Subgroups — #28557828

Order 15104.

602 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21433209	C₂	1	1	yes	maximal, characteristic
2	#21433204	C₂	1	1	yes	maximal, characteristic
3	#21432738	C₂	1	1	yes	maximal, characteristic
4	#21422883	C₂	1	2	yes	maximal, complemented
5	#21422878	C₂	1	2	yes	maximal, complemented
6	#21422875	C₂	1	2	yes	maximal, complemented
7	#21422869	C₂	1	2	yes	maximal, complemented
8	#21422849	C₂	1	1	yes	maximal, characteristic, complemented
9	#21422849	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#16837155	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#1564	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×#11745685	C₂²	1	1	yes	characteristic
13	#16837532	—	2	1	no	—
14	C₈×Dic₁₁₈	—	2	1	no	—
15	#16837481	—	2	1	no	—
16	#16837470	—	2	2	no	—
17	C₈×D₂₃₆	—	2	1	no	—
18	(C₂²⋊D₅₉)⋊C₈	—	2	2	no	—
19	#16837461	C₄	1	2	yes	—
20	#16837461	C₄	1	2	yes	—
21	#16837458	C₂²	1	2	yes	—
22	#16837454	C₂²	1	2	yes	—
23	#16837453	C₂²	1	2	yes	—
24	#16837453	C₂²	1	2	yes	—
25	#16837428	C₄	1	1	yes	characteristic
26	#16837428	C₄	1	1	yes	characteristic
27	#16837424	C₂²	1	2	yes	—
28	C₂×C₄⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
30	C₄⋊C₈×D₅₉	C₂²	1	2	yes	—
31	#16837368	C₄	1	1	yes	characteristic
32	#16837368	C₄	1	1	yes	characteristic
33	C₄×#11745664	C₂²	1	1	yes	characteristic
34	#16837155	C₂²	1	2	yes	—
35	#16837155	C₂²	1	2	yes	—
36	#16837154	C₂²	1	2	yes	—
37	#16837154	C₂²	1	2	yes	—
38	#16837152	C₂²	1	2	yes	—
39	#16837152	C₂²	1	2	yes	—
40	C₅₉×#431	C₂²	1	1	yes	characteristic
41	C₅₉×#431	C₂²	1	1	yes	characteristic
42	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
43	C₅₉×#335	C₂²	1	1	yes	characteristic
44	C₅₉×#335	C₂²	1	1	yes	characteristic
45	C₅₉×#334	C₂²	1	1	yes	characteristic
46	C₅₉×#334	C₂²	1	1	yes	characteristic
47	C₂×#11745685	C₂×C₄	1	1	yes	characteristic
48	C₂×#11745664	C₂×C₄	1	1	yes	characteristic
49	C₂×#11745664	C₂×C₄	1	1	yes	characteristic
50	C₂×#11745659	—	2	2	no	—
51	C₂²×C₅₉⋊C₈	—	2	1	no	—
52	C₂²×C₅₉⋊C₈	—	2	1	no	—
53	C₂×C₈×D₅₉	—	2	2	no	—
54	C₄×Dic₁₁₈	D₄	1	1	yes	characteristic
55	C₄×Dic₁₁₈	Q₈	1	1	yes	characteristic
56	C₄×D₂₃₆	D₄	1	1	yes	characteristic
57	C₄×D₂₃₆	Q₈	1	1	yes	characteristic
58	C₄×C₂²⋊D₅₉	D₄	1	2	yes	—
59	C₄×C₂²⋊D₅₉	Q₈	1	2	yes	—
60	#14273686	C₂×C₄	1	1	yes	characteristic
61	#14273684	C₂×C₄	1	2	yes	—
62	C₄²×D₅₉	C₂³	1	2	yes	—
63	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
64	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
65	C₄⋊(C₅₉⋊C₈)	C₂³	1	2	yes	—
66	C₄⋊(C₅₉⋊C₈)	C₂³	1	2	yes	—
67	Dic₅₉⋊C₈	—	2	2	no	—
68	Dic₅₉⋊C₈	—	2	2	no	—
69	Dic₅₉⋊C₈	C₂×C₄	1	2	yes	—
70	Dic₅₉⋊C₈	C₂×C₄	1	2	yes	—
71	Dic₅₉⋊C₈	C₂×C₄	1	2	yes	—
72	Dic₅₉⋊C₈	C₂×C₄	1	2	yes	—
73	(C₂×D₅₉)⋊C₈	—	2	2	no	—
74	(C₂×D₅₉)⋊C₈	—	2	2	no	—
75	(C₂×D₅₉)⋊C₈	C₂×C₄	1	2	yes	—
76	(C₂×D₅₉)⋊C₈	C₂×C₄	1	2	yes	—
77	(C₂×D₅₉)⋊C₈	C₂×C₄	1	2	yes	—
78	(C₂×D₅₉)⋊C₈	C₂×C₄	1	2	yes	—
79	#14273638	C₂×C₄	1	2	yes	—
80	#14273637	—	2	2	no	—
81	C₄×C₅₉⋊C₈	C₂³	1	2	yes	—
82	C₈×Dic₅₉	—	2	2	no	—
83	C₂²×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
84	C₂²×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
85	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
86	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
87	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
88	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
89	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
90	C₂²⋊C₈×C₅₉	—	2	1	no	—
91	C₂²⋊C₈×C₅₉	—	2	1	no	—
92	C₄×C₈×C₅₉	—	2	1	no	—
93	C₄×C₈×C₅₉	—	2	1	no	—
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	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₅₉	C₂×Q₈	1	1	yes	characteristic
101	C₂×C₂²⋊D₅₉	C₄⋊C₄	1	2	yes	—
102	#11745685	—	2	2	no	—
103	#11745685	—	2	2	no	—
104	C₂×D₂₃₆	C₄⋊C₄	1	1	yes	characteristic
105	C₂×C₄×D₅₉	C₂²×C₄	1	2	yes	—
106	C₂×C₄×D₅₉	C₂×D₄	1	2	yes	—
107	C₂×C₄×D₅₉	C₂×Q₈	1	2	yes	—
108	C₂×Dic₁₁₈	C₄⋊C₄	1	1	yes	characteristic
109	C₂×C₈×C₅₉	—	2	2	no	—
110	C₂×C₈×C₅₉	—	2	2	no	—
111	C₂×C₈×C₅₉	—	2	1	no	—
112	C₂×C₈×C₅₉	—	2	1	no	—
113	C₂×C₈×C₅₉	—	2	1	no	—
114	C₂×C₈×C₅₉	—	2	1	no	—
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	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
119	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
120	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
121	C₄²×C₅₉	C₂×Q₈	1	1	yes	characteristic
122	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
123	C₂²⋊Dic₅₉	C₄⋊C₄	1	2	yes	—
124	(C₂×D₅₉)⋊C₄	C₄⋊C₄	1	2	yes	—
125	(C₂×D₅₉)⋊C₄	C₄⋊C₄	1	2	yes	—
126	C₄⋊Dic₅₉	C₄⋊C₄	1	1	yes	characteristic
127	C₄⋊Dic₅₉	C₄⋊C₄	1	1	yes	characteristic
128	Dic₅₉⋊C₄	C₄⋊C₄	1	2	yes	—
129	Dic₅₉⋊C₄	C₄⋊C₄	1	2	yes	—
130	C₄×Dic₅₉	C₂²×C₄	1	2	yes	—
131	C₄×Dic₅₉	C₂×D₄	1	2	yes	—
132	C₄×Dic₅₉	C₂×Q₈	1	2	yes	—
133	#11745664	—	2	2	no	—
134	#11745664	—	2	2	no	—
135	C₂×C₅₉⋊C₈	—	2	2	no	—
136	C₂×C₅₉⋊C₈	—	2	2	no	—
137	C₂×C₅₉⋊C₈	—	8	1	no	—
138	C₂×C₅₉⋊C₈	—	8	1	no	—
139	C₂×C₅₉⋊C₈	C₂²×C₄	1	2	yes	—
140	C₂×C₅₉⋊C₈	C₂²×C₄	1	2	yes	—
141	#11745659	—	8	2	no	—
142	C₈×D₅₉	—	8	2	no	—
143	C₂³×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
144	C₂²×D₅₉	C₂×C₄⋊C₄	1	2	yes	—
145	C₂×C₄×C₅₉	—	2	1	no	—
146	C₂×C₄×C₅₉	—	2	1	no	—
147	C₂×C₄×C₅₉	—	4	1	no	—
148	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
149	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
151	C₂×C₄×C₅₉	#131	1	2	yes	—
152	C₂×C₄×C₅₉	#131	1	2	yes	—
153	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
154	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
155	C₂×C₄×C₅₉	C₂²×Q₈	1	1	yes	characteristic
156	C₂²⋊D₅₉	—	2	4	no	—
157	C₂×Dic₅₉	C₂×C₄⋊C₄	1	2	yes	—
158	C₂×Dic₅₉	C₂×C₄⋊C₄	1	2	yes	—
159	C₂×Dic₅₉	C₂×C₄⋊C₄	1	2	yes	—
160	D₂₃₆	—	2	2	no	—
161	C₄×D₅₉	—	2	2	no	—
162	C₄×D₅₉	—	2	2	no	—
163	C₄×D₅₉	—	2	2	no	—
164	C₄×D₅₉	—	2	2	no	—
165	C₄×D₅₉	—	4	2	no	—
166	Dic₁₁₈	—	2	2	no	—
167	C₈×C₅₉	—	2	1	no	—
168	C₈×C₅₉	—	2	1	no	—
169	C₈×C₅₉	—	2	1	no	—
170	C₈×C₅₉	—	2	1	no	—
171	C₈×C₅₉	—	4	1	no	—
172	C₈×C₅₉	—	4	1	no	—
173	C₈×C₅₉	—	4	1	no	—
174	C₈×C₅₉	—	4	1	no	—
175	C₅₉⋊C₈	—	2	2	no	—
176	C₅₉⋊C₈	—	2	2	no	—
177	C₅₉⋊C₈	—	4	2	no	—
178	C₅₉⋊C₈	—	4	2	no	—
179	#17812	—	59	1	no	maximal, Sylow
180	C₂²×C₅₉	—	2	1	no	—
181	C₂²×C₅₉	—	2	1	no	—
182	C₂²×C₅₉	#424	1	2	yes	—
183	C₂²×C₅₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
184	C₂×D₅₉	—	2	2	no	—
185	C₂×D₅₉	—	2	2	no	—
186	C₂×D₅₉	—	2	2	no	—
187	C₄×C₅₉	—	2	1	no	—
188	C₄×C₅₉	—	2	1	no	—
189	C₄×C₅₉	—	2	1	no	—
190	C₄×C₅₉	#424	1	2	yes	—
191	C₄×C₅₉	C₂×#131	1	1	yes	characteristic
192	C₄×C₅₉	C₂×#131	1	1	yes	characteristic
193	C₄×C₅₉	#576	1	1	yes	characteristic
194	C₄×C₅₉	#578	1	1	yes	characteristic
195	Dic₅₉	—	2	2	no	—
196	Dic₅₉	—	2	2	no	—
197	Dic₅₉	—	2	2	no	—
198	#2989	—	59	1	no	—
199	#2988	—	59	1	no	—
200	#2922	—	59	1	no	—
201	#1574	—	59	2	no	—
202	#1573	—	59	2	no	—
203	#1572	—	59	2	no	—
204	#1571	—	59	2	no	—
205	#1565	—	59	1	no	—
206	#1565	—	59	1	no	—
207	#1564	D₅₉	1	1	yes	characteristic, complemented
208	C₂×#335	—	59	1	no	—
209	C₂×C₅₉	—	2	2	no	—
210	C₂×C₅₉	C₂×#424	1	1	yes	characteristic
211	C₂×C₅₉	#2913	1	1	yes	characteristic
212	C₂×C₅₉	#2916	1	1	yes	characteristic
213	D₅₉	—	4	2	no	—
214	C₄×#41	—	59	1	no	—
215	#446	—	118	1	no	—
216	C₈×Q₈	—	118	1	no	—
217	#436	—	118	1	no	—
218	#435	—	118	2	no	—
219	C₈×D₄	—	118	1	no	—
220	C₈×D₄	—	118	2	no	—
221	#433	—	59	2	no	—
222	#433	—	59	2	no	—
223	#432	—	59	2	no	—
224	#431	—	59	2	no	—
225	#431	—	59	2	no	—
226	#431	—	59	2	no	—
227	#431	C₂×D₅₉	1	1	yes	characteristic
228	#431	C₂×D₅₉	1	1	yes	characteristic
229	#424	—	59	1	no	—
230	#424	—	59	1	no	—
231	#423	—	59	2	no	—
232	C₂×C₄⋊C₈	—	59	1	no	—
233	C₂×C₄⋊C₈	—	59	1	no	—
234	C₂×C₄⋊C₈	—	59	2	no	—
235	#408	—	59	1	no	—
236	#408	—	59	1	no	—
237	C₄×M₁₆	—	59	1	no	—
238	C₂×C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
239	#335	—	59	2	no	—
240	#335	—	59	2	no	—
241	#335	—	59	2	no	—
242	#335	—	59	2	no	—
243	#335	C₂×D₅₉	1	1	yes	characteristic
244	#335	C₂×D₅₉	1	1	yes	characteristic
245	#334	—	59	2	no	—
246	#334	—	59	2	no	—
247	#334	C₂×D₅₉	1	1	yes	characteristic
248	#334	C₂×D₅₉	1	1	yes	characteristic
249	C₅₉	#17812	1	1	yes	characteristic, complemented, Sylow
250	C₂×#41	—	59	1	no	—
251	C₂×M₁₆	—	59	1	no	—
252	C₂×M₁₆	—	59	1	no	—
253	C₂×M₁₆	—	118	2	no	—
254	C₂²×C₈	—	118	2	no	—
255	C₂²×C₈	—	118	1	no	—
256	C₂²×C₈	—	118	1	no	—
257	C₂²×C₈	C₄×D₅₉	1	1	yes	characteristic
258	C₂²×C₈	C₄×D₅₉	1	1	yes	characteristic
259	C₄×Q₈	—	59	1	no	—
260	C₄×Q₈	—	59	1	no	—
261	C₄×D₄	—	59	2	no	—
262	C₄×D₄	—	59	2	no	—
263	C₄×D₄	—	59	1	no	—
264	C₄×D₄	—	59	1	no	—
265	#117	—	59	1	no	—
266	#117	—	59	2	no	—
267	C₂×C₄²	—	59	2	no	—
268	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
269	C₄⋊C₈	—	59	2	no	—
270	C₄⋊C₈	—	59	2	no	—
271	C₄⋊C₈	—	59	2	no	—
272	C₄⋊C₈	—	59	2	no	—
273	C₄⋊C₈	—	59	2	no	—
274	C₄⋊C₈	—	59	2	no	—
275	C₄⋊C₈	—	118	2	no	—
276	C₄⋊C₈	—	118	2	no	—
277	C₄⋊C₈	—	118	1	no	—
278	C₄⋊C₈	—	118	1	no	—
279	C₄⋊C₈	C₂²×D₅₉	1	1	yes	characteristic
280	C₄⋊C₈	C₂²×D₅₉	1	1	yes	characteristic
281	C₄⋊C₈	C₂²×D₅₉	1	1	yes	characteristic
282	C₄⋊C₈	C₂²×D₅₉	1	1	yes	characteristic
283	C₂²⋊C₈	—	2	1	no	—
284	C₂²⋊C₈	—	2	1	no	—
285	C₂²⋊C₈	—	59	2	no	—
286	C₂²⋊C₈	—	59	2	no	—
287	C₂²⋊C₈	—	59	2	no	—
288	C₂²⋊C₈	—	59	2	no	—
289	C₂²⋊C₈	—	118	2	no	—
290	C₂²⋊C₈	—	118	2	no	—
291	#97	—	59	2	no	—
292	#97	—	118	2	no	—
293	C₄×C₈	—	2	1	no	—
294	C₄×C₈	—	2	1	no	—
295	C₄×C₈	—	59	2	no	—
296	C₄×C₈	—	118	2	no	—
297	C₄×C₈	C₄×D₅₉	1	1	yes	characteristic
298	C₄×C₈	C₄×D₅₉	1	1	yes	characteristic
299	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
300	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
301	#41	—	118	2	no	—
302	#41	—	118	2	no	—
303	C₂×Q₈	—	59	1	no	—
304	C₂×D₄	—	59	2	no	—
305	C₂×D₄	—	59	1	no	—
306	C₂²×C₄	—	59	2	no	—
307	C₂²×C₄	—	59	2	no	—
308	C₂²×C₄	—	59	2	no	—
309	C₂²×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
310	C₂²×C₄	D₄×D₅₉	1	1	yes	characteristic
311	C₂²×C₄	Q₈×D₅₉	1	1	yes	characteristic
312	M₁₆	—	118	2	no	—
313	M₁₆	—	118	2	no	—
314	M₁₆	—	472	2	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	—	2	1	no	—
318	C₂×C₈	—	2	1	no	—
319	C₂×C₈	—	2	1	no	—
320	C₂×C₈	—	2	1	no	—
321	C₂×C₈	—	59	2	no	—
322	C₂×C₈	—	59	2	no	—
323	C₂×C₈	—	118	2	no	—
324	C₂×C₈	—	118	2	no	—
325	C₂×C₈	—	472	2	no	—
326	C₂×C₈	—	472	1	no	—
327	C₂×C₈	—	472	1	no	—
328	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
329	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
330	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
331	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
332	C₄⋊C₄	—	59	2	no	—
333	C₄⋊C₄	—	59	2	no	—
334	C₄⋊C₄	—	59	1	no	—
335	C₄⋊C₄	—	59	1	no	—
336	C₂²⋊C₄	—	59	2	no	—
337	C₂²⋊C₄	—	59	2	no	—
338	C₂²⋊C₄	—	59	2	no	—
339	C₄²	—	59	2	no	—
340	C₄²	—	59	2	no	—
341	C₄²	—	59	2	no	—
342	C₄²	C₂×C₄×D₅₉	1	1	yes	characteristic
343	C₄²	D₄×D₅₉	1	1	yes	characteristic
344	C₄²	Q₈×D₅₉	1	1	yes	characteristic
345	C₄²	C₂³×D₅₉	1	1	yes	characteristic
346	C₂³	—	59	2	no	—
347	C₂³	C₄⋊C₄×D₅₉	1	1	yes	characteristic
348	Q₈	—	118	2	no	—
349	D₄	—	118	4	no	—
350	D₄	—	118	2	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	4	1	no	—
354	C₂×C₄	—	59	2	no	—
355	C₂×C₄	—	59	2	no	—
356	C₂×C₄	—	59	2	no	—
357	C₂×C₄	—	118	2	no	—
358	C₂×C₄	—	118	2	no	—
359	C₂×C₄	—	118	2	no	—
360	C₂×C₄	—	118	2	no	—
361	C₂×C₄	—	236	2	no	—
362	C₂×C₄	C₄⋊C₄×D₅₉	1	1	yes	characteristic
363	C₂×C₄	C₄⋊C₄×D₅₉	1	1	yes	characteristic
364	C₂×C₄	C₄⋊C₄×D₅₉	1	1	yes	characteristic
365	C₂×C₄	#14273733	1	2	yes	—
366	C₂×C₄	#14273735	1	2	yes	—
367	C₂×C₄	C₂²×C₄×D₅₉	1	1	yes	characteristic
368	C₂×C₄	C₂×D₄×D₅₉	1	1	yes	characteristic
369	C₂×C₄	C₂×Q₈×D₅₉	1	1	yes	characteristic
370	C₈	—	2	1	no	—
371	C₈	—	2	1	no	—
372	C₈	—	2	1	no	—
373	C₈	—	2	1	no	—
374	C₈	—	4	1	no	—
375	C₈	—	4	1	no	—
376	C₈	—	4	1	no	—
377	C₈	—	4	1	no	—
378	C₈	—	118	2	no	—
379	C₈	—	118	2	no	—
380	C₈	—	236	2	no	—
381	C₈	—	236	2	no	—
382	C₂²	—	2	1	no	—
383	C₂²	—	2	1	no	—
384	C₂²	—	118	2	no	—
385	C₂²	—	118	2	no	—
386	C₂²	—	118	2	no	—
387	C₂²	#16837427	1	2	yes	—
388	C₂²	C₂×C₄⋊C₄×D₅₉	1	1	yes	characteristic
389	C₄	—	2	1	no	—
390	C₄	—	2	1	no	—
391	C₄	—	2	1	no	—
392	C₄	—	118	2	no	—
393	C₄	—	118	2	no	—
394	C₄	—	118	2	no	—
395	C₄	#16837427	1	2	yes	—
396	C₄	C₂×#14273733	1	1	yes	characteristic
397	C₄	C₂×#14273735	1	1	yes	characteristic
398	C₄	#16838204	1	1	yes	characteristic
399	C₄	#16838216	1	1	yes	characteristic
400	C₂	—	2	2	no	—
401	C₂	—	236	2	no	—
402	C₂	C₂×#16837427	1	1	yes	characteristic
403	C₂	#21432693	1	1	yes	characteristic
404	C₂	#21432704	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×#1564	C₂
socle	C₂²×C₅₉	C₂²×C₄⋊C₄
prime radical	C₂×#11745685	C₂×C₄
cosocle	C₄²×C₅₉	C₂⁴
hypercenter	#1564	D₅₉
hypocenter	C₅₉	#17812
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1564

Complements

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

N	H ≅ G/N	type
4. #21422883	C₂	semidirect
5. #21422878	C₂	semidirect
6. #21422875	C₂	semidirect
7. #21422869	C₂	semidirect
8. #21422849	C₂	semidirect
9. #21422849	C₂	semidirect
10. C₂×#16837155	C₂	semidirect
11. C₅₉×#1564	C₂	semidirect
207. #1564	D₅₉	semidirect
249. C₅₉	#17812	semidirect

Maximal subgroups

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

subgroup	index
#21433209	2
#21433204	2
#21432738	2
#21422883	2
#21422878	2
#21422875	2
#21422869	2
#21422849	2
C₂×#16837155	2
C₅₉×#1564	2
#17812	59