Subgroups — #28478456

Order 15104.

606 conjugacy classes of subgroups.

The subgroup lattice has 382 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	#21426503	C₂	1	1	yes	maximal, characteristic
3	#21421951	C₂	1	4	yes	maximal, complemented
4	C₅₉×#2920	C₂	1	1	yes	maximal, characteristic
5	C₂×#14273686	C₄	1	2	yes	—
6	#16837459	—	2	1	no	—
7	#16837459	C₂²	1	2	yes	—
8	#16837455	—	2	1	no	—
9	#16837455	C₄	1	2	yes	complemented
10	#16837426	C₄	1	2	yes	complemented
11	#16837366	—	2	1	no	—
12	C₄×#11745664	—	2	1	no	—
13	#16837272	—	2	1	no	—
14	#16837268	—	2	1	no	—
15	#16837262	—	2	1	no	—
16	#16837262	—	2	1	no	—
17	C₄×C₄⋊Dic₅₉	C₄	1	2	yes	—
18	C₄×C₄⋊Dic₅₉	C₂²	1	2	yes	—
19	C₂²×C₄²×C₅₉	C₂²	1	1	yes	characteristic
20	C₅₉×#432	C₄	1	2	yes	complemented
21	C₅₉×#432	C₂²	1	2	yes	—
22	C₅₉×#431	—	2	1	no	—
23	C₅₉×#431	—	2	1	no	—
24	C₅₉×#423	—	2	1	no	—
25	C₅₉×#407	—	2	1	no	—
26	C₄×M₁₆×C₅₉	C₄	1	2	yes	complemented
27	C₂×#11745664	—	2	2	no	—
28	#14273686	—	4	4	no	—
29	C₂×C₄⋊Dic₅₉	—	2	2	no	—
30	C₂×C₄⋊Dic₅₉	—	2	2	no	—
31	C₂×C₄⋊Dic₅₉	—	2	2	no	—
32	C₂×C₂²⋊Dic₅₉	—	2	2	no	—
33	C₂×C₄×Dic₅₉	C₂×C₄	1	4	yes	—
34	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
35	C₄⋊(C₅₉⋊C₈)	C₂×C₄	1	4	yes	—
36	C₂²⋊(C₅₉⋊C₈)	—	2	2	no	—
37	C₂²⋊(C₅₉⋊C₈)	—	2	2	no	—
38	#14273638	—	2	2	no	—
39	C₄×C₅₉⋊C₈	—	2	2	no	—
40	C₅₉⋊#95	—	2	2	no	—
41	C₅₉⋊#95	—	2	2	no	—
42	C₂³×C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
43	C₂³×C₄×C₅₉	D₄	1	1	yes	characteristic
44	C₂³×C₄×C₅₉	D₄	1	1	yes	characteristic
45	C₂×M₁₆×C₅₉	—	2	2	no	—
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	D₄	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	Q₈	1	1	yes	characteristic
56	C₂×C₄²×C₅₉	Q₈	1	1	yes	characteristic
57	C₂×C₄²×C₅₉	C₂³	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	C₂×C₄	1	4	yes	—
63	C₄×C₈×C₅₉	—	2	2	no	—
64	C₂⁴×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
65	C₂²×C₄×C₅₉	—	2	2	no	—
66	C₂²×C₄×C₅₉	—	2	2	no	—
67	C₂²×C₄×C₅₉	—	4	2	no	—
68	C₂²×C₄×C₅₉	—	4	2	no	—
69	C₂²×C₄×C₅₉	C₄²	1	1	yes	characteristic
70	C₂²×C₄×C₅₉	C₄²	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	C₂²⋊C₄	1	1	yes	characteristic
77	C₂²×C₄×C₅₉	C₂²⋊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	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
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	C₂²⋊C₄	1	1	yes	characteristic
93	C₄²×C₅₉	C₂²⋊C₄	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	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	C₂×D₄	1	1	yes	characteristic
105	C₄²×C₅₉	C₂×Q₈	1	1	yes	characteristic
106	C₂²⋊Dic₅₉	—	4	4	no	—
107	C₄⋊Dic₅₉	—	4	4	no	—
108	C₄⋊Dic₅₉	—	4	4	no	—
109	C₄⋊Dic₅₉	—	4	4	no	—
110	C₄×Dic₅₉	—	4	4	no	—
111	#11745664	—	4	4	no	—
112	C₂×C₅₉⋊C₈	—	2	4	no	—
113	C₂³×C₅₉	—	2	1	no	—
114	C₂³×C₅₉	—	2	1	no	—
115	C₂³×C₅₉	—	4	1	no	—
116	C₂³×C₅₉	—	4	1	no	—
117	C₂³×C₅₉	#95	1	1	yes	characteristic
118	C₂³×C₅₉	#95	1	1	yes	characteristic
119	C₂³×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
120	C₂×C₄×C₅₉	—	2	1	no	—
121	C₂×C₄×C₅₉	—	2	1	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	—	2	2	no	—
131	C₂×C₄×C₅₉	—	2	2	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	—	4	1	no	—
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	#100	1	2	yes	—
145	C₂×C₄×C₅₉	#101	1	2	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×C₂²⋊C₄	1	1	yes	characteristic
149	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
151	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
152	C₂×Dic₅₉	—	4	4	no	—
153	C₂×Dic₅₉	—	4	4	no	—
154	C₂×Dic₅₉	—	4	4	no	—
155	C₈×C₅₉	—	4	4	no	—
156	C₅₉⋊C₈	—	4	4	no	—
157	#7953	—	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	—	2	1	no	—
166	C₂²×C₅₉	—	4	2	no	—
167	C₂²×C₅₉	—	4	2	no	—
168	C₂²×C₅₉	C₂×#95	1	1	yes	characteristic
169	C₂²×C₅₉	C₂×#100	1	1	yes	characteristic
170	C₂²×C₅₉	C₂×#101	1	1	yes	characteristic
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	—	2	1	no	—
179	C₄×C₅₉	H(3,ℤ/4)	1	2	yes	—
180	C₄×C₅₉	#343	1	2	yes	—
181	C₄×C₅₉	#343	1	2	yes	—
182	C₄×C₅₉	#421	1	2	yes	—
183	Dic₅₉	—	8	4	no	—
184	#2920	—	59	1	no	—
185	#2920	D₅₉	1	1	yes	characteristic
186	#2285	—	59	1	no	—
187	#1285	—	59	4	no	—
188	C₂×C₅₉	—	2	1	no	—
189	C₂×C₅₉	—	2	1	no	—
190	C₂×C₅₉	—	4	1	no	—
191	C₂×C₅₉	—	4	1	no	—
192	C₂×C₅₉	C₂×H(3,ℤ/4)	1	1	yes	characteristic
193	C₂×C₅₉	#1733	1	1	yes	characteristic
194	C₂×C₅₉	C₂×#343	1	1	yes	characteristic
195	C₂×#117	—	59	2	no	—
196	C₂²×C₄²	C₂×D₅₉	1	1	yes	characteristic
197	#432	—	59	2	no	—
198	#432	—	118	1	no	—
199	#432	Dic₅₉	1	2	yes	complemented
200	#432	C₂×D₅₉	1	2	yes	—
201	#431	—	2	1	no	—
202	#431	—	2	1	no	—
203	#431	—	59	2	no	—
204	#431	—	118	1	no	—
205	#423	—	2	1	no	—
206	#423	—	59	2	no	—
207	#407	—	2	1	no	—
208	#407	—	118	1	no	—
209	C₄×M₁₆	—	118	1	no	—
210	C₄×M₁₆	Dic₅₉	1	2	yes	complemented
211	#384	—	118	1	no	—
212	#382	—	118	1	no	—
213	#380	—	118	1	no	—
214	#380	—	118	1	no	—
215	C₄×C₄⋊C₄	—	59	2	no	—
216	C₄×C₄⋊C₄	—	59	2	no	—
217	C₅₉	#7953	1	1	yes	characteristic, complemented, Sylow
218	C₂³×C₄	C₄×D₅₉	1	1	yes	characteristic
219	C₂³×C₄	D₂₃₆	1	1	yes	characteristic
220	C₂³×C₄	C₂²⋊D₅₉	1	1	yes	characteristic
221	C₂×M₁₆	—	2	2	no	—
222	C₂×M₁₆	—	118	2	no	—
223	#117	—	236	4	no	—
224	C₂×C₄⋊C₄	—	118	2	no	—
225	C₂×C₄⋊C₄	—	118	2	no	—
226	C₂×C₄⋊C₄	—	118	2	no	—
227	C₂×C₂²⋊C₄	—	118	2	no	—
228	C₂×C₄²	—	59	4	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	D₂₃₆	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	C₄⋊C₈	—	59	4	no	—
244	C₄⋊C₈	—	118	2	no	—
245	C₂²⋊C₈	—	2	2	no	—
246	C₂²⋊C₈	—	2	2	no	—
247	C₂²⋊C₈	—	118	2	no	—
248	C₂²⋊C₈	—	118	2	no	—
249	#97	—	118	2	no	—
250	#97	C₂×Dic₅₉	1	4	yes	—
251	C₄×C₈	—	2	2	no	—
252	C₄×C₈	—	118	2	no	—
253	#95	—	118	2	no	—
254	#95	—	118	2	no	—
255	C₂⁴	(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
256	C₂²×C₄	—	2	2	no	—
257	C₂²×C₄	—	2	2	no	—
258	C₂²×C₄	—	4	2	no	—
259	C₂²×C₄	—	4	2	no	—
260	C₂²×C₄	—	118	4	no	—
261	C₂²×C₄	C₄×Dic₅₉	1	1	yes	characteristic
262	C₂²×C₄	C₄×Dic₅₉	1	1	yes	characteristic
263	C₂²×C₄	Dic₅₉⋊C₄	1	1	yes	characteristic
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	C₄⋊Dic₅₉	1	1	yes	characteristic
268	C₂²×C₄	C₄⋊Dic₅₉	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×D₅₉)⋊C₄	1	1	yes	characteristic
272	C₂²×C₄	(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
273	C₂²×C₄	(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
274	C₂²×C₄	C₂²⋊Dic₅₉	1	1	yes	characteristic
275	C₂²×C₄	C₂²⋊Dic₅₉	1	1	yes	characteristic
276	C₂²×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
277	C₂²×C₄	C₂×D₂₃₆	1	1	yes	characteristic
278	C₂²×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
279	M₁₆	—	4	4	no	—
280	M₁₆	—	236	4	no	—
281	C₂×C₈	—	2	4	no	—
282	C₂×C₈	—	118	4	no	—
283	C₄⋊C₄	—	236	4	no	—
284	C₄⋊C₄	—	236	4	no	—
285	C₄⋊C₄	—	236	4	no	—
286	C₂²⋊C₄	—	236	4	no	—
287	C₄²	—	236	4	no	—
288	C₄²	C₄×Dic₅₉	1	1	yes	characteristic
289	C₄²	C₄×Dic₅₉	1	1	yes	characteristic
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	C₄⋊Dic₅₉	1	1	yes	characteristic
295	C₄²	C₄⋊Dic₅₉	1	1	yes	characteristic
296	C₄²	(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
297	C₄²	(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
298	C₄²	C₂²⋊Dic₅₉	1	1	yes	characteristic
299	C₄²	C₂²⋊Dic₅₉	1	1	yes	characteristic
300	C₄²	C₂×Dic₁₁₈	1	1	yes	characteristic
301	C₄²	C₂×C₄×D₅₉	1	1	yes	characteristic
302	C₄²	C₂²×Dic₅₉	1	1	yes	characteristic
303	C₄²	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
304	C₂³	—	2	1	no	—
305	C₂³	—	2	1	no	—
306	C₂³	—	4	1	no	—
307	C₂³	—	4	1	no	—
308	C₂³	C₅₉⋊#95	1	1	yes	characteristic
309	C₂³	C₅₉⋊#95	1	1	yes	characteristic
310	C₂³	C₂×(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
311	C₂×C₄	—	2	1	no	—
312	C₂×C₄	—	2	1	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	—	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	#14273643	1	2	yes	—
339	C₂×C₄	#14273645	1	2	yes	—
340	C₂×C₄	C₂×C₄×Dic₅₉	1	1	yes	characteristic
341	C₂×C₄	C₂×(C₂×D₅₉)⋊C₄	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	C₂×C₄	C₂×C₄⋊Dic₅₉	1	1	yes	characteristic
346	C₈	—	4	4	no	—
347	C₈	—	236	4	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	—	2	1	no	—
355	C₂²	—	2	1	no	—
356	C₂²	—	4	2	no	—
357	C₂²	—	4	2	no	—
358	C₂²	C₂×C₅₉⋊#95	1	1	yes	characteristic
359	C₂²	C₂×#14273643	1	1	yes	characteristic
360	C₂²	C₂×#14273645	1	1	yes	characteristic
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	—	2	1	no	—
367	C₄	—	2	1	no	—
368	C₄	—	2	1	no	—
369	C₄	—	472	4	no	—
370	C₄	#16837158	1	2	yes	—
371	C₄	#16837170	1	2	yes	—
372	C₄	#16837170	1	2	yes	—
373	C₄	#16837418	1	2	yes	—
374	C₂	—	2	1	no	—
375	C₂	—	2	1	no	—
376	C₂	—	4	1	no	—
377	C₂	—	4	1	no	—
378	C₂	C₂×#16837158	1	1	yes	characteristic
379	C₂	#21423807	1	1	yes	characteristic
380	C₂	C₂×#16837170	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₅₉⋊#95
commutator	C₂×C₄×C₅₉	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₅₉
Fitting	C₅₉×#2920	C₂
socle	C₂²×C₅₉	C₂×#95
prime radical	C₂⁴×C₅₉	C₂²⋊C₄
cosocle	C₂×C₄²×C₅₉	C₂³
hypercenter	#2920	D₅₉
hypocenter	C₅₉	#7953
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄² ◁ #2920

Complements

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

N	H ≅ G/N	type
3. #21421951	C₂	semidirect
9. #16837455	C₄	semidirect
10. #16837426	C₄	semidirect
20. C₅₉×#432	C₄	semidirect
26. C₄×M₁₆×C₅₉	C₄	semidirect
199. #432	Dic₅₉	semidirect
210. C₄×M₁₆	Dic₅₉	semidirect
217. C₅₉	#7953	semidirect

Maximal subgroups

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

subgroup	index
#21432729	2
#21426503	2
#21421951	2
C₅₉×#2920	2
#7953	59