Subgroups — #28559908

Order 15104.

598 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21433228	C₂	1	1	yes	maximal, characteristic
2	#21433198	C₂	1	1	yes	maximal, characteristic, complemented
3	#21422987	C₂	1	2	yes	maximal, complemented
4	#21422975	C₂	1	2	yes	maximal, complemented
5	#21422968	C₂	1	2	yes	maximal, complemented
6	Q₁₆×C₅₉⋊C₈	C₂	1	2	yes	maximal, complemented
7	#21422885	C₂	1	1	yes	maximal, characteristic, complemented
8	#21422551	C₂	1	1	yes	maximal, characteristic, complemented
9	#21422478	C₂	1	1	yes	maximal, characteristic
10	#21422380	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#3107	C₂	1	1	yes	maximal, characteristic
12	#16837533	—	2	1	no	—
13	#16837533	C₂²	1	2	yes	—
14	Q₈×C₅₉⋊C₈	—	2	1	no	—
15	Q₈×C₅₉⋊C₈	C₂²	1	2	yes	—
16	Q₈×C₅₉⋊C₈	C₂²	1	2	yes	—
17	#16837480	—	2	2	no	—
18	#16837480	C₂²	1	2	yes	—
19	#16837463	—	2	2	no	—
20	#16837455	—	2	1	no	—
21	#16837455	C₂²	1	1	yes	characteristic
22	#16837455	C₂²	1	1	yes	characteristic
23	#16837426	—	2	1	no	—
24	#16837426	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
26	#16837155	C₂²	1	2	yes	—
27	#16837153	C₂²	1	2	yes	—
28	Q₈⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
29	Q₈⋊(C₅₉⋊C₈)	C₂²	1	2	yes	—
30	Q₈⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
31	Q₈⋊(C₅₉⋊C₈)	C₂²	1	2	yes	—
32	D₄⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
33	D₄⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
34	#16837124	C₂²	1	2	yes	—
35	C₈×C₅₉⋊C₈	C₂²	1	2	yes	—
36	C₅₉×#533	C₂²	1	1	yes	characteristic
37	C₄×#41×C₅₉	C₂²	1	1	yes	characteristic
38	C₅₉×#485	C₄	1	2	yes	—
39	C₅₉×#475	C₄	1	1	yes	characteristic
40	C₅₉×#474	C₄	1	1	yes	characteristic
41	C₅₉×#462	C₄	1	1	yes	characteristic
42	C₅₉×#461	C₄	1	1	yes	characteristic
43	C₅₉×#452	C₄	1	2	yes	—
44	C₄×Q₁₆×C₅₉	C₂²	1	2	yes	—
45	C₄×SD₁₆×C₅₉	C₂²	1	2	yes	—
46	C₅₉×#431	C₂²	1	1	yes	characteristic
47	C₂×#11745664	—	2	1	no	—
48	C₂×#11745664	—	2	2	no	—
49	C₂²×C₅₉⋊C₈	—	2	1	no	—
50	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
51	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
52	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
53	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
54	C₄⋊(C₅₉⋊C₈)	D₄	1	1	yes	characteristic
55	C₄⋊(C₅₉⋊C₈)	D₄	1	1	yes	characteristic
56	C₄⋊(C₅₉⋊C₈)	C₂³	1	1	yes	characteristic
57	C₄⋊(C₅₉⋊C₈)	C₂³	1	1	yes	characteristic
58	C₄⋊(C₅₉⋊C₈)	C₂³	1	2	yes	—
59	C₂²⋊(C₅₉⋊C₈)	—	2	1	no	—
60	C₂²⋊(C₅₉⋊C₈)	—	2	2	no	—
61	C₂²⋊(C₅₉⋊C₈)	D₄	1	2	yes	—
62	#14273638	—	2	2	no	—
63	C₄×C₅₉⋊C₈	—	2	1	no	—
64	C₄×C₅₉⋊C₈	—	2	1	no	—
65	C₄×C₅₉⋊C₈	—	2	2	no	—
66	C₄×C₅₉⋊C₈	—	2	2	no	—
67	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
68	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
69	C₄×C₅₉⋊C₈	C₂³	1	2	yes	—
70	C₂×#41×C₅₉	C₂×C₄	1	1	yes	characteristic
71	C₂×Q₁₆×C₅₉	C₂×C₄	1	2	yes	—
72	C₂×SD₁₆×C₅₉	C₂×C₄	1	2	yes	—
73	C₄⋊Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
74	C₄⋊Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
75	#125×C₅₉	—	2	1	no	—
76	C₂²⋊Q₈×C₅₉	—	2	1	no	—
77	C₂²⋊Q₈×C₅₉	C₂×C₄	1	2	yes	—
78	C₄×Q₈×C₅₉	—	2	1	no	—
79	C₄×Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
80	C₄×Q₈×C₅₉	C₂³	1	2	yes	—
81	C₄×Q₈×C₅₉	C₂³	1	1	yes	characteristic
82	C₄×D₄×C₅₉	—	2	1	no	—
83	C₄×D₄×C₅₉	—	2	1	no	—
84	C₄×D₄×C₅₉	C₂×C₄	1	1	yes	characteristic
85	C₄×D₄×C₅₉	C₂³	1	1	yes	characteristic
86	#117×C₅₉	—	2	1	no	—
87	#117×C₅₉	—	2	1	no	—
88	#117×C₅₉	C₂×C₄	1	1	yes	characteristic
89	C₂×C₄²×C₅₉	—	2	1	no	—
90	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
91	#107×C₅₉	C₂×C₄	1	2	yes	—
92	#106×C₅₉	C₂×C₄	1	2	yes	—
93	C₄⋊C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
94	C₄⋊C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
95	#103×C₅₉	C₂×C₄	1	2	yes	—
96	#103×C₅₉	C₂×C₄	1	2	yes	—
97	#103×C₅₉	C₂×C₄	1	2	yes	—
98	#102×C₅₉	C₂×C₄	1	2	yes	—
99	C₂²⋊C₈×C₅₉	C₂×C₄	1	2	yes	—
100	C₄×C₈×C₅₉	C₂³	1	2	yes	—
101	#41×C₅₉	—	2	2	no	—
102	#41×C₅₉	—	4	1	no	—
103	C₂×Q₈×C₅₉	—	2	1	no	—
104	C₂×Q₈×C₅₉	C₂²×C₄	1	2	yes	—
105	C₂×Q₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
106	C₂×D₄×C₅₉	—	2	1	no	—
107	C₂×D₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₅₉	—	2	1	no	—
109	C₂²×C₄×C₅₉	—	2	1	no	—
110	C₂²×C₄×C₅₉	—	2	1	no	—
111	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
112	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
114	Q₁₆×C₅₉	—	2	4	no	—
115	SD₁₆×C₅₉	—	4	2	no	—
116	C₂×C₈×C₅₉	C₂²×C₄	1	2	yes	—
117	C₂×C₈×C₅₉	C₂²×C₄	1	2	yes	—
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	1	no	—
124	C₄⋊C₄×C₅₉	—	2	2	no	—
125	C₄⋊C₄×C₅₉	C₂²×C₄	1	2	yes	—
126	C₄⋊C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
127	C₄⋊C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
128	C₂²⋊C₄×C₅₉	—	2	2	no	—
129	C₂²⋊C₄×C₅₉	—	2	1	no	—
130	C₂²⋊C₄×C₅₉	—	2	1	no	—
131	C₂²⋊C₄×C₅₉	—	2	1	no	—
132	C₄²×C₅₉	—	2	1	no	—
133	C₄²×C₅₉	—	2	1	no	—
134	C₄²×C₅₉	—	2	1	no	—
135	C₄²×C₅₉	—	2	2	no	—
136	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
137	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
138	C₄²×C₅₉	#41	1	1	yes	characteristic
139	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
140	#11745664	—	8	2	no	—
141	#11745664	—	8	1	no	—
142	C₂×C₅₉⋊C₈	—	2	4	no	—
143	C₂×C₅₉⋊C₈	—	2	1	no	—
144	C₂×C₅₉⋊C₈	—	2	1	no	—
145	C₂×C₅₉⋊C₈	—	2	1	no	—
146	C₂×C₅₉⋊C₈	—	2	1	no	—
147	C₂×C₅₉⋊C₈	—	2	2	no	—
148	C₂×C₅₉⋊C₈	C₂×D₄	1	2	yes	—
149	C₂×C₅₉⋊C₈	C₂×D₄	1	2	yes	—
150	C₂³×C₅₉	—	2	1	no	—
151	C₂³×C₅₉	C₄×D₄	1	1	yes	characteristic
152	Q₈×C₅₉	—	2	1	no	—
153	Q₈×C₅₉	—	2	2	no	—
154	Q₈×C₅₉	—	2	2	no	—
155	Q₈×C₅₉	—	4	2	no	—
156	Q₈×C₅₉	#131	1	2	yes	—
157	D₄×C₅₉	—	2	1	no	—
158	D₄×C₅₉	—	2	1	no	—
159	D₄×C₅₉	—	4	2	no	—
160	C₂×C₄×C₅₉	—	2	1	no	—
161	C₂×C₄×C₅₉	—	2	1	no	—
162	C₂×C₄×C₅₉	—	2	1	no	—
163	C₂×C₄×C₅₉	—	2	1	no	—
164	C₂×C₄×C₅₉	—	2	1	no	—
165	C₂×C₄×C₅₉	—	2	2	no	—
166	C₂×C₄×C₅₉	—	2	1	no	—
167	C₂×C₄×C₅₉	—	2	1	no	—
168	C₂×C₄×C₅₉	—	2	2	no	—
169	C₂×C₄×C₅₉	—	2	2	no	—
170	C₂×C₄×C₅₉	—	4	2	no	—
171	C₂×C₄×C₅₉	—	4	1	no	—
172	C₂×C₄×C₅₉	—	4	1	no	—
173	C₂×C₄×C₅₉	—	4	2	no	—
174	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
175	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
176	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
177	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
178	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
179	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
180	C₈×C₅₉	—	2	2	no	—
181	C₈×C₅₉	—	2	2	no	—
182	C₅₉⋊C₈	—	2	2	no	—
183	C₅₉⋊C₈	—	2	2	no	—
184	C₅₉⋊C₈	—	2	2	no	—
185	C₅₉⋊C₈	—	2	2	no	—
186	C₅₉⋊C₈	—	4	1	no	—
187	C₅₉⋊C₈	—	4	2	no	—
188	C₅₉⋊C₈	—	4	1	no	—
189	#18019	—	59	1	no	maximal, Sylow
190	C₂²×C₅₉	—	2	1	no	—
191	C₂²×C₅₉	—	2	1	no	—
192	C₂²×C₅₉	—	2	1	no	—
193	C₂²×C₅₉	—	4	1	no	—
194	C₂²×C₅₉	—	4	1	no	—
195	C₂²×C₅₉	—	4	1	no	—
196	C₂²×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
197	C₄×C₅₉	—	2	1	no	—
198	C₄×C₅₉	—	2	2	no	—
199	C₄×C₅₉	—	2	1	no	—
200	C₄×C₅₉	—	2	1	no	—
201	C₄×C₅₉	—	4	2	no	—
202	C₄×C₅₉	—	4	1	no	—
203	C₄×C₅₉	—	4	1	no	—
204	C₄×C₅₉	—	4	2	no	—
205	C₄×C₅₉	#443	1	2	yes	—
206	C₄×C₅₉	C₂×#131	1	1	yes	characteristic
207	C₄×C₅₉	#568	1	1	yes	characteristic
208	C₄×C₅₉	#577	1	1	yes	characteristic
209	C₄×C₅₉	#578	1	1	yes	characteristic
210	#3107	D₅₉	1	1	yes	characteristic
211	#2991	—	59	1	no	—
212	#2986	—	59	1	no	—
213	#1590	—	59	2	no	—
214	#1588	—	59	2	no	—
215	#1587	—	59	2	no	—
216	C₈×Q₁₆	—	59	2	no	—
217	#1574	—	59	1	no	—
218	#1493	—	59	1	no	—
219	#1476	—	59	1	no	—
220	#1450	—	59	1	no	—
221	C₂×C₅₉	—	4	1	no	—
222	C₂×C₅₉	—	8	1	no	—
223	C₂×C₅₉	#2933	1	1	yes	characteristic
224	C₂×C₅₉	#2947	1	1	yes	characteristic
225	C₂×C₅₉	C₂×#443	1	1	yes	characteristic
226	#533	C₂×D₅₉	1	1	yes	characteristic
227	C₄×#41	C₂×D₅₉	1	1	yes	characteristic
228	#485	Dic₅₉	1	2	yes	—
229	#475	Dic₅₉	1	1	yes	characteristic
230	#474	Dic₅₉	1	1	yes	characteristic
231	#462	Dic₅₉	1	1	yes	characteristic
232	#461	Dic₅₉	1	1	yes	characteristic
233	#452	Dic₅₉	1	2	yes	—
234	#446	—	59	2	no	—
235	#446	—	118	1	no	—
236	C₈×Q₈	—	59	2	no	—
237	C₈×Q₈	—	59	2	no	—
238	C₈×Q₈	—	118	1	no	—
239	C₄×Q₁₆	C₂×D₅₉	1	2	yes	—
240	C₄×SD₁₆	C₂×D₅₉	1	2	yes	—
241	#436	—	59	2	no	—
242	#436	—	118	2	no	—
243	#433	—	118	2	no	—
244	#431	—	59	1	no	—
245	#431	—	59	1	no	—
246	#431	—	118	1	no	—
247	#431	C₂×D₅₉	1	1	yes	characteristic
248	#423	—	59	1	no	—
249	#423	—	118	1	no	—
250	C₂×C₄×C₈	—	59	1	no	—
251	#335	—	59	2	no	—
252	#334	—	59	2	no	—
253	Q₈⋊C₈	—	59	1	no	—
254	Q₈⋊C₈	—	59	2	no	—
255	Q₈⋊C₈	—	59	1	no	—
256	Q₈⋊C₈	—	59	2	no	—
257	D₄⋊C₈	—	59	1	no	—
258	D₄⋊C₈	—	59	1	no	—
259	#322	—	59	2	no	—
260	C₈²	—	59	2	no	—
261	C₅₉	#18019	1	1	yes	characteristic, complemented, Sylow
262	C₂×#41	C₂×Dic₅₉	1	1	yes	characteristic
263	C₂×Q₁₆	C₂×Dic₅₉	1	2	yes	—
264	C₂×SD₁₆	C₂×Dic₅₉	1	2	yes	—
265	C₂×M₁₆	—	118	2	no	—
266	C₂×M₁₆	—	118	1	no	—
267	C₂²×C₈	—	118	1	no	—
268	C₄⋊Q₈	C₂×Dic₅₉	1	1	yes	characteristic
269	C₄⋊Q₈	C₂×Dic₅₉	1	1	yes	characteristic
270	#125	—	2	1	no	—
271	C₂²⋊Q₈	—	2	1	no	—
272	C₂²⋊Q₈	C₂×Dic₅₉	1	2	yes	—
273	C₄×Q₈	—	2	1	no	—
274	C₄×Q₈	C₂×Dic₅₉	1	1	yes	characteristic
275	C₄×Q₈	C₂²×D₅₉	1	1	yes	characteristic
276	C₄×Q₈	C₂²×D₅₉	1	2	yes	—
277	C₄×D₄	—	2	1	no	—
278	C₄×D₄	—	2	1	no	—
279	C₄×D₄	C₂×Dic₅₉	1	1	yes	characteristic
280	C₄×D₄	C₂²×D₅₉	1	1	yes	characteristic
281	#117	—	2	1	no	—
282	#117	—	2	1	no	—
283	#117	C₂×Dic₅₉	1	1	yes	characteristic
284	C₂×C₄²	—	2	1	no	—
285	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
286	#107	C₂×Dic₅₉	1	2	yes	—
287	#106	C₂×Dic₅₉	1	2	yes	—
288	C₄⋊C₈	—	59	1	no	—
289	C₄⋊C₈	—	59	1	no	—
290	C₄⋊C₈	—	59	1	no	—
291	C₄⋊C₈	—	59	1	no	—
292	C₄⋊C₈	—	59	2	no	—
293	C₄⋊C₈	—	118	2	no	—
294	C₄⋊C₈	—	118	2	no	—
295	C₄⋊C₈	—	118	2	no	—
296	C₄⋊C₈	—	118	1	no	—
297	C₄⋊C₈	C₂×Dic₅₉	1	1	yes	characteristic
298	C₄⋊C₈	C₂×Dic₅₉	1	1	yes	characteristic
299	#103	C₂×Dic₅₉	1	2	yes	—
300	#103	C₂×Dic₅₉	1	2	yes	—
301	#103	C₂×Dic₅₉	1	2	yes	—
302	#102	C₂×Dic₅₉	1	2	yes	—
303	C₂²⋊C₈	—	59	2	no	—
304	C₂²⋊C₈	—	118	2	no	—
305	C₂²⋊C₈	—	118	1	no	—
306	C₂²⋊C₈	C₂×Dic₅₉	1	2	yes	—
307	#97	—	118	2	no	—
308	C₄×C₈	—	59	2	no	—
309	C₄×C₈	—	59	1	no	—
310	C₄×C₈	—	59	1	no	—
311	C₄×C₈	—	118	2	no	—
312	C₄×C₈	—	118	2	no	—
313	C₄×C₈	—	118	1	no	—
314	C₄×C₈	—	118	1	no	—
315	C₄×C₈	C₂²×D₅₉	1	2	yes	—
316	#41	—	2	2	no	—
317	#41	—	4	1	no	—
318	C₂×Q₈	—	2	1	no	—
319	C₂×Q₈	C₂²×Dic₅₉	1	2	yes	—
320	C₂×Q₈	C₂²×Dic₅₉	1	1	yes	characteristic
321	C₂×D₄	—	2	1	no	—
322	C₂×D₄	C₂²×Dic₅₉	1	1	yes	characteristic
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	D₄×D₅₉	1	1	yes	characteristic
327	C₂²×C₄	#11745687	1	1	yes	characteristic
328	C₂²×C₄	C₂²×Dic₅₉	1	1	yes	characteristic
329	Q₁₆	—	2	4	no	—
330	SD₁₆	—	4	2	no	—
331	M₁₆	—	472	2	no	—
332	M₁₆	—	472	1	no	—
333	C₂×C₈	—	59	2	no	—
334	C₂×C₈	—	59	2	no	—
335	C₂×C₈	—	118	4	no	—
336	C₂×C₈	—	118	1	no	—
337	C₂×C₈	—	118	1	no	—
338	C₂×C₈	—	118	1	no	—
339	C₂×C₈	—	118	1	no	—
340	C₂×C₈	—	118	2	no	—
341	C₂×C₈	C₂²×Dic₅₉	1	2	yes	—
342	C₂×C₈	C₂²×Dic₅₉	1	2	yes	—
343	C₄⋊C₄	—	2	1	no	—
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	2	1	no	—
346	C₄⋊C₄	—	2	1	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	2	1	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	C₂²×Dic₅₉	1	2	yes	—
351	C₄⋊C₄	C₂²×Dic₅₉	1	1	yes	characteristic
352	C₄⋊C₄	C₂²×Dic₅₉	1	1	yes	characteristic
353	C₂²⋊C₄	—	2	2	no	—
354	C₂²⋊C₄	—	2	1	no	—
355	C₂²⋊C₄	—	2	1	no	—
356	C₂²⋊C₄	—	2	1	no	—
357	C₄²	—	2	1	no	—
358	C₄²	—	2	1	no	—
359	C₄²	—	2	1	no	—
360	C₄²	—	2	2	no	—
361	C₄²	D₄×D₅₉	1	1	yes	characteristic
362	C₄²	#11745687	1	1	yes	characteristic
363	C₄²	C₂²×Dic₅₉	1	1	yes	characteristic
364	C₄²	C₂³×D₅₉	1	1	yes	characteristic
365	C₂³	—	2	1	no	—
366	C₂³	D₄×Dic₅₉	1	1	yes	characteristic
367	Q₈	—	2	1	no	—
368	Q₈	—	2	2	no	—
369	Q₈	—	2	2	no	—
370	Q₈	—	4	2	no	—
371	Q₈	#14273734	1	2	yes	—
372	D₄	—	2	1	no	—
373	D₄	—	2	1	no	—
374	D₄	—	4	2	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	D₄×Dic₅₉	1	1	yes	characteristic
390	C₂×C₄	D₄×Dic₅₉	1	1	yes	characteristic
391	C₂×C₄	D₄×Dic₅₉	1	1	yes	characteristic
392	C₂×C₄	C₂³×Dic₅₉	1	1	yes	characteristic
393	C₂×C₄	C₂×D₄×D₅₉	1	1	yes	characteristic
394	C₂×C₄	C₂×#11745687	1	1	yes	characteristic
395	C₈	—	2	2	no	—
396	C₈	—	2	2	no	—
397	C₈	—	118	2	no	—
398	C₈	—	118	2	no	—
399	C₈	—	118	2	no	—
400	C₈	—	118	2	no	—
401	C₈	—	236	1	no	—
402	C₈	—	236	2	no	—
403	C₈	—	236	1	no	—
404	C₂²	—	2	1	no	—
405	C₂²	—	2	1	no	—
406	C₂²	—	2	1	no	—
407	C₂²	—	4	1	no	—
408	C₂²	—	4	1	no	—
409	C₂²	—	4	1	no	—
410	C₂²	C₂×D₄×Dic₅₉	1	1	yes	characteristic
411	C₄	—	2	1	no	—
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	2	2	no	—
415	C₄	—	4	1	no	—
416	C₄	—	4	1	no	—
417	C₄	—	4	2	no	—
418	C₄	—	4	2	no	—
419	C₄	#16837519	1	2	yes	—
420	C₄	C₂×#14273734	1	1	yes	characteristic
421	C₄	#16838169	1	1	yes	characteristic
422	C₄	#16838211	1	1	yes	characteristic
423	C₄	#16838218	1	1	yes	characteristic
424	C₂	—	4	1	no	—
425	C₂	—	8	1	no	—
426	C₂	#21432823	1	1	yes	characteristic
427	C₂	#21432940	1	1	yes	characteristic
428	C₂	C₂×#16837519	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×#3107	C₂
socle	C₂²×C₅₉	C₂×C₄×D₄
prime radical	C₂×#41×C₅₉	C₂×C₄
cosocle	C₄²×C₅₉	C₂⁴
hypercenter	#3107	D₅₉
hypocenter	C₅₉	#18019
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3107

Complements

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

N	H ≅ G/N	type
2. #21433198	C₂	semidirect
3. #21422987	C₂	semidirect
4. #21422975	C₂	semidirect
5. #21422968	C₂	semidirect
6. Q₁₆×C₅₉⋊C₈	C₂	semidirect
7. #21422885	C₂	semidirect
8. #21422551	C₂	semidirect
10. #21422380	C₂	semidirect
261. C₅₉	#18019	semidirect

Maximal subgroups

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

subgroup	index
#21433228	2
#21433198	2
#21422987	2
#21422975	2
#21422968	2
Q₁₆×C₅₉⋊C₈	2
#21422885	2
#21422551	2
#21422478	2
#21422380	2
C₅₉×#3107	2
#18019	59