Subgroups — C₂×C₅₉×#3209 #28472887

Order 15104.

2134 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₉×#533	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄⋊Q₈×C₅₉	C₂	1	1	yes	maximal, characteristic
3	C₅₉×#3209	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₅₉×#494	C₂	1	2	yes	maximal, complemented
5	C₂×C₅₉×#487	C₂	1	2	yes	maximal, complemented
6	C₂×C₅₉×#462	C₂	1	4	yes	maximal, complemented
7	C₂×C₅₉×#451	C₂	1	4	yes	maximal
8	C₂×C₅₉×#431	C₂	1	1	yes	maximal, characteristic
9	C₂³×Q₈×C₅₉	C₂²	1	2	yes	—
10	C₂²×Q₁₆×C₅₉	C₂²	1	8	yes	—
11	C₅₉×#533	—	2	4	no	—
12	C₅₉×#533	C₂²	1	8	yes	—
13	C₂×C₄⋊Q₈×C₅₉	—	2	1	no	—
14	C₂×C₄⋊Q₈×C₅₉	—	2	1	no	—
15	C₂×C₄⋊Q₈×C₅₉	—	2	4	no	—
16	C₂×C₄⋊Q₈×C₅₉	C₂²	1	2	yes	—
17	C₂×C₄⋊Q₈×C₅₉	C₂²	1	2	yes	—
18	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊Q₈×C₅₉	C₂²	1	8	yes	—
20	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
21	C₂×#125×C₅₉	—	2	1	no	—
22	C₂×C₂²⋊Q₈×C₅₉	—	2	1	no	—
23	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	2	yes	—
24	C₂×C₄×Q₈×C₅₉	—	2	1	no	—
25	C₂×C₄×Q₈×C₅₉	C₂²	1	2	yes	—
26	C₂×#117×C₅₉	—	2	1	no	—
27	C₂²×C₄⋊C₄×C₅₉	—	2	1	no	—
28	C₂²×C₄⋊C₄×C₅₉	—	2	1	no	—
29	C₂²×C₄²×C₅₉	C₂²	1	1	yes	characteristic
30	C₅₉×#494	C₂²	1	16	yes	complemented
31	C₅₉×#487	C₂²	1	16	yes	complemented
32	C₅₉×#462	C₂²	1	32	yes	complemented
33	C₅₉×#451	C₂²	1	32	yes	—
34	C₅₉×#431	C₂²	1	8	yes	—
35	C₂×C₄⋊C₈×C₅₉	C₂²	1	2	yes	—
36	C₂×#103×C₅₉	C₂²	1	8	yes	—
37	C₂×C₂²⋊C₈×C₅₉	C₂²	1	2	yes	—
38	C₂×C₄×C₈×C₅₉	C₂²	1	2	yes	—
39	C₂²×Q₈×C₅₉	—	2	1	no	—
40	C₂²×Q₈×C₅₉	—	2	4	no	—
41	C₂²×Q₈×C₅₉	—	2	2	no	—
42	C₂²×Q₈×C₅₉	—	4	8	no	—
43	C₂²×Q₈×C₅₉	C₂³	1	4	yes	—
44	C₂²×Q₈×C₅₉	C₂³	1	2	yes	—
45	C₂²×Q₈×C₅₉	C₂³	1	8	yes	—
46	C₂³×C₄×C₅₉	—	2	2	no	—
47	C₂³×C₄×C₅₉	D₄	1	1	yes	characteristic
48	C₂³×C₄×C₅₉	D₄	1	1	yes	characteristic
49	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
50	C₂×Q₁₆×C₅₉	—	4	16	no	—
51	C₂×Q₁₆×C₅₉	C₂³	1	32	yes	—
52	C₂²×C₈×C₅₉	C₂³	1	4	yes	—
53	C₄⋊Q₈×C₅₉	—	2	4	no	—
54	C₄⋊Q₈×C₅₉	—	2	8	no	—
55	C₄⋊Q₈×C₅₉	—	2	8	no	—
56	C₄⋊Q₈×C₅₉	—	2	4	no	—
57	C₄⋊Q₈×C₅₉	—	2	2	no	—
58	C₄⋊Q₈×C₅₉	—	2	2	no	—
59	C₄⋊Q₈×C₅₉	C₂³	1	8	yes	—
60	C₄⋊Q₈×C₅₉	C₂³	1	8	yes	—
61	C₄⋊Q₈×C₅₉	C₂³	1	4	yes	—
62	C₄⋊Q₈×C₅₉	C₂³	1	4	yes	—
63	#125×C₅₉	—	2	8	no	—
64	C₂²⋊Q₈×C₅₉	—	2	8	no	—
65	C₂²⋊Q₈×C₅₉	—	2	4	no	—
66	C₂²⋊Q₈×C₅₉	C₂³	1	8	yes	—
67	C₄×Q₈×C₅₉	—	2	8	no	—
68	C₄×Q₈×C₅₉	—	2	4	no	—
69	C₄×Q₈×C₅₉	C₂³	1	8	yes	—
70	#117×C₅₉	—	2	8	no	—
71	C₂×C₄⋊C₄×C₅₉	—	2	8	no	—
72	C₂×C₄⋊C₄×C₅₉	—	2	8	no	—
73	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
74	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
75	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
76	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
77	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
78	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
79	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
80	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
81	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
82	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
83	C₂×C₂²⋊C₄×C₅₉	—	2	2	no	—
84	C₂×C₄²×C₅₉	—	2	2	no	—
85	C₂×C₄²×C₅₉	D₄	1	1	yes	characteristic
86	C₂×C₄²×C₅₉	D₄	1	1	yes	characteristic
87	C₂×C₄²×C₅₉	D₄	1	4	yes	—
88	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
89	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
90	C₂×C₄²×C₅₉	C₂³	1	4	yes	—
91	C₄⋊C₈×C₅₉	C₂³	1	8	yes	—
92	#103×C₅₉	C₂³	1	32	yes	—
93	C₂²⋊C₈×C₅₉	C₂³	1	8	yes	—
94	C₄×C₈×C₅₉	C₂³	1	8	yes	—
95	C₂⁴×C₅₉	C₂×D₄	1	1	yes	characteristic
96	C₂×Q₈×C₅₉	—	2	2	no	—
97	C₂×Q₈×C₅₉	—	2	4	no	—
98	C₂×Q₈×C₅₉	—	2	8	no	—
99	C₂×Q₈×C₅₉	—	2	4	no	—
100	C₂×Q₈×C₅₉	—	2	8	no	—
101	C₂×Q₈×C₅₉	—	2	16	no	—
102	C₂×Q₈×C₅₉	—	4	16	no	—
103	C₂×Q₈×C₅₉	—	4	8	no	—
104	C₂×Q₈×C₅₉	—	4	16	no	—
105	C₂×Q₈×C₅₉	—	4	4	no	—
106	C₂×Q₈×C₅₉	C₂⁴	1	8	yes	—
107	C₂×Q₈×C₅₉	C₂⁴	1	4	yes	—
108	C₂²×C₄×C₅₉	—	2	4	no	—
109	C₂²×C₄×C₅₉	—	2	4	no	—
110	C₂²×C₄×C₅₉	—	2	8	no	—
111	C₂²×C₄×C₅₉	—	2	2	no	—
112	C₂²×C₄×C₅₉	—	2	2	no	—
113	C₂²×C₄×C₅₉	—	2	4	no	—
114	C₂²×C₄×C₅₉	—	4	8	no	—
115	C₂²×C₄×C₅₉	Q₁₆	1	8	yes	complemented
116	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₅₉	C₂×D₄	1	4	yes	—
118	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₅₉	C₂×D₄	1	4	yes	—
123	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
125	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
126	Q₁₆×C₅₉	—	4	32	no	—
127	C₂×C₈×C₅₉	—	2	8	no	—
128	C₂×C₈×C₅₉	C₂⁴	1	8	yes	—
129	C₄⋊C₄×C₅₉	—	2	8	no	—
130	C₄⋊C₄×C₅₉	—	2	8	no	—
131	C₄⋊C₄×C₅₉	—	2	8	no	—
132	C₄⋊C₄×C₅₉	—	2	8	no	—
133	C₄⋊C₄×C₅₉	—	2	4	no	—
134	C₄⋊C₄×C₅₉	—	2	4	no	—
135	C₄⋊C₄×C₅₉	—	2	4	no	—
136	C₄⋊C₄×C₅₉	—	2	8	no	—
137	C₄⋊C₄×C₅₉	—	2	8	no	—
138	C₄⋊C₄×C₅₉	—	2	2	no	—
139	C₄⋊C₄×C₅₉	C₂⁴	1	4	yes	—
140	C₂²⋊C₄×C₅₉	—	2	8	no	—
141	C₄²×C₅₉	—	2	8	no	—
142	C₄²×C₅₉	C₂×D₄	1	4	yes	—
143	C₄²×C₅₉	C₂×D₄	1	2	yes	—
144	C₄²×C₅₉	C₂×D₄	1	4	yes	—
145	C₄²×C₅₉	C₂×D₄	1	2	yes	—
146	C₄²×C₅₉	C₂⁴	1	2	yes	—
147	C₄²×C₅₉	C₂⁴	1	2	yes	—
148	C₂³×C₅₉	—	2	2	no	—
149	C₂³×C₅₉	—	2	2	no	—
150	C₂³×C₅₉	C₂×Q₁₆	1	4	yes	—
151	C₂³×C₅₉	C₂²×D₄	1	2	yes	—
152	C₂³×C₅₉	C₂²×D₄	1	1	yes	characteristic
153	Q₈×C₅₉	—	2	8	no	—
154	Q₈×C₅₉	—	2	16	no	—
155	Q₈×C₅₉	—	4	16	no	—
156	Q₈×C₅₉	—	4	4	no	—
157	Q₈×C₅₉	—	4	8	no	—
158	Q₈×C₅₉	—	4	8	no	—
159	C₂×C₄×C₅₉	—	2	2	no	—
160	C₂×C₄×C₅₉	—	2	2	no	—
161	C₂×C₄×C₅₉	—	2	4	no	—
162	C₂×C₄×C₅₉	—	2	8	no	—
163	C₂×C₄×C₅₉	—	2	4	no	—
164	C₂×C₄×C₅₉	—	2	4	no	—
165	C₂×C₄×C₅₉	—	2	4	no	—
166	C₂×C₄×C₅₉	—	2	8	no	—
167	C₂×C₄×C₅₉	—	4	16	no	—
168	C₂×C₄×C₅₉	—	4	8	no	—
169	C₂×C₄×C₅₉	—	4	4	no	—
170	C₂×C₄×C₅₉	—	4	4	no	—
171	C₂×C₄×C₅₉	C₂×Q₁₆	1	4	yes	—
172	C₂×C₄×C₅₉	C₂×Q₁₆	1	4	yes	—
173	C₂×C₄×C₅₉	C₂×Q₁₆	1	16	yes	complemented
174	C₂×C₄×C₅₉	#137	1	4	yes	—
175	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
176	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
177	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
178	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
179	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
180	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
181	C₂×C₄×C₅₉	H(5,𝔽₂)	1	4	yes	—
182	C₂×C₄×C₅₉	C₂⁵	1	1	yes	characteristic
183	C₈×C₅₉	—	2	8	no	—
184	C₂×#3209	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
185	C₂²×C₅₉	—	2	2	no	—
186	C₂²×C₅₉	—	2	8	no	—
187	C₂²×C₅₉	—	2	2	no	—
188	C₂²×C₅₉	#535	1	2	yes	—
189	C₂²×C₅₉	C₂²×Q₁₆	1	4	yes	—
190	C₂²×C₅₉	C₂²×Q₁₆	1	2	yes	—
191	C₂²×C₅₉	C₂×#137	1	2	yes	—
192	C₂²×C₅₉	C₂³×D₄	1	1	yes	characteristic
193	C₄×C₅₉	—	2	2	no	—
194	C₄×C₅₉	—	2	2	no	—
195	C₄×C₅₉	—	4	8	no	—
196	C₄×C₅₉	—	4	4	no	—
197	C₄×C₅₉	—	4	4	no	—
198	C₄×C₅₉	#535	1	2	yes	—
199	C₄×C₅₉	C₂²×Q₁₆	1	4	yes	—
200	C₄×C₅₉	C₂²×Q₁₆	1	4	yes	—
201	C₄×C₅₉	C₂×#137	1	4	yes	—
202	C₄×C₅₉	C₂×H(5,𝔽₂)	1	2	yes	—
203	C₂×#533	C₂×C₅₉	1	1	yes	characteristic
204	C₂²×C₄⋊Q₈	C₂×C₅₉	1	1	yes	characteristic
205	#3209	C₂×C₅₉	1	16	yes	direct product factor
206	C₂×#494	C₂×C₅₉	1	2	yes	complemented
207	C₂×#487	C₂×C₅₉	1	2	yes	complemented
208	C₂×#462	C₂×C₅₉	1	4	yes	complemented
209	C₂×#451	C₂×C₅₉	1	4	yes	—
210	C₂×#431	C₂×C₅₉	1	1	yes	characteristic
211	C₂×C₅₉	—	2	4	no	—
212	C₂×C₅₉	#3209	1	4	yes	direct product factor
213	C₂×C₅₉	C₂×#535	1	1	yes	characteristic
214	C₂×C₅₉	C₂³×Q₁₆	1	1	yes	characteristic
215	C₂×C₅₉	C₂²×#137	1	1	yes	characteristic
216	C₂³×Q₈	C₂²×C₅₉	1	2	yes	—
217	C₂²×Q₁₆	C₂²×C₅₉	1	8	yes	—
218	#533	—	2	4	no	—
219	#533	C₂²×C₅₉	1	8	yes	—
220	C₂×C₄⋊Q₈	—	2	1	no	—
221	C₂×C₄⋊Q₈	—	2	1	no	—
222	C₂×C₄⋊Q₈	—	2	4	no	—
223	C₂×C₄⋊Q₈	C₂²×C₅₉	1	2	yes	—
224	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
225	C₂×C₄⋊Q₈	C₂²×C₅₉	1	8	yes	—
226	C₂×C₄⋊Q₈	C₂²×C₅₉	1	2	yes	—
227	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
228	C₂×#125	—	2	1	no	—
229	C₂×C₂²⋊Q₈	—	2	1	no	—
230	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	2	yes	—
231	C₂×C₄×Q₈	—	2	1	no	—
232	C₂×C₄×Q₈	C₂²×C₅₉	1	2	yes	—
233	C₂×#117	—	2	1	no	—
234	C₂²×C₄⋊C₄	—	2	1	no	—
235	C₂²×C₄⋊C₄	—	2	1	no	—
236	C₂²×C₄²	C₂²×C₅₉	1	1	yes	characteristic
237	#494	C₂²×C₅₉	1	16	yes	complemented
238	#487	C₂²×C₅₉	1	16	yes	complemented
239	#462	C₂²×C₅₉	1	32	yes	complemented
240	#451	C₂²×C₅₉	1	32	yes	—
241	#431	C₂²×C₅₉	1	8	yes	—
242	C₂×C₄⋊C₈	C₂²×C₅₉	1	2	yes	—
243	C₂×#103	C₂²×C₅₉	1	8	yes	—
244	C₂×C₂²⋊C₈	C₂²×C₅₉	1	2	yes	—
245	C₂×C₄×C₈	C₂²×C₅₉	1	2	yes	—
246	C₅₉	C₂×#3209	1	1	yes	characteristic, direct product factor, Sylow
247	C₂²×Q₈	—	2	1	no	—
248	C₂²×Q₈	—	2	2	no	—
249	C₂²×Q₈	—	2	4	no	—
250	C₂²×Q₈	—	4	8	no	—
251	C₂²×Q₈	C₂³×C₅₉	1	2	yes	—
252	C₂²×Q₈	C₂³×C₅₉	1	4	yes	—
253	C₂²×Q₈	C₂³×C₅₉	1	8	yes	—
254	C₂³×C₄	—	2	2	no	—
255	C₂³×C₄	D₄×C₅₉	1	1	yes	characteristic
256	C₂³×C₄	D₄×C₅₉	1	1	yes	characteristic
257	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
258	C₂×Q₁₆	—	4	16	no	—
259	C₂×Q₁₆	C₂³×C₅₉	1	32	yes	—
260	C₂²×C₈	C₂³×C₅₉	1	4	yes	—
261	C₄⋊Q₈	—	2	8	no	—
262	C₄⋊Q₈	—	2	4	no	—
263	C₄⋊Q₈	—	2	8	no	—
264	C₄⋊Q₈	—	2	4	no	—
265	C₄⋊Q₈	—	2	2	no	—
266	C₄⋊Q₈	—	2	2	no	—
267	C₄⋊Q₈	C₂³×C₅₉	1	8	yes	—
268	C₄⋊Q₈	C₂³×C₅₉	1	8	yes	—
269	C₄⋊Q₈	C₂³×C₅₉	1	4	yes	—
270	C₄⋊Q₈	C₂³×C₅₉	1	4	yes	—
271	#125	—	2	8	no	—
272	C₂²⋊Q₈	—	2	8	no	—
273	C₂²⋊Q₈	—	2	4	no	—
274	C₂²⋊Q₈	C₂³×C₅₉	1	8	yes	—
275	C₄×Q₈	—	2	8	no	—
276	C₄×Q₈	—	2	4	no	—
277	C₄×Q₈	C₂³×C₅₉	1	8	yes	—
278	#117	—	2	8	no	—
279	C₂×C₄⋊C₄	—	2	2	no	—
280	C₂×C₄⋊C₄	—	2	8	no	—
281	C₂×C₄⋊C₄	—	2	2	no	—
282	C₂×C₄⋊C₄	—	2	2	no	—
283	C₂×C₄⋊C₄	—	2	8	no	—
284	C₂×C₄⋊C₄	—	2	2	no	—
285	C₂×C₄⋊C₄	—	2	1	no	—
286	C₂×C₄⋊C₄	—	2	1	no	—
287	C₂×C₄⋊C₄	—	2	1	no	—
288	C₂×C₄⋊C₄	—	2	2	no	—
289	C₂×C₄⋊C₄	—	2	2	no	—
290	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
291	C₂×C₂²⋊C₄	—	2	2	no	—
292	C₂×C₄²	—	2	2	no	—
293	C₂×C₄²	D₄×C₅₉	1	1	yes	characteristic
294	C₂×C₄²	D₄×C₅₉	1	1	yes	characteristic
295	C₂×C₄²	D₄×C₅₉	1	4	yes	—
296	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
297	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
298	C₂×C₄²	C₂³×C₅₉	1	4	yes	—
299	C₄⋊C₈	C₂³×C₅₉	1	8	yes	—
300	#103	C₂³×C₅₉	1	32	yes	—
301	C₂²⋊C₈	C₂³×C₅₉	1	8	yes	—
302	C₄×C₈	C₂³×C₅₉	1	8	yes	—
303	C₂⁴	C₂×D₄×C₅₉	1	1	yes	characteristic
304	C₂×Q₈	—	2	2	no	—
305	C₂×Q₈	—	2	4	no	—
306	C₂×Q₈	—	2	8	no	—
307	C₂×Q₈	—	2	4	no	—
308	C₂×Q₈	—	2	8	no	—
309	C₂×Q₈	—	2	16	no	—
310	C₂×Q₈	—	4	16	no	—
311	C₂×Q₈	—	4	8	no	—
312	C₂×Q₈	—	4	16	no	—
313	C₂×Q₈	—	4	4	no	—
314	C₂×Q₈	C₂⁴×C₅₉	1	8	yes	—
315	C₂×Q₈	C₂⁴×C₅₉	1	4	yes	—
316	C₂²×C₄	—	2	4	no	—
317	C₂²×C₄	—	2	4	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	2	8	no	—
321	C₂²×C₄	—	2	4	no	—
322	C₂²×C₄	—	4	8	no	—
323	C₂²×C₄	Q₁₆×C₅₉	1	8	yes	complemented
324	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
325	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
326	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
327	C₂²×C₄	C₂×D₄×C₅₉	1	4	yes	—
328	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
329	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
330	C₂²×C₄	C₂×D₄×C₅₉	1	4	yes	—
331	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
332	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
333	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
334	Q₁₆	—	4	32	no	—
335	C₂×C₈	—	2	8	no	—
336	C₂×C₈	C₂⁴×C₅₉	1	8	yes	—
337	C₄⋊C₄	—	2	8	no	—
338	C₄⋊C₄	—	2	8	no	—
339	C₄⋊C₄	—	2	8	no	—
340	C₄⋊C₄	—	2	8	no	—
341	C₄⋊C₄	—	2	4	no	—
342	C₄⋊C₄	—	2	4	no	—
343	C₄⋊C₄	—	2	4	no	—
344	C₄⋊C₄	—	2	8	no	—
345	C₄⋊C₄	—	2	8	no	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	C₂⁴×C₅₉	1	4	yes	—
348	C₂²⋊C₄	—	2	8	no	—
349	C₄²	—	2	8	no	—
350	C₄²	C₂×D₄×C₅₉	1	4	yes	—
351	C₄²	C₂×D₄×C₅₉	1	2	yes	—
352	C₄²	C₂×D₄×C₅₉	1	4	yes	—
353	C₄²	C₂×D₄×C₅₉	1	2	yes	—
354	C₄²	C₂⁴×C₅₉	1	2	yes	—
355	C₄²	C₂⁴×C₅₉	1	2	yes	—
356	C₂³	—	2	2	no	—
357	C₂³	—	2	2	no	—
358	C₂³	C₂×Q₁₆×C₅₉	1	4	yes	—
359	C₂³	C₂²×D₄×C₅₉	1	2	yes	—
360	C₂³	C₂²×D₄×C₅₉	1	1	yes	characteristic
361	Q₈	—	2	8	no	—
362	Q₈	—	2	16	no	—
363	Q₈	—	4	16	no	—
364	Q₈	—	4	4	no	—
365	Q₈	—	4	8	no	—
366	Q₈	—	4	8	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	4	no	—
370	C₂×C₄	—	2	8	no	—
371	C₂×C₄	—	2	4	no	—
372	C₂×C₄	—	2	4	no	—
373	C₂×C₄	—	2	4	no	—
374	C₂×C₄	—	2	8	no	—
375	C₂×C₄	—	4	16	no	—
376	C₂×C₄	—	4	8	no	—
377	C₂×C₄	—	4	4	no	—
378	C₂×C₄	—	4	4	no	—
379	C₂×C₄	C₂×Q₁₆×C₅₉	1	4	yes	—
380	C₂×C₄	C₂×Q₁₆×C₅₉	1	4	yes	—
381	C₂×C₄	C₂×Q₁₆×C₅₉	1	16	yes	complemented
382	C₂×C₄	#137×C₅₉	1	4	yes	—
383	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
384	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
385	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
386	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
387	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
388	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
389	C₂×C₄	H(5,𝔽₂)×C₅₉	1	4	yes	—
390	C₂×C₄	C₂⁵×C₅₉	1	1	yes	characteristic
391	C₈	—	2	8	no	—
392	C₂²	—	2	2	no	—
393	C₂²	—	2	2	no	—
394	C₂²	—	2	8	no	—
395	C₂²	C₅₉×#535	1	2	yes	—
396	C₂²	C₂²×Q₁₆×C₅₉	1	4	yes	—
397	C₂²	C₂²×Q₁₆×C₅₉	1	2	yes	—
398	C₂²	C₂×#137×C₅₉	1	2	yes	—
399	C₂²	C₂³×D₄×C₅₉	1	1	yes	characteristic
400	C₄	—	2	2	no	—
401	C₄	—	2	2	no	—
402	C₄	—	4	4	no	—
403	C₄	—	4	8	no	—
404	C₄	—	4	4	no	—
405	C₄	C₅₉×#535	1	2	yes	—
406	C₄	C₂²×Q₁₆×C₅₉	1	4	yes	—
407	C₄	C₂²×Q₁₆×C₅₉	1	4	yes	—
408	C₄	C₂×#137×C₅₉	1	4	yes	—
409	C₄	C₂×H(5,𝔽₂)×C₅₉	1	2	yes	—
410	C₂	—	2	4	no	—
411	C₂	C₅₉×#3209	1	4	yes	direct product factor
412	C₂	C₂×C₅₉×#535	1	1	yes	characteristic
413	C₂	C₂³×Q₁₆×C₅₉	1	1	yes	characteristic
414	C₂	C₂²×#137×C₅₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₉	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₉
prime radical	C₂⁴×C₅₉	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₉ ◁ C₂²×C₄²×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₅₉×#3209	C₂	direct (N × H)
4. C₂×C₅₉×#494	C₂	semidirect
5. C₂×C₅₉×#487	C₂	semidirect
6. C₂×C₅₉×#462	C₂	semidirect
30. C₅₉×#494	C₂²	semidirect
31. C₅₉×#487	C₂²	semidirect
32. C₅₉×#462	C₂²	semidirect
115. C₂²×C₄×C₅₉	Q₁₆	semidirect
173. C₂×C₄×C₅₉	C₂×Q₁₆	semidirect
184. C₂×#3209	C₅₉	direct (N × H)
205. #3209	C₂×C₅₉	direct (N × H)
206. C₂×#494	C₂×C₅₉	semidirect
207. C₂×#487	C₂×C₅₉	semidirect
208. C₂×#462	C₂×C₅₉	semidirect
212. C₂×C₅₉	#3209	direct (N × H)
237. #494	C₂²×C₅₉	semidirect
238. #487	C₂²×C₅₉	semidirect
239. #462	C₂²×C₅₉	semidirect
246. C₅₉	C₂×#3209	direct (N × H)
323. C₂²×C₄	Q₁₆×C₅₉	semidirect
381. C₂×C₄	C₂×Q₁₆×C₅₉	semidirect
411. C₂	C₅₉×#3209	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅₉×#533	2
C₂²×C₄⋊Q₈×C₅₉	2
C₅₉×#3209	2
C₂×C₅₉×#494	2
C₂×C₅₉×#487	2
C₂×C₅₉×#462	2
C₂×C₅₉×#451	2
C₂×C₅₉×#431	2
C₂×#3209	59

Subgroups — C2×C59×#3209 #28472887

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅₉×#3209 #28472887