Subgroups — #28558593

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	#21434116	C₂	1	1	yes	maximal, characteristic
2	#21433065	C₂	1	1	yes	maximal, characteristic, complemented
3	#21433052	C₂	1	1	yes	maximal, characteristic, complemented
4	#21422945	C₂	1	1	yes	maximal, characteristic, complemented
5	#21422938	C₂	1	1	yes	maximal, characteristic, complemented
6	#21422931	C₂	1	1	yes	maximal, characteristic, complemented
7	#21422924	C₂	1	1	yes	maximal, characteristic, complemented
8	#21422902	C₂	1	1	yes	maximal, characteristic, complemented
9	#21422895	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	#21422502	C₂	1	1	yes	maximal, characteristic, complemented
14	#21422380	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₉×#1572	C₂	1	1	yes	maximal, characteristic, complemented
16	#16837936	C₂²	1	1	yes	characteristic
17	C₄×#11745685	C₂²	1	1	yes	characteristic
18	#16837744	C₄	1	1	yes	characteristic
19	#16837727	C₄	1	1	yes	characteristic
20	#16837710	C₄	1	1	yes	characteristic
21	#16837703	C₄	1	1	yes	characteristic
22	#16837625	C₄	1	1	yes	characteristic
23	#16837618	C₄	1	1	yes	characteristic
24	#16837566	C₄	1	1	yes	characteristic
25	#16837549	C₄	1	1	yes	characteristic
26	#16837529	C₂²	1	1	yes	characteristic
27	#16837526	C₂²	1	1	yes	characteristic
28	#16837526	C₂²	1	1	yes	characteristic
29	#16837526	C₂²	1	1	yes	characteristic
30	C₄×Dic₂₃₆	C₂²	1	1	yes	characteristic
31	C₄×#11745660	C₂²	1	1	yes	characteristic
32	C₄×#11745660	C₂²	1	1	yes	characteristic
33	C₄×D₄₇₂	C₂²	1	1	yes	characteristic
34	#16837479	C₂²	1	1	yes	characteristic
35	#16837470	—	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	(C₂²⋊D₅₉)⋊C₈	—	2	1	no	—
40	(C₂²⋊D₅₉)⋊C₈	—	2	1	no	—
41	(C₂²⋊D₅₉)⋊C₈	—	2	1	no	—
42	#16837464	—	2	1	no	—
43	#16837455	C₂²	1	1	yes	characteristic
44	#16837453	—	2	1	no	—
45	#16837359	—	2	1	no	—
46	C₂×C₄×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
47	C₄×C₈×D₅₉	—	2	1	no	—
48	#16837132	C₂²	1	1	yes	characteristic
49	#16837132	C₂²	1	1	yes	characteristic
50	#16837132	C₂²	1	1	yes	characteristic
51	#16837132	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	C₈×C₅₉⋊C₈	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	C₅₉×#431	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	C₂×C₄	1	1	yes	characteristic
68	C₂×Dic₂₃₆	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×#11745659	—	2	1	no	—
73	C₂²×C₅₉⋊C₈	D₄	1	1	yes	characteristic
74	C₂²×C₅₉⋊C₈	D₄	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	#14273721	—	2	1	no	—
79	#14273719	C₂×C₄	1	1	yes	characteristic
80	#14273715	C₂×C₄	1	1	yes	characteristic
81	#14273710	—	2	1	no	—
82	#14273706	C₂×C₄	1	1	yes	characteristic
83	#14273701	C₂×C₄	1	1	yes	characteristic
84	C₄×Dic₁₁₈	C₂×C₄	1	1	yes	characteristic
85	C₄×Dic₁₁₈	C₂³	1	1	yes	characteristic
86	C₄×Dic₁₁₈	C₂³	1	1	yes	characteristic
87	C₄×D₂₃₆	C₂×C₄	1	1	yes	characteristic
88	C₄×D₂₃₆	C₂³	1	1	yes	characteristic
89	C₄×D₂₃₆	C₂³	1	1	yes	characteristic
90	C₄×C₂²⋊D₅₉	—	2	1	no	—
91	C₄×C₂²⋊D₅₉	—	2	1	no	—
92	C₄×C₂²⋊D₅₉	—	2	1	no	—
93	#14273686	C₂×C₄	1	1	yes	characteristic
94	#14273684	—	2	1	no	—
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	Dic₅₉⋊C₈	—	2	1	no	—
103	Dic₅₉⋊C₈	—	2	1	no	—
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	#14273652	C₂×C₄	1	1	yes	characteristic
109	#14273652	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	(C₂×D₅₉)⋊C₈	—	2	1	no	—
116	(C₂×D₅₉)⋊C₈	—	2	1	no	—
117	(C₂×D₅₉)⋊C₈	—	2	1	no	—
118	(C₂×D₅₉)⋊C₈	—	2	1	no	—
119	#14273637	—	2	1	no	—
120	C₄×C₅₉⋊C₈	D₄	1	1	yes	characteristic
121	C₄×C₅₉⋊C₈	D₄	1	1	yes	characteristic
122	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
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	C₂×C₄²×C₅₉	C₂³	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	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
133	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
134	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
135	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
136	C₂²⋊C₈×C₅₉	—	2	1	no	—
137	C₂²⋊C₈×C₅₉	—	2	1	no	—
138	C₂²⋊C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
139	C₂²⋊C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
140	#97×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	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	#11745685	—	2	2	no	—
150	#11745685	—	2	2	no	—
151	C₂×D₂₃₆	C₂²×C₄	1	1	yes	characteristic
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×Dic₁₁₈	C₂²×C₄	1	1	yes	characteristic
158	C₂×Dic₁₁₈	C₂²×C₄	1	1	yes	characteristic
159	C₂×C₈×C₅₉	—	2	1	no	—
160	C₂×C₈×C₅₉	—	2	1	no	—
161	C₂×C₈×C₅₉	—	2	1	no	—
162	C₂×C₈×C₅₉	—	2	1	no	—
163	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
164	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
165	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
166	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
167	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
168	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
169	C₄²×C₅₉	#41	1	1	yes	characteristic
170	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
171	C₂²⋊Dic₅₉	—	2	1	no	—
172	C₂²⋊Dic₅₉	—	2	1	no	—
173	(C₂×D₅₉)⋊C₄	—	2	1	no	—
174	(C₂×D₅₉)⋊C₄	—	2	1	no	—
175	(C₂×D₅₉)⋊C₄	—	2	1	no	—
176	(C₂×D₅₉)⋊C₄	—	2	1	no	—
177	(C₂×D₅₉)⋊C₄	—	2	1	no	—
178	(C₂×D₅₉)⋊C₄	—	2	1	no	—
179	C₄⋊Dic₅₉	C₂²×C₄	1	1	yes	characteristic
180	C₄⋊Dic₅₉	C₂²×C₄	1	1	yes	characteristic
181	C₄⋊Dic₅₉	C₂²×C₄	1	1	yes	characteristic
182	C₄⋊Dic₅₉	C₂²×C₄	1	1	yes	characteristic
183	Dic₅₉⋊C₄	—	2	1	no	—
184	Dic₅₉⋊C₄	—	2	1	no	—
185	Dic₅₉⋊C₄	—	2	1	no	—
186	Dic₅₉⋊C₄	—	2	1	no	—
187	Dic₅₉⋊C₄	—	2	1	no	—
188	Dic₅₉⋊C₄	—	2	1	no	—
189	C₄×Dic₅₉	—	2	1	no	—
190	C₄×Dic₅₉	—	2	1	no	—
191	C₄×Dic₅₉	—	2	1	no	—
192	C₄×Dic₅₉	—	2	1	no	—
193	C₂×C₅₉⋊C₈	—	2	2	no	—
194	C₂×C₅₉⋊C₈	—	2	2	no	—
195	C₂×C₅₉⋊C₈	—	2	1	no	—
196	C₂×C₅₉⋊C₈	—	2	1	no	—
197	C₂×C₅₉⋊C₈	C₂×D₄	1	1	yes	characteristic
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	Dic₂₃₆	—	2	2	no	—
202	D₄₇₂	—	2	2	no	—
203	#11745660	—	2	2	no	—
204	#11745660	—	2	2	no	—
205	#11745659	—	4	2	no	—
206	C₈×D₅₉	—	4	2	no	—
207	C₈×D₅₉	—	4	2	no	—
208	C₈×D₅₉	—	4	2	no	—
209	C₂³×C₅₉	C₄×D₄	1	1	yes	characteristic
210	C₂²×D₅₉	—	2	1	no	—
211	C₂²×D₅₉	—	2	1	no	—
212	C₂×C₄×C₅₉	—	2	1	no	—
213	C₂×C₄×C₅₉	—	2	1	no	—
214	C₂×C₄×C₅₉	—	2	1	no	—
215	C₂×C₄×C₅₉	—	2	1	no	—
216	C₂×C₄×C₅₉	—	4	1	no	—
217	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
218	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
219	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
220	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
221	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
222	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
223	C₂²⋊D₅₉	—	2	4	no	—
224	C₂²⋊D₅₉	—	4	2	no	—
225	C₂×Dic₅₉	—	2	1	no	—
226	C₂×Dic₅₉	—	2	1	no	—
227	C₂×Dic₅₉	—	2	1	no	—
228	C₂×Dic₅₉	—	2	1	no	—
229	C₂×Dic₅₉	—	2	1	no	—
230	C₂×Dic₅₉	—	2	1	no	—
231	D₂₃₆	—	2	1	no	—
232	D₂₃₆	—	2	1	no	—
233	D₂₃₆	—	2	1	no	—
234	D₂₃₆	#131	1	2	yes	—
235	C₄×D₅₉	—	2	4	no	—
236	C₄×D₅₉	—	4	2	no	—
237	C₄×D₅₉	—	4	1	no	—
238	C₄×D₅₉	—	4	1	no	—
239	C₄×D₅₉	—	4	1	no	—
240	C₄×D₅₉	—	4	1	no	—
241	Dic₁₁₈	—	2	1	no	—
242	Dic₁₁₈	—	2	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	—	2	1	no	—
248	C₈×C₅₉	—	2	1	no	—
249	C₈×C₅₉	—	4	1	no	—
250	C₈×C₅₉	—	4	1	no	—
251	C₈×C₅₉	—	4	1	no	—
252	C₈×C₅₉	—	4	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	#135	1	2	yes	—
258	C₅₉⋊C₈	#135	1	2	yes	—
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	C₂×C₄×D₄	1	1	yes	characteristic
264	C₂×D₅₉	—	2	2	no	—
265	C₂×D₅₉	—	4	1	no	—
266	C₂×D₅₉	—	4	1	no	—
267	C₂×D₅₉	—	4	1	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	C₂×#131	1	1	yes	characteristic
275	C₄×C₅₉	C₂×#131	1	1	yes	characteristic
276	C₄×C₅₉	C₂×#135	1	1	yes	characteristic
277	C₄×C₅₉	C₂×#135	1	1	yes	characteristic
278	Dic₅₉	—	2	2	no	—
279	Dic₅₉	—	4	1	no	—
280	Dic₅₉	—	4	1	no	—
281	Dic₅₉	—	4	1	no	—
282	Dic₅₉	—	4	1	no	—
283	Dic₅₉	—	4	1	no	—
284	#3102	—	59	1	no	—
285	#2966	—	59	1	no	—
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	D₅₉	1	1	yes	characteristic, complemented
296	#1488	—	59	1	no	—
297	#1482	—	59	1	no	—
298	#1450	—	59	1	no	—
299	C₂×C₅₉	—	4	1	no	—
300	C₂×C₅₉	#2929	1	1	yes	characteristic
301	C₂×C₅₉	C₄×#135	1	1	yes	characteristic
302	C₂×C₅₉	#2955	1	1	yes	characteristic
303	D₅₉	—	4	2	no	—
304	D₅₉	—	8	1	no	—
305	#529	—	59	1	no	—
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	—	59	1	no	—
316	C₈×Q₈	—	59	1	no	—
317	C₈×Q₈	—	59	1	no	—
318	C₈×Q₈	—	59	1	no	—
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	—	59	1	no	—
324	#435	—	118	1	no	—
325	C₈×D₄	—	59	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	—	118	1	no	—
331	#433	—	118	1	no	—
332	#432	C₂×D₅₉	1	1	yes	characteristic
333	#431	—	59	1	no	—
334	#431	—	118	1	no	—
335	#431	C₂×D₅₉	1	1	yes	characteristic
336	#431	C₂×D₅₉	1	1	yes	characteristic
337	#405	—	118	1	no	—
338	C₂×C₄×C₈	—	59	1	no	—
339	C₂×C₄×C₈	—	118	1	no	—
340	#335	C₂×D₅₉	1	1	yes	characteristic
341	#335	C₂×D₅₉	1	1	yes	characteristic
342	#334	C₂×D₅₉	1	1	yes	characteristic
343	#334	C₂×D₅₉	1	1	yes	characteristic
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	—	118	1	no	—
363	C₂²×C₈	—	59	1	no	—
364	C₂²×C₈	—	59	1	no	—
365	C₂²×C₈	—	118	1	no	—
366	C₂²×C₈	—	118	1	no	—
367	C₂²×C₈	—	118	1	no	—
368	#126	—	118	1	no	—
369	#125	—	59	1	no	—
370	#124	—	59	1	no	—
371	#123	—	118	1	no	—
372	C₂²⋊Q₈	—	59	1	no	—
373	#121	—	59	1	no	—
374	C₄×Q₈	—	59	1	no	—
375	C₄×Q₈	—	59	1	no	—
376	C₄×Q₈	—	59	1	no	—
377	C₄×D₄	—	59	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	—	118	1	no	—
383	#117	—	59	1	no	—
384	#117	—	118	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	—	118	1	no	—
393	C₄⋊C₈	—	118	1	no	—
394	C₄⋊C₈	—	118	1	no	—
395	C₄⋊C₈	—	118	1	no	—
396	C₄⋊C₈	—	118	1	no	—
397	C₄⋊C₈	C₄×D₅₉	1	1	yes	characteristic
398	C₄⋊C₈	C₄×D₅₉	1	1	yes	characteristic
399	C₄⋊C₈	C₂²×D₅₉	1	1	yes	characteristic
400	C₄⋊C₈	C₂²×D₅₉	1	1	yes	characteristic
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	—	118	1	no	—
414	C₂²⋊C₈	—	118	1	no	—
415	C₂²⋊C₈	—	118	1	no	—
416	C₂²⋊C₈	—	118	1	no	—
417	C₂²⋊C₈	—	118	1	no	—
418	C₂²⋊C₈	C₄×D₅₉	1	1	yes	characteristic
419	C₂²⋊C₈	C₄×D₅₉	1	1	yes	characteristic
420	#97	—	2	1	no	—
421	#97	—	118	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	—	59	1	no	—
428	C₄×C₈	—	59	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	#41	—	118	2	no	—
435	#41	—	118	2	no	—
436	C₂×Q₈	—	59	1	no	—
437	C₂×Q₈	—	59	1	no	—
438	C₂×D₄	—	59	1	no	—
439	C₂×D₄	—	59	1	no	—
440	C₂×D₄	—	118	1	no	—
441	C₂×D₄	—	118	1	no	—
442	C₂²×C₄	—	118	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	D₄×D₅₉	1	1	yes	characteristic
448	C₂²×C₄	#11745689	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	—	236	2	no	—
454	C₂×C₈	—	2	1	no	—
455	C₂×C₈	—	2	1	no	—
456	C₂×C₈	—	2	1	no	—
457	C₂×C₈	—	2	1	no	—
458	C₂×C₈	—	59	1	no	—
459	C₂×C₈	—	59	1	no	—
460	C₂×C₈	—	59	1	no	—
461	C₂×C₈	—	59	1	no	—
462	C₂×C₈	—	118	2	no	—
463	C₂×C₈	—	118	2	no	—
464	C₂×C₈	—	118	1	no	—
465	C₂×C₈	—	118	1	no	—
466	C₂×C₈	—	236	2	no	—
467	C₂×C₈	—	236	2	no	—
468	C₂×C₈	—	236	2	no	—
469	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
470	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
471	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
472	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
473	C₄⋊C₄	—	59	1	no	—
474	C₄⋊C₄	—	59	1	no	—
475	C₄⋊C₄	—	59	1	no	—
476	C₄⋊C₄	—	59	1	no	—
477	C₄⋊C₄	—	118	1	no	—
478	C₄⋊C₄	—	118	1	no	—
479	C₄⋊C₄	—	118	1	no	—
480	C₄⋊C₄	—	118	1	no	—
481	C₄⋊C₄	—	118	1	no	—
482	C₄⋊C₄	—	118	1	no	—
483	C₂²⋊C₄	—	118	1	no	—
484	C₂²⋊C₄	—	118	1	no	—
485	C₂²⋊C₄	—	118	1	no	—
486	C₂²⋊C₄	—	118	1	no	—
487	C₂²⋊C₄	—	118	1	no	—
488	C₂²⋊C₄	—	118	1	no	—
489	C₂²⋊C₄	—	118	1	no	—
490	C₂²⋊C₄	—	118	1	no	—
491	C₄²	—	118	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	D₄×D₅₉	1	1	yes	characteristic
497	C₄²	#11745689	1	1	yes	characteristic
498	C₄²	C₂³×D₅₉	1	1	yes	characteristic
499	C₂³	—	118	1	no	—
500	C₂³	—	118	1	no	—
501	C₂³	#14273689	1	1	yes	characteristic
502	Q₈	—	59	2	no	—
503	Q₈	—	118	1	no	—
504	Q₈	—	118	1	no	—
505	Q₈	—	118	1	no	—
506	D₄	—	59	2	no	—
507	D₄	—	118	4	no	—
508	D₄	—	118	1	no	—
509	D₄	—	118	1	no	—
510	D₄	—	118	1	no	—
511	D₄	—	236	2	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	—	4	1	no	—
517	C₂×C₄	—	118	4	no	—
518	C₂×C₄	—	118	1	no	—
519	C₂×C₄	—	118	1	no	—
520	C₂×C₄	—	118	1	no	—
521	C₂×C₄	—	118	1	no	—
522	C₂×C₄	—	118	1	no	—
523	C₂×C₄	—	118	1	no	—
524	C₂×C₄	—	236	2	no	—
525	C₂×C₄	—	236	1	no	—
526	C₂×C₄	—	236	1	no	—
527	C₂×C₄	—	236	1	no	—
528	C₂×C₄	—	236	1	no	—
529	C₂×C₄	#14273689	1	1	yes	characteristic
530	C₂×C₄	#14273689	1	1	yes	characteristic
531	C₂×C₄	#14273689	1	1	yes	characteristic
532	C₂×C₄	C₂²×C₄×D₅₉	1	1	yes	characteristic
533	C₂×C₄	C₂×D₄×D₅₉	1	1	yes	characteristic
534	C₂×C₄	C₂×#11745689	1	1	yes	characteristic
535	C₈	—	2	1	no	—
536	C₈	—	2	1	no	—
537	C₈	—	2	1	no	—
538	C₈	—	2	1	no	—
539	C₈	—	4	1	no	—
540	C₈	—	4	1	no	—
541	C₈	—	4	1	no	—
542	C₈	—	4	1	no	—
543	C₈	—	59	2	no	—
544	C₈	—	59	2	no	—
545	C₈	—	118	1	no	—
546	C₈	—	118	1	no	—
547	C₈	—	236	1	no	—
548	C₈	—	236	1	no	—
549	C₂²	—	2	1	no	—
550	C₂²	—	2	1	no	—
551	C₂²	—	2	1	no	—
552	C₂²	—	118	2	no	—
553	C₂²	—	236	1	no	—
554	C₂²	—	236	1	no	—
555	C₂²	—	236	1	no	—
556	C₂²	—	236	1	no	—
557	C₂²	—	236	1	no	—
558	C₂²	C₂×#14273689	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	—	118	2	no	—
564	C₄	—	236	1	no	—
565	C₄	—	236	1	no	—
566	C₄	—	236	1	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	#135×D₅₉	1	1	yes	characteristic
572	C₄	#135×D₅₉	1	1	yes	characteristic
573	C₂	—	4	1	no	—
574	C₂	—	472	1	no	—
575	C₂	—	236	2	no	—
576	C₂	#21432789	1	1	yes	characteristic
577	C₂	#21432867	1	1	yes	characteristic
578	C₂	#21432998	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×#1572	C₂
socle	C₂²×C₅₉	C₂×C₄×D₄
prime radical	#16837549	C₄
cosocle	C₄²×C₅₉	C₂⁴
hypercenter	#1572	D₅₉
hypocenter	C₅₉	#17904
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1572

Complements

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

N	H ≅ G/N	type
2. #21433065	C₂	semidirect
3. #21433052	C₂	semidirect
4. #21422945	C₂	semidirect
5. #21422938	C₂	semidirect
6. #21422931	C₂	semidirect
7. #21422924	C₂	semidirect
8. #21422902	C₂	semidirect
9. #21422895	C₂	semidirect
10. #21422895	C₂	semidirect
11. #21422890	C₂	semidirect
12. #21422528	C₂	semidirect
13. #21422502	C₂	semidirect
14. #21422380	C₂	semidirect
15. C₅₉×#1572	C₂	semidirect
295. #1572	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
#21434116	2
#21433065	2
#21433052	2
#21422945	2
#21422938	2
#21422931	2
#21422924	2
#21422902	2
#21422895	2
#21422890	2
#21422528	2
#21422502	2
#21422380	2
C₅₉×#1572	2
#17904	59