Subgroups — #28478366

Order 15104.

666 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16837459	C₂	1	1	yes	maximal, characteristic
2	C₂×#16837459	C₂	1	1	yes	maximal, characteristic
3	#21421944	C₂	1	4	yes	maximal
4	C₄×#117×C₅₉	C₂	1	1	yes	maximal, characteristic
5	#16837459	—	2	1	no	—
6	#16837459	—	2	1	no	—
7	#16837459	—	2	1	no	—
8	#16837459	—	2	1	no	—
9	#16837459	—	2	1	no	—
10	#16837459	—	2	1	no	—
11	#16837459	C₄	1	2	yes	complemented
12	#16837459	C₄	1	2	yes	complemented
13	C₂×C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
14	C₂×C₄⋊(C₅₉⋊C₈)	C₄	1	2	yes	complemented
15	C₂×C₂²⋊(C₅₉⋊C₈)	C₂²	1	2	yes	—
16	C₂×C₂²⋊(C₅₉⋊C₈)	C₂²	1	2	yes	—
17	C₂×#14273638	—	2	1	no	—
18	C₂×#14273638	C₄	1	2	yes	complemented
19	C₂×#117×C₅₉	C₄	1	2	yes	—
20	C₂²×C₄²×C₅₉	C₂²	1	1	yes	characteristic
21	C₄×C₄⋊C₄×C₅₉	—	2	1	no	—
22	C₄×C₄⋊C₄×C₅₉	—	2	1	no	—
23	C₄×C₂²⋊C₄×C₅₉	C₄	1	2	yes	—
24	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
25	C₅₉×#376	—	2	1	no	—
26	C₄³×C₅₉	—	2	1	no	—
27	C₂²×C₅₉⋊C₈	—	2	2	no	—
28	C₂²×C₅₉⋊C₈	C₂×C₄	1	4	yes	—
29	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
30	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
31	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
32	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
33	C₂²⋊(C₅₉⋊C₈)	—	2	2	no	—
34	C₂²⋊(C₅₉⋊C₈)	—	2	2	no	—
35	C₂²⋊(C₅₉⋊C₈)	—	2	2	no	—
36	C₂²⋊(C₅₉⋊C₈)	C₂×C₄	1	4	yes	—
37	#14273638	—	2	2	no	—
38	#14273638	—	2	2	no	—
39	#14273638	—	2	2	no	—
40	#14273638	—	2	2	no	—
41	C₂³×C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
42	C₂³×C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
43	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
44	#117×C₅₉	—	2	8	no	—
45	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
46	C₂×C₂²⋊C₄×C₅₉	C₂×C₄	1	4	yes	—
47	C₂×C₄²×C₅₉	—	2	2	no	—
48	C₂×C₄²×C₅₉	—	2	2	no	—
49	C₂×C₄²×C₅₉	—	2	2	no	—
50	C₂×C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
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	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	#95×C₅₉	—	2	2	no	—
63	#95×C₅₉	—	2	2	no	—
64	C₂⁴×C₅₉	C₂²×C₄	1	1	yes	characteristic
65	C₂²×C₄×C₅₉	—	2	4	no	—
66	C₂²×C₄×C₅₉	—	2	4	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	C₄²	1	1	yes	characteristic
72	C₂²×C₄×C₅₉	C₄²	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	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	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×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₅₉	C₂×Q₈	1	1	yes	characteristic
87	C₄⋊C₄×C₅₉	—	2	8	no	—
88	C₂²⋊C₄×C₅₉	—	2	4	no	—
89	C₂²⋊C₄×C₅₉	M₁₆	1	8	yes	—
90	C₄²×C₅₉	—	2	8	no	—
91	C₄²×C₅₉	—	4	4	no	—
92	C₄²×C₅₉	—	4	4	no	—
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	C₂²⋊C₄	1	1	yes	characteristic
97	C₄²×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
98	C₄²×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
99	C₄²×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
100	C₄²×C₅₉	C₂²⋊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	C₄²×C₅₉	C₄⋊C₄	1	1	yes	characteristic
107	C₄²×C₅₉	C₄⋊C₄	1	1	yes	characteristic
108	C₄²×C₅₉	C₄⋊C₄	1	1	yes	characteristic
109	C₂×C₅₉⋊C₈	—	2	4	no	—
110	C₂×C₅₉⋊C₈	—	2	4	no	—
111	C₂×C₅₉⋊C₈	—	4	4	no	—
112	C₂×C₅₉⋊C₈	—	4	4	no	—
113	C₂³×C₅₉	—	4	1	no	—
114	C₂³×C₅₉	—	4	1	no	—
115	C₂³×C₅₉	C₂×C₄²	1	1	yes	characteristic
116	C₂³×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
117	C₂³×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
118	C₂³×C₅₉	C₂×M₁₆	1	4	yes	—
119	C₂×C₄×C₅₉	—	2	2	no	—
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	—	2	2	no	—
131	C₂×C₄×C₅₉	—	2	8	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	—	4	4	no	—
139	C₂×C₄×C₅₉	—	4	4	no	—
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	#95	1	1	yes	characteristic
146	C₂×C₄×C₅₉	#95	1	1	yes	characteristic
147	C₂×C₄×C₅₉	#95	1	1	yes	characteristic
148	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
149	C₂×C₄×C₅₉	C₂×C₂²⋊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	C₅₉⋊C₈	—	4	4	no	—
153	C₅₉⋊C₈	—	4	4	no	—
154	#7930	—	59	1	no	maximal, Sylow
155	C₂²×C₅₉	—	2	1	no	—
156	C₂²×C₅₉	—	2	1	no	—
157	C₂²×C₅₉	—	2	1	no	—
158	C₂²×C₅₉	—	2	1	no	—
159	C₂²×C₅₉	—	2	1	no	—
160	C₂²×C₅₉	—	2	1	no	—
161	C₂²×C₅₉	—	4	4	no	—
162	C₂²×C₅₉	C₂×#95	1	1	yes	characteristic
163	C₂²×C₅₉	C₄×M₁₆	1	2	yes	—
164	C₂²×C₅₉	#407	1	2	yes	—
165	C₂²×C₅₉	#423	1	2	yes	—
166	C₄×C₅₉	—	2	1	no	—
167	C₄×C₅₉	—	2	1	no	—
168	C₄×C₅₉	—	2	1	no	—
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	—	4	8	no	—
177	C₄×C₅₉	#344	1	2	yes	—
178	C₄×C₅₉	#410	1	2	yes	—
179	C₂×#432	—	59	1	no	—
180	C₂×#432	—	59	1	no	—
181	C₄×#117	D₅₉	1	1	yes	characteristic
182	#1282	—	59	4	no	—
183	C₂×C₅₉	—	2	2	no	—
184	C₂×C₅₉	—	2	2	no	—
185	C₂×C₅₉	—	2	2	no	—
186	C₂×C₅₉	#1728	1	1	yes	characteristic
187	C₂×C₅₉	#1740	1	1	yes	characteristic
188	C₂×C₅₉	C₂×#344	1	1	yes	characteristic
189	C₂×#117	Dic₅₉	1	2	yes	—
190	C₂²×C₄²	C₂×D₅₉	1	1	yes	characteristic
191	#432	—	59	2	no	—
192	#432	—	59	2	no	—
193	#432	—	118	1	no	—
194	#432	—	118	1	no	—
195	#432	—	118	1	no	—
196	#432	—	118	1	no	—
197	#432	—	118	1	no	—
198	#432	—	118	1	no	—
199	C₂×C₄⋊C₈	—	59	2	no	—
200	C₂×C₄⋊C₈	—	118	1	no	—
201	C₂×C₂²⋊C₈	—	59	2	no	—
202	C₂×C₂²⋊C₈	—	59	2	no	—
203	C₂×#97	—	59	2	no	—
204	C₂×#97	—	118	1	no	—
205	C₄×C₄⋊C₄	—	2	1	no	—
206	C₄×C₄⋊C₄	—	2	1	no	—
207	C₄×C₂²⋊C₄	Dic₅₉	1	2	yes	—
208	C₄×C₂²⋊C₄	C₂×D₅₉	1	2	yes	—
209	#376	—	2	1	no	—
210	C₄³	—	2	1	no	—
211	C₅₉	#7930	1	1	yes	characteristic, complemented, Sylow
212	C₂³×C₄	C₂×Dic₅₉	1	1	yes	characteristic
213	C₂³×C₄	C₂×Dic₅₉	1	1	yes	characteristic
214	C₂³×C₄	C₂²×D₅₉	1	1	yes	characteristic
215	C₂²×C₈	—	59	4	no	—
216	C₂²×C₈	—	118	2	no	—
217	#117	—	2	8	no	—
218	C₂×C₄⋊C₄	—	2	2	no	—
219	C₂×C₂²⋊C₄	C₂×Dic₅₉	1	4	yes	—
220	C₂×C₄²	—	2	2	no	—
221	C₂×C₄²	—	2	2	no	—
222	C₂×C₄²	—	2	2	no	—
223	C₂×C₄²	Dic₁₁₈	1	1	yes	characteristic
224	C₂×C₄²	Dic₁₁₈	1	1	yes	characteristic
225	C₂×C₄²	C₄×D₅₉	1	1	yes	characteristic
226	C₂×C₄²	C₄×D₅₉	1	1	yes	characteristic
227	C₂×C₄²	C₄×D₅₉	1	1	yes	characteristic
228	C₂×C₄²	C₄×D₅₉	1	1	yes	characteristic
229	C₂×C₄²	D₂₃₆	1	1	yes	characteristic
230	C₂×C₄²	D₂₃₆	1	1	yes	characteristic
231	C₂×C₄²	C₂²⋊D₅₉	1	1	yes	characteristic
232	C₂×C₄²	C₂²⋊D₅₉	1	1	yes	characteristic
233	C₂×C₄²	C₂²⋊D₅₉	1	1	yes	characteristic
234	C₂×C₄²	C₂²⋊D₅₉	1	1	yes	characteristic
235	C₄⋊C₈	—	118	2	no	—
236	C₄⋊C₈	—	118	2	no	—
237	C₄⋊C₈	—	118	2	no	—
238	C₄⋊C₈	—	118	2	no	—
239	C₂²⋊C₈	—	59	4	no	—
240	C₂²⋊C₈	—	118	2	no	—
241	C₂²⋊C₈	—	118	2	no	—
242	C₂²⋊C₈	—	118	2	no	—
243	#97	—	118	2	no	—
244	#97	—	118	2	no	—
245	#97	—	118	2	no	—
246	#97	—	118	2	no	—
247	#95	—	2	2	no	—
248	#95	—	2	2	no	—
249	C₂⁴	C₂²×Dic₅₉	1	1	yes	characteristic
250	C₂²×C₄	—	2	4	no	—
251	C₂²×C₄	—	2	4	no	—
252	C₂²×C₄	—	4	2	no	—
253	C₂²×C₄	—	4	2	no	—
254	C₂²×C₄	C₄×Dic₅₉	1	1	yes	characteristic
255	C₂²×C₄	C₄×Dic₅₉	1	1	yes	characteristic
256	C₂²×C₄	C₄×Dic₅₉	1	1	yes	characteristic
257	C₂²×C₄	C₄×Dic₅₉	1	1	yes	characteristic
258	C₂²×C₄	C₄⋊Dic₅₉	1	1	yes	characteristic
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	C₂²⋊Dic₅₉	1	1	yes	characteristic
263	C₂²×C₄	C₂²⋊Dic₅₉	1	1	yes	characteristic
264	C₂²×C₄	C₂²⋊Dic₅₉	1	1	yes	characteristic
265	C₂²×C₄	C₂²⋊Dic₅₉	1	1	yes	characteristic
266	C₂²×C₄	C₂×Dic₁₁₈	1	1	yes	characteristic
267	C₂²×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
268	C₂²×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
269	C₂²×C₄	C₂×D₂₃₆	1	1	yes	characteristic
270	C₂²×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
271	C₂²×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
272	C₂×C₈	—	118	4	no	—
273	C₂×C₈	—	118	4	no	—
274	C₂×C₈	—	236	4	no	—
275	C₂×C₈	—	236	4	no	—
276	C₄⋊C₄	—	2	8	no	—
277	C₂²⋊C₄	—	2	4	no	—
278	C₂²⋊C₄	#11745664	1	8	yes	—
279	C₄²	—	2	8	no	—
280	C₄²	—	4	4	no	—
281	C₄²	—	4	4	no	—
282	C₄²	Dic₅₉⋊C₄	1	1	yes	characteristic
283	C₄²	Dic₅₉⋊C₄	1	1	yes	characteristic
284	C₄²	Dic₅₉⋊C₄	1	1	yes	characteristic
285	C₄²	Dic₅₉⋊C₄	1	1	yes	characteristic
286	C₄²	Dic₅₉⋊C₄	1	1	yes	characteristic
287	C₄²	Dic₅₉⋊C₄	1	1	yes	characteristic
288	C₄²	Dic₅₉⋊C₄	1	1	yes	characteristic
289	C₄²	Dic₅₉⋊C₄	1	1	yes	characteristic
290	C₄²	(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
291	C₄²	(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
292	C₄²	(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
293	C₄²	(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
294	C₄²	(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
295	C₄²	(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
296	C₄²	(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
297	C₄²	(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
298	C₂³	—	4	1	no	—
299	C₂³	—	4	1	no	—
300	C₂³	C₂×C₄×Dic₅₉	1	1	yes	characteristic
301	C₂³	C₂×C₂²⋊Dic₅₉	1	1	yes	characteristic
302	C₂³	C₂×C₄⋊Dic₅₉	1	1	yes	characteristic
303	C₂³	C₂×#11745664	1	4	yes	—
304	C₂×C₄	—	2	2	no	—
305	C₂×C₄	—	2	2	no	—
306	C₂×C₄	—	2	2	no	—
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	2	no	—
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	8	no	—
317	C₂×C₄	—	4	1	no	—
318	C₂×C₄	—	4	1	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	4	no	—
324	C₂×C₄	—	4	4	no	—
325	C₂×C₄	C₅₉⋊#95	1	1	yes	characteristic
326	C₂×C₄	C₅₉⋊#95	1	1	yes	characteristic
327	C₂×C₄	C₅₉⋊#95	1	1	yes	characteristic
328	C₂×C₄	C₅₉⋊#95	1	1	yes	characteristic
329	C₂×C₄	C₅₉⋊#95	1	1	yes	characteristic
330	C₂×C₄	C₅₉⋊#95	1	1	yes	characteristic
331	C₂×C₄	C₅₉⋊#95	1	1	yes	characteristic
332	C₂×C₄	C₅₉⋊#95	1	1	yes	characteristic
333	C₂×C₄	C₂×(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
334	C₂×C₄	C₂×(C₂×D₅₉)⋊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	C₈	—	236	4	no	—
338	C₈	—	236	4	no	—
339	C₂²	—	2	1	no	—
340	C₂²	—	2	1	no	—
341	C₂²	—	2	1	no	—
342	C₂²	—	2	1	no	—
343	C₂²	—	2	1	no	—
344	C₂²	—	2	1	no	—
345	C₂²	—	4	4	no	—
346	C₂²	C₂×C₅₉⋊#95	1	1	yes	characteristic
347	C₂²	C₄×#11745664	1	2	yes	—
348	C₂²	#16837366	1	2	yes	—
349	C₂²	#16837426	1	2	yes	—
350	C₄	—	2	1	no	—
351	C₄	—	2	1	no	—
352	C₄	—	2	1	no	—
353	C₄	—	2	1	no	—
354	C₄	—	2	1	no	—
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	—	4	8	no	—
361	C₄	#16837172	1	2	yes	—
362	C₄	#16837375	1	2	yes	—
363	C₂	—	2	2	no	—
364	C₂	—	2	2	no	—
365	C₂	—	2	2	no	—
366	C₂	#21423790	1	1	yes	characteristic
367	C₂	#21423828	1	1	yes	characteristic
368	C₂	C₂×#16837172	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×(C₂×D₅₉)⋊C₄
commutator	C₂³×C₅₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₅₉
Fitting	C₄×#117×C₅₉	C₂
socle	C₂²×C₅₉	C₂×#95
prime radical	C₂⁴×C₅₉	C₂²×C₄
cosocle	C₂³×C₄×C₅₉	C₂³
hypercenter	C₄×#117	D₅₉
hypocenter	C₅₉	#7930
LCS	G ▷ C₂³×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄² ◁ C₄×#117

Complements

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

N	H ≅ G/N	type
11. #16837459	C₄	semidirect
12. #16837459	C₄	semidirect
14. C₂×C₄⋊(C₅₉⋊C₈)	C₄	semidirect
18. C₂×#14273638	C₄	semidirect
211. C₅₉	#7930	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16837459	2
#21421944	2
C₄×#117×C₅₉	2
#7930	59