Subgroups — C₂×C₅₉×#1644 #28430592

Order 15104.

1022 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₉×#554	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅₉×#487	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅₉×#474	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅₉×#462	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₉×#1644	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₅₉×#333	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅₉×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅₉×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic
9	C₂²×Q₁₆×C₅₉	—	2	1	no	—
10	C₅₉×#554	—	2	2	no	—
11	C₅₉×#554	—	2	2	no	—
12	C₅₉×#554	—	2	2	no	—
13	C₅₉×#554	C₂²	1	4	yes	—
14	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
16	C₂×#125×C₅₉	—	2	1	no	—
17	C₂×C₂²⋊Q₈×C₅₉	—	2	1	no	—
18	C₂×C₂²⋊Q₈×C₅₉	—	2	2	no	—
19	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₅₉	—	2	1	no	—
21	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
22	C₂²×C₄⋊C₄×C₅₉	—	2	1	no	—
23	C₅₉×#487	—	2	2	no	—
24	C₅₉×#487	C₂²	1	4	yes	complemented
25	C₅₉×#474	—	2	2	no	—
26	C₅₉×#474	C₂²	1	4	yes	—
27	C₅₉×#462	—	2	2	no	—
28	C₅₉×#462	C₂²	1	4	yes	complemented
29	C₂×#107×C₅₉	—	2	1	no	—
30	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
31	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
32	C₂×#103×C₅₉	—	2	2	no	—
33	C₂×#103×C₅₉	—	2	1	no	—
34	C₂×#102×C₅₉	—	2	1	no	—
35	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
36	C₅₉×#333	C₂²	1	4	yes	complemented
37	C₅₉×Q₈⋊C₈	C₂²	1	4	yes	complemented
38	C₅₉×D₄⋊C₈	C₂²	1	4	yes	—
39	C₂²×Q₈×C₅₉	—	2	1	no	—
40	C₂²×Q₈×C₅₉	D₄	1	1	yes	characteristic
41	C₂²×Q₈×C₅₉	D₄	1	2	yes	—
42	C₂²×D₄×C₅₉	D₄	1	1	yes	characteristic
43	C₂³×C₄×C₅₉	—	2	2	no	—
44	C₂³×C₄×C₅₉	—	2	1	no	—
45	C₂×Q₁₆×C₅₉	—	2	4	no	—
46	C₂×Q₁₆×C₅₉	—	4	4	no	—
47	C₂²×C₈×C₅₉	—	2	1	no	—
48	C₂²×C₈×C₅₉	—	2	1	no	—
49	C₂²×C₈×C₅₉	—	2	1	no	—
50	C₄⋊Q₈×C₅₉	—	2	1	no	—
51	C₄⋊Q₈×C₅₉	—	2	1	no	—
52	C₄⋊Q₈×C₅₉	—	2	1	no	—
53	C₄⋊Q₈×C₅₉	—	2	1	no	—
54	C₄⋊Q₈×C₅₉	—	2	1	no	—
55	C₄⋊Q₈×C₅₉	D₄	1	2	yes	—
56	C₄⋊Q₈×C₅₉	C₂³	1	2	yes	—
57	C₄⋊Q₈×C₅₉	C₂³	1	2	yes	—
58	#125×C₅₉	—	2	4	no	—
59	#125×C₅₉	—	2	4	no	—
60	C₂²⋊Q₈×C₅₉	—	2	4	no	—
61	C₂²⋊Q₈×C₅₉	—	2	8	no	—
62	C₂²⋊Q₈×C₅₉	—	2	4	no	—
63	C₂²⋊Q₈×C₅₉	—	2	8	no	—
64	C₄×Q₈×C₅₉	—	2	1	no	—
65	C₄×Q₈×C₅₉	—	2	1	no	—
66	C₄×Q₈×C₅₉	D₄	1	2	yes	—
67	C₄×Q₈×C₅₉	C₂³	1	2	yes	—
68	C₄×D₄×C₅₉	—	2	4	no	—
69	C₄×D₄×C₅₉	—	2	4	no	—
70	C₄×D₄×C₅₉	—	2	1	no	—
71	C₄×D₄×C₅₉	—	2	1	no	—
72	C₄×D₄×C₅₉	D₄	1	2	yes	—
73	C₄×D₄×C₅₉	C₂³	1	2	yes	—
74	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
75	C₂×C₄⋊C₄×C₅₉	—	2	4	no	—
76	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
77	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
78	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
79	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
80	C₂×C₄⋊C₄×C₅₉	—	2	4	no	—
81	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
82	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
83	C₂×C₄⋊C₄×C₅₉	D₄	1	1	yes	characteristic
84	C₂×C₄⋊C₄×C₅₉	D₄	1	1	yes	characteristic
85	C₂×C₂²⋊C₄×C₅₉	—	2	2	no	—
86	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
87	C₂×C₄²×C₅₉	—	2	1	no	—
88	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
89	#107×C₅₉	—	2	4	no	—
90	C₄⋊C₈×C₅₉	—	2	1	no	—
91	C₄⋊C₈×C₅₉	—	2	1	no	—
92	C₄⋊C₈×C₅₉	C₂³	1	2	yes	—
93	C₄⋊C₈×C₅₉	C₂³	1	2	yes	—
94	#103×C₅₉	—	2	8	no	—
95	#103×C₅₉	—	2	4	no	—
96	#102×C₅₉	—	2	4	no	—
97	C₄×C₈×C₅₉	—	2	1	no	—
98	C₄×C₈×C₅₉	C₂³	1	2	yes	—
99	C₂⁴×C₅₉	—	2	1	no	—
100	C₂×Q₈×C₅₉	—	2	1	no	—
101	C₂×Q₈×C₅₉	—	2	2	no	—
102	C₂×Q₈×C₅₉	—	2	2	no	—
103	C₂×Q₈×C₅₉	—	2	2	no	—
104	C₂×Q₈×C₅₉	—	2	2	no	—
105	C₂×Q₈×C₅₉	—	4	4	no	—
106	C₂×Q₈×C₅₉	—	4	1	no	—
107	C₂×Q₈×C₅₉	—	4	2	no	—
108	C₂×Q₈×C₅₉	—	4	2	no	—
109	C₂×Q₈×C₅₉	C₂×D₄	1	2	yes	—
110	C₂×Q₈×C₅₉	C₂×D₄	1	4	yes	—
111	C₂×D₄×C₅₉	—	2	1	no	—
112	C₂×D₄×C₅₉	—	2	2	no	—
113	C₂×D₄×C₅₉	Q₁₆	1	4	yes	complemented
114	C₂×D₄×C₅₉	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₅₉	—	2	1	no	—
116	C₂²×C₄×C₅₉	—	2	1	no	—
117	C₂²×C₄×C₅₉	—	2	1	no	—
118	C₂²×C₄×C₅₉	—	2	2	no	—
119	C₂²×C₄×C₅₉	—	2	8	no	—
120	C₂²×C₄×C₅₉	—	2	2	no	—
121	C₂²×C₄×C₅₉	—	2	2	no	—
122	C₂²×C₄×C₅₉	—	4	2	no	—
123	C₂²×C₄×C₅₉	—	4	2	no	—
124	C₂²×C₄×C₅₉	—	4	1	no	—
125	C₂²×C₄×C₅₉	—	8	4	no	—
126	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
129	Q₁₆×C₅₉	—	4	8	no	—
130	C₂×C₈×C₅₉	—	2	2	no	—
131	C₂×C₈×C₅₉	—	2	2	no	—
132	C₂×C₈×C₅₉	—	2	2	no	—
133	C₂×C₈×C₅₉	—	4	2	no	—
134	C₂×C₈×C₅₉	—	4	2	no	—
135	C₂×C₈×C₅₉	—	4	2	no	—
136	C₄⋊C₄×C₅₉	—	2	8	no	—
137	C₄⋊C₄×C₅₉	—	2	8	no	—
138	C₄⋊C₄×C₅₉	—	2	1	no	—
139	C₄⋊C₄×C₅₉	—	2	2	no	—
140	C₄⋊C₄×C₅₉	—	2	2	no	—
141	C₄⋊C₄×C₅₉	—	2	2	no	—
142	C₄⋊C₄×C₅₉	—	2	1	no	—
143	C₄⋊C₄×C₅₉	—	2	2	no	—
144	C₄⋊C₄×C₅₉	—	2	2	no	—
145	C₄⋊C₄×C₅₉	—	2	2	no	—
146	C₄⋊C₄×C₅₉	—	2	2	no	—
147	C₄⋊C₄×C₅₉	—	2	2	no	—
148	C₄⋊C₄×C₅₉	—	4	1	no	—
149	C₄⋊C₄×C₅₉	—	4	1	no	—
150	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
151	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
152	C₂²⋊C₄×C₅₉	—	2	8	no	—
153	C₂²⋊C₄×C₅₉	—	2	2	no	—
154	C₂²⋊C₄×C₅₉	—	2	2	no	—
155	C₄²×C₅₉	—	2	2	no	—
156	C₄²×C₅₉	—	2	2	no	—
157	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
158	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
159	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
160	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
161	C₂³×C₅₉	—	2	2	no	—
162	C₂³×C₅₉	—	2	4	no	—
163	C₂³×C₅₉	—	4	2	no	—
164	C₂³×C₅₉	—	4	2	no	—
165	C₂³×C₅₉	#120	1	1	yes	characteristic
166	Q₈×C₅₉	—	2	2	no	—
167	Q₈×C₅₉	—	2	2	no	—
168	Q₈×C₅₉	—	4	4	no	—
169	Q₈×C₅₉	—	4	2	no	—
170	Q₈×C₅₉	—	4	2	no	—
171	Q₈×C₅₉	—	4	2	no	—
172	Q₈×C₅₉	—	8	2	no	—
173	Q₈×C₅₉	—	8	2	no	—
174	D₄×C₅₉	—	2	2	no	—
175	D₄×C₅₉	—	2	4	no	—
176	D₄×C₅₉	C₂×Q₁₆	1	4	yes	complemented
177	C₂×C₄×C₅₉	—	2	2	no	—
178	C₂×C₄×C₅₉	—	2	2	no	—
179	C₂×C₄×C₅₉	—	2	2	no	—
180	C₂×C₄×C₅₉	—	2	2	no	—
181	C₂×C₄×C₅₉	—	2	4	no	—
182	C₂×C₄×C₅₉	—	4	2	no	—
183	C₂×C₄×C₅₉	—	4	2	no	—
184	C₂×C₄×C₅₉	—	4	2	no	—
185	C₂×C₄×C₅₉	—	4	4	no	—
186	C₂×C₄×C₅₉	—	4	2	no	—
187	C₂×C₄×C₅₉	—	4	2	no	—
188	C₂×C₄×C₅₉	—	4	4	no	—
189	C₂×C₄×C₅₉	—	4	2	no	—
190	C₂×C₄×C₅₉	—	8	8	no	—
191	C₂×C₄×C₅₉	—	8	2	no	—
192	C₂×C₄×C₅₉	#120	1	1	yes	characteristic
193	C₂×C₄×C₅₉	#120	1	1	yes	characteristic
194	C₂×C₄×C₅₉	#120	1	1	yes	characteristic
195	C₂×C₄×C₅₉	C₂×Q₁₆	1	2	yes	—
196	C₂×C₄×C₅₉	#135	1	2	yes	—
197	C₂×C₄×C₅₉	AGL(1,ℤ/8)	1	2	yes	—
198	C₂×C₄×C₅₉	#137	1	2	yes	—
199	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
200	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
201	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
202	C₈×C₅₉	—	4	2	no	—
203	C₈×C₅₉	—	4	2	no	—
204	C₈×C₅₉	—	4	2	no	—
205	C₂×#1644	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
206	C₂²×C₅₉	—	2	4	no	—
207	C₂²×C₅₉	—	4	8	no	—
208	C₂²×C₅₉	—	4	2	no	—
209	C₂²×C₅₉	—	4	2	no	—
210	C₂²×C₅₉	#449	1	2	yes	—
211	C₂²×C₅₉	#451	1	2	yes	—
212	C₂²×C₅₉	#455	1	2	yes	—
213	C₂²×C₅₉	C₂×#120	1	1	yes	characteristic
214	C₄×C₅₉	—	2	1	no	—
215	C₄×C₅₉	—	2	1	no	—
216	C₄×C₅₉	—	4	2	no	—
217	C₄×C₅₉	—	4	2	no	—
218	C₄×C₅₉	—	4	2	no	—
219	C₄×C₅₉	—	4	4	no	—
220	C₄×C₅₉	—	8	2	no	—
221	C₄×C₅₉	#449	1	2	yes	—
222	C₄×C₅₉	#451	1	2	yes	—
223	C₄×C₅₉	C₂²×Q₁₆	1	1	yes	characteristic
224	C₄×C₅₉	C₂×#135	1	1	yes	characteristic
225	C₄×C₅₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
226	C₄×C₅₉	C₂×#137	1	1	yes	characteristic
227	C₂×#554	C₂×C₅₉	1	1	yes	characteristic
228	C₂×#487	C₂×C₅₉	1	1	yes	characteristic, complemented
229	C₂×#474	C₂×C₅₉	1	1	yes	characteristic
230	C₂×#462	C₂×C₅₉	1	1	yes	characteristic, complemented
231	#1644	C₂×C₅₉	1	8	yes	direct product factor
232	C₂×#333	C₂×C₅₉	1	1	yes	characteristic, complemented
233	C₂×Q₈⋊C₈	C₂×C₅₉	1	1	yes	characteristic, complemented
234	C₂×D₄⋊C₈	C₂×C₅₉	1	1	yes	characteristic
235	C₂×C₅₉	—	4	4	no	—
236	C₂×C₅₉	#1644	1	4	yes	direct product factor
237	C₂×C₅₉	C₂×#451	1	1	yes	characteristic
238	C₂×C₅₉	C₂×#449	1	1	yes	characteristic
239	C₂×C₅₉	C₂×#455	1	1	yes	characteristic
240	C₂²×Q₁₆	—	2	1	no	—
241	#554	—	2	2	no	—
242	#554	—	2	2	no	—
243	#554	—	2	2	no	—
244	#554	C₂²×C₅₉	1	4	yes	—
245	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
246	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
247	C₂×#125	—	2	1	no	—
248	C₂×C₂²⋊Q₈	—	2	1	no	—
249	C₂×C₂²⋊Q₈	—	2	2	no	—
250	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
251	C₂×C₄×D₄	—	2	1	no	—
252	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
253	C₂²×C₄⋊C₄	—	2	1	no	—
254	#487	—	2	2	no	—
255	#487	C₂²×C₅₉	1	4	yes	complemented
256	#474	—	2	2	no	—
257	#474	C₂²×C₅₉	1	4	yes	—
258	#462	—	2	2	no	—
259	#462	C₂²×C₅₉	1	4	yes	complemented
260	C₂×#107	—	2	1	no	—
261	C₂×C₄⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
262	C₂×C₄⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
263	C₂×#103	—	2	2	no	—
264	C₂×#103	—	2	1	no	—
265	C₂×#102	—	2	1	no	—
266	C₂×C₄×C₈	C₂²×C₅₉	1	1	yes	characteristic
267	#333	C₂²×C₅₉	1	4	yes	complemented
268	Q₈⋊C₈	C₂²×C₅₉	1	4	yes	complemented
269	D₄⋊C₈	C₂²×C₅₉	1	4	yes	—
270	C₅₉	C₂×#1644	1	1	yes	characteristic, direct product factor, Sylow
271	C₂²×Q₈	—	2	1	no	—
272	C₂²×Q₈	D₄×C₅₉	1	1	yes	characteristic
273	C₂²×Q₈	D₄×C₅₉	1	2	yes	—
274	C₂²×D₄	D₄×C₅₉	1	1	yes	characteristic
275	C₂³×C₄	—	2	2	no	—
276	C₂³×C₄	—	2	1	no	—
277	C₂×Q₁₆	—	2	4	no	—
278	C₂×Q₁₆	—	4	4	no	—
279	C₂²×C₈	—	2	1	no	—
280	C₂²×C₈	—	2	1	no	—
281	C₂²×C₈	—	2	1	no	—
282	C₄⋊Q₈	—	2	1	no	—
283	C₄⋊Q₈	—	2	1	no	—
284	C₄⋊Q₈	—	2	1	no	—
285	C₄⋊Q₈	—	2	1	no	—
286	C₄⋊Q₈	—	2	1	no	—
287	C₄⋊Q₈	D₄×C₅₉	1	2	yes	—
288	C₄⋊Q₈	C₂³×C₅₉	1	2	yes	—
289	C₄⋊Q₈	C₂³×C₅₉	1	2	yes	—
290	#125	—	2	4	no	—
291	#125	—	2	4	no	—
292	C₂²⋊Q₈	—	2	4	no	—
293	C₂²⋊Q₈	—	2	8	no	—
294	C₂²⋊Q₈	—	2	4	no	—
295	C₂²⋊Q₈	—	2	8	no	—
296	C₄×Q₈	—	2	1	no	—
297	C₄×Q₈	—	2	1	no	—
298	C₄×Q₈	D₄×C₅₉	1	2	yes	—
299	C₄×Q₈	C₂³×C₅₉	1	2	yes	—
300	C₄×D₄	—	2	4	no	—
301	C₄×D₄	—	2	4	no	—
302	C₄×D₄	—	2	1	no	—
303	C₄×D₄	—	2	1	no	—
304	C₄×D₄	D₄×C₅₉	1	2	yes	—
305	C₄×D₄	C₂³×C₅₉	1	2	yes	—
306	C₂×C₄⋊C₄	—	2	2	no	—
307	C₂×C₄⋊C₄	—	2	4	no	—
308	C₂×C₄⋊C₄	—	2	2	no	—
309	C₂×C₄⋊C₄	—	2	1	no	—
310	C₂×C₄⋊C₄	—	2	1	no	—
311	C₂×C₄⋊C₄	—	2	1	no	—
312	C₂×C₄⋊C₄	—	2	4	no	—
313	C₂×C₄⋊C₄	—	2	1	no	—
314	C₂×C₄⋊C₄	—	2	1	no	—
315	C₂×C₄⋊C₄	D₄×C₅₉	1	1	yes	characteristic
316	C₂×C₄⋊C₄	D₄×C₅₉	1	1	yes	characteristic
317	C₂×C₂²⋊C₄	—	2	2	no	—
318	C₂×C₂²⋊C₄	—	2	1	no	—
319	C₂×C₄²	—	2	1	no	—
320	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
321	#107	—	2	4	no	—
322	C₄⋊C₈	—	2	1	no	—
323	C₄⋊C₈	—	2	1	no	—
324	C₄⋊C₈	C₂³×C₅₉	1	2	yes	—
325	C₄⋊C₈	C₂³×C₅₉	1	2	yes	—
326	#103	—	2	8	no	—
327	#103	—	2	4	no	—
328	#102	—	2	4	no	—
329	C₄×C₈	—	2	1	no	—
330	C₄×C₈	C₂³×C₅₉	1	2	yes	—
331	C₂⁴	—	2	1	no	—
332	C₂×Q₈	—	2	1	no	—
333	C₂×Q₈	—	2	2	no	—
334	C₂×Q₈	—	2	2	no	—
335	C₂×Q₈	—	2	2	no	—
336	C₂×Q₈	—	2	2	no	—
337	C₂×Q₈	—	4	4	no	—
338	C₂×Q₈	—	4	1	no	—
339	C₂×Q₈	—	4	2	no	—
340	C₂×Q₈	—	4	2	no	—
341	C₂×Q₈	C₂×D₄×C₅₉	1	2	yes	—
342	C₂×Q₈	C₂×D₄×C₅₉	1	4	yes	—
343	C₂×D₄	—	2	1	no	—
344	C₂×D₄	—	2	2	no	—
345	C₂×D₄	Q₁₆×C₅₉	1	4	yes	complemented
346	C₂×D₄	C₂×D₄×C₅₉	1	2	yes	—
347	C₂²×C₄	—	2	1	no	—
348	C₂²×C₄	—	2	1	no	—
349	C₂²×C₄	—	2	1	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	8	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	4	2	no	—
355	C₂²×C₄	—	4	2	no	—
356	C₂²×C₄	—	4	1	no	—
357	C₂²×C₄	—	8	4	no	—
358	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
359	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
360	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
361	Q₁₆	—	4	8	no	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	2	2	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	—	4	2	no	—
366	C₂×C₈	—	4	2	no	—
367	C₂×C₈	—	4	2	no	—
368	C₄⋊C₄	—	2	8	no	—
369	C₄⋊C₄	—	2	8	no	—
370	C₄⋊C₄	—	2	1	no	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	1	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	2	2	no	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	—	4	1	no	—
381	C₄⋊C₄	—	4	1	no	—
382	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
383	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
384	C₂²⋊C₄	—	2	8	no	—
385	C₂²⋊C₄	—	2	2	no	—
386	C₂²⋊C₄	—	2	2	no	—
387	C₄²	—	2	2	no	—
388	C₄²	—	2	2	no	—
389	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
390	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
391	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
392	C₄²	C₂⁴×C₅₉	1	1	yes	characteristic
393	C₂³	—	2	4	no	—
394	C₂³	—	2	2	no	—
395	C₂³	—	4	2	no	—
396	C₂³	—	4	2	no	—
397	C₂³	#120×C₅₉	1	1	yes	characteristic
398	Q₈	—	2	2	no	—
399	Q₈	—	2	2	no	—
400	Q₈	—	4	4	no	—
401	Q₈	—	4	2	no	—
402	Q₈	—	4	2	no	—
403	Q₈	—	4	2	no	—
404	Q₈	—	8	2	no	—
405	Q₈	—	8	2	no	—
406	D₄	—	2	4	no	—
407	D₄	—	2	2	no	—
408	D₄	C₂×Q₁₆×C₅₉	1	4	yes	complemented
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	4	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	4	no	—
418	C₂×C₄	—	4	4	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	8	8	no	—
423	C₂×C₄	—	8	2	no	—
424	C₂×C₄	#120×C₅₉	1	1	yes	characteristic
425	C₂×C₄	#120×C₅₉	1	1	yes	characteristic
426	C₂×C₄	#120×C₅₉	1	1	yes	characteristic
427	C₂×C₄	C₂×Q₁₆×C₅₉	1	2	yes	—
428	C₂×C₄	#135×C₅₉	1	2	yes	—
429	C₂×C₄	AGL(1,ℤ/8)×C₅₉	1	2	yes	—
430	C₂×C₄	#137×C₅₉	1	2	yes	—
431	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
432	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
433	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
434	C₈	—	4	2	no	—
435	C₈	—	4	2	no	—
436	C₈	—	4	2	no	—
437	C₂²	—	2	4	no	—
438	C₂²	—	4	2	no	—
439	C₂²	—	4	2	no	—
440	C₂²	—	4	8	no	—
441	C₂²	C₅₉×#449	1	2	yes	—
442	C₂²	C₅₉×#451	1	2	yes	—
443	C₂²	C₅₉×#455	1	2	yes	—
444	C₂²	C₂×#120×C₅₉	1	1	yes	characteristic
445	C₄	—	2	1	no	—
446	C₄	—	2	1	no	—
447	C₄	—	4	2	no	—
448	C₄	—	4	2	no	—
449	C₄	—	4	2	no	—
450	C₄	—	4	4	no	—
451	C₄	—	8	2	no	—
452	C₄	C₅₉×#449	1	2	yes	—
453	C₄	C₅₉×#451	1	2	yes	—
454	C₄	C₂²×Q₁₆×C₅₉	1	1	yes	characteristic
455	C₄	C₂×#135×C₅₉	1	1	yes	characteristic
456	C₄	C₂×AGL(1,ℤ/8)×C₅₉	1	1	yes	characteristic
457	C₄	C₂×#137×C₅₉	1	1	yes	characteristic
458	C₂	—	4	4	no	—
459	C₂	C₅₉×#1644	1	4	yes	direct product factor
460	C₂	C₂×C₅₉×#451	1	1	yes	characteristic
461	C₂	C₂×C₅₉×#449	1	1	yes	characteristic
462	C₂	C₂×C₅₉×#455	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₉	#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₅₉
prime radical	C₂²×D₄×C₅₉	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₅₉ ◁ C₂×C₄²×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₅₉×#487	C₂	semidirect
4. C₂×C₅₉×#462	C₂	semidirect
5. C₅₉×#1644	C₂	direct (N × H)
6. C₂×C₅₉×#333	C₂	semidirect
7. C₂×C₅₉×Q₈⋊C₈	C₂	semidirect
24. C₅₉×#487	C₂²	semidirect
28. C₅₉×#462	C₂²	semidirect
36. C₅₉×#333	C₂²	semidirect
37. C₅₉×Q₈⋊C₈	C₂²	semidirect
113. C₂×D₄×C₅₉	Q₁₆	semidirect
176. D₄×C₅₉	C₂×Q₁₆	semidirect
205. C₂×#1644	C₅₉	direct (N × H)
228. C₂×#487	C₂×C₅₉	semidirect
230. C₂×#462	C₂×C₅₉	semidirect
231. #1644	C₂×C₅₉	direct (N × H)
232. C₂×#333	C₂×C₅₉	semidirect
233. C₂×Q₈⋊C₈	C₂×C₅₉	semidirect
236. C₂×C₅₉	#1644	direct (N × H)
255. #487	C₂²×C₅₉	semidirect
259. #462	C₂²×C₅₉	semidirect
267. #333	C₂²×C₅₉	semidirect
268. Q₈⋊C₈	C₂²×C₅₉	semidirect
270. C₅₉	C₂×#1644	direct (N × H)
345. C₂×D₄	Q₁₆×C₅₉	semidirect
408. D₄	C₂×Q₁₆×C₅₉	semidirect
459. C₂	C₅₉×#1644	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×#554	2
C₂×C₅₉×#487	2
C₂×C₅₉×#474	2
C₂×C₅₉×#462	2
C₅₉×#1644	2
C₂×C₅₉×#333	2
C₂×C₅₉×Q₈⋊C₈	2
C₂×C₅₉×D₄⋊C₈	2
C₂×#1644	59

Subgroups — C2×C59×#1644 #28430592

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅₉×#1644 #28430592