Subgroups — C₅₉×#62852 #28474961

Order 15104.

11618 conjugacy classes of subgroups.

The subgroup lattice has 522 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×H(5,𝔽₂)×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₉×#3500	C₂	1	8	yes	maximal, complemented
4	C₅₉×#3498	C₂	1	8	yes	maximal, complemented
5	C₅₉×#3488	C₂	1	16	yes	maximal, complemented
6	C₅₉×#3487	C₂	1	4	yes	maximal, complemented
7	C₅₉×#3484	C₂	1	12	yes	maximal, complemented
8	C₅₉×#3449	C₂	1	6	yes	maximal, complemented
9	C₂×C₅₉×#535	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	C₂²	1	2	yes	complemented
13	C₂×2₋¹⁺⁴×C₅₉	C₂²	1	4	yes	complemented
14	C₂×H(5,𝔽₂)×C₅₉	—	2	16	no	—
15	C₂×H(5,𝔽₂)×C₅₉	C₂²	1	8	yes	complemented
16	C₂×H(5,𝔽₂)×C₅₉	C₂²	1	8	yes	complemented
17	C₂×H(5,𝔽₂)×C₅₉	C₂²	1	6	yes	complemented
18	C₂×H(5,𝔽₂)×C₅₉	C₂²	1	4	yes	complemented
19	C₂²×#41×C₅₉	C₂²	1	1	yes	characteristic
20	C₂²×#41×C₅₉	C₂²	1	3	yes	complemented
21	C₂²×#41×C₅₉	C₂²	1	2	yes	complemented
22	C₂²×#41×C₅₉	C₂²	1	6	yes	complemented
23	C₂²×#41×C₅₉	C₂²	1	8	yes	complemented
24	C₂³×D₄×C₅₉	C₂²	1	3	yes	complemented
25	C₂³×D₄×C₅₉	C₂²	1	6	yes	complemented
26	C₅₉×#550	C₂²	1	32	yes	complemented
27	C₅₉×#548	C₂²	1	32	yes	complemented
28	C₅₉×#546	C₂²	1	96	yes	complemented
29	D₄²×C₅₉	C₂²	1	96	yes	complemented
30	C₅₉×#537	C₂²	1	24	yes	complemented
31	C₅₉×#536	C₂²	1	4	yes	complemented
32	C₅₉×#536	C₂²	1	12	yes	complemented
33	C₅₉×#535	C₂²	1	12	yes	complemented
34	C₅₉×#535	C₂²	1	24	yes	complemented
35	C₅₉×#535	C₂²	1	24	yes	complemented
36	C₅₉×#535	C₂²	1	24	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×#127×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×#121×C₅₉	C₂²	1	24	yes	complemented
45	C₂×#120×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	C₂⁵×C₅₉	C₂³	1	6	yes	—
52	2₋¹⁺⁴×C₅₉	—	2	32	no	—
53	2₋¹⁺⁴×C₅₉	—	2	16	no	—
54	H(5,𝔽₂)×C₅₉	—	2	64	no	—
55	H(5,𝔽₂)×C₅₉	—	2	64	no	—
56	H(5,𝔽₂)×C₅₉	—	2	32	no	—
57	H(5,𝔽₂)×C₅₉	—	2	48	no	—
58	C₂×#41×C₅₉	—	2	64	no	—
59	C₂×#41×C₅₉	—	2	16	no	—
60	C₂×#41×C₅₉	—	2	24	no	—
61	C₂×#41×C₅₉	—	2	48	no	—
62	C₂×#41×C₅₉	D₄	1	16	yes	complemented
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	16	yes	—
68	C₂×#41×C₅₉	C₂³	1	4	yes	—
69	C₂×#41×C₅₉	C₂³	1	4	yes	—
70	C₂×#41×C₅₉	C₂³	1	12	yes	complemented
71	C₂×#41×C₅₉	C₂³	1	12	yes	complemented
72	C₂×#41×C₅₉	C₂³	1	24	yes	complemented
73	C₂×#41×C₅₉	C₂³	1	8	yes	complemented
74	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
75	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
76	C₂²×Q₈×C₅₉	C₂³	1	6	yes	complemented
77	C₂²×Q₈×C₅₉	C₂³	1	8	yes	complemented
78	C₂²×D₄×C₅₉	—	2	48	no	—
79	C₂²×D₄×C₅₉	—	2	24	no	—
80	C₂²×D₄×C₅₉	C₂³	1	12	yes	—
81	C₂²×D₄×C₅₉	C₂³	1	12	yes	—
82	C₂²×D₄×C₅₉	C₂³	1	12	yes	—
83	C₂²×D₄×C₅₉	C₂³	1	6	yes	—
84	C₂²×D₄×C₅₉	C₂³	1	3	yes	—
85	C₂²×D₄×C₅₉	C₂³	1	6	yes	—
86	C₂²×D₄×C₅₉	C₂³	1	48	yes	—
87	C₂²×D₄×C₅₉	C₂³	1	3	yes	—
88	C₂²×D₄×C₅₉	C₂³	1	6	yes	complemented
89	C₂²×D₄×C₅₉	C₂³	1	24	yes	complemented
90	C₂²×D₄×C₅₉	C₂³	1	48	yes	complemented
91	C₂³×C₄×C₅₉	C₂³	1	6	yes	—
92	C₂³×C₄×C₅₉	C₂³	1	3	yes	—
93	C₂³×C₄×C₅₉	C₂³	1	12	yes	complemented
94	C₄⋊Q₈×C₅₉	C₂³	1	8	yes	complemented
95	#127×C₅₉	C₂³	1	24	yes	complemented
96	#127×C₅₉	C₂³	1	48	yes	complemented
97	#124×C₅₉	C₂³	1	24	yes	complemented
98	#124×C₅₉	C₂³	1	48	yes	complemented
99	#124×C₅₉	C₂³	1	8	yes	complemented
100	#123×C₅₉	C₂³	1	16	yes	—
101	#123×C₅₉	C₂³	1	48	yes	complemented
102	C₂²⋊Q₈×C₅₉	C₂³	1	16	yes	complemented
103	C₂²⋊Q₈×C₅₉	C₂³	1	48	yes	complemented
104	#121×C₅₉	C₂³	1	48	yes	complemented
105	#121×C₅₉	C₂³	1	96	yes	complemented
106	#121×C₅₉	C₂³	1	48	yes	complemented
107	#121×C₅₉	C₂³	1	96	yes	complemented
108	#120×C₅₉	C₂³	1	48	yes	—
109	#120×C₅₉	C₂³	1	96	yes	complemented
110	#120×C₅₉	C₂³	1	48	yes	complemented
111	C₄×Q₈×C₅₉	C₂³	1	16	yes	complemented
112	C₄×D₄×C₅₉	C₂³	1	48	yes	complemented
113	C₄×D₄×C₅₉	C₂³	1	96	yes	complemented
114	#117×C₅₉	C₂³	1	4	yes	—
115	#117×C₅₉	C₂³	1	12	yes	—
116	#117×C₅₉	C₂³	1	12	yes	complemented
117	#117×C₅₉	C₂³	1	12	yes	complemented
118	C₂×C₄⋊C₄×C₅₉	C₂³	1	12	yes	complemented
119	C₂×C₂²⋊C₄×C₅₉	C₂³	1	12	yes	—
120	C₂×C₂²⋊C₄×C₅₉	C₂³	1	48	yes	complemented
121	C₂×C₄²×C₅₉	C₂³	1	12	yes	complemented
122	C₂⁴×C₅₉	—	2	24	no	—
123	C₂⁴×C₅₉	—	8	12	no	—
124	C₂⁴×C₅₉	C₂⁴	1	24	yes	—
125	C₂⁴×C₅₉	C₂⁴	1	6	yes	—
126	C₂⁴×C₅₉	C₂⁴	1	12	yes	—
127	C₂⁴×C₅₉	C₂⁴	1	3	yes	—
128	#41×C₅₉	—	2	64	no	—
129	#41×C₅₉	—	2	32	no	—
130	#41×C₅₉	—	2	96	no	—
131	#41×C₅₉	—	2	16	no	—
132	#41×C₅₉	—	2	48	no	—
133	#41×C₅₉	—	2	48	no	—
134	#41×C₅₉	—	2	48	no	—
135	#41×C₅₉	—	2	48	no	—
136	#41×C₅₉	—	2	48	no	—
137	#41×C₅₉	C₂×D₄	1	32	yes	complemented
138	#41×C₅₉	C₂×D₄	1	32	yes	complemented
139	C₂×Q₈×C₅₉	—	2	32	no	—
140	C₂×Q₈×C₅₉	—	2	4	no	—
141	C₂×Q₈×C₅₉	—	2	24	no	—
142	C₂×Q₈×C₅₉	C₂×D₄	1	8	yes	complemented
143	C₂×Q₈×C₅₉	C₂⁴	1	2	yes	—
144	C₂×Q₈×C₅₉	C₂⁴	1	12	yes	—
145	C₂×Q₈×C₅₉	C₂⁴	1	4	yes	—
146	C₂×Q₈×C₅₉	C₂⁴	1	2	yes	—
147	C₂×Q₈×C₅₉	C₂⁴	1	4	yes	—
148	C₂×D₄×C₅₉	—	2	24	no	—
149	C₂×D₄×C₅₉	—	2	48	no	—
150	C₂×D₄×C₅₉	—	2	192	no	—
151	C₂×D₄×C₅₉	—	2	96	no	—
152	C₂×D₄×C₅₉	—	2	24	no	—
153	C₂×D₄×C₅₉	—	2	12	no	—
154	C₂×D₄×C₅₉	—	2	48	no	—
155	C₂×D₄×C₅₉	—	2	48	no	—
156	C₂×D₄×C₅₉	—	2	24	no	—
157	C₂×D₄×C₅₉	—	8	48	no	—
158	C₂×D₄×C₅₉	C₂×D₄	1	24	yes	complemented
159	C₂×D₄×C₅₉	C₂⁴	1	8	yes	—
160	C₂×D₄×C₅₉	C₂⁴	1	24	yes	—
161	C₂×D₄×C₅₉	C₂⁴	1	24	yes	—
162	C₂×D₄×C₅₉	C₂⁴	1	6	yes	—
163	C₂×D₄×C₅₉	C₂⁴	1	24	yes	—
164	C₂×D₄×C₅₉	C₂⁴	1	12	yes	—
165	C₂×D₄×C₅₉	C₂⁴	1	6	yes	—
166	C₂×D₄×C₅₉	C₂⁴	1	4	yes	—
167	C₂×D₄×C₅₉	C₂⁴	1	96	yes	—
168	C₂×D₄×C₅₉	C₂⁴	1	12	yes	—
169	C₂²×C₄×C₅₉	—	2	24	no	—
170	C₂²×C₄×C₅₉	—	2	48	no	—
171	C₂²×C₄×C₅₉	C₂×D₄	1	24	yes	complemented
172	C₂²×C₄×C₅₉	C₂⁴	1	12	yes	—
173	C₂²×C₄×C₅₉	C₂⁴	1	24	yes	—
174	C₂²×C₄×C₅₉	C₂⁴	1	24	yes	—
175	C₂²×C₄×C₅₉	C₂⁴	1	8	yes	—
176	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
177	C₂²×C₄×C₅₉	C₂⁴	1	24	yes	—
178	C₂²×C₄×C₅₉	C₂⁴	1	6	yes	—
179	C₂²×C₄×C₅₉	C₂⁴	1	6	yes	—
180	C₂²×C₄×C₅₉	C₂⁴	1	3	yes	—
181	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
182	C₄⋊C₄×C₅₉	C₂⁴	1	8	yes	—
183	C₄⋊C₄×C₅₉	C₂⁴	1	24	yes	—
184	C₄⋊C₄×C₅₉	C₂⁴	1	32	yes	—
185	C₂²⋊C₄×C₅₉	C₂⁴	1	8	yes	—
186	C₂²⋊C₄×C₅₉	C₂⁴	1	24	yes	—
187	C₂²⋊C₄×C₅₉	C₂⁴	1	96	yes	—
188	C₂²⋊C₄×C₅₉	C₂⁴	1	32	yes	—
189	C₄²×C₅₉	C₂⁴	1	8	yes	—
190	C₄²×C₅₉	C₂⁴	1	24	yes	—
191	C₂³×C₅₉	—	2	12	no	—
192	C₂³×C₅₉	—	2	24	no	—
193	C₂³×C₅₉	—	2	48	no	—
194	C₂³×C₅₉	—	4	6	no	—
195	C₂³×C₅₉	—	4	12	no	—
196	C₂³×C₅₉	—	4	24	no	—
197	C₂³×C₅₉	—	4	48	no	—
198	C₂³×C₅₉	—	8	48	no	—
199	C₂³×C₅₉	C₂²×D₄	1	12	yes	—
200	C₂³×C₅₉	C₂⁵	1	12	yes	—
201	C₂³×C₅₉	C₂⁵	1	8	yes	—
202	C₂³×C₅₉	C₂⁵	1	1	yes	characteristic
203	C₂³×C₅₉	C₂⁵	1	6	yes	—
204	Q₈×C₅₉	—	2	24	no	—
205	Q₈×C₅₉	—	2	8	no	—
206	Q₈×C₅₉	—	2	4	no	—
207	Q₈×C₅₉	—	2	4	no	—
208	Q₈×C₅₉	C₂²×D₄	1	16	yes	—
209	D₄×C₅₉	—	2	48	no	—
210	D₄×C₅₉	—	2	16	no	—
211	D₄×C₅₉	—	2	48	no	—
212	D₄×C₅₉	—	2	12	no	—
213	D₄×C₅₉	—	2	48	no	—
214	D₄×C₅₉	—	2	12	no	—
215	D₄×C₅₉	—	2	24	no	—
216	D₄×C₅₉	—	2	8	no	—
217	D₄×C₅₉	—	4	96	no	—
218	D₄×C₅₉	C₂²×D₄	1	48	yes	—
219	C₂×C₄×C₅₉	—	2	4	no	—
220	C₂×C₄×C₅₉	—	2	24	no	—
221	C₂×C₄×C₅₉	—	2	16	no	—
222	C₂×C₄×C₅₉	—	2	48	no	—
223	C₂×C₄×C₅₉	—	2	48	no	—
224	C₂×C₄×C₅₉	—	4	24	no	—
225	C₂×C₄×C₅₉	C₂²×D₄	1	12	yes	—
226	C₂×C₄×C₅₉	C₂²×D₄	1	24	yes	—
227	C₂×C₄×C₅₉	C₂²×D₄	1	4	yes	—
228	C₂×C₄×C₅₉	C₂²×D₄	1	24	yes	—
229	C₂×C₄×C₅₉	C₂⁵	1	16	yes	—
230	C₂×C₄×C₅₉	C₂⁵	1	8	yes	—
231	C₂×C₄×C₅₉	C₂⁵	1	4	yes	—
232	C₂×C₄×C₅₉	C₂⁵	1	1	yes	characteristic
233	C₂×C₄×C₅₉	C₂⁵	1	6	yes	—
234	C₂×C₄×C₅₉	C₂⁵	1	1	yes	characteristic
235	#62852	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
236	C₂²×C₅₉	—	2	12	no	—
237	C₂²×C₅₉	—	2	2	no	—
238	C₂²×C₅₉	—	2	8	no	—
239	C₂²×C₅₉	—	2	12	no	—
240	C₂²×C₅₉	—	2	16	no	—
241	C₂²×C₅₉	—	2	24	no	—
242	C₂²×C₅₉	—	4	12	no	—
243	C₂²×C₅₉	—	4	24	no	—
244	C₂²×C₅₉	—	8	24	no	—
245	C₂²×C₅₉	—	8	48	no	—
246	C₂²×C₅₉	C₂³×D₄	1	2	yes	—
247	C₂²×C₅₉	C₂³×D₄	1	12	yes	—
248	C₂²×C₅₉	C₂⁶	1	1	yes	characteristic
249	C₄×C₅₉	—	2	4	no	—
250	C₄×C₅₉	—	2	8	no	—
251	C₄×C₅₉	—	2	16	no	—
252	C₄×C₅₉	C₂³×D₄	1	2	yes	—
253	C₄×C₅₉	C₂³×D₄	1	12	yes	—
254	C₄×C₅₉	C₂³×D₄	1	2	yes	—
255	C₂×#585	C₂×C₅₉	1	1	yes	characteristic, complemented
256	C₂²×H(5,𝔽₂)	C₂×C₅₉	1	1	yes	characteristic, complemented
257	#3500	C₂×C₅₉	1	8	yes	complemented
258	#3498	C₂×C₅₉	1	8	yes	complemented
259	#3488	C₂×C₅₉	1	16	yes	complemented
260	#3487	C₂×C₅₉	1	4	yes	complemented
261	#3484	C₂×C₅₉	1	12	yes	complemented
262	#3449	C₂×C₅₉	1	6	yes	complemented
263	C₂×#535	C₂×C₅₉	1	6	yes	complemented
264	#3428	C₂×C₅₉	1	1	yes	characteristic, complemented
265	C₂×C₅₉	—	2	2	no	—
266	C₂×C₅₉	—	2	12	no	—
267	C₂×C₅₉	—	4	12	no	—
268	C₂×C₅₉	—	4	8	no	—
269	C₂×C₅₉	C₂⁴×D₄	1	1	yes	characteristic
270	C₂×C₅₉	H(7,𝔽₂)	1	2	yes	—
271	#585	—	2	16	no	—
272	C₂×2₋¹⁺⁴	C₂²×C₅₉	1	2	yes	complemented
273	C₂×2₋¹⁺⁴	C₂²×C₅₉	1	4	yes	complemented
274	C₂×H(5,𝔽₂)	—	2	16	no	—
275	C₂×H(5,𝔽₂)	C₂²×C₅₉	1	8	yes	complemented
276	C₂×H(5,𝔽₂)	C₂²×C₅₉	1	8	yes	complemented
277	C₂×H(5,𝔽₂)	C₂²×C₅₉	1	6	yes	complemented
278	C₂×H(5,𝔽₂)	C₂²×C₅₉	1	4	yes	complemented
279	C₂²×#41	C₂²×C₅₉	1	1	yes	characteristic
280	C₂²×#41	C₂²×C₅₉	1	3	yes	complemented
281	C₂²×#41	C₂²×C₅₉	1	2	yes	complemented
282	C₂²×#41	C₂²×C₅₉	1	6	yes	complemented
283	C₂²×#41	C₂²×C₅₉	1	8	yes	complemented
284	C₂³×D₄	C₂²×C₅₉	1	3	yes	complemented
285	C₂³×D₄	C₂²×C₅₉	1	6	yes	complemented
286	#550	C₂²×C₅₉	1	32	yes	complemented
287	#548	C₂²×C₅₉	1	32	yes	complemented
288	#546	C₂²×C₅₉	1	96	yes	complemented
289	D₄²	C₂²×C₅₉	1	96	yes	complemented
290	#537	C₂²×C₅₉	1	24	yes	complemented
291	#536	C₂²×C₅₉	1	4	yes	complemented
292	#536	C₂²×C₅₉	1	12	yes	complemented
293	#535	C₂²×C₅₉	1	12	yes	complemented
294	#535	C₂²×C₅₉	1	24	yes	complemented
295	#535	C₂²×C₅₉	1	24	yes	complemented
296	#535	C₂²×C₅₉	1	24	yes	complemented
297	#535	C₂²×C₅₉	1	12	yes	complemented
298	#534	C₂²×C₅₉	1	24	yes	complemented
299	#532	C₂²×C₅₉	1	24	yes	complemented
300	C₂×#127	C₂²×C₅₉	1	12	yes	complemented
301	C₂×#124	C₂²×C₅₉	1	12	yes	complemented
302	#525	C₂²×C₅₉	1	24	yes	complemented
303	#525	C₂²×C₅₉	1	24	yes	complemented
304	C₂×#121	C₂²×C₅₉	1	24	yes	complemented
305	C₂×#120	C₂²×C₅₉	1	24	yes	complemented
306	#520	C₂²×C₅₉	1	8	yes	complemented
307	#519	C₂²×C₅₉	1	2	yes	complemented
308	#518	C₂²×C₅₉	1	6	yes	complemented
309	C₄×#41	C₂²×C₅₉	1	8	yes	complemented
310	C₂×#117	C₂²×C₅₉	1	6	yes	complemented
311	C₅₉	#62852	1	1	yes	characteristic, direct product factor, Sylow
312	C₂⁵	C₂³×C₅₉	1	6	yes	—
313	2₋¹⁺⁴	—	2	32	no	—
314	2₋¹⁺⁴	—	2	16	no	—
315	H(5,𝔽₂)	—	2	64	no	—
316	H(5,𝔽₂)	—	2	64	no	—
317	H(5,𝔽₂)	—	2	32	no	—
318	H(5,𝔽₂)	—	2	48	no	—
319	C₂×#41	—	2	64	no	—
320	C₂×#41	—	2	16	no	—
321	C₂×#41	—	2	24	no	—
322	C₂×#41	—	2	48	no	—
323	C₂×#41	D₄×C₅₉	1	16	yes	complemented
324	C₂×#41	C₂³×C₅₉	1	12	yes	—
325	C₂×#41	C₂³×C₅₉	1	12	yes	—
326	C₂×#41	C₂³×C₅₉	1	12	yes	—
327	C₂×#41	C₂³×C₅₉	1	4	yes	—
328	C₂×#41	C₂³×C₅₉	1	16	yes	—
329	C₂×#41	C₂³×C₅₉	1	4	yes	—
330	C₂×#41	C₂³×C₅₉	1	4	yes	—
331	C₂×#41	C₂³×C₅₉	1	12	yes	complemented
332	C₂×#41	C₂³×C₅₉	1	12	yes	complemented
333	C₂×#41	C₂³×C₅₉	1	24	yes	complemented
334	C₂×#41	C₂³×C₅₉	1	8	yes	complemented
335	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
336	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
337	C₂²×Q₈	C₂³×C₅₉	1	6	yes	complemented
338	C₂²×Q₈	C₂³×C₅₉	1	8	yes	complemented
339	C₂²×D₄	—	2	48	no	—
340	C₂²×D₄	—	2	24	no	—
341	C₂²×D₄	C₂³×C₅₉	1	12	yes	—
342	C₂²×D₄	C₂³×C₅₉	1	12	yes	—
343	C₂²×D₄	C₂³×C₅₉	1	12	yes	—
344	C₂²×D₄	C₂³×C₅₉	1	6	yes	—
345	C₂²×D₄	C₂³×C₅₉	1	3	yes	—
346	C₂²×D₄	C₂³×C₅₉	1	6	yes	—
347	C₂²×D₄	C₂³×C₅₉	1	48	yes	—
348	C₂²×D₄	C₂³×C₅₉	1	3	yes	—
349	C₂²×D₄	C₂³×C₅₉	1	6	yes	complemented
350	C₂²×D₄	C₂³×C₅₉	1	24	yes	complemented
351	C₂²×D₄	C₂³×C₅₉	1	48	yes	complemented
352	C₂³×C₄	C₂³×C₅₉	1	6	yes	—
353	C₂³×C₄	C₂³×C₅₉	1	3	yes	—
354	C₂³×C₄	C₂³×C₅₉	1	12	yes	complemented
355	C₄⋊Q₈	C₂³×C₅₉	1	8	yes	complemented
356	#127	C₂³×C₅₉	1	24	yes	complemented
357	#127	C₂³×C₅₉	1	48	yes	complemented
358	#124	C₂³×C₅₉	1	24	yes	complemented
359	#124	C₂³×C₅₉	1	48	yes	complemented
360	#124	C₂³×C₅₉	1	8	yes	complemented
361	#123	C₂³×C₅₉	1	16	yes	—
362	#123	C₂³×C₅₉	1	48	yes	complemented
363	C₂²⋊Q₈	C₂³×C₅₉	1	16	yes	complemented
364	C₂²⋊Q₈	C₂³×C₅₉	1	48	yes	complemented
365	#121	C₂³×C₅₉	1	48	yes	complemented
366	#121	C₂³×C₅₉	1	96	yes	complemented
367	#121	C₂³×C₅₉	1	48	yes	complemented
368	#121	C₂³×C₅₉	1	96	yes	complemented
369	#120	C₂³×C₅₉	1	48	yes	—
370	#120	C₂³×C₅₉	1	96	yes	complemented
371	#120	C₂³×C₅₉	1	48	yes	complemented
372	C₄×Q₈	C₂³×C₅₉	1	16	yes	complemented
373	C₄×D₄	C₂³×C₅₉	1	48	yes	complemented
374	C₄×D₄	C₂³×C₅₉	1	96	yes	complemented
375	#117	C₂³×C₅₉	1	4	yes	—
376	#117	C₂³×C₅₉	1	12	yes	—
377	#117	C₂³×C₅₉	1	12	yes	complemented
378	#117	C₂³×C₅₉	1	12	yes	complemented
379	C₂×C₄⋊C₄	C₂³×C₅₉	1	12	yes	complemented
380	C₂×C₂²⋊C₄	C₂³×C₅₉	1	12	yes	—
381	C₂×C₂²⋊C₄	C₂³×C₅₉	1	48	yes	complemented
382	C₂×C₄²	C₂³×C₅₉	1	12	yes	complemented
383	C₂⁴	—	2	24	no	—
384	C₂⁴	—	8	12	no	—
385	C₂⁴	C₂⁴×C₅₉	1	24	yes	—
386	C₂⁴	C₂⁴×C₅₉	1	6	yes	—
387	C₂⁴	C₂⁴×C₅₉	1	12	yes	—
388	C₂⁴	C₂⁴×C₅₉	1	3	yes	—
389	#41	—	2	64	no	—
390	#41	—	2	32	no	—
391	#41	—	2	96	no	—
392	#41	—	2	16	no	—
393	#41	—	2	48	no	—
394	#41	—	2	48	no	—
395	#41	—	2	48	no	—
396	#41	—	2	48	no	—
397	#41	—	2	48	no	—
398	#41	C₂×D₄×C₅₉	1	32	yes	complemented
399	#41	C₂×D₄×C₅₉	1	32	yes	complemented
400	C₂×Q₈	—	2	32	no	—
401	C₂×Q₈	—	2	4	no	—
402	C₂×Q₈	—	2	24	no	—
403	C₂×Q₈	C₂×D₄×C₅₉	1	8	yes	complemented
404	C₂×Q₈	C₂⁴×C₅₉	1	2	yes	—
405	C₂×Q₈	C₂⁴×C₅₉	1	12	yes	—
406	C₂×Q₈	C₂⁴×C₅₉	1	4	yes	—
407	C₂×Q₈	C₂⁴×C₅₉	1	2	yes	—
408	C₂×Q₈	C₂⁴×C₅₉	1	4	yes	—
409	C₂×D₄	—	2	24	no	—
410	C₂×D₄	—	2	48	no	—
411	C₂×D₄	—	2	192	no	—
412	C₂×D₄	—	2	96	no	—
413	C₂×D₄	—	2	24	no	—
414	C₂×D₄	—	2	12	no	—
415	C₂×D₄	—	2	48	no	—
416	C₂×D₄	—	2	48	no	—
417	C₂×D₄	—	2	24	no	—
418	C₂×D₄	—	8	48	no	—
419	C₂×D₄	C₂×D₄×C₅₉	1	24	yes	complemented
420	C₂×D₄	C₂⁴×C₅₉	1	8	yes	—
421	C₂×D₄	C₂⁴×C₅₉	1	24	yes	—
422	C₂×D₄	C₂⁴×C₅₉	1	24	yes	—
423	C₂×D₄	C₂⁴×C₅₉	1	6	yes	—
424	C₂×D₄	C₂⁴×C₅₉	1	24	yes	—
425	C₂×D₄	C₂⁴×C₅₉	1	12	yes	—
426	C₂×D₄	C₂⁴×C₅₉	1	6	yes	—
427	C₂×D₄	C₂⁴×C₅₉	1	4	yes	—
428	C₂×D₄	C₂⁴×C₅₉	1	96	yes	—
429	C₂×D₄	C₂⁴×C₅₉	1	12	yes	—
430	C₂²×C₄	—	2	24	no	—
431	C₂²×C₄	—	2	48	no	—
432	C₂²×C₄	C₂×D₄×C₅₉	1	24	yes	complemented
433	C₂²×C₄	C₂⁴×C₅₉	1	12	yes	—
434	C₂²×C₄	C₂⁴×C₅₉	1	24	yes	—
435	C₂²×C₄	C₂⁴×C₅₉	1	24	yes	—
436	C₂²×C₄	C₂⁴×C₅₉	1	8	yes	—
437	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
438	C₂²×C₄	C₂⁴×C₅₉	1	24	yes	—
439	C₂²×C₄	C₂⁴×C₅₉	1	6	yes	—
440	C₂²×C₄	C₂⁴×C₅₉	1	6	yes	—
441	C₂²×C₄	C₂⁴×C₅₉	1	3	yes	—
442	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
443	C₄⋊C₄	C₂⁴×C₅₉	1	8	yes	—
444	C₄⋊C₄	C₂⁴×C₅₉	1	24	yes	—
445	C₄⋊C₄	C₂⁴×C₅₉	1	32	yes	—
446	C₂²⋊C₄	C₂⁴×C₅₉	1	8	yes	—
447	C₂²⋊C₄	C₂⁴×C₅₉	1	24	yes	—
448	C₂²⋊C₄	C₂⁴×C₅₉	1	96	yes	—
449	C₂²⋊C₄	C₂⁴×C₅₉	1	32	yes	—
450	C₄²	C₂⁴×C₅₉	1	8	yes	—
451	C₄²	C₂⁴×C₅₉	1	24	yes	—
452	C₂³	—	2	12	no	—
453	C₂³	—	2	24	no	—
454	C₂³	—	2	48	no	—
455	C₂³	—	4	6	no	—
456	C₂³	—	4	12	no	—
457	C₂³	—	4	24	no	—
458	C₂³	—	4	48	no	—
459	C₂³	—	8	48	no	—
460	C₂³	C₂²×D₄×C₅₉	1	12	yes	—
461	C₂³	C₂⁵×C₅₉	1	12	yes	—
462	C₂³	C₂⁵×C₅₉	1	8	yes	—
463	C₂³	C₂⁵×C₅₉	1	1	yes	characteristic
464	C₂³	C₂⁵×C₅₉	1	6	yes	—
465	Q₈	—	2	24	no	—
466	Q₈	—	2	8	no	—
467	Q₈	—	2	4	no	—
468	Q₈	—	2	4	no	—
469	Q₈	C₂²×D₄×C₅₉	1	16	yes	—
470	D₄	—	2	48	no	—
471	D₄	—	2	16	no	—
472	D₄	—	2	48	no	—
473	D₄	—	2	12	no	—
474	D₄	—	2	48	no	—
475	D₄	—	2	12	no	—
476	D₄	—	2	24	no	—
477	D₄	—	2	8	no	—
478	D₄	—	4	96	no	—
479	D₄	C₂²×D₄×C₅₉	1	48	yes	—
480	C₂×C₄	—	2	4	no	—
481	C₂×C₄	—	2	24	no	—
482	C₂×C₄	—	2	16	no	—
483	C₂×C₄	—	2	48	no	—
484	C₂×C₄	—	2	48	no	—
485	C₂×C₄	—	4	24	no	—
486	C₂×C₄	C₂²×D₄×C₅₉	1	12	yes	—
487	C₂×C₄	C₂²×D₄×C₅₉	1	24	yes	—
488	C₂×C₄	C₂²×D₄×C₅₉	1	4	yes	—
489	C₂×C₄	C₂²×D₄×C₅₉	1	24	yes	—
490	C₂×C₄	C₂⁵×C₅₉	1	16	yes	—
491	C₂×C₄	C₂⁵×C₅₉	1	8	yes	—
492	C₂×C₄	C₂⁵×C₅₉	1	4	yes	—
493	C₂×C₄	C₂⁵×C₅₉	1	1	yes	characteristic
494	C₂×C₄	C₂⁵×C₅₉	1	6	yes	—
495	C₂×C₄	C₂⁵×C₅₉	1	1	yes	characteristic
496	C₂²	—	2	12	no	—
497	C₂²	—	2	2	no	—
498	C₂²	—	2	8	no	—
499	C₂²	—	2	12	no	—
500	C₂²	—	2	16	no	—
501	C₂²	—	2	24	no	—
502	C₂²	—	4	12	no	—
503	C₂²	—	4	24	no	—
504	C₂²	—	8	48	no	—
505	C₂²	—	8	24	no	—
506	C₂²	C₂³×D₄×C₅₉	1	2	yes	—
507	C₂²	C₂³×D₄×C₅₉	1	12	yes	—
508	C₂²	C₂⁶×C₅₉	1	1	yes	characteristic
509	C₄	—	2	4	no	—
510	C₄	—	2	8	no	—
511	C₄	—	2	16	no	—
512	C₄	C₂³×D₄×C₅₉	1	2	yes	—
513	C₄	C₂³×D₄×C₅₉	1	12	yes	—
514	C₄	C₂³×D₄×C₅₉	1	2	yes	—
515	C₂	—	2	2	no	—
516	C₂	—	2	12	no	—
517	C₂	—	4	12	no	—
518	C₂	—	4	8	no	—
519	C₂	C₂⁴×D₄×C₅₉	1	1	yes	characteristic
520	C₂	C₅₉×H(7,𝔽₂)	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×H(5,𝔽₂)×C₅₉	C₂	semidirect
3. C₅₉×#3500	C₂	semidirect
4. C₅₉×#3498	C₂	semidirect
5. C₅₉×#3488	C₂	semidirect
6. C₅₉×#3487	C₂	semidirect
7. C₅₉×#3484	C₂	semidirect
8. C₅₉×#3449	C₂	semidirect
9. C₂×C₅₉×#535	C₂	semidirect
10. C₅₉×#3428	C₂	semidirect
12. C₂×2₋¹⁺⁴×C₅₉	C₂²	semidirect
13. C₂×2₋¹⁺⁴×C₅₉	C₂²	semidirect
15. C₂×H(5,𝔽₂)×C₅₉	C₂²	semidirect
16. C₂×H(5,𝔽₂)×C₅₉	C₂²	semidirect
17. C₂×H(5,𝔽₂)×C₅₉	C₂²	semidirect
18. C₂×H(5,𝔽₂)×C₅₉	C₂²	semidirect
20. C₂²×#41×C₅₉	C₂²	semidirect
21. C₂²×#41×C₅₉	C₂²	semidirect
22. C₂²×#41×C₅₉	C₂²	semidirect
23. C₂²×#41×C₅₉	C₂²	semidirect
24. C₂³×D₄×C₅₉	C₂²	semidirect
25. C₂³×D₄×C₅₉	C₂²	semidirect
26. C₅₉×#550	C₂²	semidirect
27. C₅₉×#548	C₂²	semidirect
28. C₅₉×#546	C₂²	semidirect
29. D₄²×C₅₉	C₂²	semidirect
30. C₅₉×#537	C₂²	semidirect
31. C₅₉×#536	C₂²	semidirect
32. C₅₉×#536	C₂²	semidirect
33. C₅₉×#535	C₂²	semidirect
34. C₅₉×#535	C₂²	semidirect
35. C₅₉×#535	C₂²	semidirect
36. C₅₉×#535	C₂²	semidirect
37. C₅₉×#535	C₂²	semidirect
38. C₅₉×#534	C₂²	semidirect
39. C₅₉×#532	C₂²	semidirect
40. C₂×#127×C₅₉	C₂²	semidirect
41. C₂×#124×C₅₉	C₂²	semidirect
42. C₅₉×#525	C₂²	semidirect
43. C₅₉×#525	C₂²	semidirect
44. C₂×#121×C₅₉	C₂²	semidirect
45. C₂×#120×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
62. C₂×#41×C₅₉	D₄	semidirect
70. C₂×#41×C₅₉	C₂³	semidirect
71. C₂×#41×C₅₉	C₂³	semidirect
72. C₂×#41×C₅₉	C₂³	semidirect
73. C₂×#41×C₅₉	C₂³	semidirect
76. C₂²×Q₈×C₅₉	C₂³	semidirect
77. C₂²×Q₈×C₅₉	C₂³	semidirect
88. C₂²×D₄×C₅₉	C₂³	semidirect
89. C₂²×D₄×C₅₉	C₂³	semidirect
90. C₂²×D₄×C₅₉	C₂³	semidirect
93. C₂³×C₄×C₅₉	C₂³	semidirect
94. C₄⋊Q₈×C₅₉	C₂³	semidirect
95. #127×C₅₉	C₂³	semidirect
96. #127×C₅₉	C₂³	semidirect
97. #124×C₅₉	C₂³	semidirect
98. #124×C₅₉	C₂³	semidirect
99. #124×C₅₉	C₂³	semidirect
101. #123×C₅₉	C₂³	semidirect
102. C₂²⋊Q₈×C₅₉	C₂³	semidirect
103. C₂²⋊Q₈×C₅₉	C₂³	semidirect
104. #121×C₅₉	C₂³	semidirect
105. #121×C₅₉	C₂³	semidirect
106. #121×C₅₉	C₂³	semidirect
107. #121×C₅₉	C₂³	semidirect
109. #120×C₅₉	C₂³	semidirect
110. #120×C₅₉	C₂³	semidirect
111. C₄×Q₈×C₅₉	C₂³	semidirect
112. C₄×D₄×C₅₉	C₂³	semidirect
113. C₄×D₄×C₅₉	C₂³	semidirect
116. #117×C₅₉	C₂³	semidirect
117. #117×C₅₉	C₂³	semidirect
118. C₂×C₄⋊C₄×C₅₉	C₂³	semidirect
120. C₂×C₂²⋊C₄×C₅₉	C₂³	semidirect
121. C₂×C₄²×C₅₉	C₂³	semidirect
137. #41×C₅₉	C₂×D₄	semidirect
138. #41×C₅₉	C₂×D₄	semidirect
142. C₂×Q₈×C₅₉	C₂×D₄	semidirect
158. C₂×D₄×C₅₉	C₂×D₄	semidirect
171. C₂²×C₄×C₅₉	C₂×D₄	semidirect
235. #62852	C₅₉	direct (N × H)
255. C₂×#585	C₂×C₅₉	semidirect
256. C₂²×H(5,𝔽₂)	C₂×C₅₉	semidirect
257. #3500	C₂×C₅₉	semidirect
258. #3498	C₂×C₅₉	semidirect
259. #3488	C₂×C₅₉	semidirect
260. #3487	C₂×C₅₉	semidirect
261. #3484	C₂×C₅₉	semidirect
262. #3449	C₂×C₅₉	semidirect
263. C₂×#535	C₂×C₅₉	semidirect
264. #3428	C₂×C₅₉	semidirect
272. C₂×2₋¹⁺⁴	C₂²×C₅₉	semidirect
273. C₂×2₋¹⁺⁴	C₂²×C₅₉	semidirect
275. C₂×H(5,𝔽₂)	C₂²×C₅₉	semidirect
276. C₂×H(5,𝔽₂)	C₂²×C₅₉	semidirect
277. C₂×H(5,𝔽₂)	C₂²×C₅₉	semidirect
278. C₂×H(5,𝔽₂)	C₂²×C₅₉	semidirect
280. C₂²×#41	C₂²×C₅₉	semidirect
281. C₂²×#41	C₂²×C₅₉	semidirect
282. C₂²×#41	C₂²×C₅₉	semidirect
283. C₂²×#41	C₂²×C₅₉	semidirect
284. C₂³×D₄	C₂²×C₅₉	semidirect
285. C₂³×D₄	C₂²×C₅₉	semidirect
286. #550	C₂²×C₅₉	semidirect
287. #548	C₂²×C₅₉	semidirect
288. #546	C₂²×C₅₉	semidirect
289. D₄²	C₂²×C₅₉	semidirect
290. #537	C₂²×C₅₉	semidirect
291. #536	C₂²×C₅₉	semidirect
292. #536	C₂²×C₅₉	semidirect
293. #535	C₂²×C₅₉	semidirect
294. #535	C₂²×C₅₉	semidirect
295. #535	C₂²×C₅₉	semidirect
296. #535	C₂²×C₅₉	semidirect
297. #535	C₂²×C₅₉	semidirect
298. #534	C₂²×C₅₉	semidirect
299. #532	C₂²×C₅₉	semidirect
300. C₂×#127	C₂²×C₅₉	semidirect
301. C₂×#124	C₂²×C₅₉	semidirect
302. #525	C₂²×C₅₉	semidirect
303. #525	C₂²×C₅₉	semidirect
304. C₂×#121	C₂²×C₅₉	semidirect
305. C₂×#120	C₂²×C₅₉	semidirect
306. #520	C₂²×C₅₉	semidirect
307. #519	C₂²×C₅₉	semidirect
308. #518	C₂²×C₅₉	semidirect
309. C₄×#41	C₂²×C₅₉	semidirect
310. C₂×#117	C₂²×C₅₉	semidirect
311. C₅₉	#62852	direct (N × H)
323. C₂×#41	D₄×C₅₉	semidirect
331. C₂×#41	C₂³×C₅₉	semidirect
332. C₂×#41	C₂³×C₅₉	semidirect
333. C₂×#41	C₂³×C₅₉	semidirect
334. C₂×#41	C₂³×C₅₉	semidirect
337. C₂²×Q₈	C₂³×C₅₉	semidirect
338. C₂²×Q₈	C₂³×C₅₉	semidirect
349. C₂²×D₄	C₂³×C₅₉	semidirect
350. C₂²×D₄	C₂³×C₅₉	semidirect
351. C₂²×D₄	C₂³×C₅₉	semidirect
354. C₂³×C₄	C₂³×C₅₉	semidirect
355. C₄⋊Q₈	C₂³×C₅₉	semidirect
356. #127	C₂³×C₅₉	semidirect
357. #127	C₂³×C₅₉	semidirect
358. #124	C₂³×C₅₉	semidirect
359. #124	C₂³×C₅₉	semidirect
360. #124	C₂³×C₅₉	semidirect
362. #123	C₂³×C₅₉	semidirect
363. C₂²⋊Q₈	C₂³×C₅₉	semidirect
364. C₂²⋊Q₈	C₂³×C₅₉	semidirect
365. #121	C₂³×C₅₉	semidirect
366. #121	C₂³×C₅₉	semidirect
367. #121	C₂³×C₅₉	semidirect
368. #121	C₂³×C₅₉	semidirect
370. #120	C₂³×C₅₉	semidirect
371. #120	C₂³×C₅₉	semidirect
372. C₄×Q₈	C₂³×C₅₉	semidirect
373. C₄×D₄	C₂³×C₅₉	semidirect
374. C₄×D₄	C₂³×C₅₉	semidirect
377. #117	C₂³×C₅₉	semidirect
378. #117	C₂³×C₅₉	semidirect
379. C₂×C₄⋊C₄	C₂³×C₅₉	semidirect
381. C₂×C₂²⋊C₄	C₂³×C₅₉	semidirect
382. C₂×C₄²	C₂³×C₅₉	semidirect
398. #41	C₂×D₄×C₅₉	semidirect
399. #41	C₂×D₄×C₅₉	semidirect
403. C₂×Q₈	C₂×D₄×C₅₉	semidirect
419. C₂×D₄	C₂×D₄×C₅₉	semidirect
432. C₂²×C₄	C₂×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×H(5,𝔽₂)×C₅₉	2
C₅₉×#3500	2
C₅₉×#3498	2
C₅₉×#3488	2
C₅₉×#3487	2
C₅₉×#3484	2
C₅₉×#3449	2
C₂×C₅₉×#535	2
C₅₉×#3428	2
#62852	59

Subgroups — C59×#62852 #28474961

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#62852 #28474961