Subgroups — C₅₉×#35165 #28447274

Order 15104.

3602 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₉×#535	C₂	1	2	yes	maximal, complemented
2	C₂×C₅₉×#532	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₄×D₄×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₉×#2847	C₂	1	4	yes	maximal, complemented
5	C₅₉×#2617	C₂	1	4	yes	maximal, complemented
6	C₅₉×#2547	C₂	1	2	yes	maximal, complemented
7	C₅₉×#2544	C₂	1	4	yes	maximal, complemented
8	C₅₉×#2541	C₂	1	2	yes	maximal, complemented
9	C₅₉×#2537	C₂	1	4	yes	maximal, complemented
10	C₅₉×#2535	C₂	1	4	yes	maximal, complemented
11	C₅₉×#2311	C₂	1	2	yes	maximal, complemented
12	C₅₉×#2285	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×#41×C₅₉	C₂²	1	2	yes	—
14	C₂³×D₄×C₅₉	C₂²	1	1	yes	characteristic
15	C₂⁴×C₄×C₅₉	C₂²	1	2	yes	—
16	C₅₉×#535	—	2	16	no	—
17	C₅₉×#532	—	2	8	no	—
18	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic, complemented
19	C₂×#127×C₅₉	C₂²	1	4	yes	—
20	C₂×#127×C₅₉	C₂²	1	1	yes	characteristic, complemented
21	C₂×#124×C₅₉	C₂²	1	4	yes	—
22	C₂×#124×C₅₉	C₂²	1	2	yes	complemented
23	C₂×#121×C₅₉	C₂²	1	8	yes	—
24	C₂×#121×C₅₉	C₂²	1	2	yes	—
25	C₂×#121×C₅₉	C₂²	1	2	yes	—
26	C₂×#121×C₅₉	C₂²	1	8	yes	complemented
27	C₂×#120×C₅₉	C₂²	1	8	yes	—
28	C₂×C₄×D₄×C₅₉	—	2	8	no	—
29	C₂×C₄×D₄×C₅₉	C₂²	1	2	yes	—
30	C₂×C₄×D₄×C₅₉	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₅₉	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₅₉	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₅₉	C₂²	1	2	yes	complemented
34	C₂×C₄×D₄×C₅₉	C₂²	1	2	yes	complemented
35	C₂×#117×C₅₉	C₂²	1	2	yes	—
36	C₂²×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
37	C₂²×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
38	C₂²×C₄²×C₅₉	C₂²	1	1	yes	characteristic
39	C₅₉×#397	C₂²	1	8	yes	complemented
40	C₅₉×#394	C₂²	1	16	yes	complemented
41	C₅₉×#392	C₂²	1	8	yes	complemented
42	C₅₉×#391	C₂²	1	4	yes	complemented
43	C₅₉×#390	C₂²	1	4	yes	complemented
44	C₅₉×#386	C₂²	1	8	yes	—
45	C₅₉×#386	C₂²	1	16	yes	complemented
46	C₅₉×#384	C₂²	1	2	yes	complemented
47	C₅₉×#382	C₂²	1	2	yes	complemented
48	C₅₉×#380	C₂²	1	2	yes	—
49	C₅₉×#380	C₂²	1	2	yes	—
50	C₅₉×#380	C₂²	1	8	yes	complemented
51	C₅₉×#380	C₂²	1	8	yes	complemented
52	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	complemented
53	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	complemented
54	C₂⁵×C₅₉	C₂³	1	2	yes	—
55	C₂×#41×C₅₉	—	2	8	no	—
56	C₂×#41×C₅₉	—	2	8	no	—
57	C₂×#41×C₅₉	—	2	8	no	—
58	C₂²×Q₈×C₅₉	C₂³	1	2	yes	—
59	C₂²×D₄×C₅₉	—	2	4	no	—
60	C₂²×D₄×C₅₉	—	2	4	no	—
61	C₂²×D₄×C₅₉	D₄	1	8	yes	complemented
62	C₂²×D₄×C₅₉	C₂³	1	4	yes	—
63	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
64	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
65	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
66	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
67	C₂²×D₄×C₅₉	C₂³	1	16	yes	—
68	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
69	C₂³×C₄×C₅₉	—	2	8	no	—
70	C₂³×C₄×C₅₉	—	4	8	no	—
71	C₂³×C₄×C₅₉	C₂³	1	4	yes	—
72	C₂³×C₄×C₅₉	C₂³	1	4	yes	—
73	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
75	C₂³×C₄×C₅₉	C₂³	1	4	yes	—
76	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
77	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
78	C₄⋊Q₈×C₅₉	—	2	4	no	—
79	#127×C₅₉	—	2	16	no	—
80	#127×C₅₉	—	2	4	no	—
81	#124×C₅₉	—	2	16	no	—
82	#124×C₅₉	—	2	8	no	—
83	#121×C₅₉	—	2	32	no	—
84	#121×C₅₉	—	2	8	no	—
85	#121×C₅₉	—	2	8	no	—
86	#121×C₅₉	—	4	16	no	—
87	#120×C₅₉	—	2	32	no	—
88	C₄×D₄×C₅₉	—	2	8	no	—
89	C₄×D₄×C₅₉	—	2	8	no	—
90	C₄×D₄×C₅₉	—	2	8	no	—
91	C₄×D₄×C₅₉	—	2	8	no	—
92	C₄×D₄×C₅₉	—	2	8	no	—
93	C₄×D₄×C₅₉	—	2	8	no	—
94	#117×C₅₉	—	2	8	no	—
95	C₂×C₄⋊C₄×C₅₉	—	2	4	no	—
96	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
97	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
98	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
99	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
100	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
101	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
102	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
103	C₂×C₂²⋊C₄×C₅₉	—	2	8	no	—
104	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
105	C₂×C₂²⋊C₄×C₅₉	C₂³	1	16	yes	—
106	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
107	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
108	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
109	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
110	C₂×C₂²⋊C₄×C₅₉	C₂³	1	16	yes	—
111	C₂×C₄²×C₅₉	D₄	1	8	yes	complemented
112	C₂×C₄²×C₅₉	C₂³	1	4	yes	—
113	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
114	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
115	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
116	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
117	#95×C₅₉	C₂³	1	4	yes	—
118	#95×C₅₉	C₂³	1	4	yes	—
119	#95×C₅₉	C₂³	1	16	yes	—
120	C₂⁴×C₅₉	—	2	4	no	—
121	C₂⁴×C₅₉	—	2	4	no	—
122	C₂⁴×C₅₉	—	4	4	no	—
123	C₂⁴×C₅₉	—	4	4	no	—
124	C₂⁴×C₅₉	C₂×D₄	1	8	yes	—
125	C₂⁴×C₅₉	C₂⁴	1	4	yes	—
126	C₂⁴×C₅₉	C₂⁴	1	4	yes	—
127	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
128	#41×C₅₉	—	4	32	no	—
129	C₂×Q₈×C₅₉	—	2	4	no	—
130	C₂×Q₈×C₅₉	—	2	4	no	—
131	C₂×Q₈×C₅₉	—	2	4	no	—
132	C₂×D₄×C₅₉	—	2	8	no	—
133	C₂×D₄×C₅₉	—	2	8	no	—
134	C₂×D₄×C₅₉	—	2	8	no	—
135	C₂×D₄×C₅₉	—	2	32	no	—
136	C₂×D₄×C₅₉	—	2	32	no	—
137	C₂×D₄×C₅₉	—	2	4	no	—
138	C₂×D₄×C₅₉	—	2	4	no	—
139	C₂×D₄×C₅₉	—	2	4	no	—
140	C₂×D₄×C₅₉	—	2	4	no	—
141	C₂×D₄×C₅₉	—	2	4	no	—
142	C₂×D₄×C₅₉	—	2	4	no	—
143	C₂×D₄×C₅₉	—	2	4	no	—
144	C₂×D₄×C₅₉	—	2	4	no	—
145	C₂×D₄×C₅₉	—	2	4	no	—
146	C₂×D₄×C₅₉	—	2	8	no	—
147	C₂×D₄×C₅₉	—	4	4	no	—
148	C₂×D₄×C₅₉	—	4	16	no	—
149	C₂×D₄×C₅₉	—	4	16	no	—
150	C₂×D₄×C₅₉	C₂×D₄	1	8	yes	—
151	C₂×D₄×C₅₉	C₂×D₄	1	8	yes	—
152	C₂²×C₄×C₅₉	—	2	4	no	—
153	C₂²×C₄×C₅₉	—	2	4	no	—
154	C₂²×C₄×C₅₉	—	2	8	no	—
155	C₂²×C₄×C₅₉	—	2	8	no	—
156	C₂²×C₄×C₅₉	—	2	8	no	—
157	C₂²×C₄×C₅₉	—	2	8	no	—
158	C₂²×C₄×C₅₉	—	2	8	no	—
159	C₂²×C₄×C₅₉	—	2	16	no	—
160	C₂²×C₄×C₅₉	—	4	8	no	—
161	C₂²×C₄×C₅₉	—	4	4	no	—
162	C₂²×C₄×C₅₉	—	4	2	no	—
163	C₂²×C₄×C₅₉	—	4	32	no	—
164	C₂²×C₄×C₅₉	C₂×D₄	1	4	yes	—
165	C₂²×C₄×C₅₉	C₂×D₄	1	4	yes	—
166	C₂²×C₄×C₅₉	C₂×D₄	1	4	yes	—
167	C₂²×C₄×C₅₉	C₂×D₄	1	4	yes	—
168	C₂²×C₄×C₅₉	#41	1	4	yes	—
169	C₂²×C₄×C₅₉	C₂⁴	1	8	yes	—
170	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
171	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
172	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
173	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
174	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
175	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
176	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
177	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
178	C₄⋊C₄×C₅₉	—	2	4	no	—
179	C₄⋊C₄×C₅₉	—	2	4	no	—
180	C₄⋊C₄×C₅₉	—	2	8	no	—
181	C₄⋊C₄×C₅₉	—	2	4	no	—
182	C₄⋊C₄×C₅₉	—	2	4	no	—
183	C₄⋊C₄×C₅₉	—	2	8	no	—
184	C₄⋊C₄×C₅₉	—	4	4	no	—
185	C₂²⋊C₄×C₅₉	—	2	8	no	—
186	C₂²⋊C₄×C₅₉	—	2	32	no	—
187	C₂²⋊C₄×C₅₉	—	2	8	no	—
188	C₂²⋊C₄×C₅₉	—	2	8	no	—
189	C₂²⋊C₄×C₅₉	—	2	8	no	—
190	C₂²⋊C₄×C₅₉	—	2	8	no	—
191	C₂²⋊C₄×C₅₉	—	4	16	no	—
192	C₄²×C₅₉	—	2	8	no	—
193	C₄²×C₅₉	C₂×D₄	1	4	yes	—
194	C₄²×C₅₉	C₂×D₄	1	4	yes	—
195	C₄²×C₅₉	C₂×D₄	1	4	yes	—
196	C₄²×C₅₉	C₂×D₄	1	4	yes	—
197	C₂³×C₅₉	—	2	2	no	—
198	C₂³×C₅₉	—	2	2	no	—
199	C₂³×C₅₉	—	2	16	no	—
200	C₂³×C₅₉	—	2	4	no	—
201	C₂³×C₅₉	—	2	4	no	—
202	C₂³×C₅₉	—	2	8	no	—
203	C₂³×C₅₉	—	2	8	no	—
204	C₂³×C₅₉	—	2	4	no	—
205	C₂³×C₅₉	—	2	4	no	—
206	C₂³×C₅₉	—	2	4	no	—
207	C₂³×C₅₉	—	2	8	no	—
208	C₂³×C₅₉	—	2	8	no	—
209	C₂³×C₅₉	—	4	16	no	—
210	C₂³×C₅₉	—	4	8	no	—
211	C₂³×C₅₉	—	4	8	no	—
212	C₂³×C₅₉	—	4	16	no	—
213	C₂³×C₅₉	C₂²×D₄	1	8	yes	—
214	C₂³×C₅₉	C₂²×D₄	1	2	yes	—
215	C₂³×C₅₉	C₂²×D₄	1	2	yes	—
216	C₂³×C₅₉	C₂×#41	1	2	yes	—
217	C₂³×C₅₉	C₂⁵	1	1	yes	characteristic
218	Q₈×C₅₉	—	4	8	no	—
219	D₄×C₅₉	—	2	16	no	—
220	D₄×C₅₉	—	2	16	no	—
221	D₄×C₅₉	—	4	8	no	—
222	D₄×C₅₉	—	4	16	no	—
223	D₄×C₅₉	—	4	8	no	—
224	D₄×C₅₉	—	4	8	no	—
225	D₄×C₅₉	—	8	32	no	—
226	C₂×C₄×C₅₉	—	2	2	no	—
227	C₂×C₄×C₅₉	—	2	2	no	—
228	C₂×C₄×C₅₉	—	2	2	no	—
229	C₂×C₄×C₅₉	—	2	8	no	—
230	C₂×C₄×C₅₉	—	2	8	no	—
231	C₂×C₄×C₅₉	—	2	4	no	—
232	C₂×C₄×C₅₉	—	2	4	no	—
233	C₂×C₄×C₅₉	—	2	4	no	—
234	C₂×C₄×C₅₉	—	2	4	no	—
235	C₂×C₄×C₅₉	—	2	8	no	—
236	C₂×C₄×C₅₉	—	2	8	no	—
237	C₂×C₄×C₅₉	—	2	8	no	—
238	C₂×C₄×C₅₉	—	4	4	no	—
239	C₂×C₄×C₅₉	—	4	16	no	—
240	C₂×C₄×C₅₉	—	4	8	no	—
241	C₂×C₄×C₅₉	—	4	16	no	—
242	C₂×C₄×C₅₉	—	4	16	no	—
243	C₂×C₄×C₅₉	#121	1	16	yes	complemented
244	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
245	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
246	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
247	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
248	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
249	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
250	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
251	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
252	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
253	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
254	C₂×C₄×C₅₉	H(5,𝔽₂)	1	4	yes	—
255	#35165	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
256	C₂²×C₅₉	—	2	2	no	—
257	C₂²×C₅₉	—	2	2	no	—
258	C₂²×C₅₉	—	2	4	no	—
259	C₂²×C₅₉	—	2	4	no	—
260	C₂²×C₅₉	—	2	8	no	—
261	C₂²×C₅₉	—	2	16	no	—
262	C₂²×C₅₉	—	4	32	no	—
263	C₂²×C₅₉	—	4	4	no	—
264	C₂²×C₅₉	—	4	4	no	—
265	C₂²×C₅₉	—	4	8	no	—
266	C₂²×C₅₉	—	4	4	no	—
267	C₂²×C₅₉	—	4	4	no	—
268	C₂²×C₅₉	—	4	4	no	—
269	C₂²×C₅₉	—	4	8	no	—
270	C₂²×C₅₉	—	4	8	no	—
271	C₂²×C₅₉	C₂×#121	1	4	yes	—
272	C₂²×C₅₉	C₂³×D₄	1	1	yes	characteristic
273	C₂²×C₅₉	C₂³×D₄	1	1	yes	characteristic
274	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
275	C₂²×C₅₉	C₂×H(5,𝔽₂)	1	2	yes	—
276	C₂²×C₅₉	#585	1	2	yes	—
277	C₄×C₅₉	—	2	2	no	—
278	C₄×C₅₉	—	2	2	no	—
279	C₄×C₅₉	—	2	2	no	—
280	C₄×C₅₉	—	4	4	no	—
281	C₄×C₅₉	—	4	4	no	—
282	C₄×C₅₉	—	4	8	no	—
283	C₄×C₅₉	C₂×#121	1	4	yes	—
284	C₄×C₅₉	C₂×#121	1	4	yes	—
285	C₄×C₅₉	#535	1	4	yes	complemented
286	C₂×#535	C₂×C₅₉	1	2	yes	complemented
287	C₂×#532	C₂×C₅₉	1	1	yes	characteristic, complemented
288	C₂²×C₄×D₄	C₂×C₅₉	1	1	yes	characteristic, complemented
289	#2847	C₂×C₅₉	1	4	yes	complemented
290	#2617	C₂×C₅₉	1	4	yes	complemented
291	#2547	C₂×C₅₉	1	2	yes	complemented
292	#2544	C₂×C₅₉	1	4	yes	complemented
293	#2541	C₂×C₅₉	1	2	yes	complemented
294	#2537	C₂×C₅₉	1	4	yes	complemented
295	#2535	C₂×C₅₉	1	4	yes	complemented
296	#2311	C₂×C₅₉	1	2	yes	complemented
297	#2285	C₂×C₅₉	1	1	yes	characteristic, complemented
298	C₂×C₅₉	—	2	4	no	—
299	C₂×C₅₉	—	4	8	no	—
300	C₂×C₅₉	—	8	4	no	—
301	C₂×C₅₉	C₂²×#121	1	1	yes	characteristic
302	C₂×C₅₉	C₂×#535	1	1	yes	characteristic
303	C₂×C₅₉	#3449	1	1	yes	characteristic
304	C₂×C₅₉	#3496	1	2	yes	—
305	C₂×C₅₉	#3506	1	2	yes	—
306	C₂²×#41	C₂²×C₅₉	1	2	yes	—
307	C₂³×D₄	C₂²×C₅₉	1	1	yes	characteristic
308	C₂⁴×C₄	C₂²×C₅₉	1	2	yes	—
309	#535	—	2	16	no	—
310	#532	—	2	8	no	—
311	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic, complemented
312	C₂×#127	C₂²×C₅₉	1	4	yes	—
313	C₂×#127	C₂²×C₅₉	1	1	yes	characteristic, complemented
314	C₂×#124	C₂²×C₅₉	1	4	yes	—
315	C₂×#124	C₂²×C₅₉	1	2	yes	complemented
316	C₂×#121	C₂²×C₅₉	1	2	yes	—
317	C₂×#121	C₂²×C₅₉	1	2	yes	—
318	C₂×#121	C₂²×C₅₉	1	8	yes	—
319	C₂×#121	C₂²×C₅₉	1	8	yes	complemented
320	C₂×#120	C₂²×C₅₉	1	8	yes	—
321	C₂×C₄×D₄	—	2	8	no	—
322	C₂×C₄×D₄	C₂²×C₅₉	1	2	yes	—
323	C₂×C₄×D₄	C₂²×C₅₉	1	2	yes	—
324	C₂×C₄×D₄	C₂²×C₅₉	1	2	yes	—
325	C₂×C₄×D₄	C₂²×C₅₉	1	2	yes	—
326	C₂×C₄×D₄	C₂²×C₅₉	1	2	yes	complemented
327	C₂×C₄×D₄	C₂²×C₅₉	1	2	yes	complemented
328	C₂×#117	C₂²×C₅₉	1	2	yes	—
329	C₂²×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
330	C₂²×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
331	C₂²×C₄²	C₂²×C₅₉	1	1	yes	characteristic
332	#397	C₂²×C₅₉	1	8	yes	complemented
333	#394	C₂²×C₅₉	1	16	yes	complemented
334	#392	C₂²×C₅₉	1	8	yes	complemented
335	#391	C₂²×C₅₉	1	4	yes	complemented
336	#390	C₂²×C₅₉	1	4	yes	complemented
337	#386	C₂²×C₅₉	1	8	yes	—
338	#386	C₂²×C₅₉	1	16	yes	complemented
339	#384	C₂²×C₅₉	1	2	yes	complemented
340	#382	C₂²×C₅₉	1	2	yes	complemented
341	#380	C₂²×C₅₉	1	2	yes	—
342	#380	C₂²×C₅₉	1	2	yes	—
343	#380	C₂²×C₅₉	1	8	yes	complemented
344	#380	C₂²×C₅₉	1	8	yes	complemented
345	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	complemented
346	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	complemented
347	C₅₉	#35165	1	1	yes	characteristic, direct product factor, Sylow
348	C₂⁵	C₂³×C₅₉	1	2	yes	—
349	C₂×#41	—	2	8	no	—
350	C₂×#41	—	2	8	no	—
351	C₂×#41	—	2	8	no	—
352	C₂²×Q₈	C₂³×C₅₉	1	2	yes	—
353	C₂²×D₄	—	2	4	no	—
354	C₂²×D₄	—	2	4	no	—
355	C₂²×D₄	D₄×C₅₉	1	8	yes	complemented
356	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
357	C₂²×D₄	C₂³×C₅₉	1	4	yes	—
358	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
359	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
360	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
361	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
362	C₂²×D₄	C₂³×C₅₉	1	16	yes	—
363	C₂³×C₄	—	2	8	no	—
364	C₂³×C₄	—	4	8	no	—
365	C₂³×C₄	C₂³×C₅₉	1	4	yes	—
366	C₂³×C₄	C₂³×C₅₉	1	4	yes	—
367	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
368	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
369	C₂³×C₄	C₂³×C₅₉	1	4	yes	—
370	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
371	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
372	C₄⋊Q₈	—	2	4	no	—
373	#127	—	2	16	no	—
374	#127	—	2	4	no	—
375	#124	—	2	16	no	—
376	#124	—	2	8	no	—
377	#121	—	2	32	no	—
378	#121	—	2	8	no	—
379	#121	—	2	8	no	—
380	#121	—	4	16	no	—
381	#120	—	2	32	no	—
382	C₄×D₄	—	2	8	no	—
383	C₄×D₄	—	2	8	no	—
384	C₄×D₄	—	2	8	no	—
385	C₄×D₄	—	2	8	no	—
386	C₄×D₄	—	2	8	no	—
387	C₄×D₄	—	2	8	no	—
388	#117	—	2	8	no	—
389	C₂×C₄⋊C₄	—	2	4	no	—
390	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
391	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
392	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
393	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
394	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
395	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
396	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
397	C₂×C₂²⋊C₄	—	2	8	no	—
398	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
399	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
400	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
401	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
402	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
403	C₂×C₂²⋊C₄	C₂³×C₅₉	1	16	yes	—
404	C₂×C₂²⋊C₄	C₂³×C₅₉	1	16	yes	—
405	C₂×C₄²	D₄×C₅₉	1	8	yes	complemented
406	C₂×C₄²	C₂³×C₅₉	1	4	yes	—
407	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
408	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
409	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
410	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
411	#95	C₂³×C₅₉	1	4	yes	—
412	#95	C₂³×C₅₉	1	4	yes	—
413	#95	C₂³×C₅₉	1	16	yes	—
414	C₂⁴	—	2	4	no	—
415	C₂⁴	—	2	4	no	—
416	C₂⁴	—	4	4	no	—
417	C₂⁴	—	4	4	no	—
418	C₂⁴	C₂×D₄×C₅₉	1	8	yes	—
419	C₂⁴	C₂⁴×C₅₉	1	4	yes	—
420	C₂⁴	C₂⁴×C₅₉	1	4	yes	—
421	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
422	#41	—	4	32	no	—
423	C₂×Q₈	—	2	4	no	—
424	C₂×Q₈	—	2	4	no	—
425	C₂×Q₈	—	2	4	no	—
426	C₂×D₄	—	2	8	no	—
427	C₂×D₄	—	2	8	no	—
428	C₂×D₄	—	2	8	no	—
429	C₂×D₄	—	2	32	no	—
430	C₂×D₄	—	2	32	no	—
431	C₂×D₄	—	2	4	no	—
432	C₂×D₄	—	2	4	no	—
433	C₂×D₄	—	2	4	no	—
434	C₂×D₄	—	2	4	no	—
435	C₂×D₄	—	2	4	no	—
436	C₂×D₄	—	2	4	no	—
437	C₂×D₄	—	2	4	no	—
438	C₂×D₄	—	2	4	no	—
439	C₂×D₄	—	2	4	no	—
440	C₂×D₄	—	2	8	no	—
441	C₂×D₄	—	4	4	no	—
442	C₂×D₄	—	4	16	no	—
443	C₂×D₄	—	4	16	no	—
444	C₂×D₄	C₂×D₄×C₅₉	1	8	yes	—
445	C₂×D₄	C₂×D₄×C₅₉	1	8	yes	—
446	C₂²×C₄	—	2	4	no	—
447	C₂²×C₄	—	2	4	no	—
448	C₂²×C₄	—	2	8	no	—
449	C₂²×C₄	—	2	8	no	—
450	C₂²×C₄	—	2	8	no	—
451	C₂²×C₄	—	2	8	no	—
452	C₂²×C₄	—	2	8	no	—
453	C₂²×C₄	—	2	16	no	—
454	C₂²×C₄	—	4	8	no	—
455	C₂²×C₄	—	4	4	no	—
456	C₂²×C₄	—	4	2	no	—
457	C₂²×C₄	—	4	32	no	—
458	C₂²×C₄	C₂×D₄×C₅₉	1	4	yes	—
459	C₂²×C₄	C₂×D₄×C₅₉	1	4	yes	—
460	C₂²×C₄	C₂×D₄×C₅₉	1	4	yes	—
461	C₂²×C₄	C₂×D₄×C₅₉	1	4	yes	—
462	C₂²×C₄	#41×C₅₉	1	4	yes	—
463	C₂²×C₄	C₂⁴×C₅₉	1	8	yes	—
464	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
465	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
466	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
467	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
468	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
469	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
470	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
471	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
472	C₄⋊C₄	—	2	4	no	—
473	C₄⋊C₄	—	2	4	no	—
474	C₄⋊C₄	—	2	8	no	—
475	C₄⋊C₄	—	2	4	no	—
476	C₄⋊C₄	—	2	4	no	—
477	C₄⋊C₄	—	2	8	no	—
478	C₄⋊C₄	—	4	4	no	—
479	C₂²⋊C₄	—	2	8	no	—
480	C₂²⋊C₄	—	2	32	no	—
481	C₂²⋊C₄	—	2	8	no	—
482	C₂²⋊C₄	—	2	8	no	—
483	C₂²⋊C₄	—	2	8	no	—
484	C₂²⋊C₄	—	2	8	no	—
485	C₂²⋊C₄	—	4	16	no	—
486	C₄²	—	2	8	no	—
487	C₄²	C₂×D₄×C₅₉	1	4	yes	—
488	C₄²	C₂×D₄×C₅₉	1	4	yes	—
489	C₄²	C₂×D₄×C₅₉	1	4	yes	—
490	C₄²	C₂×D₄×C₅₉	1	4	yes	—
491	C₂³	—	2	2	no	—
492	C₂³	—	2	2	no	—
493	C₂³	—	2	16	no	—
494	C₂³	—	2	4	no	—
495	C₂³	—	2	4	no	—
496	C₂³	—	2	8	no	—
497	C₂³	—	2	8	no	—
498	C₂³	—	2	4	no	—
499	C₂³	—	2	4	no	—
500	C₂³	—	2	4	no	—
501	C₂³	—	2	8	no	—
502	C₂³	—	2	8	no	—
503	C₂³	—	4	16	no	—
504	C₂³	—	4	8	no	—
505	C₂³	—	4	16	no	—
506	C₂³	—	4	8	no	—
507	C₂³	C₂²×D₄×C₅₉	1	8	yes	—
508	C₂³	C₂²×D₄×C₅₉	1	2	yes	—
509	C₂³	C₂²×D₄×C₅₉	1	2	yes	—
510	C₂³	C₂×#41×C₅₉	1	2	yes	—
511	C₂³	C₂⁵×C₅₉	1	1	yes	characteristic
512	Q₈	—	4	8	no	—
513	D₄	—	2	16	no	—
514	D₄	—	2	16	no	—
515	D₄	—	4	8	no	—
516	D₄	—	4	16	no	—
517	D₄	—	4	8	no	—
518	D₄	—	4	8	no	—
519	D₄	—	8	32	no	—
520	C₂×C₄	—	2	2	no	—
521	C₂×C₄	—	2	2	no	—
522	C₂×C₄	—	2	2	no	—
523	C₂×C₄	—	2	8	no	—
524	C₂×C₄	—	2	8	no	—
525	C₂×C₄	—	2	4	no	—
526	C₂×C₄	—	2	4	no	—
527	C₂×C₄	—	2	4	no	—
528	C₂×C₄	—	2	4	no	—
529	C₂×C₄	—	2	8	no	—
530	C₂×C₄	—	2	8	no	—
531	C₂×C₄	—	2	8	no	—
532	C₂×C₄	—	4	4	no	—
533	C₂×C₄	—	4	16	no	—
534	C₂×C₄	—	4	8	no	—
535	C₂×C₄	—	4	16	no	—
536	C₂×C₄	—	4	16	no	—
537	C₂×C₄	#121×C₅₉	1	16	yes	complemented
538	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
539	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
540	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
541	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
542	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
543	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
544	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
545	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
546	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
547	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
548	C₂×C₄	H(5,𝔽₂)×C₅₉	1	4	yes	—
549	C₂²	—	2	4	no	—
550	C₂²	—	2	2	no	—
551	C₂²	—	2	2	no	—
552	C₂²	—	2	4	no	—
553	C₂²	—	2	8	no	—
554	C₂²	—	2	16	no	—
555	C₂²	—	4	32	no	—
556	C₂²	—	4	8	no	—
557	C₂²	—	4	4	no	—
558	C₂²	—	4	4	no	—
559	C₂²	—	4	8	no	—
560	C₂²	—	4	4	no	—
561	C₂²	—	4	4	no	—
562	C₂²	—	4	4	no	—
563	C₂²	—	4	8	no	—
564	C₂²	C₂×#121×C₅₉	1	4	yes	—
565	C₂²	C₂³×D₄×C₅₉	1	1	yes	characteristic
566	C₂²	C₂³×D₄×C₅₉	1	1	yes	characteristic
567	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
568	C₂²	C₂×H(5,𝔽₂)×C₅₉	1	2	yes	—
569	C₂²	C₅₉×#585	1	2	yes	—
570	C₄	—	2	2	no	—
571	C₄	—	2	2	no	—
572	C₄	—	2	2	no	—
573	C₄	—	4	4	no	—
574	C₄	—	4	4	no	—
575	C₄	—	4	8	no	—
576	C₄	C₂×#121×C₅₉	1	4	yes	—
577	C₄	C₂×#121×C₅₉	1	4	yes	—
578	C₄	C₅₉×#535	1	4	yes	complemented
579	C₂	—	2	4	no	—
580	C₂	—	4	8	no	—
581	C₂	—	8	4	no	—
582	C₂	C₂²×#121×C₅₉	1	1	yes	characteristic
583	C₂	C₂×C₅₉×#535	1	1	yes	characteristic
584	C₂	C₅₉×#3449	1	1	yes	characteristic
585	C₂	C₅₉×#3496	1	2	yes	—
586	C₂	C₅₉×#3506	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₅₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₉
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×#535	C₂	semidirect
2. C₂×C₅₉×#532	C₂	semidirect
3. C₂²×C₄×D₄×C₅₉	C₂	semidirect
4. C₅₉×#2847	C₂	semidirect
5. C₅₉×#2617	C₂	semidirect
6. C₅₉×#2547	C₂	semidirect
7. C₅₉×#2544	C₂	semidirect
8. C₅₉×#2541	C₂	semidirect
9. C₅₉×#2537	C₂	semidirect
10. C₅₉×#2535	C₂	semidirect
11. C₅₉×#2311	C₂	semidirect
12. C₅₉×#2285	C₂	semidirect
18. C₂×C₄⋊Q₈×C₅₉	C₂²	semidirect
20. C₂×#127×C₅₉	C₂²	semidirect
22. C₂×#124×C₅₉	C₂²	semidirect
26. C₂×#121×C₅₉	C₂²	semidirect
33. C₂×C₄×D₄×C₅₉	C₂²	semidirect
34. C₂×C₄×D₄×C₅₉	C₂²	semidirect
39. C₅₉×#397	C₂²	semidirect
40. C₅₉×#394	C₂²	semidirect
41. C₅₉×#392	C₂²	semidirect
42. C₅₉×#391	C₂²	semidirect
43. C₅₉×#390	C₂²	semidirect
45. C₅₉×#386	C₂²	semidirect
46. C₅₉×#384	C₂²	semidirect
47. C₅₉×#382	C₂²	semidirect
50. C₅₉×#380	C₂²	semidirect
51. C₅₉×#380	C₂²	semidirect
52. C₄×C₄⋊C₄×C₅₉	C₂²	semidirect
53. C₄×C₄⋊C₄×C₅₉	C₂²	semidirect
61. C₂²×D₄×C₅₉	D₄	semidirect
111. C₂×C₄²×C₅₉	D₄	semidirect
243. C₂×C₄×C₅₉	#121	semidirect
255. #35165	C₅₉	direct (N × H)
285. C₄×C₅₉	#535	semidirect
286. C₂×#535	C₂×C₅₉	semidirect
287. C₂×#532	C₂×C₅₉	semidirect
288. C₂²×C₄×D₄	C₂×C₅₉	semidirect
289. #2847	C₂×C₅₉	semidirect
290. #2617	C₂×C₅₉	semidirect
291. #2547	C₂×C₅₉	semidirect
292. #2544	C₂×C₅₉	semidirect
293. #2541	C₂×C₅₉	semidirect
294. #2537	C₂×C₅₉	semidirect
295. #2535	C₂×C₅₉	semidirect
296. #2311	C₂×C₅₉	semidirect
297. #2285	C₂×C₅₉	semidirect
311. C₂×C₄⋊Q₈	C₂²×C₅₉	semidirect
313. C₂×#127	C₂²×C₅₉	semidirect
315. C₂×#124	C₂²×C₅₉	semidirect
319. C₂×#121	C₂²×C₅₉	semidirect
326. C₂×C₄×D₄	C₂²×C₅₉	semidirect
327. C₂×C₄×D₄	C₂²×C₅₉	semidirect
332. #397	C₂²×C₅₉	semidirect
333. #394	C₂²×C₅₉	semidirect
334. #392	C₂²×C₅₉	semidirect
335. #391	C₂²×C₅₉	semidirect
336. #390	C₂²×C₅₉	semidirect
338. #386	C₂²×C₅₉	semidirect
339. #384	C₂²×C₅₉	semidirect
340. #382	C₂²×C₅₉	semidirect
343. #380	C₂²×C₅₉	semidirect
344. #380	C₂²×C₅₉	semidirect
345. C₄×C₄⋊C₄	C₂²×C₅₉	semidirect
346. C₄×C₄⋊C₄	C₂²×C₅₉	semidirect
347. C₅₉	#35165	direct (N × H)
355. C₂²×D₄	D₄×C₅₉	semidirect
405. C₂×C₄²	D₄×C₅₉	semidirect
537. C₂×C₄	#121×C₅₉	semidirect
578. C₄	C₅₉×#535	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅₉×#535	2
C₂×C₅₉×#532	2
C₂²×C₄×D₄×C₅₉	2
C₅₉×#2847	2
C₅₉×#2617	2
C₅₉×#2547	2
C₅₉×#2544	2
C₅₉×#2541	2
C₅₉×#2537	2
C₅₉×#2535	2
C₅₉×#2311	2
C₅₉×#2285	2
#35165	59

Subgroups — C59×#35165 #28447274

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#35165 #28447274