—
111	C₄⋊C₄×C₅₉	—	2	3	no	—
112	C₄⋊C₄×C₅₉	C₂²⋊C₄	1	3	yes	—
113	C₄⋊C₄×C₅₉	C₂²⋊C₄	1	3	yes	—
114	C₄⋊C₄×C₅₉	C₂²×C₄	1	3	yes	—
115	C₄⋊C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
116	C₂²⋊C₄×C₅₉	—	2	3	no	—
117	C₂²⋊C₄×C₅₉	—	2	3	no	—
118	C₂²⋊C₄×C₅₉	—	2	1	no	—
119	C₂²⋊C₄×C₅₉	C₂²⋊C₄	1	6	yes	—
120	C₄²×C₅₉	—	2	3	no	—
121	C₄²×C₅₉	—	2	6	no	—
122	C₄²×C₅₉	—	2	3	no	—
123	C₄²×C₅₉	—	2	3	no	—
124	C₄²×C₅₉	C₂²×C₄	1	3	yes	—
125	C₄²×C₅₉	C₂×D₄	1	3	yes	—
126	C₄²×C₅₉	C₂×D₄	1	3	yes	—
127	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
128	C₂³×C₅₉	—	2	1	no	—
129	C₂³×C₅₉	C₂×C₂²⋊C₄	1	3	yes	—
130	Q₈×C₅₉	—	2	3	no	—
131	Q₈×C₅₉	—	2	12	no	—
132	Q₈×C₅₉	C₂²⋊C₈	1	4	yes	—
133	Q₈×C₅₉	C₂²×C₈	1	6	yes	—
134	D₄×C₅₉	—	2	12	no	—
135	D₄×C₅₉	—	2	1	no	—
136	D₄×C₅₉	C₂²⋊C₈	1	12	yes	—
137	D₄×C₅₉	C₂²×C₈	1	2	yes	—
138	C₂×C₄×C₅₉	—	2	3	no	—
139	C₂×C₄×C₅₉	—	2	12	no	—
140	C₂×C₄×C₅₉	—	2	3	no	—
141	C₂×C₄×C₅₉	—	2	3	no	—
142	C₂×C₄×C₅₉	—	2	12	no	—
143	C₂×C₄×C₅₉	—	2	1	no	—
144	C₂×C₄×C₅₉	—	2	3	no	—
145	C₂×C₄×C₅₉	—	4	3	no	—
146	C₂×C₄×C₅₉	—	4	1	no	—
147	C₂×C₄×C₅₉	—	4	1	no	—
148	C₂×C₄×C₅₉	—	8	3	no	—
149	C₂×C₄×C₅₉	—	8	3	no	—
150	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	3	yes	—
151	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	3	yes	—
152	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	3	yes	—
153	C₂×C₄×C₅₉	C₂²×C₈	1	6	yes	—
154	C₂×C₄×C₅₉	C₂×M₁₆	1	6	yes	—
155	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
156	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
157	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
158	C₈×C₅₉	—	2	2	no	—
159	C₈×C₅₉	—	4	3	no	—
160	C₈×C₅₉	—	4	3	no	—
161	C₈×C₅₉	—	4	1	no	—
162	#17439	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
163	C₂²×C₅₉	—	2	3	no	—
164	C₂²×C₅₉	—	2	3	no	—
165	C₂²×C₅₉	—	2	2	no	—
166	C₂²×C₅₉	—	4	1	no	—
167	C₂²×C₅₉	—	4	1	no	—
168	C₂²×C₅₉	C₂×C₂²⋊C₈	1	6	yes	—
169	C₂²×C₅₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
170	C₄×C₅₉	—	2	6	no	—
171	C₄×C₅₉	—	2	3	no	—
172	C₄×C₅₉	—	2	1	no	—
173	C₄×C₅₉	—	2	3	no	—
174	C₄×C₅₉	—	4	1	no	—
175	C₄×C₅₉	—	4	3	no	—
176	C₄×C₅₉	C₂×C₂²⋊C₈	1	6	yes	—
177	C₄×C₅₉	C₂³×C₈	1	1	yes	characteristic
178	C₄×C₅₉	C₂²×M₁₆	1	1	yes	characteristic
179	C₄×C₅₉	#577	1	1	yes	characteristic
180	C₄×C₅₉	#578	1	1	yes	characteristic
181	C₄×2₋¹⁺⁴	C₂×C₅₉	1	1	yes	characteristic
182	#2988	C₂×C₅₉	1	1	yes	characteristic, complemented
183	C₈×#41	C₂×C₅₉	1	1	yes	characteristic, complemented
184	#1479	C₂×C₅₉	1	3	yes	complemented
185	#1477	C₂×C₅₉	1	3	yes	complemented
186	#1476	C₂×C₅₉	1	3	yes	complemented
187	C₂×Q₈⋊C₈	C₂×C₅₉	1	3	yes	complemented
188	C₂×C₅₉	—	2	6	no	—
189	C₂×C₅₉	—	4	2	no	—
190	C₂×C₅₉	C₂²×C₂²⋊C₈	1	1	yes	characteristic
191	C₂×C₅₉	#2898	1	1	yes	characteristic
192	C₂×C₅₉	#2901	1	1	yes	characteristic
193	C₂×2₋¹⁺⁴	C₄×C₅₉	1	1	yes	characteristic
194	#520	—	2	3	no	—
195	#520	C₄×C₅₉	1	3	yes	—
196	#520	C₄×C₅₉	1	1	yes	characteristic
197	#519	—	2	1	no	—
198	#519	C₄×C₅₉	1	3	yes	—
199	C₄×#41	—	2	3	no	—
200	C₄×#41	C₂²×C₅₉	1	3	yes	—
201	C₄×#41	C₂²×C₅₉	1	1	yes	characteristic
202	C₂×C₄×Q₈	—	2	1	no	—
203	C₂×C₄×Q₈	C₂²×C₅₉	1	3	yes	—
204	C₈×Q₈	—	2	1	no	—
205	C₈×Q₈	—	2	1	no	—
206	C₈×D₄	—	2	3	no	—
207	C₈×D₄	—	2	3	no	—
208	#431	C₂²×C₅₉	1	3	yes	—
209	#431	C₂²×C₅₉	1	3	yes	—
210	C₂×C₄⋊C₈	C₂²×C₅₉	1	3	yes	—
211	C₂×C₄×C₈	C₂²×C₅₉	1	3	yes	—
212	Q₈⋊C₈	C₂²×C₅₉	1	3	yes	—
213	Q₈⋊C₈	C₂²×C₅₉	1	6	yes	—
214	Q₈⋊C₈	C₂²×C₅₉	1	3	yes	—
215	D₄⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
216	D₄⋊C₈	C₂²×C₅₉	1	3	yes	—
217	C₅₉	#17439	1	1	yes	characteristic, direct product factor, Sylow
218	2₋¹⁺⁴	—	2	4	no	—
219	2₋¹⁺⁴	C₈×C₅₉	1	8	yes	complemented
220	C₂×#41	—	2	3	no	—
221	C₂×#41	C₂×C₄×C₅₉	1	3	yes	—
222	C₂×#41	C₂×C₄×C₅₉	1	1	yes	characteristic
223	C₂²×Q₈	—	2	1	no	—
224	C₂²×Q₈	C₂×C₄×C₅₉	1	3	yes	—
225	C₂²×C₈	—	2	3	no	—
226	C₂²×C₈	—	2	3	no	—
227	C₄×Q₈	—	2	1	no	—
228	C₄×Q₈	—	2	3	no	—
229	C₄×Q₈	—	2	3	no	—
230	C₄×Q₈	—	2	3	no	—
231	C₄×Q₈	—	2	3	no	—
232	C₄×Q₈	C₂×C₄×C₅₉	1	6	yes	—
233	C₄×Q₈	C₂×C₄×C₅₉	1	3	yes	—
234	C₄×Q₈	D₄×C₅₉	1	1	yes	characteristic
235	C₄×Q₈	D₄×C₅₉	1	1	yes	characteristic
236	C₄×Q₈	C₂³×C₅₉	1	3	yes	—
237	C₄×D₄	—	2	3	no	—
238	C₄×D₄	—	2	3	no	—
239	C₄×D₄	—	2	3	no	—
240	C₄×D₄	—	2	6	no	—
241	C₄×D₄	C₂×C₄×C₅₉	1	3	yes	—
242	C₄×D₄	D₄×C₅₉	1	3	yes	—
243	C₄×D₄	D₄×C₅₉	1	3	yes	—
244	C₄×D₄	C₂³×C₅₉	1	1	yes	characteristic
245	#117	—	2	3	no	—
246	#117	—	2	6	no	—
247	#117	—	2	3	no	—
248	#117	C₂×C₄×C₅₉	1	3	yes	—
249	#117	C₂×C₄×C₅₉	1	3	yes	—
250	C₂×C₄⋊C₄	—	2	3	no	—
251	C₂×C₄⋊C₄	—	2	3	no	—
252	C₂×C₄⋊C₄	C₂×C₄×C₅₉	1	3	yes	—
253	C₂×C₄²	—	2	3	no	—
254	C₂×C₄²	—	2	3	no	—
255	C₂×C₄²	C₂³×C₅₉	1	3	yes	—
256	C₄⋊C₈	—	2	3	no	—
257	C₄⋊C₈	—	2	3	no	—
258	C₄⋊C₈	C₂³×C₅₉	1	3	yes	—
259	C₄⋊C₈	C₂³×C₅₉	1	1	yes	characteristic
260	C₂²⋊C₈	—	2	3	no	—
261	C₂²⋊C₈	—	2	3	no	—
262	C₄×C₈	—	2	3	no	—
263	C₄×C₈	—	2	3	no	—
264	C₄×C₈	C₂³×C₅₉	1	1	yes	characteristic
265	C₄×C₈	C₂³×C₅₉	1	3	yes	—
266	#41	—	2	24	no	—
267	#41	—	2	6	no	—
268	#41	C₂×C₈×C₅₉	1	4	yes	—
269	#41	C₂×C₈×C₅₉	1	12	yes	complemented
270	#41	M₁₆×C₅₉	1	4	yes	—
271	C₂×Q₈	—	2	8	no	—
272	C₂×Q₈	—	2	3	no	—
273	C₂×Q₈	—	2	6	no	—
274	C₂×Q₈	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
275	C₂×Q₈	C₂×C₈×C₅₉	1	12	yes	complemented
276	C₂×Q₈	C₂²×C₄×C₅₉	1	3	yes	—
277	C₂×D₄	—	2	3	no	—
278	C₂×D₄	C₂²⋊C₄×C₅₉	1	3	yes	—
279	C₂×D₄	C₂²×C₄×C₅₉	1	1	yes	characteristic
280	C₂²×C₄	—	2	3	no	—
281	C₂²×C₄	—	2	3	no	—
282	C₂²×C₄	—	2	3	no	—
283	C₂²×C₄	—	2	1	no	—
284	C₂²×C₄	—	2	3	no	—
285	C₂²×C₄	C₂²×C₄×C₅₉	1	3	yes	—
286	C₂²×C₄	C₂×D₄×C₅₉	1	3	yes	—
287	C₂²×C₄	C₂×D₄×C₅₉	1	3	yes	—
288	C₂×C₈	—	2	1	no	—
289	C₂×C₈	—	2	1	no	—
290	C₂×C₈	—	2	3	no	—
291	C₂×C₈	—	2	3	no	—
292	C₂×C₈	—	4	6	no	—
293	C₂×C₈	—	8	3	no	—
294	C₄⋊C₄	—	2	6	no	—
295	C₄⋊C₄	—	2	3	no	—
296	C₄⋊C₄	—	2	3	no	—
297	C₄⋊C₄	—	2	3	no	—
298	C₄⋊C₄	C₂²⋊C₄×C₅₉	1	3	yes	—
299	C₄⋊C₄	C₂²⋊C₄×C₅₉	1	3	yes	—
300	C₄⋊C₄	C₂²×C₄×C₅₉	1	3	yes	—
301	C₄⋊C₄	C₂²×C₄×C₅₉	1	1	yes	characteristic
302	C₂²⋊C₄	—	2	3	no	—
303	C₂²⋊C₄	—	2	3	no	—
304	C₂²⋊C₄	—	2	1	no	—
305	C₂²⋊C₄	C₂²⋊C₄×C₅₉	1	6	yes	—
306	C₄²	—	2	3	no	—
307	C₄²	—	2	6	no	—
308	C₄²	—	2	3	no	—
309	C₄²	—	2	3	no	—
310	C₄²	C₂²×C₄×C₅₉	1	3	yes	—
311	C₄²	C₂×D₄×C₅₉	1	3	yes	—
312	C₄²	C₂×D₄×C₅₉	1	3	yes	—
313	C₄²	C₂⁴×C₅₉	1	1	yes	characteristic
314	C₂³	—	2	1	no	—
315	C₂³	C₂×C₂²⋊C₄×C₅₉	1	3	yes	—
316	Q₈	—	2	12	no	—
317	Q₈	—	2	3	no	—
318	Q₈	C₂²⋊C₈×C₅₉	1	4	yes	—
319	Q₈	C₂²×C₈×C₅₉	1	6	yes	—
320	D₄	—	2	12	no	—
321	D₄	—	2	1	no	—
322	D₄	C₂²⋊C₈×C₅₉	1	12	yes	—
323	D₄	C₂²×C₈×C₅₉	1	2	yes	—
324	C₂×C₄	—	2	12	no	—
325	C₂×C₄	—	2	3	no	—
326	C₂×C₄	—	2	12	no	—
327	C₂×C₄	—	2	3	no	—
328	C₂×C₄	—	2	3	no	—
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	—	2	3	no	—
331	C₂×C₄	—	4	3	no	—
332	C₂×C₄	—	4	1	no	—
333	C₂×C₄	—	4	1	no	—
334	C₂×C₄	—	8	3	no	—
335	C₂×C₄	—	8	3	no	—
336	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	3	yes	—
337	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	3	yes	—
338	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	3	yes	—
339	C₂×C₄	C₂²×C₈×C₅₉	1	6	yes	—
340	C₂×C₄	C₂×M₁₆×C₅₉	1	6	yes	—
341	C₂×C₄	C₂³×C₄×C₅₉	1	1	yes	characteristic
342	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
343	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
344	C₈	—	2	2	no	—
345	C₈	—	4	3	no	—
346	C₈	—	4	3	no	—
347	C₈	—	4	1	no	—
348	C₂²	—	2	3	no	—
349	C₂²	—	2	3	no	—
350	C₂²	—	2	2	no	—
351	C₂²	—	4	1	no	—
352	C₂²	—	4	1	no	—
353	C₂²	C₂×C₂²⋊C₈×C₅₉	1	6	yes	—
354	C₂²	C₂²×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
355	C₄	—	2	6	no	—
356	C₄	—	2	3	no	—
357	C₄	—	2	1	no	—
358	C₄	—	2	3	no	—
359	C₄	—	4	1	no	—
360	C₄	—	4	3	no	—
361	C₄	C₂×C₂²⋊C₈×C₅₉	1	6	yes	—
362	C₄	C₂³×C₈×C₅₉	1	1	yes	characteristic
363	C₄	C₂²×M₁₆×C₅₉	1	1	yes	characteristic
364	C₄	C₅₉×#577	1	1	yes	characteristic
365	C₄	C₅₉×#578	1	1	yes	characteristic
366	C₂	—	2	6	no	—
367	C₂	—	4	2	no	—
368	C₂	C₂²×C₂²⋊C₈×C₅₉	1	1	yes	characteristic
369	C₂	C₅₉×#2898	1	1	yes	characteristic
370	C₂	C₅₉×#2901	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅₉	C₂²×D₄
commutator	C₄	C₂³×C₈×C₅₉
Frattini, cosocle	C₄²	C₂⁴×C₅₉
socle	C₂²×C₅₉	C₂²×C₂²⋊C₄
prime radical	C₂×2₋¹⁺⁴×C₅₉	C₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅₉ ◁ C₄×#41×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅₉×#2988	C₂	semidirect
3. C₈×#41×C₅₉	C₂	semidirect
4. C₅₉×#1479	C₂	semidirect
5. C₅₉×#1477	C₂	semidirect
6. C₅₉×#1476	C₂	semidirect
7. C₂×C₅₉×Q₈⋊C₈	C₂	semidirect
33. 2₋¹⁺⁴×C₅₉	C₈	semidirect
83. #41×C₅₉	C₂×C₈	semidirect
89. C₂×Q₈×C₅₉	C₂×C₈	semidirect
162. #17439	C₅₉	direct (N × H)
182. #2988	C₂×C₅₉	semidirect
183. C₈×#41	C₂×C₅₉	semidirect
184. #1479	C₂×C₅₉	semidirect
185. #1477	C₂×C₅₉	semidirect
186. #1476	C₂×C₅₉	semidirect
187. C₂×Q₈⋊C₈	C₂×C₅₉	semidirect
217. C₅₉	#17439	direct (N × H)
219. 2₋¹⁺⁴	C₈×C₅₉	semidirect
269. #41	C₂×C₈×C₅₉	semidirect
275. C₂×Q₈	C₂×C₈×C₅₉	semidirect

Maximal subgroups

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

subgroup	index
C₄×2₋¹⁺⁴×C₅₉	2
C₅₉×#2988	2
C₈×#41×C₅₉	2
C₅₉×#1479	2
C₅₉×#1477	2
C₅₉×#1476	2
C₂×C₅₉×Q₈⋊C₈	2
#17439	59

Subgroups — C59×#17439 #28429548

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#17439 #28429548