Subgroups — #21438666

Order 7552.

1032 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16838156	C₂	1	2	yes	maximal, complemented
2	#16838146	C₂	1	2	yes	maximal, complemented
3	#16838125	C₂	1	2	yes	maximal, complemented
4	#16838075	C₂	1	4	yes	maximal, complemented
5	D₄×Dic₁₁₈	C₂	1	2	yes	maximal, complemented
6	#16838061	C₂	1	2	yes	maximal, complemented
7	#16838048	C₂	1	2	yes	maximal, complemented
8	#16838027	C₂	1	2	yes	maximal, complemented
9	#16838023	C₂	1	2	yes	maximal, complemented
10	#16838018	C₂	1	4	yes	maximal, complemented
11	#16837989	C₂	1	2	yes	maximal, complemented
12	#16837978	C₂	1	2	yes	maximal, complemented
13	#16837959	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#14273715	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₉×#529	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#11745685	C₂²	1	2	yes	—
17	C₂²×Dic₁₁₈	C₂²	1	1	yes	characteristic
18	C₂²×Dic₁₁₈	C₂²	1	2	yes	complemented
19	C₂²×D₂₃₆	C₂²	1	1	yes	characteristic
20	#14273727	C₂²	1	1	yes	characteristic, complemented
21	#14273727	C₂²	1	1	yes	characteristic, complemented
22	#14273727	C₂²	1	2	yes	complemented
23	#14273726	C₂²	1	4	yes	complemented
24	#14273722	C₂²	1	4	yes	complemented
25	#14273722	C₂²	1	4	yes	complemented
26	#14273722	C₂²	1	4	yes	complemented
27	#14273719	C₂²	1	2	yes	complemented
28	#14273715	C₂²	1	2	yes	—
29	#14273715	C₂²	1	2	yes	—
30	#14273715	C₂²	1	2	yes	—
31	#14273715	C₂²	1	2	yes	—
32	#14273715	C₂²	1	2	yes	—
33	#14273713	C₂²	1	4	yes	complemented
34	#14273713	C₂²	1	4	yes	complemented
35	#14273712	C₂²	1	4	yes	—
36	#14273711	C₂²	1	4	yes	complemented
37	#14273711	C₂²	1	4	yes	complemented
38	#14273709	C₂²	1	4	yes	complemented
39	#14273707	C₂²	1	4	yes	complemented
40	#14273707	C₂²	1	4	yes	complemented
41	#14273706	C₂²	1	2	yes	—
42	#14273706	C₂²	1	2	yes	—
43	#14273706	C₂²	1	2	yes	complemented
44	#14273705	C₂²	1	4	yes	complemented
45	#14273705	C₂²	1	4	yes	complemented
46	#14273704	C₂²	1	4	yes	—
47	#14273704	C₂²	1	4	yes	complemented
48	#14273703	C₂²	1	4	yes	complemented
49	#14273701	C₂²	1	2	yes	—
50	#14273700	C₂²	1	4	yes	—
51	#14273699	C₂²	1	4	yes	complemented
52	#14273695	C₂²	1	4	yes	—
53	C₄×Dic₁₁₈	C₂²	1	2	yes	complemented
54	C₄×Dic₁₁₈	C₂²	1	2	yes	complemented
55	C₄×Dic₁₁₈	C₂²	1	2	yes	complemented
56	C₄×D₂₃₆	C₂²	1	2	yes	—
57	D₄×Dic₅₉	C₂²	1	4	yes	—
58	(C₂²⋊D₅₉)⋊C₄	C₂²	1	4	yes	complemented
59	#14273686	C₂²	1	2	yes	—
60	#14273685	C₂²	1	4	yes	complemented
61	C₂×(C₂×D₅₉)⋊C₄	C₂²	1	2	yes	—
62	C₂×(C₂×D₅₉)⋊C₄	C₂²	1	2	yes	—
63	C₂²⋊C₄×D₅₉	C₂²	1	4	yes	—
64	#126×C₅₉	C₂²	1	2	yes	complemented
65	#125×C₅₉	C₂²	1	1	yes	characteristic, complemented
66	#124×C₅₉	C₂²	1	1	yes	characteristic, complemented
67	#123×C₅₉	C₂²	1	2	yes	—
68	C₂²⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
69	#121×C₅₉	C₂²	1	1	yes	characteristic
70	C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic, complemented
71	C₄×D₄×C₅₉	C₂²	1	2	yes	—
72	C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic, complemented
73	#117×C₅₉	C₂²	1	2	yes	complemented
74	C₂×C₄²×C₅₉	C₂²	1	1	yes	characteristic
75	C₂³×D₅₉	C₂³	1	2	yes	—
76	C₂×Q₈×C₅₉	C₂³	1	1	yes	characteristic
77	C₂×D₄×C₅₉	C₂³	1	2	yes	—
78	C₂×D₄×C₅₉	C₂³	1	1	yes	characteristic
79	C₂²×C₄×C₅₉	C₂³	1	1	yes	characteristic
80	C₂²×C₄×C₅₉	C₂³	1	1	yes	characteristic
81	C₂²×C₄×C₅₉	C₂³	1	2	yes	—
82	C₂²×C₄×C₅₉	C₂³	1	1	yes	characteristic
83	C₂×C₂²⋊D₅₉	C₂³	1	4	yes	—
84	C₂×C₂²⋊D₅₉	C₂³	1	4	yes	—
85	C₂²×Dic₅₉	C₂³	1	2	yes	—
86	C₂²×Dic₅₉	C₂³	1	4	yes	—
87	#11745685	—	4	4	no	—
88	C₂×D₂₃₆	—	4	2	no	—
89	C₂×D₂₃₆	C₂³	1	2	yes	—
90	C₂×D₂₃₆	C₂³	1	2	yes	—
91	C₂×C₄×D₅₉	C₂³	1	4	yes	—
92	C₂×C₄×D₅₉	C₂³	1	4	yes	—
93	C₂×Dic₁₁₈	—	4	2	no	—
94	C₂×Dic₁₁₈	—	4	4	no	—
95	C₂×Dic₁₁₈	C₂³	1	2	yes	—
96	C₂×Dic₁₁₈	C₂³	1	2	yes	—
97	C₂×Dic₁₁₈	C₂³	1	2	yes	—
98	C₂×Dic₁₁₈	C₂³	1	4	yes	—
99	C₂×Dic₁₁₈	C₂³	1	2	yes	—
100	C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
101	C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
102	C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
103	C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
104	C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
105	C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
106	C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
107	C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
108	C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
109	C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
110	C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
111	C₄²×C₅₉	C₂³	1	1	yes	characteristic
112	C₄²×C₅₉	C₂³	1	1	yes	characteristic
113	C₄²×C₅₉	C₂³	1	1	yes	characteristic
114	C₄²×C₅₉	C₂³	1	1	yes	characteristic
115	C₄²×C₅₉	C₂³	1	2	yes	—
116	C₂²⋊Dic₅₉	C₂³	1	4	yes	—
117	C₂²⋊Dic₅₉	C₂³	1	4	yes	—
118	(C₂×D₅₉)⋊C₄	C₂³	1	4	yes	—
119	(C₂×D₅₉)⋊C₄	C₂³	1	4	yes	—
120	(C₂×D₅₉)⋊C₄	C₂³	1	4	yes	—
121	(C₂×D₅₉)⋊C₄	C₂³	1	4	yes	—
122	(C₂×D₅₉)⋊C₄	C₂³	1	4	yes	—
123	(C₂×D₅₉)⋊C₄	C₂³	1	4	yes	—
124	(C₂×D₅₉)⋊C₄	C₂³	1	4	yes	—
125	(C₂×D₅₉)⋊C₄	C₂³	1	4	yes	—
126	C₄⋊Dic₅₉	C₂³	1	4	yes	—
127	C₄⋊Dic₅₉	C₂³	1	2	yes	—
128	C₄⋊Dic₅₉	C₂³	1	2	yes	—
129	C₄⋊Dic₅₉	C₂³	1	4	yes	—
130	C₄⋊Dic₅₉	C₂³	1	2	yes	—
131	C₄⋊Dic₅₉	C₂³	1	2	yes	—
132	Dic₅₉⋊C₄	C₂³	1	4	yes	—
133	Dic₅₉⋊C₄	C₂³	1	4	yes	—
134	Dic₅₉⋊C₄	C₂³	1	4	yes	—
135	Dic₅₉⋊C₄	C₂³	1	4	yes	—
136	C₄×Dic₅₉	C₂³	1	4	yes	—
137	C₄×Dic₅₉	C₂³	1	4	yes	—
138	C₂³×C₅₉	C₂⁴	1	2	yes	—
139	C₂³×C₅₉	C₂⁴	1	1	yes	characteristic
140	C₂²×D₅₉	—	2	4	no	—
141	C₂²×D₅₉	—	4	2	no	—
142	C₂²×D₅₉	—	4	2	no	—
143	C₂²×D₅₉	C₂⁴	1	4	yes	—
144	Q₈×C₅₉	—	4	1	no	—
145	D₄×C₅₉	—	2	4	no	—
146	D₄×C₅₉	—	4	1	no	—
147	C₂×C₄×C₅₉	—	2	2	no	—
148	C₂×C₄×C₅₉	—	2	2	no	—
149	C₂×C₄×C₅₉	—	2	4	no	—
150	C₂×C₄×C₅₉	—	4	1	no	—
151	C₂×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
152	C₂×C₄×C₅₉	C₂⁴	1	2	yes	—
153	C₂×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
154	C₂×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
155	C₂×C₄×C₅₉	C₂⁴	1	2	yes	—
156	C₂×C₄×C₅₉	C₂⁴	1	2	yes	—
157	C₂×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
158	C₂×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
159	C₂×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
160	C₂²⋊D₅₉	—	4	4	no	—
161	C₂²⋊D₅₉	—	4	4	no	—
162	C₂×Dic₅₉	—	4	2	no	—
163	C₂×Dic₅₉	—	4	4	no	—
164	C₂×Dic₅₉	C₂⁴	1	4	yes	—
165	C₂×Dic₅₉	C₂⁴	1	4	yes	—
166	C₂×Dic₅₉	C₂⁴	1	4	yes	—
167	D₂₃₆	—	2	4	no	—
168	D₂₃₆	—	4	2	no	—
169	C₄×D₅₉	—	4	4	no	—
170	C₄×D₅₉	—	4	4	no	—
171	Dic₁₁₈	—	2	4	no	—
172	Dic₁₁₈	—	2	4	no	—
173	Dic₁₁₈	—	4	2	no	—
174	Dic₁₁₈	—	4	4	no	—
175	Dic₁₁₈	—	4	2	no	—
176	C₂²×C₅₉	—	2	1	no	—
177	C₂²×C₅₉	—	2	1	no	—
178	C₂²×C₅₉	—	2	2	no	—
179	C₂²×C₅₉	—	2	2	no	—
180	C₂²×C₅₉	—	2	2	no	—
181	C₂²×C₅₉	2₋¹⁺⁴	1	2	yes	—
182	C₂²×C₅₉	C₂⁵	1	1	yes	characteristic
183	C₂×D₅₉	—	2	4	no	—
184	C₂×D₅₉	—	2	4	no	—
185	C₂×D₅₉	—	2	4	no	—
186	C₂×D₅₉	—	8	4	no	—
187	C₄×C₅₉	—	2	2	no	—
188	C₄×C₅₉	—	2	1	no	—
189	C₄×C₅₉	—	2	1	no	—
190	C₄×C₅₉	—	2	1	no	—
191	C₄×C₅₉	—	2	2	no	—
192	C₄×C₅₉	—	2	1	no	—
193	C₄×C₅₉	—	2	2	no	—
194	C₄×C₅₉	—	2	1	no	—
195	C₄×C₅₉	H(5,𝔽₂)	1	2	yes	—
196	Dic₅₉	—	2	4	no	—
197	Dic₅₉	—	2	4	no	—
198	Dic₅₉	—	2	4	no	—
199	#3561	—	59	1	no	maximal, Sylow
200	C₂×C₅₉	—	2	2	no	—
201	C₂×C₅₉	—	4	2	no	—
202	C₂×C₅₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
203	C₂×C₅₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
204	C₂×C₅₉	#585	1	1	yes	characteristic
205	D₅₉	—	4	4	no	—
206	#563	—	59	2	no	—
207	#562	—	59	2	no	—
208	#556	—	59	2	no	—
209	#551	—	59	4	no	—
210	D₄×Q₈	—	59	2	no	—
211	#548	—	59	2	no	—
212	#546	—	59	2	no	—
213	#543	—	59	2	no	—
214	#542	—	59	4	no	—
215	#542	—	59	2	no	—
216	#538	—	59	2	no	—
217	#536	—	59	2	no	—
218	#533	—	59	1	no	—
219	#529	D₅₉	1	1	yes	characteristic, complemented
220	C₂×#124	—	59	1	no	—
221	C₅₉	#3561	1	1	yes	characteristic, complemented, Sylow
222	C₂×#41	—	59	2	no	—
223	C₂²×Q₈	—	59	1	no	—
224	C₂²×Q₈	—	59	2	no	—
225	C₂²×D₄	—	59	1	no	—
226	C₄⋊Q₈	—	59	4	no	—
227	C₄⋊Q₈	—	59	1	no	—
228	C₄⋊Q₈	—	59	1	no	—
229	C₄⋊Q₈	—	59	2	no	—
230	#126	—	59	4	no	—
231	#126	—	59	4	no	—
232	#126	—	59	4	no	—
233	#126	C₂×D₅₉	1	2	yes	complemented
234	#125	—	59	2	no	—
235	#125	C₂×D₅₉	1	1	yes	characteristic, complemented
236	#124	—	59	4	no	—
237	#124	—	59	4	no	—
238	#124	—	59	2	no	—
239	#124	—	59	2	no	—
240	#124	—	59	2	no	—
241	#124	—	59	2	no	—
242	#124	—	59	2	no	—
243	#124	C₂×D₅₉	1	1	yes	characteristic, complemented
244	#123	—	59	4	no	—
245	#123	—	59	4	no	—
246	#123	—	59	4	no	—
247	#123	—	59	4	no	—
248	#123	C₂×D₅₉	1	2	yes	—
249	C₂²⋊Q₈	—	59	4	no	—
250	C₂²⋊Q₈	—	59	2	no	—
251	C₂²⋊Q₈	—	59	2	no	—
252	C₂²⋊Q₈	—	59	2	no	—
253	C₂²⋊Q₈	—	59	4	no	—
254	C₂²⋊Q₈	—	59	4	no	—
255	C₂²⋊Q₈	—	59	4	no	—
256	C₂²⋊Q₈	—	59	4	no	—
257	C₂²⋊Q₈	—	59	4	no	—
258	C₂²⋊Q₈	—	59	4	no	—
259	C₂²⋊Q₈	C₂×D₅₉	1	1	yes	characteristic
260	#121	—	59	4	no	—
261	#121	—	59	2	no	—
262	#121	—	59	4	no	—
263	#121	C₂×D₅₉	1	1	yes	characteristic
264	#120	—	59	4	no	—
265	C₄×Q₈	—	59	2	no	—
266	C₄×Q₈	—	59	2	no	—
267	C₄×Q₈	—	59	2	no	—
268	C₄×Q₈	C₂×D₅₉	1	1	yes	characteristic, complemented
269	C₄×D₄	—	59	4	no	—
270	C₄×D₄	—	59	4	no	—
271	C₄×D₄	—	59	2	no	—
272	C₄×D₄	C₂×D₅₉	1	2	yes	—
273	C₄×D₄	C₂×D₅₉	1	1	yes	characteristic, complemented
274	#117	—	59	2	no	—
275	#117	—	59	4	no	—
276	#117	C₂×D₅₉	1	2	yes	complemented
277	C₂×C₂²⋊C₄	—	59	2	no	—
278	C₂×C₂²⋊C₄	—	59	2	no	—
279	C₂×C₂²⋊C₄	—	59	4	no	—
280	C₂×C₄²	C₂×D₅₉	1	1	yes	characteristic
281	C₂⁴	—	59	2	no	—
282	#41	—	236	4	no	—
283	C₂×Q₈	—	59	2	no	—
284	C₂×Q₈	—	59	2	no	—
285	C₂×Q₈	—	59	2	no	—
286	C₂×Q₈	—	59	4	no	—
287	C₂×Q₈	—	59	2	no	—
288	C₂×Q₈	—	236	2	no	—
289	C₂×Q₈	—	236	4	no	—
290	C₂×Q₈	C₂²×D₅₉	1	1	yes	characteristic
291	C₂×D₄	—	59	4	no	—
292	C₂×D₄	—	59	4	no	—
293	C₂×D₄	—	59	2	no	—
294	C₂×D₄	—	59	2	no	—
295	C₂×D₄	—	236	2	no	—
296	C₂×D₄	C₂²×D₅₉	1	2	yes	—
297	C₂×D₄	C₂²×D₅₉	1	1	yes	characteristic
298	C₂²×C₄	—	59	2	no	—
299	C₂²×C₄	—	59	4	no	—
300	C₂²×C₄	—	59	4	no	—
301	C₂²×C₄	—	59	4	no	—
302	C₂²×C₄	C₂²×D₅₉	1	1	yes	characteristic
303	C₂²×C₄	C₂²×D₅₉	1	1	yes	characteristic
304	C₂²×C₄	C₂²×D₅₉	1	2	yes	—
305	C₂²×C₄	C₂²×D₅₉	1	1	yes	characteristic
306	C₄⋊C₄	—	59	4	no	—
307	C₄⋊C₄	—	59	2	no	—
308	C₄⋊C₄	—	59	2	no	—
309	C₄⋊C₄	—	59	2	no	—
310	C₄⋊C₄	—	59	4	no	—
311	C₄⋊C₄	—	59	4	no	—
312	C₄⋊C₄	—	59	4	no	—
313	C₄⋊C₄	—	59	4	no	—
314	C₄⋊C₄	—	59	4	no	—
315	C₄⋊C₄	—	59	2	no	—
316	C₄⋊C₄	C₂²×D₅₉	1	2	yes	—
317	C₄⋊C₄	C₂²×D₅₉	1	2	yes	—
318	C₄⋊C₄	C₂²×D₅₉	1	2	yes	—
319	C₄⋊C₄	C₂²×D₅₉	1	2	yes	—
320	C₄⋊C₄	C₂²×D₅₉	1	1	yes	characteristic
321	C₄⋊C₄	C₂²×D₅₉	1	1	yes	characteristic
322	C₂²⋊C₄	—	59	4	no	—
323	C₂²⋊C₄	—	59	4	no	—
324	C₂²⋊C₄	—	59	4	no	—
325	C₂²⋊C₄	—	59	4	no	—
326	C₂²⋊C₄	—	59	4	no	—
327	C₂²⋊C₄	—	59	4	no	—
328	C₂²⋊C₄	—	59	4	no	—
329	C₂²⋊C₄	—	59	4	no	—
330	C₂²⋊C₄	—	59	4	no	—
331	C₂²⋊C₄	—	59	4	no	—
332	C₂²⋊C₄	C₂²×D₅₉	1	2	yes	—
333	C₂²⋊C₄	C₂²×D₅₉	1	2	yes	—
334	C₂²⋊C₄	C₂²×D₅₉	1	2	yes	—
335	C₂²⋊C₄	C₂²×D₅₉	1	2	yes	—
336	C₂²⋊C₄	C₂²×D₅₉	1	2	yes	—
337	C₄²	—	59	4	no	—
338	C₄²	—	59	4	no	—
339	C₄²	C₂²×D₅₉	1	1	yes	characteristic
340	C₄²	C₂²×D₅₉	1	1	yes	characteristic
341	C₄²	C₂²×D₅₉	1	1	yes	characteristic
342	C₄²	C₂²×D₅₉	1	1	yes	characteristic
343	C₄²	C₂²×D₅₉	1	2	yes	—
344	C₂³	—	59	4	no	—
345	C₂³	—	118	4	no	—
346	C₂³	—	236	2	no	—
347	C₂³	—	236	2	no	—
348	C₂³	C₂³×D₅₉	1	2	yes	—
349	C₂³	C₂³×D₅₉	1	1	yes	characteristic
350	Q₈	—	4	1	no	—
351	Q₈	—	118	4	no	—
352	Q₈	—	118	4	no	—
353	Q₈	—	236	2	no	—
354	Q₈	—	236	4	no	—
355	Q₈	—	236	2	no	—
356	D₄	—	2	4	no	—
357	D₄	—	4	1	no	—
358	D₄	—	118	4	no	—
359	D₄	—	236	2	no	—
360	D₄	—	236	4	no	—
361	D₄	—	236	4	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	4	1	no	—
366	C₂×C₄	—	59	4	no	—
367	C₂×C₄	—	59	4	no	—
368	C₂×C₄	—	59	4	no	—
369	C₂×C₄	—	236	4	no	—
370	C₂×C₄	—	236	4	no	—
371	C₂×C₄	—	236	4	no	—
372	C₂×C₄	—	236	2	no	—
373	C₂×C₄	C₂³×D₅₉	1	1	yes	characteristic
374	C₂×C₄	C₂³×D₅₉	1	2	yes	—
375	C₂×C₄	C₂³×D₅₉	1	1	yes	characteristic
376	C₂×C₄	C₂³×D₅₉	1	1	yes	characteristic
377	C₂×C₄	C₂³×D₅₉	1	1	yes	characteristic
378	C₂×C₄	C₂³×D₅₉	1	1	yes	characteristic
379	C₂×C₄	C₂³×D₅₉	1	2	yes	—
380	C₂×C₄	C₂³×D₅₉	1	2	yes	—
381	C₂×C₄	C₂³×D₅₉	1	1	yes	characteristic
382	C₂²	—	2	1	no	—
383	C₂²	—	2	1	no	—
384	C₂²	—	2	2	no	—
385	C₂²	—	2	2	no	—
386	C₂²	—	2	2	no	—
387	C₂²	—	118	4	no	—
388	C₂²	—	118	4	no	—
389	C₂²	—	118	4	no	—
390	C₂²	—	472	4	no	—
391	C₂²	#14273774	1	2	yes	—
392	C₂²	C₂⁴×D₅₉	1	1	yes	characteristic
393	C₄	—	2	2	no	—
394	C₄	—	2	1	no	—
395	C₄	—	2	1	no	—
396	C₄	—	2	1	no	—
397	C₄	—	2	2	no	—
398	C₄	—	2	1	no	—
399	C₄	—	2	1	no	—
400	C₄	—	2	2	no	—
401	C₄	—	118	4	no	—
402	C₄	—	118	4	no	—
403	C₄	—	118	4	no	—
404	C₄	#14273773	1	2	yes	—
405	C₂	—	2	2	no	—
406	C₂	—	4	2	no	—
407	C₂	—	236	4	no	—
408	C₂	C₂×#14273773	1	1	yes	characteristic
409	C₂	C₂×#14273774	1	1	yes	characteristic
410	C₂	#16838238	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₅₉
commutator, socle	C₂²×C₅₉	C₂⁵
Fitting	C₅₉×#529	C₂
hypercenter	#529	D₅₉
hypocenter	C₅₉	#3561
LCS	G ▷ C₂²×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂² ◁ #529

Complements

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

N	H ≅ G/N	type
1. #16838156	C₂	semidirect
2. #16838146	C₂	semidirect
3. #16838125	C₂	semidirect
4. #16838075	C₂	semidirect
5. D₄×Dic₁₁₈	C₂	semidirect
6. #16838061	C₂	semidirect
7. #16838048	C₂	semidirect
8. #16838027	C₂	semidirect
9. #16838023	C₂	semidirect
10. #16838018	C₂	semidirect
11. #16837989	C₂	semidirect
12. #16837978	C₂	semidirect
13. #16837959	C₂	semidirect
14. C₂×#14273715	C₂	semidirect
15. C₅₉×#529	C₂	semidirect
18. C₂²×Dic₁₁₈	C₂²	semidirect
20. #14273727	C₂²	semidirect
21. #14273727	C₂²	semidirect
22. #14273727	C₂²	semidirect
23. #14273726	C₂²	semidirect
24. #14273722	C₂²	semidirect
25. #14273722	C₂²	semidirect
26. #14273722	C₂²	semidirect
27. #14273719	C₂²	semidirect
33. #14273713	C₂²	semidirect
34. #14273713	C₂²	semidirect
36. #14273711	C₂²	semidirect
37. #14273711	C₂²	semidirect
38. #14273709	C₂²	semidirect
39. #14273707	C₂²	semidirect
40. #14273707	C₂²	semidirect
43. #14273706	C₂²	semidirect
44. #14273705	C₂²	semidirect
45. #14273705	C₂²	semidirect
47. #14273704	C₂²	semidirect
48. #14273703	C₂²	semidirect
51. #14273699	C₂²	semidirect
53. C₄×Dic₁₁₈	C₂²	semidirect
54. C₄×Dic₁₁₈	C₂²	semidirect
55. C₄×Dic₁₁₈	C₂²	semidirect
58. (C₂²⋊D₅₉)⋊C₄	C₂²	semidirect
60. #14273685	C₂²	semidirect
64. #126×C₅₉	C₂²	semidirect
65. #125×C₅₉	C₂²	semidirect
66. #124×C₅₉	C₂²	semidirect
70. C₄×Q₈×C₅₉	C₂²	semidirect
72. C₄×D₄×C₅₉	C₂²	semidirect
73. #117×C₅₉	C₂²	semidirect
219. #529	D₅₉	semidirect
221. C₅₉	#3561	semidirect
233. #126	C₂×D₅₉	semidirect
235. #125	C₂×D₅₉	semidirect
243. #124	C₂×D₅₉	semidirect
268. C₄×Q₈	C₂×D₅₉	semidirect
273. C₄×D₄	C₂×D₅₉	semidirect
276. #117	C₂×D₅₉	semidirect