Subgroups — C₅₉×#34633 #28446742

Order 15104.

3166 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₉×#532	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅₉×#525	C₂	1	2	yes	maximal, complemented
3	C₂²×#117×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₉×#2621	C₂	1	2	yes	maximal, complemented
5	C₅₉×#2620	C₂	1	4	yes	maximal, complemented
6	C₅₉×#2619	C₂	1	2	yes	maximal, complemented
7	C₅₉×#2618	C₂	1	4	yes	maximal, complemented
8	C₅₉×#2617	C₂	1	4	yes	maximal, complemented
9	C₅₉×#2392	C₂	1	8	yes	maximal, complemented
10	C₅₉×#2297	C₂	1	2	yes	maximal, complemented
11	C₅₉×#2285	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₅₉	C₂²	1	2	yes	—
13	C₂⁴×C₄×C₅₉	C₂²	1	1	yes	characteristic
14	C₅₉×#532	—	2	8	no	—
15	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic, complemented
16	C₂×#127×C₅₉	C₂²	1	1	yes	characteristic, complemented
17	C₂×#124×C₅₉	C₂²	1	2	yes	complemented
18	C₅₉×#525	—	2	16	no	—
19	C₂×#123×C₅₉	C₂²	1	4	yes	—
20	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	4	yes	—
21	C₂×#121×C₅₉	C₂²	1	4	yes	—
22	C₂×#121×C₅₉	C₂²	1	4	yes	—
23	C₂×#120×C₅₉	C₂²	1	4	yes	—
24	C₂×C₄×D₄×C₅₉	C₂²	1	8	yes	—
25	C₂×C₄×D₄×C₅₉	C₂²	1	4	yes	complemented
26	C₂×#117×C₅₉	—	2	8	no	—
27	C₂×#117×C₅₉	C₂²	1	2	yes	—
28	C₂×#117×C₅₉	C₂²	1	2	yes	—
29	C₂×#117×C₅₉	C₂²	1	2	yes	—
30	C₂×#117×C₅₉	C₂²	1	4	yes	—
31	C₂²×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
32	C₂²×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
33	C₂²×C₄²×C₅₉	C₂²	1	1	yes	characteristic
34	C₂²×C₄²×C₅₉	C₂²	1	1	yes	characteristic
35	C₅₉×#398	C₂²	1	8	yes	complemented
36	C₅₉×#397	C₂²	1	8	yes	—
37	C₅₉×#396	C₂²	1	16	yes	complemented
38	C₅₉×#394	C₂²	1	16	yes	—
39	C₅₉×#394	C₂²	1	8	yes	complemented
40	C₅₉×#392	C₂²	1	8	yes	—
41	C₅₉×#391	C₂²	1	4	yes	complemented
42	C₅₉×#390	C₂²	1	4	yes	complemented
43	C₅₉×#386	C₂²	1	8	yes	—
44	C₅₉×#384	C₂²	1	2	yes	complemented
45	C₅₉×#382	C₂²	1	2	yes	complemented
46	C₅₉×#380	C₂²	1	4	yes	—
47	C₄×C₄⋊C₄×C₅₉	C₂²	1	4	yes	complemented
48	C₄×C₂²⋊C₄×C₅₉	C₂²	1	8	yes	complemented
49	C₂⁵×C₅₉	C₂³	1	1	yes	characteristic
50	C₂×#41×C₅₉	—	2	8	no	—
51	C₂×#41×C₅₉	—	2	8	no	—
52	C₂×#41×C₅₉	—	2	8	no	—
53	C₂²×Q₈×C₅₉	C₂³	1	2	yes	—
54	C₂²×D₄×C₅₉	C₂³	1	4	yes	—
55	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
56	C₂²×D₄×C₅₉	C₂³	1	8	yes	—
57	C₂²×D₄×C₅₉	C₂³	1	4	yes	—
58	C₂³×C₄×C₅₉	—	2	4	no	—
59	C₂³×C₄×C₅₉	—	2	4	no	—
60	C₂³×C₄×C₅₉	D₄	1	8	yes	complemented
61	C₂³×C₄×C₅₉	C₂³	1	4	yes	—
62	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
64	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
65	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
66	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
67	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
68	C₄⋊Q₈×C₅₉	—	2	4	no	—
69	#127×C₅₉	—	2	4	no	—
70	#124×C₅₉	—	2	8	no	—
71	#123×C₅₉	—	2	16	no	—
72	C₂²⋊Q₈×C₅₉	—	2	16	no	—
73	#121×C₅₉	—	2	16	no	—
74	#121×C₅₉	—	2	16	no	—
75	#120×C₅₉	—	2	16	no	—
76	C₄×D₄×C₅₉	—	2	32	no	—
77	C₄×D₄×C₅₉	—	2	16	no	—
78	#117×C₅₉	—	2	8	no	—
79	#117×C₅₉	—	2	16	no	—
80	#117×C₅₉	—	2	8	no	—
81	#117×C₅₉	—	2	8	no	—
82	C₂×C₄⋊C₄×C₅₉	—	2	8	no	—
83	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
84	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
85	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
86	C₂×C₄⋊C₄×C₅₉	C₂³	1	8	yes	—
87	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
88	C₂×C₄⋊C₄×C₅₉	C₂³	1	8	yes	—
89	C₂×C₂²⋊C₄×C₅₉	—	2	8	no	—
90	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
91	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
92	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
93	C₂×C₂²⋊C₄×C₅₉	C₂³	1	8	yes	—
94	C₂×C₂²⋊C₄×C₅₉	C₂³	1	8	yes	—
95	C₂×C₂²⋊C₄×C₅₉	C₂³	1	8	yes	—
96	C₂×C₂²⋊C₄×C₅₉	C₂³	1	16	yes	—
97	C₂×C₄²×C₅₉	—	2	4	no	—
98	C₂×C₄²×C₅₉	D₄	1	8	yes	complemented
99	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
100	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
101	C₂×C₄²×C₅₉	C₂³	1	4	yes	—
102	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
103	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
104	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
105	#95×C₅₉	C₂³	1	16	yes	—
106	#95×C₅₉	C₂³	1	8	yes	—
107	C₂⁴×C₅₉	—	2	2	no	—
108	C₂⁴×C₅₉	—	2	2	no	—
109	C₂⁴×C₅₉	—	4	4	no	—
110	C₂⁴×C₅₉	C₂×D₄	1	4	yes	—
111	C₂⁴×C₅₉	C₂⁴	1	4	yes	—
112	C₂⁴×C₅₉	C₂⁴	1	2	yes	—
113	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
114	#41×C₅₉	—	4	32	no	—
115	C₂×Q₈×C₅₉	—	2	4	no	—
116	C₂×Q₈×C₅₉	—	2	4	no	—
117	C₂×Q₈×C₅₉	—	2	4	no	—
118	C₂×D₄×C₅₉	—	2	16	no	—
119	C₂×D₄×C₅₉	—	2	8	no	—
120	C₂×D₄×C₅₉	—	2	8	no	—
121	C₂×D₄×C₅₉	—	2	8	no	—
122	C₂×D₄×C₅₉	—	2	8	no	—
123	C₂×D₄×C₅₉	—	2	4	no	—
124	C₂×D₄×C₅₉	—	2	4	no	—
125	C₂×D₄×C₅₉	—	2	4	no	—
126	C₂×D₄×C₅₉	—	4	8	no	—
127	C₂×D₄×C₅₉	—	4	16	no	—
128	C₂²×C₄×C₅₉	—	2	2	no	—
129	C₂²×C₄×C₅₉	—	2	2	no	—
130	C₂²×C₄×C₅₉	—	2	32	no	—
131	C₂²×C₄×C₅₉	—	2	4	no	—
132	C₂²×C₄×C₅₉	—	2	4	no	—
133	C₂²×C₄×C₅₉	—	2	4	no	—
134	C₂²×C₄×C₅₉	—	2	4	no	—
135	C₂²×C₄×C₅₉	—	2	4	no	—
136	C₂²×C₄×C₅₉	—	2	8	no	—
137	C₂²×C₄×C₅₉	—	2	8	no	—
138	C₂²×C₄×C₅₉	—	2	8	no	—
139	C₂²×C₄×C₅₉	—	4	4	no	—
140	C₂²×C₄×C₅₉	—	4	4	no	—
141	C₂²×C₄×C₅₉	C₂×D₄	1	8	yes	—
142	C₂²×C₄×C₅₉	C₂×D₄	1	8	yes	—
143	C₂²×C₄×C₅₉	C₂×D₄	1	4	yes	—
144	C₂²×C₄×C₅₉	C₂×D₄	1	8	yes	—
145	C₂²×C₄×C₅₉	C₂×D₄	1	4	yes	—
146	C₂²×C₄×C₅₉	C₂×D₄	1	4	yes	—
147	C₂²×C₄×C₅₉	#41	1	4	yes	—
148	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
149	C₂²×C₄×C₅₉	C₂⁴	1	8	yes	—
150	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
151	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
152	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
153	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
154	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
155	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
156	C₄⋊C₄×C₅₉	—	2	8	no	—
157	C₄⋊C₄×C₅₉	—	2	8	no	—
158	C₄⋊C₄×C₅₉	—	2	8	no	—
159	C₄⋊C₄×C₅₉	—	2	8	no	—
160	C₄⋊C₄×C₅₉	—	2	16	no	—
161	C₄⋊C₄×C₅₉	—	4	8	no	—
162	C₂²⋊C₄×C₅₉	—	2	8	no	—
163	C₂²⋊C₄×C₅₉	—	2	16	no	—
164	C₂²⋊C₄×C₅₉	—	2	8	no	—
165	C₂²⋊C₄×C₅₉	—	2	8	no	—
166	C₂²⋊C₄×C₅₉	—	2	16	no	—
167	C₂²⋊C₄×C₅₉	—	2	16	no	—
168	C₂²⋊C₄×C₅₉	—	4	16	no	—
169	C₄²×C₅₉	—	2	4	no	—
170	C₄²×C₅₉	—	2	4	no	—
171	C₄²×C₅₉	—	2	8	no	—
172	C₄²×C₅₉	C₂×D₄	1	8	yes	—
173	C₄²×C₅₉	C₂×D₄	1	4	yes	—
174	C₄²×C₅₉	C₂×D₄	1	4	yes	—
175	C₂³×C₅₉	—	2	4	no	—
176	C₂³×C₅₉	—	2	8	no	—
177	C₂³×C₅₉	—	2	2	no	—
178	C₂³×C₅₉	—	2	2	no	—
179	C₂³×C₅₉	—	2	8	no	—
180	C₂³×C₅₉	—	2	4	no	—
181	C₂³×C₅₉	—	2	4	no	—
182	C₂³×C₅₉	—	2	4	no	—
183	C₂³×C₅₉	—	2	16	no	—
184	C₂³×C₅₉	—	4	8	no	—
185	C₂³×C₅₉	—	4	8	no	—
186	C₂³×C₅₉	—	4	8	no	—
187	C₂³×C₅₉	C₂²×D₄	1	4	yes	—
188	C₂³×C₅₉	C₂²×D₄	1	2	yes	—
189	C₂³×C₅₉	C₂²×D₄	1	2	yes	—
190	C₂³×C₅₉	C₂×#41	1	2	yes	—
191	C₂³×C₅₉	C₂⁵	1	1	yes	characteristic
192	Q₈×C₅₉	—	4	8	no	—
193	D₄×C₅₉	—	4	16	no	—
194	D₄×C₅₉	—	4	32	no	—
195	D₄×C₅₉	—	4	16	no	—
196	D₄×C₅₉	—	4	8	no	—
197	C₂×C₄×C₅₉	—	2	8	no	—
198	C₂×C₄×C₅₉	—	2	2	no	—
199	C₂×C₄×C₅₉	—	2	2	no	—
200	C₂×C₄×C₅₉	—	2	4	no	—
201	C₂×C₄×C₅₉	—	2	4	no	—
202	C₂×C₄×C₅₉	—	2	16	no	—
203	C₂×C₄×C₅₉	—	2	16	no	—
204	C₂×C₄×C₅₉	—	2	4	no	—
205	C₂×C₄×C₅₉	—	2	8	no	—
206	C₂×C₄×C₅₉	—	2	4	no	—
207	C₂×C₄×C₅₉	—	2	4	no	—
208	C₂×C₄×C₅₉	—	2	4	no	—
209	C₂×C₄×C₅₉	—	2	8	no	—
210	C₂×C₄×C₅₉	—	2	16	no	—
211	C₂×C₄×C₅₉	—	4	8	no	—
212	C₂×C₄×C₅₉	—	4	8	no	—
213	C₂×C₄×C₅₉	—	4	16	no	—
214	C₂×C₄×C₅₉	#121	1	16	yes	—
215	C₂×C₄×C₅₉	C₂²×D₄	1	4	yes	—
216	C₂×C₄×C₅₉	C₂²×D₄	1	4	yes	—
217	C₂×C₄×C₅₉	C₂²×D₄	1	4	yes	—
218	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
219	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
220	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
221	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
222	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
223	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
224	#34633	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
225	C₂²×C₅₉	—	2	4	no	—
226	C₂²×C₅₉	—	2	4	no	—
227	C₂²×C₅₉	—	2	4	no	—
228	C₂²×C₅₉	—	2	4	no	—
229	C₂²×C₅₉	—	2	8	no	—
230	C₂²×C₅₉	—	4	16	no	—
231	C₂²×C₅₉	—	4	4	no	—
232	C₂²×C₅₉	—	4	4	no	—
233	C₂²×C₅₉	—	4	4	no	—
234	C₂²×C₅₉	—	4	8	no	—
235	C₂²×C₅₉	—	4	8	no	—
236	C₂²×C₅₉	—	4	8	no	—
237	C₂²×C₅₉	C₂×#121	1	4	yes	—
238	C₂²×C₅₉	C₂³×D₄	1	1	yes	characteristic
239	C₂²×C₅₉	C₂³×D₄	1	1	yes	characteristic
240	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
241	C₂²×C₅₉	#585	1	4	yes	—
242	C₄×C₅₉	—	2	4	no	—
243	C₄×C₅₉	—	2	4	no	—
244	C₄×C₅₉	—	2	4	no	—
245	C₄×C₅₉	—	4	4	no	—
246	C₄×C₅₉	—	4	4	no	—
247	C₄×C₅₉	—	4	8	no	—
248	C₄×C₅₉	C₂×#121	1	4	yes	—
249	C₄×C₅₉	C₂×#121	1	4	yes	—
250	C₂×#532	C₂×C₅₉	1	1	yes	characteristic, complemented
251	C₂×#525	C₂×C₅₉	1	2	yes	complemented
252	C₂²×#117	C₂×C₅₉	1	1	yes	characteristic, complemented
253	#2621	C₂×C₅₉	1	2	yes	complemented
254	#2620	C₂×C₅₉	1	4	yes	complemented
255	#2619	C₂×C₅₉	1	2	yes	complemented
256	#2618	C₂×C₅₉	1	4	yes	complemented
257	#2617	C₂×C₅₉	1	4	yes	complemented
258	#2392	C₂×C₅₉	1	8	yes	complemented
259	#2297	C₂×C₅₉	1	2	yes	complemented
260	#2285	C₂×C₅₉	1	1	yes	characteristic, complemented
261	C₂×C₅₉	—	2	4	no	—
262	C₂×C₅₉	—	4	4	no	—
263	C₂×C₅₉	—	8	4	no	—
264	C₂×C₅₉	C₂²×#121	1	1	yes	characteristic
265	C₂×C₅₉	#3449	1	2	yes	—
266	C₂×C₅₉	#3449	1	2	yes	—
267	C₂×C₅₉	#3455	1	2	yes	—
268	C₂²×#41	C₂²×C₅₉	1	2	yes	—
269	C₂⁴×C₄	C₂²×C₅₉	1	1	yes	characteristic
270	#532	—	2	8	no	—
271	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic, complemented
272	C₂×#127	C₂²×C₅₉	1	1	yes	characteristic, complemented
273	C₂×#124	C₂²×C₅₉	1	2	yes	complemented
274	#525	—	2	16	no	—
275	C₂×#123	C₂²×C₅₉	1	4	yes	—
276	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	4	yes	—
277	C₂×#121	C₂²×C₅₉	1	4	yes	—
278	C₂×#121	C₂²×C₅₉	1	4	yes	—
279	C₂×#120	C₂²×C₅₉	1	4	yes	—
280	C₂×C₄×D₄	C₂²×C₅₉	1	8	yes	—
281	C₂×C₄×D₄	C₂²×C₅₉	1	4	yes	complemented
282	C₂×#117	—	2	8	no	—
283	C₂×#117	C₂²×C₅₉	1	2	yes	—
284	C₂×#117	C₂²×C₅₉	1	2	yes	—
285	C₂×#117	C₂²×C₅₉	1	4	yes	—
286	C₂×#117	C₂²×C₅₉	1	2	yes	—
287	C₂²×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
288	C₂²×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
289	C₂²×C₄²	C₂²×C₅₉	1	1	yes	characteristic
290	C₂²×C₄²	C₂²×C₅₉	1	1	yes	characteristic
291	#398	C₂²×C₅₉	1	8	yes	complemented
292	#397	C₂²×C₅₉	1	8	yes	—
293	#396	C₂²×C₅₉	1	16	yes	complemented
294	#394	C₂²×C₅₉	1	16	yes	—
295	#394	C₂²×C₅₉	1	8	yes	complemented
296	#392	C₂²×C₅₉	1	8	yes	—
297	#391	C₂²×C₅₉	1	4	yes	complemented
298	#390	C₂²×C₅₉	1	4	yes	complemented
299	#386	C₂²×C₅₉	1	8	yes	—
300	#384	C₂²×C₅₉	1	2	yes	complemented
301	#382	C₂²×C₅₉	1	2	yes	complemented
302	#380	C₂²×C₅₉	1	4	yes	—
303	C₄×C₄⋊C₄	C₂²×C₅₉	1	4	yes	complemented
304	C₄×C₂²⋊C₄	C₂²×C₅₉	1	8	yes	complemented
305	C₅₉	#34633	1	1	yes	characteristic, direct product factor, Sylow
306	C₂⁵	C₂³×C₅₉	1	1	yes	characteristic
307	C₂×#41	—	2	8	no	—
308	C₂×#41	—	2	8	no	—
309	C₂×#41	—	2	8	no	—
310	C₂²×Q₈	C₂³×C₅₉	1	2	yes	—
311	C₂²×D₄	C₂³×C₅₉	1	4	yes	—
312	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
313	C₂²×D₄	C₂³×C₅₉	1	8	yes	—
314	C₂²×D₄	C₂³×C₅₉	1	4	yes	—
315	C₂³×C₄	—	2	4	no	—
316	C₂³×C₄	—	2	4	no	—
317	C₂³×C₄	D₄×C₅₉	1	8	yes	complemented
318	C₂³×C₄	C₂³×C₅₉	1	4	yes	—
319	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
320	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
321	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
322	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
323	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
324	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
325	C₄⋊Q₈	—	2	4	no	—
326	#127	—	2	4	no	—
327	#124	—	2	8	no	—
328	#123	—	2	16	no	—
329	C₂²⋊Q₈	—	2	16	no	—
330	#121	—	2	16	no	—
331	#121	—	2	16	no	—
332	#120	—	2	16	no	—
333	C₄×D₄	—	2	32	no	—
334	C₄×D₄	—	2	16	no	—
335	#117	—	2	8	no	—
336	#117	—	2	16	no	—
337	#117	—	2	8	no	—
338	#117	—	2	8	no	—
339	C₂×C₄⋊C₄	—	2	8	no	—
340	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
341	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
342	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
343	C₂×C₄⋊C₄	C₂³×C₅₉	1	8	yes	—
344	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
345	C₂×C₄⋊C₄	C₂³×C₅₉	1	8	yes	—
346	C₂×C₂²⋊C₄	—	2	8	no	—
347	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
348	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
349	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
350	C₂×C₂²⋊C₄	C₂³×C₅₉	1	8	yes	—
351	C₂×C₂²⋊C₄	C₂³×C₅₉	1	8	yes	—
352	C₂×C₂²⋊C₄	C₂³×C₅₉	1	8	yes	—
353	C₂×C₂²⋊C₄	C₂³×C₅₉	1	16	yes	—
354	C₂×C₄²	—	2	4	no	—
355	C₂×C₄²	D₄×C₅₉	1	8	yes	complemented
356	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
357	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
358	C₂×C₄²	C₂³×C₅₉	1	4	yes	—
359	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
360	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
361	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
362	#95	C₂³×C₅₉	1	16	yes	—
363	#95	C₂³×C₅₉	1	8	yes	—
364	C₂⁴	—	2	2	no	—
365	C₂⁴	—	2	2	no	—
366	C₂⁴	—	4	4	no	—
367	C₂⁴	C₂×D₄×C₅₉	1	4	yes	—
368	C₂⁴	C₂⁴×C₅₉	1	4	yes	—
369	C₂⁴	C₂⁴×C₅₉	1	2	yes	—
370	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
371	#41	—	4	32	no	—
372	C₂×Q₈	—	2	4	no	—
373	C₂×Q₈	—	2	4	no	—
374	C₂×Q₈	—	2	4	no	—
375	C₂×D₄	—	2	16	no	—
376	C₂×D₄	—	2	8	no	—
377	C₂×D₄	—	2	8	no	—
378	C₂×D₄	—	2	8	no	—
379	C₂×D₄	—	2	8	no	—
380	C₂×D₄	—	2	4	no	—
381	C₂×D₄	—	2	4	no	—
382	C₂×D₄	—	2	4	no	—
383	C₂×D₄	—	4	8	no	—
384	C₂×D₄	—	4	16	no	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	2	2	no	—
387	C₂²×C₄	—	2	32	no	—
388	C₂²×C₄	—	2	4	no	—
389	C₂²×C₄	—	2	4	no	—
390	C₂²×C₄	—	2	4	no	—
391	C₂²×C₄	—	2	4	no	—
392	C₂²×C₄	—	2	4	no	—
393	C₂²×C₄	—	2	8	no	—
394	C₂²×C₄	—	2	8	no	—
395	C₂²×C₄	—	2	8	no	—
396	C₂²×C₄	—	4	4	no	—
397	C₂²×C₄	—	4	4	no	—
398	C₂²×C₄	C₂×D₄×C₅₉	1	8	yes	—
399	C₂²×C₄	C₂×D₄×C₅₉	1	8	yes	—
400	C₂²×C₄	C₂×D₄×C₅₉	1	4	yes	—
401	C₂²×C₄	C₂×D₄×C₅₉	1	8	yes	—
402	C₂²×C₄	C₂×D₄×C₅₉	1	4	yes	—
403	C₂²×C₄	C₂×D₄×C₅₉	1	4	yes	—
404	C₂²×C₄	#41×C₅₉	1	4	yes	—
405	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
406	C₂²×C₄	C₂⁴×C₅₉	1	8	yes	—
407	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
408	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
409	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
410	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
411	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
412	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
413	C₄⋊C₄	—	2	8	no	—
414	C₄⋊C₄	—	2	8	no	—
415	C₄⋊C₄	—	2	8	no	—
416	C₄⋊C₄	—	2	8	no	—
417	C₄⋊C₄	—	2	16	no	—
418	C₄⋊C₄	—	4	8	no	—
419	C₂²⋊C₄	—	2	8	no	—
420	C₂²⋊C₄	—	2	16	no	—
421	C₂²⋊C₄	—	2	8	no	—
422	C₂²⋊C₄	—	2	8	no	—
423	C₂²⋊C₄	—	2	16	no	—
424	C₂²⋊C₄	—	2	16	no	—
425	C₂²⋊C₄	—	4	16	no	—
426	C₄²	—	2	4	no	—
427	C₄²	—	2	4	no	—
428	C₄²	—	2	8	no	—
429	C₄²	C₂×D₄×C₅₉	1	8	yes	—
430	C₄²	C₂×D₄×C₅₉	1	4	yes	—
431	C₄²	C₂×D₄×C₅₉	1	4	yes	—
432	C₂³	—	2	4	no	—
433	C₂³	—	2	8	no	—
434	C₂³	—	2	2	no	—
435	C₂³	—	2	2	no	—
436	C₂³	—	2	8	no	—
437	C₂³	—	2	4	no	—
438	C₂³	—	2	4	no	—
439	C₂³	—	2	4	no	—
440	C₂³	—	2	16	no	—
441	C₂³	—	4	8	no	—
442	C₂³	—	4	8	no	—
443	C₂³	—	4	8	no	—
444	C₂³	C₂²×D₄×C₅₉	1	4	yes	—
445	C₂³	C₂²×D₄×C₅₉	1	2	yes	—
446	C₂³	C₂²×D₄×C₅₉	1	2	yes	—
447	C₂³	C₂×#41×C₅₉	1	2	yes	—
448	C₂³	C₂⁵×C₅₉	1	1	yes	characteristic
449	Q₈	—	4	8	no	—
450	D₄	—	4	16	no	—
451	D₄	—	4	32	no	—
452	D₄	—	4	16	no	—
453	D₄	—	4	8	no	—
454	C₂×C₄	—	2	8	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	4	no	—
458	C₂×C₄	—	2	4	no	—
459	C₂×C₄	—	2	16	no	—
460	C₂×C₄	—	2	16	no	—
461	C₂×C₄	—	2	4	no	—
462	C₂×C₄	—	2	8	no	—
463	C₂×C₄	—	2	4	no	—
464	C₂×C₄	—	2	4	no	—
465	C₂×C₄	—	2	4	no	—
466	C₂×C₄	—	2	8	no	—
467	C₂×C₄	—	2	16	no	—
468	C₂×C₄	—	4	8	no	—
469	C₂×C₄	—	4	8	no	—
470	C₂×C₄	—	4	16	no	—
471	C₂×C₄	#121×C₅₉	1	16	yes	—
472	C₂×C₄	C₂²×D₄×C₅₉	1	4	yes	—
473	C₂×C₄	C₂²×D₄×C₅₉	1	4	yes	—
474	C₂×C₄	C₂²×D₄×C₅₉	1	4	yes	—
475	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
476	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
477	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
478	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
479	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
480	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
481	C₂²	—	2	4	no	—
482	C₂²	—	2	4	no	—
483	C₂²	—	2	4	no	—
484	C₂²	—	2	4	no	—
485	C₂²	—	2	8	no	—
486	C₂²	—	4	16	no	—
487	C₂²	—	4	4	no	—
488	C₂²	—	4	4	no	—
489	C₂²	—	4	4	no	—
490	C₂²	—	4	8	no	—
491	C₂²	—	4	8	no	—
492	C₂²	—	4	8	no	—
493	C₂²	C₂×#121×C₅₉	1	4	yes	—
494	C₂²	C₂³×D₄×C₅₉	1	1	yes	characteristic
495	C₂²	C₂³×D₄×C₅₉	1	1	yes	characteristic
496	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
497	C₂²	C₅₉×#585	1	4	yes	—
498	C₄	—	2	4	no	—
499	C₄	—	2	4	no	—
500	C₄	—	2	4	no	—
501	C₄	—	4	4	no	—
502	C₄	—	4	4	no	—
503	C₄	—	4	8	no	—
504	C₄	C₂×#121×C₅₉	1	4	yes	—
505	C₄	C₂×#121×C₅₉	1	4	yes	—
506	C₂	—	2	4	no	—
507	C₂	—	4	4	no	—
508	C₂	—	8	4	no	—
509	C₂	C₂²×#121×C₅₉	1	1	yes	characteristic
510	C₂	C₅₉×#3449	1	2	yes	—
511	C₂	C₅₉×#3449	1	2	yes	—
512	C₂	C₅₉×#3455	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₅₉	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₉
socle	C₂³×C₅₉	C₂⁵
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅₉×#532	C₂	semidirect
2. C₂×C₅₉×#525	C₂	semidirect
3. C₂²×#117×C₅₉	C₂	semidirect
4. C₅₉×#2621	C₂	semidirect
5. C₅₉×#2620	C₂	semidirect
6. C₅₉×#2619	C₂	semidirect
7. C₅₉×#2618	C₂	semidirect
8. C₅₉×#2617	C₂	semidirect
9. C₅₉×#2392	C₂	semidirect
10. C₅₉×#2297	C₂	semidirect
11. C₅₉×#2285	C₂	semidirect
15. C₂×C₄⋊Q₈×C₅₉	C₂²	semidirect
16. C₂×#127×C₅₉	C₂²	semidirect
17. C₂×#124×C₅₉	C₂²	semidirect
25. C₂×C₄×D₄×C₅₉	C₂²	semidirect
35. C₅₉×#398	C₂²	semidirect
37. C₅₉×#396	C₂²	semidirect
39. C₅₉×#394	C₂²	semidirect
41. C₅₉×#391	C₂²	semidirect
42. C₅₉×#390	C₂²	semidirect
44. C₅₉×#384	C₂²	semidirect
45. C₅₉×#382	C₂²	semidirect
47. C₄×C₄⋊C₄×C₅₉	C₂²	semidirect
48. C₄×C₂²⋊C₄×C₅₉	C₂²	semidirect
60. C₂³×C₄×C₅₉	D₄	semidirect
98. C₂×C₄²×C₅₉	D₄	semidirect
224. #34633	C₅₉	direct (N × H)
250. C₂×#532	C₂×C₅₉	semidirect
251. C₂×#525	C₂×C₅₉	semidirect
252. C₂²×#117	C₂×C₅₉	semidirect
253. #2621	C₂×C₅₉	semidirect
254. #2620	C₂×C₅₉	semidirect
255. #2619	C₂×C₅₉	semidirect
256. #2618	C₂×C₅₉	semidirect
257. #2617	C₂×C₅₉	semidirect
258. #2392	C₂×C₅₉	semidirect
259. #2297	C₂×C₅₉	semidirect
260. #2285	C₂×C₅₉	semidirect
271. C₂×C₄⋊Q₈	C₂²×C₅₉	semidirect
272. C₂×#127	C₂²×C₅₉	semidirect
273. C₂×#124	C₂²×C₅₉	semidirect
281. C₂×C₄×D₄	C₂²×C₅₉	semidirect
291. #398	C₂²×C₅₉	semidirect
293. #396	C₂²×C₅₉	semidirect
295. #394	C₂²×C₅₉	semidirect
297. #391	C₂²×C₅₉	semidirect
298. #390	C₂²×C₅₉	semidirect
300. #384	C₂²×C₅₉	semidirect
301. #382	C₂²×C₅₉	semidirect
303. C₄×C₄⋊C₄	C₂²×C₅₉	semidirect
304. C₄×C₂²⋊C₄	C₂²×C₅₉	semidirect
305. C₅₉	#34633	direct (N × H)
317. C₂³×C₄	D₄×C₅₉	semidirect
355. C₂×C₄²	D₄×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×#532	2
C₂×C₅₉×#525	2
C₂²×#117×C₅₉	2
C₅₉×#2621	2
C₅₉×#2620	2
C₅₉×#2619	2
C₅₉×#2618	2
C₅₉×#2617	2
C₅₉×#2392	2
C₅₉×#2297	2
C₅₉×#2285	2
#34633	59

Subgroups — C59×#34633 #28446742

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#34633 #28446742