Subgroups — C₅₉×#35350 #28447459

Order 15104.

4142 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#120×C₅₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅₉×#518	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₉×#2482	C₂	1	4	yes	maximal, complemented
4	C₅₉×#2418	C₂	1	16	yes	maximal, complemented
5	C₅₉×#2405	C₂	1	4	yes	maximal, complemented
6	C₅₉×#2315	C₂	1	2	yes	maximal, complemented
7	C₅₉×#2308	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅₉×#379	C₂	1	2	yes	maximal, complemented
9	C₂⁶×C₅₉	C₂²	1	1	yes	characteristic
10	C₂³×D₄×C₅₉	C₂²	1	1	yes	characteristic
11	C₂³×D₄×C₅₉	C₂²	1	2	yes	—
12	C₂×#123×C₅₉	C₂²	1	8	yes	complemented
13	C₂×#120×C₅₉	—	2	8	no	—
14	C₂×#120×C₅₉	C₂²	1	8	yes	—
15	C₅₉×#518	—	2	8	no	—
16	C₂×C₄×D₄×C₅₉	C₂²	1	8	yes	complemented
17	C₂×#117×C₅₉	C₂²	1	2	yes	complemented
18	C₂²×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
19	C₂²×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
20	C₂²×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
21	C₂²×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
22	C₂²×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	complemented
23	C₂²×C₂²⋊C₄×C₅₉	C₂²	1	8	yes	complemented
24	C₅₉×#399	C₂²	1	8	yes	complemented
25	C₅₉×#397	C₂²	1	8	yes	complemented
26	C₅₉×#394	C₂²	1	16	yes	complemented
27	C₅₉×#388	C₂²	1	16	yes	complemented
28	C₅₉×#386	C₂²	1	8	yes	complemented
29	C₅₉×#386	C₂²	1	8	yes	complemented
30	C₅₉×#385	C₂²	1	8	yes	complemented
31	C₅₉×#385	C₂²	1	8	yes	complemented
32	C₅₉×#381	C₂²	1	2	yes	complemented
33	C₅₉×#380	C₂²	1	8	yes	complemented
34	C₅₉×#379	C₂²	1	8	yes	—
35	C₅₉×#379	C₂²	1	8	yes	complemented
36	C₅₉×#379	C₂²	1	2	yes	complemented
37	C₂⁵×C₅₉	—	2	4	no	—
38	C₂⁵×C₅₉	—	2	8	no	—
39	C₂⁵×C₅₉	—	4	8	no	—
40	C₂⁵×C₅₉	C₂³	1	2	yes	—
41	C₂⁵×C₅₉	C₂³	1	4	yes	—
42	C₂⁵×C₅₉	C₂³	1	1	yes	characteristic
43	C₂⁵×C₅₉	C₂³	1	1	yes	characteristic
44	C₂²×D₄×C₅₉	—	2	8	no	—
45	C₂²×D₄×C₅₉	—	2	8	no	—
46	C₂²×D₄×C₅₉	—	4	8	no	—
47	C₂²×D₄×C₅₉	D₄	1	8	yes	—
48	C₂²×D₄×C₅₉	C₂³	1	8	yes	—
49	C₂²×D₄×C₅₉	C₂³	1	4	yes	—
50	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₅₉	C₂³	1	4	yes	—
52	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
53	C₂³×C₄×C₅₉	C₂³	1	4	yes	—
54	C₂³×C₄×C₅₉	C₂³	1	4	yes	complemented
55	#123×C₅₉	—	4	16	no	—
56	#120×C₅₉	—	2	32	no	—
57	C₄×D₄×C₅₉	—	2	32	no	—
58	#117×C₅₉	—	2	8	no	—
59	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	complemented
60	C₂×C₄⋊C₄×C₅₉	C₂³	1	16	yes	complemented
61	C₂×C₂²⋊C₄×C₅₉	—	2	8	no	—
62	C₂×C₂²⋊C₄×C₅₉	—	2	4	no	—
63	C₂×C₂²⋊C₄×C₅₉	—	2	8	no	—
64	C₂×C₂²⋊C₄×C₅₉	—	2	8	no	—
65	C₂×C₂²⋊C₄×C₅₉	—	2	8	no	—
66	C₂×C₂²⋊C₄×C₅₉	—	4	16	no	—
67	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
68	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
69	C₂×C₂²⋊C₄×C₅₉	C₂³	1	16	yes	—
70	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
71	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
72	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
73	C₂×C₂²⋊C₄×C₅₉	C₂³	1	8	yes	—
74	C₂×C₂²⋊C₄×C₅₉	C₂³	1	16	yes	—
75	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	complemented
76	C₂×C₂²⋊C₄×C₅₉	C₂³	1	8	yes	complemented
77	C₂×C₄²×C₅₉	C₂³	1	4	yes	complemented
78	#95×C₅₉	C₂³	1	16	yes	complemented
79	#95×C₅₉	C₂³	1	8	yes	complemented
80	C₂⁴×C₅₉	—	2	4	no	—
81	C₂⁴×C₅₉	—	2	8	no	—
82	C₂⁴×C₅₉	—	2	16	no	—
83	C₂⁴×C₅₉	—	2	8	no	—
84	C₂⁴×C₅₉	—	2	4	no	—
85	C₂⁴×C₅₉	—	2	8	no	—
86	C₂⁴×C₅₉	—	2	8	no	—
87	C₂⁴×C₅₉	—	2	8	no	—
88	C₂⁴×C₅₉	—	4	4	no	—
89	C₂⁴×C₅₉	—	4	8	no	—
90	C₂⁴×C₅₉	—	4	4	no	—
91	C₂⁴×C₅₉	—	4	4	no	—
92	C₂⁴×C₅₉	—	4	32	no	—
93	C₂⁴×C₅₉	—	4	64	no	—
94	C₂⁴×C₅₉	—	4	16	no	—
95	C₂⁴×C₅₉	C₂×D₄	1	4	yes	—
96	C₂⁴×C₅₉	C₂×D₄	1	4	yes	—
97	C₂⁴×C₅₉	#41	1	8	yes	—
98	C₂⁴×C₅₉	C₂⁴	1	2	yes	—
99	C₂⁴×C₅₉	C₂⁴	1	4	yes	—
100	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
101	C₂⁴×C₅₉	C₂⁴	1	2	yes	—
102	C₂×D₄×C₅₉	—	2	32	no	—
103	C₂×D₄×C₅₉	—	2	8	no	—
104	C₂×D₄×C₅₉	—	2	8	no	—
105	C₂×D₄×C₅₉	—	2	16	no	—
106	C₂×D₄×C₅₉	—	2	16	no	—
107	C₂×D₄×C₅₉	—	4	8	no	—
108	C₂×D₄×C₅₉	—	4	32	no	—
109	C₂×D₄×C₅₉	C₂×D₄	1	16	yes	—
110	C₂²×C₄×C₅₉	—	2	4	no	—
111	C₂²×C₄×C₅₉	—	2	4	no	—
112	C₂²×C₄×C₅₉	—	2	8	no	—
113	C₂²×C₄×C₅₉	—	2	8	no	—
114	C₂²×C₄×C₅₉	—	2	8	no	—
115	C₂²×C₄×C₅₉	—	4	4	no	—
116	C₂²×C₄×C₅₉	—	4	8	no	—
117	C₂²×C₄×C₅₉	—	4	8	no	—
118	C₂²×C₄×C₅₉	—	4	8	no	—
119	C₂²×C₄×C₅₉	C₂×D₄	1	4	yes	—
120	C₂²×C₄×C₅₉	C₂⁴	1	8	yes	—
121	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
122	C₂²×C₄×C₅₉	C₂⁴	1	8	yes	—
123	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
124	C₄⋊C₄×C₅₉	—	2	8	no	—
125	C₄⋊C₄×C₅₉	—	4	16	no	—
126	C₂²⋊C₄×C₅₉	—	2	8	no	—
127	C₂²⋊C₄×C₅₉	—	2	8	no	—
128	C₂²⋊C₄×C₅₉	—	2	8	no	—
129	C₂²⋊C₄×C₅₉	—	2	8	no	—
130	C₂²⋊C₄×C₅₉	—	2	8	no	—
131	C₂²⋊C₄×C₅₉	—	2	8	no	—
132	C₂²⋊C₄×C₅₉	—	2	32	no	—
133	C₂²⋊C₄×C₅₉	—	2	16	no	—
134	C₂²⋊C₄×C₅₉	—	4	16	no	—
135	C₂²⋊C₄×C₅₉	—	4	8	no	—
136	C₄²×C₅₉	—	2	8	no	—
137	C₂³×C₅₉	—	2	8	no	—
138	C₂³×C₅₉	—	2	4	no	—
139	C₂³×C₅₉	—	2	16	no	—
140	C₂³×C₅₉	—	2	32	no	—
141	C₂³×C₅₉	—	2	4	no	—
142	C₂³×C₅₉	—	2	4	no	—
143	C₂³×C₅₉	—	2	8	no	—
144	C₂³×C₅₉	—	2	8	no	—
145	C₂³×C₅₉	—	2	8	no	—
146	C₂³×C₅₉	—	2	4	no	—
147	C₂³×C₅₉	—	2	8	no	—
148	C₂³×C₅₉	—	4	8	no	—
149	C₂³×C₅₉	—	4	16	no	—
150	C₂³×C₅₉	—	4	8	no	—
151	C₂³×C₅₉	—	4	32	no	—
152	C₂³×C₅₉	—	4	32	no	—
153	C₂³×C₅₉	—	4	32	no	—
154	C₂³×C₅₉	—	4	8	no	—
155	C₂³×C₅₉	—	4	16	no	—
156	C₂³×C₅₉	—	4	128	no	—
157	C₂³×C₅₉	—	4	8	no	—
158	C₂³×C₅₉	—	4	16	no	—
159	C₂³×C₅₉	—	8	8	no	—
160	C₂³×C₅₉	#123	1	16	yes	complemented
161	C₂³×C₅₉	C₂²×D₄	1	4	yes	—
162	C₂³×C₅₉	C₂²×D₄	1	2	yes	—
163	C₂³×C₅₉	C₂²×D₄	1	4	yes	—
164	C₂³×C₅₉	C₂×#41	1	4	yes	—
165	C₂³×C₅₉	C₂×#41	1	4	yes	—
166	C₂³×C₅₉	C₂×#41	1	4	yes	—
167	C₂³×C₅₉	H(5,𝔽₂)	1	8	yes	—
168	C₂³×C₅₉	C₂⁵	1	1	yes	characteristic
169	D₄×C₅₉	—	2	32	no	—
170	D₄×C₅₉	—	4	32	no	—
171	C₂×C₄×C₅₉	—	2	8	no	—
172	C₂×C₄×C₅₉	—	2	4	no	—
173	C₂×C₄×C₅₉	—	2	8	no	—
174	C₂×C₄×C₅₉	—	2	4	no	—
175	C₂×C₄×C₅₉	—	2	8	no	—
176	C₂×C₄×C₅₉	—	2	16	no	—
177	C₂×C₄×C₅₉	—	2	16	no	—
178	C₂×C₄×C₅₉	—	2	8	no	—
179	C₂×C₄×C₅₉	—	4	8	no	—
180	C₂×C₄×C₅₉	—	8	8	no	—
181	C₂×C₄×C₅₉	—	8	8	no	—
182	C₂×C₄×C₅₉	—	8	8	no	—
183	C₂×C₄×C₅₉	C₂²×D₄	1	4	yes	—
184	#35350	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
185	C₂²×C₅₉	—	2	4	no	—
186	C₂²×C₅₉	—	2	8	no	—
187	C₂²×C₅₉	—	2	8	no	—
188	C₂²×C₅₉	—	2	8	no	—
189	C₂²×C₅₉	—	2	8	no	—
190	C₂²×C₅₉	—	2	4	no	—
191	C₂²×C₅₉	—	2	8	no	—
192	C₂²×C₅₉	—	2	8	no	—
193	C₂²×C₅₉	—	2	16	no	—
194	C₂²×C₅₉	—	4	16	no	—
195	C₂²×C₅₉	—	4	32	no	—
196	C₂²×C₅₉	—	4	64	no	—
197	C₂²×C₅₉	—	4	4	no	—
198	C₂²×C₅₉	—	4	4	no	—
199	C₂²×C₅₉	—	4	8	no	—
200	C₂²×C₅₉	—	4	8	no	—
201	C₂²×C₅₉	—	8	8	no	—
202	C₂²×C₅₉	C₂×#123	1	4	yes	—
203	C₂²×C₅₉	C₂×#123	1	8	yes	—
204	C₂²×C₅₉	C₂³×D₄	1	1	yes	characteristic
205	C₂²×C₅₉	C₂²×#41	1	2	yes	—
206	C₂²×C₅₉	C₂×H(5,𝔽₂)	1	4	yes	—
207	C₄×C₅₉	—	2	4	no	—
208	C₄×C₅₉	—	4	4	no	—
209	C₄×C₅₉	—	4	8	no	—
210	C₄×C₅₉	—	4	8	no	—
211	C₂²×#120	C₂×C₅₉	1	1	yes	characteristic
212	C₂×#518	C₂×C₅₉	1	1	yes	characteristic, complemented
213	#2482	C₂×C₅₉	1	4	yes	complemented
214	#2418	C₂×C₅₉	1	16	yes	complemented
215	#2405	C₂×C₅₉	1	4	yes	complemented
216	#2315	C₂×C₅₉	1	2	yes	complemented
217	#2308	C₂×C₅₉	1	1	yes	characteristic, complemented
218	C₂×#379	C₂×C₅₉	1	2	yes	complemented
219	C₂×C₅₉	—	2	4	no	—
220	C₂×C₅₉	—	2	8	no	—
221	C₂×C₅₉	—	4	8	no	—
222	C₂×C₅₉	—	4	4	no	—
223	C₂×C₅₉	C₂²×#123	1	1	yes	characteristic
224	C₂×C₅₉	#3484	1	2	yes	—
225	C₂×C₅₉	#3490	1	4	yes	—
226	C₂⁶	C₂²×C₅₉	1	1	yes	characteristic
227	C₂³×D₄	C₂²×C₅₉	1	1	yes	characteristic
228	C₂³×D₄	C₂²×C₅₉	1	2	yes	—
229	C₂×#123	C₂²×C₅₉	1	8	yes	complemented
230	C₂×#120	—	2	8	no	—
231	C₂×#120	C₂²×C₅₉	1	8	yes	—
232	#518	—	2	8	no	—
233	C₂×C₄×D₄	C₂²×C₅₉	1	8	yes	complemented
234	C₂×#117	C₂²×C₅₉	1	2	yes	complemented
235	C₂²×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
236	C₂²×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
237	C₂²×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
238	C₂²×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
239	C₂²×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	complemented
240	C₂²×C₂²⋊C₄	C₂²×C₅₉	1	8	yes	complemented
241	#399	C₂²×C₅₉	1	8	yes	complemented
242	#397	C₂²×C₅₉	1	8	yes	complemented
243	#394	C₂²×C₅₉	1	16	yes	complemented
244	#388	C₂²×C₅₉	1	16	yes	complemented
245	#386	C₂²×C₅₉	1	8	yes	complemented
246	#386	C₂²×C₅₉	1	8	yes	complemented
247	#385	C₂²×C₅₉	1	8	yes	complemented
248	#385	C₂²×C₅₉	1	8	yes	complemented
249	#381	C₂²×C₅₉	1	2	yes	complemented
250	#380	C₂²×C₅₉	1	8	yes	complemented
251	#379	C₂²×C₅₉	1	8	yes	—
252	#379	C₂²×C₅₉	1	8	yes	complemented
253	#379	C₂²×C₅₉	1	2	yes	complemented
254	C₅₉	#35350	1	1	yes	characteristic, direct product factor, Sylow
255	C₂⁵	—	2	4	no	—
256	C₂⁵	—	2	8	no	—
257	C₂⁵	—	4	8	no	—
258	C₂⁵	C₂³×C₅₉	1	2	yes	—
259	C₂⁵	C₂³×C₅₉	1	4	yes	—
260	C₂⁵	C₂³×C₅₉	1	1	yes	characteristic
261	C₂⁵	C₂³×C₅₉	1	1	yes	characteristic
262	C₂²×D₄	—	2	8	no	—
263	C₂²×D₄	—	2	8	no	—
264	C₂²×D₄	—	4	8	no	—
265	C₂²×D₄	D₄×C₅₉	1	8	yes	—
266	C₂²×D₄	C₂³×C₅₉	1	8	yes	—
267	C₂²×D₄	C₂³×C₅₉	1	4	yes	—
268	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
269	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
270	C₂³×C₄	C₂³×C₅₉	1	4	yes	—
271	C₂³×C₄	C₂³×C₅₉	1	4	yes	—
272	C₂³×C₄	C₂³×C₅₉	1	4	yes	complemented
273	#123	—	4	16	no	—
274	#120	—	2	32	no	—
275	C₄×D₄	—	2	32	no	—
276	#117	—	2	8	no	—
277	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	complemented
278	C₂×C₄⋊C₄	C₂³×C₅₉	1	16	yes	complemented
279	C₂×C₂²⋊C₄	—	2	8	no	—
280	C₂×C₂²⋊C₄	—	2	4	no	—
281	C₂×C₂²⋊C₄	—	2	8	no	—
282	C₂×C₂²⋊C₄	—	2	8	no	—
283	C₂×C₂²⋊C₄	—	2	8	no	—
284	C₂×C₂²⋊C₄	—	4	16	no	—
285	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
286	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
287	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
288	C₂×C₂²⋊C₄	C₂³×C₅₉	1	8	yes	—
289	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
290	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
291	C₂×C₂²⋊C₄	C₂³×C₅₉	1	16	yes	—
292	C₂×C₂²⋊C₄	C₂³×C₅₉	1	16	yes	—
293	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	complemented
294	C₂×C₂²⋊C₄	C₂³×C₅₉	1	8	yes	complemented
295	C₂×C₄²	C₂³×C₅₉	1	4	yes	complemented
296	#95	C₂³×C₅₉	1	16	yes	complemented
297	#95	C₂³×C₅₉	1	8	yes	complemented
298	C₂⁴	—	2	4	no	—
299	C₂⁴	—	2	8	no	—
300	C₂⁴	—	2	16	no	—
301	C₂⁴	—	2	8	no	—
302	C₂⁴	—	2	4	no	—
303	C₂⁴	—	2	8	no	—
304	C₂⁴	—	2	8	no	—
305	C₂⁴	—	2	8	no	—
306	C₂⁴	—	4	4	no	—
307	C₂⁴	—	4	8	no	—
308	C₂⁴	—	4	4	no	—
309	C₂⁴	—	4	4	no	—
310	C₂⁴	—	4	32	no	—
311	C₂⁴	—	4	64	no	—
312	C₂⁴	—	4	16	no	—
313	C₂⁴	C₂×D₄×C₅₉	1	4	yes	—
314	C₂⁴	C₂×D₄×C₅₉	1	4	yes	—
315	C₂⁴	#41×C₅₉	1	8	yes	—
316	C₂⁴	C₂⁴×C₅₉	1	2	yes	—
317	C₂⁴	C₂⁴×C₅₉	1	4	yes	—
318	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
319	C₂⁴	C₂⁴×C₅₉	1	2	yes	—
320	C₂×D₄	—	2	32	no	—
321	C₂×D₄	—	2	8	no	—
322	C₂×D₄	—	2	8	no	—
323	C₂×D₄	—	2	16	no	—
324	C₂×D₄	—	2	16	no	—
325	C₂×D₄	—	4	8	no	—
326	C₂×D₄	—	4	32	no	—
327	C₂×D₄	C₂×D₄×C₅₉	1	16	yes	—
328	C₂²×C₄	—	2	4	no	—
329	C₂²×C₄	—	2	4	no	—
330	C₂²×C₄	—	2	8	no	—
331	C₂²×C₄	—	2	8	no	—
332	C₂²×C₄	—	2	8	no	—
333	C₂²×C₄	—	4	4	no	—
334	C₂²×C₄	—	4	8	no	—
335	C₂²×C₄	—	4	8	no	—
336	C₂²×C₄	—	4	8	no	—
337	C₂²×C₄	C₂×D₄×C₅₉	1	4	yes	—
338	C₂²×C₄	C₂⁴×C₅₉	1	8	yes	—
339	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
340	C₂²×C₄	C₂⁴×C₅₉	1	8	yes	—
341	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
342	C₄⋊C₄	—	2	8	no	—
343	C₄⋊C₄	—	4	16	no	—
344	C₂²⋊C₄	—	2	8	no	—
345	C₂²⋊C₄	—	2	8	no	—
346	C₂²⋊C₄	—	2	8	no	—
347	C₂²⋊C₄	—	2	8	no	—
348	C₂²⋊C₄	—	2	8	no	—
349	C₂²⋊C₄	—	2	8	no	—
350	C₂²⋊C₄	—	2	32	no	—
351	C₂²⋊C₄	—	2	16	no	—
352	C₂²⋊C₄	—	4	16	no	—
353	C₂²⋊C₄	—	4	8	no	—
354	C₄²	—	2	8	no	—
355	C₂³	—	2	8	no	—
356	C₂³	—	2	4	no	—
357	C₂³	—	2	16	no	—
358	C₂³	—	2	32	no	—
359	C₂³	—	2	4	no	—
360	C₂³	—	2	4	no	—
361	C₂³	—	2	8	no	—
362	C₂³	—	2	8	no	—
363	C₂³	—	2	8	no	—
364	C₂³	—	2	4	no	—
365	C₂³	—	2	8	no	—
366	C₂³	—	4	8	no	—
367	C₂³	—	4	16	no	—
368	C₂³	—	4	8	no	—
369	C₂³	—	4	32	no	—
370	C₂³	—	4	32	no	—
371	C₂³	—	4	32	no	—
372	C₂³	—	4	8	no	—
373	C₂³	—	4	16	no	—
374	C₂³	—	4	128	no	—
375	C₂³	—	4	8	no	—
376	C₂³	—	4	16	no	—
377	C₂³	—	8	8	no	—
378	C₂³	#123×C₅₉	1	16	yes	complemented
379	C₂³	C₂²×D₄×C₅₉	1	4	yes	—
380	C₂³	C₂²×D₄×C₅₉	1	2	yes	—
381	C₂³	C₂²×D₄×C₅₉	1	4	yes	—
382	C₂³	C₂×#41×C₅₉	1	4	yes	—
383	C₂³	C₂×#41×C₅₉	1	4	yes	—
384	C₂³	C₂×#41×C₅₉	1	4	yes	—
385	C₂³	H(5,𝔽₂)×C₅₉	1	8	yes	—
386	C₂³	C₂⁵×C₅₉	1	1	yes	characteristic
387	D₄	—	2	32	no	—
388	D₄	—	4	32	no	—
389	C₂×C₄	—	2	8	no	—
390	C₂×C₄	—	2	4	no	—
391	C₂×C₄	—	2	8	no	—
392	C₂×C₄	—	2	4	no	—
393	C₂×C₄	—	2	8	no	—
394	C₂×C₄	—	2	16	no	—
395	C₂×C₄	—	2	16	no	—
396	C₂×C₄	—	2	8	no	—
397	C₂×C₄	—	4	8	no	—
398	C₂×C₄	—	8	8	no	—
399	C₂×C₄	—	8	8	no	—
400	C₂×C₄	—	8	8	no	—
401	C₂×C₄	C₂²×D₄×C₅₉	1	4	yes	—
402	C₂²	—	2	4	no	—
403	C₂²	—	2	8	no	—
404	C₂²	—	2	8	no	—
405	C₂²	—	2	8	no	—
406	C₂²	—	2	8	no	—
407	C₂²	—	2	4	no	—
408	C₂²	—	2	8	no	—
409	C₂²	—	2	8	no	—
410	C₂²	—	2	16	no	—
411	C₂²	—	4	16	no	—
412	C₂²	—	4	32	no	—
413	C₂²	—	4	64	no	—
414	C₂²	—	4	4	no	—
415	C₂²	—	4	4	no	—
416	C₂²	—	4	8	no	—
417	C₂²	—	4	8	no	—
418	C₂²	—	8	8	no	—
419	C₂²	C₂×#123×C₅₉	1	4	yes	—
420	C₂²	C₂×#123×C₅₉	1	8	yes	—
421	C₂²	C₂³×D₄×C₅₉	1	1	yes	characteristic
422	C₂²	C₂²×#41×C₅₉	1	2	yes	—
423	C₂²	C₂×H(5,𝔽₂)×C₅₉	1	4	yes	—
424	C₄	—	2	4	no	—
425	C₄	—	4	4	no	—
426	C₄	—	4	8	no	—
427	C₄	—	4	8	no	—
428	C₂	—	2	4	no	—
429	C₂	—	2	8	no	—
430	C₂	—	4	8	no	—
431	C₂	—	4	4	no	—
432	C₂	C₂²×#123×C₅₉	1	1	yes	characteristic
433	C₂	C₅₉×#3484	1	2	yes	—
434	C₂	C₅₉×#3490	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₅₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₉
prime radical	C₂²×#120×C₅₉	C₂
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
2. C₂×C₅₉×#518	C₂	semidirect
3. C₅₉×#2482	C₂	semidirect
4. C₅₉×#2418	C₂	semidirect
5. C₅₉×#2405	C₂	semidirect
6. C₅₉×#2315	C₂	semidirect
7. C₅₉×#2308	C₂	semidirect
8. C₂×C₅₉×#379	C₂	semidirect
12. C₂×#123×C₅₉	C₂²	semidirect
16. C₂×C₄×D₄×C₅₉	C₂²	semidirect
17. C₂×#117×C₅₉	C₂²	semidirect
22. C₂²×C₂²⋊C₄×C₅₉	C₂²	semidirect
23. C₂²×C₂²⋊C₄×C₅₉	C₂²	semidirect
24. C₅₉×#399	C₂²	semidirect
25. C₅₉×#397	C₂²	semidirect
26. C₅₉×#394	C₂²	semidirect
27. C₅₉×#388	C₂²	semidirect
28. C₅₉×#386	C₂²	semidirect
29. C₅₉×#386	C₂²	semidirect
30. C₅₉×#385	C₂²	semidirect
31. C₅₉×#385	C₂²	semidirect
32. C₅₉×#381	C₂²	semidirect
33. C₅₉×#380	C₂²	semidirect
35. C₅₉×#379	C₂²	semidirect
36. C₅₉×#379	C₂²	semidirect
54. C₂³×C₄×C₅₉	C₂³	semidirect
59. C₂×C₄⋊C₄×C₅₉	C₂³	semidirect
60. C₂×C₄⋊C₄×C₅₉	C₂³	semidirect
75. C₂×C₂²⋊C₄×C₅₉	C₂³	semidirect
76. C₂×C₂²⋊C₄×C₅₉	C₂³	semidirect
77. C₂×C₄²×C₅₉	C₂³	semidirect
78. #95×C₅₉	C₂³	semidirect
79. #95×C₅₉	C₂³	semidirect
160. C₂³×C₅₉	#123	semidirect
184. #35350	C₅₉	direct (N × H)
212. C₂×#518	C₂×C₅₉	semidirect
213. #2482	C₂×C₅₉	semidirect
214. #2418	C₂×C₅₉	semidirect
215. #2405	C₂×C₅₉	semidirect
216. #2315	C₂×C₅₉	semidirect
217. #2308	C₂×C₅₉	semidirect
218. C₂×#379	C₂×C₅₉	semidirect
229. C₂×#123	C₂²×C₅₉	semidirect
233. C₂×C₄×D₄	C₂²×C₅₉	semidirect
234. C₂×#117	C₂²×C₅₉	semidirect
239. C₂²×C₂²⋊C₄	C₂²×C₅₉	semidirect
240. C₂²×C₂²⋊C₄	C₂²×C₅₉	semidirect
241. #399	C₂²×C₅₉	semidirect
242. #397	C₂²×C₅₉	semidirect
243. #394	C₂²×C₅₉	semidirect
244. #388	C₂²×C₅₉	semidirect
245. #386	C₂²×C₅₉	semidirect
246. #386	C₂²×C₅₉	semidirect
247. #385	C₂²×C₅₉	semidirect
248. #385	C₂²×C₅₉	semidirect
249. #381	C₂²×C₅₉	semidirect
250. #380	C₂²×C₅₉	semidirect
252. #379	C₂²×C₅₉	semidirect
253. #379	C₂²×C₅₉	semidirect
254. C₅₉	#35350	direct (N × H)
272. C₂³×C₄	C₂³×C₅₉	semidirect
277. C₂×C₄⋊C₄	C₂³×C₅₉	semidirect
278. C₂×C₄⋊C₄	C₂³×C₅₉	semidirect
293. C₂×C₂²⋊C₄	C₂³×C₅₉	semidirect
294. C₂×C₂²⋊C₄	C₂³×C₅₉	semidirect
295. C₂×C₄²	C₂³×C₅₉	semidirect
296. #95	C₂³×C₅₉	semidirect
297. #95	C₂³×C₅₉	semidirect
378. C₂³	#123×C₅₉	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#120×C₅₉	2
C₂×C₅₉×#518	2
C₅₉×#2482	2
C₅₉×#2418	2
C₅₉×#2405	2
C₅₉×#2315	2
C₅₉×#2308	2
C₂×C₅₉×#379	2
#35350	59

Subgroups — C59×#35350 #28447459

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#35350 #28447459