Subgroups — #28741893

Order 15104.

692 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16837819	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#14273667	C₂	1	1	yes	maximal, characteristic, complemented
3	#21425928	C₂	1	2	yes	maximal, complemented
4	#21425922	C₂	1	2	yes	maximal, complemented
5	#21425922	C₂	1	2	yes	maximal, complemented
6	D₄×C₅₉⋊C₁₆	C₂	1	2	yes	maximal, complemented
7	#21425855	C₂	1	1	yes	maximal, characteristic, complemented
8	#21425710	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₂²⋊(C₅₉⋊C₁₆)	C₂	1	1	yes	maximal, characteristic, complemented
10	#21425693	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#2929	C₂	1	1	yes	maximal, characteristic
12	#16837819	—	2	4	no	—
13	C₂×#14273667	—	2	4	no	—
14	C₂×#14273667	C₂²	1	2	yes	—
15	C₂×#14273667	C₂²	1	1	yes	characteristic
16	C₂×#14273667	C₂²	1	1	yes	characteristic
17	C₂×#14273667	C₂²	1	2	yes	complemented
18	C₂²×C₅₉⋊C₁₆	C₂²	1	2	yes	—
19	C₂²×C₅₉⋊C₁₆	C₂²	1	1	yes	characteristic
20	C₂²×C₅₉⋊C₁₆	C₂²	1	1	yes	characteristic
21	C₂²×C₅₉⋊C₁₆	C₂²	1	2	yes	complemented
22	C₄⋊(C₅₉⋊C₁₆)	C₂²	1	2	yes	complemented
23	C₄⋊(C₅₉⋊C₁₆)	C₂²	1	2	yes	complemented
24	C₂²⋊(C₅₉⋊C₁₆)	C₂²	1	1	yes	characteristic
25	C₂²⋊(C₅₉⋊C₁₆)	C₂²	1	1	yes	characteristic
26	C₂²⋊(C₅₉⋊C₁₆)	C₂²	1	1	yes	characteristic
27	C₂²⋊(C₅₉⋊C₁₆)	C₂²	1	1	yes	characteristic
28	C₂²⋊(C₅₉⋊C₁₆)	C₂²	1	2	yes	complemented
29	C₂²⋊(C₅₉⋊C₁₆)	C₂²	1	2	yes	complemented
30	#16837178	C₂²	1	2	yes	complemented
31	C₄×C₅₉⋊C₁₆	C₂²	1	2	yes	complemented
32	C₂×#131×C₅₉	C₂²	1	1	yes	characteristic
33	C₂³×C₈×C₅₉	C₂²	1	1	yes	characteristic
34	C₅₉×#525	C₄	1	1	yes	characteristic
35	C₅₉×#435	C₄	1	2	yes	—
36	C₅₉×#435	C₄	1	2	yes	—
37	C₈×D₄×C₅₉	C₂²	1	2	yes	—
38	C₈×D₄×C₅₉	C₂²	1	2	yes	—
39	C₅₉×#424	C₄	1	1	yes	characteristic
40	C₅₉×#408	C₄	1	1	yes	characteristic
41	C₅₉×#407	C₄	1	1	yes	characteristic
42	C₅₉×#405	C₂²	1	1	yes	characteristic
43	#14273667	—	2	2	no	—
44	#14273667	—	2	4	no	—
45	#14273667	—	2	4	no	—
46	#14273667	D₄	1	4	yes	complemented
47	C₂×C₅₉⋊C₁₆	—	2	2	no	—
48	C₂×C₅₉⋊C₁₆	—	2	2	no	—
49	C₂×C₅₉⋊C₁₆	—	2	4	no	—
50	C₂×C₅₉⋊C₁₆	—	2	4	no	—
51	C₂×C₅₉⋊C₁₆	C₂³	1	1	yes	characteristic
52	C₂×C₅₉⋊C₁₆	C₂³	1	1	yes	characteristic
53	C₂×C₅₉⋊C₁₆	C₂³	1	1	yes	characteristic
54	C₂×C₅₉⋊C₁₆	C₂³	1	1	yes	characteristic
55	C₂×C₅₉⋊C₁₆	C₂³	1	2	yes	—
56	C₂×C₅₉⋊C₁₆	C₂³	1	2	yes	—
57	C₂×#41×C₅₉	C₂×C₄	1	1	yes	characteristic
58	C₂³×C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
59	#131×C₅₉	—	2	2	no	—
60	#131×C₅₉	—	2	2	no	—
61	C₂×M₁₆×C₅₉	C₂×C₄	1	1	yes	characteristic
62	C₂×M₁₆×C₅₉	C₂×C₄	1	1	yes	characteristic
63	C₂×M₁₆×C₅₉	C₂×C₄	1	2	yes	—
64	C₂²×C₈×C₅₉	—	2	2	no	—
65	C₂²×C₈×C₅₉	—	2	2	no	—
66	C₂²×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
67	C₂²×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
68	C₂²×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
69	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
70	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
72	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
73	#123×C₅₉	C₈	1	2	yes	—
74	C₂²⋊Q₈×C₅₉	C₈	1	1	yes	characteristic
75	C₂²⋊Q₈×C₅₉	C₈	1	1	yes	characteristic
76	#121×C₅₉	C₈	1	1	yes	characteristic
77	#121×C₅₉	C₈	1	1	yes	characteristic
78	#120×C₅₉	C₈	1	2	yes	—
79	C₄×D₄×C₅₉	C₂×C₄	1	2	yes	—
80	C₄×D₄×C₅₉	C₂×C₄	1	2	yes	—
81	#117×C₅₉	C₂×C₄	1	1	yes	characteristic
82	C₄⋊C₈×C₅₉	C₂×C₄	1	2	yes	—
83	C₄⋊C₈×C₅₉	C₂×C₄	1	2	yes	—
84	C₂²⋊C₈×C₅₉	C₂×C₄	1	2	yes	—
85	C₂²⋊C₈×C₅₉	C₂×C₄	1	2	yes	—
86	C₂²⋊C₈×C₅₉	C₂×C₄	1	2	yes	—
87	C₂²⋊C₈×C₅₉	C₂×C₄	1	2	yes	—
88	#97×C₅₉	C₂×C₄	1	2	yes	—
89	C₄×C₈×C₅₉	C₂³	1	2	yes	—
90	C₂⁴×C₅₉	C₂×C₈	1	1	yes	characteristic
91	#41×C₅₉	—	2	2	no	—
92	#41×C₅₉	—	2	2	no	—
93	C₂×Q₈×C₅₉	C₂×C₈	1	1	yes	characteristic
94	C₂×D₄×C₅₉	C₂×C₈	1	2	yes	—
95	C₂×D₄×C₅₉	C₂×C₈	1	2	yes	—
96	C₂×D₄×C₅₉	C₂×C₈	1	1	yes	characteristic
97	C₂×D₄×C₅₉	C₂×C₈	1	2	yes	—
98	C₂²×C₄×C₅₉	—	2	2	no	—
99	C₂²×C₄×C₅₉	—	2	2	no	—
100	C₂²×C₄×C₅₉	C₂×C₈	1	1	yes	characteristic
101	C₂²×C₄×C₅₉	C₂×C₈	1	1	yes	characteristic
102	C₂²×C₄×C₅₉	C₂×C₈	1	1	yes	characteristic
103	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₅₉	C₂²×C₄	1	2	yes	—
106	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
107	M₁₆×C₅₉	—	2	2	no	—
108	M₁₆×C₅₉	—	2	2	no	—
109	M₁₆×C₅₉	—	2	4	no	—
110	C₂×C₈×C₅₉	—	2	2	no	—
111	C₂×C₈×C₅₉	—	2	2	no	—
112	C₂×C₈×C₅₉	—	2	2	no	—
113	C₂×C₈×C₅₉	—	2	1	no	—
114	C₂×C₈×C₅₉	—	2	1	no	—
115	C₂×C₈×C₅₉	—	2	2	no	—
116	C₂×C₈×C₅₉	—	2	1	no	—
117	C₂×C₈×C₅₉	—	2	1	no	—
118	C₂×C₈×C₅₉	—	2	2	no	—
119	C₂×C₈×C₅₉	C₂²×C₄	1	2	yes	—
120	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₈×C₅₉	C₂²×C₄	1	2	yes	—
123	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
124	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
125	C₂×C₈×C₅₉	#41	1	2	yes	—
126	C₂×C₈×C₅₉	C₂⁴	1	1	yes	characteristic
127	C₄⋊C₄×C₅₉	C₂×C₈	1	1	yes	characteristic
128	C₄⋊C₄×C₅₉	C₂×C₈	1	1	yes	characteristic
129	C₄⋊C₄×C₅₉	C₂×C₈	1	2	yes	—
130	C₄⋊C₄×C₅₉	C₂×C₈	1	2	yes	—
131	C₂²⋊C₄×C₅₉	C₂×C₈	1	2	yes	—
132	C₂²⋊C₄×C₅₉	C₂×C₈	1	2	yes	—
133	C₂²⋊C₄×C₅₉	C₂×C₈	1	2	yes	—
134	C₂²⋊C₄×C₅₉	C₂×C₈	1	2	yes	—
135	C₂²⋊C₄×C₅₉	C₂×C₈	1	2	yes	—
136	C₄²×C₅₉	C₂²×C₄	1	2	yes	—
137	C₅₉⋊C₁₆	—	2	1	no	—
138	C₅₉⋊C₁₆	—	2	1	no	—
139	C₅₉⋊C₁₆	—	2	2	no	—
140	C₅₉⋊C₁₆	—	2	1	no	—
141	C₅₉⋊C₁₆	—	2	1	no	—
142	C₅₉⋊C₁₆	C₂×D₄	1	4	yes	—
143	C₂³×C₅₉	—	2	2	no	—
144	C₂³×C₅₉	—	2	2	no	—
145	C₂³×C₅₉	—	4	1	no	—
146	C₂³×C₅₉	C₂²×C₈	1	1	yes	characteristic
147	C₂³×C₅₉	C₂²×C₈	1	2	yes	—
148	C₂³×C₅₉	C₂²×C₈	1	1	yes	characteristic
149	C₂³×C₅₉	C₂²×C₈	1	1	yes	characteristic
150	Q₈×C₅₉	—	2	2	no	—
151	D₄×C₅₉	—	2	4	no	—
152	D₄×C₅₉	—	2	4	no	—
153	D₄×C₅₉	—	2	2	no	—
154	D₄×C₅₉	—	4	2	no	—
155	C₂×C₄×C₅₉	—	2	2	no	—
156	C₂×C₄×C₅₉	—	2	1	no	—
157	C₂×C₄×C₅₉	—	2	1	no	—
158	C₂×C₄×C₅₉	—	2	2	no	—
159	C₂×C₄×C₅₉	—	2	1	no	—
160	C₂×C₄×C₅₉	—	2	1	no	—
161	C₂×C₄×C₅₉	—	2	2	no	—
162	C₂×C₄×C₅₉	—	2	2	no	—
163	C₂×C₄×C₅₉	—	2	2	no	—
164	C₂×C₄×C₅₉	C₄×D₄	1	2	yes	—
165	C₂×C₄×C₅₉	C₂²×C₈	1	2	yes	—
166	C₂×C₄×C₅₉	C₂²×C₈	1	2	yes	—
167	C₂×C₄×C₅₉	C₂²×C₈	1	1	yes	characteristic
168	C₂×C₄×C₅₉	C₂²×C₈	1	1	yes	characteristic
169	C₂×C₄×C₅₉	C₂²×C₈	1	2	yes	—
170	C₂×C₄×C₅₉	C₂²×C₈	1	1	yes	characteristic
171	C₂×C₄×C₅₉	#131	1	2	yes	—
172	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
173	C₈×C₅₉	—	2	1	no	—
174	C₈×C₅₉	—	2	1	no	—
175	C₈×C₅₉	—	2	2	no	—
176	C₈×C₅₉	—	2	2	no	—
177	C₈×C₅₉	C₄×D₄	1	2	yes	—
178	C₈×C₅₉	C₂²×D₄	1	1	yes	characteristic
179	C₈×C₅₉	C₂×#41	1	1	yes	characteristic
180	#33436	—	59	1	no	maximal, Sylow
181	C₂²×C₅₉	—	2	1	no	—
182	C₂²×C₅₉	—	2	1	no	—
183	C₂²×C₅₉	—	2	1	no	—
184	C₂²×C₅₉	—	2	1	no	—
185	C₂²×C₅₉	—	2	2	no	—
186	C₂²×C₅₉	—	2	1	no	—
187	C₂²×C₅₉	—	2	1	no	—
188	C₂²×C₅₉	—	2	2	no	—
189	C₂²×C₅₉	—	2	1	no	—
190	C₂²×C₅₉	—	2	2	no	—
191	C₂²×C₅₉	—	4	4	no	—
192	C₂²×C₅₉	C₈×D₄	1	2	yes	—
193	C₂²×C₅₉	#504	1	2	yes	complemented
194	C₂²×C₅₉	C₂³×C₈	1	1	yes	characteristic
195	C₄×C₅₉	—	2	2	no	—
196	C₄×C₅₉	—	2	2	no	—
197	C₄×C₅₉	—	2	1	no	—
198	C₄×C₅₉	—	2	1	no	—
199	C₄×C₅₉	—	2	2	no	—
200	C₄×C₅₉	C₈×D₄	1	2	yes	—
201	C₄×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
202	C₄×C₅₉	C₂×#131	1	1	yes	characteristic
203	C₂×#504	—	59	1	no	—
204	C₂²×M₃₂	—	59	1	no	—
205	#2929	D₅₉	1	1	yes	characteristic
206	#2169	—	59	2	no	—
207	#2168	—	59	2	no	—
208	#2168	—	59	2	no	—
209	D₄×C₁₆	—	59	2	no	—
210	#2151	—	59	1	no	—
211	#2113	—	59	1	no	—
212	C₂×C₂²⋊C₁₆	—	59	1	no	—
213	#2108	—	59	1	no	—
214	C₂×C₅₉	—	2	2	no	—
215	C₂×C₅₉	—	2	2	no	—
216	C₂×C₅₉	—	4	2	no	—
217	C₂×C₅₉	—	4	1	no	—
218	C₂×C₅₉	C₂×C₈×D₄	1	1	yes	characteristic
219	C₂×C₅₉	C₂×#504	1	1	yes	characteristic
220	C₂×C₅₉	#3407	1	1	yes	characteristic
221	C₂×#131	C₂×D₅₉	1	1	yes	characteristic
222	C₂³×C₈	C₂×D₅₉	1	1	yes	characteristic
223	#525	Dic₅₉	1	1	yes	characteristic
224	#504	—	118	4	no	—
225	C₂×M₃₂	—	59	1	no	—
226	C₂×M₃₂	—	59	1	no	—
227	C₂×M₃₂	—	59	2	no	—
228	C₂×M₃₂	—	59	2	no	—
229	C₂×M₃₂	—	118	4	no	—
230	C₂²×C₁₆	—	59	1	no	—
231	C₂²×C₁₆	—	59	1	no	—
232	C₂²×C₁₆	—	59	2	no	—
233	C₂²×C₁₆	—	59	2	no	—
234	#435	Dic₅₉	1	2	yes	—
235	#435	Dic₅₉	1	2	yes	—
236	C₈×D₄	C₂×D₅₉	1	2	yes	—
237	C₈×D₄	C₂×D₅₉	1	2	yes	—
238	#424	Dic₅₉	1	1	yes	characteristic
239	#408	Dic₅₉	1	1	yes	characteristic
240	#407	Dic₅₉	1	1	yes	characteristic
241	#405	C₂×D₅₉	1	1	yes	characteristic
242	C₄⋊C₁₆	—	59	2	no	—
243	C₄⋊C₁₆	—	59	2	no	—
244	C₂²⋊C₁₆	—	59	1	no	—
245	C₂²⋊C₁₆	—	59	1	no	—
246	C₂²⋊C₁₆	—	59	1	no	—
247	C₂²⋊C₁₆	—	59	1	no	—
248	C₂²⋊C₁₆	—	59	2	no	—
249	C₂²⋊C₁₆	—	59	2	no	—
250	#346	—	59	2	no	—
251	C₄×C₁₆	—	59	2	no	—
252	C₅₉	#33436	1	1	yes	characteristic, complemented, Sylow
253	C₂×#41	C₂×Dic₅₉	1	1	yes	characteristic
254	C₂³×C₄	C₂×Dic₅₉	1	1	yes	characteristic
255	#131	—	2	2	no	—
256	#131	—	2	2	no	—
257	C₂×M₁₆	C₂×Dic₅₉	1	1	yes	characteristic
258	C₂×M₁₆	C₂×Dic₅₉	1	2	yes	—
259	C₂×M₁₆	C₂×Dic₅₉	1	1	yes	characteristic
260	C₂²×C₈	—	2	2	no	—
261	C₂²×C₈	—	2	2	no	—
262	C₂²×C₈	C₂×Dic₅₉	1	1	yes	characteristic
263	C₂²×C₈	C₂×Dic₅₉	1	1	yes	characteristic
264	C₂²×C₈	C₂×Dic₅₉	1	1	yes	characteristic
265	C₂²×C₈	C₂²×D₅₉	1	1	yes	characteristic
266	C₂²×C₈	C₂²×D₅₉	1	1	yes	characteristic
267	C₂²×C₈	C₂²×D₅₉	1	2	yes	—
268	C₂²×C₈	C₂²×D₅₉	1	1	yes	characteristic
269	#123	C₅₉⋊C₈	1	2	yes	—
270	C₂²⋊Q₈	C₅₉⋊C₈	1	1	yes	characteristic
271	C₂²⋊Q₈	C₅₉⋊C₈	1	1	yes	characteristic
272	#121	C₅₉⋊C₈	1	1	yes	characteristic
273	#121	C₅₉⋊C₈	1	1	yes	characteristic
274	#120	C₅₉⋊C₈	1	2	yes	—
275	C₄×D₄	C₂×Dic₅₉	1	2	yes	—
276	C₄×D₄	C₂×Dic₅₉	1	2	yes	—
277	#117	C₂×Dic₅₉	1	1	yes	characteristic
278	M₃₂	—	59	4	no	—
279	M₃₂	—	118	4	no	—
280	M₃₂	—	118	4	no	—
281	M₃₂	—	118	2	no	—
282	C₂×C₁₆	—	59	2	no	—
283	C₂×C₁₆	—	59	1	no	—
284	C₂×C₁₆	—	59	1	no	—
285	C₂×C₁₆	—	59	1	no	—
286	C₂×C₁₆	—	59	1	no	—
287	C₂×C₁₆	—	59	2	no	—
288	C₂×C₁₆	—	118	4	no	—
289	C₂×C₁₆	—	118	4	no	—
290	C₂×C₁₆	—	118	2	no	—
291	C₂×C₁₆	—	118	2	no	—
292	C₄⋊C₈	C₂×Dic₅₉	1	2	yes	—
293	C₄⋊C₈	C₂×Dic₅₉	1	2	yes	—
294	C₂²⋊C₈	C₂×Dic₅₉	1	2	yes	—
295	C₂²⋊C₈	C₂×Dic₅₉	1	2	yes	—
296	C₂²⋊C₈	C₂×Dic₅₉	1	2	yes	—
297	C₂²⋊C₈	C₂×Dic₅₉	1	2	yes	—
298	#97	C₂×Dic₅₉	1	2	yes	—
299	C₄×C₈	C₂²×D₅₉	1	2	yes	—
300	C₂⁴	C₂×C₅₉⋊C₈	1	1	yes	characteristic
301	#41	—	2	2	no	—
302	#41	—	2	2	no	—
303	C₂×Q₈	C₂×C₅₉⋊C₈	1	1	yes	characteristic
304	C₂×D₄	C₂×C₅₉⋊C₈	1	2	yes	—
305	C₂×D₄	C₂×C₅₉⋊C₈	1	2	yes	—
306	C₂×D₄	C₂×C₅₉⋊C₈	1	1	yes	characteristic
307	C₂×D₄	C₂×C₅₉⋊C₈	1	2	yes	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	C₂×C₅₉⋊C₈	1	1	yes	characteristic
311	C₂²×C₄	C₂×C₅₉⋊C₈	1	1	yes	characteristic
312	C₂²×C₄	C₂×C₅₉⋊C₈	1	1	yes	characteristic
313	C₂²×C₄	C₂²×Dic₅₉	1	1	yes	characteristic
314	C₂²×C₄	C₂²×Dic₅₉	1	1	yes	characteristic
315	C₂²×C₄	C₂²×Dic₅₉	1	2	yes	—
316	C₂²×C₄	C₂²×Dic₅₉	1	1	yes	characteristic
317	M₁₆	—	2	2	no	—
318	M₁₆	—	2	2	no	—
319	M₁₆	—	2	4	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	2	1	no	—
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	—	2	1	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	D₄×D₅₉	1	2	yes	—
330	C₂×C₈	#11745687	1	2	yes	—
331	C₂×C₈	C₂²×Dic₅₉	1	2	yes	—
332	C₂×C₈	C₂²×Dic₅₉	1	1	yes	characteristic
333	C₂×C₈	C₂²×Dic₅₉	1	1	yes	characteristic
334	C₂×C₈	C₂²×Dic₅₉	1	2	yes	—
335	C₂×C₈	C₂²×Dic₅₉	1	1	yes	characteristic
336	C₂×C₈	C₂³×D₅₉	1	1	yes	characteristic
337	C₄⋊C₄	C₂×C₅₉⋊C₈	1	1	yes	characteristic
338	C₄⋊C₄	C₂×C₅₉⋊C₈	1	1	yes	characteristic
339	C₄⋊C₄	C₂×C₅₉⋊C₈	1	2	yes	—
340	C₄⋊C₄	C₂×C₅₉⋊C₈	1	2	yes	—
341	C₂²⋊C₄	C₂×C₅₉⋊C₈	1	2	yes	—
342	C₂²⋊C₄	C₂×C₅₉⋊C₈	1	2	yes	—
343	C₂²⋊C₄	C₂×C₅₉⋊C₈	1	2	yes	—
344	C₂²⋊C₄	C₂×C₅₉⋊C₈	1	2	yes	—
345	C₂²⋊C₄	C₂×C₅₉⋊C₈	1	2	yes	—
346	C₄²	C₂²×Dic₅₉	1	2	yes	—
347	C₁₆	—	59	4	no	—
348	C₁₆	—	118	1	no	—
349	C₁₆	—	118	2	no	—
350	C₁₆	—	118	1	no	—
351	C₁₆	—	118	1	no	—
352	C₁₆	—	118	1	no	—
353	C₂³	—	2	2	no	—
354	C₂³	—	2	2	no	—
355	C₂³	—	4	1	no	—
356	C₂³	C₂²×C₅₉⋊C₈	1	1	yes	characteristic
357	C₂³	C₂²×C₅₉⋊C₈	1	2	yes	—
358	C₂³	C₂²×C₅₉⋊C₈	1	1	yes	characteristic
359	C₂³	C₂²×C₅₉⋊C₈	1	1	yes	characteristic
360	Q₈	—	2	2	no	—
361	D₄	—	2	4	no	—
362	D₄	—	2	4	no	—
363	D₄	—	2	2	no	—
364	D₄	—	4	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	D₄×Dic₅₉	1	2	yes	—
375	C₂×C₄	C₂²×C₅₉⋊C₈	1	2	yes	—
376	C₂×C₄	C₂²×C₅₉⋊C₈	1	2	yes	—
377	C₂×C₄	C₂²×C₅₉⋊C₈	1	1	yes	characteristic
378	C₂×C₄	C₂²×C₅₉⋊C₈	1	1	yes	characteristic
379	C₂×C₄	C₂²×C₅₉⋊C₈	1	2	yes	—
380	C₂×C₄	C₂²×C₅₉⋊C₈	1	1	yes	characteristic
381	C₂×C₄	#14273734	1	2	yes	—
382	C₂×C₄	C₂³×Dic₅₉	1	1	yes	characteristic
383	C₈	—	2	2	no	—
384	C₈	—	2	1	no	—
385	C₈	—	2	1	no	—
386	C₈	—	2	2	no	—
387	C₈	D₄×Dic₅₉	1	2	yes	—
388	C₈	C₂×D₄×D₅₉	1	1	yes	characteristic
389	C₈	C₂×#11745687	1	1	yes	characteristic
390	C₂²	—	2	1	no	—
391	C₂²	—	2	1	no	—
392	C₂²	—	2	1	no	—
393	C₂²	—	2	1	no	—
394	C₂²	—	2	2	no	—
395	C₂²	—	2	1	no	—
396	C₂²	—	2	1	no	—
397	C₂²	—	2	2	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	2	2	no	—
400	C₂²	—	4	4	no	—
401	C₂²	D₄×C₅₉⋊C₈	1	2	yes	—
402	C₂²	#16837819	1	2	yes	complemented
403	C₂²	C₂³×C₅₉⋊C₈	1	1	yes	characteristic
404	C₄	—	2	2	no	—
405	C₄	—	2	2	no	—
406	C₄	—	2	1	no	—
407	C₄	—	2	1	no	—
408	C₄	—	2	2	no	—
409	C₄	D₄×C₅₉⋊C₈	1	2	yes	—
410	C₄	C₂×D₄×Dic₅₉	1	1	yes	characteristic
411	C₄	C₂×#14273734	1	1	yes	characteristic
412	C₂	—	2	2	no	—
413	C₂	—	2	2	no	—
414	C₂	—	4	1	no	—
415	C₂	—	4	2	no	—
416	C₂	C₂×D₄×C₅₉⋊C₈	1	1	yes	characteristic
417	C₂	C₂×#16837819	1	1	yes	characteristic
418	C₂	#21437199	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₅₉
commutator, socle	C₂²×C₅₉	C₂³×C₈
Fitting	C₅₉×#2929	C₂
prime radical	C₅₉×#525	C₄
cosocle	C₂×C₈×C₅₉	C₂⁴
hypercenter	#2929	D₅₉
hypocenter	C₅₉	#33436
LCS	G ▷ C₂²×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₈ ◁ #2929

Complements

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

N	H ≅ G/N	type
1. C₂×#16837819	C₂	semidirect
2. C₂²×#14273667	C₂	semidirect
3. #21425928	C₂	semidirect
4. #21425922	C₂	semidirect
5. #21425922	C₂	semidirect
6. D₄×C₅₉⋊C₁₆	C₂	semidirect
7. #21425855	C₂	semidirect
8. #21425710	C₂	semidirect
9. C₂×C₂²⋊(C₅₉⋊C₁₆)	C₂	semidirect
10. #21425693	C₂	semidirect
17. C₂×#14273667	C₂²	semidirect
21. C₂²×C₅₉⋊C₁₆	C₂²	semidirect
22. C₄⋊(C₅₉⋊C₁₆)	C₂²	semidirect
23. C₄⋊(C₅₉⋊C₁₆)	C₂²	semidirect
28. C₂²⋊(C₅₉⋊C₁₆)	C₂²	semidirect
29. C₂²⋊(C₅₉⋊C₁₆)	C₂²	semidirect
30. #16837178	C₂²	semidirect
31. C₄×C₅₉⋊C₁₆	C₂²	semidirect
46. #14273667	D₄	semidirect
193. C₂²×C₅₉	#504	semidirect
252. C₅₉	#33436	semidirect
402. C₂²	#16837819	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16837819	2
C₂²×#14273667	2
#21425928	2
#21425922	2
D₄×C₅₉⋊C₁₆	2
#21425855	2
#21425710	2
C₂×C₂²⋊(C₅₉⋊C₁₆)	2
#21425693	2
C₅₉×#2929	2
#33436	59