Subgroups — #28596513

Order 15104.

750 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21433878	C₂	1	1	yes	maximal, characteristic
2	C₄×#14273733	C₂	1	1	yes	maximal, characteristic
3	#21425041	C₂	1	1	yes	maximal, characteristic, complemented
4	#21424869	C₂	1	1	yes	maximal, characteristic, complemented
5	#21424692	C₂	1	2	yes	maximal, complemented
6	#21424370	C₂	1	2	yes	maximal
7	#21424113	C₂	1	1	yes	maximal, characteristic
8	#21423976	C₂	1	2	yes	maximal, complemented
9	C₈×C₄⋊Dic₅₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#21423935	C₂	1	2	yes	maximal
11	C₅₉×#2960	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14273733	C₂²	1	1	yes	characteristic
13	C₂×#14273733	C₂²	1	1	yes	characteristic
14	C₄×#11745685	C₂²	1	1	yes	characteristic
15	#16837706	C₄	1	2	yes	complemented
16	#16837699	C₄	1	2	yes	complemented
17	#16837694	C₄	1	1	yes	characteristic, complemented
18	#16837689	C₄	1	1	yes	characteristic, complemented
19	#16837684	C₄	1	1	yes	characteristic, complemented
20	#16837679	C₄	1	1	yes	characteristic, complemented
21	C₂×#14273662	C₂²	1	2	yes	—
22	#16837438	C₂²	1	2	yes	—
23	C₂×C₄⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
24	C₂×#14273653	C₂²	1	2	yes	—
25	#16837396	C₂²	1	2	yes	—
26	#16837357	C₂²	1	1	yes	characteristic
27	#16837357	C₂²	1	1	yes	characteristic
28	#16837356	—	2	1	no	—
29	#16837356	—	2	1	no	—
30	C₄×#11745664	C₂²	1	1	yes	characteristic
31	C₄×#11745659	—	2	1	no	—
32	C₂×C₈×Dic₅₉	C₂²	1	2	yes	—
33	C₄×C₈×D₅₉	—	2	1	no	—
34	C₄×C₄⋊Dic₅₉	C₂²	1	1	yes	characteristic
35	#16837166	C₂²	1	2	yes	—
36	#16837163	C₂²	1	2	yes	—
37	#16837161	C₂²	1	2	yes	—
38	#16837161	C₂²	1	2	yes	—
39	#16837156	C₂²	1	2	yes	—
40	C₅₉×#533	C₂²	1	1	yes	characteristic
41	C₅₉×#446	—	2	1	no	—
42	C₅₉×#446	—	2	1	no	—
43	C₈×Q₈×C₅₉	—	2	1	no	—
44	C₈×Q₈×C₅₉	—	2	1	no	—
45	C₅₉×#424	C₂²	1	2	yes	—
46	C₅₉×#423	C₂²	1	1	yes	characteristic
47	C₅₉×#405	C₂²	1	2	yes	—
48	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
49	C₂×#11745685	C₂³	1	1	yes	characteristic
50	#14273733	—	2	2	no	—
51	#14273733	—	2	2	no	—
52	#14273733	—	2	2	no	—
53	#14273733	Q₈	1	4	yes	complemented
54	C₂×#11745664	C₂³	1	1	yes	characteristic
55	C₂×#11745664	C₂³	1	1	yes	characteristic
56	C₂×#11745659	—	2	1	no	—
57	C₂×#11745659	—	2	1	no	—
58	C₂²×C₅₉⋊C₈	C₂³	1	2	yes	—
59	C₂×C₈×D₅₉	—	2	1	no	—
60	C₂×C₈×D₅₉	—	2	1	no	—
61	C₄×Dic₁₁₈	C₂×C₄	1	1	yes	characteristic
62	C₄×Dic₁₁₈	C₂×C₄	1	1	yes	characteristic
63	C₄×D₂₃₆	C₂×C₄	1	1	yes	characteristic
64	C₄×D₂₃₆	C₂×C₄	1	1	yes	characteristic
65	C₄×C₂²⋊D₅₉	—	2	1	no	—
66	C₄×C₂²⋊D₅₉	—	2	1	no	—
67	#14273686	C₂³	1	1	yes	characteristic
68	#14273684	—	2	1	no	—
69	C₂×C₄⋊Dic₅₉	—	2	1	no	—
70	C₂×C₄×Dic₅₉	C₂³	1	2	yes	—
71	C₄²×D₅₉	—	2	1	no	—
72	#14273662	—	2	4	no	—
73	#14273660	C₂×C₄	1	2	yes	—
74	#14273660	C₂×C₄	1	2	yes	—
75	#14273658	C₂×C₄	1	2	yes	—
76	#14273658	C₂×C₄	1	2	yes	—
77	C₄⋊(C₅₉⋊C₈)	C₂×C₄	1	1	yes	characteristic
78	C₄⋊(C₅₉⋊C₈)	C₂×C₄	1	1	yes	characteristic
79	C₄⋊(C₅₉⋊C₈)	C₂×C₄	1	2	yes	—
80	#14273653	—	2	4	no	—
81	#14273650	C₂×C₄	1	2	yes	—
82	#14273650	C₂×C₄	1	2	yes	—
83	#14273647	C₂×C₄	1	2	yes	—
84	#14273647	C₂×C₄	1	2	yes	—
85	#14273638	—	2	1	no	—
86	#14273637	—	2	1	no	—
87	#14273637	—	2	1	no	—
88	C₄×C₅₉⋊C₈	—	2	1	no	—
89	C₈×Dic₅₉	—	2	1	no	—
90	C₈×Dic₅₉	—	2	1	no	—
91	C₈×Dic₅₉	—	2	4	no	—
92	C₅₉⋊#95	—	2	1	no	—
93	C₂×M₁₆×C₅₉	C₂³	1	2	yes	—
94	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
95	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
96	C₄⋊Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
97	C₄⋊Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
98	#125×C₅₉	C₂×C₄	1	2	yes	—
99	C₂²⋊Q₈×C₅₉	—	2	1	no	—
100	C₂²⋊Q₈×C₅₉	—	2	1	no	—
101	C₄×Q₈×C₅₉	—	2	1	no	—
102	C₄×Q₈×C₅₉	—	2	1	no	—
103	#117×C₅₉	C₂³	1	2	yes	—
104	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
105	C₄⋊C₈×C₅₉	—	2	2	no	—
106	C₄⋊C₈×C₅₉	—	2	2	no	—
107	C₄⋊C₈×C₅₉	—	2	1	no	—
108	C₄⋊C₈×C₅₉	—	2	1	no	—
109	#97×C₅₉	—	2	2	no	—
110	C₄×C₈×C₅₉	—	2	2	no	—
111	C₄×C₈×C₅₉	D₄	1	1	yes	characteristic
112	C₄×C₈×C₅₉	D₄	1	1	yes	characteristic
113	C₄×C₈×C₅₉	D₄	1	1	yes	characteristic
114	C₄×C₈×C₅₉	D₄	1	1	yes	characteristic
115	C₂×Q₈×C₅₉	—	2	1	no	—
116	C₂×Q₈×C₅₉	—	2	1	no	—
117	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
118	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
119	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
120	C₂×C₂²⋊D₅₉	—	2	1	no	—
121	C₂²×Dic₅₉	—	2	2	no	—
122	#11745685	—	2	1	no	—
123	#11745685	—	2	1	no	—
124	#11745685	C₂×Q₈	1	2	yes	—
125	#11745685	#41	1	2	yes	—
126	C₂×D₂₃₆	C₂²×C₄	1	1	yes	characteristic
127	C₂×C₄×D₅₉	—	2	1	no	—
128	C₂×C₄×D₅₉	—	2	1	no	—
129	C₂×C₄×D₅₉	—	2	1	no	—
130	C₂×Dic₁₁₈	C₂²×C₄	1	1	yes	characteristic
131	M₁₆×C₅₉	—	2	2	no	—
132	M₁₆×C₅₉	—	2	2	no	—
133	C₂×C₈×C₅₉	—	2	1	no	—
134	C₂×C₈×C₅₉	—	2	1	no	—
135	C₂×C₈×C₅₉	—	2	2	no	—
136	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
137	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
138	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
139	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
140	C₂×C₈×C₅₉	C₂×Q₈	1	2	yes	—
141	C₂×C₈×C₅₉	#41	1	2	yes	—
142	C₄⋊C₄×C₅₉	—	2	2	no	—
143	C₄⋊C₄×C₅₉	—	2	2	no	—
144	C₄⋊C₄×C₅₉	—	2	1	no	—
145	C₄⋊C₄×C₅₉	—	2	1	no	—
146	C₄⋊C₄×C₅₉	C₂²×C₄	1	2	yes	—
147	C₄⋊C₄×C₅₉	C₂²×C₄	1	2	yes	—
148	C₂²⋊C₄×C₅₉	—	2	2	no	—
149	C₄²×C₅₉	—	2	2	no	—
150	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
151	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
152	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
153	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
154	C₂²⋊Dic₅₉	—	2	1	no	—
155	(C₂×D₅₉)⋊C₄	—	2	1	no	—
156	(C₂×D₅₉)⋊C₄	—	2	1	no	—
157	C₄⋊Dic₅₉	—	2	4	no	—
158	C₄⋊Dic₅₉	C₂²×C₄	1	1	yes	characteristic
159	C₄⋊Dic₅₉	C₂²×C₄	1	1	yes	characteristic
160	Dic₅₉⋊C₄	—	2	1	no	—
161	Dic₅₉⋊C₄	—	2	1	no	—
162	C₄×Dic₅₉	—	2	1	no	—
163	C₄×Dic₅₉	—	2	1	no	—
164	C₄×Dic₅₉	—	2	1	no	—
165	C₄×Dic₅₉	—	2	2	no	—
166	C₄×Dic₅₉	—	2	2	no	—
167	#11745664	—	2	1	no	—
168	#11745664	—	2	1	no	—
169	#11745664	C₂×Q₈	1	2	yes	—
170	#11745664	#41	1	2	yes	—
171	C₂×C₅₉⋊C₈	—	2	1	no	—
172	C₂×C₅₉⋊C₈	—	2	1	no	—
173	C₂×C₅₉⋊C₈	—	2	2	no	—
174	C₂×C₅₉⋊C₈	—	2	2	no	—
175	C₂×C₅₉⋊C₈	C₂²×C₄	1	2	yes	—
176	C₂×C₅₉⋊C₈	C₂²×C₄	1	2	yes	—
177	#11745659	—	2	4	no	—
178	#11745659	—	2	4	no	—
179	C₈×D₅₉	—	2	4	no	—
180	C₈×D₅₉	—	2	4	no	—
181	C₂³×C₅₉	C₂×#41	1	1	yes	characteristic
182	C₂²×D₅₉	—	2	1	no	—
183	Q₈×C₅₉	—	4	2	no	—
184	Q₈×C₅₉	—	4	2	no	—
185	C₂×C₄×C₅₉	—	2	2	no	—
186	C₂×C₄×C₅₉	—	2	2	no	—
187	C₂×C₄×C₅₉	—	2	2	no	—
188	C₂×C₄×C₅₉	—	4	1	no	—
189	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
190	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
191	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
192	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
193	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
194	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₅₉	C₂²×Q₈	1	1	yes	characteristic
196	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
197	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
198	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
199	C₂²⋊D₅₉	—	2	2	no	—
200	C₂²⋊D₅₉	—	2	2	no	—
201	C₂×Dic₅₉	—	2	1	no	—
202	C₂×Dic₅₉	—	2	4	no	—
203	C₂×Dic₅₉	—	2	1	no	—
204	C₂×Dic₅₉	—	2	1	no	—
205	C₂×Dic₅₉	—	4	2	no	—
206	C₂×Dic₅₉	—	4	2	no	—
207	D₂₃₆	—	2	1	no	—
208	D₂₃₆	C₄×Q₈	1	2	yes	—
209	C₄×D₅₉	—	2	2	no	—
210	C₄×D₅₉	—	2	2	no	—
211	C₄×D₅₉	—	4	2	no	—
212	C₄×D₅₉	—	4	2	no	—
213	Dic₁₁₈	—	2	1	no	—
214	Dic₁₁₈	C₄×Q₈	1	2	yes	—
215	C₈×C₅₉	—	2	1	no	—
216	C₈×C₅₉	—	2	1	no	—
217	C₈×C₅₉	—	4	2	no	—
218	C₈×C₅₉	C₂²⋊Q₈	1	2	yes	—
219	C₈×C₅₉	C₂²⋊Q₈	1	2	yes	—
220	C₅₉⋊C₈	—	2	2	no	—
221	C₅₉⋊C₈	—	2	2	no	—
222	C₅₉⋊C₈	—	2	2	no	—
223	C₅₉⋊C₈	—	2	2	no	—
224	#21627	—	59	1	no	maximal, Sylow
225	C₂²×C₅₉	—	2	1	no	—
226	C₂²×C₅₉	—	2	1	no	—
227	C₂²×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
228	C₂²×C₅₉	#529	1	1	yes	characteristic
229	C₂²×C₅₉	#533	1	1	yes	characteristic
230	C₂×D₅₉	—	2	2	no	—
231	C₂×D₅₉	—	4	1	no	—
232	C₂×D₅₉	—	4	1	no	—
233	C₄×C₅₉	—	2	1	no	—
234	C₄×C₅₉	—	2	1	no	—
235	C₄×C₅₉	—	2	1	no	—
236	C₄×C₅₉	—	4	2	no	—
237	C₄×C₅₉	—	4	2	no	—
238	C₄×C₅₉	#443	1	2	yes	—
239	C₄×C₅₉	C₂×C₄×Q₈	1	1	yes	characteristic
240	C₄×C₅₉	C₄×#41	1	1	yes	characteristic
241	C₄×C₅₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
242	C₄×C₅₉	#525	1	1	yes	characteristic
243	Dic₅₉	—	2	2	no	—
244	Dic₅₉	—	4	4	no	—
245	Dic₅₉	—	4	1	no	—
246	Dic₅₉	—	4	1	no	—
247	#3076	—	59	1	no	—
248	#2960	D₅₉	1	1	yes	characteristic, complemented
249	C₄×#131	—	59	1	no	—
250	#1986	—	59	1	no	—
251	#1950	—	59	1	no	—
252	#1922	—	59	2	no	—
253	#1866	—	59	2	no	—
254	#1806	—	59	1	no	—
255	#1772	—	59	2	no	—
256	C₈×C₄⋊C₄	—	59	1	no	—
257	#1764	—	59	2	no	—
258	C₂×C₅₉	—	2	1	no	—
259	C₂×C₅₉	—	2	1	no	—
260	C₂×C₅₉	C₄×C₂²⋊Q₈	1	1	yes	characteristic
261	C₂×C₅₉	C₂×#443	1	1	yes	characteristic
262	C₂×C₅₉	#2955	1	1	yes	characteristic
263	D₅₉	—	4	2	no	—
264	C₂×#131	—	59	1	no	—
265	C₂×#131	—	59	1	no	—
266	#533	C₂×D₅₉	1	1	yes	characteristic
267	C₄×#41	—	59	1	no	—
268	#479	—	59	2	no	—
269	#478	—	59	2	no	—
270	#477	—	59	1	no	—
271	#476	—	59	1	no	—
272	#475	—	59	1	no	—
273	#474	—	59	1	no	—
274	#446	—	2	1	no	—
275	#446	—	2	1	no	—
276	C₈×Q₈	—	2	1	no	—
277	C₈×Q₈	—	2	1	no	—
278	C₂×#108	—	59	2	no	—
279	#427	—	59	2	no	—
280	#424	C₂×D₅₉	1	2	yes	—
281	#423	C₂×D₅₉	1	1	yes	characteristic
282	C₂×C₄⋊C₈	—	59	1	no	—
283	C₂×#104	—	59	2	no	—
284	#416	—	59	2	no	—
285	#405	—	59	1	no	—
286	#405	—	59	1	no	—
287	#405	—	118	1	no	—
288	#405	—	118	1	no	—
289	#405	C₂×D₅₉	1	2	yes	—
290	C₄×M₁₆	—	59	1	no	—
291	C₄×M₁₆	—	118	1	no	—
292	C₂×C₄×C₈	—	59	2	no	—
293	C₂×C₄×C₈	—	118	1	no	—
294	C₂×C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
295	C₄×C₄⋊C₄	—	59	1	no	—
296	#341	—	59	2	no	—
297	#339	—	59	2	no	—
298	#339	—	59	2	no	—
299	#339	—	59	2	no	—
300	#336	—	59	2	no	—
301	C₅₉	#21627	1	1	yes	characteristic, complemented, Sylow
302	C₂×#41	—	59	1	no	—
303	#131	—	59	4	no	—
304	#131	—	118	2	no	—
305	#131	—	118	2	no	—
306	#131	—	118	2	no	—
307	C₂×M₁₆	—	59	1	no	—
308	C₂×M₁₆	—	59	1	no	—
309	C₂×M₁₆	—	118	1	no	—
310	C₂×M₁₆	—	118	1	no	—
311	C₂×M₁₆	C₂²×D₅₉	1	2	yes	—
312	C₂²×C₈	—	59	2	no	—
313	C₂²×C₈	—	118	1	no	—
314	C₂²×C₈	—	118	1	no	—
315	C₂²×C₈	C₂²×D₅₉	1	1	yes	characteristic
316	C₂²×C₈	C₂²×D₅₉	1	1	yes	characteristic
317	C₄⋊Q₈	C₄×D₅₉	1	1	yes	characteristic
318	C₄⋊Q₈	C₄×D₅₉	1	1	yes	characteristic
319	#125	C₄×D₅₉	1	2	yes	—
320	C₂²⋊Q₈	—	2	1	no	—
321	C₂²⋊Q₈	—	2	1	no	—
322	C₄×Q₈	—	2	1	no	—
323	C₄×Q₈	—	2	1	no	—
324	C₄×Q₈	—	59	1	no	—
325	C₄×Q₈	—	59	1	no	—
326	C₄×D₄	—	59	1	no	—
327	C₄×D₄	—	59	1	no	—
328	C₄×D₄	—	118	1	no	—
329	C₄×D₄	—	118	1	no	—
330	#117	—	59	1	no	—
331	#117	—	118	1	no	—
332	#117	C₂²×D₅₉	1	2	yes	—
333	C₂×C₄⋊C₄	—	118	1	no	—
334	C₂×C₄²	—	59	2	no	—
335	C₂×C₄²	—	118	1	no	—
336	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
337	#108	—	118	4	no	—
338	#107	—	59	2	no	—
339	#107	—	59	2	no	—
340	#106	—	59	2	no	—
341	#106	—	59	2	no	—
342	C₄⋊C₈	—	2	2	no	—
343	C₄⋊C₈	—	2	2	no	—
344	C₄⋊C₈	—	2	1	no	—
345	C₄⋊C₈	—	2	1	no	—
346	C₄⋊C₈	—	59	1	no	—
347	C₄⋊C₈	—	59	1	no	—
348	C₄⋊C₈	—	59	2	no	—
349	#104	—	118	4	no	—
350	#103	—	59	2	no	—
351	#103	—	59	2	no	—
352	#102	—	59	2	no	—
353	#102	—	59	2	no	—
354	#97	—	2	2	no	—
355	#97	—	118	1	no	—
356	#97	—	118	1	no	—
357	#97	—	118	1	no	—
358	C₄×C₈	—	2	2	no	—
359	C₄×C₈	—	118	4	no	—
360	C₄×C₈	—	118	1	no	—
361	C₄×C₈	—	118	1	no	—
362	C₄×C₈	—	118	1	no	—
363	C₄×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
364	C₄×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
365	C₄×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
366	C₄×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
367	#95	—	118	1	no	—
368	#41	—	59	2	no	—
369	#41	—	59	2	no	—
370	#41	—	118	1	no	—
371	#41	—	118	1	no	—
372	C₂×Q₈	—	2	1	no	—
373	C₂×Q₈	—	2	1	no	—
374	C₂×Q₈	—	59	1	no	—
375	C₂×D₄	—	59	1	no	—
376	C₂×D₄	—	118	1	no	—
377	C₂²×C₄	—	118	1	no	—
378	C₂²×C₄	—	118	2	no	—
379	C₂²×C₄	—	118	1	no	—
380	C₂²×C₄	—	118	1	no	—
381	C₂²×C₄	#11745685	1	1	yes	characteristic
382	C₂²×C₄	#11745685	1	1	yes	characteristic
383	C₂²×C₄	C₂³×D₅₉	1	1	yes	characteristic
384	M₁₆	—	2	2	no	—
385	M₁₆	—	2	2	no	—
386	M₁₆	—	59	2	no	—
387	M₁₆	—	59	2	no	—
388	M₁₆	—	118	4	no	—
389	M₁₆	—	118	1	no	—
390	M₁₆	—	118	1	no	—
391	M₁₆	—	118	4	no	—
392	C₂×C₈	—	2	1	no	—
393	C₂×C₈	—	2	1	no	—
394	C₂×C₈	—	2	2	no	—
395	C₂×C₈	—	59	2	no	—
396	C₂×C₈	—	59	2	no	—
397	C₂×C₈	—	118	4	no	—
398	C₂×C₈	—	118	1	no	—
399	C₂×C₈	—	118	1	no	—
400	C₂×C₈	—	118	2	no	—
401	C₂×C₈	—	118	2	no	—
402	C₂×C₈	—	118	4	no	—
403	C₂×C₈	Q₈×D₅₉	1	2	yes	—
404	C₂×C₈	#11745689	1	2	yes	—
405	C₂×C₈	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
406	C₂×C₈	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
407	C₂×C₈	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
408	C₂×C₈	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
409	C₄⋊C₄	—	2	2	no	—
410	C₄⋊C₄	—	2	2	no	—
411	C₄⋊C₄	—	2	1	no	—
412	C₄⋊C₄	—	2	1	no	—
413	C₄⋊C₄	—	59	1	no	—
414	C₄⋊C₄	—	59	1	no	—
415	C₄⋊C₄	—	118	4	no	—
416	C₄⋊C₄	—	118	1	no	—
417	C₄⋊C₄	—	118	1	no	—
418	C₄⋊C₄	C₂×C₄×D₅₉	1	2	yes	—
419	C₄⋊C₄	C₂×C₄×D₅₉	1	2	yes	—
420	C₂²⋊C₄	—	2	2	no	—
421	C₂²⋊C₄	—	118	1	no	—
422	C₂²⋊C₄	—	118	1	no	—
423	C₂²⋊C₄	—	118	1	no	—
424	C₄²	—	2	2	no	—
425	C₄²	—	118	1	no	—
426	C₄²	—	118	1	no	—
427	C₄²	—	118	1	no	—
428	C₄²	—	118	2	no	—
429	C₄²	—	118	2	no	—
430	C₄²	C₂×C₄×D₅₉	1	1	yes	characteristic
431	C₄²	C₂×C₄×D₅₉	1	1	yes	characteristic
432	C₄²	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
433	C₄²	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
434	C₂³	—	118	1	no	—
435	C₂³	C₂×#11745685	1	1	yes	characteristic
436	Q₈	—	4	2	no	—
437	Q₈	—	4	2	no	—
438	Q₈	—	59	2	no	—
439	Q₈	—	118	1	no	—
440	D₄	—	59	2	no	—
441	D₄	—	118	2	no	—
442	D₄	—	118	2	no	—
443	D₄	—	118	1	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	4	1	no	—
448	C₂×C₄	—	118	1	no	—
449	C₂×C₄	—	118	2	no	—
450	C₂×C₄	—	118	2	no	—
451	C₂×C₄	—	118	4	no	—
452	C₂×C₄	—	118	1	no	—
453	C₂×C₄	—	118	1	no	—
454	C₂×C₄	—	236	2	no	—
455	C₂×C₄	—	236	2	no	—
456	C₂×C₄	—	236	2	no	—
457	C₂×C₄	—	236	2	no	—
458	C₂×C₄	C₄×C₂²⋊D₅₉	1	1	yes	characteristic
459	C₂×C₄	C₄×C₂²⋊D₅₉	1	1	yes	characteristic
460	C₂×C₄	C₄×C₂²⋊D₅₉	1	1	yes	characteristic
461	C₂×C₄	C₄×C₂²⋊D₅₉	1	1	yes	characteristic
462	C₂×C₄	C₂²×C₄×D₅₉	1	1	yes	characteristic
463	C₂×C₄	C₂²×C₂²⋊D₅₉	1	1	yes	characteristic
464	C₂×C₄	C₂×Q₈×D₅₉	1	1	yes	characteristic
465	C₂×C₄	#41×D₅₉	1	1	yes	characteristic
466	C₂×C₄	#41×D₅₉	1	1	yes	characteristic
467	C₂×C₄	C₂×#11745689	1	1	yes	characteristic
468	C₈	—	2	1	no	—
469	C₈	—	2	1	no	—
470	C₈	—	4	2	no	—
471	C₈	—	118	2	no	—
472	C₈	—	118	2	no	—
473	C₈	—	118	2	no	—
474	C₈	—	118	2	no	—
475	C₈	#14273703	1	2	yes	—
476	C₈	#14273703	1	2	yes	—
477	C₂²	—	2	1	no	—
478	C₂²	—	2	1	no	—
479	C₂²	—	118	2	no	—
480	C₂²	—	236	1	no	—
481	C₂²	—	236	1	no	—
482	C₂²	C₂×C₄×C₂²⋊D₅₉	1	1	yes	characteristic
483	C₂²	#16837939	1	1	yes	characteristic
484	C₂²	#16837956	1	1	yes	characteristic
485	C₄	—	2	1	no	—
486	C₄	—	2	1	no	—
487	C₄	—	2	1	no	—
488	C₄	—	4	2	no	—
489	C₄	—	4	2	no	—
490	C₄	—	118	2	no	—
491	C₄	—	236	4	no	—
492	C₄	—	236	1	no	—
493	C₄	—	236	1	no	—
494	C₄	#16837517	1	2	yes	—
495	C₄	C₄×Q₈×D₅₉	1	1	yes	characteristic
496	C₄	C₄×#11745689	1	1	yes	characteristic
497	C₄	C₂×#14273703	1	1	yes	characteristic
498	C₄	#16837909	1	1	yes	characteristic
499	C₂	—	2	1	no	—
500	C₂	—	2	1	no	—
501	C₂	—	236	2	no	—
502	C₂	C₄×#14273703	1	1	yes	characteristic
503	C₂	C₂×#16837517	1	1	yes	characteristic
504	C₂	#21432997	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂×C₂²⋊D₅₉
commutator	C₂×C₄×C₅₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₅₉
Fitting	C₅₉×#2960	C₂
socle	C₂²×C₅₉	C₂×C₄×D₄
prime radical	C₂×#11745685	C₂³
cosocle	C₂²×C₄×C₅₉	C₂⁴
hypercenter	#2960	D₅₉
hypocenter	C₅₉	#21627
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈ ◁ #2960

Complements

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

N	H ≅ G/N	type
3. #21425041	C₂	semidirect
4. #21424869	C₂	semidirect
5. #21424692	C₂	semidirect
8. #21423976	C₂	semidirect
9. C₈×C₄⋊Dic₅₉	C₂	semidirect
11. C₅₉×#2960	C₂	semidirect
15. #16837706	C₄	semidirect
16. #16837699	C₄	semidirect
17. #16837694	C₄	semidirect
18. #16837689	C₄	semidirect
19. #16837684	C₄	semidirect
20. #16837679	C₄	semidirect
53. #14273733	Q₈	semidirect
248. #2960	D₅₉	semidirect
301. C₅₉	#21627	semidirect

Maximal subgroups

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

subgroup	index
#21433878	2
C₄×#14273733	2
#21425041	2
#21424869	2
#21424692	2
#21424370	2
#21424113	2
#21423976	2
C₈×C₄⋊Dic₅₉	2
#21423935	2
C₅₉×#2960	2
#21627	59