Subgroups — C₂×#21437198 #29495157

Order 15104.

2074 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#14273733	C₂	1	1	yes	maximal, characteristic
2	#21437198	C₂	1	16	yes	maximal, direct product factor
3	C₂×#16837820	C₂	1	4	yes	maximal, complemented
4	C₂×#16837818	C₂	1	4	yes	maximal, complemented
5	C₂²×#14273667	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×M₃₂×D₅₉	C₂	1	4	yes	maximal, complemented
7	C₂²×M₃₂×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#11745685	C₄	1	1	yes	characteristic
9	C₂×#14273733	C₄	1	2	yes	—
10	C₂×#14273733	C₄	1	2	yes	—
11	C₂×#14273733	C₄	1	8	yes	—
12	C₂×#14273733	C₂²	1	2	yes	—
13	C₂×#14273733	C₂²	1	2	yes	—
14	C₂×#14273733	C₂²	1	8	yes	—
15	C₂²×#11745664	C₄	1	1	yes	characteristic
16	C₂²×#11745659	C₄	1	2	yes	—
17	C₂²×C₈×D₅₉	C₂²	1	2	yes	—
18	#16837820	C₂²	1	32	yes	complemented
19	#16837818	C₂²	1	32	yes	complemented
20	C₂×#14273667	C₂²	1	2	yes	—
21	C₂×#14273667	C₂²	1	2	yes	complemented
22	C₂×#14273667	C₂²	1	8	yes	complemented
23	C₂×#14273666	C₂²	1	8	yes	complemented
24	M₃₂×D₅₉	C₂²	1	32	yes	complemented
25	C₂²×C₅₉⋊C₁₆	C₂²	1	2	yes	complemented
26	C₂×C₁₆×D₅₉	C₂²	1	8	yes	complemented
27	C₂³×C₈×C₅₉	C₂²	1	1	yes	characteristic
28	C₂×M₃₂×C₅₉	C₂²	1	2	yes	—
29	C₂×M₃₂×C₅₉	C₂²	1	2	yes	complemented
30	C₂×M₃₂×C₅₉	C₂²	1	8	yes	complemented
31	C₂²×C₁₆×C₅₉	C₂²	1	2	yes	complemented
32	C₂×#11745685	C₈	1	2	yes	—
33	C₂×#11745685	C₈	1	2	yes	—
34	C₂×#11745685	C₈	1	8	yes	—
35	C₂×#11745685	C₂×C₄	1	2	yes	—
36	C₂×#11745685	C₂×C₄	1	2	yes	—
37	C₂×#11745685	C₂×C₄	1	8	yes	—
38	C₂²×Dic₁₁₈	C₈	1	1	yes	characteristic
39	C₂²×D₂₃₆	C₈	1	1	yes	characteristic
40	C₂²×C₂²⋊D₅₉	C₈	1	2	yes	—
41	C₂²×C₄×D₅₉	C₂×C₄	1	2	yes	—
42	#14273733	C₂×C₄	1	8	yes	—
43	#14273733	C₂×C₄	1	8	yes	—
44	#14273733	C₂×C₄	1	16	yes	—
45	#14273733	C₂×C₄	1	16	yes	—
46	#14273733	C₂³	1	8	yes	—
47	#14273733	C₂³	1	8	yes	—
48	C₂×#11745664	C₂×C₄	1	2	yes	—
49	C₂×#11745664	C₂×C₄	1	2	yes	—
50	C₂×#11745664	C₂×C₄	1	8	yes	—
51	C₂×#11745659	C₂×C₄	1	4	yes	—
52	C₂×#11745659	C₂×C₄	1	4	yes	—
53	C₂×#11745659	C₂×C₄	1	16	yes	—
54	C₂²×C₅₉⋊C₈	C₂×C₄	1	2	yes	—
55	C₂×C₈×D₅₉	C₂×C₄	1	8	yes	—
56	C₂×C₈×D₅₉	C₂×C₄	1	4	yes	—
57	C₂×C₈×D₅₉	C₂³	1	4	yes	—
58	C₂×C₈×D₅₉	C₂³	1	8	yes	—
59	#14273667	C₂³	1	8	yes	—
60	#14273667	C₂³	1	8	yes	complemented
61	#14273666	C₂³	1	32	yes	complemented
62	C₂×C₅₉⋊C₁₆	C₂³	1	4	yes	—
63	C₂×C₅₉⋊C₁₆	C₂³	1	8	yes	complemented
64	C₁₆×D₅₉	C₂³	1	32	yes	complemented
65	C₂³×C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
66	C₂²×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
67	C₂²×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
68	C₂²×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
69	C₂²×C₈×C₅₉	C₂×C₄	1	4	yes	—
70	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
73	C₂²×C₈×C₅₉	C₂³	1	4	yes	—
74	M₃₂×C₅₉	C₂³	1	8	yes	—
75	M₃₂×C₅₉	C₂³	1	8	yes	complemented
76	C₂×C₁₆×C₅₉	C₂³	1	4	yes	—
77	C₂×C₁₆×C₅₉	C₂³	1	8	yes	complemented
78	C₂⁴×C₅₉	C₂×C₈	1	1	yes	characteristic
79	C₂³×D₅₉	C₂×C₈	1	2	yes	—
80	C₂²×C₄×C₅₉	C₂×C₈	1	1	yes	characteristic
81	C₂²×C₄×C₅₉	C₂×C₈	1	1	yes	characteristic
82	C₂²×C₄×C₅₉	C₂×C₈	1	1	yes	characteristic
83	C₂²×C₄×C₅₉	C₂×C₈	1	4	yes	—
84	C₂²×C₄×C₅₉	C₂²×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	4	yes	—
88	C₂×C₂²⋊D₅₉	C₂×C₈	1	4	yes	—
89	C₂×C₂²⋊D₅₉	C₂×C₈	1	4	yes	—
90	C₂×C₂²⋊D₅₉	C₂×C₈	1	16	yes	—
91	C₂²×Dic₅₉	C₂×C₈	1	2	yes	—
92	#11745685	C₂×C₈	1	8	yes	—
93	#11745685	C₂×C₈	1	8	yes	—
94	#11745685	C₂×C₈	1	16	yes	—
95	#11745685	C₂×C₈	1	16	yes	—
96	#11745685	C₂²×C₄	1	8	yes	—
97	#11745685	C₂²×C₄	1	8	yes	—
98	C₂×D₂₃₆	C₂×C₈	1	2	yes	—
99	C₂×D₂₃₆	C₂×C₈	1	2	yes	—
100	C₂×D₂₃₆	C₂×C₈	1	8	yes	—
101	C₂×C₄×D₅₉	C₂×C₈	1	4	yes	—
102	C₂×C₄×D₅₉	C₂×C₈	1	8	yes	—
103	C₂×C₄×D₅₉	C₂²×C₄	1	4	yes	—
104	C₂×C₄×D₅₉	C₂²×C₄	1	8	yes	—
105	C₂×Dic₁₁₈	C₂×C₈	1	8	yes	—
106	C₂×Dic₁₁₈	C₂×C₈	1	2	yes	—
107	C₂×Dic₁₁₈	C₂×C₈	1	2	yes	—
108	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₈×C₅₉	C₂²×C₄	1	2	yes	—
110	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
111	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₈×C₅₉	C₂²×C₄	1	4	yes	—
113	C₂×C₈×C₅₉	C₂²×C₄	1	2	yes	—
114	C₂×C₈×C₅₉	C₂²×C₄	1	2	yes	—
115	C₂×C₈×C₅₉	C₂²×C₄	1	4	yes	—
116	C₂×C₈×C₅₉	C₂²×C₄	1	4	yes	—
117	C₂×C₈×C₅₉	C₂⁴	1	2	yes	—
118	C₂×C₈×C₅₉	C₂⁴	1	2	yes	—
119	C₂×C₈×C₅₉	C₂⁴	1	2	yes	—
120	C₂×C₈×C₅₉	C₂⁴	1	1	yes	characteristic
121	#11745664	C₂²×C₄	1	8	yes	—
122	#11745664	C₂²×C₄	1	8	yes	—
123	C₂×C₅₉⋊C₈	C₂²×C₄	1	4	yes	—
124	C₂×C₅₉⋊C₈	C₂²×C₄	1	8	yes	—
125	#11745659	C₂²×C₄	1	16	yes	—
126	#11745659	C₂²×C₄	1	16	yes	—
127	C₈×D₅₉	C₂²×C₄	1	8	yes	—
128	C₈×D₅₉	C₂²×C₄	1	16	yes	—
129	C₈×D₅₉	C₂⁴	1	8	yes	—
130	C₁₆×C₅₉	C₂⁴	1	8	yes	—
131	C₅₉⋊C₁₆	C₂⁴	1	8	yes	—
132	C₂³×C₅₉	—	4	2	no	—
133	C₂³×C₅₉	C₂²×C₈	1	1	yes	characteristic
134	C₂³×C₅₉	C₂²×C₈	1	1	yes	characteristic
135	C₂³×C₅₉	C₂²×C₈	1	1	yes	characteristic
136	C₂³×C₅₉	C₂²×C₈	1	4	yes	—
137	C₂²×D₅₉	—	4	4	no	—
138	C₂²×D₅₉	C₂²×C₈	1	4	yes	—
139	C₂²×D₅₉	C₂²×C₈	1	8	yes	—
140	C₂×C₄×C₅₉	C₂²×C₈	1	4	yes	—
141	C₂×C₄×C₅₉	C₂²×C₈	1	1	yes	characteristic
142	C₂×C₄×C₅₉	C₂²×C₈	1	1	yes	characteristic
143	C₂×C₄×C₅₉	C₂²×C₈	1	2	yes	—
144	C₂×C₄×C₅₉	C₂²×C₈	1	1	yes	characteristic
145	C₂×C₄×C₅₉	C₂²×C₈	1	4	yes	—
146	C₂×C₄×C₅₉	C₂²×C₈	1	4	yes	—
147	C₂×C₄×C₅₉	C₂²×C₈	1	2	yes	—
148	C₂×C₄×C₅₉	C₂²×C₈	1	2	yes	—
149	C₂×C₄×C₅₉	C₂³×C₄	1	2	yes	—
150	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
151	C₂×C₄×C₅₉	C₂³×C₄	1	2	yes	—
152	C₂×C₄×C₅₉	C₂³×C₄	1	2	yes	—
153	C₂²⋊D₅₉	C₂²×C₈	1	16	yes	—
154	C₂²⋊D₅₉	C₂²×C₈	1	16	yes	—
155	C₂×Dic₅₉	C₂²×C₈	1	8	yes	—
156	C₂×Dic₅₉	C₂²×C₈	1	4	yes	—
157	D₂₃₆	C₂²×C₈	1	8	yes	—
158	D₂₃₆	C₂²×C₈	1	8	yes	—
159	C₄×D₅₉	C₂²×C₈	1	16	yes	—
160	C₄×D₅₉	C₂²×C₈	1	8	yes	—
161	C₄×D₅₉	C₂³×C₄	1	8	yes	—
162	Dic₁₁₈	C₂²×C₈	1	8	yes	—
163	Dic₁₁₈	C₂²×C₈	1	8	yes	—
164	C₈×C₅₉	C₂³×C₄	1	2	yes	—
165	C₈×C₅₉	C₂³×C₄	1	1	yes	characteristic
166	C₈×C₅₉	C₂³×C₄	1	2	yes	—
167	C₈×C₅₉	C₂³×C₄	1	2	yes	—
168	C₈×C₅₉	C₂⁵	1	1	yes	characteristic
169	C₅₉⋊C₈	C₂³×C₄	1	8	yes	—
170	C₂×#3407	—	59	1	no	maximal, Sylow
171	C₂²×C₅₉	—	2	2	no	—
172	C₂²×C₅₉	—	2	2	no	—
173	C₂²×C₅₉	—	2	2	no	—
174	C₂²×C₅₉	—	4	4	no	—
175	C₂²×C₅₉	C₂³×C₈	1	2	yes	—
176	C₂²×C₅₉	C₂³×C₈	1	2	yes	—
177	C₂²×C₅₉	C₂³×C₈	1	2	yes	—
178	C₂²×C₅₉	C₂³×C₈	1	1	yes	characteristic
179	C₂×D₅₉	—	2	8	no	—
180	C₂×D₅₉	—	4	8	no	—
181	C₂×D₅₉	C₂³×C₈	1	8	yes	—
182	C₄×C₅₉	C₂³×C₈	1	2	yes	—
183	C₄×C₅₉	C₂³×C₈	1	2	yes	—
184	C₄×C₅₉	C₂³×C₈	1	2	yes	—
185	C₄×C₅₉	C₂³×C₈	1	1	yes	characteristic
186	C₄×C₅₉	C₂⁴×C₄	1	1	yes	characteristic
187	Dic₅₉	C₂³×C₈	1	8	yes	—
188	C₂²×#131	—	59	1	no	—
189	#3407	—	59	16	no	—
190	C₂×#504	—	59	4	no	—
191	C₂×#504	—	59	4	no	—
192	C₂²×M₃₂	—	59	4	no	—
193	C₂²×M₃₂	—	59	1	no	—
194	C₂²×M₃₂	D₅₉	1	1	yes	characteristic, complemented
195	C₂×C₅₉	—	2	2	no	—
196	C₂×C₅₉	—	2	2	no	—
197	C₂×C₅₉	—	2	2	no	—
198	C₂×C₅₉	#3407	1	2	yes	complemented
199	C₂×C₅₉	C₂⁴×C₈	1	1	yes	characteristic
200	D₅₉	—	2	8	no	—
201	C₂²×#41	—	59	1	no	—
202	C₂×#131	—	59	2	no	—
203	C₂×#131	—	59	2	no	—
204	C₂×#131	—	59	8	no	—
205	C₂×#131	—	59	2	no	—
206	C₂×#131	—	59	2	no	—
207	C₂×#131	—	59	8	no	—
208	C₂²×M₁₆	—	59	1	no	—
209	C₂²×M₁₆	—	59	2	no	—
210	C₂³×C₈	—	59	2	no	—
211	C₂³×C₈	C₂×D₅₉	1	1	yes	characteristic
212	#504	—	59	32	no	—
213	#504	—	59	32	no	—
214	C₂×M₃₂	—	59	2	no	—
215	C₂×M₃₂	—	59	2	no	—
216	C₂×M₃₂	—	59	8	no	—
217	C₂×M₃₂	—	59	32	no	—
218	C₂×M₃₂	—	59	8	no	—
219	C₂×M₃₂	C₂×D₅₉	1	2	yes	—
220	C₂×M₃₂	C₂×D₅₉	1	2	yes	complemented
221	C₂×M₃₂	C₂×D₅₉	1	8	yes	complemented
222	C₂²×C₁₆	—	59	2	no	—
223	C₂²×C₁₆	—	59	8	no	—
224	C₂²×C₁₆	C₂×D₅₉	1	2	yes	complemented
225	C₅₉	C₂×#3407	1	1	yes	characteristic, complemented, Sylow
226	C₂×#41	—	59	2	no	—
227	C₂×#41	—	59	2	no	—
228	C₂×#41	—	59	8	no	—
229	C₂×#41	—	59	2	no	—
230	C₂×#41	—	59	2	no	—
231	C₂×#41	—	59	8	no	—
232	C₂²×Q₈	—	59	1	no	—
233	C₂²×D₄	—	59	2	no	—
234	C₂²×D₄	—	59	1	no	—
235	C₂³×C₄	—	59	2	no	—
236	C₂³×C₄	C₄×D₅₉	1	1	yes	characteristic
237	#131	—	59	8	no	—
238	#131	—	59	8	no	—
239	#131	—	59	16	no	—
240	#131	—	59	16	no	—
241	#131	—	59	8	no	—
242	#131	—	59	8	no	—
243	C₂×M₁₆	—	59	2	no	—
244	C₂×M₁₆	—	59	2	no	—
245	C₂×M₁₆	—	59	8	no	—
246	C₂×M₁₆	—	59	4	no	—
247	C₂×M₁₆	—	59	4	no	—
248	C₂×M₁₆	—	59	16	no	—
249	C₂²×C₈	—	59	2	no	—
250	C₂²×C₈	—	59	8	no	—
251	C₂²×C₈	—	59	4	no	—
252	C₂²×C₈	—	59	8	no	—
253	C₂²×C₈	—	59	4	no	—
254	C₂²×C₈	C₄×D₅₉	1	1	yes	characteristic
255	C₂²×C₈	C₄×D₅₉	1	1	yes	characteristic
256	C₂²×C₈	C₄×D₅₉	1	1	yes	characteristic
257	C₂²×C₈	C₄×D₅₉	1	4	yes	—
258	C₂²×C₈	C₂²×D₅₉	1	4	yes	—
259	C₂²×C₈	C₂²×D₅₉	1	1	yes	characteristic
260	C₂²×C₈	C₂²×D₅₉	1	1	yes	characteristic
261	C₂²×C₈	C₂²×D₅₉	1	1	yes	characteristic
262	M₃₂	—	59	8	no	—
263	M₃₂	—	59	8	no	—
264	M₃₂	—	59	32	no	—
265	M₃₂	C₂²×D₅₉	1	8	yes	—
266	M₃₂	C₂²×D₅₉	1	8	yes	complemented
267	C₂×C₁₆	—	59	8	no	—
268	C₂×C₁₆	—	59	4	no	—
269	C₂×C₁₆	—	59	32	no	—
270	C₂×C₁₆	C₂²×D₅₉	1	4	yes	—
271	C₂×C₁₆	C₂²×D₅₉	1	8	yes	complemented
272	C₂⁴	—	59	2	no	—
273	C₂⁴	C₈×D₅₉	1	1	yes	characteristic
274	#41	—	59	8	no	—
275	#41	—	59	8	no	—
276	#41	—	59	16	no	—
277	#41	—	59	16	no	—
278	#41	—	59	8	no	—
279	#41	—	59	8	no	—
280	C₂×Q₈	—	59	8	no	—
281	C₂×Q₈	—	59	2	no	—
282	C₂×Q₈	—	59	2	no	—
283	C₂×D₄	—	59	4	no	—
284	C₂×D₄	—	59	4	no	—
285	C₂×D₄	—	59	16	no	—
286	C₂×D₄	—	59	2	no	—
287	C₂×D₄	—	59	2	no	—
288	C₂×D₄	—	59	8	no	—
289	C₂²×C₄	—	59	2	no	—
290	C₂²×C₄	—	59	4	no	—
291	C₂²×C₄	—	59	8	no	—
292	C₂²×C₄	—	59	8	no	—
293	C₂²×C₄	—	59	4	no	—
294	C₂²×C₄	C₈×D₅₉	1	1	yes	characteristic
295	C₂²×C₄	C₈×D₅₉	1	1	yes	characteristic
296	C₂²×C₄	C₈×D₅₉	1	1	yes	characteristic
297	C₂²×C₄	C₈×D₅₉	1	4	yes	—
298	C₂²×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
299	C₂²×C₄	C₂×C₄×D₅₉	1	4	yes	—
300	C₂²×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
301	C₂²×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
302	M₁₆	—	59	8	no	—
303	M₁₆	—	59	8	no	—
304	M₁₆	—	59	16	no	—
305	M₁₆	—	59	16	no	—
306	C₂×C₈	—	59	8	no	—
307	C₂×C₈	—	59	4	no	—
308	C₂×C₈	—	59	16	no	—
309	C₂×C₈	—	59	8	no	—
310	C₂×C₈	—	59	8	no	—
311	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
312	C₂×C₈	C₂×C₄×D₅₉	1	2	yes	—
313	C₂×C₈	C₂×C₄×D₅₉	1	4	yes	—
314	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
315	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
316	C₂×C₈	C₂×C₄×D₅₉	1	4	yes	—
317	C₂×C₈	C₂×C₄×D₅₉	1	4	yes	—
318	C₂×C₈	C₂×C₄×D₅₉	1	2	yes	—
319	C₂×C₈	C₂×C₄×D₅₉	1	2	yes	—
320	C₂×C₈	C₂³×D₅₉	1	2	yes	—
321	C₂×C₈	C₂³×D₅₉	1	2	yes	—
322	C₂×C₈	C₂³×D₅₉	1	2	yes	—
323	C₂×C₈	C₂³×D₅₉	1	1	yes	characteristic
324	C₁₆	—	59	8	no	—
325	C₁₆	C₂³×D₅₉	1	8	yes	—
326	C₂³	—	4	2	no	—
327	C₂³	—	59	4	no	—
328	C₂³	—	59	8	no	—
329	C₂³	—	236	4	no	—
330	C₂³	C₂×C₈×D₅₉	1	1	yes	characteristic
331	C₂³	C₂×C₈×D₅₉	1	1	yes	characteristic
332	C₂³	C₂×C₈×D₅₉	1	1	yes	characteristic
333	C₂³	C₂×C₈×D₅₉	1	4	yes	—
334	Q₈	—	59	8	no	—
335	Q₈	—	59	8	no	—
336	D₄	—	59	16	no	—
337	D₄	—	59	16	no	—
338	D₄	—	59	8	no	—
339	D₄	—	59	8	no	—
340	C₂×C₄	—	59	8	no	—
341	C₂×C₄	—	59	4	no	—
342	C₂×C₄	—	59	16	no	—
343	C₂×C₄	—	59	8	no	—
344	C₂×C₄	—	59	8	no	—
345	C₂×C₄	C₂×C₈×D₅₉	1	2	yes	—
346	C₂×C₄	C₂×C₈×D₅₉	1	1	yes	characteristic
347	C₂×C₄	C₂×C₈×D₅₉	1	4	yes	—
348	C₂×C₄	C₂×C₈×D₅₉	1	1	yes	characteristic
349	C₂×C₄	C₂×C₈×D₅₉	1	1	yes	characteristic
350	C₂×C₄	C₂×C₈×D₅₉	1	4	yes	—
351	C₂×C₄	C₂×C₈×D₅₉	1	4	yes	—
352	C₂×C₄	C₂×C₈×D₅₉	1	2	yes	—
353	C₂×C₄	C₂×C₈×D₅₉	1	2	yes	—
354	C₂×C₄	C₂²×C₄×D₅₉	1	2	yes	—
355	C₂×C₄	C₂²×C₄×D₅₉	1	1	yes	characteristic
356	C₂×C₄	C₂²×C₄×D₅₉	1	2	yes	—
357	C₂×C₄	C₂²×C₄×D₅₉	1	2	yes	—
358	C₈	—	59	8	no	—
359	C₈	C₂²×C₄×D₅₉	1	2	yes	—
360	C₈	C₂²×C₄×D₅₉	1	1	yes	characteristic
361	C₈	C₂²×C₄×D₅₉	1	2	yes	—
362	C₈	C₂²×C₄×D₅₉	1	2	yes	—
363	C₈	C₂⁴×D₅₉	1	1	yes	characteristic
364	C₂²	—	2	2	no	—
365	C₂²	—	2	2	no	—
366	C₂²	—	2	2	no	—
367	C₂²	—	4	4	no	—
368	C₂²	—	59	8	no	—
369	C₂²	—	118	8	no	—
370	C₂²	—	236	8	no	—
371	C₂²	C₂²×C₈×D₅₉	1	2	yes	—
372	C₂²	C₂²×C₈×D₅₉	1	2	yes	—
373	C₂²	C₂²×C₈×D₅₉	1	2	yes	—
374	C₂²	C₂²×C₈×D₅₉	1	1	yes	characteristic
375	C₄	—	59	8	no	—
376	C₄	C₂²×C₈×D₅₉	1	2	yes	—
377	C₄	C₂²×C₈×D₅₉	1	1	yes	characteristic
378	C₄	C₂²×C₈×D₅₉	1	2	yes	—
379	C₄	C₂²×C₈×D₅₉	1	2	yes	—
380	C₄	C₂³×C₄×D₅₉	1	1	yes	characteristic
381	C₂	—	2	2	no	—
382	C₂	—	2	2	no	—
383	C₂	—	2	2	no	—
384	C₂	—	118	8	no	—
385	C₂	#21437198	1	2	yes	direct product factor
386	C₂	C₂³×C₈×D₅₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂³×D₅₉
commutator	C₂×C₅₉	C₂⁴×C₈
Frattini	C₈	C₂⁴×D₅₉
Fitting	C₂²×M₃₂×C₅₉	C₂
socle	C₂²×C₅₉	C₂³×C₈
prime radical	C₂²×#11745685	C₄
cosocle	C₈×C₅₉	C₂⁵
hypercenter	C₂²×M₃₂	D₅₉
hypocenter	C₅₉	C₂×#3407
LCS	G ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×M₃₂

Complements

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

N	H ≅ G/N	type
2. #21437198	C₂	direct (N × H)
3. C₂×#16837820	C₂	semidirect
4. C₂×#16837818	C₂	semidirect
5. C₂²×#14273667	C₂	semidirect
6. C₂×M₃₂×D₅₉	C₂	semidirect
7. C₂²×M₃₂×C₅₉	C₂	semidirect
18. #16837820	C₂²	semidirect
19. #16837818	C₂²	semidirect
21. C₂×#14273667	C₂²	semidirect
22. C₂×#14273667	C₂²	semidirect
23. C₂×#14273666	C₂²	semidirect
24. M₃₂×D₅₉	C₂²	semidirect
25. C₂²×C₅₉⋊C₁₆	C₂²	semidirect
26. C₂×C₁₆×D₅₉	C₂²	semidirect
29. C₂×M₃₂×C₅₉	C₂²	semidirect
30. C₂×M₃₂×C₅₉	C₂²	semidirect
31. C₂²×C₁₆×C₅₉	C₂²	semidirect
60. #14273667	C₂³	semidirect
61. #14273666	C₂³	semidirect
63. C₂×C₅₉⋊C₁₆	C₂³	semidirect
64. C₁₆×D₅₉	C₂³	semidirect
75. M₃₂×C₅₉	C₂³	semidirect
77. C₂×C₁₆×C₅₉	C₂³	semidirect
194. C₂²×M₃₂	D₅₉	semidirect
198. C₂×C₅₉	#3407	semidirect
220. C₂×M₃₂	C₂×D₅₉	semidirect
221. C₂×M₃₂	C₂×D₅₉	semidirect
224. C₂²×C₁₆	C₂×D₅₉	semidirect
225. C₅₉	C₂×#3407	semidirect
266. M₃₂	C₂²×D₅₉	semidirect
271. C₂×C₁₆	C₂²×D₅₉	semidirect
385. C₂	#21437198	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#14273733	2
#21437198	2
C₂×#16837820	2
C₂×#16837818	2
C₂²×#14273667	2
C₂×M₃₂×D₅₉	2
C₂²×M₃₂×C₅₉	2
C₂×#3407	59

Subgroups — C2×#21437198 #29495157

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#21437198 #29495157