Subgroups — #28557841

Order 15104.

638 conjugacy classes of subgroups.

The subgroup lattice has 376 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	#21422877	C₂	1	4	yes	maximal, complemented
4	#21422874	C₂	1	4	yes	maximal, complemented
5	#21422854	C₂	1	2	yes	maximal, complemented
6	#21422851	C₂	1	2	yes	maximal, complemented
7	C₅₉×#2920	C₂	1	1	yes	maximal, characteristic
8	#16837459	—	2	1	no	—
9	#16837459	C₂²	1	2	yes	—
10	#16837455	—	2	1	no	—
11	#16837455	C₄	1	2	yes	—
12	#16837455	C₄	1	2	yes	—
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)	C₄	1	2	yes	—
18	#16837366	—	2	1	no	—
19	C₂×C₂²⋊(C₅₉⋊C₈)	C₄	1	2	yes	—
20	C₄×#11745664	—	2	1	no	—
21	C₂×C₄×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
23	#16837154	C₂²	1	8	yes	complemented
24	#16837152	C₂²	1	8	yes	complemented
25	C₂²×C₄²×C₅₉	C₂²	1	1	yes	characteristic
26	C₅₉×#432	—	2	1	no	—
27	C₅₉×#432	C₂²	1	2	yes	—
28	C₅₉×#431	—	2	1	no	—
29	C₅₉×#431	C₂²	1	2	yes	—
30	C₅₉×#423	C₂²	1	2	yes	—
31	C₅₉×#407	—	2	1	no	—
32	C₄×M₁₆×C₅₉	—	2	1	no	—
33	C₂×#11745664	—	2	2	no	—
34	C₂²×C₅₉⋊C₈	C₂×C₄	1	2	yes	—
35	C₂²×C₅₉⋊C₈	C₂×C₄	1	2	yes	—
36	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
37	C₄⋊(C₅₉⋊C₈)	C₂×C₄	1	4	yes	—
38	C₄⋊(C₅₉⋊C₈)	C₂×C₄	1	4	yes	—
39	C₄⋊(C₅₉⋊C₈)	C₂³	1	4	yes	—
40	C₂²⋊(C₅₉⋊C₈)	—	2	2	no	—
41	C₂²⋊(C₅₉⋊C₈)	—	2	2	no	—
42	C₂²⋊(C₅₉⋊C₈)	C₂×C₄	1	4	yes	—
43	C₂²⋊(C₅₉⋊C₈)	C₂×C₄	1	4	yes	—
44	#14273638	—	2	2	no	—
45	C₄×C₅₉⋊C₈	—	2	2	no	—
46	C₄×C₅₉⋊C₈	C₂×C₄	1	2	yes	—
47	C₄×C₅₉⋊C₈	C₂×C₄	1	2	yes	—
48	C₄×C₅₉⋊C₈	C₂³	1	2	yes	—
49	C₄×C₅₉⋊C₈	C₂³	1	2	yes	—
50	C₂³×C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
51	C₂³×C₄×C₅₉	D₄	1	1	yes	characteristic
52	C₂³×C₄×C₅₉	Q₈	1	1	yes	characteristic
53	C₂×M₁₆×C₅₉	—	2	2	no	—
54	C₂×C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄²×C₅₉	D₄	1	1	yes	characteristic
58	C₂×C₄²×C₅₉	D₄	1	1	yes	characteristic
59	C₂×C₄²×C₅₉	D₄	1	1	yes	characteristic
60	C₂×C₄²×C₅₉	Q₈	1	1	yes	characteristic
61	C₂×C₄²×C₅₉	Q₈	1	1	yes	characteristic
62	C₂×C₄²×C₅₉	Q₈	1	1	yes	characteristic
63	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
64	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
65	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
66	C₄⋊C₈×C₅₉	—	2	2	no	—
67	C₄⋊C₈×C₅₉	C₂³	1	4	yes	—
68	C₂²⋊C₈×C₅₉	—	2	2	no	—
69	C₂²⋊C₈×C₅₉	—	2	2	no	—
70	#97×C₅₉	—	2	2	no	—
71	C₄×C₈×C₅₉	—	2	2	no	—
72	C₂⁴×C₅₉	C₄⋊C₄	1	1	yes	characteristic
73	C₂²×C₄×C₅₉	—	2	4	no	—
74	C₂²×C₄×C₅₉	—	4	2	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	M₁₆×C₅₉	—	4	4	no	—
95	C₂×C₈×C₅₉	—	2	4	no	—
96	C₄²×C₅₉	C₄⋊C₄	1	1	yes	characteristic
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	C₂²×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	C₂×D₄	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×Q₈	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	C₂⁴	1	1	yes	characteristic
112	#11745664	—	4	4	no	—
113	C₂×C₅₉⋊C₈	—	2	4	no	—
114	C₂×C₅₉⋊C₈	—	4	2	no	—
115	C₂×C₅₉⋊C₈	—	4	2	no	—
116	C₂×C₅₉⋊C₈	C₂²×C₄	1	4	yes	—
117	C₂×C₅₉⋊C₈	C₂²×C₄	1	4	yes	—
118	C₂³×C₅₉	—	2	2	no	—
119	C₂³×C₅₉	—	4	1	no	—
120	C₂³×C₅₉	—	4	1	no	—
121	C₂³×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
122	C₂³×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
123	C₂³×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
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	—	4	1	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	—	4	1	no	—
140	C₂×C₄×C₅₉	—	4	1	no	—
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	C₂×C₄⋊C₄	1	1	yes	characteristic
149	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₅₉	#135	1	4	yes	—
151	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
152	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
153	C₂×C₄×C₅₉	C₂²×Q₈	1	1	yes	characteristic
154	C₈×C₅₉	—	4	4	no	—
155	C₅₉⋊C₈	—	2	4	no	—
156	C₅₉⋊C₈	—	2	4	no	—
157	C₅₉⋊C₈	—	4	4	no	—
158	#17815	—	59	1	no	maximal, Sylow
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	—	2	1	no	—
166	C₂²×C₅₉	—	2	1	no	—
167	C₂²×C₅₉	—	4	4	no	—
168	C₂²×C₅₉	#427	1	2	yes	—
169	C₂²×C₅₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
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	—	2	1	no	—
177	C₄×C₅₉	—	2	1	no	—
178	C₄×C₅₉	#427	1	2	yes	—
179	C₄×C₅₉	#430	1	2	yes	—
180	C₄×C₅₉	#568	1	2	yes	—
181	C₄×C₅₉	C₂×#135	1	2	yes	—
182	#2920	—	59	1	no	—
183	#2920	D₅₉	1	1	yes	characteristic
184	C₂×#431	—	59	1	no	—
185	#1572	—	59	4	no	—
186	#1572	—	59	4	no	—
187	#1567	—	59	2	no	—
188	#1566	—	59	2	no	—
189	C₂×C₅₉	—	2	2	no	—
190	C₂×C₅₉	—	4	1	no	—
191	C₂×C₅₉	—	4	1	no	—
192	C₂×C₅₉	#2905	1	1	yes	characteristic
193	C₂×C₅₉	C₂×#427	1	1	yes	characteristic
194	C₂×C₅₉	C₂×#430	1	1	yes	characteristic
195	C₂²×C₄²	C₂×D₅₉	1	1	yes	characteristic
196	#432	—	2	1	no	—
197	#432	—	59	2	no	—
198	#432	—	118	1	no	—
199	#432	C₂×D₅₉	1	2	yes	—
200	#431	—	2	1	no	—
201	#431	—	59	2	no	—
202	#431	—	59	2	no	—
203	#431	—	59	2	no	—
204	#431	—	59	2	no	—
205	#431	—	59	2	no	—
206	#431	—	118	1	no	—
207	#431	C₂×D₅₉	1	2	yes	—
208	#423	—	59	2	no	—
209	#423	C₂×D₅₉	1	2	yes	—
210	C₂×C₄⋊C₈	—	59	2	no	—
211	#407	—	2	1	no	—
212	#407	—	118	1	no	—
213	C₂×C₂²⋊C₈	—	59	2	no	—
214	C₄×M₁₆	—	2	1	no	—
215	C₄×M₁₆	—	118	1	no	—
216	C₂×C₄×C₈	—	59	1	no	—
217	C₂×C₄×C₈	—	59	1	no	—
218	#335	—	59	8	no	—
219	#334	—	59	8	no	—
220	C₅₉	#17815	1	1	yes	characteristic, complemented, Sylow
221	C₂³×C₄	Dic₁₁₈	1	1	yes	characteristic
222	C₂³×C₄	C₄×D₅₉	1	1	yes	characteristic
223	C₂³×C₄	C₂²⋊D₅₉	1	1	yes	characteristic
224	C₂×M₁₆	—	2	2	no	—
225	C₂×M₁₆	—	118	2	no	—
226	C₂²×C₈	—	59	2	no	—
227	C₂²×C₈	—	59	2	no	—
228	C₂×C₄²	Dic₁₁₈	1	1	yes	characteristic
229	C₂×C₄²	Dic₁₁₈	1	1	yes	characteristic
230	C₂×C₄²	Dic₁₁₈	1	1	yes	characteristic
231	C₂×C₄²	C₄×D₅₉	1	1	yes	characteristic
232	C₂×C₄²	C₄×D₅₉	1	1	yes	characteristic
233	C₂×C₄²	C₄×D₅₉	1	1	yes	characteristic
234	C₂×C₄²	C₂²⋊D₅₉	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	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
239	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
240	C₄⋊C₈	—	2	2	no	—
241	C₄⋊C₈	—	59	4	no	—
242	C₄⋊C₈	—	59	4	no	—
243	C₄⋊C₈	—	59	4	no	—
244	C₄⋊C₈	—	118	2	no	—
245	C₄⋊C₈	C₂²×D₅₉	1	4	yes	—
246	C₂²⋊C₈	—	2	2	no	—
247	C₂²⋊C₈	—	2	2	no	—
248	C₂²⋊C₈	—	59	4	no	—
249	C₂²⋊C₈	—	59	4	no	—
250	C₂²⋊C₈	—	118	2	no	—
251	C₂²⋊C₈	—	118	2	no	—
252	#97	—	2	2	no	—
253	#97	—	118	2	no	—
254	C₄×C₈	—	2	2	no	—
255	C₄×C₈	—	59	2	no	—
256	C₄×C₈	—	59	2	no	—
257	C₄×C₈	—	59	2	no	—
258	C₄×C₈	—	59	2	no	—
259	C₄×C₈	—	118	2	no	—
260	C₂⁴	Dic₅₉⋊C₄	1	1	yes	characteristic
261	C₂²×C₄	—	2	4	no	—
262	C₂²×C₄	—	4	2	no	—
263	C₂²×C₄	—	4	2	no	—
264	C₂²×C₄	Dic₅₉⋊C₄	1	1	yes	characteristic
265	C₂²×C₄	Dic₅₉⋊C₄	1	1	yes	characteristic
266	C₂²×C₄	Dic₅₉⋊C₄	1	1	yes	characteristic
267	C₂²×C₄	Dic₅₉⋊C₄	1	1	yes	characteristic
268	C₂²×C₄	Dic₅₉⋊C₄	1	1	yes	characteristic
269	C₂²×C₄	Dic₅₉⋊C₄	1	1	yes	characteristic
270	C₂²×C₄	Dic₅₉⋊C₄	1	1	yes	characteristic
271	C₂²×C₄	Dic₅₉⋊C₄	1	1	yes	characteristic
272	C₂²×C₄	Dic₅₉⋊C₄	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×Dic₁₁₈	1	1	yes	characteristic
276	C₂²×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
277	C₂²×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
278	C₂²×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
279	C₂²×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
280	C₂²×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
281	C₂²×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
282	M₁₆	—	4	4	no	—
283	M₁₆	—	236	4	no	—
284	C₂×C₈	—	2	4	no	—
285	C₂×C₈	—	59	4	no	—
286	C₂×C₈	—	59	4	no	—
287	C₂×C₈	—	118	4	no	—
288	C₂×C₈	—	236	2	no	—
289	C₂×C₈	—	236	2	no	—
290	C₄²	Dic₅₉⋊C₄	1	1	yes	characteristic
291	C₄²	Dic₅₉⋊C₄	1	1	yes	characteristic
292	C₄²	Dic₅₉⋊C₄	1	1	yes	characteristic
293	C₄²	Dic₅₉⋊C₄	1	1	yes	characteristic
294	C₄²	Dic₅₉⋊C₄	1	1	yes	characteristic
295	C₄²	Dic₅₉⋊C₄	1	1	yes	characteristic
296	C₄²	C₂×Dic₁₁₈	1	1	yes	characteristic
297	C₄²	C₂×Dic₁₁₈	1	1	yes	characteristic
298	C₄²	C₂×Dic₁₁₈	1	1	yes	characteristic
299	C₄²	C₂×C₄×D₅₉	1	1	yes	characteristic
300	C₄²	C₂×C₄×D₅₉	1	1	yes	characteristic
301	C₄²	C₂×C₄×D₅₉	1	1	yes	characteristic
302	C₄²	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
303	C₄²	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
304	C₄²	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
305	C₄²	C₂³×D₅₉	1	1	yes	characteristic
306	C₂³	—	2	2	no	—
307	C₂³	—	4	1	no	—
308	C₂³	—	4	1	no	—
309	C₂³	C₂×Dic₅₉⋊C₄	1	1	yes	characteristic
310	C₂³	C₂×Dic₅₉⋊C₄	1	1	yes	characteristic
311	C₂³	C₂×Dic₅₉⋊C₄	1	1	yes	characteristic
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	—	4	1	no	—
327	C₂×C₄	—	4	1	no	—
328	C₂×C₄	—	4	1	no	—
329	C₂×C₄	C₂×Dic₅₉⋊C₄	1	1	yes	characteristic
330	C₂×C₄	C₂×Dic₅₉⋊C₄	1	1	yes	characteristic
331	C₂×C₄	C₂×Dic₅₉⋊C₄	1	1	yes	characteristic
332	C₂×C₄	C₂×Dic₅₉⋊C₄	1	1	yes	characteristic
333	C₂×C₄	C₂×Dic₅₉⋊C₄	1	1	yes	characteristic
334	C₂×C₄	C₂×Dic₅₉⋊C₄	1	1	yes	characteristic
335	C₂×C₄	C₂×Dic₅₉⋊C₄	1	1	yes	characteristic
336	C₂×C₄	C₂×Dic₅₉⋊C₄	1	1	yes	characteristic
337	C₂×C₄	C₂×Dic₅₉⋊C₄	1	1	yes	characteristic
338	C₂×C₄	#14273747	1	4	yes	—
339	C₂×C₄	C₂²×C₄×D₅₉	1	1	yes	characteristic
340	C₂×C₄	C₂²×C₂²⋊D₅₉	1	1	yes	characteristic
341	C₂×C₄	C₂²×Dic₁₁₈	1	1	yes	characteristic
342	C₈	—	4	4	no	—
343	C₈	—	118	4	no	—
344	C₈	—	118	4	no	—
345	C₈	—	236	4	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	—	2	1	no	—
352	C₂²	—	2	1	no	—
353	C₂²	—	2	1	no	—
354	C₂²	—	4	4	no	—
355	C₂²	#16837438	1	2	yes	—
356	C₂²	C₂²×Dic₅₉⋊C₄	1	1	yes	characteristic
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	—	2	1	no	—
363	C₄	—	2	1	no	—
364	C₄	—	2	1	no	—
365	C₄	#16837438	1	2	yes	—
366	C₄	#16837450	1	2	yes	—
367	C₄	#16838168	1	2	yes	—
368	C₄	C₂×#14273747	1	2	yes	—
369	C₂	—	2	2	no	—
370	C₂	—	4	1	no	—
371	C₂	—	4	1	no	—
372	C₂	#21432659	1	1	yes	characteristic
373	C₂	C₂×#16837438	1	1	yes	characteristic
374	C₂	C₂×#16837450	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₅₉
commutator	C₂×C₄×C₅₉	C₂³×C₄
Frattini	C₄²	C₂³×D₅₉
Fitting	C₅₉×#2920	C₂
socle	C₂²×C₅₉	C₂²×C₄⋊C₄
prime radical	C₂⁴×C₅₉	C₄⋊C₄
cosocle	C₄²×C₅₉	C₂⁴
hypercenter	#2920	D₅₉
hypocenter	C₅₉	#17815
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄² ◁ #2920

Complements

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

N	H ≅ G/N	type
3. #21422877	C₂	semidirect
4. #21422874	C₂	semidirect
5. #21422854	C₂	semidirect
6. #21422851	C₂	semidirect
23. #16837154	C₂²	semidirect
24. #16837152	C₂²	semidirect
220. C₅₉	#17815	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
#21422877	2
#21422874	2
#21422854	2
#21422851	2
C₅₉×#2920	2
#17815	59