Subgroups — #28558591

Order 15104.

634 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	#21434108	C₂	1	1	yes	maximal, characteristic
2	C₈×#11745685	C₂	1	1	yes	maximal, characteristic, complemented
3	#21422944	C₂	1	1	yes	maximal, characteristic, complemented
4	#21422937	C₂	1	1	yes	maximal, characteristic, complemented
5	#21422930	C₂	1	1	yes	maximal, characteristic, complemented
6	#21422923	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈×#11745672	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈×#11745671	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈×#11745670	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×#11745669	C₂	1	1	yes	maximal, characteristic, complemented
11	#21422877	C₂	1	1	yes	maximal, characteristic, complemented
12	#21422528	C₂	1	1	yes	maximal, characteristic, complemented
13	#21422504	C₂	1	1	yes	maximal, characteristic, complemented
14	#21422379	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₉×#2966	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×#11745685	C₂²	1	1	yes	characteristic
17	#16837740	C₄	1	1	yes	characteristic
18	#16837723	C₄	1	1	yes	characteristic
19	#16837706	C₄	1	1	yes	characteristic
20	#16837699	C₄	1	1	yes	characteristic
21	#16837621	C₄	1	1	yes	characteristic
22	#16837614	C₄	1	1	yes	characteristic
23	#16837562	C₄	1	1	yes	characteristic
24	#16837545	C₄	1	1	yes	characteristic
25	C₈×Dic₁₁₈	C₂²	1	1	yes	characteristic
26	C₈×Dic₁₁₈	C₂²	1	1	yes	characteristic
27	C₄×#11745672	C₂²	1	1	yes	characteristic
28	C₄×#11745671	C₂²	1	1	yes	characteristic
29	C₄×#11745670	C₂²	1	1	yes	characteristic
30	C₄×#11745669	C₂²	1	1	yes	characteristic
31	C₈×D₂₃₆	C₂²	1	1	yes	characteristic
32	C₈×D₂₃₆	C₂²	1	1	yes	characteristic
33	C₈×C₂²⋊D₅₉	—	2	1	no	—
34	C₈×C₂²⋊D₅₉	—	2	1	no	—
35	#16837455	C₂²	1	1	yes	characteristic
36	#16837455	C₂²	1	1	yes	characteristic
37	#16837455	C₂²	1	1	yes	characteristic
38	#16837453	—	2	1	no	—
39	C₄×C₈×D₅₉	—	2	1	no	—
40	#16837154	C₂²	1	1	yes	characteristic
41	#16837154	C₂²	1	1	yes	characteristic
42	#16837152	C₂²	1	1	yes	characteristic
43	#16837152	C₂²	1	1	yes	characteristic
44	Q₈⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
45	Q₈⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
46	#16837132	C₂²	1	1	yes	characteristic
47	#16837132	C₂²	1	1	yes	characteristic
48	D₄⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
49	D₄⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
50	#16837129	C₂²	1	1	yes	characteristic
51	#16837129	C₂²	1	1	yes	characteristic
52	#16837123	C₂²	1	1	yes	characteristic
53	#16837123	C₂²	1	1	yes	characteristic
54	C₈×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
55	C₈×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
56	C₅₉×#529	C₂²	1	1	yes	characteristic
57	C₅₉×#446	C₂²	1	1	yes	characteristic
58	C₈×Q₈×C₅₉	C₂²	1	1	yes	characteristic
59	C₅₉×#436	C₂²	1	1	yes	characteristic
60	C₅₉×#435	—	2	1	no	—
61	C₈×D₄×C₅₉	—	2	1	no	—
62	C₈×D₄×C₅₉	C₂²	1	1	yes	characteristic
63	C₅₉×#433	—	2	1	no	—
64	C₅₉×#432	C₂²	1	1	yes	characteristic
65	C₅₉×#405	—	2	1	no	—
66	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
67	C₂×#11745685	C₂×C₄	1	1	yes	characteristic
68	C₂×#11745672	C₂×C₄	1	1	yes	characteristic
69	C₂×#11745670	C₂×C₄	1	1	yes	characteristic
70	C₂×#11745671	C₂×C₄	1	1	yes	characteristic
71	C₂×#11745669	C₂×C₄	1	1	yes	characteristic
72	C₂×C₈×D₅₉	—	2	1	no	—
73	C₂×C₈×D₅₉	—	2	1	no	—
74	C₄×Dic₁₁₈	C₂×C₄	1	1	yes	characteristic
75	C₄×Dic₁₁₈	C₂³	1	1	yes	characteristic
76	C₄×D₂₃₆	C₂×C₄	1	1	yes	characteristic
77	C₄×D₂₃₆	C₂³	1	1	yes	characteristic
78	C₄×C₂²⋊D₅₉	—	2	1	no	—
79	C₄×C₂²⋊D₅₉	—	2	1	no	—
80	#14273686	C₂×C₄	1	1	yes	characteristic
81	#14273684	—	2	1	no	—
82	C₄²×D₅₉	—	2	1	no	—
83	#14273660	C₂×C₄	1	1	yes	characteristic
84	#14273660	C₂×C₄	1	1	yes	characteristic
85	#14273658	C₂×C₄	1	1	yes	characteristic
86	#14273658	C₂×C₄	1	1	yes	characteristic
87	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
88	C₄⋊(C₅₉⋊C₈)	C₂×C₄	1	1	yes	characteristic
89	C₄⋊(C₅₉⋊C₈)	C₂×C₄	1	1	yes	characteristic
90	C₄⋊(C₅₉⋊C₈)	C₂³	1	1	yes	characteristic
91	C₄⋊(C₅₉⋊C₈)	C₂³	1	1	yes	characteristic
92	Dic₅₉⋊C₈	—	2	1	no	—
93	Dic₅₉⋊C₈	—	2	1	no	—
94	#14273651	C₂×C₄	1	1	yes	characteristic
95	#14273651	C₂×C₄	1	1	yes	characteristic
96	#14273650	C₂×C₄	1	1	yes	characteristic
97	#14273650	C₂×C₄	1	1	yes	characteristic
98	#14273648	C₂×C₄	1	1	yes	characteristic
99	#14273648	C₂×C₄	1	1	yes	characteristic
100	#14273647	C₂×C₄	1	1	yes	characteristic
101	#14273647	C₂×C₄	1	1	yes	characteristic
102	C₂²⋊(C₅₉⋊C₈)	—	2	1	no	—
103	C₂²⋊(C₅₉⋊C₈)	—	2	1	no	—
104	C₂²⋊(C₅₉⋊C₈)	C₂×C₄	1	1	yes	characteristic
105	C₂²⋊(C₅₉⋊C₈)	C₂×C₄	1	1	yes	characteristic
106	(C₂×D₅₉)⋊C₈	—	2	1	no	—
107	(C₂×D₅₉)⋊C₈	—	2	1	no	—
108	C₄×C₅₉⋊C₈	—	2	1	no	—
109	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
110	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
111	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
112	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
113	C₈×Dic₅₉	—	2	1	no	—
114	C₈×Dic₅₉	—	2	1	no	—
115	C₂×M₁₆×C₅₉	—	2	1	no	—
116	C₂²×C₈×C₅₉	—	2	1	no	—
117	C₂²×C₈×C₅₉	D₄	1	1	yes	characteristic
118	C₂²×C₈×C₅₉	D₄	1	1	yes	characteristic
119	#126×C₅₉	—	2	1	no	—
120	#125×C₅₉	C₂×C₄	1	1	yes	characteristic
121	#124×C₅₉	C₂×C₄	1	1	yes	characteristic
122	#123×C₅₉	—	2	1	no	—
123	C₂²⋊Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
124	#121×C₅₉	C₂×C₄	1	1	yes	characteristic
125	C₄×Q₈×C₅₉	C₂³	1	1	yes	characteristic
126	C₄×D₄×C₅₉	—	2	1	no	—
127	C₄×D₄×C₅₉	C₂³	1	1	yes	characteristic
128	#117×C₅₉	—	2	1	no	—
129	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
130	C₄⋊C₈×C₅₉	—	2	1	no	—
131	C₄⋊C₈×C₅₉	—	2	1	no	—
132	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
133	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
134	C₂²⋊C₈×C₅₉	—	2	1	no	—
135	C₂²⋊C₈×C₅₉	—	2	1	no	—
136	C₂²⋊C₈×C₅₉	—	2	1	no	—
137	#97×C₅₉	—	2	1	no	—
138	#97×C₅₉	—	2	1	no	—
139	C₄×C₈×C₅₉	—	2	1	no	—
140	C₄×C₈×C₅₉	D₄	1	1	yes	characteristic
141	C₄×C₈×C₅₉	D₄	1	1	yes	characteristic
142	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
144	C₂×Q₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
145	C₂×D₄×C₅₉	—	2	1	no	—
146	C₂×D₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
147	C₂²×C₄×C₅₉	—	2	1	no	—
148	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
149	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
151	C₂×C₂²⋊D₅₉	—	2	1	no	—
152	#11745685	—	2	2	no	—
153	#11745685	—	2	2	no	—
154	C₂×D₂₃₆	C₂²×C₄	1	1	yes	characteristic
155	C₂×C₄×D₅₉	—	2	1	no	—
156	C₂×C₄×D₅₉	—	2	1	no	—
157	C₂×C₄×D₅₉	—	2	1	no	—
158	C₂×Dic₁₁₈	C₂²×C₄	1	1	yes	characteristic
159	M₁₆×C₅₉	—	4	2	no	—
160	C₂×C₈×C₅₉	—	2	2	no	—
161	C₂×C₈×C₅₉	—	2	2	no	—
162	C₂×C₈×C₅₉	—	2	1	no	—
163	C₂×C₈×C₅₉	—	2	1	no	—
164	C₂×C₈×C₅₉	—	4	2	no	—
165	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
166	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
167	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
168	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
169	C₄⋊C₄×C₅₉	—	2	1	no	—
170	C₄⋊C₄×C₅₉	—	2	1	no	—
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	C₂²⋊C₄×C₅₉	—	2	1	no	—
176	C₂²⋊C₄×C₅₉	—	2	1	no	—
177	C₂²⋊C₄×C₅₉	—	2	1	no	—
178	C₂²⋊C₄×C₅₉	—	2	1	no	—
179	C₂²⋊C₄×C₅₉	—	2	1	no	—
180	C₄²×C₅₉	—	2	1	no	—
181	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
182	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
183	C₄²×C₅₉	#41	1	1	yes	characteristic
184	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
185	C₂²⋊Dic₅₉	—	2	1	no	—
186	#11745672	—	2	2	no	—
187	#11745671	—	2	2	no	—
188	#11745670	—	2	2	no	—
189	#11745669	—	2	2	no	—
190	(C₂×D₅₉)⋊C₄	—	2	1	no	—
191	(C₂×D₅₉)⋊C₄	—	2	1	no	—
192	C₄⋊Dic₅₉	C₂²×C₄	1	1	yes	characteristic
193	C₄⋊Dic₅₉	C₂²×C₄	1	1	yes	characteristic
194	Dic₅₉⋊C₄	—	2	1	no	—
195	Dic₅₉⋊C₄	—	2	1	no	—
196	C₄×Dic₅₉	—	2	1	no	—
197	C₄×Dic₅₉	—	2	1	no	—
198	C₄×Dic₅₉	—	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	C₂²×C₄	1	1	yes	characteristic
204	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
205	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
206	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
207	C₈×D₅₉	—	4	2	no	—
208	C₈×D₅₉	—	4	2	no	—
209	C₂³×C₅₉	—	2	1	no	—
210	C₂³×C₅₉	C₄×D₄	1	1	yes	characteristic
211	C₂²×D₅₉	—	2	1	no	—
212	Q₈×C₅₉	—	2	1	no	—
213	Q₈×C₅₉	—	2	1	no	—
214	D₄×C₅₉	—	2	1	no	—
215	D₄×C₅₉	—	2	1	no	—
216	D₄×C₅₉	—	4	2	no	—
217	C₂×C₄×C₅₉	—	2	1	no	—
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	—	2	1	no	—
223	C₂×C₄×C₅₉	—	2	1	no	—
224	C₂×C₄×C₅₉	—	4	1	no	—
225	C₂×C₄×C₅₉	—	4	1	no	—
226	C₂×C₄×C₅₉	—	4	1	no	—
227	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
228	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
229	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
230	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
231	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
232	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
233	C₂²⋊D₅₉	—	2	4	no	—
234	C₂×Dic₅₉	—	2	1	no	—
235	C₂×Dic₅₉	—	2	1	no	—
236	C₂×Dic₅₉	—	2	1	no	—
237	D₂₃₆	—	2	1	no	—
238	D₂₃₆	#131	1	2	yes	—
239	C₄×D₅₉	—	2	4	no	—
240	C₄×D₅₉	—	4	2	no	—
241	C₄×D₅₉	—	4	1	no	—
242	C₄×D₅₉	—	4	1	no	—
243	Dic₁₁₈	—	2	1	no	—
244	Dic₁₁₈	#131	1	2	yes	—
245	C₈×C₅₉	—	2	1	no	—
246	C₈×C₅₉	—	2	1	no	—
247	C₈×C₅₉	—	4	1	no	—
248	C₈×C₅₉	—	4	1	no	—
249	C₈×C₅₉	#135	1	2	yes	—
250	C₈×C₅₉	#135	1	2	yes	—
251	C₅₉⋊C₈	—	2	1	no	—
252	C₅₉⋊C₈	—	2	1	no	—
253	C₅₉⋊C₈	—	2	1	no	—
254	C₅₉⋊C₈	—	2	1	no	—
255	C₅₉⋊C₈	—	4	1	no	—
256	C₅₉⋊C₈	—	4	1	no	—
257	C₅₉⋊C₈	—	4	1	no	—
258	C₅₉⋊C₈	—	4	1	no	—
259	#17904	—	59	1	no	maximal, Sylow
260	C₂²×C₅₉	—	2	1	no	—
261	C₂²×C₅₉	—	2	1	no	—
262	C₂²×C₅₉	—	2	1	no	—
263	C₂²×C₅₉	—	4	1	no	—
264	C₂²×C₅₉	—	4	1	no	—
265	C₂²×C₅₉	—	4	1	no	—
266	C₂²×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
267	C₂×D₅₉	—	2	2	no	—
268	C₂×D₅₉	—	4	1	no	—
269	C₂×D₅₉	—	4	1	no	—
270	C₄×C₅₉	—	2	1	no	—
271	C₄×C₅₉	—	2	1	no	—
272	C₄×C₅₉	—	2	1	no	—
273	C₄×C₅₉	—	2	1	no	—
274	C₄×C₅₉	—	4	1	no	—
275	C₄×C₅₉	—	4	1	no	—
276	C₄×C₅₉	—	4	1	no	—
277	C₄×C₅₉	C₂×#131	1	1	yes	characteristic
278	C₄×C₅₉	C₂×#131	1	1	yes	characteristic
279	C₄×C₅₉	C₂×#135	1	1	yes	characteristic
280	C₄×C₅₉	C₂×#135	1	1	yes	characteristic
281	Dic₅₉	—	2	2	no	—
282	Dic₅₉	—	4	1	no	—
283	Dic₅₉	—	4	1	no	—
284	#3102	—	59	1	no	—
285	#2966	D₅₉	1	1	yes	characteristic, complemented
286	C₈×#41	—	59	1	no	—
287	#1584	—	59	1	no	—
288	#1583	—	59	1	no	—
289	#1582	—	59	1	no	—
290	#1581	—	59	1	no	—
291	C₈×Q₁₆	—	59	1	no	—
292	C₈×SD₁₆	—	59	1	no	—
293	C₈×SD₁₆	—	59	1	no	—
294	C₈×D₈	—	59	1	no	—
295	#1572	—	59	1	no	—
296	#1488	—	59	1	no	—
297	#1482	—	59	1	no	—
298	#1450	—	59	1	no	—
299	C₂×C₅₉	—	4	1	no	—
300	C₂×C₅₉	—	8	1	no	—
301	C₂×C₅₉	#2929	1	1	yes	characteristic
302	C₂×C₅₉	C₄×#135	1	1	yes	characteristic
303	C₂×C₅₉	#2955	1	1	yes	characteristic
304	D₅₉	—	4	2	no	—
305	#529	C₂×D₅₉	1	1	yes	characteristic
306	C₄×#41	—	59	1	no	—
307	#485	—	59	1	no	—
308	#482	—	59	1	no	—
309	#479	—	59	1	no	—
310	#478	—	59	1	no	—
311	#464	—	59	1	no	—
312	#463	—	59	1	no	—
313	#452	—	59	1	no	—
314	#449	—	59	1	no	—
315	#446	C₂×D₅₉	1	1	yes	characteristic
316	C₈×Q₈	—	59	1	no	—
317	C₈×Q₈	—	59	1	no	—
318	C₈×Q₈	C₂×D₅₉	1	1	yes	characteristic
319	C₄×Q₁₆	—	59	1	no	—
320	C₄×SD₁₆	—	59	1	no	—
321	C₄×SD₁₆	—	59	1	no	—
322	C₄×D₈	—	59	1	no	—
323	#436	C₂×D₅₉	1	1	yes	characteristic
324	#435	—	2	1	no	—
325	C₈×D₄	—	2	1	no	—
326	C₈×D₄	—	59	1	no	—
327	C₈×D₄	—	59	1	no	—
328	C₈×D₄	—	118	1	no	—
329	C₈×D₄	—	118	1	no	—
330	C₈×D₄	C₂×D₅₉	1	1	yes	characteristic
331	#433	—	2	1	no	—
332	#432	C₂×D₅₉	1	1	yes	characteristic
333	#431	—	59	1	no	—
334	#431	—	59	1	no	—
335	#431	—	59	1	no	—
336	#431	—	118	1	no	—
337	#405	—	2	1	no	—
338	C₂×C₄×C₈	—	118	1	no	—
339	C₂×C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
340	#335	—	59	1	no	—
341	#335	—	59	1	no	—
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	D₄⋊C₈	—	59	1	no	—
349	D₄⋊C₈	—	59	1	no	—
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	—	59	1	no	—
356	C₅₉	#17904	1	1	yes	characteristic, complemented, Sylow
357	C₂×#41	—	59	1	no	—
358	C₂×Q₁₆	—	59	1	no	—
359	C₂×SD₁₆	—	59	1	no	—
360	C₂×SD₁₆	—	59	1	no	—
361	C₂×D₈	—	59	1	no	—
362	C₂×M₁₆	—	2	1	no	—
363	C₂²×C₈	—	2	1	no	—
364	C₂²×C₈	—	118	1	no	—
365	C₂²×C₈	—	118	1	no	—
366	C₂²×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
367	C₂²×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
368	#126	—	2	1	no	—
369	#125	C₄×D₅₉	1	1	yes	characteristic
370	#124	C₄×D₅₉	1	1	yes	characteristic
371	#123	—	2	1	no	—
372	C₂²⋊Q₈	C₄×D₅₉	1	1	yes	characteristic
373	#121	C₄×D₅₉	1	1	yes	characteristic
374	C₄×Q₈	—	59	1	no	—
375	C₄×Q₈	—	59	1	no	—
376	C₄×Q₈	C₂²×D₅₉	1	1	yes	characteristic
377	C₄×D₄	—	2	1	no	—
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	C₄×D₄	C₂²×D₅₉	1	1	yes	characteristic
383	#117	—	2	1	no	—
384	#117	—	59	1	no	—
385	#117	—	118	1	no	—
386	C₂×C₄²	—	118	1	no	—
387	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
388	#107	—	59	1	no	—
389	#107	—	59	1	no	—
390	#106	—	59	1	no	—
391	#106	—	59	1	no	—
392	C₄⋊C₈	—	2	1	no	—
393	C₄⋊C₈	—	2	1	no	—
394	C₄⋊C₈	—	59	1	no	—
395	C₄⋊C₈	—	59	1	no	—
396	C₄⋊C₈	—	59	1	no	—
397	C₄⋊C₈	—	59	1	no	—
398	C₄⋊C₈	—	118	1	no	—
399	C₄⋊C₈	—	118	1	no	—
400	C₄⋊C₈	—	118	1	no	—
401	C₄⋊C₈	C₂²×D₅₉	1	1	yes	characteristic
402	C₄⋊C₈	C₂²×D₅₉	1	1	yes	characteristic
403	#103	—	59	1	no	—
404	#103	—	59	1	no	—
405	#103	—	59	1	no	—
406	#103	—	59	1	no	—
407	#102	—	59	1	no	—
408	#102	—	59	1	no	—
409	#102	—	59	1	no	—
410	#102	—	59	1	no	—
411	C₂²⋊C₈	—	2	1	no	—
412	C₂²⋊C₈	—	2	1	no	—
413	C₂²⋊C₈	—	2	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	C₂²⋊C₈	—	118	1	no	—
420	#97	—	2	1	no	—
421	#97	—	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	—	59	1	no	—
427	C₄×C₈	—	118	1	no	—
428	C₄×C₈	—	118	1	no	—
429	C₄×C₈	—	118	1	no	—
430	C₄×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
431	C₄×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
432	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
433	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
434	#41	—	118	2	no	—
435	#41	—	118	2	no	—
436	C₂×Q₈	—	59	1	no	—
437	C₂×Q₈	C₂×C₄×D₅₉	1	1	yes	characteristic
438	C₂×D₄	—	2	1	no	—
439	C₂×D₄	—	59	1	no	—
440	C₂×D₄	—	118	1	no	—
441	C₂×D₄	C₂×C₄×D₅₉	1	1	yes	characteristic
442	C₂²×C₄	—	2	1	no	—
443	C₂²×C₄	—	118	1	no	—
444	C₂²×C₄	—	118	1	no	—
445	C₂²×C₄	—	118	1	no	—
446	C₂²×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
447	C₂²×C₄	#11745685	1	1	yes	characteristic
448	C₂²×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
449	Q₁₆	—	118	2	no	—
450	SD₁₆	—	118	2	no	—
451	SD₁₆	—	118	2	no	—
452	D₈	—	118	2	no	—
453	M₁₆	—	4	2	no	—
454	C₂×C₈	—	2	2	no	—
455	C₂×C₈	—	2	2	no	—
456	C₂×C₈	—	2	1	no	—
457	C₂×C₈	—	2	1	no	—
458	C₂×C₈	—	4	2	no	—
459	C₂×C₈	—	59	1	no	—
460	C₂×C₈	—	59	1	no	—
461	C₂×C₈	—	59	1	no	—
462	C₂×C₈	—	59	1	no	—
463	C₂×C₈	—	118	1	no	—
464	C₂×C₈	—	118	1	no	—
465	C₂×C₈	—	118	1	no	—
466	C₂×C₈	—	118	1	no	—
467	C₂×C₈	—	236	2	no	—
468	C₂×C₈	—	236	2	no	—
469	C₂×C₈	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
470	C₂×C₈	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
471	C₂×C₈	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
472	C₂×C₈	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
473	C₄⋊C₄	—	2	1	no	—
474	C₄⋊C₄	—	2	1	no	—
475	C₄⋊C₄	—	2	1	no	—
476	C₄⋊C₄	—	2	1	no	—
477	C₄⋊C₄	—	59	1	no	—
478	C₄⋊C₄	—	59	1	no	—
479	C₄⋊C₄	—	118	1	no	—
480	C₄⋊C₄	—	118	1	no	—
481	C₄⋊C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
482	C₄⋊C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
483	C₂²⋊C₄	—	2	1	no	—
484	C₂²⋊C₄	—	2	1	no	—
485	C₂²⋊C₄	—	2	1	no	—
486	C₂²⋊C₄	—	2	1	no	—
487	C₂²⋊C₄	—	2	1	no	—
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	—	118	1	no	—
493	C₄²	—	118	1	no	—
494	C₄²	—	118	1	no	—
495	C₄²	C₂×C₄×D₅₉	1	1	yes	characteristic
496	C₄²	#11745685	1	1	yes	characteristic
497	C₄²	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
498	C₄²	C₂³×D₅₉	1	1	yes	characteristic
499	C₂³	—	2	1	no	—
500	C₂³	—	118	1	no	—
501	C₂³	C₄×C₂²⋊D₅₉	1	1	yes	characteristic
502	Q₈	—	2	1	no	—
503	Q₈	—	2	1	no	—
504	Q₈	—	59	2	no	—
505	Q₈	—	118	1	no	—
506	D₄	—	2	1	no	—
507	D₄	—	2	1	no	—
508	D₄	—	4	2	no	—
509	D₄	—	59	2	no	—
510	D₄	—	118	4	no	—
511	D₄	—	118	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	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	—	2	1	no	—
519	C₂×C₄	—	4	1	no	—
520	C₂×C₄	—	4	1	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	118	4	no	—
523	C₂×C₄	—	118	1	no	—
524	C₂×C₄	—	118	1	no	—
525	C₂×C₄	—	118	1	no	—
526	C₂×C₄	—	236	2	no	—
527	C₂×C₄	—	236	1	no	—
528	C₂×C₄	—	236	1	no	—
529	C₂×C₄	C₄×C₂²⋊D₅₉	1	1	yes	characteristic
530	C₂×C₄	C₄×C₂²⋊D₅₉	1	1	yes	characteristic
531	C₂×C₄	C₄×C₂²⋊D₅₉	1	1	yes	characteristic
532	C₂×C₄	C₂²×C₄×D₅₉	1	1	yes	characteristic
533	C₂×C₄	C₂²×C₂²⋊D₅₉	1	1	yes	characteristic
534	C₂×C₄	C₂×#11745685	1	1	yes	characteristic
535	C₈	—	2	1	no	—
536	C₈	—	2	1	no	—
537	C₈	—	4	1	no	—
538	C₈	—	4	1	no	—
539	C₈	—	118	1	no	—
540	C₈	—	118	1	no	—
541	C₈	—	118	1	no	—
542	C₈	—	118	1	no	—
543	C₈	—	236	1	no	—
544	C₈	—	236	1	no	—
545	C₈	—	236	1	no	—
546	C₈	—	236	1	no	—
547	C₈	#14273747	1	2	yes	—
548	C₈	#14273747	1	2	yes	—
549	C₂²	—	2	1	no	—
550	C₂²	—	2	1	no	—
551	C₂²	—	2	1	no	—
552	C₂²	—	4	1	no	—
553	C₂²	—	4	1	no	—
554	C₂²	—	4	1	no	—
555	C₂²	—	118	2	no	—
556	C₂²	—	236	1	no	—
557	C₂²	—	236	1	no	—
558	C₂²	C₂×C₄×C₂²⋊D₅₉	1	1	yes	characteristic
559	C₄	—	2	1	no	—
560	C₄	—	2	1	no	—
561	C₄	—	2	1	no	—
562	C₄	—	2	1	no	—
563	C₄	—	4	1	no	—
564	C₄	—	4	1	no	—
565	C₄	—	4	1	no	—
566	C₄	—	118	2	no	—
567	C₄	—	236	1	no	—
568	C₄	—	236	1	no	—
569	C₄	#131×D₅₉	1	1	yes	characteristic
570	C₄	#131×D₅₉	1	1	yes	characteristic
571	C₄	C₂×#14273747	1	1	yes	characteristic
572	C₄	C₂×#14273747	1	1	yes	characteristic
573	C₂	—	4	1	no	—
574	C₂	—	8	1	no	—
575	C₂	—	236	2	no	—
576	C₂	#21432788	1	1	yes	characteristic
577	C₂	C₄×#14273747	1	1	yes	characteristic
578	C₂	#21432997	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂×C₂²⋊D₅₉
commutator	C₂×C₄×C₅₉	C₂³×C₄
Frattini	C₄²	C₂³×D₅₉
Fitting	C₅₉×#2966	C₂
socle	C₂²×C₅₉	C₂×C₄×D₄
prime radical	#16837545	C₄
cosocle	C₄²×C₅₉	C₂⁴
hypercenter	#2966	D₅₉
hypocenter	C₅₉	#17904
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈ ◁ #2966

Complements

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

N	H ≅ G/N	type
2. C₈×#11745685	C₂	semidirect
3. #21422944	C₂	semidirect
4. #21422937	C₂	semidirect
5. #21422930	C₂	semidirect
6. #21422923	C₂	semidirect
7. C₈×#11745672	C₂	semidirect
8. C₈×#11745671	C₂	semidirect
9. C₈×#11745670	C₂	semidirect
10. C₈×#11745669	C₂	semidirect
11. #21422877	C₂	semidirect
12. #21422528	C₂	semidirect
13. #21422504	C₂	semidirect
14. #21422379	C₂	semidirect
15. C₅₉×#2966	C₂	semidirect
285. #2966	D₅₉	semidirect
356. C₅₉	#17904	semidirect

Maximal subgroups

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

subgroup	index
#21434108	2
C₈×#11745685	2
#21422944	2
#21422937	2
#21422930	2
#21422923	2
C₈×#11745672	2
C₈×#11745671	2
C₈×#11745670	2
C₈×#11745669	2
#21422877	2
#21422528	2
#21422504	2
#21422379	2
C₅₉×#2966	2
#17904	59