Subgroups — #28478824

Order 15104.

696 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21426494	C₂	1	1	yes	maximal, characteristic
2	C₄×#14273686	C₂	1	1	yes	maximal, characteristic
3	#21421981	C₂	1	4	yes	maximal
4	C₅₉×#2920	C₂	1	1	yes	maximal, characteristic
5	C₂×#14273686	—	2	1	no	—
6	#16837270	C₄	1	2	yes	complemented
7	#16837268	C₄	1	2	yes	complemented
8	#16837265	—	2	1	no	—
9	#16837262	—	2	1	no	—
10	C₄×C₄⋊Dic₅₉	—	2	1	no	—
11	C₄×C₄⋊Dic₅₉	—	2	1	no	—
12	C₄×C₄⋊Dic₅₉	C₄	1	2	yes	complemented
13	C₄×C₂²⋊Dic₅₉	—	2	1	no	—
14	C₄×C₂²⋊Dic₅₉	C₂²	1	2	yes	—
15	C₄×C₂²⋊Dic₅₉	C₂²	1	2	yes	—
16	#16837248	—	2	1	no	—
17	#16837248	C₄	1	2	yes	complemented
18	C₄²×Dic₅₉	—	2	1	no	—
19	C₂²×C₄²×C₅₉	C₂²	1	1	yes	characteristic
20	C₅₉×#432	—	2	1	no	—
21	C₅₉×#432	—	2	1	no	—
22	C₅₉×#431	—	2	1	no	—
23	C₅₉×#431	—	2	1	no	—
24	C₅₉×#423	C₄	1	2	yes	complemented
25	C₅₉×#407	C₂²	1	2	yes	—
26	C₄×M₁₆×C₅₉	C₄	1	2	yes	complemented
27	#14273686	—	2	8	no	—
28	C₂×C₄⋊Dic₅₉	—	2	2	no	—
29	C₂×C₄⋊Dic₅₉	—	2	2	no	—
30	C₂×C₂²⋊Dic₅₉	—	2	2	no	—
31	C₂×C₂²⋊Dic₅₉	—	2	2	no	—
32	C₂×C₄×Dic₅₉	—	2	2	no	—
33	C₂×C₄×Dic₅₉	—	2	2	no	—
34	C₂×C₄×Dic₅₉	—	2	2	no	—
35	C₂×C₄×Dic₅₉	—	2	2	no	—
36	C₅₉⋊#95	—	2	2	no	—
37	C₅₉⋊#95	—	2	2	no	—
38	C₅₉⋊#95	—	2	2	no	—
39	C₅₉⋊#95	—	2	2	no	—
40	C₅₉⋊#95	C₂×C₄	1	4	yes	—
41	C₅₉⋊#95	C₂×C₄	1	4	yes	—
42	C₂³×C₄×C₅₉	D₄	1	1	yes	characteristic
43	C₂³×C₄×C₅₉	D₄	1	1	yes	characteristic
44	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
45	C₂×M₁₆×C₅₉	C₂×C₄	1	4	yes	—
46	C₂×C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄²×C₅₉	D₄	1	1	yes	characteristic
53	C₂×C₄²×C₅₉	D₄	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	Q₈	1	1	yes	characteristic
57	C₂×C₄²×C₅₉	Q₈	1	1	yes	characteristic
58	C₄⋊C₈×C₅₉	—	2	2	no	—
59	C₄⋊C₈×C₅₉	—	2	2	no	—
60	C₂²⋊C₈×C₅₉	—	2	2	no	—
61	C₂²⋊C₈×C₅₉	—	2	2	no	—
62	#97×C₅₉	—	2	2	no	—
63	C₄×C₈×C₅₉	—	2	2	no	—
64	C₂⁴×C₅₉	C₂×D₄	1	1	yes	characteristic
65	C₂²×C₄×C₅₉	—	2	4	no	—
66	C₂²×C₄×C₅₉	—	4	2	no	—
67	C₂²×C₄×C₅₉	—	4	2	no	—
68	C₂²×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
69	C₂²×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
70	C₂²×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
71	C₂²×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
72	C₂²×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
73	C₂²×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
74	C₂²×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
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	C₂²×C₄	1	1	yes	characteristic
81	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
82	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₄×C₅₉	C₂×Q₈	1	1	yes	characteristic
86	C₂²×Dic₅₉	—	2	4	no	—
87	C₂²×Dic₅₉	—	2	4	no	—
88	M₁₆×C₅₉	—	4	4	no	—
89	C₂×C₈×C₅₉	—	2	4	no	—
90	C₄²×C₅₉	C₄²	1	1	yes	characteristic
91	C₄²×C₅₉	C₄²	1	1	yes	characteristic
92	C₄²×C₅₉	C₄²	1	1	yes	characteristic
93	C₄²×C₅₉	C₄²	1	1	yes	characteristic
94	C₄²×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
95	C₄²×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
96	C₄²×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
97	C₄²×C₅₉	C₂²⋊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	C₄⋊C₄	1	1	yes	characteristic
104	C₄²×C₅₉	C₄⋊C₄	1	1	yes	characteristic
105	C₄²×C₅₉	C₄⋊C₄	1	1	yes	characteristic
106	C₂²⋊Dic₅₉	—	2	8	no	—
107	C₂²⋊Dic₅₉	—	4	4	no	—
108	C₄⋊Dic₅₉	—	2	8	no	—
109	C₄⋊Dic₅₉	—	4	4	no	—
110	C₄×Dic₅₉	—	2	8	no	—
111	C₄×Dic₅₉	—	4	4	no	—
112	C₄×Dic₅₉	—	4	4	no	—
113	C₄×Dic₅₉	—	4	4	no	—
114	C₂³×C₅₉	—	2	2	no	—
115	C₂³×C₅₉	—	2	2	no	—
116	C₂³×C₅₉	—	4	1	no	—
117	C₂³×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
118	C₂³×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
119	C₂³×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
120	C₂×C₄×C₅₉	—	2	2	no	—
121	C₂×C₄×C₅₉	—	2	2	no	—
122	C₂×C₄×C₅₉	—	2	2	no	—
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	—	4	1	no	—
131	C₂×C₄×C₅₉	—	4	1	no	—
132	C₂×C₄×C₅₉	—	4	1	no	—
133	C₂×C₄×C₅₉	—	4	1	no	—
134	C₂×C₄×C₅₉	—	4	1	no	—
135	C₂×C₄×C₅₉	—	4	1	no	—
136	C₂×C₄×C₅₉	—	4	1	no	—
137	C₂×C₄×C₅₉	#95	1	1	yes	characteristic
138	C₂×C₄×C₅₉	#95	1	1	yes	characteristic
139	C₂×C₄×C₅₉	#95	1	1	yes	characteristic
140	C₂×C₄×C₅₉	#95	1	1	yes	characteristic
141	C₂×C₄×C₅₉	#95	1	1	yes	characteristic
142	C₂×C₄×C₅₉	#95	1	1	yes	characteristic
143	C₂×C₄×C₅₉	#95	1	1	yes	characteristic
144	C₂×C₄×C₅₉	#95	1	1	yes	characteristic
145	C₂×C₄×C₅₉	#104	1	4	yes	—
146	C₂×C₄×C₅₉	C₂×C₄²	1	1	yes	characteristic
147	C₂×C₄×C₅₉	C₂×C₂²⋊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×Dic₅₉	—	2	8	no	—
151	C₂×Dic₅₉	—	4	4	no	—
152	C₂×Dic₅₉	—	4	4	no	—
153	C₂×Dic₅₉	—	4	4	no	—
154	C₂×Dic₅₉	—	4	4	no	—
155	C₂×Dic₅₉	—	4	4	no	—
156	C₈×C₅₉	—	4	4	no	—
157	#8052	—	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	C₂×#95	1	1	yes	characteristic
167	C₂²×C₅₉	C₂×#104	1	2	yes	—
168	C₂²×C₅₉	#421	1	2	yes	—
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	—	2	1	no	—
177	C₄×C₅₉	—	2	1	no	—
178	C₄×C₅₉	#339	1	2	yes	—
179	C₄×C₅₉	#339	1	2	yes	—
180	C₄×C₅₉	#410	1	2	yes	—
181	Dic₅₉	—	4	8	no	—
182	Dic₅₉	—	8	4	no	—
183	#2920	D₅₉	1	1	yes	characteristic
184	#2283	—	59	1	no	—
185	C₄×#117	—	59	1	no	—
186	#1297	—	59	4	no	—
187	C₂×C₅₉	—	2	2	no	—
188	C₂×C₅₉	—	2	2	no	—
189	C₂×C₅₉	—	4	1	no	—
190	C₂×C₅₉	C₂×#339	1	1	yes	characteristic
191	C₂×C₅₉	#1733	1	1	yes	characteristic
192	C₂×C₅₉	#1740	1	1	yes	characteristic
193	C₂×#117	—	118	1	no	—
194	C₂²×C₄²	C₂×D₅₉	1	1	yes	characteristic
195	#432	—	2	1	no	—
196	#432	—	2	1	no	—
197	#431	—	2	1	no	—
198	#431	—	2	1	no	—
199	#423	Dic₅₉	1	2	yes	complemented
200	#407	C₂×D₅₉	1	2	yes	—
201	C₄×M₁₆	Dic₅₉	1	2	yes	complemented
202	#383	—	59	2	no	—
203	#382	—	59	2	no	—
204	#381	—	118	1	no	—
205	#380	—	118	1	no	—
206	C₄×C₄⋊C₄	—	59	2	no	—
207	C₄×C₄⋊C₄	—	118	1	no	—
208	C₄×C₄⋊C₄	—	118	1	no	—
209	C₄×C₂²⋊C₄	—	59	2	no	—
210	C₄×C₂²⋊C₄	—	59	2	no	—
211	C₄×C₂²⋊C₄	—	118	1	no	—
212	#376	—	59	2	no	—
213	#376	—	118	1	no	—
214	C₄³	—	118	1	no	—
215	C₅₉	#8052	1	1	yes	characteristic, complemented, Sylow
216	C₂³×C₄	D₂₃₆	1	1	yes	characteristic
217	C₂³×C₄	D₂₃₆	1	1	yes	characteristic
218	C₂³×C₄	C₂²×D₅₉	1	1	yes	characteristic
219	C₂×M₁₆	C₂×Dic₅₉	1	4	yes	—
220	#117	—	118	8	no	—
221	C₂×C₄⋊C₄	—	118	2	no	—
222	C₂×C₄⋊C₄	—	118	2	no	—
223	C₂×C₂²⋊C₄	—	118	2	no	—
224	C₂×C₂²⋊C₄	—	118	2	no	—
225	C₂×C₄²	—	118	2	no	—
226	C₂×C₄²	—	118	2	no	—
227	C₂×C₄²	—	118	2	no	—
228	C₂×C₄²	—	118	2	no	—
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	C₄×D₅₉	1	1	yes	characteristic
235	C₂×C₄²	C₂×Dic₅₉	1	1	yes	characteristic
236	C₂×C₄²	C₂×Dic₅₉	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	C₂×C₄²	C₂²⋊D₅₉	1	1	yes	characteristic
241	C₄⋊C₈	—	2	2	no	—
242	C₄⋊C₈	—	2	2	no	—
243	C₂²⋊C₈	—	2	2	no	—
244	C₂²⋊C₈	—	2	2	no	—
245	#97	—	2	2	no	—
246	C₄×C₈	—	2	2	no	—
247	#95	—	59	4	no	—
248	#95	—	59	4	no	—
249	#95	—	118	2	no	—
250	#95	—	118	2	no	—
251	#95	—	118	2	no	—
252	#95	—	118	2	no	—
253	C₂⁴	C₂×D₂₃₆	1	1	yes	characteristic
254	C₂²×C₄	—	2	4	no	—
255	C₂²×C₄	—	4	2	no	—
256	C₂²×C₄	—	4	2	no	—
257	C₂²×C₄	—	118	4	no	—
258	C₂²×C₄	—	118	4	no	—
259	C₂²×C₄	C₄⋊Dic₅₉	1	1	yes	characteristic
260	C₂²×C₄	C₄⋊Dic₅₉	1	1	yes	characteristic
261	C₂²×C₄	C₄⋊Dic₅₉	1	1	yes	characteristic
262	C₂²×C₄	C₄⋊Dic₅₉	1	1	yes	characteristic
263	C₂²×C₄	(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
264	C₂²×C₄	(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
265	C₂²×C₄	(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
266	C₂²×C₄	(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
267	C₂²×C₄	(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
268	C₂²×C₄	(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
269	C₂²×C₄	(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
270	C₂²×C₄	(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
271	C₂²×C₄	C₂×Dic₁₁₈	1	1	yes	characteristic
272	C₂²×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
273	C₂²×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
274	C₂²×C₄	C₂²×Dic₅₉	1	1	yes	characteristic
275	C₂²×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
276	C₂²×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
277	M₁₆	—	4	4	no	—
278	C₂×C₈	—	2	4	no	—
279	C₄⋊C₄	—	118	8	no	—
280	C₄⋊C₄	—	236	4	no	—
281	C₂²⋊C₄	—	118	8	no	—
282	C₂²⋊C₄	—	236	4	no	—
283	C₄²	—	118	8	no	—
284	C₄²	—	236	4	no	—
285	C₄²	—	236	4	no	—
286	C₄²	—	236	4	no	—
287	C₄²	C₄×Dic₅₉	1	1	yes	characteristic
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	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	Dic₅₉⋊C₄	1	1	yes	characteristic
297	C₄²	Dic₅₉⋊C₄	1	1	yes	characteristic
298	C₄²	Dic₅₉⋊C₄	1	1	yes	characteristic
299	C₄²	C₂²⋊Dic₅₉	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	C₂³	—	2	2	no	—
304	C₂³	—	2	2	no	—
305	C₂³	—	4	1	no	—
306	C₂³	C₂×(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
307	C₂³	C₂×(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
308	C₂³	C₂×C₄⋊Dic₅₉	1	1	yes	characteristic
309	C₂×C₄	—	2	2	no	—
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	—	4	1	no	—
320	C₂×C₄	—	4	1	no	—
321	C₂×C₄	—	4	1	no	—
322	C₂×C₄	—	4	1	no	—
323	C₂×C₄	—	4	1	no	—
324	C₂×C₄	—	4	1	no	—
325	C₂×C₄	—	4	1	no	—
326	C₂×C₄	—	118	8	no	—
327	C₂×C₄	—	236	4	no	—
328	C₂×C₄	—	236	4	no	—
329	C₂×C₄	—	236	4	no	—
330	C₂×C₄	—	236	4	no	—
331	C₂×C₄	—	236	4	no	—
332	C₂×C₄	C₅₉⋊#95	1	1	yes	characteristic
333	C₂×C₄	C₅₉⋊#95	1	1	yes	characteristic
334	C₂×C₄	C₅₉⋊#95	1	1	yes	characteristic
335	C₂×C₄	C₅₉⋊#95	1	1	yes	characteristic
336	C₂×C₄	C₅₉⋊#95	1	1	yes	characteristic
337	C₂×C₄	C₅₉⋊#95	1	1	yes	characteristic
338	C₂×C₄	C₅₉⋊#95	1	1	yes	characteristic
339	C₂×C₄	C₅₉⋊#95	1	1	yes	characteristic
340	C₂×C₄	#14273653	1	4	yes	—
341	C₂×C₄	C₂×C₄×Dic₅₉	1	1	yes	characteristic
342	C₂×C₄	C₂×C₂²⋊Dic₅₉	1	1	yes	characteristic
343	C₂×C₄	C₂×Dic₅₉⋊C₄	1	1	yes	characteristic
344	C₂×C₄	C₂×Dic₅₉⋊C₄	1	1	yes	characteristic
345	C₈	—	4	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	—	4	4	no	—
354	C₂²	C₂×C₅₉⋊#95	1	1	yes	characteristic
355	C₂²	C₂×#14273653	1	2	yes	—
356	C₂²	#16837418	1	2	yes	—
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	—	2	1	no	—
366	C₄	—	472	4	no	—
367	C₄	—	236	8	no	—
368	C₄	#16837163	1	2	yes	—
369	C₄	#16837163	1	2	yes	—
370	C₄	#16837376	1	2	yes	—
371	C₂	—	2	2	no	—
372	C₂	—	2	2	no	—
373	C₂	—	4	1	no	—
374	C₂	C₂×#16837163	1	1	yes	characteristic
375	C₂	#21423807	1	1	yes	characteristic
376	C₂	#21423829	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×C₂²⋊Dic₅₉
commutator	C₂×C₄×C₅₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₅₉
Fitting	C₅₉×#2920	C₂
socle	C₂²×C₅₉	C₂×#95
prime radical	C₂⁴×C₅₉	C₂×D₄
cosocle	C₂³×C₄×C₅₉	C₂³
hypercenter	#2920	D₅₉
hypocenter	C₅₉	#8052
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂²×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
6. #16837270	C₄	semidirect
7. #16837268	C₄	semidirect
12. C₄×C₄⋊Dic₅₉	C₄	semidirect
17. #16837248	C₄	semidirect
24. C₅₉×#423	C₄	semidirect
26. C₄×M₁₆×C₅₉	C₄	semidirect
199. #423	Dic₅₉	semidirect
201. C₄×M₁₆	Dic₅₉	semidirect
215. C₅₉	#8052	semidirect

Maximal subgroups

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

subgroup	index
#21426494	2
C₄×#14273686	2
#21421981	2
C₅₉×#2920	2
#8052	59