Subgroups — C₂×C₅₉×#1506 #28429649

Order 15104.

1130 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₉×#533	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅₉×#432	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅₉×#376	C₂	1	1	yes	maximal, characteristic
4	C₅₉×#1506	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₅₉×#328	C₂	1	4	yes	maximal
6	C₅₉×#533	—	2	2	no	—
7	C₅₉×#533	—	2	2	no	—
8	C₅₉×#533	C₄	1	4	yes	complemented
9	C₅₉×#533	C₂²	1	4	yes	—
10	C₂×C₄⋊Q₈×C₅₉	C₄	1	1	yes	characteristic, complemented
11	C₂×C₄⋊Q₈×C₅₉	C₄	1	1	yes	characteristic, complemented
12	C₂×#125×C₅₉	—	2	1	no	—
13	C₂×C₂²⋊Q₈×C₅₉	—	2	1	no	—
14	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	2	yes	—
15	C₂×C₄×Q₈×C₅₉	—	2	1	no	—
16	C₂×C₄×Q₈×C₅₉	C₄	1	2	yes	complemented
17	C₂×#117×C₅₉	—	2	1	no	—
18	C₂²×C₄²×C₅₉	—	2	1	no	—
19	C₂²×C₄²×C₅₉	C₂²	1	1	yes	characteristic
20	C₅₉×#432	—	2	2	no	—
21	C₅₉×#432	C₂²	1	4	yes	—
22	C₂×C₄⋊C₈×C₅₉	—	2	1	no	—
23	C₂×C₂²⋊C₈×C₅₉	C₂²	1	2	yes	—
24	C₂×#97×C₅₉	—	2	1	no	—
25	C₅₉×#376	—	2	2	no	—
26	C₅₉×#376	C₂²	1	4	yes	—
27	C₂×#95×C₅₉	—	2	1	no	—
28	C₂×#95×C₅₉	C₂²	1	2	yes	—
29	C₅₉×#328	C₂²	1	16	yes	—
30	C₂²×Q₈×C₅₉	—	2	1	no	—
31	C₂²×Q₈×C₅₉	C₂×C₄	1	2	yes	—
32	C₂³×C₄×C₅₉	—	2	2	no	—
33	C₂³×C₄×C₅₉	D₄	1	1	yes	characteristic
34	C₂³×C₄×C₅₉	D₄	1	1	yes	characteristic
35	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
36	C₂²×C₈×C₅₉	—	2	2	no	—
37	C₄⋊Q₈×C₅₉	—	2	2	no	—
38	C₄⋊Q₈×C₅₉	—	2	2	no	—
39	C₄⋊Q₈×C₅₉	C₂×C₄	1	4	yes	complemented
40	C₄⋊Q₈×C₅₉	C₂×C₄	1	4	yes	complemented
41	#125×C₅₉	—	2	4	no	—
42	#125×C₅₉	—	2	4	no	—
43	C₂²⋊Q₈×C₅₉	—	2	4	no	—
44	C₂²⋊Q₈×C₅₉	—	2	4	no	—
45	C₂²⋊Q₈×C₅₉	—	2	2	no	—
46	C₂²⋊Q₈×C₅₉	—	2	2	no	—
47	C₂²⋊Q₈×C₅₉	C₂×C₄	1	4	yes	—
48	C₂²⋊Q₈×C₅₉	C₂³	1	4	yes	—
49	C₄×Q₈×C₅₉	—	2	4	no	—
50	C₄×Q₈×C₅₉	—	2	4	no	—
51	C₄×Q₈×C₅₉	—	2	4	no	—
52	C₄×Q₈×C₅₉	C₂×C₄	1	8	yes	complemented
53	#117×C₅₉	—	2	4	no	—
54	#117×C₅₉	—	2	4	no	—
55	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
56	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
57	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
58	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
59	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
60	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	2	yes	—
61	C₂×C₂²⋊C₄×C₅₉	—	2	2	no	—
62	C₂×C₄²×C₅₉	—	2	8	no	—
63	C₂×C₄²×C₅₉	—	2	2	no	—
64	C₂×C₄²×C₅₉	—	2	4	no	—
65	C₂×C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄²×C₅₉	C₂×C₄	1	2	yes	—
68	C₂×C₄²×C₅₉	D₄	1	2	yes	—
69	C₂×C₄²×C₅₉	D₄	1	1	yes	characteristic
70	C₂×C₄²×C₅₉	D₄	1	1	yes	characteristic
71	C₂×C₄²×C₅₉	D₄	1	2	yes	—
72	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
73	C₄⋊C₈×C₅₉	—	2	4	no	—
74	C₂²⋊C₈×C₅₉	—	2	2	no	—
75	C₂²⋊C₈×C₅₉	C₂³	1	4	yes	—
76	#97×C₅₉	—	2	4	no	—
77	#95×C₅₉	—	2	4	no	—
78	#95×C₅₉	—	2	2	no	—
79	#95×C₅₉	C₂³	1	4	yes	—
80	C₂⁴×C₅₉	C₂×D₄	1	1	yes	characteristic
81	C₂×Q₈×C₅₉	—	2	2	no	—
82	C₂×Q₈×C₅₉	—	2	4	no	—
83	C₂×Q₈×C₅₉	—	4	4	no	—
84	C₂×Q₈×C₅₉	—	4	4	no	—
85	C₂×Q₈×C₅₉	C₂²×C₄	1	4	yes	—
86	C₂²×C₄×C₅₉	—	2	4	no	—
87	C₂²×C₄×C₅₉	—	2	4	no	—
88	C₂²×C₄×C₅₉	—	2	8	no	—
89	C₂²×C₄×C₅₉	—	2	2	no	—
90	C₂²×C₄×C₅₉	—	2	2	no	—
91	C₂²×C₄×C₅₉	—	2	4	no	—
92	C₂²×C₄×C₅₉	—	4	2	no	—
93	C₂²×C₄×C₅₉	—	4	4	no	—
94	C₂²×C₄×C₅₉	—	4	4	no	—
95	C₂²×C₄×C₅₉	C₂²⋊C₄	1	2	yes	—
96	C₂²×C₄×C₅₉	C₂²⋊C₄	1	2	yes	—
97	C₂²×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
98	C₂²×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
99	C₂²×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
100	C₂²×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
101	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
104	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
109	C₂×C₈×C₅₉	—	2	4	no	—
110	C₂×C₈×C₅₉	—	4	4	no	—
111	C₄⋊C₄×C₅₉	—	2	4	no	—
112	C₄⋊C₄×C₅₉	—	2	4	no	—
113	C₄⋊C₄×C₅₉	—	2	4	no	—
114	C₄⋊C₄×C₅₉	—	2	4	no	—
115	C₄⋊C₄×C₅₉	—	2	8	no	—
116	C₄⋊C₄×C₅₉	—	2	2	no	—
117	C₄⋊C₄×C₅₉	—	2	4	no	—
118	C₄⋊C₄×C₅₉	C₂²×C₄	1	4	yes	—
119	C₂²⋊C₄×C₅₉	—	2	4	no	—
120	C₂²⋊C₄×C₅₉	—	2	4	no	—
121	C₄²×C₅₉	—	2	16	no	—
122	C₄²×C₅₉	—	2	8	no	—
123	C₄²×C₅₉	C₂²⋊C₄	1	2	yes	—
124	C₄²×C₅₉	C₂²⋊C₄	1	2	yes	—
125	C₄²×C₅₉	C₂²⋊C₄	1	2	yes	—
126	C₄²×C₅₉	C₂²⋊C₄	1	2	yes	—
127	C₄²×C₅₉	C₂²×C₄	1	2	yes	—
128	C₄²×C₅₉	C₂²×C₄	1	2	yes	—
129	C₄²×C₅₉	C₂×D₄	1	2	yes	—
130	C₄²×C₅₉	C₂×D₄	1	2	yes	—
131	C₂³×C₅₉	—	2	2	no	—
132	C₂³×C₅₉	—	2	2	no	—
133	C₂³×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
134	C₂³×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
135	C₂³×C₅₉	#137	1	4	yes	—
136	C₂³×C₅₉	C₂²×D₄	1	1	yes	characteristic
137	Q₈×C₅₉	—	4	4	no	—
138	Q₈×C₅₉	—	4	4	no	—
139	Q₈×C₅₉	—	4	8	no	—
140	C₂×C₄×C₅₉	—	2	4	no	—
141	C₂×C₄×C₅₉	—	2	2	no	—
142	C₂×C₄×C₅₉	—	2	2	no	—
143	C₂×C₄×C₅₉	—	2	4	no	—
144	C₂×C₄×C₅₉	—	2	2	no	—
145	C₂×C₄×C₅₉	—	2	2	no	—
146	C₂×C₄×C₅₉	—	2	2	no	—
147	C₂×C₄×C₅₉	—	2	4	no	—
148	C₂×C₄×C₅₉	—	2	4	no	—
149	C₂×C₄×C₅₉	—	2	8	no	—
150	C₂×C₄×C₅₉	—	2	4	no	—
151	C₂×C₄×C₅₉	—	2	4	no	—
152	C₂×C₄×C₅₉	—	4	1	no	—
153	C₂×C₄×C₅₉	—	4	1	no	—
154	C₂×C₄×C₅₉	—	4	1	no	—
155	C₂×C₄×C₅₉	—	4	1	no	—
156	C₂×C₄×C₅₉	—	4	4	no	—
157	C₂×C₄×C₅₉	—	4	16	no	—
158	C₂×C₄×C₅₉	—	4	4	no	—
159	C₂×C₄×C₅₉	—	4	4	no	—
160	C₂×C₄×C₅₉	—	4	4	no	—
161	C₂×C₄×C₅₉	#104	1	4	yes	—
162	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	2	yes	—
163	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
164	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
165	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	2	yes	—
166	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	2	yes	—
167	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	2	yes	—
168	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
169	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
170	C₈×C₅₉	—	4	4	no	—
171	C₂×#1506	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
172	C₂²×C₅₉	—	2	1	no	—
173	C₂²×C₅₉	—	2	1	no	—
174	C₂²×C₅₉	—	2	1	no	—
175	C₂²×C₅₉	—	2	1	no	—
176	C₂²×C₅₉	—	2	8	no	—
177	C₂²×C₅₉	#410	1	2	yes	—
178	C₂²×C₅₉	#419	1	2	yes	—
179	C₂²×C₅₉	#419	1	2	yes	—
180	C₂²×C₅₉	C₂×#104	1	2	yes	—
181	C₂²×C₅₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
182	C₂²×C₅₉	C₂×#137	1	2	yes	—
183	C₄×C₅₉	—	2	1	no	—
184	C₄×C₅₉	—	2	1	no	—
185	C₄×C₅₉	—	2	1	no	—
186	C₄×C₅₉	—	2	1	no	—
187	C₄×C₅₉	—	2	2	no	—
188	C₄×C₅₉	—	2	2	no	—
189	C₄×C₅₉	—	2	2	no	—
190	C₄×C₅₉	—	4	8	no	—
191	C₄×C₅₉	—	4	4	no	—
192	C₄×C₅₉	—	4	4	no	—
193	C₄×C₅₉	C₂×#104	1	4	yes	—
194	C₂×#533	C₂×C₅₉	1	1	yes	characteristic
195	C₂×#432	C₂×C₅₉	1	1	yes	characteristic
196	C₂×#376	C₂×C₅₉	1	1	yes	characteristic
197	#1506	C₂×C₅₉	1	8	yes	direct product factor
198	C₂×#328	C₂×C₅₉	1	4	yes	—
199	C₂×C₅₉	—	2	2	no	—
200	C₂×C₅₉	—	2	2	no	—
201	C₂×C₅₉	#1506	1	4	yes	direct product factor
202	C₂×C₅₉	C₂×#410	1	1	yes	characteristic
203	C₂×C₅₉	C₂×#419	1	1	yes	characteristic
204	C₂×C₅₉	C₂²×#104	1	1	yes	characteristic
205	#533	—	2	2	no	—
206	#533	—	2	2	no	—
207	#533	C₄×C₅₉	1	4	yes	complemented
208	#533	C₂²×C₅₉	1	4	yes	—
209	C₂×C₄⋊Q₈	C₄×C₅₉	1	1	yes	characteristic, complemented
210	C₂×C₄⋊Q₈	C₄×C₅₉	1	1	yes	characteristic, complemented
211	C₂×#125	—	2	1	no	—
212	C₂×C₂²⋊Q₈	—	2	1	no	—
213	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	2	yes	—
214	C₂×C₄×Q₈	—	2	1	no	—
215	C₂×C₄×Q₈	C₄×C₅₉	1	2	yes	complemented
216	C₂×#117	—	2	1	no	—
217	C₂²×C₄²	—	2	1	no	—
218	C₂²×C₄²	C₂²×C₅₉	1	1	yes	characteristic
219	#432	—	2	2	no	—
220	#432	C₂²×C₅₉	1	4	yes	—
221	C₂×C₄⋊C₈	—	2	1	no	—
222	C₂×C₂²⋊C₈	C₂²×C₅₉	1	2	yes	—
223	C₂×#97	—	2	1	no	—
224	#376	—	2	2	no	—
225	#376	C₂²×C₅₉	1	4	yes	—
226	C₂×#95	—	2	1	no	—
227	C₂×#95	C₂²×C₅₉	1	2	yes	—
228	#328	C₂²×C₅₉	1	16	yes	—
229	C₅₉	C₂×#1506	1	1	yes	characteristic, direct product factor, Sylow
230	C₂²×Q₈	—	2	1	no	—
231	C₂²×Q₈	C₂×C₄×C₅₉	1	2	yes	—
232	C₂³×C₄	—	2	2	no	—
233	C₂³×C₄	D₄×C₅₉	1	1	yes	characteristic
234	C₂³×C₄	D₄×C₅₉	1	1	yes	characteristic
235	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
236	C₂²×C₈	—	2	2	no	—
237	C₄⋊Q₈	—	2	2	no	—
238	C₄⋊Q₈	—	2	2	no	—
239	C₄⋊Q₈	C₂×C₄×C₅₉	1	4	yes	complemented
240	C₄⋊Q₈	C₂×C₄×C₅₉	1	4	yes	complemented
241	#125	—	2	4	no	—
242	#125	—	2	4	no	—
243	C₂²⋊Q₈	—	2	4	no	—
244	C₂²⋊Q₈	—	2	4	no	—
245	C₂²⋊Q₈	—	2	2	no	—
246	C₂²⋊Q₈	—	2	2	no	—
247	C₂²⋊Q₈	C₂×C₄×C₅₉	1	4	yes	—
248	C₂²⋊Q₈	C₂³×C₅₉	1	4	yes	—
249	C₄×Q₈	—	2	4	no	—
250	C₄×Q₈	—	2	4	no	—
251	C₄×Q₈	—	2	4	no	—
252	C₄×Q₈	C₂×C₄×C₅₉	1	8	yes	complemented
253	#117	—	2	4	no	—
254	#117	—	2	4	no	—
255	C₂×C₄⋊C₄	—	2	1	no	—
256	C₂×C₄⋊C₄	—	2	1	no	—
257	C₂×C₄⋊C₄	—	2	1	no	—
258	C₂×C₄⋊C₄	—	2	2	no	—
259	C₂×C₄⋊C₄	—	2	2	no	—
260	C₂×C₄⋊C₄	C₂×C₄×C₅₉	1	2	yes	—
261	C₂×C₂²⋊C₄	—	2	2	no	—
262	C₂×C₄²	—	2	8	no	—
263	C₂×C₄²	—	2	2	no	—
264	C₂×C₄²	—	2	4	no	—
265	C₂×C₄²	C₂×C₄×C₅₉	1	1	yes	characteristic
266	C₂×C₄²	C₂×C₄×C₅₉	1	1	yes	characteristic
267	C₂×C₄²	C₂×C₄×C₅₉	1	2	yes	—
268	C₂×C₄²	D₄×C₅₉	1	2	yes	—
269	C₂×C₄²	D₄×C₅₉	1	1	yes	characteristic
270	C₂×C₄²	D₄×C₅₉	1	1	yes	characteristic
271	C₂×C₄²	D₄×C₅₉	1	2	yes	—
272	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
273	C₄⋊C₈	—	2	4	no	—
274	C₂²⋊C₈	—	2	2	no	—
275	C₂²⋊C₈	C₂³×C₅₉	1	4	yes	—
276	#97	—	2	4	no	—
277	#95	—	2	4	no	—
278	#95	—	2	2	no	—
279	#95	C₂³×C₅₉	1	4	yes	—
280	C₂⁴	C₂×D₄×C₅₉	1	1	yes	characteristic
281	C₂×Q₈	—	2	2	no	—
282	C₂×Q₈	—	2	4	no	—
283	C₂×Q₈	—	4	4	no	—
284	C₂×Q₈	—	4	4	no	—
285	C₂×Q₈	C₂²×C₄×C₅₉	1	4	yes	—
286	C₂²×C₄	—	2	4	no	—
287	C₂²×C₄	—	2	4	no	—
288	C₂²×C₄	—	2	8	no	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	2	4	no	—
292	C₂²×C₄	—	4	2	no	—
293	C₂²×C₄	—	4	4	no	—
294	C₂²×C₄	—	4	4	no	—
295	C₂²×C₄	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
296	C₂²×C₄	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
297	C₂²×C₄	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
298	C₂²×C₄	C₂²⋊C₄×C₅₉	1	2	yes	—
299	C₂²×C₄	C₂²⋊C₄×C₅₉	1	2	yes	—
300	C₂²×C₄	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
301	C₂²×C₄	C₂²×C₄×C₅₉	1	1	yes	characteristic
302	C₂²×C₄	C₂²×C₄×C₅₉	1	1	yes	characteristic
303	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
304	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
305	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
306	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
307	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
308	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
309	C₂×C₈	—	2	4	no	—
310	C₂×C₈	—	4	4	no	—
311	C₄⋊C₄	—	2	4	no	—
312	C₄⋊C₄	—	2	4	no	—
313	C₄⋊C₄	—	2	4	no	—
314	C₄⋊C₄	—	2	4	no	—
315	C₄⋊C₄	—	2	8	no	—
316	C₄⋊C₄	—	2	2	no	—
317	C₄⋊C₄	—	2	4	no	—
318	C₄⋊C₄	C₂²×C₄×C₅₉	1	4	yes	—
319	C₂²⋊C₄	—	2	4	no	—
320	C₂²⋊C₄	—	2	4	no	—
321	C₄²	—	2	16	no	—
322	C₄²	—	2	8	no	—
323	C₄²	C₂²⋊C₄×C₅₉	1	2	yes	—
324	C₄²	C₂²⋊C₄×C₅₉	1	2	yes	—
325	C₄²	C₂²⋊C₄×C₅₉	1	2	yes	—
326	C₄²	C₂²⋊C₄×C₅₉	1	2	yes	—
327	C₄²	C₂²×C₄×C₅₉	1	2	yes	—
328	C₄²	C₂²×C₄×C₅₉	1	2	yes	—
329	C₄²	C₂×D₄×C₅₉	1	2	yes	—
330	C₄²	C₂×D₄×C₅₉	1	2	yes	—
331	C₂³	—	2	2	no	—
332	C₂³	—	2	2	no	—
333	C₂³	C₂×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
334	C₂³	C₂×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
335	C₂³	#137×C₅₉	1	4	yes	—
336	C₂³	C₂²×D₄×C₅₉	1	1	yes	characteristic
337	Q₈	—	4	4	no	—
338	Q₈	—	4	4	no	—
339	Q₈	—	4	8	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	4	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	4	no	—
347	C₂×C₄	—	2	4	no	—
348	C₂×C₄	—	2	4	no	—
349	C₂×C₄	—	2	8	no	—
350	C₂×C₄	—	2	4	no	—
351	C₂×C₄	—	2	4	no	—
352	C₂×C₄	—	4	1	no	—
353	C₂×C₄	—	4	1	no	—
354	C₂×C₄	—	4	1	no	—
355	C₂×C₄	—	4	1	no	—
356	C₂×C₄	—	4	16	no	—
357	C₂×C₄	—	4	4	no	—
358	C₂×C₄	—	4	4	no	—
359	C₂×C₄	—	4	4	no	—
360	C₂×C₄	—	4	4	no	—
361	C₂×C₄	#104×C₅₉	1	4	yes	—
362	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	2	yes	—
363	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
364	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
365	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	2	yes	—
366	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	2	yes	—
367	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	2	yes	—
368	C₂×C₄	C₂³×C₄×C₅₉	1	1	yes	characteristic
369	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
370	C₈	—	4	4	no	—
371	C₂²	—	2	8	no	—
372	C₂²	—	2	1	no	—
373	C₂²	—	2	1	no	—
374	C₂²	—	2	1	no	—
375	C₂²	—	2	1	no	—
376	C₂²	C₅₉×#410	1	2	yes	—
377	C₂²	C₅₉×#419	1	2	yes	—
378	C₂²	C₅₉×#419	1	2	yes	—
379	C₂²	C₂×#104×C₅₉	1	2	yes	—
380	C₂²	C₂²×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
381	C₂²	C₂×#137×C₅₉	1	2	yes	—
382	C₄	—	2	1	no	—
383	C₄	—	2	1	no	—
384	C₄	—	2	1	no	—
385	C₄	—	2	1	no	—
386	C₄	—	2	2	no	—
387	C₄	—	2	2	no	—
388	C₄	—	2	2	no	—
389	C₄	—	4	8	no	—
390	C₄	—	4	4	no	—
391	C₄	—	4	4	no	—
392	C₄	C₂×#104×C₅₉	1	4	yes	—
393	C₂	—	2	2	no	—
394	C₂	—	2	2	no	—
395	C₂	C₅₉×#1506	1	4	yes	direct product factor
396	C₂	C₂×C₅₉×#410	1	1	yes	characteristic
397	C₂	C₂×C₅₉×#419	1	1	yes	characteristic
398	C₂	C₂²×#104×C₅₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₉	C₂×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₅₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅₉
prime radical	C₂⁴×C₅₉	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₅₉ ◁ C₂²×C₄²×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₅₉×#1506	C₂	direct (N × H)
8. C₅₉×#533	C₄	semidirect
10. C₂×C₄⋊Q₈×C₅₉	C₄	semidirect
11. C₂×C₄⋊Q₈×C₅₉	C₄	semidirect
16. C₂×C₄×Q₈×C₅₉	C₄	semidirect
39. C₄⋊Q₈×C₅₉	C₂×C₄	semidirect
40. C₄⋊Q₈×C₅₉	C₂×C₄	semidirect
52. C₄×Q₈×C₅₉	C₂×C₄	semidirect
171. C₂×#1506	C₅₉	direct (N × H)
197. #1506	C₂×C₅₉	direct (N × H)
201. C₂×C₅₉	#1506	direct (N × H)
207. #533	C₄×C₅₉	semidirect
209. C₂×C₄⋊Q₈	C₄×C₅₉	semidirect
210. C₂×C₄⋊Q₈	C₄×C₅₉	semidirect
215. C₂×C₄×Q₈	C₄×C₅₉	semidirect
229. C₅₉	C₂×#1506	direct (N × H)
239. C₄⋊Q₈	C₂×C₄×C₅₉	semidirect
240. C₄⋊Q₈	C₂×C₄×C₅₉	semidirect
252. C₄×Q₈	C₂×C₄×C₅₉	semidirect
395. C₂	C₅₉×#1506	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅₉×#533	2
C₂×C₅₉×#432	2
C₂×C₅₉×#376	2
C₅₉×#1506	2
C₂×C₅₉×#328	2
C₂×#1506	59

Subgroups — C2×C59×#1506 #28429649

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅₉×#1506 #28429649