Subgroups — #28558777

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	#21434157	C₂	1	1	yes	maximal, characteristic
2	#21433205	C₂	1	1	yes	maximal, characteristic, complemented
3	#21433174	C₂	1	1	yes	maximal, characteristic, complemented
4	#21422973	C₂	1	1	yes	maximal, characteristic, complemented
5	#21422959	C₂	1	1	yes	maximal, characteristic, complemented
6	#21422938	C₂	1	1	yes	maximal, characteristic, complemented
7	#21422924	C₂	1	1	yes	maximal, characteristic, complemented
8	#21422919	C₂	1	1	yes	maximal, characteristic, complemented
9	#21422907	C₂	1	1	yes	maximal, characteristic, complemented
10	#21422895	C₂	1	1	yes	maximal, characteristic, complemented
11	#21422890	C₂	1	1	yes	maximal, characteristic, complemented
12	#21422528	C₂	1	1	yes	maximal, characteristic, complemented
13	#21422494	C₂	1	1	yes	maximal, characteristic, complemented
14	#21422396	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₉×#1573	C₂	1	1	yes	maximal, characteristic, complemented
16	#16837952	C₂²	1	1	yes	characteristic
17	C₄×#11745685	C₂²	1	1	yes	characteristic
18	#16837727	C₄	1	1	yes	characteristic
19	#16837727	C₄	1	1	yes	characteristic
20	#16837698	C₄	1	1	yes	characteristic
21	#16837693	C₄	1	1	yes	characteristic
22	#16837603	C₄	1	1	yes	characteristic
23	#16837598	C₄	1	1	yes	characteristic
24	#16837549	C₄	1	1	yes	characteristic
25	#16837549	C₄	1	1	yes	characteristic
26	#16837526	C₂²	1	1	yes	characteristic
27	#16837526	C₂²	1	1	yes	characteristic
28	C₄×#11745660	C₂²	1	1	yes	characteristic
29	C₄×#11745660	C₂²	1	1	yes	characteristic
30	C₄×D₄₇₂	C₂²	1	1	yes	characteristic
31	C₄×D₄₇₂	C₂²	1	1	yes	characteristic
32	#16837479	C₂²	1	1	yes	characteristic
33	#16837479	C₂²	1	1	yes	characteristic
34	#16837475	—	2	1	no	—
35	#16837475	—	2	1	no	—
36	#16837467	C₂²	1	1	yes	characteristic
37	#16837467	C₂²	1	1	yes	characteristic
38	#16837467	C₂²	1	1	yes	characteristic
39	#16837467	C₂²	1	1	yes	characteristic
40	C₈×C₂²⋊D₅₉	—	2	1	no	—
41	C₈×C₂²⋊D₅₉	—	2	1	no	—
42	#16837455	C₂²	1	1	yes	characteristic
43	#16837455	C₂²	1	1	yes	characteristic
44	#16837454	—	2	1	no	—
45	C₄⋊C₈×D₅₉	—	2	1	no	—
46	#16837367	—	2	1	no	—
47	#16837367	—	2	1	no	—
48	#16837132	C₂²	1	1	yes	characteristic
49	#16837132	C₂²	1	1	yes	characteristic
50	#16837129	C₂²	1	1	yes	characteristic
51	#16837129	C₂²	1	1	yes	characteristic
52	#16837129	C₂²	1	1	yes	characteristic
53	#16837129	C₂²	1	1	yes	characteristic
54	#16837129	C₂²	1	1	yes	characteristic
55	#16837129	C₂²	1	1	yes	characteristic
56	#16837124	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	C₅₉×#432	C₂²	1	1	yes	characteristic
61	C₅₉×#431	C₂²	1	1	yes	characteristic
62	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
63	C₅₉×#335	C₂²	1	1	yes	characteristic
64	C₅₉×#335	C₂²	1	1	yes	characteristic
65	C₅₉×#334	C₂²	1	1	yes	characteristic
66	C₅₉×#334	C₂²	1	1	yes	characteristic
67	C₂×#11745685	—	2	1	no	—
68	C₂×#11745685	C₂×C₄	1	1	yes	characteristic
69	C₂×#11745660	C₂×C₄	1	1	yes	characteristic
70	C₂×#11745660	C₂×C₄	1	1	yes	characteristic
71	C₂×D₄₇₂	C₂×C₄	1	1	yes	characteristic
72	C₂×D₄₇₂	C₂×C₄	1	1	yes	characteristic
73	C₂×#11745659	—	2	1	no	—
74	C₂×#11745659	—	2	1	no	—
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	#14273727	C₂×C₄	1	1	yes	characteristic
80	#14273724	C₂×C₄	1	1	yes	characteristic
81	#14273715	—	2	1	no	—
82	#14273701	—	2	1	no	—
83	#14273701	C₂×C₄	1	1	yes	characteristic
84	#14273701	C₂×C₄	1	1	yes	characteristic
85	C₄×Dic₁₁₈	C₂×C₄	1	1	yes	characteristic
86	C₄×Dic₁₁₈	C₂³	1	1	yes	characteristic
87	C₄×D₂₃₆	—	2	1	no	—
88	C₄×D₂₃₆	C₂×C₄	1	1	yes	characteristic
89	C₄×D₂₃₆	C₂³	1	1	yes	characteristic
90	C₄×D₂₃₆	C₂³	1	1	yes	characteristic
91	C₄×D₂₃₆	C₂³	1	1	yes	characteristic
92	C₄×C₂²⋊D₅₉	—	2	1	no	—
93	C₄×C₂²⋊D₅₉	—	2	1	no	—
94	#14273686	C₂×C₄	1	1	yes	characteristic
95	#14273684	—	2	1	no	—
96	C₄²×D₅₉	—	2	1	no	—
97	#14273661	C₂×C₄	1	1	yes	characteristic
98	#14273661	C₂×C₄	1	1	yes	characteristic
99	#14273659	C₂×C₄	1	1	yes	characteristic
100	#14273659	C₂×C₄	1	1	yes	characteristic
101	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
102	C₄⋊(C₅₉⋊C₈)	D₄	1	1	yes	characteristic
103	C₄⋊(C₅₉⋊C₈)	D₄	1	1	yes	characteristic
104	Dic₅₉⋊C₈	—	2	1	no	—
105	Dic₅₉⋊C₈	—	2	1	no	—
106	#14273652	C₂×C₄	1	1	yes	characteristic
107	#14273652	C₂×C₄	1	1	yes	characteristic
108	#14273649	C₂×C₄	1	1	yes	characteristic
109	#14273649	C₂×C₄	1	1	yes	characteristic
110	#14273649	C₂×C₄	1	1	yes	characteristic
111	#14273649	C₂×C₄	1	1	yes	characteristic
112	#14273649	C₂×C₄	1	1	yes	characteristic
113	#14273649	C₂×C₄	1	1	yes	characteristic
114	C₂²⋊(C₅₉⋊C₈)	—	2	1	no	—
115	C₂²⋊(C₅₉⋊C₈)	D₄	1	1	yes	characteristic
116	C₂²⋊(C₅₉⋊C₈)	D₄	1	1	yes	characteristic
117	(C₂×D₅₉)⋊C₈	—	2	1	no	—
118	(C₂×D₅₉)⋊C₈	—	2	1	no	—
119	(C₂×D₅₉)⋊C₈	—	2	1	no	—
120	(C₂×D₅₉)⋊C₈	—	2	1	no	—
121	(C₂×D₅₉)⋊C₈	—	2	1	no	—
122	(C₂×D₅₉)⋊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	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
127	C₈×Dic₅₉	—	2	1	no	—
128	C₈×Dic₅₉	—	2	1	no	—
129	C₂²×C₈×C₅₉	—	2	1	no	—
130	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
131	C₄⋊C₈×C₅₉	—	2	1	no	—
132	C₄⋊C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
133	C₄⋊C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
134	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
135	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
136	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
137	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
138	C₂²⋊C₈×C₅₉	—	2	1	no	—
139	C₂²⋊C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
140	C₂²⋊C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
141	#97×C₅₉	—	2	1	no	—
142	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
144	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
145	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
147	C₂×C₂²⋊D₅₉	—	2	1	no	—
148	C₂×C₂²⋊D₅₉	—	2	1	no	—
149	C₂×C₂²⋊D₅₉	—	2	1	no	—
150	#11745685	—	2	2	no	—
151	#11745685	—	2	2	no	—
152	#11745685	—	8	1	no	—
153	#11745685	—	8	1	no	—
154	C₂×D₂₃₆	—	2	1	no	—
155	C₂×D₂₃₆	—	2	1	no	—
156	C₂×D₂₃₆	C₂²×C₄	1	1	yes	characteristic
157	C₂×D₂₃₆	C₂²×C₄	1	1	yes	characteristic
158	C₂×D₂₃₆	C₂²×C₄	1	1	yes	characteristic
159	C₂×C₄×D₅₉	—	2	1	no	—
160	C₂×C₄×D₅₉	—	2	1	no	—
161	C₂×C₄×D₅₉	—	2	1	no	—
162	C₂×C₄×D₅₉	—	2	1	no	—
163	C₂×C₄×D₅₉	—	2	1	no	—
164	C₂×Dic₁₁₈	—	2	1	no	—
165	C₂×Dic₁₁₈	C₂²×C₄	1	1	yes	characteristic
166	C₂×C₈×C₅₉	—	2	1	no	—
167	C₂×C₈×C₅₉	—	2	1	no	—
168	C₂×C₈×C₅₉	—	2	1	no	—
169	C₂×C₈×C₅₉	—	2	1	no	—
170	C₂×C₈×C₅₉	—	8	1	no	—
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	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
175	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
176	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
177	C₄²×C₅₉	#41	1	1	yes	characteristic
178	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
179	C₂²⋊Dic₅₉	—	2	1	no	—
180	(C₂×D₅₉)⋊C₄	—	2	1	no	—
181	(C₂×D₅₉)⋊C₄	—	2	1	no	—
182	(C₂×D₅₉)⋊C₄	—	2	1	no	—
183	(C₂×D₅₉)⋊C₄	—	2	1	no	—
184	(C₂×D₅₉)⋊C₄	—	2	1	no	—
185	(C₂×D₅₉)⋊C₄	—	2	1	no	—
186	C₄⋊Dic₅₉	—	2	1	no	—
187	C₄⋊Dic₅₉	C₂²×C₄	1	1	yes	characteristic
188	C₄⋊Dic₅₉	C₂²×C₄	1	1	yes	characteristic
189	C₄⋊Dic₅₉	C₂²×C₄	1	1	yes	characteristic
190	C₄⋊Dic₅₉	C₂²×C₄	1	1	yes	characteristic
191	Dic₅₉⋊C₄	—	2	1	no	—
192	Dic₅₉⋊C₄	—	2	1	no	—
193	C₄×Dic₅₉	—	2	1	no	—
194	C₄×Dic₅₉	—	2	1	no	—
195	C₄×Dic₅₉	—	2	1	no	—
196	C₂×C₅₉⋊C₈	—	2	1	no	—
197	C₂×C₅₉⋊C₈	—	2	1	no	—
198	C₂×C₅₉⋊C₈	C₂×D₄	1	1	yes	characteristic
199	C₂×C₅₉⋊C₈	C₂×D₄	1	1	yes	characteristic
200	C₂×C₅₉⋊C₈	C₂×D₄	1	1	yes	characteristic
201	C₂×C₅₉⋊C₈	C₂×D₄	1	1	yes	characteristic
202	D₄₇₂	—	2	2	no	—
203	D₄₇₂	—	2	2	no	—
204	#11745660	—	2	2	no	—
205	#11745660	—	2	2	no	—
206	#11745659	—	8	1	no	—
207	#11745659	—	8	1	no	—
208	C₈×D₅₉	—	8	1	no	—
209	C₈×D₅₉	—	8	1	no	—
210	C₈×D₅₉	—	8	1	no	—
211	C₈×D₅₉	—	8	1	no	—
212	C₂³×C₅₉	C₄×D₄	1	1	yes	characteristic
213	C₂²×D₅₉	—	2	1	no	—
214	C₂²×D₅₉	—	2	1	no	—
215	C₂²×D₅₉	—	2	1	no	—
216	C₂×C₄×C₅₉	—	2	1	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	—	4	1	no	—
221	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
222	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
223	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
224	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
225	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
226	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
227	C₂²⋊D₅₉	—	2	4	no	—
228	C₂²⋊D₅₉	—	8	1	no	—
229	C₂²⋊D₅₉	—	8	1	no	—
230	C₂×Dic₅₉	—	2	1	no	—
231	C₂×Dic₅₉	—	2	1	no	—
232	C₂×Dic₅₉	—	2	1	no	—
233	C₂×Dic₅₉	—	2	1	no	—
234	C₂×Dic₅₉	—	2	1	no	—
235	D₂₃₆	—	2	1	no	—
236	D₂₃₆	—	2	1	no	—
237	D₂₃₆	—	2	1	no	—
238	D₂₃₆	—	2	1	no	—
239	D₂₃₆	—	2	1	no	—
240	D₂₃₆	—	8	1	no	—
241	D₂₃₆	—	8	1	no	—
242	D₂₃₆	#131	1	2	yes	—
243	C₄×D₅₉	—	2	4	no	—
244	C₄×D₅₉	—	4	1	no	—
245	C₄×D₅₉	—	4	1	no	—
246	C₄×D₅₉	—	4	1	no	—
247	C₄×D₅₉	—	4	1	no	—
248	C₄×D₅₉	—	4	1	no	—
249	C₄×D₅₉	—	4	1	no	—
250	C₄×D₅₉	—	8	1	no	—
251	Dic₁₁₈	—	2	1	no	—
252	Dic₁₁₈	—	8	1	no	—
253	Dic₁₁₈	#131	1	2	yes	—
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	C₈×C₅₉	—	4	1	no	—
259	C₈×C₅₉	—	4	1	no	—
260	C₈×C₅₉	—	4	1	no	—
261	C₈×C₅₉	—	4	1	no	—
262	C₅₉⋊C₈	—	2	1	no	—
263	C₅₉⋊C₈	—	2	1	no	—
264	C₅₉⋊C₈	—	2	1	no	—
265	C₅₉⋊C₈	—	2	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	1	no	—
271	C₂²×C₅₉	—	2	1	no	—
272	C₂²×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
273	C₂×D₅₉	—	2	2	no	—
274	C₂×D₅₉	—	4	1	no	—
275	C₂×D₅₉	—	4	1	no	—
276	C₂×D₅₉	—	4	1	no	—
277	C₂×D₅₉	—	4	1	no	—
278	C₂×D₅₉	—	4	1	no	—
279	C₂×D₅₉	—	4	1	no	—
280	C₂×D₅₉	—	4	1	no	—
281	C₂×D₅₉	—	4	1	no	—
282	C₄×C₅₉	—	2	1	no	—
283	C₄×C₅₉	—	2	1	no	—
284	C₄×C₅₉	—	2	1	no	—
285	C₄×C₅₉	—	2	1	no	—
286	C₄×C₅₉	C₂×#131	1	1	yes	characteristic
287	C₄×C₅₉	C₂×#131	1	1	yes	characteristic
288	C₄×C₅₉	#576	1	1	yes	characteristic
289	C₄×C₅₉	#577	1	1	yes	characteristic
290	Dic₅₉	—	2	2	no	—
291	Dic₅₉	—	4	1	no	—
292	Dic₅₉	—	4	1	no	—
293	Dic₅₉	—	4	1	no	—
294	Dic₅₉	—	4	1	no	—
295	#3106	—	59	1	no	—
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	D₅₉	1	1	yes	characteristic, complemented
307	#1488	—	59	1	no	—
308	#1480	—	59	1	no	—
309	#1454	—	59	1	no	—
310	C₂×C₅₉	—	4	1	no	—
311	C₂×C₅₉	#2929	1	1	yes	characteristic
312	C₂×C₅₉	#2946	1	1	yes	characteristic
313	C₂×C₅₉	#2957	1	1	yes	characteristic
314	D₅₉	—	4	2	no	—
315	D₅₉	—	8	1	no	—
316	D₅₉	—	8	1	no	—
317	#532	—	59	1	no	—
318	C₄×#41	—	59	1	no	—
319	#482	—	59	1	no	—
320	#482	—	59	1	no	—
321	#477	—	59	1	no	—
322	#476	—	59	1	no	—
323	#460	—	59	1	no	—
324	#459	—	59	1	no	—
325	#449	—	59	1	no	—
326	#449	—	59	1	no	—
327	C₈×Q₈	—	59	1	no	—
328	C₈×Q₈	—	59	1	no	—
329	C₄×SD₁₆	—	59	1	no	—
330	C₄×SD₁₆	—	59	1	no	—
331	C₄×D₈	—	59	1	no	—
332	C₄×D₈	—	59	1	no	—
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	C₂×D₅₉	1	1	yes	characteristic
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	—	118	1	no	—
349	C₂×C₄⋊C₈	C₂×D₅₉	1	1	yes	characteristic
350	#408	—	118	1	no	—
351	#408	—	118	1	no	—
352	#335	C₂×D₅₉	1	1	yes	characteristic
353	#335	C₂×D₅₉	1	1	yes	characteristic
354	#334	C₂×D₅₉	1	1	yes	characteristic
355	#334	C₂×D₅₉	1	1	yes	characteristic
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	—	59	1	no	—
370	C₂×#41	—	118	1	no	—
371	C₂×SD₁₆	—	59	1	no	—
372	C₂×SD₁₆	—	59	1	no	—
373	C₂×D₈	—	59	1	no	—
374	C₂×D₈	—	59	1	no	—
375	C₂×M₁₆	—	118	1	no	—
376	C₂×M₁₆	—	118	1	no	—
377	C₂²×C₈	—	2	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	—	59	1	no	—
383	#127	—	59	1	no	—
384	#124	—	118	1	no	—
385	#121	—	59	1	no	—
386	#121	—	59	1	no	—
387	#121	—	118	1	no	—
388	C₄×Q₈	—	59	1	no	—
389	C₄×Q₈	—	59	1	no	—
390	C₄×D₄	—	59	1	no	—
391	C₄×D₄	—	59	1	no	—
392	C₄×D₄	—	59	1	no	—
393	C₄×D₄	—	59	1	no	—
394	C₄×D₄	—	118	1	no	—
395	C₄×D₄	—	118	1	no	—
396	C₄×D₄	—	118	1	no	—
397	#117	—	59	1	no	—
398	#117	—	118	1	no	—
399	C₂×C₄²	—	118	1	no	—
400	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
401	#107	—	59	1	no	—
402	#107	—	59	1	no	—
403	#106	—	59	1	no	—
404	#106	—	59	1	no	—
405	C₄⋊C₈	—	2	1	no	—
406	C₄⋊C₈	—	59	1	no	—
407	C₄⋊C₈	—	59	1	no	—
408	C₄⋊C₈	—	118	1	no	—
409	C₄⋊C₈	—	118	1	no	—
410	C₄⋊C₈	—	118	1	no	—
411	C₄⋊C₈	C₄×D₅₉	1	1	yes	characteristic
412	C₄⋊C₈	C₄×D₅₉	1	1	yes	characteristic
413	C₄⋊C₈	C₂²×D₅₉	1	1	yes	characteristic
414	C₄⋊C₈	C₂²×D₅₉	1	1	yes	characteristic
415	C₄⋊C₈	C₂²×D₅₉	1	1	yes	characteristic
416	C₄⋊C₈	C₂²×D₅₉	1	1	yes	characteristic
417	#103	—	59	1	no	—
418	#103	—	59	1	no	—
419	#102	—	59	1	no	—
420	#102	—	59	1	no	—
421	#102	—	59	1	no	—
422	#102	—	59	1	no	—
423	#102	—	59	1	no	—
424	#102	—	59	1	no	—
425	C₂²⋊C₈	—	2	1	no	—
426	C₂²⋊C₈	—	59	1	no	—
427	C₂²⋊C₈	—	59	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	C₄×D₅₉	1	1	yes	characteristic
436	C₂²⋊C₈	C₄×D₅₉	1	1	yes	characteristic
437	#97	—	2	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	—	118	2	no	—
447	#41	—	118	2	no	—
448	#41	—	472	1	no	—
449	#41	—	472	1	no	—
450	C₂×Q₈	—	59	1	no	—
451	C₂×Q₈	—	118	1	no	—
452	C₂×D₄	—	59	1	no	—
453	C₂×D₄	—	59	1	no	—
454	C₂×D₄	—	59	1	no	—
455	C₂×D₄	—	118	1	no	—
456	C₂×D₄	—	118	1	no	—
457	C₂×D₄	—	118	1	no	—
458	C₂×D₄	—	118	1	no	—
459	C₂×D₄	—	118	1	no	—
460	C₂²×C₄	—	118	1	no	—
461	C₂²×C₄	—	118	1	no	—
462	C₂²×C₄	—	118	1	no	—
463	C₂²×C₄	—	118	1	no	—
464	C₂²×C₄	—	118	1	no	—
465	C₂²×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
466	C₂²×C₄	D₄×D₅₉	1	1	yes	characteristic
467	C₂²×C₄	#11745689	1	1	yes	characteristic
468	SD₁₆	—	118	2	no	—
469	SD₁₆	—	118	2	no	—
470	D₈	—	118	2	no	—
471	D₈	—	118	2	no	—
472	M₁₆	—	472	1	no	—
473	M₁₆	—	472	1	no	—
474	C₂×C₈	—	2	1	no	—
475	C₂×C₈	—	2	1	no	—
476	C₂×C₈	—	2	1	no	—
477	C₂×C₈	—	2	1	no	—
478	C₂×C₈	—	8	1	no	—
479	C₂×C₈	—	59	1	no	—
480	C₂×C₈	—	59	1	no	—
481	C₂×C₈	—	59	1	no	—
482	C₂×C₈	—	59	1	no	—
483	C₂×C₈	—	118	1	no	—
484	C₂×C₈	—	118	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	C₂×C₄×D₅₉	1	1	yes	characteristic
490	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
491	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
492	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
493	C₄⋊C₄	—	59	1	no	—
494	C₄⋊C₄	—	59	1	no	—
495	C₄⋊C₄	—	59	1	no	—
496	C₄⋊C₄	—	59	1	no	—
497	C₄⋊C₄	—	118	1	no	—
498	C₄⋊C₄	—	118	1	no	—
499	C₄⋊C₄	—	118	1	no	—
500	C₂²⋊C₄	—	118	1	no	—
501	C₂²⋊C₄	—	118	1	no	—
502	C₂²⋊C₄	—	118	1	no	—
503	C₂²⋊C₄	—	118	1	no	—
504	C₂²⋊C₄	—	118	1	no	—
505	C₂²⋊C₄	—	118	1	no	—
506	C₂²⋊C₄	—	118	1	no	—
507	C₄²	—	118	1	no	—
508	C₄²	—	118	1	no	—
509	C₄²	—	118	1	no	—
510	C₄²	C₂×C₄×D₅₉	1	1	yes	characteristic
511	C₄²	D₄×D₅₉	1	1	yes	characteristic
512	C₄²	#11745689	1	1	yes	characteristic
513	C₄²	C₂³×D₅₉	1	1	yes	characteristic
514	C₂³	—	118	1	no	—
515	C₂³	—	118	1	no	—
516	C₂³	—	118	1	no	—
517	C₂³	#14273689	1	1	yes	characteristic
518	Q₈	—	59	2	no	—
519	Q₈	—	118	1	no	—
520	Q₈	—	472	1	no	—
521	D₄	—	59	2	no	—
522	D₄	—	118	4	no	—
523	D₄	—	118	1	no	—
524	D₄	—	118	1	no	—
525	D₄	—	118	1	no	—
526	D₄	—	118	1	no	—
527	D₄	—	118	1	no	—
528	D₄	—	472	1	no	—
529	D₄	—	472	1	no	—
530	D₄	—	472	1	no	—
531	D₄	—	472	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	4	1	no	—
537	C₂×C₄	—	118	4	no	—
538	C₂×C₄	—	118	1	no	—
539	C₂×C₄	—	118	1	no	—
540	C₂×C₄	—	118	1	no	—
541	C₂×C₄	—	118	1	no	—
542	C₂×C₄	—	118	1	no	—
543	C₂×C₄	—	472	1	no	—
544	C₂×C₄	—	236	1	no	—
545	C₂×C₄	—	236	1	no	—
546	C₂×C₄	—	236	1	no	—
547	C₂×C₄	—	236	1	no	—
548	C₂×C₄	—	236	1	no	—
549	C₂×C₄	—	236	1	no	—
550	C₂×C₄	#14273689	1	1	yes	characteristic
551	C₂×C₄	#14273689	1	1	yes	characteristic
552	C₂×C₄	#14273689	1	1	yes	characteristic
553	C₂×C₄	C₂²×C₄×D₅₉	1	1	yes	characteristic
554	C₂×C₄	C₂×D₄×D₅₉	1	1	yes	characteristic
555	C₂×C₄	C₂×#11745689	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	—	4	1	no	—
561	C₈	—	4	1	no	—
562	C₈	—	4	1	no	—
563	C₈	—	4	1	no	—
564	C₈	—	118	1	no	—
565	C₈	—	118	1	no	—
566	C₈	—	118	1	no	—
567	C₈	—	118	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	—	118	2	no	—
574	C₂²	—	236	1	no	—
575	C₂²	—	236	1	no	—
576	C₂²	—	236	1	no	—
577	C₂²	—	236	1	no	—
578	C₂²	—	236	1	no	—
579	C₂²	—	236	1	no	—
580	C₂²	—	236	1	no	—
581	C₂²	—	236	1	no	—
582	C₂²	C₂×#14273689	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	—	118	2	no	—
588	C₄	—	236	1	no	—
589	C₄	—	236	1	no	—
590	C₄	—	236	1	no	—
591	C₄	—	236	1	no	—
592	C₄	#131×D₅₉	1	1	yes	characteristic
593	C₄	#131×D₅₉	1	1	yes	characteristic
594	C₄	#16838206	1	1	yes	characteristic
595	C₄	#16838211	1	1	yes	characteristic
596	C₂	—	4	1	no	—
597	C₂	—	472	1	no	—
598	C₂	—	472	1	no	—
599	C₂	—	236	2	no	—
600	C₂	#21432789	1	1	yes	characteristic
601	C₂	#21432926	1	1	yes	characteristic
602	C₂	#21433012	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₅₉
commutator	C₂×C₄×C₅₉	C₂³×C₄
Frattini	C₄²	C₂³×D₅₉
Fitting	C₅₉×#1573	C₂
socle	C₂²×C₅₉	C₂×C₄×D₄
prime radical	#21434157	C₂
cosocle	C₄²×C₅₉	C₂⁴
hypercenter	#1573	D₅₉
hypocenter	C₅₉	#17920
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1573

Complements

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

N	H ≅ G/N	type
2. #21433205	C₂	semidirect
3. #21433174	C₂	semidirect
4. #21422973	C₂	semidirect
5. #21422959	C₂	semidirect
6. #21422938	C₂	semidirect
7. #21422924	C₂	semidirect
8. #21422919	C₂	semidirect
9. #21422907	C₂	semidirect
10. #21422895	C₂	semidirect
11. #21422890	C₂	semidirect
12. #21422528	C₂	semidirect
13. #21422494	C₂	semidirect
14. #21422396	C₂	semidirect
15. C₅₉×#1573	C₂	semidirect
306. #1573	D₅₉	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
#21434157	2
#21433205	2
#21433174	2
#21422973	2
#21422959	2
#21422938	2
#21422924	2
#21422919	2
#21422907	2
#21422895	2
#21422890	2
#21422528	2
#21422494	2
#21422396	2
C₅₉×#1573	2
#17920	59