Subgroups — C₅₉×#62859 #28474968

Order 15104.

10986 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₉×#585	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×2₋¹⁺⁴×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₉×#3500	C₂	1	8	yes	maximal, complemented
4	C₅₉×#3499	C₂	1	8	yes	maximal, complemented
5	C₅₉×#3489	C₂	1	16	yes	maximal, complemented
6	C₅₉×#3486	C₂	1	4	yes	maximal, complemented
7	C₅₉×#3485	C₂	1	12	yes	maximal, complemented
8	C₅₉×#3449	C₂	1	6	yes	maximal, complemented
9	C₂×C₅₉×#536	C₂	1	6	yes	maximal, complemented
10	C₅₉×#3428	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#585	—	2	16	no	—
12	C₂×2₋¹⁺⁴×C₅₉	—	2	16	no	—
13	C₂×2₋¹⁺⁴×C₅₉	C₂²	1	2	yes	—
14	C₂×2₋¹⁺⁴×C₅₉	C₂²	1	8	yes	complemented
15	C₂×2₋¹⁺⁴×C₅₉	C₂²	1	8	yes	complemented
16	C₂×2₋¹⁺⁴×C₅₉	C₂²	1	4	yes	complemented
17	C₂×H(5,𝔽₂)×C₅₉	C₂²	1	6	yes	—
18	C₂×H(5,𝔽₂)×C₅₉	C₂²	1	4	yes	complemented
19	C₂²×#41×C₅₉	C₂²	1	6	yes	—
20	C₂²×#41×C₅₉	C₂²	1	1	yes	characteristic
21	C₂²×#41×C₅₉	C₂²	1	3	yes	complemented
22	C₂²×#41×C₅₉	C₂²	1	6	yes	complemented
23	C₂²×#41×C₅₉	C₂²	1	8	yes	complemented
24	C₂³×Q₈×C₅₉	C₂²	1	3	yes	complemented
25	C₂³×Q₈×C₅₉	C₂²	1	2	yes	complemented
26	D₄×Q₈×C₅₉	C₂²	1	32	yes	complemented
27	C₅₉×#548	C₂²	1	32	yes	complemented
28	C₅₉×#547	C₂²	1	96	yes	complemented
29	C₅₉×#546	C₂²	1	96	yes	complemented
30	C₅₉×#537	C₂²	1	24	yes	complemented
31	C₅₉×#536	C₂²	1	12	yes	complemented
32	C₅₉×#536	C₂²	1	24	yes	complemented
33	C₅₉×#536	C₂²	1	24	yes	complemented
34	C₅₉×#536	C₂²	1	24	yes	complemented
35	C₅₉×#536	C₂²	1	12	yes	complemented
36	C₅₉×#535	C₂²	1	4	yes	complemented
37	C₅₉×#535	C₂²	1	12	yes	complemented
38	C₅₉×#534	C₂²	1	24	yes	complemented
39	C₅₉×#532	C₂²	1	24	yes	complemented
40	C₂×C₄⋊Q₈×C₅₉	C₂²	1	12	yes	complemented
41	C₂×#124×C₅₉	C₂²	1	12	yes	complemented
42	C₅₉×#525	C₂²	1	24	yes	complemented
43	C₅₉×#525	C₂²	1	24	yes	complemented
44	C₂×#123×C₅₉	C₂²	1	24	yes	complemented
45	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	24	yes	complemented
46	C₅₉×#520	C₂²	1	8	yes	complemented
47	C₅₉×#519	C₂²	1	2	yes	complemented
48	C₅₉×#518	C₂²	1	6	yes	complemented
49	C₄×#41×C₅₉	C₂²	1	8	yes	complemented
50	C₂×#117×C₅₉	C₂²	1	6	yes	complemented
51	2₋¹⁺⁴×C₅₉	—	2	64	no	—
52	2₋¹⁺⁴×C₅₉	—	2	64	no	—
53	2₋¹⁺⁴×C₅₉	—	2	32	no	—
54	2₋¹⁺⁴×C₅₉	—	2	16	no	—
55	H(5,𝔽₂)×C₅₉	—	2	32	no	—
56	H(5,𝔽₂)×C₅₉	—	2	48	no	—
57	C₂×#41×C₅₉	—	2	64	no	—
58	C₂×#41×C₅₉	—	2	48	no	—
59	C₂×#41×C₅₉	—	2	48	no	—
60	C₂×#41×C₅₉	—	2	24	no	—
61	C₂×#41×C₅₉	D₄	1	16	yes	complemented
62	C₂×#41×C₅₉	C₂³	1	12	yes	—
63	C₂×#41×C₅₉	C₂³	1	12	yes	—
64	C₂×#41×C₅₉	C₂³	1	12	yes	—
65	C₂×#41×C₅₉	C₂³	1	12	yes	—
66	C₂×#41×C₅₉	C₂³	1	4	yes	—
67	C₂×#41×C₅₉	C₂³	1	12	yes	—
68	C₂×#41×C₅₉	C₂³	1	48	yes	—
69	C₂×#41×C₅₉	C₂³	1	24	yes	—
70	C₂×#41×C₅₉	C₂³	1	8	yes	—
71	C₂×#41×C₅₉	C₂³	1	4	yes	—
72	C₂×#41×C₅₉	C₂³	1	4	yes	—
73	C₂²×Q₈×C₅₉	—	2	16	no	—
74	C₂²×Q₈×C₅₉	—	2	24	no	—
75	C₂²×Q₈×C₅₉	C₂³	1	12	yes	—
76	C₂²×Q₈×C₅₉	C₂³	1	12	yes	—
77	C₂²×Q₈×C₅₉	C₂³	1	6	yes	—
78	C₂²×Q₈×C₅₉	C₂³	1	3	yes	—
79	C₂²×Q₈×C₅₉	C₂³	1	6	yes	—
80	C₂²×Q₈×C₅₉	C₂³	1	16	yes	—
81	C₂²×Q₈×C₅₉	C₂³	1	8	yes	—
82	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
83	C₂²×D₄×C₅₉	C₂³	1	12	yes	—
84	C₂²×D₄×C₅₉	C₂³	1	6	yes	—
85	C₂²×D₄×C₅₉	C₂³	1	6	yes	—
86	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
87	C₂²×D₄×C₅₉	C₂³	1	24	yes	—
88	C₂²×D₄×C₅₉	C₂³	1	3	yes	—
89	C₂³×C₄×C₅₉	C₂³	1	12	yes	—
90	C₂³×C₄×C₅₉	C₂³	1	6	yes	—
91	C₂³×C₄×C₅₉	C₂³	1	6	yes	—
92	C₂³×C₄×C₅₉	C₂³	1	3	yes	—
93	C₄⋊Q₈×C₅₉	C₂³	1	24	yes	—
94	C₄⋊Q₈×C₅₉	C₂³	1	48	yes	—
95	#127×C₅₉	C₂³	1	8	yes	—
96	#124×C₅₉	C₂³	1	24	yes	—
97	#124×C₅₉	C₂³	1	48	yes	—
98	#124×C₅₉	C₂³	1	8	yes	—
99	#123×C₅₉	C₂³	1	48	yes	—
100	#123×C₅₉	C₂³	1	96	yes	—
101	#123×C₅₉	C₂³	1	48	yes	—
102	C₂²⋊Q₈×C₅₉	C₂³	1	48	yes	—
103	C₂²⋊Q₈×C₅₉	C₂³	1	96	yes	—
104	C₂²⋊Q₈×C₅₉	C₂³	1	48	yes	—
105	#121×C₅₉	C₂³	1	16	yes	—
106	#121×C₅₉	C₂³	1	48	yes	—
107	#121×C₅₉	C₂³	1	96	yes	—
108	#120×C₅₉	C₂³	1	16	yes	—
109	#120×C₅₉	C₂³	1	48	yes	—
110	C₄×Q₈×C₅₉	C₂³	1	16	yes	—
111	C₄×D₄×C₅₉	C₂³	1	48	yes	—
112	C₄×D₄×C₅₉	C₂³	1	96	yes	—
113	#117×C₅₉	C₂³	1	4	yes	—
114	#117×C₅₉	C₂³	1	12	yes	—
115	#117×C₅₉	C₂³	1	12	yes	—
116	#117×C₅₉	C₂³	1	12	yes	—
117	C₂×C₄⋊C₄×C₅₉	C₂³	1	12	yes	—
118	C₂×C₄⋊C₄×C₅₉	C₂³	1	48	yes	—
119	C₂×C₂²⋊C₄×C₅₉	C₂³	1	12	yes	—
120	C₂×C₂²⋊C₄×C₅₉	C₂³	1	48	yes	—
121	C₂×C₄²×C₅₉	C₂³	1	12	yes	—
122	C₂⁴×C₅₉	C₂⁴	1	12	yes	—
123	C₂⁴×C₅₉	C₂⁴	1	2	yes	—
124	C₂⁴×C₅₉	C₂⁴	1	3	yes	—
125	#41×C₅₉	—	2	32	no	—
126	#41×C₅₉	—	2	96	no	—
127	#41×C₅₉	—	2	192	no	—
128	#41×C₅₉	—	2	48	no	—
129	#41×C₅₉	—	2	16	no	—
130	#41×C₅₉	—	2	48	no	—
131	#41×C₅₉	—	2	48	no	—
132	#41×C₅₉	—	2	48	no	—
133	#41×C₅₉	—	2	48	no	—
134	#41×C₅₉	C₂×D₄	1	32	yes	—
135	#41×C₅₉	C₂×D₄	1	32	yes	—
136	C₂×Q₈×C₅₉	—	2	64	no	—
137	C₂×Q₈×C₅₉	—	2	32	no	—
138	C₂×Q₈×C₅₉	—	2	24	no	—
139	C₂×Q₈×C₅₉	—	2	12	no	—
140	C₂×Q₈×C₅₉	—	2	48	no	—
141	C₂×Q₈×C₅₉	—	2	48	no	—
142	C₂×Q₈×C₅₉	—	2	24	no	—
143	C₂×Q₈×C₅₉	C₂×D₄	1	8	yes	—
144	C₂×Q₈×C₅₉	C₂⁴	1	6	yes	—
145	C₂×Q₈×C₅₉	C₂⁴	1	24	yes	—
146	C₂×Q₈×C₅₉	C₂⁴	1	12	yes	—
147	C₂×Q₈×C₅₉	C₂⁴	1	6	yes	—
148	C₂×Q₈×C₅₉	C₂⁴	1	4	yes	—
149	C₂×Q₈×C₅₉	C₂⁴	1	4	yes	—
150	C₂×D₄×C₅₉	—	2	24	no	—
151	C₂×D₄×C₅₉	—	2	48	no	—
152	C₂×D₄×C₅₉	—	2	96	no	—
153	C₂×D₄×C₅₉	—	2	4	no	—
154	C₂×D₄×C₅₉	—	2	24	no	—
155	C₂×D₄×C₅₉	C₂×D₄	1	24	yes	—
156	C₂×D₄×C₅₉	C₂⁴	1	24	yes	—
157	C₂×D₄×C₅₉	C₂⁴	1	8	yes	—
158	C₂×D₄×C₅₉	C₂⁴	1	2	yes	—
159	C₂×D₄×C₅₉	C₂⁴	1	24	yes	—
160	C₂×D₄×C₅₉	C₂⁴	1	12	yes	—
161	C₂×D₄×C₅₉	C₂⁴	1	4	yes	—
162	C₂×D₄×C₅₉	C₂⁴	1	2	yes	—
163	C₂×D₄×C₅₉	C₂⁴	1	32	yes	—
164	C₂×D₄×C₅₉	C₂⁴	1	12	yes	—
165	C₂²×C₄×C₅₉	—	2	24	no	—
166	C₂²×C₄×C₅₉	—	2	24	no	—
167	C₂²×C₄×C₅₉	—	2	48	no	—
168	C₂²×C₄×C₅₉	C₂×D₄	1	24	yes	—
169	C₂²×C₄×C₅₉	C₂⁴	1	24	yes	—
170	C₂²×C₄×C₅₉	C₂⁴	1	12	yes	—
171	C₂²×C₄×C₅₉	C₂⁴	1	24	yes	—
172	C₂²×C₄×C₅₉	C₂⁴	1	24	yes	—
173	C₂²×C₄×C₅₉	C₂⁴	1	8	yes	—
174	C₂²×C₄×C₅₉	C₂⁴	1	6	yes	—
175	C₂²×C₄×C₅₉	C₂⁴	1	24	yes	—
176	C₂²×C₄×C₅₉	C₂⁴	1	6	yes	—
177	C₂²×C₄×C₅₉	C₂⁴	1	6	yes	—
178	C₂²×C₄×C₅₉	C₂⁴	1	3	yes	—
179	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
180	C₄⋊C₄×C₅₉	C₂⁴	1	8	yes	—
181	C₄⋊C₄×C₅₉	C₂⁴	1	96	yes	—
182	C₄⋊C₄×C₅₉	C₂⁴	1	24	yes	—
183	C₂²⋊C₄×C₅₉	C₂⁴	1	8	yes	—
184	C₂²⋊C₄×C₅₉	C₂⁴	1	96	yes	—
185	C₂²⋊C₄×C₅₉	C₂⁴	1	24	yes	—
186	C₂²⋊C₄×C₅₉	C₂⁴	1	32	yes	—
187	C₄²×C₅₉	C₂⁴	1	8	yes	—
188	C₄²×C₅₉	C₂⁴	1	24	yes	—
189	C₂³×C₅₉	—	2	4	no	—
190	C₂³×C₅₉	—	2	24	no	—
191	C₂³×C₅₉	—	4	6	no	—
192	C₂³×C₅₉	—	4	4	no	—
193	C₂³×C₅₉	—	4	24	no	—
194	C₂³×C₅₉	C₂²×D₄	1	12	yes	—
195	C₂³×C₅₉	C₂⁵	1	8	yes	—
196	C₂³×C₅₉	C₂⁵	1	4	yes	—
197	C₂³×C₅₉	C₂⁵	1	1	yes	characteristic
198	C₂³×C₅₉	C₂⁵	1	6	yes	—
199	Q₈×C₅₉	—	2	12	no	—
200	Q₈×C₅₉	—	2	48	no	—
201	Q₈×C₅₉	—	2	12	no	—
202	Q₈×C₅₉	—	2	24	no	—
203	Q₈×C₅₉	—	2	8	no	—
204	Q₈×C₅₉	C₂²×D₄	1	16	yes	—
205	D₄×C₅₉	—	2	16	no	—
206	D₄×C₅₉	—	2	48	no	—
207	D₄×C₅₉	—	2	48	no	—
208	D₄×C₅₉	—	2	24	no	—
209	D₄×C₅₉	—	2	8	no	—
210	D₄×C₅₉	—	2	4	no	—
211	D₄×C₅₉	—	2	4	no	—
212	D₄×C₅₉	—	4	32	no	—
213	D₄×C₅₉	C₂²×D₄	1	48	yes	—
214	C₂×C₄×C₅₉	—	2	12	no	—
215	C₂×C₄×C₅₉	—	2	24	no	—
216	C₂×C₄×C₅₉	—	2	48	no	—
217	C₂×C₄×C₅₉	—	2	16	no	—
218	C₂×C₄×C₅₉	—	2	48	no	—
219	C₂×C₄×C₅₉	—	2	48	no	—
220	C₂×C₄×C₅₉	—	4	24	no	—
221	C₂×C₄×C₅₉	C₂²×D₄	1	12	yes	—
222	C₂×C₄×C₅₉	C₂²×D₄	1	24	yes	—
223	C₂×C₄×C₅₉	C₂²×D₄	1	4	yes	—
224	C₂×C₄×C₅₉	C₂²×D₄	1	24	yes	—
225	C₂×C₄×C₅₉	C₂⁵	1	16	yes	—
226	C₂×C₄×C₅₉	C₂⁵	1	12	yes	—
227	C₂×C₄×C₅₉	C₂⁵	1	8	yes	—
228	C₂×C₄×C₅₉	C₂⁵	1	1	yes	characteristic
229	C₂×C₄×C₅₉	C₂⁵	1	6	yes	—
230	C₂×C₄×C₅₉	C₂⁵	1	1	yes	characteristic
231	#62859	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
232	C₂²×C₅₉	—	2	12	no	—
233	C₂²×C₅₉	—	2	2	no	—
234	C₂²×C₅₉	—	2	4	no	—
235	C₂²×C₅₉	—	2	8	no	—
236	C₂²×C₅₉	—	2	8	no	—
237	C₂²×C₅₉	—	2	16	no	—
238	C₂²×C₅₉	—	4	12	no	—
239	C₂²×C₅₉	—	4	8	no	—
240	C₂²×C₅₉	—	8	24	no	—
241	C₂²×C₅₉	C₂³×D₄	1	2	yes	—
242	C₂²×C₅₉	C₂³×D₄	1	12	yes	—
243	C₂²×C₅₉	C₂⁶	1	1	yes	characteristic
244	C₄×C₅₉	—	2	8	no	—
245	C₄×C₅₉	—	2	12	no	—
246	C₄×C₅₉	—	2	16	no	—
247	C₄×C₅₉	C₂³×D₄	1	2	yes	—
248	C₄×C₅₉	C₂³×D₄	1	12	yes	—
249	C₄×C₅₉	C₂³×D₄	1	2	yes	—
250	C₂×#585	C₂×C₅₉	1	1	yes	characteristic, complemented
251	C₂²×2₋¹⁺⁴	C₂×C₅₉	1	1	yes	characteristic, complemented
252	#3500	C₂×C₅₉	1	8	yes	complemented
253	#3499	C₂×C₅₉	1	8	yes	complemented
254	#3489	C₂×C₅₉	1	16	yes	complemented
255	#3486	C₂×C₅₉	1	4	yes	complemented
256	#3485	C₂×C₅₉	1	12	yes	complemented
257	#3449	C₂×C₅₉	1	6	yes	complemented
258	C₂×#536	C₂×C₅₉	1	6	yes	complemented
259	#3428	C₂×C₅₉	1	1	yes	characteristic, complemented
260	C₂×C₅₉	—	2	2	no	—
261	C₂×C₅₉	—	2	12	no	—
262	C₂×C₅₉	—	4	4	no	—
263	C₂×C₅₉	—	4	8	no	—
264	C₂×C₅₉	C₂⁴×D₄	1	1	yes	characteristic
265	C₂×C₅₉	2₋¹⁺⁶	1	2	yes	—
266	#585	—	2	16	no	—
267	C₂×2₋¹⁺⁴	—	2	16	no	—
268	C₂×2₋¹⁺⁴	C₂²×C₅₉	1	2	yes	—
269	C₂×2₋¹⁺⁴	C₂²×C₅₉	1	8	yes	complemented
270	C₂×2₋¹⁺⁴	C₂²×C₅₉	1	8	yes	complemented
271	C₂×2₋¹⁺⁴	C₂²×C₅₉	1	4	yes	complemented
272	C₂×H(5,𝔽₂)	C₂²×C₅₉	1	6	yes	—
273	C₂×H(5,𝔽₂)	C₂²×C₅₉	1	4	yes	complemented
274	C₂²×#41	C₂²×C₅₉	1	6	yes	—
275	C₂²×#41	C₂²×C₅₉	1	1	yes	characteristic
276	C₂²×#41	C₂²×C₅₉	1	3	yes	complemented
277	C₂²×#41	C₂²×C₅₉	1	6	yes	complemented
278	C₂²×#41	C₂²×C₅₉	1	8	yes	complemented
279	C₂³×Q₈	C₂²×C₅₉	1	3	yes	complemented
280	C₂³×Q₈	C₂²×C₅₉	1	2	yes	complemented
281	D₄×Q₈	C₂²×C₅₉	1	32	yes	complemented
282	#548	C₂²×C₅₉	1	32	yes	complemented
283	#547	C₂²×C₅₉	1	96	yes	complemented
284	#546	C₂²×C₅₉	1	96	yes	complemented
285	#537	C₂²×C₅₉	1	24	yes	complemented
286	#536	C₂²×C₅₉	1	12	yes	complemented
287	#536	C₂²×C₅₉	1	24	yes	complemented
288	#536	C₂²×C₅₉	1	24	yes	complemented
289	#536	C₂²×C₅₉	1	24	yes	complemented
290	#536	C₂²×C₅₉	1	12	yes	complemented
291	#535	C₂²×C₅₉	1	4	yes	complemented
292	#535	C₂²×C₅₉	1	12	yes	complemented
293	#534	C₂²×C₅₉	1	24	yes	complemented
294	#532	C₂²×C₅₉	1	24	yes	complemented
295	C₂×C₄⋊Q₈	C₂²×C₅₉	1	12	yes	complemented
296	C₂×#124	C₂²×C₅₉	1	12	yes	complemented
297	#525	C₂²×C₅₉	1	24	yes	complemented
298	#525	C₂²×C₅₉	1	24	yes	complemented
299	C₂×#123	C₂²×C₅₉	1	24	yes	complemented
300	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	24	yes	complemented
301	#520	C₂²×C₅₉	1	8	yes	complemented
302	#519	C₂²×C₅₉	1	2	yes	complemented
303	#518	C₂²×C₅₉	1	6	yes	complemented
304	C₄×#41	C₂²×C₅₉	1	8	yes	complemented
305	C₂×#117	C₂²×C₅₉	1	6	yes	complemented
306	C₅₉	#62859	1	1	yes	characteristic, direct product factor, Sylow
307	2₋¹⁺⁴	—	2	64	no	—
308	2₋¹⁺⁴	—	2	64	no	—
309	2₋¹⁺⁴	—	2	32	no	—
310	2₋¹⁺⁴	—	2	16	no	—
311	H(5,𝔽₂)	—	2	32	no	—
312	H(5,𝔽₂)	—	2	48	no	—
313	C₂×#41	—	2	64	no	—
314	C₂×#41	—	2	48	no	—
315	C₂×#41	—	2	48	no	—
316	C₂×#41	—	2	24	no	—
317	C₂×#41	D₄×C₅₉	1	16	yes	complemented
318	C₂×#41	C₂³×C₅₉	1	12	yes	—
319	C₂×#41	C₂³×C₅₉	1	12	yes	—
320	C₂×#41	C₂³×C₅₉	1	12	yes	—
321	C₂×#41	C₂³×C₅₉	1	12	yes	—
322	C₂×#41	C₂³×C₅₉	1	4	yes	—
323	C₂×#41	C₂³×C₅₉	1	12	yes	—
324	C₂×#41	C₂³×C₅₉	1	48	yes	—
325	C₂×#41	C₂³×C₅₉	1	24	yes	—
326	C₂×#41	C₂³×C₅₉	1	8	yes	—
327	C₂×#41	C₂³×C₅₉	1	4	yes	—
328	C₂×#41	C₂³×C₅₉	1	4	yes	—
329	C₂²×Q₈	—	2	16	no	—
330	C₂²×Q₈	—	2	24	no	—
331	C₂²×Q₈	C₂³×C₅₉	1	12	yes	—
332	C₂²×Q₈	C₂³×C₅₉	1	12	yes	—
333	C₂²×Q₈	C₂³×C₅₉	1	6	yes	—
334	C₂²×Q₈	C₂³×C₅₉	1	3	yes	—
335	C₂²×Q₈	C₂³×C₅₉	1	6	yes	—
336	C₂²×Q₈	C₂³×C₅₉	1	16	yes	—
337	C₂²×Q₈	C₂³×C₅₉	1	8	yes	—
338	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
339	C₂²×D₄	C₂³×C₅₉	1	12	yes	—
340	C₂²×D₄	C₂³×C₅₉	1	6	yes	—
341	C₂²×D₄	C₂³×C₅₉	1	6	yes	—
342	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
343	C₂²×D₄	C₂³×C₅₉	1	24	yes	—
344	C₂²×D₄	C₂³×C₅₉	1	3	yes	—
345	C₂³×C₄	C₂³×C₅₉	1	12	yes	—
346	C₂³×C₄	C₂³×C₅₉	1	6	yes	—
347	C₂³×C₄	C₂³×C₅₉	1	6	yes	—
348	C₂³×C₄	C₂³×C₅₉	1	3	yes	—
349	C₄⋊Q₈	C₂³×C₅₉	1	24	yes	—
350	C₄⋊Q₈	C₂³×C₅₉	1	48	yes	—
351	#127	C₂³×C₅₉	1	8	yes	—
352	#124	C₂³×C₅₉	1	24	yes	—
353	#124	C₂³×C₅₉	1	48	yes	—
354	#124	C₂³×C₅₉	1	8	yes	—
355	#123	C₂³×C₅₉	1	48	yes	—
356	#123	C₂³×C₅₉	1	96	yes	—
357	#123	C₂³×C₅₉	1	48	yes	—
358	C₂²⋊Q₈	C₂³×C₅₉	1	48	yes	—
359	C₂²⋊Q₈	C₂³×C₅₉	1	96	yes	—
360	C₂²⋊Q₈	C₂³×C₅₉	1	48	yes	—
361	#121	C₂³×C₅₉	1	16	yes	—
362	#121	C₂³×C₅₉	1	48	yes	—
363	#121	C₂³×C₅₉	1	96	yes	—
364	#120	C₂³×C₅₉	1	16	yes	—
365	#120	C₂³×C₅₉	1	48	yes	—
366	C₄×Q₈	C₂³×C₅₉	1	16	yes	—
367	C₄×D₄	C₂³×C₅₉	1	48	yes	—
368	C₄×D₄	C₂³×C₅₉	1	96	yes	—
369	#117	C₂³×C₅₉	1	4	yes	—
370	#117	C₂³×C₅₉	1	12	yes	—
371	#117	C₂³×C₅₉	1	12	yes	—
372	#117	C₂³×C₅₉	1	12	yes	—
373	C₂×C₄⋊C₄	C₂³×C₅₉	1	12	yes	—
374	C₂×C₄⋊C₄	C₂³×C₅₉	1	48	yes	—
375	C₂×C₂²⋊C₄	C₂³×C₅₉	1	12	yes	—
376	C₂×C₂²⋊C₄	C₂³×C₅₉	1	48	yes	—
377	C₂×C₄²	C₂³×C₅₉	1	12	yes	—
378	C₂⁴	C₂⁴×C₅₉	1	12	yes	—
379	C₂⁴	C₂⁴×C₅₉	1	2	yes	—
380	C₂⁴	C₂⁴×C₅₉	1	3	yes	—
381	#41	—	2	32	no	—
382	#41	—	2	96	no	—
383	#41	—	2	192	no	—
384	#41	—	2	48	no	—
385	#41	—	2	16	no	—
386	#41	—	2	48	no	—
387	#41	—	2	48	no	—
388	#41	—	2	48	no	—
389	#41	—	2	48	no	—
390	#41	C₂×D₄×C₅₉	1	32	yes	—
391	#41	C₂×D₄×C₅₉	1	32	yes	—
392	C₂×Q₈	—	2	64	no	—
393	C₂×Q₈	—	2	32	no	—
394	C₂×Q₈	—	2	24	no	—
395	C₂×Q₈	—	2	12	no	—
396	C₂×Q₈	—	2	48	no	—
397	C₂×Q₈	—	2	48	no	—
398	C₂×Q₈	—	2	24	no	—
399	C₂×Q₈	C₂×D₄×C₅₉	1	8	yes	—
400	C₂×Q₈	C₂⁴×C₅₉	1	6	yes	—
401	C₂×Q₈	C₂⁴×C₅₉	1	24	yes	—
402	C₂×Q₈	C₂⁴×C₅₉	1	12	yes	—
403	C₂×Q₈	C₂⁴×C₅₉	1	6	yes	—
404	C₂×Q₈	C₂⁴×C₅₉	1	4	yes	—
405	C₂×Q₈	C₂⁴×C₅₉	1	4	yes	—
406	C₂×D₄	—	2	24	no	—
407	C₂×D₄	—	2	48	no	—
408	C₂×D₄	—	2	96	no	—
409	C₂×D₄	—	2	4	no	—
410	C₂×D₄	—	2	24	no	—
411	C₂×D₄	C₂×D₄×C₅₉	1	24	yes	—
412	C₂×D₄	C₂⁴×C₅₉	1	24	yes	—
413	C₂×D₄	C₂⁴×C₅₉	1	8	yes	—
414	C₂×D₄	C₂⁴×C₅₉	1	2	yes	—
415	C₂×D₄	C₂⁴×C₅₉	1	24	yes	—
416	C₂×D₄	C₂⁴×C₅₉	1	12	yes	—
417	C₂×D₄	C₂⁴×C₅₉	1	4	yes	—
418	C₂×D₄	C₂⁴×C₅₉	1	2	yes	—
419	C₂×D₄	C₂⁴×C₅₉	1	32	yes	—
420	C₂×D₄	C₂⁴×C₅₉	1	12	yes	—
421	C₂²×C₄	—	2	24	no	—
422	C₂²×C₄	—	2	24	no	—
423	C₂²×C₄	—	2	48	no	—
424	C₂²×C₄	C₂×D₄×C₅₉	1	24	yes	—
425	C₂²×C₄	C₂⁴×C₅₉	1	24	yes	—
426	C₂²×C₄	C₂⁴×C₅₉	1	12	yes	—
427	C₂²×C₄	C₂⁴×C₅₉	1	24	yes	—
428	C₂²×C₄	C₂⁴×C₅₉	1	24	yes	—
429	C₂²×C₄	C₂⁴×C₅₉	1	8	yes	—
430	C₂²×C₄	C₂⁴×C₅₉	1	6	yes	—
431	C₂²×C₄	C₂⁴×C₅₉	1	24	yes	—
432	C₂²×C₄	C₂⁴×C₅₉	1	6	yes	—
433	C₂²×C₄	C₂⁴×C₅₉	1	6	yes	—
434	C₂²×C₄	C₂⁴×C₅₉	1	3	yes	—
435	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
436	C₄⋊C₄	C₂⁴×C₅₉	1	8	yes	—
437	C₄⋊C₄	C₂⁴×C₅₉	1	96	yes	—
438	C₄⋊C₄	C₂⁴×C₅₉	1	24	yes	—
439	C₂²⋊C₄	C₂⁴×C₅₉	1	8	yes	—
440	C₂²⋊C₄	C₂⁴×C₅₉	1	96	yes	—
441	C₂²⋊C₄	C₂⁴×C₅₉	1	24	yes	—
442	C₂²⋊C₄	C₂⁴×C₅₉	1	32	yes	—
443	C₄²	C₂⁴×C₅₉	1	8	yes	—
444	C₄²	C₂⁴×C₅₉	1	24	yes	—
445	C₂³	—	2	4	no	—
446	C₂³	—	2	24	no	—
447	C₂³	—	4	6	no	—
448	C₂³	—	4	4	no	—
449	C₂³	—	4	24	no	—
450	C₂³	C₂²×D₄×C₅₉	1	12	yes	—
451	C₂³	C₂⁵×C₅₉	1	8	yes	—
452	C₂³	C₂⁵×C₅₉	1	4	yes	—
453	C₂³	C₂⁵×C₅₉	1	1	yes	characteristic
454	C₂³	C₂⁵×C₅₉	1	6	yes	—
455	Q₈	—	2	12	no	—
456	Q₈	—	2	48	no	—
457	Q₈	—	2	12	no	—
458	Q₈	—	2	24	no	—
459	Q₈	—	2	8	no	—
460	Q₈	C₂²×D₄×C₅₉	1	16	yes	—
461	D₄	—	2	16	no	—
462	D₄	—	2	48	no	—
463	D₄	—	2	48	no	—
464	D₄	—	2	24	no	—
465	D₄	—	2	8	no	—
466	D₄	—	2	4	no	—
467	D₄	—	2	4	no	—
468	D₄	—	4	32	no	—
469	D₄	C₂²×D₄×C₅₉	1	48	yes	—
470	C₂×C₄	—	2	12	no	—
471	C₂×C₄	—	2	24	no	—
472	C₂×C₄	—	2	48	no	—
473	C₂×C₄	—	2	16	no	—
474	C₂×C₄	—	2	48	no	—
475	C₂×C₄	—	2	48	no	—
476	C₂×C₄	—	4	24	no	—
477	C₂×C₄	C₂²×D₄×C₅₉	1	12	yes	—
478	C₂×C₄	C₂²×D₄×C₅₉	1	24	yes	—
479	C₂×C₄	C₂²×D₄×C₅₉	1	4	yes	—
480	C₂×C₄	C₂²×D₄×C₅₉	1	24	yes	—
481	C₂×C₄	C₂⁵×C₅₉	1	16	yes	—
482	C₂×C₄	C₂⁵×C₅₉	1	12	yes	—
483	C₂×C₄	C₂⁵×C₅₉	1	8	yes	—
484	C₂×C₄	C₂⁵×C₅₉	1	1	yes	characteristic
485	C₂×C₄	C₂⁵×C₅₉	1	6	yes	—
486	C₂×C₄	C₂⁵×C₅₉	1	1	yes	characteristic
487	C₂²	—	2	12	no	—
488	C₂²	—	2	2	no	—
489	C₂²	—	2	4	no	—
490	C₂²	—	2	8	no	—
491	C₂²	—	2	8	no	—
492	C₂²	—	2	16	no	—
493	C₂²	—	4	12	no	—
494	C₂²	—	4	8	no	—
495	C₂²	—	8	24	no	—
496	C₂²	C₂³×D₄×C₅₉	1	2	yes	—
497	C₂²	C₂³×D₄×C₅₉	1	12	yes	—
498	C₂²	C₂⁶×C₅₉	1	1	yes	characteristic
499	C₄	—	2	8	no	—
500	C₄	—	2	12	no	—
501	C₄	—	2	16	no	—
502	C₄	C₂³×D₄×C₅₉	1	2	yes	—
503	C₄	C₂³×D₄×C₅₉	1	12	yes	—
504	C₄	C₂³×D₄×C₅₉	1	2	yes	—
505	C₂	—	2	2	no	—
506	C₂	—	2	12	no	—
507	C₂	—	4	4	no	—
508	C₂	—	4	8	no	—
509	C₂	C₂⁴×D₄×C₅₉	1	1	yes	characteristic
510	C₂	C₅₉×2₋¹⁺⁶	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₅₉	C₂⁶
commutator, Frattini, cosocle	C₂²	C₂⁶×C₅₉
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅₉×#585	C₂	semidirect
2. C₂²×2₋¹⁺⁴×C₅₉	C₂	semidirect
3. C₅₉×#3500	C₂	semidirect
4. C₅₉×#3499	C₂	semidirect
5. C₅₉×#3489	C₂	semidirect
6. C₅₉×#3486	C₂	semidirect
7. C₅₉×#3485	C₂	semidirect
8. C₅₉×#3449	C₂	semidirect
9. C₂×C₅₉×#536	C₂	semidirect
10. C₅₉×#3428	C₂	semidirect
14. C₂×2₋¹⁺⁴×C₅₉	C₂²	semidirect
15. C₂×2₋¹⁺⁴×C₅₉	C₂²	semidirect
16. C₂×2₋¹⁺⁴×C₅₉	C₂²	semidirect
18. C₂×H(5,𝔽₂)×C₅₉	C₂²	semidirect
21. C₂²×#41×C₅₉	C₂²	semidirect
22. C₂²×#41×C₅₉	C₂²	semidirect
23. C₂²×#41×C₅₉	C₂²	semidirect
24. C₂³×Q₈×C₅₉	C₂²	semidirect
25. C₂³×Q₈×C₅₉	C₂²	semidirect
26. D₄×Q₈×C₅₉	C₂²	semidirect
27. C₅₉×#548	C₂²	semidirect
28. C₅₉×#547	C₂²	semidirect
29. C₅₉×#546	C₂²	semidirect
30. C₅₉×#537	C₂²	semidirect
31. C₅₉×#536	C₂²	semidirect
32. C₅₉×#536	C₂²	semidirect
33. C₅₉×#536	C₂²	semidirect
34. C₅₉×#536	C₂²	semidirect
35. C₅₉×#536	C₂²	semidirect
36. C₅₉×#535	C₂²	semidirect
37. C₅₉×#535	C₂²	semidirect
38. C₅₉×#534	C₂²	semidirect
39. C₅₉×#532	C₂²	semidirect
40. C₂×C₄⋊Q₈×C₅₉	C₂²	semidirect
41. C₂×#124×C₅₉	C₂²	semidirect
42. C₅₉×#525	C₂²	semidirect
43. C₅₉×#525	C₂²	semidirect
44. C₂×#123×C₅₉	C₂²	semidirect
45. C₂×C₂²⋊Q₈×C₅₉	C₂²	semidirect
46. C₅₉×#520	C₂²	semidirect
47. C₅₉×#519	C₂²	semidirect
48. C₅₉×#518	C₂²	semidirect
49. C₄×#41×C₅₉	C₂²	semidirect
50. C₂×#117×C₅₉	C₂²	semidirect
61. C₂×#41×C₅₉	D₄	semidirect
231. #62859	C₅₉	direct (N × H)
250. C₂×#585	C₂×C₅₉	semidirect
251. C₂²×2₋¹⁺⁴	C₂×C₅₉	semidirect
252. #3500	C₂×C₅₉	semidirect
253. #3499	C₂×C₅₉	semidirect
254. #3489	C₂×C₅₉	semidirect
255. #3486	C₂×C₅₉	semidirect
256. #3485	C₂×C₅₉	semidirect
257. #3449	C₂×C₅₉	semidirect
258. C₂×#536	C₂×C₅₉	semidirect
259. #3428	C₂×C₅₉	semidirect
269. C₂×2₋¹⁺⁴	C₂²×C₅₉	semidirect
270. C₂×2₋¹⁺⁴	C₂²×C₅₉	semidirect
271. C₂×2₋¹⁺⁴	C₂²×C₅₉	semidirect
273. C₂×H(5,𝔽₂)	C₂²×C₅₉	semidirect
276. C₂²×#41	C₂²×C₅₉	semidirect
277. C₂²×#41	C₂²×C₅₉	semidirect
278. C₂²×#41	C₂²×C₅₉	semidirect
279. C₂³×Q₈	C₂²×C₅₉	semidirect
280. C₂³×Q₈	C₂²×C₅₉	semidirect
281. D₄×Q₈	C₂²×C₅₉	semidirect
282. #548	C₂²×C₅₉	semidirect
283. #547	C₂²×C₅₉	semidirect
284. #546	C₂²×C₅₉	semidirect
285. #537	C₂²×C₅₉	semidirect
286. #536	C₂²×C₅₉	semidirect
287. #536	C₂²×C₅₉	semidirect
288. #536	C₂²×C₅₉	semidirect
289. #536	C₂²×C₅₉	semidirect
290. #536	C₂²×C₅₉	semidirect
291. #535	C₂²×C₅₉	semidirect
292. #535	C₂²×C₅₉	semidirect
293. #534	C₂²×C₅₉	semidirect
294. #532	C₂²×C₅₉	semidirect
295. C₂×C₄⋊Q₈	C₂²×C₅₉	semidirect
296. C₂×#124	C₂²×C₅₉	semidirect
297. #525	C₂²×C₅₉	semidirect
298. #525	C₂²×C₅₉	semidirect
299. C₂×#123	C₂²×C₅₉	semidirect
300. C₂×C₂²⋊Q₈	C₂²×C₅₉	semidirect
301. #520	C₂²×C₅₉	semidirect
302. #519	C₂²×C₅₉	semidirect
303. #518	C₂²×C₅₉	semidirect
304. C₄×#41	C₂²×C₅₉	semidirect
305. C₂×#117	C₂²×C₅₉	semidirect
306. C₅₉	#62859	direct (N × H)
317. C₂×#41	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×#585	2
C₂²×2₋¹⁺⁴×C₅₉	2
C₅₉×#3500	2
C₅₉×#3499	2
C₅₉×#3489	2
C₅₉×#3486	2
C₅₉×#3485	2
C₅₉×#3449	2
C₂×C₅₉×#536	2
C₅₉×#3428	2
#62859	59

Subgroups — C59×#62859 #28474968

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#62859 #28474968