Subgroups — C₅₉×#62245 #28474354

Order 15104.

2422 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₉×#3496	C₂	1	2	yes	maximal, complemented
2	C₅₉×#3334	C₂	1	4	yes	maximal, complemented
3	C₅₉×#3294	C₂	1	8	yes	maximal, complemented
4	D₄×D₈×C₅₉	C₂	1	4	yes	maximal, complemented
5	C₅₉×#3245	C₂	1	2	yes	maximal, complemented
6	C₅₉×#3186	C₂	1	4	yes	maximal, complemented
7	C₅₉×#3169	C₂	1	2	yes	maximal, complemented
8	C₂×C₅₉×#466	C₂	1	4	yes	maximal, complemented
9	C₂×C₈×D₄×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×H(5,𝔽₂)×C₅₉	—	2	2	no	—
11	C₂²×D₈×C₅₉	C₂²	1	4	yes	complemented
12	C₂³×C₈×C₅₉	C₂²	1	2	yes	complemented
13	C₅₉×#547	C₂²	1	8	yes	complemented
14	C₅₉×#546	—	2	8	no	—
15	D₄²×C₅₉	C₂²	1	8	yes	complemented
16	C₅₉×#537	—	2	2	no	—
17	C₅₉×#534	—	2	4	no	—
18	C₅₉×#532	C₂²	1	4	yes	complemented
19	C₂×#121×C₅₉	C₂²	1	8	yes	complemented
20	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
21	C₅₉×#500	C₂²	1	2	yes	complemented
22	C₅₉×#493	C₂²	1	2	yes	complemented
23	C₅₉×#486	C₂²	1	4	yes	complemented
24	C₅₉×#480	C₂²	1	16	yes	complemented
25	C₅₉×#474	C₂²	1	8	yes	complemented
26	C₅₉×#466	C₂²	1	8	yes	complemented
27	C₅₉×#466	C₂²	1	8	yes	complemented
28	C₅₉×#466	C₂²	1	4	yes	complemented
29	C₅₉×#466	C₂²	1	8	yes	complemented
30	C₅₉×#466	C₂²	1	4	yes	complemented
31	C₅₉×#459	C₂²	1	8	yes	complemented
32	C₅₉×#447	C₂²	1	16	yes	complemented
33	C₄×D₈×C₅₉	C₂²	1	4	yes	complemented
34	C₄×D₈×C₅₉	C₂²	1	4	yes	complemented
35	C₈×D₄×C₅₉	C₂²	1	4	yes	complemented
36	C₈×D₄×C₅₉	C₂²	1	4	yes	complemented
37	C₂×#107×C₅₉	C₂²	1	4	yes	complemented
38	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic, complemented
39	C₂×#102×C₅₉	C₂²	1	8	yes	complemented
40	C₂×C₂²⋊C₈×C₅₉	C₂²	1	2	yes	complemented
41	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic, complemented
42	H(5,𝔽₂)×C₅₉	—	4	16	no	—
43	C₂×#41×C₅₉	—	2	8	no	—
44	C₂×#41×C₅₉	—	2	4	no	—
45	C₂²×D₄×C₅₉	—	2	8	no	—
46	C₂²×D₄×C₅₉	—	2	8	no	—
47	C₂²×D₄×C₅₉	D₄	1	1	yes	characteristic
48	C₂²×D₄×C₅₉	C₂³	1	8	yes	—
49	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
50	C₂×D₈×C₅₉	—	4	8	no	—
51	C₂×D₈×C₅₉	C₂³	1	4	yes	—
52	C₂×D₈×C₅₉	C₂³	1	4	yes	—
53	C₂×D₈×C₅₉	C₂³	1	8	yes	—
54	C₂²×C₈×C₅₉	—	4	4	no	—
55	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₅₉	C₂³	1	4	yes	—
57	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
58	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
59	C₂²×C₈×C₅₉	C₂³	1	4	yes	—
60	C₄⋊Q₈×C₅₉	C₂³	1	4	yes	—
61	#127×C₅₉	C₂³	1	4	yes	—
62	#124×C₅₉	—	2	4	no	—
63	#123×C₅₉	—	2	16	no	—
64	C₂²⋊Q₈×C₅₉	—	2	8	no	—
65	#121×C₅₉	—	2	8	no	—
66	#121×C₅₉	—	2	8	no	—
67	#121×C₅₉	—	2	4	no	—
68	#121×C₅₉	—	2	8	no	—
69	#121×C₅₉	C₂³	1	16	yes	—
70	#121×C₅₉	C₂³	1	8	yes	—
71	#120×C₅₉	—	2	16	no	—
72	C₄×D₄×C₅₉	—	2	4	no	—
73	C₄×D₄×C₅₉	D₄	1	4	yes	—
74	C₄×D₄×C₅₉	C₂³	1	8	yes	—
75	C₄×D₄×C₅₉	C₂³	1	4	yes	—
76	C₂×C₄⋊C₄×C₅₉	D₄	1	1	yes	characteristic
77	C₂×C₄⋊C₄×C₅₉	C₂³	1	8	yes	—
78	C₂×C₂²⋊C₄×C₅₉	—	2	8	no	—
79	C₂×C₂²⋊C₄×C₅₉	D₄	1	2	yes	—
80	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
81	#107×C₅₉	C₂³	1	4	yes	—
82	#107×C₅₉	C₂³	1	8	yes	—
83	#107×C₅₉	C₂³	1	4	yes	—
84	C₄⋊C₈×C₅₉	C₂³	1	4	yes	—
85	#102×C₅₉	C₂³	1	8	yes	—
86	#102×C₅₉	C₂³	1	16	yes	—
87	#102×C₅₉	C₂³	1	8	yes	—
88	C₂²⋊C₈×C₅₉	C₂³	1	8	yes	—
89	C₄×C₈×C₅₉	C₂³	1	2	yes	—
90	C₄×C₈×C₅₉	C₂³	1	2	yes	—
91	C₂⁴×C₅₉	—	2	8	no	—
92	C₂⁴×C₅₉	C₂×D₄	1	2	yes	—
93	#41×C₅₉	—	4	32	no	—
94	#41×C₅₉	—	4	16	no	—
95	C₂×Q₈×C₅₉	—	2	4	no	—
96	C₂×D₄×C₅₉	—	2	16	no	—
97	C₂×D₄×C₅₉	—	2	8	no	—
98	C₂×D₄×C₅₉	—	2	4	no	—
99	C₂×D₄×C₅₉	—	2	4	no	—
100	C₂×D₄×C₅₉	—	2	8	no	—
101	C₂×D₄×C₅₉	—	4	8	no	—
102	C₂×D₄×C₅₉	—	4	8	no	—
103	C₂×D₄×C₅₉	—	4	32	no	—
104	C₂×D₄×C₅₉	—	4	32	no	—
105	C₂×D₄×C₅₉	D₈	1	8	yes	complemented
106	C₂×D₄×C₅₉	C₂×D₄	1	4	yes	—
107	C₂×D₄×C₅₉	C₂⁴	1	8	yes	—
108	C₂²×C₄×C₅₉	—	2	8	no	—
109	C₂²×C₄×C₅₉	—	2	8	no	—
110	C₂²×C₄×C₅₉	—	4	2	no	—
111	C₂²×C₄×C₅₉	—	4	2	no	—
112	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₅₉	C₂×D₄	1	4	yes	—
114	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
117	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
118	D₈×C₅₉	—	2	8	no	—
119	D₈×C₅₉	—	4	8	no	—
120	D₈×C₅₉	—	4	4	no	—
121	C₂×C₈×C₅₉	—	2	2	no	—
122	C₂×C₈×C₅₉	—	2	8	no	—
123	C₂×C₈×C₅₉	—	4	4	no	—
124	C₂×C₈×C₅₉	—	4	2	no	—
125	C₂×C₈×C₅₉	—	4	1	no	—
126	C₂×C₈×C₅₉	C₂⁴	1	2	yes	—
127	C₂×C₈×C₅₉	C₂⁴	1	1	yes	characteristic
128	C₂×C₈×C₅₉	C₂⁴	1	4	yes	—
129	C₂×C₈×C₅₉	C₂⁴	1	1	yes	characteristic
130	C₄⋊C₄×C₅₉	—	2	8	no	—
131	C₄⋊C₄×C₅₉	—	2	4	no	—
132	C₄⋊C₄×C₅₉	C₂×D₄	1	4	yes	—
133	C₄⋊C₄×C₅₉	C₂⁴	1	8	yes	—
134	C₂²⋊C₄×C₅₉	—	2	8	no	—
135	C₂²⋊C₄×C₅₉	—	2	16	no	—
136	C₂²⋊C₄×C₅₉	—	2	8	no	—
137	C₂²⋊C₄×C₅₉	C₂×D₄	1	8	yes	—
138	C₄²×C₅₉	C₂×D₄	1	2	yes	—
139	C₄²×C₅₉	C₂⁴	1	2	yes	—
140	C₂³×C₅₉	—	2	8	no	—
141	C₂³×C₅₉	—	4	2	no	—
142	C₂³×C₅₉	—	4	2	no	—
143	C₂³×C₅₉	—	4	16	no	—
144	C₂³×C₅₉	—	8	8	no	—
145	C₂³×C₅₉	—	8	8	no	—
146	C₂³×C₅₉	C₂×D₈	1	8	yes	complemented
147	C₂³×C₅₉	C₂²×D₄	1	4	yes	—
148	C₂³×C₅₉	C₂²×D₄	1	1	yes	characteristic
149	Q₈×C₅₉	—	4	8	no	—
150	D₄×C₅₉	—	2	8	no	—
151	D₄×C₅₉	—	2	8	no	—
152	D₄×C₅₉	—	4	32	no	—
153	D₄×C₅₉	—	4	16	no	—
154	D₄×C₅₉	—	4	8	no	—
155	D₄×C₅₉	—	8	4	no	—
156	D₄×C₅₉	—	8	8	no	—
157	D₄×C₅₉	C₂×D₈	1	16	yes	complemented
158	C₂×C₄×C₅₉	—	2	1	no	—
159	C₂×C₄×C₅₉	—	2	4	no	—
160	C₂×C₄×C₅₉	—	2	1	no	—
161	C₂×C₄×C₅₉	—	2	4	no	—
162	C₂×C₄×C₅₉	—	2	8	no	—
163	C₂×C₄×C₅₉	—	4	4	no	—
164	C₂×C₄×C₅₉	—	4	2	no	—
165	C₂×C₄×C₅₉	—	4	1	no	—
166	C₂×C₄×C₅₉	—	4	16	no	—
167	C₂×C₄×C₅₉	—	4	16	no	—
168	C₂×C₄×C₅₉	C₂×D₈	1	4	yes	complemented
169	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
170	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
171	C₂×C₄×C₅₉	C₂²×D₄	1	4	yes	—
172	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
173	C₂×C₄×C₅₉	C₂⁵	1	1	yes	characteristic
174	C₈×C₅₉	—	2	1	no	—
175	C₈×C₅₉	—	2	4	no	—
176	C₈×C₅₉	—	2	2	no	—
177	C₈×C₅₉	H(5,𝔽₂)	1	2	yes	complemented
178	#62245	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
179	C₂²×C₅₉	—	2	1	no	—
180	C₂²×C₅₉	—	2	4	no	—
181	C₂²×C₅₉	—	2	1	no	—
182	C₂²×C₅₉	—	2	4	no	—
183	C₂²×C₅₉	—	4	8	no	—
184	C₂²×C₅₉	—	4	8	no	—
185	C₂²×C₅₉	—	4	8	no	—
186	C₂²×C₅₉	—	4	8	no	—
187	C₂²×C₅₉	—	16	16	no	—
188	C₂²×C₅₉	C₂²×D₈	1	8	yes	—
189	C₂²×C₅₉	C₂²×D₈	1	2	yes	—
190	C₂²×C₅₉	C₂³×D₄	1	1	yes	characteristic
191	C₄×C₅₉	—	2	2	no	—
192	C₄×C₅₉	—	2	1	no	—
193	C₄×C₅₉	—	2	4	no	—
194	C₄×C₅₉	—	4	8	no	—
195	C₄×C₅₉	C₂²×D₈	1	4	yes	—
196	C₄×C₅₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
197	C₄×C₅₉	#585	1	1	yes	characteristic
198	#3496	C₂×C₅₉	1	2	yes	complemented
199	#3334	C₂×C₅₉	1	4	yes	complemented
200	#3294	C₂×C₅₉	1	8	yes	complemented
201	D₄×D₈	C₂×C₅₉	1	4	yes	complemented
202	#3245	C₂×C₅₉	1	2	yes	complemented
203	#3186	C₂×C₅₉	1	4	yes	complemented
204	#3169	C₂×C₅₉	1	2	yes	complemented
205	C₂×#466	C₂×C₅₉	1	4	yes	complemented
206	C₂×C₈×D₄	C₂×C₅₉	1	1	yes	characteristic, complemented
207	C₂×C₅₉	—	2	2	no	—
208	C₂×C₅₉	—	2	8	no	—
209	C₂×C₅₉	—	8	8	no	—
210	C₂×C₅₉	#3496	1	1	yes	characteristic
211	C₂×C₅₉	C₂³×D₈	1	1	yes	characteristic
212	C₂×C₅₉	#3584	1	1	yes	characteristic
213	C₂×H(5,𝔽₂)	—	2	2	no	—
214	C₂²×D₈	C₂²×C₅₉	1	4	yes	complemented
215	C₂³×C₈	C₂²×C₅₉	1	2	yes	complemented
216	#547	C₂²×C₅₉	1	8	yes	complemented
217	#546	—	2	8	no	—
218	D₄²	C₂²×C₅₉	1	8	yes	complemented
219	#537	—	2	2	no	—
220	#534	—	2	4	no	—
221	#532	C₂²×C₅₉	1	4	yes	complemented
222	C₂×#121	C₂²×C₅₉	1	8	yes	complemented
223	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
224	#500	C₂²×C₅₉	1	2	yes	complemented
225	#493	C₂²×C₅₉	1	2	yes	complemented
226	#486	C₂²×C₅₉	1	4	yes	complemented
227	#480	C₂²×C₅₉	1	16	yes	complemented
228	#474	C₂²×C₅₉	1	8	yes	complemented
229	#466	C₂²×C₅₉	1	8	yes	complemented
230	#466	C₂²×C₅₉	1	4	yes	complemented
231	#466	C₂²×C₅₉	1	4	yes	complemented
232	#466	C₂²×C₅₉	1	8	yes	complemented
233	#466	C₂²×C₅₉	1	8	yes	complemented
234	#459	C₂²×C₅₉	1	8	yes	complemented
235	#447	C₂²×C₅₉	1	16	yes	complemented
236	C₄×D₈	C₂²×C₅₉	1	4	yes	complemented
237	C₄×D₈	C₂²×C₅₉	1	4	yes	complemented
238	C₈×D₄	C₂²×C₅₉	1	4	yes	complemented
239	C₈×D₄	C₂²×C₅₉	1	4	yes	complemented
240	C₂×#107	C₂²×C₅₉	1	4	yes	complemented
241	C₂×C₄⋊C₈	C₂²×C₅₉	1	1	yes	characteristic, complemented
242	C₂×#102	C₂²×C₅₉	1	8	yes	complemented
243	C₂×C₂²⋊C₈	C₂²×C₅₉	1	2	yes	complemented
244	C₂×C₄×C₈	C₂²×C₅₉	1	1	yes	characteristic, complemented
245	C₅₉	#62245	1	1	yes	characteristic, direct product factor, Sylow
246	H(5,𝔽₂)	—	4	16	no	—
247	C₂×#41	—	2	8	no	—
248	C₂×#41	—	2	4	no	—
249	C₂²×D₄	—	2	8	no	—
250	C₂²×D₄	—	2	8	no	—
251	C₂²×D₄	D₄×C₅₉	1	1	yes	characteristic
252	C₂²×D₄	C₂³×C₅₉	1	8	yes	—
253	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
254	C₂×D₈	—	4	8	no	—
255	C₂×D₈	C₂³×C₅₉	1	4	yes	—
256	C₂×D₈	C₂³×C₅₉	1	8	yes	—
257	C₂×D₈	C₂³×C₅₉	1	4	yes	—
258	C₂²×C₈	—	4	4	no	—
259	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
260	C₂²×C₈	C₂³×C₅₉	1	4	yes	—
261	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
262	C₂²×C₈	C₂³×C₅₉	1	4	yes	—
263	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
264	C₄⋊Q₈	C₂³×C₅₉	1	4	yes	—
265	#127	C₂³×C₅₉	1	4	yes	—
266	#124	—	2	4	no	—
267	#123	—	2	16	no	—
268	C₂²⋊Q₈	—	2	8	no	—
269	#121	—	2	8	no	—
270	#121	—	2	8	no	—
271	#121	—	2	4	no	—
272	#121	—	2	8	no	—
273	#121	C₂³×C₅₉	1	8	yes	—
274	#121	C₂³×C₅₉	1	16	yes	—
275	#120	—	2	16	no	—
276	C₄×D₄	—	2	4	no	—
277	C₄×D₄	D₄×C₅₉	1	4	yes	—
278	C₄×D₄	C₂³×C₅₉	1	8	yes	—
279	C₄×D₄	C₂³×C₅₉	1	4	yes	—
280	C₂×C₄⋊C₄	D₄×C₅₉	1	1	yes	characteristic
281	C₂×C₄⋊C₄	C₂³×C₅₉	1	8	yes	—
282	C₂×C₂²⋊C₄	—	2	8	no	—
283	C₂×C₂²⋊C₄	D₄×C₅₉	1	2	yes	—
284	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
285	#107	C₂³×C₅₉	1	4	yes	—
286	#107	C₂³×C₅₉	1	8	yes	—
287	#107	C₂³×C₅₉	1	4	yes	—
288	C₄⋊C₈	C₂³×C₅₉	1	4	yes	—
289	#102	C₂³×C₅₉	1	8	yes	—
290	#102	C₂³×C₅₉	1	16	yes	—
291	#102	C₂³×C₅₉	1	8	yes	—
292	C₂²⋊C₈	C₂³×C₅₉	1	8	yes	—
293	C₄×C₈	C₂³×C₅₉	1	2	yes	—
294	C₄×C₈	C₂³×C₅₉	1	2	yes	—
295	C₂⁴	—	2	8	no	—
296	C₂⁴	C₂×D₄×C₅₉	1	2	yes	—
297	#41	—	4	32	no	—
298	#41	—	4	16	no	—
299	C₂×Q₈	—	2	4	no	—
300	C₂×D₄	—	2	16	no	—
301	C₂×D₄	—	2	8	no	—
302	C₂×D₄	—	2	4	no	—
303	C₂×D₄	—	2	4	no	—
304	C₂×D₄	—	2	8	no	—
305	C₂×D₄	—	4	8	no	—
306	C₂×D₄	—	4	8	no	—
307	C₂×D₄	—	4	32	no	—
308	C₂×D₄	—	4	32	no	—
309	C₂×D₄	D₈×C₅₉	1	8	yes	complemented
310	C₂×D₄	C₂×D₄×C₅₉	1	4	yes	—
311	C₂×D₄	C₂⁴×C₅₉	1	8	yes	—
312	C₂²×C₄	—	2	8	no	—
313	C₂²×C₄	—	2	8	no	—
314	C₂²×C₄	—	4	2	no	—
315	C₂²×C₄	—	4	2	no	—
316	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
317	C₂²×C₄	C₂×D₄×C₅₉	1	4	yes	—
318	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
319	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
320	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
321	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
322	D₈	—	2	8	no	—
323	D₈	—	4	8	no	—
324	D₈	—	4	4	no	—
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	—	2	8	no	—
327	C₂×C₈	—	4	4	no	—
328	C₂×C₈	—	4	2	no	—
329	C₂×C₈	—	4	1	no	—
330	C₂×C₈	C₂⁴×C₅₉	1	2	yes	—
331	C₂×C₈	C₂⁴×C₅₉	1	1	yes	characteristic
332	C₂×C₈	C₂⁴×C₅₉	1	4	yes	—
333	C₂×C₈	C₂⁴×C₅₉	1	1	yes	characteristic
334	C₄⋊C₄	—	2	8	no	—
335	C₄⋊C₄	—	2	4	no	—
336	C₄⋊C₄	C₂×D₄×C₅₉	1	4	yes	—
337	C₄⋊C₄	C₂⁴×C₅₉	1	8	yes	—
338	C₂²⋊C₄	—	2	8	no	—
339	C₂²⋊C₄	—	2	16	no	—
340	C₂²⋊C₄	—	2	8	no	—
341	C₂²⋊C₄	C₂×D₄×C₅₉	1	8	yes	—
342	C₄²	C₂×D₄×C₅₉	1	2	yes	—
343	C₄²	C₂⁴×C₅₉	1	2	yes	—
344	C₂³	—	2	8	no	—
345	C₂³	—	4	2	no	—
346	C₂³	—	4	2	no	—
347	C₂³	—	4	16	no	—
348	C₂³	—	8	8	no	—
349	C₂³	—	8	8	no	—
350	C₂³	C₂×D₈×C₅₉	1	8	yes	complemented
351	C₂³	C₂²×D₄×C₅₉	1	4	yes	—
352	C₂³	C₂²×D₄×C₅₉	1	1	yes	characteristic
353	Q₈	—	4	8	no	—
354	D₄	—	2	8	no	—
355	D₄	—	2	8	no	—
356	D₄	—	4	32	no	—
357	D₄	—	4	16	no	—
358	D₄	—	4	8	no	—
359	D₄	—	8	4	no	—
360	D₄	—	8	8	no	—
361	D₄	C₂×D₈×C₅₉	1	16	yes	complemented
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	4	no	—
366	C₂×C₄	—	2	8	no	—
367	C₂×C₄	—	4	4	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	1	no	—
370	C₂×C₄	—	4	16	no	—
371	C₂×C₄	—	4	16	no	—
372	C₂×C₄	C₂×D₈×C₅₉	1	4	yes	complemented
373	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
374	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
375	C₂×C₄	C₂²×D₄×C₅₉	1	4	yes	—
376	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
377	C₂×C₄	C₂⁵×C₅₉	1	1	yes	characteristic
378	C₈	—	2	1	no	—
379	C₈	—	2	4	no	—
380	C₈	—	2	2	no	—
381	C₈	H(5,𝔽₂)×C₅₉	1	2	yes	complemented
382	C₂²	—	2	1	no	—
383	C₂²	—	2	4	no	—
384	C₂²	—	2	1	no	—
385	C₂²	—	2	4	no	—
386	C₂²	—	4	8	no	—
387	C₂²	—	4	8	no	—
388	C₂²	—	4	8	no	—
389	C₂²	—	4	8	no	—
390	C₂²	—	16	16	no	—
391	C₂²	C₂²×D₈×C₅₉	1	8	yes	—
392	C₂²	C₂²×D₈×C₅₉	1	2	yes	—
393	C₂²	C₂³×D₄×C₅₉	1	1	yes	characteristic
394	C₄	—	2	2	no	—
395	C₄	—	2	1	no	—
396	C₄	—	2	4	no	—
397	C₄	—	4	8	no	—
398	C₄	C₂²×D₈×C₅₉	1	4	yes	—
399	C₄	C₂×H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
400	C₄	C₅₉×#585	1	1	yes	characteristic
401	C₂	—	2	2	no	—
402	C₂	—	2	8	no	—
403	C₂	—	8	8	no	—
404	C₂	C₅₉×#3496	1	1	yes	characteristic
405	C₂	C₂³×D₈×C₅₉	1	1	yes	characteristic
406	C₂	C₅₉×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₉ ◁ C₂×C₄×D₄×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₉×#3496	C₂	semidirect
2. C₅₉×#3334	C₂	semidirect
3. C₅₉×#3294	C₂	semidirect
4. D₄×D₈×C₅₉	C₂	semidirect
5. C₅₉×#3245	C₂	semidirect
6. C₅₉×#3186	C₂	semidirect
7. C₅₉×#3169	C₂	semidirect
8. C₂×C₅₉×#466	C₂	semidirect
9. C₂×C₈×D₄×C₅₉	C₂	semidirect
11. C₂²×D₈×C₅₉	C₂²	semidirect
12. C₂³×C₈×C₅₉	C₂²	semidirect
13. C₅₉×#547	C₂²	semidirect
15. D₄²×C₅₉	C₂²	semidirect
18. C₅₉×#532	C₂²	semidirect
19. C₂×#121×C₅₉	C₂²	semidirect
21. C₅₉×#500	C₂²	semidirect
22. C₅₉×#493	C₂²	semidirect
23. C₅₉×#486	C₂²	semidirect
24. C₅₉×#480	C₂²	semidirect
25. C₅₉×#474	C₂²	semidirect
26. C₅₉×#466	C₂²	semidirect
27. C₅₉×#466	C₂²	semidirect
28. C₅₉×#466	C₂²	semidirect
29. C₅₉×#466	C₂²	semidirect
30. C₅₉×#466	C₂²	semidirect
31. C₅₉×#459	C₂²	semidirect
32. C₅₉×#447	C₂²	semidirect
33. C₄×D₈×C₅₉	C₂²	semidirect
34. C₄×D₈×C₅₉	C₂²	semidirect
35. C₈×D₄×C₅₉	C₂²	semidirect
36. C₈×D₄×C₅₉	C₂²	semidirect
37. C₂×#107×C₅₉	C₂²	semidirect
38. C₂×C₄⋊C₈×C₅₉	C₂²	semidirect
39. C₂×#102×C₅₉	C₂²	semidirect
40. C₂×C₂²⋊C₈×C₅₉	C₂²	semidirect
41. C₂×C₄×C₈×C₅₉	C₂²	semidirect
105. C₂×D₄×C₅₉	D₈	semidirect
146. C₂³×C₅₉	C₂×D₈	semidirect
157. D₄×C₅₉	C₂×D₈	semidirect
168. C₂×C₄×C₅₉	C₂×D₈	semidirect
177. C₈×C₅₉	H(5,𝔽₂)	semidirect
178. #62245	C₅₉	direct (N × H)
198. #3496	C₂×C₅₉	semidirect
199. #3334	C₂×C₅₉	semidirect
200. #3294	C₂×C₅₉	semidirect
201. D₄×D₈	C₂×C₅₉	semidirect
202. #3245	C₂×C₅₉	semidirect
203. #3186	C₂×C₅₉	semidirect
204. #3169	C₂×C₅₉	semidirect
205. C₂×#466	C₂×C₅₉	semidirect
206. C₂×C₈×D₄	C₂×C₅₉	semidirect
214. C₂²×D₈	C₂²×C₅₉	semidirect
215. C₂³×C₈	C₂²×C₅₉	semidirect
216. #547	C₂²×C₅₉	semidirect
218. D₄²	C₂²×C₅₉	semidirect
221. #532	C₂²×C₅₉	semidirect
222. C₂×#121	C₂²×C₅₉	semidirect
224. #500	C₂²×C₅₉	semidirect
225. #493	C₂²×C₅₉	semidirect
226. #486	C₂²×C₅₉	semidirect
227. #480	C₂²×C₅₉	semidirect
228. #474	C₂²×C₅₉	semidirect
229. #466	C₂²×C₅₉	semidirect
230. #466	C₂²×C₅₉	semidirect
231. #466	C₂²×C₅₉	semidirect
232. #466	C₂²×C₅₉	semidirect
233. #466	C₂²×C₅₉	semidirect
234. #459	C₂²×C₅₉	semidirect
235. #447	C₂²×C₅₉	semidirect
236. C₄×D₈	C₂²×C₅₉	semidirect
237. C₄×D₈	C₂²×C₅₉	semidirect
238. C₈×D₄	C₂²×C₅₉	semidirect
239. C₈×D₄	C₂²×C₅₉	semidirect
240. C₂×#107	C₂²×C₅₉	semidirect
241. C₂×C₄⋊C₈	C₂²×C₅₉	semidirect
242. C₂×#102	C₂²×C₅₉	semidirect
243. C₂×C₂²⋊C₈	C₂²×C₅₉	semidirect
244. C₂×C₄×C₈	C₂²×C₅₉	semidirect
245. C₅₉	#62245	direct (N × H)
309. C₂×D₄	D₈×C₅₉	semidirect
350. C₂³	C₂×D₈×C₅₉	semidirect
361. D₄	C₂×D₈×C₅₉	semidirect
372. C₂×C₄	C₂×D₈×C₅₉	semidirect
381. C₈	H(5,𝔽₂)×C₅₉	semidirect

Maximal subgroups

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

subgroup	index
C₅₉×#3496	2
C₅₉×#3334	2
C₅₉×#3294	2
D₄×D₈×C₅₉	2
C₅₉×#3245	2
C₅₉×#3186	2
C₅₉×#3169	2
C₂×C₅₉×#466	2
C₂×C₈×D₄×C₅₉	2
#62245	59

Subgroups — C59×#62245 #28474354

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#62245 #28474354