Subgroups — #28558133

Order 15104.

702 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21433206	C₂	1	1	yes	maximal, characteristic
2	#21433175	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#14273759	C₂	1	1	yes	maximal, characteristic
4	#21422915	C₂	1	1	yes	maximal, characteristic, complemented
5	#21422913	C₂	1	1	yes	maximal, characteristic, complemented
6	#21422907	C₂	1	1	yes	maximal, characteristic, complemented
7	#21422906	C₂	1	1	yes	maximal, characteristic, complemented
8	#21422900	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈×#11745660	C₂	1	1	yes	maximal, characteristic, complemented
10	#21422893	C₂	1	1	yes	maximal, characteristic, complemented
11	#21422847	C₂	1	1	yes	maximal, characteristic, complemented
12	#21422477	C₂	1	1	yes	maximal, characteristic
13	Q₈⋊C₈×D₅₉	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈×#11745659	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈×Q₁₆×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#14273759	C₄	1	1	yes	characteristic
17	C₄×#11745689	C₂²	1	1	yes	characteristic
18	C₄×Q₈×D₅₉	C₂²	1	1	yes	characteristic
19	Q₈×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
20	Q₈×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
21	C₈×Dic₁₁₈	—	2	1	no	—
22	C₈×Dic₁₁₈	C₂²	1	1	yes	characteristic
23	#16837526	—	2	1	no	—
24	#16837526	C₂²	1	1	yes	characteristic
25	#16837509	C₄	1	1	yes	characteristic
26	#16837506	C₄	1	1	yes	characteristic
27	#16837505	C₄	1	1	yes	characteristic
28	#16837501	C₄	1	1	yes	characteristic
29	C₄×#11745672	C₂²	1	1	yes	characteristic
30	C₄×#11745660	C₂²	1	1	yes	characteristic
31	C₄×#11745671	C₂²	1	1	yes	characteristic
32	C₈×D₂₃₆	—	2	1	no	—
33	C₈×D₂₃₆	C₂²	1	1	yes	characteristic
34	#16837467	—	2	1	no	—
35	#16837467	C₂²	1	1	yes	characteristic
36	#16837454	—	2	1	no	—
37	#16837454	C₂²	1	1	yes	characteristic
38	#16837453	—	2	1	no	—
39	#16837453	—	2	1	no	—
40	#16837453	C₂²	1	1	yes	characteristic
41	#16837443	C₄	1	1	yes	characteristic
42	C₄⋊C₈×D₅₉	—	2	1	no	—
43	C₄⋊C₈×D₅₉	C₂²	1	1	yes	characteristic
44	#16837409	C₄	1	1	yes	characteristic
45	#16837402	C₄	1	1	yes	characteristic
46	C₄×#11745659	C₂²	1	1	yes	characteristic
47	C₄×C₈×D₅₉	C₂²	1	1	yes	characteristic
48	#16837154	C₂²	1	1	yes	characteristic
49	#16837153	C₂²	1	1	yes	characteristic
50	#16837152	C₂²	1	1	yes	characteristic
51	#16837134	C₂²	1	1	yes	characteristic
52	Q₈⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
53	Q₈⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
54	#16837132	C₂²	1	1	yes	characteristic
55	#16837131	C₂²	1	1	yes	characteristic
56	#16837129	C₂²	1	1	yes	characteristic
57	#16837124	C₂²	1	1	yes	characteristic
58	#16837123	C₂²	1	1	yes	characteristic
59	C₈×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
60	C₈×Q₈×C₅₉	C₂²	1	1	yes	characteristic
61	C₈×Q₈×C₅₉	C₂²	1	1	yes	characteristic
62	C₄×Q₁₆×C₅₉	C₂²	1	1	yes	characteristic
63	C₅₉×#335	C₂²	1	1	yes	characteristic
64	C₅₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
65	C₅₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
66	C₈²×C₅₉	C₂²	1	1	yes	characteristic
67	C₂×#11745689	C₂×C₄	1	1	yes	characteristic
68	C₂×Q₈×D₅₉	C₂×C₄	1	1	yes	characteristic
69	#14273759	C₈	1	8	yes	complemented
70	C₂×#11745672	C₂×C₄	1	1	yes	characteristic
71	C₂×#11745660	C₂×C₄	1	1	yes	characteristic
72	C₂×#11745671	C₂×C₄	1	1	yes	characteristic
73	C₂×#11745659	C₂×C₄	1	1	yes	characteristic
74	C₂×#11745659	C₂×C₄	1	1	yes	characteristic
75	C₂×C₈×D₅₉	—	2	1	no	—
76	C₂×C₈×D₅₉	—	2	1	no	—
77	C₂×C₈×D₅₉	—	2	1	no	—
78	C₂×C₈×D₅₉	—	2	1	no	—
79	Q₈×Dic₅₉	C₂×C₄	1	1	yes	characteristic
80	Q₈×Dic₅₉	C₂×C₄	1	1	yes	characteristic
81	C₄×Dic₁₁₈	—	2	1	no	—
82	C₄×Dic₁₁₈	C₂³	1	1	yes	characteristic
83	#14273692	—	2	1	no	—
84	#14273692	C₂×C₄	1	1	yes	characteristic
85	C₄×D₂₃₆	—	2	1	no	—
86	C₄×D₂₃₆	C₂³	1	1	yes	characteristic
87	#14273689	—	2	1	no	—
88	#14273689	C₂×C₄	1	1	yes	characteristic
89	#14273685	—	2	1	no	—
90	#14273685	C₂×C₄	1	1	yes	characteristic
91	C₄⋊C₄×D₅₉	—	2	1	no	—
92	C₄⋊C₄×D₅₉	C₂×C₄	1	1	yes	characteristic
93	C₄²×D₅₉	—	2	1	no	—
94	C₄²×D₅₉	—	2	1	no	—
95	C₄²×D₅₉	C₂³	1	1	yes	characteristic
96	#14273660	C₂×C₄	1	1	yes	characteristic
97	#14273659	C₂×C₄	1	1	yes	characteristic
98	#14273658	C₂×C₄	1	1	yes	characteristic
99	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
100	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
101	C₄⋊(C₅₉⋊C₈)	C₂³	1	1	yes	characteristic
102	C₄⋊(C₅₉⋊C₈)	C₂³	1	1	yes	characteristic
103	Dic₅₉⋊C₈	—	2	1	no	—
104	Dic₅₉⋊C₈	—	2	1	no	—
105	Dic₅₉⋊C₈	—	2	1	no	—
106	Dic₅₉⋊C₈	D₄	1	1	yes	characteristic
107	Dic₅₉⋊C₈	D₄	1	1	yes	characteristic
108	#14273652	C₂×C₄	1	1	yes	characteristic
109	#14273651	C₂×C₄	1	1	yes	characteristic
110	#14273651	C₂×C₄	1	1	yes	characteristic
111	#14273650	C₂×C₄	1	1	yes	characteristic
112	#14273649	C₂×C₄	1	1	yes	characteristic
113	#14273647	C₂×C₄	1	1	yes	characteristic
114	(C₂×D₅₉)⋊C₈	—	2	1	no	—
115	(C₂×D₅₉)⋊C₈	—	2	1	no	—
116	(C₂×D₅₉)⋊C₈	—	2	1	no	—
117	(C₂×D₅₉)⋊C₈	D₄	1	1	yes	characteristic
118	(C₂×D₅₉)⋊C₈	D₄	1	1	yes	characteristic
119	#14273637	C₂×C₄	1	1	yes	characteristic
120	#14273637	C₂×C₄	1	1	yes	characteristic
121	C₄×C₅₉⋊C₈	—	2	1	no	—
122	C₄×C₅₉⋊C₈	—	2	1	no	—
123	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
124	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
125	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
126	C₈×Dic₅₉	—	2	1	no	—
127	C₈×Dic₅₉	—	2	1	no	—
128	C₈×Dic₅₉	—	2	1	no	—
129	C₈×Dic₅₉	—	2	1	no	—
130	C₂×Q₁₆×C₅₉	C₂×C₄	1	1	yes	characteristic
131	C₄×Q₈×C₅₉	C₂³	1	1	yes	characteristic
132	C₄×Q₈×C₅₉	C₂³	1	1	yes	characteristic
133	#107×C₅₉	C₂×C₄	1	1	yes	characteristic
134	C₄⋊C₈×C₅₉	—	2	1	no	—
135	C₄⋊C₈×C₅₉	—	2	1	no	—
136	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
137	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
138	#103×C₅₉	C₂×C₄	1	1	yes	characteristic
139	#103×C₅₉	C₂×C₄	1	1	yes	characteristic
140	C₄×C₈×C₅₉	—	2	1	no	—
141	C₄×C₈×C₅₉	—	2	1	no	—
142	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
144	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
145	C₂×Q₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
146	C₂×Q₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
147	#11745689	—	2	2	no	—
148	#11745689	C₂×C₈	1	4	yes	—
149	Q₈×D₅₉	—	2	2	no	—
150	Q₈×D₅₉	C₂×C₈	1	4	yes	complemented
151	C₂×D₂₃₆	—	2	1	no	—
152	C₂×D₂₃₆	C₂²×C₄	1	1	yes	characteristic
153	C₂×C₄×D₅₉	—	2	1	no	—
154	C₂×C₄×D₅₉	—	2	1	no	—
155	C₂×C₄×D₅₉	—	2	1	no	—
156	C₂×C₄×D₅₉	—	2	1	no	—
157	C₂×C₄×D₅₉	—	2	1	no	—
158	C₂×C₄×D₅₉	C₂²×C₄	1	1	yes	characteristic
159	C₂×C₄×D₅₉	C₂×D₄	1	1	yes	characteristic
160	C₂×C₄×D₅₉	#41	1	1	yes	characteristic
161	C₂×Dic₁₁₈	—	2	1	no	—
162	C₂×Dic₁₁₈	C₂²×C₄	1	1	yes	characteristic
163	Q₁₆×C₅₉	C₂×C₈	1	4	yes	complemented
164	C₂×C₈×C₅₉	—	2	1	no	—
165	C₂×C₈×C₅₉	—	2	1	no	—
166	C₂×C₈×C₅₉	—	2	1	no	—
167	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
168	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
169	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
170	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
171	C₄⋊C₄×C₅₉	—	2	1	no	—
172	C₄⋊C₄×C₅₉	—	2	1	no	—
173	C₄⋊C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
174	C₄⋊C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
175	C₄²×C₅₉	—	2	1	no	—
176	C₄²×C₅₉	—	2	1	no	—
177	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
178	#11745672	C₂×C₈	1	4	yes	complemented
179	#11745671	C₂×C₈	1	4	yes	complemented
180	(C₂×D₅₉)⋊C₄	—	2	1	no	—
181	(C₂×D₅₉)⋊C₄	—	2	1	no	—
182	(C₂×D₅₉)⋊C₄	—	2	1	no	—
183	C₄⋊Dic₅₉	—	2	1	no	—
184	C₄⋊Dic₅₉	—	2	1	no	—
185	C₄⋊Dic₅₉	C₂²×C₄	1	1	yes	characteristic
186	C₄⋊Dic₅₉	C₂²×C₄	1	1	yes	characteristic
187	Dic₅₉⋊C₄	—	2	1	no	—
188	Dic₅₉⋊C₄	—	2	1	no	—
189	Dic₅₉⋊C₄	—	2	1	no	—
190	C₄×Dic₅₉	—	2	1	no	—
191	C₄×Dic₅₉	—	2	1	no	—
192	C₄×Dic₅₉	—	2	1	no	—
193	C₄×Dic₅₉	—	2	1	no	—
194	C₄×Dic₅₉	—	2	1	no	—
195	C₄×Dic₅₉	C₂²×C₄	1	1	yes	characteristic
196	C₄×Dic₅₉	C₂×D₄	1	1	yes	characteristic
197	C₄×Dic₅₉	#41	1	1	yes	characteristic
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	C₂²×C₄	1	1	yes	characteristic
202	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
203	C₂×C₅₉⋊C₈	C₂×D₄	1	1	yes	characteristic
204	C₂×C₅₉⋊C₈	C₂×D₄	1	1	yes	characteristic
205	#11745660	C₂×C₈	1	4	yes	complemented
206	#11745659	—	2	2	no	—
207	#11745659	C₂×C₈	1	4	yes	complemented
208	C₈×D₅₉	—	4	2	no	—
209	C₈×D₅₉	—	8	1	no	—
210	C₈×D₅₉	—	8	1	no	—
211	C₈×D₅₉	—	8	1	no	—
212	C₂²×D₅₉	—	2	1	no	—
213	C₂²×D₅₉	C₄×D₄	1	1	yes	characteristic
214	Q₈×C₅₉	—	2	1	no	—
215	Q₈×C₅₉	—	2	1	no	—
216	Q₈×C₅₉	C₂²×C₈	1	2	yes	—
217	Q₈×C₅₉	C₂²×C₈	1	2	yes	—
218	C₂×C₄×C₅₉	—	2	1	no	—
219	C₂×C₄×C₅₉	—	2	1	no	—
220	C₂×C₄×C₅₉	—	2	1	no	—
221	C₂×C₄×C₅₉	—	2	1	no	—
222	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
223	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
224	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
225	C₂×Dic₅₉	—	2	1	no	—
226	C₂×Dic₅₉	—	2	1	no	—
227	C₂×Dic₅₉	—	2	1	no	—
228	C₂×Dic₅₉	C₄×D₄	1	1	yes	characteristic
229	C₂×Dic₅₉	C₄×D₄	1	1	yes	characteristic
230	C₂×Dic₅₉	C₄×D₄	1	1	yes	characteristic
231	D₂₃₆	—	2	4	no	—
232	D₂₃₆	—	2	1	no	—
233	D₂₃₆	C₂²×C₈	1	2	yes	—
234	C₄×D₅₉	—	2	4	no	—
235	C₄×D₅₉	—	2	1	no	—
236	C₄×D₅₉	—	2	1	no	—
237	C₄×D₅₉	—	2	4	no	—
238	C₄×D₅₉	—	4	1	no	—
239	C₄×D₅₉	—	4	1	no	—
240	C₄×D₅₉	—	4	1	no	—
241	C₄×D₅₉	—	8	1	no	—
242	C₄×D₅₉	—	8	1	no	—
243	C₄×D₅₉	C₂²×C₈	1	2	yes	—
244	C₄×D₅₉	#131	1	2	yes	—
245	Dic₁₁₈	—	2	1	no	—
246	Dic₁₁₈	—	2	4	no	—
247	Dic₁₁₈	C₂²×C₈	1	2	yes	—
248	C₈×C₅₉	—	2	2	no	—
249	C₈×C₅₉	—	2	1	no	—
250	C₈×C₅₉	—	2	1	no	—
251	C₈×C₅₉	—	2	1	no	—
252	C₈×C₅₉	—	4	1	no	—
253	C₈×C₅₉	—	4	1	no	—
254	C₈×C₅₉	C₂²×C₈	1	2	yes	—
255	C₅₉⋊C₈	—	2	1	no	—
256	C₅₉⋊C₈	—	2	1	no	—
257	C₅₉⋊C₈	—	2	1	no	—
258	C₅₉⋊C₈	—	4	1	no	—
259	C₅₉⋊C₈	—	4	1	no	—
260	C₅₉⋊C₈	—	4	1	no	—
261	C₅₉⋊C₈	C₂²×C₈	1	2	yes	—
262	#17853	—	59	1	no	maximal, Sylow
263	C₂²×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
264	C₂×D₅₉	—	2	1	no	—
265	C₂×D₅₉	—	2	1	no	—
266	C₂×D₅₉	—	2	2	no	—
267	C₂×D₅₉	—	4	1	no	—
268	C₂×D₅₉	—	4	1	no	—
269	C₂×D₅₉	C₈×D₄	1	2	yes	—
270	C₄×C₅₉	—	2	2	no	—
271	C₄×C₅₉	—	2	2	no	—
272	C₄×C₅₉	—	2	1	no	—
273	C₄×C₅₉	—	4	1	no	—
274	C₄×C₅₉	—	4	1	no	—
275	C₄×C₅₉	C₂³×C₈	1	1	yes	characteristic
276	C₄×C₅₉	C₂×#131	1	1	yes	characteristic
277	C₄×C₅₉	#577	1	1	yes	characteristic
278	C₄×C₅₉	#578	1	1	yes	characteristic
279	Dic₅₉	—	2	2	no	—
280	Dic₅₉	—	2	1	no	—
281	Dic₅₉	—	2	1	no	—
282	Dic₅₉	—	4	1	no	—
283	Dic₅₉	—	4	1	no	—
284	Dic₅₉	C₈×D₄	1	2	yes	—
285	#2988	—	59	1	no	—
286	#2982	—	59	1	no	—
287	C₄×#137	—	59	1	no	—
288	#1579	—	59	1	no	—
289	#1579	—	59	1	no	—
290	SD₁₆⋊C₈	—	59	1	no	—
291	SD₁₆⋊C₈	—	59	1	no	—
292	C₈×Q₁₆	—	59	1	no	—
293	C₈×Q₁₆	D₅₉	1	1	yes	characteristic, complemented
294	C₈×SD₁₆	—	59	1	no	—
295	C₈×SD₁₆	—	59	1	no	—
296	#1565	—	59	1	no	—
297	#1476	—	59	1	no	—
298	C₂×Q₈⋊C₈	—	59	1	no	—
299	C₈×M₁₆	—	59	1	no	—
300	C₂×C₅₉	C₂×C₈×D₄	1	1	yes	characteristic
301	C₂×C₅₉	#2947	1	1	yes	characteristic
302	C₂×C₅₉	#2956	1	1	yes	characteristic
303	D₅₉	—	2	2	no	—
304	D₅₉	—	4	2	no	—
305	C₂×#137	—	59	1	no	—
306	C₄×#41	—	59	1	no	—
307	C₂×C₄×Q₈	—	59	1	no	—
308	C₈×Q₈	—	59	1	no	—
309	C₈×Q₈	—	59	1	no	—
310	C₈×Q₈	—	59	1	no	—
311	C₈×Q₈	—	59	1	no	—
312	C₈×Q₈	—	118	1	no	—
313	C₈×Q₈	—	118	1	no	—
314	C₈×Q₈	C₂×D₅₉	1	1	yes	characteristic
315	C₈×Q₈	C₂×D₅₉	1	1	yes	characteristic
316	#441	—	59	1	no	—
317	#441	—	59	1	no	—
318	#440	—	59	1	no	—
319	#440	—	59	1	no	—
320	C₄×Q₁₆	—	59	1	no	—
321	C₄×Q₁₆	C₂×D₅₉	1	1	yes	characteristic
322	C₄×SD₁₆	—	59	1	no	—
323	C₄×SD₁₆	—	59	1	no	—
324	C₈×D₄	—	59	1	no	—
325	C₈×D₄	—	59	1	no	—
326	C₈×D₄	—	118	1	no	—
327	C₈×D₄	—	118	1	no	—
328	#431	—	59	1	no	—
329	#431	—	59	1	no	—
330	#431	—	118	1	no	—
331	#431	—	118	1	no	—
332	#431	—	118	1	no	—
333	#428	—	59	1	no	—
334	C₂×C₄⋊C₈	—	59	1	no	—
335	C₂×C₄⋊C₈	—	118	1	no	—
336	#419	—	59	1	no	—
337	#417	—	59	1	no	—
338	C₄×M₁₆	—	59	1	no	—
339	C₂×C₄×C₈	—	59	1	no	—
340	#335	—	59	1	no	—
341	#335	C₂×D₅₉	1	1	yes	characteristic
342	#334	—	59	1	no	—
343	#334	—	59	1	no	—
344	Q₈⋊C₈	—	59	1	no	—
345	Q₈⋊C₈	—	59	1	no	—
346	Q₈⋊C₈	—	59	1	no	—
347	Q₈⋊C₈	—	59	1	no	—
348	Q₈⋊C₈	C₂×D₅₉	1	1	yes	characteristic
349	Q₈⋊C₈	C₂×D₅₉	1	1	yes	characteristic
350	D₄⋊C₈	—	59	1	no	—
351	D₄⋊C₈	—	59	1	no	—
352	#322	—	59	1	no	—
353	#322	—	59	1	no	—
354	C₈²	—	59	1	no	—
355	C₈²	C₂×D₅₉	1	1	yes	characteristic
356	C₅₉	#17853	1	1	yes	characteristic, complemented, Sylow
357	C₂×#41	—	59	1	no	—
358	C₂²×Q₈	—	59	1	no	—
359	#137	—	59	8	no	—
360	C₂×Q₁₆	—	59	1	no	—
361	C₂×Q₁₆	C₄×D₅₉	1	1	yes	characteristic
362	C₂×SD₁₆	—	59	1	no	—
363	C₂×SD₁₆	—	59	1	no	—
364	C₂×M₁₆	—	59	1	no	—
365	C₂×M₁₆	—	59	1	no	—
366	C₂²×C₈	—	118	1	no	—
367	C₂²×C₈	—	118	1	no	—
368	C₂²×C₈	—	118	1	no	—
369	C₂²×C₈	—	118	1	no	—
370	C₄×Q₈	—	59	1	no	—
371	C₄×Q₈	—	59	1	no	—
372	C₄×Q₈	—	59	1	no	—
373	C₄×Q₈	—	59	1	no	—
374	C₄×Q₈	—	118	1	no	—
375	C₄×Q₈	—	118	1	no	—
376	C₄×Q₈	C₂²×D₅₉	1	1	yes	characteristic
377	C₄×Q₈	C₂²×D₅₉	1	1	yes	characteristic
378	C₄×D₄	—	59	1	no	—
379	C₄×D₄	—	59	1	no	—
380	C₄×D₄	—	118	1	no	—
381	C₄×D₄	—	118	1	no	—
382	#117	—	59	1	no	—
383	#117	—	118	1	no	—
384	C₂×C₄⋊C₄	—	59	1	no	—
385	C₂×C₄⋊C₄	—	118	1	no	—
386	C₂×C₄²	—	59	1	no	—
387	C₂×C₄²	—	118	1	no	—
388	C₂×C₄²	—	118	1	no	—
389	#107	—	59	1	no	—
390	#107	C₄×D₅₉	1	1	yes	characteristic
391	#106	—	59	1	no	—
392	#106	—	59	1	no	—
393	C₄⋊C₈	—	2	1	no	—
394	C₄⋊C₈	—	2	1	no	—
395	C₄⋊C₈	—	59	1	no	—
396	C₄⋊C₈	—	59	1	no	—
397	C₄⋊C₈	—	59	1	no	—
398	C₄⋊C₈	—	59	1	no	—
399	C₄⋊C₈	—	118	1	no	—
400	C₄⋊C₈	—	118	1	no	—
401	C₄⋊C₈	—	118	1	no	—
402	C₄⋊C₈	—	118	1	no	—
403	C₄⋊C₈	—	118	1	no	—
404	C₄⋊C₈	C₂²×D₅₉	1	1	yes	characteristic
405	C₄⋊C₈	C₂²×D₅₉	1	1	yes	characteristic
406	#103	—	59	1	no	—
407	#103	—	59	1	no	—
408	#103	—	59	1	no	—
409	#103	—	59	1	no	—
410	#103	C₄×D₅₉	1	1	yes	characteristic
411	#103	C₄×D₅₉	1	1	yes	characteristic
412	#102	—	59	1	no	—
413	#102	—	59	1	no	—
414	C₂²⋊C₈	—	59	1	no	—
415	C₂²⋊C₈	—	59	1	no	—
416	C₂²⋊C₈	—	118	1	no	—
417	C₂²⋊C₈	—	118	1	no	—
418	C₂²⋊C₈	—	118	1	no	—
419	#97	—	59	1	no	—
420	#97	—	59	1	no	—
421	C₄×C₈	—	2	1	no	—
422	C₄×C₈	—	2	1	no	—
423	C₄×C₈	—	59	1	no	—
424	C₄×C₈	—	59	1	no	—
425	C₄×C₈	—	59	1	no	—
426	C₄×C₈	—	118	1	no	—
427	C₄×C₈	—	118	1	no	—
428	C₄×C₈	—	118	1	no	—
429	C₄×C₈	—	118	1	no	—
430	C₄×C₈	—	118	1	no	—
431	C₄×C₈	—	118	1	no	—
432	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
433	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
434	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
435	#41	—	59	4	no	—
436	#41	—	118	2	no	—
437	C₂×Q₈	—	59	4	no	—
438	C₂×Q₈	—	59	1	no	—
439	C₂×Q₈	—	118	1	no	—
440	C₂×Q₈	—	118	2	no	—
441	C₂×Q₈	C₂×C₄×D₅₉	1	1	yes	characteristic
442	C₂×Q₈	C₂×C₄×D₅₉	1	1	yes	characteristic
443	C₂×D₄	—	59	1	no	—
444	C₂×D₄	—	118	1	no	—
445	C₂²×C₄	—	59	1	no	—
446	C₂²×C₄	—	59	1	no	—
447	C₂²×C₄	—	59	1	no	—
448	C₂²×C₄	—	118	1	no	—
449	C₂²×C₄	—	118	1	no	—
450	C₂²×C₄	—	118	1	no	—
451	C₂²×C₄	—	118	1	no	—
452	C₂²×C₄	—	118	1	no	—
453	Q₁₆	—	59	4	no	—
454	Q₁₆	C₈×D₅₉	1	4	yes	complemented
455	SD₁₆	—	59	4	no	—
456	SD₁₆	—	59	4	no	—
457	M₁₆	—	59	4	no	—
458	M₁₆	—	118	2	no	—
459	C₂×C₈	—	2	1	no	—
460	C₂×C₈	—	2	1	no	—
461	C₂×C₈	—	2	1	no	—
462	C₂×C₈	—	59	1	no	—
463	C₂×C₈	—	59	1	no	—
464	C₂×C₈	—	59	1	no	—
465	C₂×C₈	—	59	1	no	—
466	C₂×C₈	—	118	1	no	—
467	C₂×C₈	—	118	1	no	—
468	C₂×C₈	—	118	1	no	—
469	C₂×C₈	—	472	1	no	—
470	C₂×C₈	—	472	1	no	—
471	C₂×C₈	—	472	1	no	—
472	C₂×C₈	—	236	2	no	—
473	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
474	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
475	C₂×C₈	D₄×D₅₉	1	1	yes	characteristic
476	C₂×C₈	D₄×D₅₉	1	1	yes	characteristic
477	C₄⋊C₄	—	2	1	no	—
478	C₄⋊C₄	—	2	1	no	—
479	C₄⋊C₄	—	59	1	no	—
480	C₄⋊C₄	—	59	1	no	—
481	C₄⋊C₄	—	118	1	no	—
482	C₄⋊C₄	—	118	1	no	—
483	C₄⋊C₄	—	118	1	no	—
484	C₄⋊C₄	—	118	1	no	—
485	C₄⋊C₄	—	118	1	no	—
486	C₄⋊C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
487	C₄⋊C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
488	C₂²⋊C₄	—	118	1	no	—
489	C₂²⋊C₄	—	118	1	no	—
490	C₂²⋊C₄	—	118	1	no	—
491	C₄²	—	2	1	no	—
492	C₄²	—	2	1	no	—
493	C₄²	—	59	1	no	—
494	C₄²	—	59	1	no	—
495	C₄²	—	59	1	no	—
496	C₄²	—	118	1	no	—
497	C₄²	—	118	1	no	—
498	C₄²	—	118	1	no	—
499	C₄²	—	118	1	no	—
500	C₄²	—	118	1	no	—
501	C₄²	C₂³×D₅₉	1	1	yes	characteristic
502	C₂³	—	59	1	no	—
503	C₂³	—	118	1	no	—
504	Q₈	—	2	1	no	—
505	Q₈	—	2	1	no	—
506	Q₈	—	59	2	no	—
507	Q₈	—	118	4	no	—
508	Q₈	—	118	1	no	—
509	Q₈	C₂×C₈×D₅₉	1	2	yes	—
510	Q₈	C₂×C₈×D₅₉	1	2	yes	—
511	D₄	—	59	2	no	—
512	D₄	—	118	4	no	—
513	D₄	—	118	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	59	1	no	—
519	C₂×C₄	—	59	2	no	—
520	C₂×C₄	—	59	2	no	—
521	C₂×C₄	—	59	1	no	—
522	C₂×C₄	—	59	1	no	—
523	C₂×C₄	—	118	4	no	—
524	C₂×C₄	—	118	4	no	—
525	C₂×C₄	—	118	1	no	—
526	C₂×C₄	—	118	1	no	—
527	C₂×C₄	—	118	1	no	—
528	C₂×C₄	—	118	1	no	—
529	C₂×C₄	—	118	1	no	—
530	C₂×C₄	—	472	1	no	—
531	C₂×C₄	—	472	1	no	—
532	C₂×C₄	—	236	1	no	—
533	C₂×C₄	—	236	1	no	—
534	C₂×C₄	—	236	1	no	—
535	C₂×C₄	C₂²×C₄×D₅₉	1	1	yes	characteristic
536	C₂×C₄	C₂×D₄×D₅₉	1	1	yes	characteristic
537	C₂×C₄	#41×D₅₉	1	1	yes	characteristic
538	C₈	—	2	2	no	—
539	C₈	—	2	1	no	—
540	C₈	—	2	1	no	—
541	C₈	—	2	1	no	—
542	C₈	—	4	1	no	—
543	C₈	—	4	1	no	—
544	C₈	—	59	2	no	—
545	C₈	—	118	1	no	—
546	C₈	—	118	1	no	—
547	C₈	—	118	1	no	—
548	C₈	—	236	1	no	—
549	C₈	—	236	1	no	—
550	C₈	—	236	1	no	—
551	C₈	C₂×C₈×D₅₉	1	2	yes	—
552	C₂²	—	59	2	no	—
553	C₂²	—	118	1	no	—
554	C₂²	—	118	1	no	—
555	C₂²	—	118	2	no	—
556	C₂²	—	236	1	no	—
557	C₂²	—	236	1	no	—
558	C₂²	C₄×D₄×D₅₉	1	1	yes	characteristic
559	C₄	—	2	1	no	—
560	C₄	—	2	2	no	—
561	C₄	—	2	2	no	—
562	C₄	—	4	1	no	—
563	C₄	—	4	1	no	—
564	C₄	—	59	2	no	—
565	C₄	—	118	1	no	—
566	C₄	—	118	1	no	—
567	C₄	—	118	2	no	—
568	C₄	—	236	1	no	—
569	C₄	—	236	1	no	—
570	C₄	C₂²×C₈×D₅₉	1	1	yes	characteristic
571	C₄	#131×D₅₉	1	1	yes	characteristic
572	C₄	#16838209	1	1	yes	characteristic
573	C₄	#16838215	1	1	yes	characteristic
574	C₂	—	118	2	no	—
575	C₂	—	236	2	no	—
576	C₂	C₈×D₄×D₅₉	1	1	yes	characteristic
577	C₂	#21432934	1	1	yes	characteristic
578	C₂	#21433001	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₅₉
commutator	C₄×C₅₉	C₂³×C₈
Frattini	C₄²	C₂³×D₅₉
Fitting	C₈×Q₁₆×C₅₉	C₂
socle	C₂²×C₅₉	C₂×C₄×D₄
prime radical	C₂×#11745689	C₂×C₄
cosocle	C₄²×C₅₉	C₂⁴
hypercenter	C₈×Q₁₆	D₅₉
hypocenter	C₅₉	#17853
LCS	G ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ C₈×Q₁₆

Complements

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

N	H ≅ G/N	type
2. #21433175	C₂	semidirect
4. #21422915	C₂	semidirect
5. #21422913	C₂	semidirect
6. #21422907	C₂	semidirect
7. #21422906	C₂	semidirect
8. #21422900	C₂	semidirect
9. C₈×#11745660	C₂	semidirect
10. #21422893	C₂	semidirect
11. #21422847	C₂	semidirect
13. Q₈⋊C₈×D₅₉	C₂	semidirect
14. C₈×#11745659	C₂	semidirect
15. C₈×Q₁₆×C₅₉	C₂	semidirect
69. #14273759	C₈	semidirect
150. Q₈×D₅₉	C₂×C₈	semidirect
163. Q₁₆×C₅₉	C₂×C₈	semidirect
178. #11745672	C₂×C₈	semidirect
179. #11745671	C₂×C₈	semidirect
205. #11745660	C₂×C₈	semidirect
207. #11745659	C₂×C₈	semidirect
293. C₈×Q₁₆	D₅₉	semidirect
356. C₅₉	#17853	semidirect
454. Q₁₆	C₈×D₅₉	semidirect

Maximal subgroups

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

subgroup	index
#21433206	2
#21433175	2
C₄×#14273759	2
#21422915	2
#21422913	2
#21422907	2
#21422906	2
#21422900	2
C₈×#11745660	2
#21422893	2
#21422847	2
#21422477	2
Q₈⋊C₈×D₅₉	2
C₈×#11745659	2
C₈×Q₁₆×C₅₉	2
#17853	59