Subgroups — C₅₉×#23456 #28435565

Order 15104.

1362 conjugacy classes of subgroups.

The subgroup lattice has 496 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	C₂×C₅₉×#418	C₂	1	1	yes	maximal, characteristic
3	C₂²×#102×C₅₉	C₂	1	1	yes	maximal, characteristic
4	C₅₉×#2309	C₂	1	1	yes	maximal, characteristic
5	C₅₉×#2025	C₂	1	4	yes	maximal, complemented
6	C₅₉×#2023	C₂	1	4	yes	maximal, complemented
7	C₅₉×#1736	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₉×#1735	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₉×#1729	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×D₄×C₅₉	C₂²	1	1	yes	characteristic
11	C₂²×M₁₆×C₅₉	C₂²	1	1	yes	characteristic
12	C₂³×C₈×C₅₉	C₂²	1	1	yes	characteristic
13	C₅₉×#544	—	2	4	no	—
14	C₅₉×#544	—	2	4	no	—
15	C₂×C₄⋊Q₈×C₅₉	—	2	1	no	—
16	C₂×C₄⋊Q₈×C₅₉	C₂²	1	2	yes	complemented
17	C₂×#125×C₅₉	—	2	1	no	—
18	C₂×#125×C₅₉	C₂²	1	2	yes	complemented
19	C₂×C₂²⋊Q₈×C₅₉	—	2	2	no	—
20	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
21	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
22	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
23	C₂²×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
24	C₅₉×#418	—	2	4	no	—
25	C₂×#102×C₅₉	—	2	4	no	—
26	C₂×#102×C₅₉	C₂²	1	2	yes	—
27	C₂×#102×C₅₉	C₂²	1	4	yes	—
28	C₂×#102×C₅₉	C₂²	1	2	yes	—
29	C₅₉×#390	—	2	1	no	—
30	C₅₉×#390	—	2	1	no	—
31	C₅₉×#390	C₂²	1	4	yes	—
32	C₅₉×#379	—	2	2	no	—
33	C₅₉×#340	C₂²	1	2	yes	complemented
34	C₅₉×#340	C₂²	1	2	yes	complemented
35	C₅₉×#340	C₂²	1	4	yes	complemented
36	C₅₉×#336	C₂²	1	4	yes	complemented
37	C₂⁵×C₅₉	—	2	1	no	—
38	C₂²×Q₈×C₅₉	—	2	2	no	—
39	C₂²×D₄×C₅₉	—	2	2	no	—
40	C₂²×D₄×C₅₉	—	2	2	no	—
41	C₂²×D₄×C₅₉	—	2	1	no	—
42	C₂²×D₄×C₅₉	—	2	2	no	—
43	C₂²×D₄×C₅₉	—	2	2	no	—
44	C₂²×D₄×C₅₉	—	2	2	no	—
45	C₂²×D₄×C₅₉	Q₈	1	4	yes	complemented
46	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
47	C₂³×C₄×C₅₉	—	2	1	no	—
48	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
49	C₂×M₁₆×C₅₉	—	2	2	no	—
50	C₂×M₁₆×C₅₉	—	2	2	no	—
51	C₂×M₁₆×C₅₉	—	2	2	no	—
52	C₂²×C₈×C₅₉	—	2	2	no	—
53	C₂²×C₈×C₅₉	—	2	2	no	—
54	C₂²×C₈×C₅₉	—	2	2	no	—
55	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
56	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
57	C₄⋊Q₈×C₅₉	—	2	8	no	—
58	C₄⋊Q₈×C₅₉	—	2	4	no	—
59	C₄⋊Q₈×C₅₉	—	2	4	no	—
60	#125×C₅₉	—	2	8	no	—
61	#125×C₅₉	—	2	4	no	—
62	#125×C₅₉	—	2	4	no	—
63	C₂²⋊Q₈×C₅₉	—	2	16	no	—
64	#117×C₅₉	—	2	2	no	—
65	#117×C₅₉	—	2	2	no	—
66	#117×C₅₉	—	2	2	no	—
67	#117×C₅₉	—	2	2	no	—
68	#117×C₅₉	—	2	2	no	—
69	#117×C₅₉	D₄	1	4	yes	—
70	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
71	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
72	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
73	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
74	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
75	C₂×C₄⋊C₄×C₅₉	D₄	1	1	yes	characteristic
76	C₂×C₄⋊C₄×C₅₉	D₄	1	1	yes	characteristic
77	C₂×C₄⋊C₄×C₅₉	D₄	1	4	yes	—
78	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
79	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
80	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
82	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
83	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
84	C₂×C₂²⋊C₄×C₅₉	—	2	4	no	—
85	C₂×C₂²⋊C₄×C₅₉	—	2	4	no	—
86	C₂×C₂²⋊C₄×C₅₉	D₄	1	2	yes	—
87	C₂×C₄²×C₅₉	—	2	1	no	—
88	C₂×C₄²×C₅₉	—	2	1	no	—
89	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
90	#102×C₅₉	—	2	8	no	—
91	#102×C₅₉	—	2	4	no	—
92	#102×C₅₉	—	2	4	no	—
93	C₂⁴×C₅₉	—	2	2	no	—
94	C₂⁴×C₅₉	—	2	4	no	—
95	C₂⁴×C₅₉	—	4	2	no	—
96	C₂⁴×C₅₉	—	4	2	no	—
97	C₂⁴×C₅₉	—	8	2	no	—
98	C₂⁴×C₅₉	—	8	2	no	—
99	C₂⁴×C₅₉	C₂×D₄	1	1	yes	characteristic
100	C₂×Q₈×C₅₉	—	2	8	no	—
101	C₂×Q₈×C₅₉	—	8	4	no	—
102	C₂×D₄×C₅₉	—	2	8	no	—
103	C₂×D₄×C₅₉	—	2	8	no	—
104	C₂×D₄×C₅₉	—	2	4	no	—
105	C₂×D₄×C₅₉	—	2	2	no	—
106	C₂×D₄×C₅₉	—	2	2	no	—
107	C₂×D₄×C₅₉	—	2	2	no	—
108	C₂×D₄×C₅₉	—	2	2	no	—
109	C₂×D₄×C₅₉	—	2	2	no	—
110	C₂×D₄×C₅₉	—	4	2	no	—
111	C₂×D₄×C₅₉	—	4	4	no	—
112	C₂×D₄×C₅₉	—	4	4	no	—
113	C₂×D₄×C₅₉	—	4	2	no	—
114	C₂×D₄×C₅₉	C₂×Q₈	1	4	yes	—
115	C₂²×C₄×C₅₉	—	2	1	no	—
116	C₂²×C₄×C₅₉	—	2	1	no	—
117	C₂²×C₄×C₅₉	—	2	2	no	—
118	C₂²×C₄×C₅₉	—	2	4	no	—
119	C₂²×C₄×C₅₉	—	2	2	no	—
120	C₂²×C₄×C₅₉	—	8	2	no	—
121	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
122	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
123	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
126	C₂²×C₄×C₅₉	C₂×Q₈	1	2	yes	—
127	C₂²×C₄×C₅₉	#41	1	2	yes	—
128	C₂²×C₄×C₅₉	#41	1	2	yes	—
129	C₂²×C₄×C₅₉	#41	1	2	yes	—
130	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
131	M₁₆×C₅₉	—	4	4	no	—
132	C₂×C₈×C₅₉	—	2	2	no	—
133	C₂×C₈×C₅₉	—	2	2	no	—
134	C₂×C₈×C₅₉	—	2	2	no	—
135	C₂×C₈×C₅₉	—	2	2	no	—
136	C₂×C₈×C₅₉	—	2	2	no	—
137	C₂×C₈×C₅₉	—	2	2	no	—
138	C₂×C₈×C₅₉	—	4	4	no	—
139	C₄⋊C₄×C₅₉	—	2	8	no	—
140	C₄⋊C₄×C₅₉	—	2	8	no	—
141	C₄⋊C₄×C₅₉	—	2	8	no	—
142	C₄⋊C₄×C₅₉	—	2	4	no	—
143	C₄⋊C₄×C₅₉	—	2	2	no	—
144	C₄⋊C₄×C₅₉	—	2	2	no	—
145	C₄⋊C₄×C₅₉	—	2	2	no	—
146	C₄⋊C₄×C₅₉	—	2	1	no	—
147	C₄⋊C₄×C₅₉	—	2	1	no	—
148	C₄⋊C₄×C₅₉	—	2	2	no	—
149	C₄⋊C₄×C₅₉	—	2	2	no	—
150	C₄⋊C₄×C₅₉	C₂×D₄	1	4	yes	—
151	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
152	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
153	C₂²⋊C₄×C₅₉	—	2	4	no	—
154	C₂²⋊C₄×C₅₉	—	2	4	no	—
155	C₂²⋊C₄×C₅₉	—	4	2	no	—
156	C₂²⋊C₄×C₅₉	—	8	4	no	—
157	C₂²⋊C₄×C₅₉	—	8	4	no	—
158	C₄²×C₅₉	—	2	4	no	—
159	C₄²×C₅₉	—	2	2	no	—
160	C₄²×C₅₉	—	2	2	no	—
161	C₄²×C₅₉	—	4	2	no	—
162	C₂³×C₅₉	—	2	2	no	—
163	C₂³×C₅₉	—	2	2	no	—
164	C₂³×C₅₉	—	2	4	no	—
165	C₂³×C₅₉	—	4	2	no	—
166	C₂³×C₅₉	—	4	2	no	—
167	C₂³×C₅₉	—	4	4	no	—
168	C₂³×C₅₉	—	4	4	no	—
169	C₂³×C₅₉	—	4	8	no	—
170	C₂³×C₅₉	—	8	8	no	—
171	C₂³×C₅₉	—	8	8	no	—
172	C₂³×C₅₉	—	8	4	no	—
173	C₂³×C₅₉	—	8	4	no	—
174	C₂³×C₅₉	#120	1	2	yes	—
175	C₂³×C₅₉	C₂²⋊Q₈	1	2	yes	—
176	C₂³×C₅₉	#124	1	2	yes	—
177	C₂³×C₅₉	C₂²×D₄	1	1	yes	characteristic
178	Q₈×C₅₉	—	8	8	no	—
179	D₄×C₅₉	—	2	4	no	—
180	D₄×C₅₉	—	2	4	no	—
181	D₄×C₅₉	—	4	2	no	—
182	D₄×C₅₉	—	4	2	no	—
183	D₄×C₅₉	—	4	8	no	—
184	C₂×C₄×C₅₉	—	2	2	no	—
185	C₂×C₄×C₅₉	—	2	2	no	—
186	C₂×C₄×C₅₉	—	2	2	no	—
187	C₂×C₄×C₅₉	—	2	2	no	—
188	C₂×C₄×C₅₉	—	2	4	no	—
189	C₂×C₄×C₅₉	—	2	4	no	—
190	C₂×C₄×C₅₉	—	2	4	no	—
191	C₂×C₄×C₅₉	—	4	4	no	—
192	C₂×C₄×C₅₉	—	4	2	no	—
193	C₂×C₄×C₅₉	—	4	2	no	—
194	C₂×C₄×C₅₉	—	4	2	no	—
195	C₂×C₄×C₅₉	—	4	2	no	—
196	C₂×C₄×C₅₉	—	4	2	no	—
197	C₂×C₄×C₅₉	—	8	4	no	—
198	C₂×C₄×C₅₉	#120	1	2	yes	—
199	C₂×C₄×C₅₉	C₂²⋊Q₈	1	4	yes	—
200	C₂×C₄×C₅₉	C₂²⋊Q₈	1	4	yes	—
201	C₂×C₄×C₅₉	C₂²⋊Q₈	1	2	yes	—
202	C₂×C₄×C₅₉	#124	1	4	yes	—
203	C₂×C₄×C₅₉	#124	1	4	yes	—
204	C₂×C₄×C₅₉	#124	1	2	yes	—
205	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
206	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
207	C₂×C₄×C₅₉	C₂²×Q₈	1	1	yes	characteristic
208	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
209	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
210	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
211	C₈×C₅₉	—	4	2	no	—
212	C₈×C₅₉	—	4	2	no	—
213	#23456	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
214	C₂²×C₅₉	—	2	4	no	—
215	C₂²×C₅₉	—	2	4	no	—
216	C₂²×C₅₉	—	2	2	no	—
217	C₂²×C₅₉	—	2	2	no	—
218	C₂²×C₅₉	—	4	8	no	—
219	C₂²×C₅₉	—	4	4	no	—
220	C₂²×C₅₉	—	8	16	no	—
221	C₂²×C₅₉	—	8	4	no	—
222	C₂²×C₅₉	—	8	2	no	—
223	C₂²×C₅₉	—	8	2	no	—
224	C₂²×C₅₉	#393	1	4	yes	—
225	C₂²×C₅₉	C₂×#120	1	1	yes	characteristic
226	C₂²×C₅₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
227	C₂²×C₅₉	C₂×#124	1	1	yes	characteristic
228	C₂²×C₅₉	#576	1	2	yes	—
229	C₂²×C₅₉	#577	1	2	yes	—
230	C₄×C₅₉	—	4	2	no	—
231	C₄×C₅₉	—	4	4	no	—
232	C₄×C₅₉	—	4	2	no	—
233	C₄×C₅₉	—	4	2	no	—
234	C₄×C₅₉	—	4	2	no	—
235	C₄×C₅₉	—	8	2	no	—
236	C₄×C₅₉	#393	1	4	yes	—
237	C₄×C₅₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
238	C₄×C₅₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
239	C₄×C₅₉	C₂×#124	1	1	yes	characteristic
240	C₄×C₅₉	C₂×#124	1	1	yes	characteristic
241	C₂×#544	C₂×C₅₉	1	1	yes	characteristic, complemented
242	C₂×#418	C₂×C₅₉	1	1	yes	characteristic
243	C₂²×#102	C₂×C₅₉	1	1	yes	characteristic
244	#2309	C₂×C₅₉	1	1	yes	characteristic
245	#2025	C₂×C₅₉	1	4	yes	complemented
246	#2023	C₂×C₅₉	1	4	yes	complemented
247	#1736	C₂×C₅₉	1	1	yes	characteristic, complemented
248	#1735	C₂×C₅₉	1	1	yes	characteristic, complemented
249	#1729	C₂×C₅₉	1	1	yes	characteristic, complemented
250	C₂×C₅₉	—	2	4	no	—
251	C₂×C₅₉	—	8	4	no	—
252	C₂×C₅₉	C₂×#393	1	1	yes	characteristic
253	C₂×C₅₉	#3008	1	1	yes	characteristic
254	C₂×C₅₉	#3010	1	1	yes	characteristic
255	C₂×C₅₉	#3081	1	2	yes	—
256	C₂×C₅₉	#3136	1	2	yes	—
257	C₂³×D₄	C₂²×C₅₉	1	1	yes	characteristic
258	C₂²×M₁₆	C₂²×C₅₉	1	1	yes	characteristic
259	C₂³×C₈	C₂²×C₅₉	1	1	yes	characteristic
260	#544	—	2	4	no	—
261	#544	—	2	4	no	—
262	C₂×C₄⋊Q₈	—	2	1	no	—
263	C₂×C₄⋊Q₈	C₂²×C₅₉	1	2	yes	complemented
264	C₂×#125	—	2	1	no	—
265	C₂×#125	C₂²×C₅₉	1	2	yes	complemented
266	C₂×C₂²⋊Q₈	—	2	2	no	—
267	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
268	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
269	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
270	C₂²×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
271	#418	—	2	4	no	—
272	C₂×#102	—	2	4	no	—
273	C₂×#102	C₂²×C₅₉	1	4	yes	—
274	C₂×#102	C₂²×C₅₉	1	2	yes	—
275	C₂×#102	C₂²×C₅₉	1	2	yes	—
276	#390	—	2	1	no	—
277	#390	—	2	1	no	—
278	#390	C₂²×C₅₉	1	4	yes	—
279	#379	—	2	2	no	—
280	#340	C₂²×C₅₉	1	2	yes	complemented
281	#340	C₂²×C₅₉	1	2	yes	complemented
282	#340	C₂²×C₅₉	1	4	yes	complemented
283	#336	C₂²×C₅₉	1	4	yes	complemented
284	C₅₉	#23456	1	1	yes	characteristic, direct product factor, Sylow
285	C₂⁵	—	2	1	no	—
286	C₂²×Q₈	—	2	2	no	—
287	C₂²×D₄	—	2	2	no	—
288	C₂²×D₄	—	2	2	no	—
289	C₂²×D₄	—	2	1	no	—
290	C₂²×D₄	—	2	2	no	—
291	C₂²×D₄	—	2	2	no	—
292	C₂²×D₄	—	2	2	no	—
293	C₂²×D₄	Q₈×C₅₉	1	4	yes	complemented
294	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
295	C₂³×C₄	—	2	1	no	—
296	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
297	C₂×M₁₆	—	2	2	no	—
298	C₂×M₁₆	—	2	2	no	—
299	C₂×M₁₆	—	2	2	no	—
300	C₂²×C₈	—	2	2	no	—
301	C₂²×C₈	—	2	2	no	—
302	C₂²×C₈	—	2	2	no	—
303	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
304	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
305	C₄⋊Q₈	—	2	8	no	—
306	C₄⋊Q₈	—	2	4	no	—
307	C₄⋊Q₈	—	2	4	no	—
308	#125	—	2	8	no	—
309	#125	—	2	4	no	—
310	#125	—	2	4	no	—
311	C₂²⋊Q₈	—	2	16	no	—
312	#117	—	2	2	no	—
313	#117	—	2	2	no	—
314	#117	—	2	2	no	—
315	#117	—	2	2	no	—
316	#117	—	2	2	no	—
317	#117	D₄×C₅₉	1	4	yes	—
318	C₂×C₄⋊C₄	—	2	1	no	—
319	C₂×C₄⋊C₄	—	2	2	no	—
320	C₂×C₄⋊C₄	—	2	2	no	—
321	C₂×C₄⋊C₄	—	2	2	no	—
322	C₂×C₄⋊C₄	—	2	2	no	—
323	C₂×C₄⋊C₄	D₄×C₅₉	1	1	yes	characteristic
324	C₂×C₄⋊C₄	D₄×C₅₉	1	1	yes	characteristic
325	C₂×C₄⋊C₄	D₄×C₅₉	1	4	yes	—
326	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
327	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
328	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
329	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
330	C₂×C₂²⋊C₄	—	2	1	no	—
331	C₂×C₂²⋊C₄	—	2	1	no	—
332	C₂×C₂²⋊C₄	—	2	4	no	—
333	C₂×C₂²⋊C₄	—	2	4	no	—
334	C₂×C₂²⋊C₄	D₄×C₅₉	1	2	yes	—
335	C₂×C₄²	—	2	1	no	—
336	C₂×C₄²	—	2	1	no	—
337	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
338	#102	—	2	8	no	—
339	#102	—	2	4	no	—
340	#102	—	2	4	no	—
341	C₂⁴	—	2	2	no	—
342	C₂⁴	—	2	4	no	—
343	C₂⁴	—	4	2	no	—
344	C₂⁴	—	4	2	no	—
345	C₂⁴	—	8	2	no	—
346	C₂⁴	—	8	2	no	—
347	C₂⁴	C₂×D₄×C₅₉	1	1	yes	characteristic
348	C₂×Q₈	—	2	8	no	—
349	C₂×Q₈	—	8	4	no	—
350	C₂×D₄	—	2	8	no	—
351	C₂×D₄	—	2	8	no	—
352	C₂×D₄	—	2	4	no	—
353	C₂×D₄	—	2	2	no	—
354	C₂×D₄	—	2	2	no	—
355	C₂×D₄	—	2	2	no	—
356	C₂×D₄	—	2	2	no	—
357	C₂×D₄	—	2	2	no	—
358	C₂×D₄	—	4	2	no	—
359	C₂×D₄	—	4	2	no	—
360	C₂×D₄	—	4	4	no	—
361	C₂×D₄	—	4	4	no	—
362	C₂×D₄	C₂×Q₈×C₅₉	1	4	yes	—
363	C₂²×C₄	—	2	1	no	—
364	C₂²×C₄	—	2	1	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	4	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	8	2	no	—
369	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
370	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
371	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
372	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
373	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
374	C₂²×C₄	C₂×Q₈×C₅₉	1	2	yes	—
375	C₂²×C₄	#41×C₅₉	1	2	yes	—
376	C₂²×C₄	#41×C₅₉	1	2	yes	—
377	C₂²×C₄	#41×C₅₉	1	2	yes	—
378	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
379	M₁₆	—	4	4	no	—
380	C₂×C₈	—	2	2	no	—
381	C₂×C₈	—	2	2	no	—
382	C₂×C₈	—	2	2	no	—
383	C₂×C₈	—	2	2	no	—
384	C₂×C₈	—	2	2	no	—
385	C₂×C₈	—	2	2	no	—
386	C₂×C₈	—	4	4	no	—
387	C₄⋊C₄	—	2	8	no	—
388	C₄⋊C₄	—	2	8	no	—
389	C₄⋊C₄	—	2	8	no	—
390	C₄⋊C₄	—	2	4	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	2	2	no	—
393	C₄⋊C₄	—	2	2	no	—
394	C₄⋊C₄	—	2	1	no	—
395	C₄⋊C₄	—	2	1	no	—
396	C₄⋊C₄	—	2	2	no	—
397	C₄⋊C₄	—	2	2	no	—
398	C₄⋊C₄	C₂×D₄×C₅₉	1	4	yes	—
399	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
400	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
401	C₂²⋊C₄	—	2	4	no	—
402	C₂²⋊C₄	—	2	4	no	—
403	C₂²⋊C₄	—	4	2	no	—
404	C₂²⋊C₄	—	8	4	no	—
405	C₂²⋊C₄	—	8	4	no	—
406	C₄²	—	2	4	no	—
407	C₄²	—	2	2	no	—
408	C₄²	—	2	2	no	—
409	C₄²	—	4	2	no	—
410	C₂³	—	2	2	no	—
411	C₂³	—	2	2	no	—
412	C₂³	—	2	4	no	—
413	C₂³	—	4	8	no	—
414	C₂³	—	4	2	no	—
415	C₂³	—	4	2	no	—
416	C₂³	—	4	4	no	—
417	C₂³	—	4	4	no	—
418	C₂³	—	8	8	no	—
419	C₂³	—	8	4	no	—
420	C₂³	—	8	4	no	—
421	C₂³	—	8	8	no	—
422	C₂³	#120×C₅₉	1	2	yes	—
423	C₂³	C₂²⋊Q₈×C₅₉	1	2	yes	—
424	C₂³	#124×C₅₉	1	2	yes	—
425	C₂³	C₂²×D₄×C₅₉	1	1	yes	characteristic
426	Q₈	—	8	8	no	—
427	D₄	—	2	4	no	—
428	D₄	—	2	4	no	—
429	D₄	—	4	8	no	—
430	D₄	—	4	2	no	—
431	D₄	—	4	2	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	4	no	—
437	C₂×C₄	—	2	4	no	—
438	C₂×C₄	—	2	4	no	—
439	C₂×C₄	—	4	4	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	8	4	no	—
446	C₂×C₄	#120×C₅₉	1	2	yes	—
447	C₂×C₄	C₂²⋊Q₈×C₅₉	1	2	yes	—
448	C₂×C₄	C₂²⋊Q₈×C₅₉	1	4	yes	—
449	C₂×C₄	C₂²⋊Q₈×C₅₉	1	4	yes	—
450	C₂×C₄	#124×C₅₉	1	2	yes	—
451	C₂×C₄	#124×C₅₉	1	4	yes	—
452	C₂×C₄	#124×C₅₉	1	4	yes	—
453	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
454	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
455	C₂×C₄	C₂²×Q₈×C₅₉	1	1	yes	characteristic
456	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
457	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
458	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
459	C₈	—	4	2	no	—
460	C₈	—	4	2	no	—
461	C₂²	—	2	2	no	—
462	C₂²	—	2	2	no	—
463	C₂²	—	2	4	no	—
464	C₂²	—	2	4	no	—
465	C₂²	—	4	8	no	—
466	C₂²	—	4	4	no	—
467	C₂²	—	8	16	no	—
468	C₂²	—	8	2	no	—
469	C₂²	—	8	2	no	—
470	C₂²	—	8	4	no	—
471	C₂²	C₅₉×#393	1	4	yes	—
472	C₂²	C₂×#120×C₅₉	1	1	yes	characteristic
473	C₂²	C₂×C₂²⋊Q₈×C₅₉	1	1	yes	characteristic
474	C₂²	C₂×#124×C₅₉	1	1	yes	characteristic
475	C₂²	C₅₉×#576	1	2	yes	—
476	C₂²	C₅₉×#577	1	2	yes	—
477	C₄	—	4	2	no	—
478	C₄	—	4	4	no	—
479	C₄	—	4	2	no	—
480	C₄	—	4	2	no	—
481	C₄	—	4	2	no	—
482	C₄	—	8	2	no	—
483	C₄	C₅₉×#393	1	4	yes	—
484	C₄	C₂×C₂²⋊Q₈×C₅₉	1	1	yes	characteristic
485	C₄	C₂×C₂²⋊Q₈×C₅₉	1	1	yes	characteristic
486	C₄	C₂×#124×C₅₉	1	1	yes	characteristic
487	C₄	C₂×#124×C₅₉	1	1	yes	characteristic
488	C₂	—	2	4	no	—
489	C₂	—	8	4	no	—
490	C₂	C₂×C₅₉×#393	1	1	yes	characteristic
491	C₂	C₅₉×#3008	1	1	yes	characteristic
492	C₂	C₅₉×#3010	1	1	yes	characteristic
493	C₂	C₅₉×#3081	1	2	yes	—
494	C₂	C₅₉×#3136	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₅₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅₉
prime radical	C₂³×D₄×C₅₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₉ ◁ C₂×#117×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅₉×#544	C₂	semidirect
5. C₅₉×#2025	C₂	semidirect
6. C₅₉×#2023	C₂	semidirect
7. C₅₉×#1736	C₂	semidirect
8. C₅₉×#1735	C₂	semidirect
9. C₅₉×#1729	C₂	semidirect
16. C₂×C₄⋊Q₈×C₅₉	C₂²	semidirect
18. C₂×#125×C₅₉	C₂²	semidirect
33. C₅₉×#340	C₂²	semidirect
34. C₅₉×#340	C₂²	semidirect
35. C₅₉×#340	C₂²	semidirect
36. C₅₉×#336	C₂²	semidirect
45. C₂²×D₄×C₅₉	Q₈	semidirect
213. #23456	C₅₉	direct (N × H)
241. C₂×#544	C₂×C₅₉	semidirect
245. #2025	C₂×C₅₉	semidirect
246. #2023	C₂×C₅₉	semidirect
247. #1736	C₂×C₅₉	semidirect
248. #1735	C₂×C₅₉	semidirect
249. #1729	C₂×C₅₉	semidirect
263. C₂×C₄⋊Q₈	C₂²×C₅₉	semidirect
265. C₂×#125	C₂²×C₅₉	semidirect
280. #340	C₂²×C₅₉	semidirect
281. #340	C₂²×C₅₉	semidirect
282. #340	C₂²×C₅₉	semidirect
283. #336	C₂²×C₅₉	semidirect
284. C₅₉	#23456	direct (N × H)
293. C₂²×D₄	Q₈×C₅₉	semidirect

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
C₂×C₅₉×#418	2
C₂²×#102×C₅₉	2
C₅₉×#2309	2
C₅₉×#2025	2
C₅₉×#2023	2
C₅₉×#1736	2
C₅₉×#1735	2
C₅₉×#1729	2
#23456	59

Subgroups — C59×#23456 #28435565

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#23456 #28435565