Subgroups — #28558781

Order 15104.

638 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21433207	C₂	1	1	yes	maximal, characteristic, complemented
2	#21433172	C₂	1	1	yes	maximal, characteristic, complemented
3	#21422975	C₂	1	1	yes	maximal, characteristic, complemented
4	#21422961	C₂	1	1	yes	maximal, characteristic, complemented
5	#21422940	C₂	1	1	yes	maximal, characteristic, complemented
6	#21422926	C₂	1	1	yes	maximal, characteristic, complemented
7	#21422920	C₂	1	1	yes	maximal, characteristic, complemented
8	SD₁₆⋊(C₅₉⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
9	SD₁₆×C₅₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
10	D₈×C₅₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	#21422881	C₂	1	1	yes	maximal, characteristic, complemented
12	#21422530	C₂	1	1	yes	maximal, characteristic, complemented
13	#21422495	C₂	1	1	yes	maximal, characteristic, complemented
14	#21422396	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₉×#3106	C₂	1	1	yes	maximal, characteristic
16	Q₈×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
17	Q₈×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
18	#16837480	C₂²	1	1	yes	characteristic
19	#16837480	C₂²	1	1	yes	characteristic
20	#16837474	—	2	1	no	—
21	#16837474	—	2	1	no	—
22	D₄×C₅₉⋊C₈	—	2	1	no	—
23	D₄×C₅₉⋊C₈	—	2	1	no	—
24	D₄×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
25	D₄×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
26	D₄×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
27	D₄×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
28	#16837459	C₂²	1	1	yes	characteristic
29	#16837455	—	2	1	no	—
30	#16837455	C₂²	1	1	yes	characteristic
31	#16837455	C₂²	1	1	yes	characteristic
32	C₂×C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
33	C₂×C₄⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
34	#16837369	—	2	1	no	—
35	#16837369	—	2	1	no	—
36	#16837155	C₂²	1	1	yes	characteristic
37	#16837155	C₂²	1	1	yes	characteristic
38	#16837153	C₂²	1	1	yes	characteristic
39	#16837153	C₂²	1	1	yes	characteristic
40	Q₈⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
41	Q₈⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
42	D₄⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
43	D₄⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
44	D₄⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
45	D₄⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
46	D₄⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
47	D₄⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
48	#16837124	C₂²	1	1	yes	characteristic
49	#16837124	C₂²	1	1	yes	characteristic
50	#16837123	C₂²	1	1	yes	characteristic
51	C₈×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
52	C₅₉×#532	C₂²	1	1	yes	characteristic
53	C₄×#41×C₅₉	C₂²	1	1	yes	characteristic
54	C₅₉×#482	C₄	1	1	yes	characteristic
55	C₅₉×#482	C₄	1	1	yes	characteristic
56	C₅₉×#477	C₄	1	1	yes	characteristic
57	C₅₉×#476	C₄	1	1	yes	characteristic
58	C₅₉×#460	C₄	1	1	yes	characteristic
59	C₅₉×#459	C₄	1	1	yes	characteristic
60	C₅₉×#449	C₄	1	1	yes	characteristic
61	C₅₉×#449	C₄	1	1	yes	characteristic
62	C₄×SD₁₆×C₅₉	C₂²	1	1	yes	characteristic
63	C₄×SD₁₆×C₅₉	C₂²	1	1	yes	characteristic
64	C₄×D₈×C₅₉	C₂²	1	1	yes	characteristic
65	C₄×D₈×C₅₉	C₂²	1	1	yes	characteristic
66	C₅₉×#431	C₂²	1	1	yes	characteristic
67	C₂×#11745664	—	2	1	no	—
68	C₂×#11745664	—	2	1	no	—
69	C₂²×C₅₉⋊C₈	—	2	1	no	—
70	C₂²×C₅₉⋊C₈	—	2	1	no	—
71	C₂²×C₅₉⋊C₈	—	2	1	no	—
72	C₂²×C₅₉⋊C₈	—	2	1	no	—
73	C₂²×C₅₉⋊C₈	—	2	1	no	—
74	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
75	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
76	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
77	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
78	C₄⋊(C₅₉⋊C₈)	D₄	1	1	yes	characteristic
79	C₄⋊(C₅₉⋊C₈)	D₄	1	1	yes	characteristic
80	C₄⋊(C₅₉⋊C₈)	C₂³	1	1	yes	characteristic
81	C₄⋊(C₅₉⋊C₈)	C₂³	1	1	yes	characteristic
82	C₄⋊(C₅₉⋊C₈)	C₂³	1	1	yes	characteristic
83	C₄⋊(C₅₉⋊C₈)	C₂³	1	1	yes	characteristic
84	C₂²⋊(C₅₉⋊C₈)	—	2	1	no	—
85	C₂²⋊(C₅₉⋊C₈)	—	2	1	no	—
86	C₂²⋊(C₅₉⋊C₈)	—	2	1	no	—
87	C₂²⋊(C₅₉⋊C₈)	—	2	1	no	—
88	C₂²⋊(C₅₉⋊C₈)	—	2	1	no	—
89	C₂²⋊(C₅₉⋊C₈)	—	2	1	no	—
90	C₂²⋊(C₅₉⋊C₈)	—	2	1	no	—
91	C₂²⋊(C₅₉⋊C₈)	—	2	1	no	—
92	C₂²⋊(C₅₉⋊C₈)	D₄	1	1	yes	characteristic
93	C₂²⋊(C₅₉⋊C₈)	D₄	1	1	yes	characteristic
94	#14273638	—	2	1	no	—
95	C₄×C₅₉⋊C₈	—	2	1	no	—
96	C₄×C₅₉⋊C₈	—	2	1	no	—
97	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
98	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
99	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
100	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
101	C₂×#41×C₅₉	—	2	1	no	—
102	C₂×#41×C₅₉	C₂×C₄	1	1	yes	characteristic
103	C₂×SD₁₆×C₅₉	C₂×C₄	1	1	yes	characteristic
104	C₂×SD₁₆×C₅₉	C₂×C₄	1	1	yes	characteristic
105	C₂×D₈×C₅₉	C₂×C₄	1	1	yes	characteristic
106	C₂×D₈×C₅₉	C₂×C₄	1	1	yes	characteristic
107	C₄⋊Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
108	#127×C₅₉	C₂×C₄	1	1	yes	characteristic
109	#124×C₅₉	—	2	1	no	—
110	#121×C₅₉	—	2	1	no	—
111	#121×C₅₉	C₂×C₄	1	1	yes	characteristic
112	#121×C₅₉	C₂×C₄	1	1	yes	characteristic
113	C₄×Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
114	C₄×Q₈×C₅₉	C₂³	1	1	yes	characteristic
115	C₄×D₄×C₅₉	—	2	1	no	—
116	C₄×D₄×C₅₉	—	2	1	no	—
117	C₄×D₄×C₅₉	—	2	1	no	—
118	C₄×D₄×C₅₉	C₂×C₄	1	1	yes	characteristic
119	C₄×D₄×C₅₉	C₂³	1	1	yes	characteristic
120	C₄×D₄×C₅₉	C₂³	1	1	yes	characteristic
121	C₄×D₄×C₅₉	C₂³	1	1	yes	characteristic
122	#117×C₅₉	—	2	1	no	—
123	#117×C₅₉	C₂×C₄	1	1	yes	characteristic
124	C₂×C₄²×C₅₉	—	2	1	no	—
125	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
126	#107×C₅₉	C₂×C₄	1	1	yes	characteristic
127	#107×C₅₉	C₂×C₄	1	1	yes	characteristic
128	#106×C₅₉	C₂×C₄	1	1	yes	characteristic
129	#106×C₅₉	C₂×C₄	1	1	yes	characteristic
130	C₄⋊C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
131	C₄⋊C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
132	#103×C₅₉	C₂×C₄	1	1	yes	characteristic
133	#103×C₅₉	C₂×C₄	1	1	yes	characteristic
134	#102×C₅₉	C₂×C₄	1	1	yes	characteristic
135	#102×C₅₉	C₂×C₄	1	1	yes	characteristic
136	#102×C₅₉	C₂×C₄	1	1	yes	characteristic
137	#102×C₅₉	C₂×C₄	1	1	yes	characteristic
138	#102×C₅₉	C₂×C₄	1	1	yes	characteristic
139	#102×C₅₉	C₂×C₄	1	1	yes	characteristic
140	C₂²⋊C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
141	C₂²⋊C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
142	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
144	#41×C₅₉	—	2	2	no	—
145	#41×C₅₉	—	2	2	no	—
146	#41×C₅₉	—	8	1	no	—
147	#41×C₅₉	—	8	1	no	—
148	C₂×Q₈×C₅₉	—	2	1	no	—
149	C₂×Q₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
150	C₂×D₄×C₅₉	—	2	1	no	—
151	C₂×D₄×C₅₉	—	2	1	no	—
152	C₂×D₄×C₅₉	—	2	1	no	—
153	C₂×D₄×C₅₉	—	2	1	no	—
154	C₂×D₄×C₅₉	—	2	1	no	—
155	C₂×D₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
156	C₂×D₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
157	C₂×D₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
158	C₂²×C₄×C₅₉	—	2	1	no	—
159	C₂²×C₄×C₅₉	—	2	1	no	—
160	C₂²×C₄×C₅₉	—	2	1	no	—
161	C₂²×C₄×C₅₉	—	2	1	no	—
162	C₂²×C₄×C₅₉	—	2	1	no	—
163	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
164	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
166	SD₁₆×C₅₉	—	2	2	no	—
167	SD₁₆×C₅₉	—	2	2	no	—
168	D₈×C₅₉	—	2	2	no	—
169	D₈×C₅₉	—	2	2	no	—
170	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
171	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
172	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
173	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
174	C₄⋊C₄×C₅₉	—	2	1	no	—
175	C₄⋊C₄×C₅₉	—	2	1	no	—
176	C₄⋊C₄×C₅₉	—	2	1	no	—
177	C₄⋊C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
178	C₄⋊C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
179	C₄⋊C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
180	C₄⋊C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
181	C₂²⋊C₄×C₅₉	—	2	1	no	—
182	C₂²⋊C₄×C₅₉	—	2	1	no	—
183	C₂²⋊C₄×C₅₉	—	2	1	no	—
184	C₂²⋊C₄×C₅₉	—	2	1	no	—
185	C₂²⋊C₄×C₅₉	—	2	1	no	—
186	C₂²⋊C₄×C₅₉	—	2	1	no	—
187	C₂²⋊C₄×C₅₉	—	2	1	no	—
188	C₄²×C₅₉	—	2	1	no	—
189	C₄²×C₅₉	—	2	1	no	—
190	C₄²×C₅₉	—	2	1	no	—
191	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
192	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
193	C₄²×C₅₉	#41	1	1	yes	characteristic
194	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
195	#11745664	—	8	1	no	—
196	#11745664	—	8	1	no	—
197	C₂×C₅₉⋊C₈	—	2	1	no	—
198	C₂×C₅₉⋊C₈	—	2	1	no	—
199	C₂×C₅₉⋊C₈	—	2	1	no	—
200	C₂×C₅₉⋊C₈	—	2	1	no	—
201	C₂×C₅₉⋊C₈	—	2	1	no	—
202	C₂×C₅₉⋊C₈	—	2	1	no	—
203	C₂×C₅₉⋊C₈	—	8	1	no	—
204	C₂×C₅₉⋊C₈	—	8	1	no	—
205	C₂×C₅₉⋊C₈	—	8	1	no	—
206	C₂×C₅₉⋊C₈	—	8	1	no	—
207	C₂×C₅₉⋊C₈	—	8	1	no	—
208	C₂×C₅₉⋊C₈	C₂×D₄	1	1	yes	characteristic
209	C₂×C₅₉⋊C₈	C₂×D₄	1	1	yes	characteristic
210	C₂×C₅₉⋊C₈	C₂×D₄	1	1	yes	characteristic
211	C₂×C₅₉⋊C₈	C₂×D₄	1	1	yes	characteristic
212	C₂³×C₅₉	—	2	1	no	—
213	C₂³×C₅₉	—	2	1	no	—
214	C₂³×C₅₉	—	2	1	no	—
215	C₂³×C₅₉	C₄×D₄	1	1	yes	characteristic
216	Q₈×C₅₉	—	2	1	no	—
217	Q₈×C₅₉	—	8	1	no	—
218	Q₈×C₅₉	#131	1	2	yes	—
219	D₄×C₅₉	—	2	4	no	—
220	D₄×C₅₉	—	2	1	no	—
221	D₄×C₅₉	—	2	1	no	—
222	D₄×C₅₉	—	2	1	no	—
223	D₄×C₅₉	—	2	1	no	—
224	D₄×C₅₉	—	2	1	no	—
225	D₄×C₅₉	—	8	1	no	—
226	D₄×C₅₉	—	8	1	no	—
227	D₄×C₅₉	—	8	1	no	—
228	D₄×C₅₉	—	8	1	no	—
229	D₄×C₅₉	#131	1	2	yes	—
230	C₂×C₄×C₅₉	—	2	4	no	—
231	C₂×C₄×C₅₉	—	2	1	no	—
232	C₂×C₄×C₅₉	—	2	1	no	—
233	C₂×C₄×C₅₉	—	2	1	no	—
234	C₂×C₄×C₅₉	—	2	1	no	—
235	C₂×C₄×C₅₉	—	2	1	no	—
236	C₂×C₄×C₅₉	—	2	1	no	—
237	C₂×C₄×C₅₉	—	2	1	no	—
238	C₂×C₄×C₅₉	—	2	1	no	—
239	C₂×C₄×C₅₉	—	2	1	no	—
240	C₂×C₄×C₅₉	—	4	1	no	—
241	C₂×C₄×C₅₉	—	4	1	no	—
242	C₂×C₄×C₅₉	—	4	1	no	—
243	C₂×C₄×C₅₉	—	4	1	no	—
244	C₂×C₄×C₅₉	—	4	1	no	—
245	C₂×C₄×C₅₉	—	4	1	no	—
246	C₂×C₄×C₅₉	—	4	1	no	—
247	C₂×C₄×C₅₉	—	8	1	no	—
248	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
249	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
250	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
251	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
252	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
253	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
254	C₈×C₅₉	—	2	1	no	—
255	C₈×C₅₉	—	2	1	no	—
256	C₈×C₅₉	—	2	1	no	—
257	C₈×C₅₉	—	2	1	no	—
258	C₅₉⋊C₈	—	2	1	no	—
259	C₅₉⋊C₈	—	2	1	no	—
260	C₅₉⋊C₈	—	2	1	no	—
261	C₅₉⋊C₈	—	2	1	no	—
262	C₅₉⋊C₈	—	4	1	no	—
263	C₅₉⋊C₈	—	4	1	no	—
264	C₅₉⋊C₈	—	4	1	no	—
265	C₅₉⋊C₈	—	4	1	no	—
266	C₅₉⋊C₈	—	4	1	no	—
267	C₅₉⋊C₈	—	4	1	no	—
268	#17920	—	59	1	no	maximal, Sylow
269	C₂²×C₅₉	—	2	1	no	—
270	C₂²×C₅₉	—	2	2	no	—
271	C₂²×C₅₉	—	2	1	no	—
272	C₂²×C₅₉	—	2	1	no	—
273	C₂²×C₅₉	—	4	1	no	—
274	C₂²×C₅₉	—	4	1	no	—
275	C₂²×C₅₉	—	4	1	no	—
276	C₂²×C₅₉	—	4	1	no	—
277	C₂²×C₅₉	—	4	1	no	—
278	C₂²×C₅₉	—	4	1	no	—
279	C₂²×C₅₉	—	4	1	no	—
280	C₂²×C₅₉	—	4	1	no	—
281	C₂²×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
282	C₄×C₅₉	—	2	1	no	—
283	C₄×C₅₉	—	2	2	no	—
284	C₄×C₅₉	—	2	1	no	—
285	C₄×C₅₉	—	2	1	no	—
286	C₄×C₅₉	—	2	1	no	—
287	C₄×C₅₉	—	4	1	no	—
288	C₄×C₅₉	—	4	1	no	—
289	C₄×C₅₉	—	4	1	no	—
290	C₄×C₅₉	—	4	1	no	—
291	C₄×C₅₉	C₂×#131	1	1	yes	characteristic
292	C₄×C₅₉	C₂×#131	1	1	yes	characteristic
293	C₄×C₅₉	#576	1	1	yes	characteristic
294	C₄×C₅₉	#577	1	1	yes	characteristic
295	#3106	D₅₉	1	1	yes	characteristic
296	#2988	—	59	1	no	—
297	#2981	—	59	1	no	—
298	#1588	—	59	1	no	—
299	#1586	—	59	1	no	—
300	#1583	—	59	1	no	—
301	#1581	—	59	1	no	—
302	#1580	—	59	1	no	—
303	SD₁₆⋊C₈	—	59	1	no	—
304	C₈×SD₁₆	—	59	1	no	—
305	C₈×D₈	—	59	1	no	—
306	#1573	—	59	1	no	—
307	#1488	—	59	1	no	—
308	#1480	—	59	1	no	—
309	#1454	—	59	1	no	—
310	C₂×C₅₉	—	4	1	no	—
311	C₂×C₅₉	—	4	2	no	—
312	C₂×C₅₉	—	8	1	no	—
313	C₂×C₅₉	—	8	1	no	—
314	C₂×C₅₉	#2929	1	1	yes	characteristic
315	C₂×C₅₉	#2946	1	1	yes	characteristic
316	C₂×C₅₉	#2957	1	1	yes	characteristic
317	#532	C₂×D₅₉	1	1	yes	characteristic
318	C₄×#41	C₂×D₅₉	1	1	yes	characteristic
319	#482	Dic₅₉	1	1	yes	characteristic
320	#482	Dic₅₉	1	1	yes	characteristic
321	#477	Dic₅₉	1	1	yes	characteristic
322	#476	Dic₅₉	1	1	yes	characteristic
323	#460	Dic₅₉	1	1	yes	characteristic
324	#459	Dic₅₉	1	1	yes	characteristic
325	#449	Dic₅₉	1	1	yes	characteristic
326	#449	Dic₅₉	1	1	yes	characteristic
327	C₈×Q₈	—	59	1	no	—
328	C₈×Q₈	—	59	1	no	—
329	C₄×SD₁₆	C₂×D₅₉	1	1	yes	characteristic
330	C₄×SD₁₆	C₂×D₅₉	1	1	yes	characteristic
331	C₄×D₈	C₂×D₅₉	1	1	yes	characteristic
332	C₄×D₈	C₂×D₅₉	1	1	yes	characteristic
333	#436	—	59	1	no	—
334	#436	—	59	1	no	—
335	#435	—	118	1	no	—
336	#435	—	118	1	no	—
337	C₈×D₄	—	59	1	no	—
338	C₈×D₄	—	59	1	no	—
339	C₈×D₄	—	59	1	no	—
340	C₈×D₄	—	59	1	no	—
341	C₈×D₄	—	118	1	no	—
342	C₈×D₄	—	118	1	no	—
343	#432	—	59	1	no	—
344	#431	—	59	1	no	—
345	#431	—	59	1	no	—
346	#431	—	118	1	no	—
347	#431	C₂×D₅₉	1	1	yes	characteristic
348	C₂×C₄⋊C₈	—	59	1	no	—
349	C₂×C₄⋊C₈	—	118	1	no	—
350	#408	—	118	1	no	—
351	#408	—	118	1	no	—
352	#335	—	59	1	no	—
353	#335	—	59	1	no	—
354	#334	—	59	1	no	—
355	#334	—	59	1	no	—
356	Q₈⋊C₈	—	59	1	no	—
357	Q₈⋊C₈	—	59	1	no	—
358	D₄⋊C₈	—	59	1	no	—
359	D₄⋊C₈	—	59	1	no	—
360	D₄⋊C₈	—	59	1	no	—
361	D₄⋊C₈	—	59	1	no	—
362	D₄⋊C₈	—	59	1	no	—
363	D₄⋊C₈	—	59	1	no	—
364	#322	—	59	1	no	—
365	#322	—	59	1	no	—
366	#322	—	59	1	no	—
367	C₈²	—	59	1	no	—
368	C₅₉	#17920	1	1	yes	characteristic, complemented, Sylow
369	C₂×#41	—	2	1	no	—
370	C₂×#41	C₂×Dic₅₉	1	1	yes	characteristic
371	C₂×SD₁₆	C₂×Dic₅₉	1	1	yes	characteristic
372	C₂×SD₁₆	C₂×Dic₅₉	1	1	yes	characteristic
373	C₂×D₈	C₂×Dic₅₉	1	1	yes	characteristic
374	C₂×D₈	C₂×Dic₅₉	1	1	yes	characteristic
375	C₂×M₁₆	—	118	1	no	—
376	C₂×M₁₆	—	118	1	no	—
377	C₂²×C₈	—	118	1	no	—
378	C₂²×C₈	—	118	1	no	—
379	C₂²×C₈	—	118	1	no	—
380	C₂²×C₈	—	118	1	no	—
381	C₂²×C₈	—	118	1	no	—
382	C₄⋊Q₈	C₂×Dic₅₉	1	1	yes	characteristic
383	#127	C₂×Dic₅₉	1	1	yes	characteristic
384	#124	—	2	1	no	—
385	#121	—	2	1	no	—
386	#121	C₂×Dic₅₉	1	1	yes	characteristic
387	#121	C₂×Dic₅₉	1	1	yes	characteristic
388	C₄×Q₈	C₂×Dic₅₉	1	1	yes	characteristic
389	C₄×Q₈	C₂²×D₅₉	1	1	yes	characteristic
390	C₄×D₄	—	2	1	no	—
391	C₄×D₄	—	2	1	no	—
392	C₄×D₄	—	2	1	no	—
393	C₄×D₄	C₂×Dic₅₉	1	1	yes	characteristic
394	C₄×D₄	C₂²×D₅₉	1	1	yes	characteristic
395	C₄×D₄	C₂²×D₅₉	1	1	yes	characteristic
396	C₄×D₄	C₂²×D₅₉	1	1	yes	characteristic
397	#117	—	2	1	no	—
398	#117	C₂×Dic₅₉	1	1	yes	characteristic
399	C₂×C₄²	—	2	1	no	—
400	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
401	#107	C₂×Dic₅₉	1	1	yes	characteristic
402	#107	C₂×Dic₅₉	1	1	yes	characteristic
403	#106	C₂×Dic₅₉	1	1	yes	characteristic
404	#106	C₂×Dic₅₉	1	1	yes	characteristic
405	C₄⋊C₈	—	59	1	no	—
406	C₄⋊C₈	—	59	1	no	—
407	C₄⋊C₈	—	59	1	no	—
408	C₄⋊C₈	—	59	1	no	—
409	C₄⋊C₈	—	59	1	no	—
410	C₄⋊C₈	—	59	1	no	—
411	C₄⋊C₈	—	118	1	no	—
412	C₄⋊C₈	—	118	1	no	—
413	C₄⋊C₈	—	118	1	no	—
414	C₄⋊C₈	—	118	1	no	—
415	C₄⋊C₈	C₂×Dic₅₉	1	1	yes	characteristic
416	C₄⋊C₈	C₂×Dic₅₉	1	1	yes	characteristic
417	#103	C₂×Dic₅₉	1	1	yes	characteristic
418	#103	C₂×Dic₅₉	1	1	yes	characteristic
419	#102	C₂×Dic₅₉	1	1	yes	characteristic
420	#102	C₂×Dic₅₉	1	1	yes	characteristic
421	#102	C₂×Dic₅₉	1	1	yes	characteristic
422	#102	C₂×Dic₅₉	1	1	yes	characteristic
423	#102	C₂×Dic₅₉	1	1	yes	characteristic
424	#102	C₂×Dic₅₉	1	1	yes	characteristic
425	C₂²⋊C₈	—	59	1	no	—
426	C₂²⋊C₈	—	59	1	no	—
427	C₂²⋊C₈	—	118	1	no	—
428	C₂²⋊C₈	—	118	1	no	—
429	C₂²⋊C₈	—	118	1	no	—
430	C₂²⋊C₈	—	118	1	no	—
431	C₂²⋊C₈	—	118	1	no	—
432	C₂²⋊C₈	—	118	1	no	—
433	C₂²⋊C₈	—	118	1	no	—
434	C₂²⋊C₈	—	118	1	no	—
435	C₂²⋊C₈	C₂×Dic₅₉	1	1	yes	characteristic
436	C₂²⋊C₈	C₂×Dic₅₉	1	1	yes	characteristic
437	#97	—	118	1	no	—
438	C₄×C₈	—	59	1	no	—
439	C₄×C₈	—	59	1	no	—
440	C₄×C₈	—	59	1	no	—
441	C₄×C₈	—	59	1	no	—
442	C₄×C₈	—	118	1	no	—
443	C₄×C₈	—	118	1	no	—
444	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
445	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
446	#41	—	2	2	no	—
447	#41	—	2	2	no	—
448	#41	—	8	1	no	—
449	#41	—	8	1	no	—
450	C₂×Q₈	—	2	1	no	—
451	C₂×Q₈	C₂²×Dic₅₉	1	1	yes	characteristic
452	C₂×D₄	—	2	1	no	—
453	C₂×D₄	—	2	1	no	—
454	C₂×D₄	—	2	1	no	—
455	C₂×D₄	—	2	1	no	—
456	C₂×D₄	—	2	1	no	—
457	C₂×D₄	C₂²×Dic₅₉	1	1	yes	characteristic
458	C₂×D₄	C₂²×Dic₅₉	1	1	yes	characteristic
459	C₂×D₄	C₂²×Dic₅₉	1	1	yes	characteristic
460	C₂²×C₄	—	2	1	no	—
461	C₂²×C₄	—	2	1	no	—
462	C₂²×C₄	—	2	1	no	—
463	C₂²×C₄	—	2	1	no	—
464	C₂²×C₄	—	2	1	no	—
465	C₂²×C₄	D₄×D₅₉	1	1	yes	characteristic
466	C₂²×C₄	#11745687	1	1	yes	characteristic
467	C₂²×C₄	C₂²×Dic₅₉	1	1	yes	characteristic
468	SD₁₆	—	2	2	no	—
469	SD₁₆	—	2	2	no	—
470	D₈	—	2	2	no	—
471	D₈	—	2	2	no	—
472	M₁₆	—	472	1	no	—
473	M₁₆	—	472	1	no	—
474	C₂×C₈	—	59	1	no	—
475	C₂×C₈	—	59	1	no	—
476	C₂×C₈	—	59	1	no	—
477	C₂×C₈	—	59	1	no	—
478	C₂×C₈	—	118	1	no	—
479	C₂×C₈	—	118	1	no	—
480	C₂×C₈	—	118	1	no	—
481	C₂×C₈	—	118	1	no	—
482	C₂×C₈	—	118	1	no	—
483	C₂×C₈	—	118	1	no	—
484	C₂×C₈	—	472	1	no	—
485	C₂×C₈	—	472	1	no	—
486	C₂×C₈	—	472	1	no	—
487	C₂×C₈	—	472	1	no	—
488	C₂×C₈	—	472	1	no	—
489	C₂×C₈	C₂²×Dic₅₉	1	1	yes	characteristic
490	C₂×C₈	C₂²×Dic₅₉	1	1	yes	characteristic
491	C₂×C₈	C₂²×Dic₅₉	1	1	yes	characteristic
492	C₂×C₈	C₂²×Dic₅₉	1	1	yes	characteristic
493	C₄⋊C₄	—	2	1	no	—
494	C₄⋊C₄	—	2	1	no	—
495	C₄⋊C₄	—	2	1	no	—
496	C₄⋊C₄	C₂²×Dic₅₉	1	1	yes	characteristic
497	C₄⋊C₄	C₂²×Dic₅₉	1	1	yes	characteristic
498	C₄⋊C₄	C₂²×Dic₅₉	1	1	yes	characteristic
499	C₄⋊C₄	C₂²×Dic₅₉	1	1	yes	characteristic
500	C₂²⋊C₄	—	2	1	no	—
501	C₂²⋊C₄	—	2	1	no	—
502	C₂²⋊C₄	—	2	1	no	—
503	C₂²⋊C₄	—	2	1	no	—
504	C₂²⋊C₄	—	2	1	no	—
505	C₂²⋊C₄	—	2	1	no	—
506	C₂²⋊C₄	—	2	1	no	—
507	C₄²	—	2	1	no	—
508	C₄²	—	2	1	no	—
509	C₄²	—	2	1	no	—
510	C₄²	D₄×D₅₉	1	1	yes	characteristic
511	C₄²	#11745687	1	1	yes	characteristic
512	C₄²	C₂²×Dic₅₉	1	1	yes	characteristic
513	C₄²	C₂³×D₅₉	1	1	yes	characteristic
514	C₂³	—	2	1	no	—
515	C₂³	—	2	1	no	—
516	C₂³	—	2	1	no	—
517	C₂³	D₄×Dic₅₉	1	1	yes	characteristic
518	Q₈	—	2	1	no	—
519	Q₈	—	8	1	no	—
520	Q₈	#14273734	1	2	yes	—
521	D₄	—	2	4	no	—
522	D₄	—	2	1	no	—
523	D₄	—	2	1	no	—
524	D₄	—	2	1	no	—
525	D₄	—	2	1	no	—
526	D₄	—	2	1	no	—
527	D₄	—	8	1	no	—
528	D₄	—	8	1	no	—
529	D₄	—	8	1	no	—
530	D₄	—	8	1	no	—
531	D₄	#14273734	1	2	yes	—
532	C₂×C₄	—	2	4	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	4	1	no	—
543	C₂×C₄	—	4	1	no	—
544	C₂×C₄	—	4	1	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	4	1	no	—
549	C₂×C₄	—	8	1	no	—
550	C₂×C₄	D₄×Dic₅₉	1	1	yes	characteristic
551	C₂×C₄	D₄×Dic₅₉	1	1	yes	characteristic
552	C₂×C₄	D₄×Dic₅₉	1	1	yes	characteristic
553	C₂×C₄	C₂³×Dic₅₉	1	1	yes	characteristic
554	C₂×C₄	C₂×D₄×D₅₉	1	1	yes	characteristic
555	C₂×C₄	C₂×#11745687	1	1	yes	characteristic
556	C₈	—	2	1	no	—
557	C₈	—	2	1	no	—
558	C₈	—	2	1	no	—
559	C₈	—	2	1	no	—
560	C₈	—	118	1	no	—
561	C₈	—	118	1	no	—
562	C₈	—	118	1	no	—
563	C₈	—	118	1	no	—
564	C₈	—	236	1	no	—
565	C₈	—	236	1	no	—
566	C₈	—	236	1	no	—
567	C₈	—	236	1	no	—
568	C₈	—	236	1	no	—
569	C₈	—	236	1	no	—
570	C₂²	—	2	1	no	—
571	C₂²	—	2	1	no	—
572	C₂²	—	2	1	no	—
573	C₂²	—	2	2	no	—
574	C₂²	—	4	1	no	—
575	C₂²	—	4	1	no	—
576	C₂²	—	4	1	no	—
577	C₂²	—	4	1	no	—
578	C₂²	—	4	1	no	—
579	C₂²	—	4	1	no	—
580	C₂²	—	4	1	no	—
581	C₂²	—	4	1	no	—
582	C₂²	C₂×D₄×Dic₅₉	1	1	yes	characteristic
583	C₄	—	2	1	no	—
584	C₄	—	2	1	no	—
585	C₄	—	2	1	no	—
586	C₄	—	2	1	no	—
587	C₄	—	2	2	no	—
588	C₄	—	4	1	no	—
589	C₄	—	4	1	no	—
590	C₄	—	4	1	no	—
591	C₄	—	4	1	no	—
592	C₄	C₂×#14273734	1	1	yes	characteristic
593	C₄	C₂×#14273734	1	1	yes	characteristic
594	C₄	#16838206	1	1	yes	characteristic
595	C₄	#16838212	1	1	yes	characteristic
596	C₂	—	4	1	no	—
597	C₂	—	4	2	no	—
598	C₂	—	8	1	no	—
599	C₂	—	8	1	no	—
600	C₂	#21432791	1	1	yes	characteristic
601	C₂	#21432929	1	1	yes	characteristic
602	C₂	#21433013	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₅₉
commutator	C₂×C₄×C₅₉	C₂³×C₄
Frattini	C₄²	C₂³×D₅₉
Fitting, prime radical	C₅₉×#3106	C₂
socle	C₂²×C₅₉	C₂×C₄×D₄
cosocle	C₄²×C₅₉	C₂⁴
hypercenter	#3106	D₅₉
hypocenter	C₅₉	#17920
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3106

Complements

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

N	H ≅ G/N	type
1. #21433207	C₂	semidirect
2. #21433172	C₂	semidirect
3. #21422975	C₂	semidirect
4. #21422961	C₂	semidirect
5. #21422940	C₂	semidirect
6. #21422926	C₂	semidirect
7. #21422920	C₂	semidirect
8. SD₁₆⋊(C₅₉⋊C₈)	C₂	semidirect
9. SD₁₆×C₅₉⋊C₈	C₂	semidirect
10. D₈×C₅₉⋊C₈	C₂	semidirect
11. #21422881	C₂	semidirect
12. #21422530	C₂	semidirect
13. #21422495	C₂	semidirect
14. #21422396	C₂	semidirect
368. C₅₉	#17920	semidirect

Maximal subgroups

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

subgroup	index
#21433207	2
#21433172	2
#21422975	2
#21422961	2
#21422940	2
#21422926	2
#21422920	2
SD₁₆⋊(C₅₉⋊C₈)	2
SD₁₆×C₅₉⋊C₈	2
D₈×C₅₉⋊C₈	2
#21422881	2
#21422530	2
#21422495	2
#21422396	2
C₅₉×#3106	2
#17920	59