Subgroups — #28557763

Order 15104.

668 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21432729	C₂	1	1	yes	maximal, characteristic
2	C₂×#16837455	C₂	1	1	yes	maximal, characteristic
3	#21422876	C₂	1	4	yes	maximal, complemented
4	#21422871	C₂	1	2	yes	maximal, complemented
5	#21422867	C₂	1	2	yes	maximal, complemented
6	#21422844	C₂	1	4	yes	maximal, complemented
7	C₂×C₅₉×#431	C₂	1	1	yes	maximal, characteristic
8	#16837459	—	2	1	no	—
9	#16837459	C₂²	1	2	yes	—
10	#16837455	—	2	1	no	—
11	#16837455	—	2	1	no	—
12	#16837455	—	2	1	no	—
13	#16837455	C₂²	1	2	yes	—
14	#16837455	C₂²	1	2	yes	—
15	#16837455	C₂²	1	2	yes	—
16	#16837426	C₂²	1	2	yes	—
17	C₂×C₄⋊(C₅₉⋊C₈)	C₂²	1	2	yes	—
18	#16837366	—	2	1	no	—
19	C₂×C₂²⋊(C₅₉⋊C₈)	—	2	1	no	—
20	C₄×#11745664	—	2	1	no	—
21	C₂×C₄×C₅₉⋊C₈	—	2	1	no	—
22	#16837155	C₂²	1	8	yes	complemented
23	#16837153	C₂²	1	8	yes	complemented
24	C₂²×C₄²×C₅₉	C₂²	1	1	yes	characteristic
25	C₅₉×#431	C₄	1	2	yes	—
26	C₅₉×#431	C₄	1	2	yes	—
27	C₅₉×#431	C₂²	1	1	yes	characteristic
28	C₅₉×#431	C₂²	1	1	yes	characteristic
29	C₅₉×#431	C₂²	1	2	yes	—
30	C₂×C₄⋊C₈×C₅₉	C₄	1	2	yes	—
31	C₂×C₂²⋊C₈×C₅₉	C₄	1	2	yes	—
32	C₂×C₄×C₈×C₅₉	C₂²	1	2	yes	—
33	C₂×#11745664	—	2	2	no	—
34	C₂²×C₅₉⋊C₈	—	2	2	no	—
35	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
36	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
37	C₄⋊(C₅₉⋊C₈)	C₂³	1	4	yes	—
38	C₄⋊(C₅₉⋊C₈)	C₂³	1	4	yes	—
39	C₂²⋊(C₅₉⋊C₈)	—	2	2	no	—
40	C₂²⋊(C₅₉⋊C₈)	—	2	2	no	—
41	C₂²⋊(C₅₉⋊C₈)	—	2	2	no	—
42	C₂²⋊(C₅₉⋊C₈)	—	2	2	no	—
43	#14273638	—	2	2	no	—
44	C₄×C₅₉⋊C₈	—	2	2	no	—
45	C₄×C₅₉⋊C₈	—	2	2	no	—
46	C₄×C₅₉⋊C₈	—	2	2	no	—
47	C₂³×C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
48	C₂³×C₄×C₅₉	D₄	1	1	yes	characteristic
49	C₂³×C₄×C₅₉	Q₈	1	1	yes	characteristic
50	C₂²×C₈×C₅₉	C₂×C₄	1	4	yes	—
51	C₂×C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄²×C₅₉	D₄	1	1	yes	characteristic
55	C₂×C₄²×C₅₉	D₄	1	1	yes	characteristic
56	C₂×C₄²×C₅₉	D₄	1	1	yes	characteristic
57	C₂×C₄²×C₅₉	Q₈	1	1	yes	characteristic
58	C₂×C₄²×C₅₉	Q₈	1	1	yes	characteristic
59	C₂×C₄²×C₅₉	Q₈	1	1	yes	characteristic
60	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
61	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
62	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
63	C₄⋊C₈×C₅₉	C₂×C₄	1	2	yes	—
64	C₄⋊C₈×C₅₉	C₂×C₄	1	2	yes	—
65	C₄⋊C₈×C₅₉	C₂×C₄	1	4	yes	—
66	C₂²⋊C₈×C₅₉	C₂×C₄	1	2	yes	—
67	C₂²⋊C₈×C₅₉	C₂×C₄	1	2	yes	—
68	C₂²⋊C₈×C₅₉	C₂×C₄	1	4	yes	—
69	C₄×C₈×C₅₉	C₂×C₄	1	4	yes	—
70	C₄×C₈×C₅₉	C₂³	1	2	yes	—
71	C₄×C₈×C₅₉	C₂³	1	2	yes	—
72	C₂⁴×C₅₉	C₄⋊C₄	1	1	yes	characteristic
73	C₂²×C₄×C₅₉	—	2	4	no	—
74	C₂²×C₄×C₅₉	—	2	4	no	—
75	C₂²×C₄×C₅₉	—	4	2	no	—
76	C₂²×C₄×C₅₉	C₄⋊C₄	1	1	yes	characteristic
77	C₂²×C₄×C₅₉	C₄⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₅₉	C₄⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₅₉	C₄⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₅₉	C₄⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₅₉	C₄⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₅₉	C₄⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₅₉	C₄⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₅₉	C₄⋊C₄	1	1	yes	characteristic
85	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₅₉	C₂×Q₈	1	1	yes	characteristic
92	C₂²×C₄×C₅₉	C₂×Q₈	1	1	yes	characteristic
93	C₂²×C₄×C₅₉	C₂×Q₈	1	1	yes	characteristic
94	C₂×C₈×C₅₉	—	2	8	no	—
95	C₂×C₈×C₅₉	C₂²×C₄	1	4	yes	—
96	C₂×C₈×C₅₉	C₂²×C₄	1	4	yes	—
97	C₄²×C₅₉	C₄⋊C₄	1	1	yes	characteristic
98	C₄²×C₅₉	C₄⋊C₄	1	1	yes	characteristic
99	C₄²×C₅₉	C₄⋊C₄	1	1	yes	characteristic
100	C₄²×C₅₉	C₄⋊C₄	1	1	yes	characteristic
101	C₄²×C₅₉	C₄⋊C₄	1	1	yes	characteristic
102	C₄²×C₅₉	C₄⋊C₄	1	1	yes	characteristic
103	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
104	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
105	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
106	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
107	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
108	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
109	C₄²×C₅₉	C₂×Q₈	1	1	yes	characteristic
110	C₄²×C₅₉	C₂×Q₈	1	1	yes	characteristic
111	C₄²×C₅₉	C₂×Q₈	1	1	yes	characteristic
112	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
113	#11745664	—	4	4	no	—
114	C₂×C₅₉⋊C₈	—	2	4	no	—
115	C₂×C₅₉⋊C₈	—	2	4	no	—
116	C₂×C₅₉⋊C₈	—	4	4	no	—
117	C₂³×C₅₉	—	2	2	no	—
118	C₂³×C₅₉	—	2	2	no	—
119	C₂³×C₅₉	—	4	1	no	—
120	C₂³×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
121	C₂³×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
122	C₂³×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
123	C₂×C₄×C₅₉	—	2	2	no	—
124	C₂×C₄×C₅₉	—	2	2	no	—
125	C₂×C₄×C₅₉	—	2	2	no	—
126	C₂×C₄×C₅₉	—	2	2	no	—
127	C₂×C₄×C₅₉	—	2	2	no	—
128	C₂×C₄×C₅₉	—	2	2	no	—
129	C₂×C₄×C₅₉	—	2	2	no	—
130	C₂×C₄×C₅₉	—	2	2	no	—
131	C₂×C₄×C₅₉	—	2	2	no	—
132	C₂×C₄×C₅₉	—	2	2	no	—
133	C₂×C₄×C₅₉	—	2	2	no	—
134	C₂×C₄×C₅₉	—	2	2	no	—
135	C₂×C₄×C₅₉	—	2	2	no	—
136	C₂×C₄×C₅₉	—	4	1	no	—
137	C₂×C₄×C₅₉	—	4	1	no	—
138	C₂×C₄×C₅₉	—	4	1	no	—
139	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
140	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
141	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
142	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
143	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
144	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
145	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
146	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
147	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
148	C₂×C₄×C₅₉	#131	1	4	yes	—
149	C₂×C₄×C₅₉	#135	1	4	yes	—
150	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
151	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
152	C₂×C₄×C₅₉	C₂²×Q₈	1	1	yes	characteristic
153	C₈×C₅₉	—	2	4	no	—
154	C₈×C₅₉	—	2	4	no	—
155	C₅₉⋊C₈	—	4	4	no	—
156	C₅₉⋊C₈	—	4	4	no	—
157	#17803	—	59	1	no	maximal, Sylow
158	C₂²×C₅₉	—	2	1	no	—
159	C₂²×C₅₉	—	2	1	no	—
160	C₂²×C₅₉	—	2	1	no	—
161	C₂²×C₅₉	—	2	1	no	—
162	C₂²×C₅₉	—	2	1	no	—
163	C₂²×C₅₉	—	2	1	no	—
164	C₂²×C₅₉	—	2	1	no	—
165	C₂²×C₅₉	—	4	4	no	—
166	C₂²×C₅₉	#424	1	2	yes	—
167	C₂²×C₅₉	#427	1	2	yes	—
168	C₂²×C₅₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
169	C₄×C₅₉	—	2	1	no	—
170	C₄×C₅₉	—	2	1	no	—
171	C₄×C₅₉	—	2	1	no	—
172	C₄×C₅₉	—	2	1	no	—
173	C₄×C₅₉	—	2	1	no	—
174	C₄×C₅₉	—	2	1	no	—
175	C₄×C₅₉	—	2	1	no	—
176	C₄×C₅₉	#424	1	2	yes	—
177	C₄×C₅₉	#427	1	2	yes	—
178	C₄×C₅₉	#430	1	2	yes	—
179	C₄×C₅₉	C₂×#131	1	2	yes	—
180	C₄×C₅₉	C₂×#135	1	2	yes	—
181	#2920	—	59	1	no	—
182	C₂×#431	—	59	1	no	—
183	C₂×#431	D₅₉	1	1	yes	characteristic
184	#1572	—	59	4	no	—
185	#1571	—	59	2	no	—
186	#1570	—	59	2	no	—
187	#1564	—	59	4	no	—
188	C₂×C₅₉	—	2	2	no	—
189	C₂×C₅₉	—	2	2	no	—
190	C₂×C₅₉	—	4	1	no	—
191	C₂×C₅₉	C₂×#424	1	1	yes	characteristic
192	C₂×C₅₉	C₂×#427	1	1	yes	characteristic
193	C₂×C₅₉	C₂×#430	1	1	yes	characteristic
194	C₂²×C₄²	C₂×D₅₉	1	1	yes	characteristic
195	#432	—	59	2	no	—
196	#432	—	118	1	no	—
197	#431	—	59	2	no	—
198	#431	—	59	2	no	—
199	#431	—	59	2	no	—
200	#431	—	118	1	no	—
201	#431	—	118	1	no	—
202	#431	—	118	1	no	—
203	#431	Dic₅₉	1	2	yes	—
204	#431	Dic₅₉	1	2	yes	—
205	#431	C₂×D₅₉	1	1	yes	characteristic
206	#431	C₂×D₅₉	1	1	yes	characteristic
207	#431	C₂×D₅₉	1	2	yes	—
208	#423	—	59	2	no	—
209	C₂×C₄⋊C₈	—	59	2	no	—
210	C₂×C₄⋊C₈	Dic₅₉	1	2	yes	—
211	#407	—	118	1	no	—
212	C₂×C₂²⋊C₈	—	118	1	no	—
213	C₂×C₂²⋊C₈	Dic₅₉	1	2	yes	—
214	C₄×M₁₆	—	118	1	no	—
215	C₂×C₄×C₈	—	118	1	no	—
216	C₂×C₄×C₈	C₂×D₅₉	1	2	yes	—
217	#335	—	59	8	no	—
218	#334	—	59	8	no	—
219	C₅₉	#17803	1	1	yes	characteristic, complemented, Sylow
220	C₂³×C₄	Dic₁₁₈	1	1	yes	characteristic
221	C₂³×C₄	D₂₃₆	1	1	yes	characteristic
222	C₂³×C₄	C₂×Dic₅₉	1	1	yes	characteristic
223	C₂×M₁₆	—	118	2	no	—
224	C₂²×C₈	—	118	2	no	—
225	C₂²×C₈	C₂×Dic₅₉	1	4	yes	—
226	C₂×C₄²	Dic₁₁₈	1	1	yes	characteristic
227	C₂×C₄²	Dic₁₁₈	1	1	yes	characteristic
228	C₂×C₄²	Dic₁₁₈	1	1	yes	characteristic
229	C₂×C₄²	D₂₃₆	1	1	yes	characteristic
230	C₂×C₄²	D₂₃₆	1	1	yes	characteristic
231	C₂×C₄²	D₂₃₆	1	1	yes	characteristic
232	C₂×C₄²	C₂×Dic₅₉	1	1	yes	characteristic
233	C₂×C₄²	C₂×Dic₅₉	1	1	yes	characteristic
234	C₂×C₄²	C₂×Dic₅₉	1	1	yes	characteristic
235	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
236	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
237	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
238	C₄⋊C₈	—	59	4	no	—
239	C₄⋊C₈	—	59	4	no	—
240	C₄⋊C₈	—	118	2	no	—
241	C₄⋊C₈	—	118	2	no	—
242	C₄⋊C₈	C₂×Dic₅₉	1	2	yes	—
243	C₄⋊C₈	C₂×Dic₅₉	1	2	yes	—
244	C₄⋊C₈	C₂×Dic₅₉	1	4	yes	—
245	C₂²⋊C₈	—	118	2	no	—
246	C₂²⋊C₈	—	118	2	no	—
247	C₂²⋊C₈	—	118	2	no	—
248	C₂²⋊C₈	—	118	2	no	—
249	C₂²⋊C₈	C₂×Dic₅₉	1	2	yes	—
250	C₂²⋊C₈	C₂×Dic₅₉	1	2	yes	—
251	C₂²⋊C₈	C₂×Dic₅₉	1	4	yes	—
252	#97	—	118	2	no	—
253	C₄×C₈	—	118	2	no	—
254	C₄×C₈	—	118	2	no	—
255	C₄×C₈	—	118	2	no	—
256	C₄×C₈	C₂×Dic₅₉	1	4	yes	—
257	C₄×C₈	C₂²×D₅₉	1	2	yes	—
258	C₄×C₈	C₂²×D₅₉	1	2	yes	—
259	C₂⁴	C₄⋊Dic₅₉	1	1	yes	characteristic
260	C₂²×C₄	—	2	4	no	—
261	C₂²×C₄	—	2	4	no	—
262	C₂²×C₄	—	4	2	no	—
263	C₂²×C₄	C₄⋊Dic₅₉	1	1	yes	characteristic
264	C₂²×C₄	C₄⋊Dic₅₉	1	1	yes	characteristic
265	C₂²×C₄	C₄⋊Dic₅₉	1	1	yes	characteristic
266	C₂²×C₄	C₄⋊Dic₅₉	1	1	yes	characteristic
267	C₂²×C₄	C₄⋊Dic₅₉	1	1	yes	characteristic
268	C₂²×C₄	C₄⋊Dic₅₉	1	1	yes	characteristic
269	C₂²×C₄	C₄⋊Dic₅₉	1	1	yes	characteristic
270	C₂²×C₄	C₄⋊Dic₅₉	1	1	yes	characteristic
271	C₂²×C₄	C₄⋊Dic₅₉	1	1	yes	characteristic
272	C₂²×C₄	C₂×Dic₁₁₈	1	1	yes	characteristic
273	C₂²×C₄	C₂×Dic₁₁₈	1	1	yes	characteristic
274	C₂²×C₄	C₂×Dic₁₁₈	1	1	yes	characteristic
275	C₂²×C₄	C₂×D₂₃₆	1	1	yes	characteristic
276	C₂²×C₄	C₂×D₂₃₆	1	1	yes	characteristic
277	C₂²×C₄	C₂×D₂₃₆	1	1	yes	characteristic
278	C₂²×C₄	C₂²×Dic₅₉	1	1	yes	characteristic
279	C₂²×C₄	C₂²×Dic₅₉	1	1	yes	characteristic
280	C₂²×C₄	C₂²×Dic₅₉	1	1	yes	characteristic
281	M₁₆	—	236	4	no	—
282	C₂×C₈	—	2	8	no	—
283	C₂×C₈	—	118	4	no	—
284	C₂×C₈	—	118	4	no	—
285	C₂×C₈	—	236	4	no	—
286	C₂×C₈	C₂²×Dic₅₉	1	4	yes	—
287	C₂×C₈	C₂²×Dic₅₉	1	4	yes	—
288	C₄²	C₄⋊Dic₅₉	1	1	yes	characteristic
289	C₄²	C₄⋊Dic₅₉	1	1	yes	characteristic
290	C₄²	C₄⋊Dic₅₉	1	1	yes	characteristic
291	C₄²	C₄⋊Dic₅₉	1	1	yes	characteristic
292	C₄²	C₄⋊Dic₅₉	1	1	yes	characteristic
293	C₄²	C₄⋊Dic₅₉	1	1	yes	characteristic
294	C₄²	C₂×Dic₁₁₈	1	1	yes	characteristic
295	C₄²	C₂×Dic₁₁₈	1	1	yes	characteristic
296	C₄²	C₂×Dic₁₁₈	1	1	yes	characteristic
297	C₄²	C₂×D₂₃₆	1	1	yes	characteristic
298	C₄²	C₂×D₂₃₆	1	1	yes	characteristic
299	C₄²	C₂×D₂₃₆	1	1	yes	characteristic
300	C₄²	C₂²×Dic₅₉	1	1	yes	characteristic
301	C₄²	C₂²×Dic₅₉	1	1	yes	characteristic
302	C₄²	C₂²×Dic₅₉	1	1	yes	characteristic
303	C₄²	C₂³×D₅₉	1	1	yes	characteristic
304	C₂³	—	2	2	no	—
305	C₂³	—	2	2	no	—
306	C₂³	—	4	1	no	—
307	C₂³	C₂×C₄⋊Dic₅₉	1	1	yes	characteristic
308	C₂³	C₂×C₄⋊Dic₅₉	1	1	yes	characteristic
309	C₂³	C₂×C₄⋊Dic₅₉	1	1	yes	characteristic
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	4	1	no	—
324	C₂×C₄	—	4	1	no	—
325	C₂×C₄	—	4	1	no	—
326	C₂×C₄	C₂×C₄⋊Dic₅₉	1	1	yes	characteristic
327	C₂×C₄	C₂×C₄⋊Dic₅₉	1	1	yes	characteristic
328	C₂×C₄	C₂×C₄⋊Dic₅₉	1	1	yes	characteristic
329	C₂×C₄	C₂×C₄⋊Dic₅₉	1	1	yes	characteristic
330	C₂×C₄	C₂×C₄⋊Dic₅₉	1	1	yes	characteristic
331	C₂×C₄	C₂×C₄⋊Dic₅₉	1	1	yes	characteristic
332	C₂×C₄	C₂×C₄⋊Dic₅₉	1	1	yes	characteristic
333	C₂×C₄	C₂×C₄⋊Dic₅₉	1	1	yes	characteristic
334	C₂×C₄	C₂×C₄⋊Dic₅₉	1	1	yes	characteristic
335	C₂×C₄	#14273734	1	4	yes	—
336	C₂×C₄	#14273749	1	4	yes	—
337	C₂×C₄	C₂³×Dic₅₉	1	1	yes	characteristic
338	C₂×C₄	C₂²×D₂₃₆	1	1	yes	characteristic
339	C₂×C₄	C₂²×Dic₁₁₈	1	1	yes	characteristic
340	C₈	—	2	4	no	—
341	C₈	—	2	4	no	—
342	C₈	—	236	4	no	—
343	C₈	—	236	4	no	—
344	C₂²	—	2	1	no	—
345	C₂²	—	2	1	no	—
346	C₂²	—	2	1	no	—
347	C₂²	—	2	1	no	—
348	C₂²	—	2	1	no	—
349	C₂²	—	2	1	no	—
350	C₂²	—	2	1	no	—
351	C₂²	—	4	4	no	—
352	C₂²	#16837429	1	2	yes	—
353	C₂²	#16837440	1	2	yes	—
354	C₂²	C₂²×C₄⋊Dic₅₉	1	1	yes	characteristic
355	C₄	—	2	1	no	—
356	C₄	—	2	1	no	—
357	C₄	—	2	1	no	—
358	C₄	—	2	1	no	—
359	C₄	—	2	1	no	—
360	C₄	—	2	1	no	—
361	C₄	—	2	1	no	—
362	C₄	#16837429	1	2	yes	—
363	C₄	#16837440	1	2	yes	—
364	C₄	#16837451	1	2	yes	—
365	C₄	C₂×#14273734	1	2	yes	—
366	C₄	C₂×#14273749	1	2	yes	—
367	C₂	—	2	2	no	—
368	C₂	—	2	2	no	—
369	C₂	—	4	1	no	—
370	C₂	C₂×#16837429	1	1	yes	characteristic
371	C₂	C₂×#16837440	1	1	yes	characteristic
372	C₂	C₂×#16837451	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	C₂×D₂₃₆
commutator	C₂×C₄×C₅₉	C₂³×C₄
Frattini	C₄²	C₂³×D₅₉
Fitting	C₂×C₅₉×#431	C₂
socle	C₂²×C₅₉	C₂²×C₄⋊C₄
prime radical	C₂⁴×C₅₉	C₄⋊C₄
cosocle	C₄²×C₅₉	C₂⁴
hypercenter	C₂×#431	D₅₉
hypocenter	C₅₉	#17803
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₄² ◁ C₂²×C₄² ◁ C₂×#431

Complements

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

N	H ≅ G/N	type
3. #21422876	C₂	semidirect
4. #21422871	C₂	semidirect
5. #21422867	C₂	semidirect
6. #21422844	C₂	semidirect
22. #16837155	C₂²	semidirect
23. #16837153	C₂²	semidirect
219. C₅₉	#17803	semidirect

Maximal subgroups

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

subgroup	index
#21432729	2
C₂×#16837455	2
#21422876	2
#21422871	2
#21422867	2
#21422844	2
C₂×C₅₉×#431	2
#17803	59