Subgroups — #28559359

Order 15104.

600 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21433191	C₂	1	1	yes	maximal, characteristic, complemented
2	#21433172	C₂	1	1	yes	maximal, characteristic
3	#21422999	C₂	1	2	yes	maximal, complemented
4	#21422987	C₂	1	2	yes	maximal, complemented
5	SD₁₆⋊(C₅₉⋊C₈)	C₂	1	2	yes	maximal, complemented
6	SD₁₆×C₅₉⋊C₈	C₂	1	2	yes	maximal, complemented
7	#21422859	C₂	1	1	yes	maximal, characteristic, complemented
8	#21422569	C₂	1	1	yes	maximal, characteristic, complemented
9	#21422565	C₂	1	1	yes	maximal, characteristic
10	#21422379	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#3167	C₂	1	1	yes	maximal, characteristic
12	#16837533	—	2	2	no	—
13	#16837533	C₂²	1	2	yes	—
14	Q₈×C₅₉⋊C₈	C₂²	1	2	yes	—
15	#16837480	C₂²	1	2	yes	—
16	#16837474	—	2	2	no	—
17	D₄×C₅₉⋊C₈	C₂²	1	2	yes	—
18	#16837463	—	2	2	no	—
19	#16837459	C₂²	1	1	yes	characteristic
20	#16837459	C₂²	1	1	yes	characteristic
21	#16837455	C₂²	1	1	yes	characteristic
22	#16837455	C₂²	1	1	yes	characteristic
23	#16837369	—	2	2	no	—
24	#16837155	C₂²	1	2	yes	—
25	#16837153	C₂²	1	2	yes	—
26	Q₈⋊(C₅₉⋊C₈)	C₂²	1	2	yes	—
27	Q₈⋊(C₅₉⋊C₈)	C₂²	1	2	yes	—
28	D₄⋊(C₅₉⋊C₈)	C₂²	1	2	yes	—
29	D₄⋊(C₅₉⋊C₈)	C₂²	1	2	yes	—
30	#16837123	C₂²	1	1	yes	characteristic
31	#16837123	C₂²	1	1	yes	characteristic
32	C₈×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
33	C₈×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
34	C₅₉×#533	C₂²	1	1	yes	characteristic
35	C₅₉×#532	C₂²	1	1	yes	characteristic
36	C₅₉×#498	C₄	1	1	yes	characteristic
37	C₅₉×#492	C₄	1	1	yes	characteristic
38	C₅₉×#487	C₄	1	1	yes	characteristic
39	C₅₉×#486	C₄	1	1	yes	characteristic
40	C₅₉×#465	C₄	1	2	yes	—
41	C₅₉×#465	C₄	1	2	yes	—
42	C₄×SD₁₆×C₅₉	C₂²	1	2	yes	—
43	C₄×SD₁₆×C₅₉	C₂²	1	2	yes	—
44	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
45	C₂×#11745664	—	2	2	no	—
46	C₂²×C₅₉⋊C₈	—	2	2	no	—
47	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
48	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
49	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
50	C₄⋊(C₅₉⋊C₈)	D₄	1	2	yes	—
51	C₄⋊(C₅₉⋊C₈)	C₂³	1	2	yes	—
52	C₄⋊(C₅₉⋊C₈)	C₂³	1	2	yes	—
53	C₂²⋊(C₅₉⋊C₈)	—	2	1	no	—
54	C₂²⋊(C₅₉⋊C₈)	—	2	1	no	—
55	C₂²⋊(C₅₉⋊C₈)	—	2	1	no	—
56	C₂²⋊(C₅₉⋊C₈)	—	2	2	no	—
57	C₂²⋊(C₅₉⋊C₈)	—	2	2	no	—
58	C₂²⋊(C₅₉⋊C₈)	D₄	1	2	yes	—
59	#14273638	—	2	1	no	—
60	#14273638	—	2	1	no	—
61	#14273638	—	2	2	no	—
62	C₄×C₅₉⋊C₈	—	2	2	no	—
63	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
64	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
65	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
66	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
67	C₂×#41×C₅₉	—	2	1	no	—
68	C₂×SD₁₆×C₅₉	C₂×C₄	1	2	yes	—
69	C₂×SD₁₆×C₅₉	C₂×C₄	1	2	yes	—
70	C₂²×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
71	C₂²×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
72	C₄⋊Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
73	C₄⋊Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
74	C₄⋊Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
75	#127×C₅₉	C₂×C₄	1	1	yes	characteristic
76	#125×C₅₉	—	2	1	no	—
77	#124×C₅₉	—	2	1	no	—
78	C₂²⋊Q₈×C₅₉	—	2	1	no	—
79	C₂²⋊Q₈×C₅₉	C₂×C₄	1	2	yes	—
80	#121×C₅₉	—	2	1	no	—
81	#121×C₅₉	C₂×C₄	1	2	yes	—
82	C₄×Q₈×C₅₉	—	2	1	no	—
83	C₄×Q₈×C₅₉	C₂³	1	2	yes	—
84	C₄×D₄×C₅₉	—	2	1	no	—
85	C₄×D₄×C₅₉	C₂³	1	2	yes	—
86	#117×C₅₉	—	2	1	no	—
87	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
88	#106×C₅₉	C₂×C₄	1	2	yes	—
89	#106×C₅₉	C₂×C₄	1	2	yes	—
90	#103×C₅₉	C₂×C₄	1	2	yes	—
91	#103×C₅₉	C₂×C₄	1	2	yes	—
92	#102×C₅₉	C₂×C₄	1	2	yes	—
93	#102×C₅₉	C₂×C₄	1	2	yes	—
94	C₄×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
95	C₄×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
96	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
97	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
98	#41×C₅₉	—	8	2	no	—
99	C₂×Q₈×C₅₉	—	2	1	no	—
100	C₂×Q₈×C₅₉	—	2	1	no	—
101	C₂×Q₈×C₅₉	C₂²×C₄	1	2	yes	—
102	C₂×D₄×C₅₉	—	2	2	no	—
103	C₂×D₄×C₅₉	—	2	1	no	—
104	C₂×D₄×C₅₉	—	2	1	no	—
105	C₂×D₄×C₅₉	C₂²×C₄	1	2	yes	—
106	C₂²×C₄×C₅₉	—	2	2	no	—
107	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
110	SD₁₆×C₅₉	—	2	4	no	—
111	SD₁₆×C₅₉	—	2	4	no	—
112	C₂×C₈×C₅₉	—	2	2	no	—
113	C₂×C₈×C₅₉	—	2	2	no	—
114	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
118	C₄⋊C₄×C₅₉	—	2	1	no	—
119	C₄⋊C₄×C₅₉	—	2	1	no	—
120	C₄⋊C₄×C₅₉	—	2	1	no	—
121	C₄⋊C₄×C₅₉	—	2	1	no	—
122	C₄⋊C₄×C₅₉	—	2	2	no	—
123	C₄⋊C₄×C₅₉	—	2	2	no	—
124	C₄⋊C₄×C₅₉	C₂²×C₄	1	2	yes	—
125	C₄⋊C₄×C₅₉	C₂²×C₄	1	2	yes	—
126	C₂²⋊C₄×C₅₉	—	2	2	no	—
127	C₂²⋊C₄×C₅₉	—	2	2	no	—
128	C₂²⋊C₄×C₅₉	—	2	2	no	—
129	C₄²×C₅₉	—	2	2	no	—
130	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
131	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
132	C₄²×C₅₉	#41	1	1	yes	characteristic
133	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
134	#11745664	—	8	2	no	—
135	C₂×C₅₉⋊C₈	—	2	2	no	—
136	C₂×C₅₉⋊C₈	—	2	2	no	—
137	C₂×C₅₉⋊C₈	—	2	1	no	—
138	C₂×C₅₉⋊C₈	—	2	1	no	—
139	C₂×C₅₉⋊C₈	—	8	2	no	—
140	C₂×C₅₉⋊C₈	C₂×D₄	1	2	yes	—
141	C₂×C₅₉⋊C₈	C₂×D₄	1	2	yes	—
142	C₂³×C₅₉	—	2	2	no	—
143	C₂³×C₅₉	C₄×D₄	1	1	yes	characteristic
144	Q₈×C₅₉	—	2	2	no	—
145	Q₈×C₅₉	—	2	2	no	—
146	Q₈×C₅₉	—	8	1	no	—
147	Q₈×C₅₉	—	8	1	no	—
148	D₄×C₅₉	—	2	2	no	—
149	D₄×C₅₉	—	2	2	no	—
150	D₄×C₅₉	—	8	1	no	—
151	D₄×C₅₉	—	8	1	no	—
152	D₄×C₅₉	—	8	2	no	—
153	C₂×C₄×C₅₉	—	2	1	no	—
154	C₂×C₄×C₅₉	—	2	1	no	—
155	C₂×C₄×C₅₉	—	2	2	no	—
156	C₂×C₄×C₅₉	—	2	2	no	—
157	C₂×C₄×C₅₉	—	2	2	no	—
158	C₂×C₄×C₅₉	—	2	2	no	—
159	C₂×C₄×C₅₉	—	4	1	no	—
160	C₂×C₄×C₅₉	—	4	2	no	—
161	C₂×C₄×C₅₉	—	4	2	no	—
162	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
163	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
164	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
165	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
166	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
167	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
168	C₈×C₅₉	—	2	1	no	—
169	C₈×C₅₉	—	2	1	no	—
170	C₈×C₅₉	#131	1	2	yes	—
171	C₈×C₅₉	#131	1	2	yes	—
172	C₅₉⋊C₈	—	2	2	no	—
173	C₅₉⋊C₈	—	2	2	no	—
174	C₅₉⋊C₈	—	4	1	no	—
175	C₅₉⋊C₈	—	4	1	no	—
176	C₅₉⋊C₈	—	4	2	no	—
177	C₅₉⋊C₈	—	4	2	no	—
178	#17971	—	59	1	no	maximal, Sylow
179	C₂²×C₅₉	—	2	1	no	—
180	C₂²×C₅₉	—	2	1	no	—
181	C₂²×C₅₉	—	2	1	no	—
182	C₂²×C₅₉	—	4	2	no	—
183	C₂²×C₅₉	—	4	2	no	—
184	C₂²×C₅₉	—	4	2	no	—
185	C₂²×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
186	C₄×C₅₉	—	2	1	no	—
187	C₄×C₅₉	—	2	1	no	—
188	C₄×C₅₉	—	2	1	no	—
189	C₄×C₅₉	—	2	1	no	—
190	C₄×C₅₉	—	4	2	no	—
191	C₄×C₅₉	—	4	2	no	—
192	C₄×C₅₉	—	4	2	no	—
193	C₄×C₅₉	C₂×#131	1	1	yes	characteristic
194	C₄×C₅₉	C₂×#131	1	1	yes	characteristic
195	C₄×C₅₉	#577	1	2	yes	—
196	#3167	D₅₉	1	1	yes	characteristic
197	#2985	—	59	1	no	—
198	#2981	—	59	1	no	—
199	#1592	—	59	2	no	—
200	#1590	—	59	2	no	—
201	SD₁₆⋊C₈	—	59	2	no	—
202	C₈×SD₁₆	—	59	2	no	—
203	#1568	—	59	1	no	—
204	#1497	—	59	1	no	—
205	#1496	—	59	1	no	—
206	#1450	—	59	1	no	—
207	C₂×C₅₉	—	4	1	no	—
208	C₂×C₅₉	—	8	2	no	—
209	C₂×C₅₉	#2931	1	1	yes	characteristic
210	C₂×C₅₉	#2949	1	1	yes	characteristic
211	C₂×C₅₉	#2957	1	1	yes	characteristic
212	#533	C₂×D₅₉	1	1	yes	characteristic
213	#532	C₂×D₅₉	1	1	yes	characteristic
214	#498	Dic₅₉	1	1	yes	characteristic
215	#492	Dic₅₉	1	1	yes	characteristic
216	#487	Dic₅₉	1	1	yes	characteristic
217	#486	Dic₅₉	1	1	yes	characteristic
218	#465	Dic₅₉	1	2	yes	—
219	#465	Dic₅₉	1	2	yes	—
220	#446	—	59	2	no	—
221	#446	—	118	2	no	—
222	C₈×Q₈	—	59	2	no	—
223	C₄×SD₁₆	C₂×D₅₉	1	2	yes	—
224	C₄×SD₁₆	C₂×D₅₉	1	2	yes	—
225	#436	—	59	2	no	—
226	#435	—	118	2	no	—
227	C₈×D₄	—	59	2	no	—
228	#433	—	118	2	no	—
229	#432	—	59	1	no	—
230	#432	—	59	1	no	—
231	#431	—	59	1	no	—
232	#431	—	59	1	no	—
233	#408	—	118	2	no	—
234	C₂×C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
235	#335	—	59	2	no	—
236	#334	—	59	2	no	—
237	Q₈⋊C₈	—	59	2	no	—
238	Q₈⋊C₈	—	59	2	no	—
239	D₄⋊C₈	—	59	2	no	—
240	D₄⋊C₈	—	59	2	no	—
241	#322	—	59	1	no	—
242	#322	—	59	1	no	—
243	C₈²	—	59	1	no	—
244	C₈²	—	59	1	no	—
245	C₅₉	#17971	1	1	yes	characteristic, complemented, Sylow
246	C₂×#41	—	2	1	no	—
247	C₂×SD₁₆	C₂×Dic₅₉	1	2	yes	—
248	C₂×SD₁₆	C₂×Dic₅₉	1	2	yes	—
249	C₂×M₁₆	—	118	2	no	—
250	C₂²×C₈	—	118	2	no	—
251	C₂²×C₈	C₂×Dic₅₉	1	1	yes	characteristic
252	C₂²×C₈	C₂×Dic₅₉	1	1	yes	characteristic
253	C₄⋊Q₈	C₂×Dic₅₉	1	1	yes	characteristic
254	C₄⋊Q₈	C₂×Dic₅₉	1	1	yes	characteristic
255	C₄⋊Q₈	C₂×Dic₅₉	1	1	yes	characteristic
256	#127	C₂×Dic₅₉	1	1	yes	characteristic
257	#125	—	2	1	no	—
258	#124	—	2	1	no	—
259	C₂²⋊Q₈	—	2	1	no	—
260	C₂²⋊Q₈	C₂×Dic₅₉	1	2	yes	—
261	#121	—	2	1	no	—
262	#121	C₂×Dic₅₉	1	2	yes	—
263	C₄×Q₈	—	2	1	no	—
264	C₄×Q₈	C₂²×D₅₉	1	2	yes	—
265	C₄×D₄	—	2	1	no	—
266	C₄×D₄	C₂²×D₅₉	1	2	yes	—
267	#117	—	2	1	no	—
268	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
269	#106	C₂×Dic₅₉	1	2	yes	—
270	#106	C₂×Dic₅₉	1	2	yes	—
271	C₄⋊C₈	—	59	2	no	—
272	C₄⋊C₈	—	59	2	no	—
273	C₄⋊C₈	—	59	2	no	—
274	C₄⋊C₈	—	118	2	no	—
275	C₄⋊C₈	—	118	2	no	—
276	C₄⋊C₈	—	118	1	no	—
277	#103	C₂×Dic₅₉	1	2	yes	—
278	#103	C₂×Dic₅₉	1	2	yes	—
279	#102	C₂×Dic₅₉	1	2	yes	—
280	#102	C₂×Dic₅₉	1	2	yes	—
281	C₂²⋊C₈	—	59	2	no	—
282	C₂²⋊C₈	—	118	2	no	—
283	C₂²⋊C₈	—	118	2	no	—
284	C₂²⋊C₈	—	118	1	no	—
285	C₂²⋊C₈	—	118	1	no	—
286	C₂²⋊C₈	—	118	1	no	—
287	#97	—	118	2	no	—
288	#97	—	118	1	no	—
289	#97	—	118	1	no	—
290	C₄×C₈	—	59	1	no	—
291	C₄×C₈	—	59	1	no	—
292	C₄×C₈	—	59	1	no	—
293	C₄×C₈	—	59	1	no	—
294	C₄×C₈	—	118	2	no	—
295	C₄×C₈	C₂×Dic₅₉	1	1	yes	characteristic
296	C₄×C₈	C₂×Dic₅₉	1	1	yes	characteristic
297	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
298	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
299	#41	—	8	2	no	—
300	C₂×Q₈	—	2	1	no	—
301	C₂×Q₈	—	2	1	no	—
302	C₂×Q₈	C₂²×Dic₅₉	1	2	yes	—
303	C₂×D₄	—	2	2	no	—
304	C₂×D₄	—	2	1	no	—
305	C₂×D₄	—	2	1	no	—
306	C₂×D₄	C₂²×Dic₅₉	1	2	yes	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	D₄×D₅₉	1	1	yes	characteristic
309	C₂²×C₄	#11745687	1	1	yes	characteristic
310	C₂²×C₄	C₂²×Dic₅₉	1	1	yes	characteristic
311	SD₁₆	—	2	4	no	—
312	SD₁₆	—	2	4	no	—
313	M₁₆	—	472	2	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	59	2	no	—
317	C₂×C₈	—	59	2	no	—
318	C₂×C₈	—	118	2	no	—
319	C₂×C₈	—	118	2	no	—
320	C₂×C₈	—	118	1	no	—
321	C₂×C₈	—	118	1	no	—
322	C₂×C₈	—	472	2	no	—
323	C₂×C₈	C₂²×Dic₅₉	1	1	yes	characteristic
324	C₂×C₈	C₂²×Dic₅₉	1	1	yes	characteristic
325	C₂×C₈	C₂²×Dic₅₉	1	1	yes	characteristic
326	C₂×C₈	C₂²×Dic₅₉	1	1	yes	characteristic
327	C₄⋊C₄	—	2	1	no	—
328	C₄⋊C₄	—	2	1	no	—
329	C₄⋊C₄	—	2	1	no	—
330	C₄⋊C₄	—	2	1	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	C₂²×Dic₅₉	1	2	yes	—
334	C₄⋊C₄	C₂²×Dic₅₉	1	2	yes	—
335	C₂²⋊C₄	—	2	2	no	—
336	C₂²⋊C₄	—	2	2	no	—
337	C₂²⋊C₄	—	2	2	no	—
338	C₄²	—	2	2	no	—
339	C₄²	D₄×D₅₉	1	1	yes	characteristic
340	C₄²	#11745687	1	1	yes	characteristic
341	C₄²	C₂²×Dic₅₉	1	1	yes	characteristic
342	C₄²	C₂³×D₅₉	1	1	yes	characteristic
343	C₂³	—	2	2	no	—
344	C₂³	D₄×Dic₅₉	1	1	yes	characteristic
345	Q₈	—	2	2	no	—
346	Q₈	—	2	2	no	—
347	Q₈	—	8	1	no	—
348	Q₈	—	8	1	no	—
349	D₄	—	2	2	no	—
350	D₄	—	2	2	no	—
351	D₄	—	8	1	no	—
352	D₄	—	8	1	no	—
353	D₄	—	8	2	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	D₄×Dic₅₉	1	1	yes	characteristic
364	C₂×C₄	D₄×Dic₅₉	1	1	yes	characteristic
365	C₂×C₄	D₄×Dic₅₉	1	1	yes	characteristic
366	C₂×C₄	C₂³×Dic₅₉	1	1	yes	characteristic
367	C₂×C₄	C₂×D₄×D₅₉	1	1	yes	characteristic
368	C₂×C₄	C₂×#11745687	1	1	yes	characteristic
369	C₈	—	2	1	no	—
370	C₈	—	2	1	no	—
371	C₈	—	118	2	no	—
372	C₈	—	118	2	no	—
373	C₈	—	236	1	no	—
374	C₈	—	236	1	no	—
375	C₈	—	236	2	no	—
376	C₈	—	236	2	no	—
377	C₈	#14273734	1	2	yes	—
378	C₈	#14273734	1	2	yes	—
379	C₂²	—	2	1	no	—
380	C₂²	—	2	1	no	—
381	C₂²	—	2	1	no	—
382	C₂²	—	4	2	no	—
383	C₂²	—	4	2	no	—
384	C₂²	—	4	2	no	—
385	C₂²	C₂×D₄×Dic₅₉	1	1	yes	characteristic
386	C₄	—	2	1	no	—
387	C₄	—	2	1	no	—
388	C₄	—	2	1	no	—
389	C₄	—	2	1	no	—
390	C₄	—	4	2	no	—
391	C₄	—	4	2	no	—
392	C₄	—	4	2	no	—
393	C₄	C₂×#14273734	1	1	yes	characteristic
394	C₄	C₂×#14273734	1	1	yes	characteristic
395	C₄	#16838208	1	2	yes	—
396	C₂	—	4	1	no	—
397	C₂	—	8	2	no	—
398	C₂	#21432808	1	1	yes	characteristic
399	C₂	#21432956	1	1	yes	characteristic
400	C₂	#21433013	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×#3167	C₂
socle	C₂²×C₅₉	C₂×C₄×D₄
prime radical	C₅₉×#532	C₂²
cosocle	C₄²×C₅₉	C₂⁴
hypercenter	#3167	D₅₉
hypocenter	C₅₉	#17971
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3167

Complements

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

N	H ≅ G/N	type
1. #21433191	C₂	semidirect
3. #21422999	C₂	semidirect
4. #21422987	C₂	semidirect
5. SD₁₆⋊(C₅₉⋊C₈)	C₂	semidirect
6. SD₁₆×C₅₉⋊C₈	C₂	semidirect
7. #21422859	C₂	semidirect
8. #21422569	C₂	semidirect
10. #21422379	C₂	semidirect
245. C₅₉	#17971	semidirect

Maximal subgroups

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

subgroup	index
#21433191	2
#21433172	2
#21422999	2
#21422987	2
SD₁₆⋊(C₅₉⋊C₈)	2
SD₁₆×C₅₉⋊C₈	2
#21422859	2
#21422569	2
#21422565	2
#21422379	2
C₅₉×#3167	2
#17971	59