Subgroups — #28572521

Order 15104.

656 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21434655	C₂	1	1	yes	maximal, characteristic
2	#21433901	C₂	1	1	yes	maximal, characteristic, complemented
3	#21433568	C₂	1	1	yes	maximal, characteristic
4	#21423526	C₂	1	2	yes	maximal, complemented
5	#21423512	C₂	1	2	yes	maximal, complemented
6	#21423478	C₂	1	2	yes	maximal, complemented
7	#21423444	C₂	1	2	yes	maximal, complemented
8	#21422852	C₂	1	1	yes	maximal, characteristic, complemented
9	#21422784	C₂	1	1	yes	maximal, characteristic, complemented
10	#21422771	C₂	1	1	yes	maximal, characteristic
11	C₂×C₈×Q₈×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14273758	—	2	1	no	—
13	#16837959	C₂²	1	1	yes	characteristic
14	#16837952	C₂²	1	1	yes	characteristic
15	#16837800	C₂²	1	1	yes	characteristic
16	#16837775	C₂²	1	1	yes	characteristic
17	#16837753	C₂²	1	1	yes	characteristic
18	#16837749	C₂²	1	1	yes	characteristic
19	#16837709	—	2	2	no	—
20	#16837697	C₂²	1	2	yes	—
21	#16837687	C₂²	1	2	yes	—
22	#16837631	—	2	1	no	—
23	#16837631	—	2	1	no	—
24	#16837624	—	2	2	no	—
25	#16837612	C₂²	1	2	yes	—
26	#16837602	C₂²	1	2	yes	—
27	C₄×#11745660	—	2	1	no	—
28	C₄×#11745660	—	2	1	no	—
29	#16837442	—	2	1	no	—
30	#16837426	C₂²	1	1	yes	characteristic
31	#16837426	C₂²	1	1	yes	characteristic
32	#16837411	—	2	1	no	—
33	#16837401	—	2	1	no	—
34	#16837153	C₂²	1	2	yes	—
35	#16837153	C₂²	1	2	yes	—
36	#16837150	C₂²	1	2	yes	—
37	#16837149	C₂²	1	2	yes	—
38	#16837147	C₂²	1	2	yes	—
39	#16837145	C₂²	1	2	yes	—
40	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
41	C₈×Q₈×C₅₉	—	2	1	no	—
42	C₈×Q₈×C₅₉	—	2	1	no	—
43	C₈×Q₈×C₅₉	C₂²	1	2	yes	—
44	C₈×Q₈×C₅₉	C₂²	1	2	yes	—
45	C₂×C₄⋊C₈×C₅₉	—	2	1	no	—
46	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
47	C₂×C₄×C₈×C₅₉	—	2	1	no	—
48	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
49	C₂×#11745685	—	2	1	no	—
50	#14273758	—	4	4	no	—
51	C₂×#11745672	—	2	2	no	—
52	C₂×#11745660	—	2	1	no	—
53	C₂×#11745660	—	2	1	no	—
54	C₂×#11745671	—	2	2	no	—
55	C₂×#11745664	—	2	1	no	—
56	C₂×#11745664	—	2	1	no	—
57	#14273727	C₂³	1	1	yes	characteristic
58	#14273727	C₂³	1	1	yes	characteristic
59	#14273727	C₂³	1	1	yes	characteristic
60	#14273724	C₂³	1	1	yes	characteristic
61	#14273719	—	2	1	no	—
62	#14273715	—	2	1	no	—
63	#14273706	—	2	1	no	—
64	#14273706	—	2	1	no	—
65	#14273701	—	2	1	no	—
66	#14273701	—	2	1	no	—
67	C₄×Dic₁₁₈	—	2	1	no	—
68	C₄×Dic₁₁₈	—	2	1	no	—
69	C₄×D₂₃₆	—	2	1	no	—
70	C₄×D₂₃₆	—	2	1	no	—
71	#14273686	—	2	1	no	—
72	#14273660	—	2	2	no	—
73	#14273659	—	2	1	no	—
74	#14273659	—	2	1	no	—
75	#14273658	—	2	2	no	—
76	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
77	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
78	C₄⋊(C₅₉⋊C₈)	C₂³	1	2	yes	—
79	C₄⋊(C₅₉⋊C₈)	C₂³	1	2	yes	—
80	#14273652	—	2	1	no	—
81	#14273652	—	2	1	no	—
82	#14273651	—	2	2	no	—
83	#14273651	—	2	2	no	—
84	#14273650	—	2	2	no	—
85	#14273649	—	2	1	no	—
86	#14273649	—	2	1	no	—
87	#14273647	—	2	2	no	—
88	C₂²×Q₈×C₅₉	D₄	1	1	yes	characteristic
89	C₂²×C₈×C₅₉	—	2	1	no	—
90	C₂²×C₈×C₅₉	D₄	1	1	yes	characteristic
91	C₂²×C₈×C₅₉	D₄	1	1	yes	characteristic
92	C₄×Q₈×C₅₉	—	2	1	no	—
93	C₄×Q₈×C₅₉	—	2	1	no	—
94	C₄×Q₈×C₅₉	D₄	1	2	yes	—
95	C₄×Q₈×C₅₉	C₂³	1	2	yes	—
96	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
97	C₂×C₄⋊C₄×C₅₉	D₄	1	1	yes	characteristic
98	C₂×C₄²×C₅₉	—	2	1	no	—
99	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
100	C₄⋊C₈×C₅₉	—	2	2	no	—
101	C₄⋊C₈×C₅₉	—	2	2	no	—
102	C₄⋊C₈×C₅₉	—	2	1	no	—
103	C₄⋊C₈×C₅₉	C₂³	1	2	yes	—
104	C₄×C₈×C₅₉	—	2	2	no	—
105	C₄×C₈×C₅₉	—	2	2	no	—
106	C₄×C₈×C₅₉	D₄	1	1	yes	characteristic
107	C₄×C₈×C₅₉	D₄	1	1	yes	characteristic
108	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
109	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
110	C₂×Q₈×C₅₉	—	2	1	no	—
111	C₂×Q₈×C₅₉	—	2	2	no	—
112	C₂×Q₈×C₅₉	SD₁₆	1	4	yes	complemented
113	C₂×Q₈×C₅₉	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₅₉	—	2	1	no	—
115	C₂²×C₄×C₅₉	—	2	1	no	—
116	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
119	C₂×C₂²⋊D₅₉	—	4	1	no	—
120	#11745685	—	4	2	no	—
121	#11745685	—	4	2	no	—
122	C₂×D₂₃₆	—	2	1	no	—
123	C₂×D₂₃₆	—	2	1	no	—
124	C₂×D₂₃₆	—	2	1	no	—
125	C₂×C₄×D₅₉	—	4	1	no	—
126	C₂×Dic₁₁₈	—	2	1	no	—
127	C₂×Dic₁₁₈	—	2	1	no	—
128	C₂×Dic₁₁₈	—	2	1	no	—
129	C₂×C₈×C₅₉	—	2	2	no	—
130	C₂×C₈×C₅₉	—	2	2	no	—
131	C₂×C₈×C₅₉	—	4	1	no	—
132	C₂×C₈×C₅₉	—	4	2	no	—
133	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
134	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
135	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
136	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
137	C₄⋊C₄×C₅₉	—	2	2	no	—
138	C₄⋊C₄×C₅₉	—	2	1	no	—
139	C₄⋊C₄×C₅₉	—	2	2	no	—
140	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
141	C₄²×C₅₉	—	2	2	no	—
142	C₄²×C₅₉	—	2	2	no	—
143	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
144	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
145	C₄²×C₅₉	#41	1	1	yes	characteristic
146	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
147	C₂²⋊Dic₅₉	—	4	1	no	—
148	#11745672	—	4	4	no	—
149	#11745671	—	4	4	no	—
150	(C₂×D₅₉)⋊C₄	—	4	1	no	—
151	(C₂×D₅₉)⋊C₄	—	4	1	no	—
152	C₄⋊Dic₅₉	—	2	1	no	—
153	C₄⋊Dic₅₉	—	2	1	no	—
154	C₄⋊Dic₅₉	—	2	1	no	—
155	C₄⋊Dic₅₉	—	2	1	no	—
156	C₄⋊Dic₅₉	—	2	1	no	—
157	C₄⋊Dic₅₉	—	2	1	no	—
158	Dic₅₉⋊C₄	—	4	1	no	—
159	Dic₅₉⋊C₄	—	4	1	no	—
160	C₄×Dic₅₉	—	4	1	no	—
161	#11745664	—	4	2	no	—
162	#11745664	—	4	2	no	—
163	C₂×C₅₉⋊C₈	—	2	2	no	—
164	C₂×C₅₉⋊C₈	—	2	2	no	—
165	#11745660	—	4	2	no	—
166	#11745660	—	4	2	no	—
167	C₂³×C₅₉	#121	1	1	yes	characteristic
168	C₂²×D₅₉	—	4	1	no	—
169	Q₈×C₅₉	—	2	2	no	—
170	Q₈×C₅₉	—	2	4	no	—
171	Q₈×C₅₉	C₂×SD₁₆	1	4	yes	—
172	C₂×C₄×C₅₉	—	2	2	no	—
173	C₂×C₄×C₅₉	—	2	4	no	—
174	C₂×C₄×C₅₉	—	2	1	no	—
175	C₂×C₄×C₅₉	—	2	1	no	—
176	C₂×C₄×C₅₉	—	2	2	no	—
177	C₂×C₄×C₅₉	—	4	1	no	—
178	C₂×C₄×C₅₉	—	4	2	no	—
179	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
180	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
181	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
182	C₂×C₄×C₅₉	C₂×SD₁₆	1	2	yes	—
183	C₂×C₄×C₅₉	#135	1	2	yes	—
184	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
185	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
186	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
187	C₂²⋊D₅₉	—	8	2	no	—
188	C₂×Dic₅₉	—	4	1	no	—
189	C₂×Dic₅₉	—	4	1	no	—
190	C₂×Dic₅₉	—	4	1	no	—
191	D₂₃₆	—	4	1	no	—
192	D₂₃₆	—	4	1	no	—
193	D₂₃₆	—	4	1	no	—
194	D₂₃₆	—	4	1	no	—
195	D₂₃₆	—	8	1	no	—
196	C₄×D₅₉	—	8	2	no	—
197	Dic₁₁₈	—	4	1	no	—
198	Dic₁₁₈	—	4	1	no	—
199	Dic₁₁₈	—	4	1	no	—
200	Dic₁₁₈	—	4	1	no	—
201	Dic₁₁₈	—	8	1	no	—
202	C₈×C₅₉	—	2	1	no	—
203	C₈×C₅₉	—	2	1	no	—
204	C₈×C₅₉	—	2	1	no	—
205	C₈×C₅₉	—	4	2	no	—
206	C₈×C₅₉	#137	1	2	yes	complemented
207	C₅₉⋊C₈	—	4	2	no	—
208	C₅₉⋊C₈	—	4	2	no	—
209	#19260	—	59	1	no	maximal, Sylow
210	C₂²×C₅₉	—	2	1	no	—
211	C₂²×C₅₉	—	2	1	no	—
212	C₂²×C₅₉	#465	1	2	yes	—
213	C₂²×C₅₉	C₂×#121	1	1	yes	characteristic
214	C₂×D₅₉	—	8	1	no	—
215	C₂×D₅₉	—	8	1	no	—
216	C₂×D₅₉	—	8	1	no	—
217	C₄×C₅₉	—	2	1	no	—
218	C₄×C₅₉	—	2	4	no	—
219	C₄×C₅₉	—	2	1	no	—
220	C₄×C₅₉	—	2	1	no	—
221	C₄×C₅₉	—	4	2	no	—
222	C₄×C₅₉	#465	1	2	yes	—
223	C₄×C₅₉	C₂²×SD₁₆	1	1	yes	characteristic
224	C₄×C₅₉	C₂×#135	1	1	yes	characteristic
225	C₄×C₅₉	C₂×#137	1	1	yes	characteristic
226	C₄×C₅₉	#575	1	1	yes	characteristic
227	Dic₅₉	—	8	1	no	—
228	Dic₅₉	—	8	1	no	—
229	Dic₅₉	—	8	1	no	—
230	#3167	—	59	1	no	—
231	#3078	—	59	1	no	—
232	#3037	—	59	1	no	—
233	C₂×C₈×Q₈	D₅₉	1	1	yes	characteristic, complemented
234	#1680	—	59	2	no	—
235	#1678	—	59	2	no	—
236	#1672	—	59	2	no	—
237	#1666	—	59	2	no	—
238	#1566	—	59	1	no	—
239	#1550	—	59	1	no	—
240	#1547	—	59	1	no	—
241	C₂×C₅₉	—	2	2	no	—
242	C₂×C₅₉	#3037	1	1	yes	characteristic
243	C₂×C₅₉	C₂×#465	1	1	yes	characteristic
244	C₂×C₅₉	#3067	1	1	yes	characteristic
245	D₅₉	—	16	1	no	—
246	C₂×#137	—	118	1	no	—
247	#533	—	59	1	no	—
248	#532	—	59	1	no	—
249	C₂×C₄×Q₈	C₂×D₅₉	1	1	yes	characteristic
250	#498	—	59	1	no	—
251	#492	—	59	1	no	—
252	#487	—	59	1	no	—
253	#486	—	59	1	no	—
254	#479	—	118	2	no	—
255	#477	—	59	2	no	—
256	#475	—	59	2	no	—
257	#465	—	118	1	no	—
258	#465	—	118	1	no	—
259	#464	—	118	2	no	—
260	#462	—	59	2	no	—
261	#460	—	59	2	no	—
262	C₈×Q₈	—	2	1	no	—
263	C₈×Q₈	—	2	1	no	—
264	C₈×Q₈	C₂×D₅₉	1	2	yes	—
265	C₈×Q₈	C₂×D₅₉	1	2	yes	—
266	C₄×SD₁₆	—	118	1	no	—
267	C₄×SD₁₆	—	118	1	no	—
268	#428	—	118	1	no	—
269	#423	—	59	1	no	—
270	#423	—	59	1	no	—
271	C₂×C₄⋊C₈	—	2	1	no	—
272	C₂×C₄⋊C₈	C₂×D₅₉	1	1	yes	characteristic
273	#419	—	118	1	no	—
274	#417	—	118	1	no	—
275	C₂×C₄×C₈	—	2	1	no	—
276	C₂×C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
277	#334	—	59	2	no	—
278	#334	—	59	2	no	—
279	#333	—	59	2	no	—
280	#332	—	59	2	no	—
281	#332	—	59	2	no	—
282	#331	—	59	2	no	—
283	C₅₉	#19260	1	1	yes	characteristic, complemented, Sylow
284	C₂×#41	—	118	1	no	—
285	C₂²×Q₈	D₂₃₆	1	1	yes	characteristic
286	#137	—	236	4	no	—
287	C₂×Q₁₆	—	118	2	no	—
288	C₂×SD₁₆	—	118	2	no	—
289	C₂×SD₁₆	—	118	1	no	—
290	C₂×SD₁₆	—	118	1	no	—
291	C₂×M₁₆	—	118	1	no	—
292	C₂×M₁₆	—	118	1	no	—
293	C₂²×C₈	—	2	1	no	—
294	C₂²×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
295	C₂²×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
296	C₄⋊Q₈	—	59	1	no	—
297	C₄⋊Q₈	—	59	1	no	—
298	C₄⋊Q₈	—	59	1	no	—
299	#127	—	59	1	no	—
300	#125	—	118	1	no	—
301	#124	—	118	1	no	—
302	C₂²⋊Q₈	—	118	1	no	—
303	C₂²⋊Q₈	—	118	1	no	—
304	#121	—	118	1	no	—
305	#121	—	118	1	no	—
306	C₄×Q₈	—	2	1	no	—
307	C₄×Q₈	—	2	1	no	—
308	C₄×Q₈	—	118	1	no	—
309	C₄×Q₈	—	118	1	no	—
310	C₄×Q₈	D₂₃₆	1	2	yes	—
311	C₄×Q₈	C₂²×D₅₉	1	2	yes	—
312	C₄×D₄	—	118	1	no	—
313	C₄×D₄	—	118	1	no	—
314	#117	—	118	1	no	—
315	C₂×C₄⋊C₄	—	2	1	no	—
316	C₂×C₄⋊C₄	D₂₃₆	1	1	yes	characteristic
317	C₂×C₄²	—	2	1	no	—
318	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
319	#107	—	118	2	no	—
320	#106	—	118	1	no	—
321	#106	—	118	1	no	—
322	#106	—	118	2	no	—
323	C₄⋊C₈	—	2	2	no	—
324	C₄⋊C₈	—	2	2	no	—
325	C₄⋊C₈	—	2	1	no	—
326	C₄⋊C₈	—	59	2	no	—
327	C₄⋊C₈	—	59	2	no	—
328	C₄⋊C₈	—	118	1	no	—
329	C₄⋊C₈	—	118	1	no	—
330	C₄⋊C₈	C₂²×D₅₉	1	2	yes	—
331	#103	—	118	2	no	—
332	#103	—	118	2	no	—
333	#103	—	118	1	no	—
334	#103	—	118	1	no	—
335	#103	—	118	2	no	—
336	#102	—	118	1	no	—
337	#102	—	118	1	no	—
338	#102	—	118	2	no	—
339	C₄×C₈	—	2	2	no	—
340	C₄×C₈	—	2	2	no	—
341	C₄×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
342	C₄×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
343	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
344	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
345	#41	—	236	2	no	—
346	#41	—	236	2	no	—
347	C₂×Q₈	—	2	1	no	—
348	C₂×Q₈	—	2	2	no	—
349	C₂×Q₈	—	118	1	no	—
350	C₂×Q₈	—	118	1	no	—
351	C₂×Q₈	—	118	1	no	—
352	C₂×Q₈	#11745660	1	4	yes	complemented
353	C₂×Q₈	C₂×D₂₃₆	1	2	yes	—
354	C₂×D₄	—	118	1	no	—
355	C₂×D₄	—	118	1	no	—
356	C₂×D₄	—	118	1	no	—
357	C₂×D₄	—	236	1	no	—
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	—	2	1	no	—
360	C₂²×C₄	—	236	1	no	—
361	C₂²×C₄	C₂×D₂₃₆	1	1	yes	characteristic
362	C₂²×C₄	#11745685	1	1	yes	characteristic
363	C₂²×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
364	Q₁₆	—	236	4	no	—
365	SD₁₆	—	236	2	no	—
366	SD₁₆	—	236	4	no	—
367	SD₁₆	—	236	2	no	—
368	M₁₆	—	236	2	no	—
369	M₁₆	—	236	2	no	—
370	C₂×C₈	—	2	2	no	—
371	C₂×C₈	—	2	2	no	—
372	C₂×C₈	—	4	1	no	—
373	C₂×C₈	—	4	2	no	—
374	C₂×C₈	—	118	2	no	—
375	C₂×C₈	—	118	2	no	—
376	C₂×C₈	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
377	C₂×C₈	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
378	C₂×C₈	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
379	C₂×C₈	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
380	C₄⋊C₄	—	2	2	no	—
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	2	2	no	—
383	C₄⋊C₄	—	118	1	no	—
384	C₄⋊C₄	—	118	1	no	—
385	C₄⋊C₄	—	118	1	no	—
386	C₄⋊C₄	—	118	1	no	—
387	C₄⋊C₄	—	118	1	no	—
388	C₄⋊C₄	—	118	1	no	—
389	C₄⋊C₄	—	236	1	no	—
390	C₄⋊C₄	—	236	1	no	—
391	C₄⋊C₄	C₂×D₂₃₆	1	2	yes	—
392	C₂²⋊C₄	—	236	1	no	—
393	C₂²⋊C₄	—	236	1	no	—
394	C₂²⋊C₄	—	236	1	no	—
395	C₄²	—	2	2	no	—
396	C₄²	—	2	2	no	—
397	C₄²	—	236	1	no	—
398	C₄²	C₂×D₂₃₆	1	1	yes	characteristic
399	C₄²	#11745685	1	1	yes	characteristic
400	C₄²	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
401	C₄²	C₂³×D₅₉	1	1	yes	characteristic
402	C₂³	—	236	1	no	—
403	C₂³	#14273701	1	1	yes	characteristic
404	Q₈	—	2	2	no	—
405	Q₈	—	2	4	no	—
406	Q₈	—	472	1	no	—
407	Q₈	—	236	1	no	—
408	Q₈	—	236	1	no	—
409	Q₈	—	236	1	no	—
410	Q₈	—	236	1	no	—
411	Q₈	C₂×#11745660	1	4	yes	—
412	D₄	—	472	1	no	—
413	D₄	—	472	2	no	—
414	D₄	—	236	1	no	—
415	D₄	—	236	1	no	—
416	D₄	—	236	1	no	—
417	D₄	—	236	1	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	4	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	4	1	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	472	2	no	—
426	C₂×C₄	—	236	1	no	—
427	C₂×C₄	—	236	1	no	—
428	C₂×C₄	—	236	1	no	—
429	C₂×C₄	#14273701	1	1	yes	characteristic
430	C₂×C₄	#14273701	1	1	yes	characteristic
431	C₂×C₄	#14273701	1	1	yes	characteristic
432	C₂×C₄	C₂×#11745660	1	2	yes	—
433	C₂×C₄	#14273749	1	2	yes	—
434	C₂×C₄	C₂²×C₂²⋊D₅₉	1	1	yes	characteristic
435	C₂×C₄	C₂²×D₂₃₆	1	1	yes	characteristic
436	C₂×C₄	C₂×#11745685	1	1	yes	characteristic
437	C₈	—	2	1	no	—
438	C₈	—	2	1	no	—
439	C₈	—	2	1	no	—
440	C₈	—	4	2	no	—
441	C₈	—	236	2	no	—
442	C₈	—	236	2	no	—
443	C₈	#14273758	1	2	yes	complemented
444	C₂²	—	2	1	no	—
445	C₂²	—	2	1	no	—
446	C₂²	—	472	1	no	—
447	C₂²	—	472	1	no	—
448	C₂²	—	472	1	no	—
449	C₂²	#16837631	1	2	yes	—
450	C₂²	C₂×#14273701	1	1	yes	characteristic
451	C₄	—	2	4	no	—
452	C₄	—	2	1	no	—
453	C₄	—	2	1	no	—
454	C₄	—	2	1	no	—
455	C₄	—	4	2	no	—
456	C₄	—	472	1	no	—
457	C₄	—	472	1	no	—
458	C₄	—	472	1	no	—
459	C₄	#16837631	1	2	yes	—
460	C₄	C₂²×#11745660	1	1	yes	characteristic
461	C₄	C₂×#14273749	1	1	yes	characteristic
462	C₄	C₂×#14273758	1	1	yes	characteristic
463	C₄	#16838200	1	1	yes	characteristic
464	C₂	—	2	2	no	—
465	C₂	—	944	1	no	—
466	C₂	#21433568	1	1	yes	characteristic
467	C₂	C₂×#16837631	1	1	yes	characteristic
468	C₂	#21433816	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#14273701
commutator, cosocle	C₄²×C₅₉	C₂⁴
Frattini	C₄²	C₂³×D₅₉
Fitting	C₂×C₈×Q₈×C₅₉	C₂
socle	C₂²×C₅₉	C₂×#121
prime radical	#16837952	C₂²
hypercenter	C₂×C₈×Q₈	D₅₉
hypocenter	C₅₉	#19260
LCS	G ▷ C₄²×C₅₉ ▷ C₂²×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₈×Q₈

Complements

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

N	H ≅ G/N	type
2. #21433901	C₂	semidirect
4. #21423526	C₂	semidirect
5. #21423512	C₂	semidirect
6. #21423478	C₂	semidirect
7. #21423444	C₂	semidirect
8. #21422852	C₂	semidirect
9. #21422784	C₂	semidirect
11. C₂×C₈×Q₈×C₅₉	C₂	semidirect
112. C₂×Q₈×C₅₉	SD₁₆	semidirect
206. C₈×C₅₉	#137	semidirect
233. C₂×C₈×Q₈	D₅₉	semidirect
283. C₅₉	#19260	semidirect
352. C₂×Q₈	#11745660	semidirect
443. C₈	#14273758	semidirect

Maximal subgroups

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

subgroup	index
#21434655	2
#21433901	2
#21433568	2
#21423526	2
#21423512	2
#21423478	2
#21423444	2
#21422852	2
#21422784	2
#21422771	2
C₂×C₈×Q₈×C₅₉	2
#19260	59