Subgroups — #28615057

Order 15104.

642 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21425037	C₂	1	1	yes	maximal, characteristic, complemented
2	#21425033	C₂	1	1	yes	maximal, characteristic, complemented
3	#21424815	C₂	1	1	yes	maximal, characteristic, complemented
4	#21424815	C₂	1	1	yes	maximal, characteristic, complemented
5	#21424711	C₂	1	1	yes	maximal, characteristic
6	#21424704	C₂	1	1	yes	maximal, characteristic
7	#21424704	C₂	1	1	yes	maximal, characteristic
8	#21424704	C₂	1	1	yes	maximal, characteristic
9	#21424662	C₂	1	1	yes	maximal, characteristic, complemented
10	#21424655	C₂	1	1	yes	maximal, characteristic, complemented
11	#21424655	C₂	1	1	yes	maximal, characteristic, complemented
12	#21424655	C₂	1	1	yes	maximal, characteristic, complemented
13	#21424167	C₂	1	1	yes	maximal, characteristic
14	#21424080	C₂	1	1	yes	maximal, characteristic
15	C₅₉×#2396	C₂	1	1	yes	maximal, characteristic
16	C₂×C₄⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
22	C₂×C₂²⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
23	C₂×C₂²⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
24	C₂×C₂²⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
25	C₂×C₂²⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
26	C₂×#14273638	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
30	#16837157	C₂²	1	1	yes	characteristic
31	#16837157	C₂²	1	1	yes	characteristic
32	#16837157	C₂²	1	1	yes	characteristic
33	#16837157	C₂²	1	1	yes	characteristic
34	#16837157	C₂²	1	1	yes	characteristic
35	#16837157	C₂²	1	1	yes	characteristic
36	#16837157	C₂²	1	1	yes	characteristic
37	#16837157	C₂²	1	1	yes	characteristic
38	#16837157	C₂²	1	1	yes	characteristic
39	#16837157	C₂²	1	1	yes	characteristic
40	#16837157	C₂²	1	1	yes	characteristic
41	#16837157	C₂²	1	1	yes	characteristic
42	#16837157	C₂²	1	1	yes	characteristic
43	#16837157	C₂²	1	1	yes	characteristic
44	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
45	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
46	C₅₉×#400	C₄	1	1	yes	characteristic
47	C₅₉×#399	C₄	1	1	yes	characteristic
48	C₅₉×#398	C₄	1	1	yes	characteristic
49	C₅₉×#398	C₄	1	1	yes	characteristic
50	C₅₉×#396	C₄	1	1	yes	characteristic
51	C₅₉×#396	C₄	1	1	yes	characteristic
52	C₅₉×#395	C₄	1	1	yes	characteristic
53	C₅₉×#393	C₄	1	1	yes	characteristic
54	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
55	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
56	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
57	C₄×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
58	C₄×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
59	C₂²×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
60	C₂²×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
61	C₂²×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
62	C₂²×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
63	C₂²×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
64	C₂²×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
65	C₂²×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
66	C₂²×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
67	C₄⋊(C₅₉⋊C₈)	—	4	1	no	—
68	C₄⋊(C₅₉⋊C₈)	—	4	1	no	—
69	C₄⋊(C₅₉⋊C₈)	—	4	1	no	—
70	C₄⋊(C₅₉⋊C₈)	—	4	1	no	—
71	C₄⋊(C₅₉⋊C₈)	—	4	1	no	—
72	C₄⋊(C₅₉⋊C₈)	—	4	1	no	—
73	C₂²⋊(C₅₉⋊C₈)	—	4	1	no	—
74	C₂²⋊(C₅₉⋊C₈)	—	4	1	no	—
75	C₂²⋊(C₅₉⋊C₈)	—	4	1	no	—
76	C₂²⋊(C₅₉⋊C₈)	—	4	1	no	—
77	#14273638	—	4	1	no	—
78	C₄×C₅₉⋊C₈	—	4	1	no	—
79	C₄×C₅₉⋊C₈	—	4	1	no	—
80	C₄×C₅₉⋊C₈	—	4	1	no	—
81	C₂²×Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
82	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
83	C₄×Q₈×C₅₉	—	4	1	no	—
84	C₄×Q₈×C₅₉	—	4	1	no	—
85	#117×C₅₉	—	4	1	no	—
86	#117×C₅₉	—	4	1	no	—
87	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
89	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
91	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
92	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
93	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
94	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
95	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
96	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
97	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
98	C₂×C₂²⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
99	C₂×C₂²⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
100	C₂×C₂²⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
101	C₂×C₂²⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
102	C₂×C₂²⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
103	C₂×C₂²⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
104	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
105	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
106	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
107	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
108	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
109	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
110	#95×C₅₉	C₂×C₄	1	1	yes	characteristic
111	#95×C₅₉	C₂×C₄	1	1	yes	characteristic
112	#95×C₅₉	C₂×C₄	1	1	yes	characteristic
113	#95×C₅₉	C₂×C₄	1	1	yes	characteristic
114	#95×C₅₉	C₂×C₄	1	1	yes	characteristic
115	#95×C₅₉	C₂×C₄	1	1	yes	characteristic
116	#95×C₅₉	C₂×C₄	1	1	yes	characteristic
117	#95×C₅₉	C₂×C₄	1	1	yes	characteristic
118	#95×C₅₉	C₂×C₄	1	1	yes	characteristic
119	#95×C₅₉	C₂×C₄	1	1	yes	characteristic
120	C₂⁴×C₅₉	C₂²×C₄	1	1	yes	characteristic
121	C₂×Q₈×C₅₉	—	2	2	no	—
122	C₂×Q₈×C₅₉	—	4	1	no	—
123	C₂×Q₈×C₅₉	—	4	1	no	—
124	C₂²×C₄×C₅₉	—	2	1	no	—
125	C₂²×C₄×C₅₉	—	2	1	no	—
126	C₂²×C₄×C₅₉	—	2	1	no	—
127	C₂²×C₄×C₅₉	—	2	1	no	—
128	C₂²×C₄×C₅₉	—	2	1	no	—
129	C₂²×C₄×C₅₉	—	2	1	no	—
130	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
131	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
132	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
133	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
134	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
135	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
136	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
137	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
138	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
139	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
140	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
141	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
142	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
143	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
144	C₄⋊C₄×C₅₉	—	2	2	no	—
145	C₄⋊C₄×C₅₉	—	2	2	no	—
146	C₄⋊C₄×C₅₉	—	2	2	no	—
147	C₄⋊C₄×C₅₉	—	2	2	no	—
148	C₄⋊C₄×C₅₉	—	2	2	no	—
149	C₄⋊C₄×C₅₉	—	4	1	no	—
150	C₄⋊C₄×C₅₉	—	4	1	no	—
151	C₄⋊C₄×C₅₉	—	4	1	no	—
152	C₄⋊C₄×C₅₉	—	4	1	no	—
153	C₄⋊C₄×C₅₉	—	4	1	no	—
154	C₄⋊C₄×C₅₉	—	4	1	no	—
155	C₂²⋊C₄×C₅₉	—	2	2	no	—
156	C₂²⋊C₄×C₅₉	—	2	2	no	—
157	C₂²⋊C₄×C₅₉	—	2	2	no	—
158	C₂²⋊C₄×C₅₉	—	4	1	no	—
159	C₂²⋊C₄×C₅₉	—	4	1	no	—
160	C₂²⋊C₄×C₅₉	—	4	1	no	—
161	C₄²×C₅₉	—	2	1	no	—
162	C₄²×C₅₉	—	2	1	no	—
163	C₄²×C₅₉	—	2	1	no	—
164	C₄²×C₅₉	—	2	1	no	—
165	C₄²×C₅₉	—	2	1	no	—
166	C₄²×C₅₉	—	2	1	no	—
167	C₄²×C₅₉	—	2	1	no	—
168	C₄²×C₅₉	—	2	1	no	—
169	C₄²×C₅₉	—	2	1	no	—
170	C₄²×C₅₉	—	2	1	no	—
171	C₄²×C₅₉	—	2	1	no	—
172	C₄²×C₅₉	—	2	1	no	—
173	C₂×C₅₉⋊C₈	—	2	1	no	—
174	C₂×C₅₉⋊C₈	—	2	1	no	—
175	C₂×C₅₉⋊C₈	—	2	1	no	—
176	C₂×C₅₉⋊C₈	—	2	1	no	—
177	C₂×C₅₉⋊C₈	—	2	1	no	—
178	C₂×C₅₉⋊C₈	—	2	1	no	—
179	C₂×C₅₉⋊C₈	—	2	1	no	—
180	C₂×C₅₉⋊C₈	—	2	1	no	—
181	C₂×C₅₉⋊C₈	—	2	1	no	—
182	C₂×C₅₉⋊C₈	—	2	1	no	—
183	C₂×C₅₉⋊C₈	—	2	1	no	—
184	C₂×C₅₉⋊C₈	—	2	1	no	—
185	C₂×C₅₉⋊C₈	—	2	1	no	—
186	C₂×C₅₉⋊C₈	—	2	1	no	—
187	C₂×C₅₉⋊C₈	—	2	1	no	—
188	C₂×C₅₉⋊C₈	—	2	1	no	—
189	C₂×C₅₉⋊C₈	—	2	1	no	—
190	C₂×C₅₉⋊C₈	—	2	1	no	—
191	C₂×C₅₉⋊C₈	—	2	1	no	—
192	C₂×C₅₉⋊C₈	—	2	1	no	—
193	C₂×C₅₉⋊C₈	—	2	1	no	—
194	C₂×C₅₉⋊C₈	—	2	1	no	—
195	C₂×C₅₉⋊C₈	—	2	1	no	—
196	C₂×C₅₉⋊C₈	—	2	1	no	—
197	C₂³×C₅₉	—	2	1	no	—
198	C₂³×C₅₉	—	2	1	no	—
199	C₂³×C₅₉	—	2	1	no	—
200	C₂³×C₅₉	—	2	1	no	—
201	C₂³×C₅₉	—	2	1	no	—
202	C₂³×C₅₉	—	2	1	no	—
203	C₂³×C₅₉	—	2	1	no	—
204	C₂³×C₅₉	C₂³×C₄	1	1	yes	characteristic
205	Q₈×C₅₉	—	4	4	no	—
206	C₂×C₄×C₅₉	—	2	1	no	—
207	C₂×C₄×C₅₉	—	2	1	no	—
208	C₂×C₄×C₅₉	—	2	1	no	—
209	C₂×C₄×C₅₉	—	2	1	no	—
210	C₂×C₄×C₅₉	—	2	1	no	—
211	C₂×C₄×C₅₉	—	2	1	no	—
212	C₂×C₄×C₅₉	—	2	1	no	—
213	C₂×C₄×C₅₉	—	2	1	no	—
214	C₂×C₄×C₅₉	—	2	1	no	—
215	C₂×C₄×C₅₉	—	2	1	no	—
216	C₂×C₄×C₅₉	—	2	1	no	—
217	C₂×C₄×C₅₉	—	2	1	no	—
218	C₂×C₄×C₅₉	—	2	1	no	—
219	C₂×C₄×C₅₉	—	2	1	no	—
220	C₂×C₄×C₅₉	—	2	1	no	—
221	C₂×C₄×C₅₉	—	2	1	no	—
222	C₂×C₄×C₅₉	—	2	1	no	—
223	C₂×C₄×C₅₉	—	2	1	no	—
224	C₂×C₄×C₅₉	—	2	1	no	—
225	C₂×C₄×C₅₉	—	2	1	no	—
226	C₂×C₄×C₅₉	—	2	1	no	—
227	C₂×C₄×C₅₉	—	2	1	no	—
228	C₂×C₄×C₅₉	—	2	1	no	—
229	C₂×C₄×C₅₉	—	2	1	no	—
230	C₂×C₄×C₅₉	—	2	1	no	—
231	C₂×C₄×C₅₉	—	2	1	no	—
232	C₂×C₄×C₅₉	—	2	1	no	—
233	C₂×C₄×C₅₉	—	2	1	no	—
234	C₂×C₄×C₅₉	—	2	1	no	—
235	C₂×C₄×C₅₉	—	2	1	no	—
236	C₂×C₄×C₅₉	—	2	1	no	—
237	C₂×C₄×C₅₉	—	2	1	no	—
238	C₂×C₄×C₅₉	—	2	1	no	—
239	C₂×C₄×C₅₉	—	2	1	no	—
240	C₂×C₄×C₅₉	—	2	1	no	—
241	C₂×C₄×C₅₉	—	2	1	no	—
242	C₂×C₄×C₅₉	—	4	1	no	—
243	C₂×C₄×C₅₉	—	4	1	no	—
244	C₂×C₄×C₅₉	—	4	1	no	—
245	C₂×C₄×C₅₉	—	4	1	no	—
246	C₂×C₄×C₅₉	#131	1	2	yes	—
247	C₂×C₄×C₅₉	#131	1	2	yes	—
248	C₂×C₄×C₅₉	#131	1	2	yes	—
249	C₂×C₄×C₅₉	H(5,𝔽₂)	1	1	yes	characteristic
250	C₂×C₄×C₅₉	H(5,𝔽₂)	1	1	yes	characteristic
251	C₂×C₄×C₅₉	H(5,𝔽₂)	1	1	yes	characteristic
252	C₂×C₄×C₅₉	2₋¹⁺⁴	1	1	yes	characteristic
253	C₂×C₄×C₅₉	2₋¹⁺⁴	1	1	yes	characteristic
254	C₂×C₄×C₅₉	2₋¹⁺⁴	1	1	yes	characteristic
255	C₅₉⋊C₈	—	4	1	no	—
256	C₅₉⋊C₈	—	4	1	no	—
257	C₅₉⋊C₈	—	4	1	no	—
258	C₅₉⋊C₈	—	4	1	no	—
259	C₅₉⋊C₈	—	4	1	no	—
260	C₅₉⋊C₈	—	4	1	no	—
261	C₅₉⋊C₈	—	4	1	no	—
262	C₅₉⋊C₈	—	4	1	no	—
263	#23338	—	59	1	no	maximal, Sylow
264	C₂²×C₅₉	—	4	1	no	—
265	C₂²×C₅₉	—	4	1	no	—
266	C₂²×C₅₉	—	4	1	no	—
267	C₂²×C₅₉	—	4	1	no	—
268	C₂²×C₅₉	—	4	1	no	—
269	C₂²×C₅₉	—	4	1	no	—
270	C₂²×C₅₉	—	4	1	no	—
271	C₂²×C₅₉	#518	1	1	yes	characteristic
272	C₂²×C₅₉	#519	1	1	yes	characteristic
273	C₂²×C₅₉	#520	1	1	yes	characteristic
274	C₂²×C₅₉	C₂×#131	1	1	yes	characteristic
275	C₂²×C₅₉	C₂×#131	1	1	yes	characteristic
276	C₂²×C₅₉	C₂×#131	1	1	yes	characteristic
277	C₂²×C₅₉	#568	1	1	yes	characteristic
278	C₄×C₅₉	—	2	2	no	—
279	C₄×C₅₉	—	2	2	no	—
280	C₄×C₅₉	—	2	2	no	—
281	C₄×C₅₉	—	4	1	no	—
282	C₄×C₅₉	—	4	1	no	—
283	C₄×C₅₉	—	4	1	no	—
284	C₄×C₅₉	—	4	1	no	—
285	C₄×C₅₉	—	4	1	no	—
286	C₄×C₅₉	—	4	1	no	—
287	C₄×C₅₉	—	4	1	no	—
288	C₄×C₅₉	—	4	1	no	—
289	C₄×C₅₉	—	4	1	no	—
290	C₄×C₅₉	—	4	1	no	—
291	C₄×C₅₉	#562	1	1	yes	characteristic
292	C₄×C₅₉	#562	1	1	yes	characteristic
293	C₄×C₅₉	#563	1	1	yes	characteristic
294	C₄×C₅₉	#563	1	1	yes	characteristic
295	#2396	D₅₉	1	1	yes	characteristic
296	#1985	—	59	1	no	—
297	#1984	—	59	1	no	—
298	#1939	—	59	1	no	—
299	#1939	—	59	1	no	—
300	#1924	—	59	1	no	—
301	#1923	—	59	1	no	—
302	#1923	—	59	1	no	—
303	#1923	—	59	1	no	—
304	#1917	—	59	1	no	—
305	#1916	—	59	1	no	—
306	#1916	—	59	1	no	—
307	#1916	—	59	1	no	—
308	#1818	—	59	1	no	—
309	#1798	—	59	1	no	—
310	C₂×C₅₉	—	8	1	no	—
311	C₂×C₅₉	#2378	1	1	yes	characteristic
312	C₂×C₅₉	#2976	1	1	yes	characteristic
313	C₂×C₅₉	#2979	1	1	yes	characteristic
314	C₂×C₅₉	#2985	1	1	yes	characteristic
315	C₂×C₅₉	#2986	1	1	yes	characteristic
316	C₂×C₅₉	#2992	1	1	yes	characteristic
317	C₂×C₅₉	#2994	1	1	yes	characteristic
318	C₂×C₄×Q₈	C₂×D₅₉	1	1	yes	characteristic
319	C₂×#117	C₂×D₅₉	1	1	yes	characteristic
320	C₂×C₄⋊C₈	—	59	1	no	—
321	C₂×C₄⋊C₈	—	59	1	no	—
322	C₂×C₄⋊C₈	—	59	1	no	—
323	C₂×C₄⋊C₈	—	59	1	no	—
324	C₂×C₄⋊C₈	—	59	1	no	—
325	C₂×C₄⋊C₈	—	59	1	no	—
326	C₂×C₂²⋊C₈	—	59	1	no	—
327	C₂×C₂²⋊C₈	—	59	1	no	—
328	C₂×C₂²⋊C₈	—	59	1	no	—
329	C₂×C₂²⋊C₈	—	59	1	no	—
330	C₂×#97	—	59	1	no	—
331	C₂×C₄×C₈	—	59	1	no	—
332	C₂×C₄×C₈	—	59	1	no	—
333	C₂×C₄×C₈	—	59	1	no	—
334	#400	Dic₅₉	1	1	yes	characteristic
335	#399	Dic₅₉	1	1	yes	characteristic
336	#398	Dic₅₉	1	1	yes	characteristic
337	#398	Dic₅₉	1	1	yes	characteristic
338	#396	Dic₅₉	1	1	yes	characteristic
339	#396	Dic₅₉	1	1	yes	characteristic
340	#395	Dic₅₉	1	1	yes	characteristic
341	#393	Dic₅₉	1	1	yes	characteristic
342	C₄×C₄⋊C₄	C₂×D₅₉	1	1	yes	characteristic
343	C₄×C₄⋊C₄	C₂×D₅₉	1	1	yes	characteristic
344	C₄×C₄⋊C₄	C₂×D₅₉	1	1	yes	characteristic
345	C₄×C₂²⋊C₄	C₂×D₅₉	1	1	yes	characteristic
346	C₄×C₂²⋊C₄	C₂×D₅₉	1	1	yes	characteristic
347	#336	—	59	1	no	—
348	#336	—	59	1	no	—
349	#336	—	59	1	no	—
350	#336	—	59	1	no	—
351	#336	—	59	1	no	—
352	#336	—	59	1	no	—
353	#336	—	59	1	no	—
354	#336	—	59	1	no	—
355	#336	—	59	1	no	—
356	#336	—	59	1	no	—
357	#336	—	59	1	no	—
358	#336	—	59	1	no	—
359	#336	—	59	1	no	—
360	#336	—	59	1	no	—
361	C₅₉	#23338	1	1	yes	characteristic, complemented, Sylow
362	C₂²×Q₈	C₂×Dic₅₉	1	1	yes	characteristic
363	C₂³×C₄	C₂²×D₅₉	1	1	yes	characteristic
364	C₂²×C₈	—	59	1	no	—
365	C₂²×C₈	—	59	1	no	—
366	C₂²×C₈	—	59	1	no	—
367	C₂²×C₈	—	59	1	no	—
368	C₂²×C₈	—	59	1	no	—
369	C₂²×C₈	—	59	1	no	—
370	C₂²×C₈	—	59	1	no	—
371	C₂²×C₈	—	59	1	no	—
372	C₄×Q₈	—	4	1	no	—
373	C₄×Q₈	—	4	1	no	—
374	#117	—	4	1	no	—
375	#117	—	4	1	no	—
376	C₂×C₄⋊C₄	C₂×Dic₅₉	1	1	yes	characteristic
377	C₂×C₄⋊C₄	C₂×Dic₅₉	1	1	yes	characteristic
378	C₂×C₄⋊C₄	C₂×Dic₅₉	1	1	yes	characteristic
379	C₂×C₄⋊C₄	C₂×Dic₅₉	1	1	yes	characteristic
380	C₂×C₄⋊C₄	C₂×Dic₅₉	1	1	yes	characteristic
381	C₂×C₄⋊C₄	C₂×Dic₅₉	1	1	yes	characteristic
382	C₂×C₄⋊C₄	C₂×Dic₅₉	1	1	yes	characteristic
383	C₂×C₄⋊C₄	C₂×Dic₅₉	1	1	yes	characteristic
384	C₂×C₄⋊C₄	C₂×Dic₅₉	1	1	yes	characteristic
385	C₂×C₄⋊C₄	C₂×Dic₅₉	1	1	yes	characteristic
386	C₂×C₄⋊C₄	C₂×Dic₅₉	1	1	yes	characteristic
387	C₂×C₂²⋊C₄	C₂×Dic₅₉	1	1	yes	characteristic
388	C₂×C₂²⋊C₄	C₂×Dic₅₉	1	1	yes	characteristic
389	C₂×C₂²⋊C₄	C₂×Dic₅₉	1	1	yes	characteristic
390	C₂×C₂²⋊C₄	C₂×Dic₅₉	1	1	yes	characteristic
391	C₂×C₂²⋊C₄	C₂×Dic₅₉	1	1	yes	characteristic
392	C₂×C₂²⋊C₄	C₂×Dic₅₉	1	1	yes	characteristic
393	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
394	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
395	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
396	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
397	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
398	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
399	C₄⋊C₈	—	236	1	no	—
400	C₄⋊C₈	—	236	1	no	—
401	C₄⋊C₈	—	236	1	no	—
402	C₄⋊C₈	—	236	1	no	—
403	C₄⋊C₈	—	236	1	no	—
404	C₄⋊C₈	—	236	1	no	—
405	C₂²⋊C₈	—	236	1	no	—
406	C₂²⋊C₈	—	236	1	no	—
407	C₂²⋊C₈	—	236	1	no	—
408	C₂²⋊C₈	—	236	1	no	—
409	#97	—	236	1	no	—
410	C₄×C₈	—	236	1	no	—
411	C₄×C₈	—	236	1	no	—
412	C₄×C₈	—	236	1	no	—
413	#95	C₂×Dic₅₉	1	1	yes	characteristic
414	#95	C₂×Dic₅₉	1	1	yes	characteristic
415	#95	C₂×Dic₅₉	1	1	yes	characteristic
416	#95	C₂×Dic₅₉	1	1	yes	characteristic
417	#95	C₂×Dic₅₉	1	1	yes	characteristic
418	#95	C₂×Dic₅₉	1	1	yes	characteristic
419	#95	C₂×Dic₅₉	1	1	yes	characteristic
420	#95	C₂×Dic₅₉	1	1	yes	characteristic
421	#95	C₂×Dic₅₉	1	1	yes	characteristic
422	#95	C₂×Dic₅₉	1	1	yes	characteristic
423	C₂⁴	C₂²×Dic₅₉	1	1	yes	characteristic
424	C₂×Q₈	—	2	2	no	—
425	C₂×Q₈	—	4	1	no	—
426	C₂×Q₈	—	4	1	no	—
427	C₂²×C₄	—	2	1	no	—
428	C₂²×C₄	—	2	1	no	—
429	C₂²×C₄	—	2	1	no	—
430	C₂²×C₄	—	2	1	no	—
431	C₂²×C₄	—	2	1	no	—
432	C₂²×C₄	—	2	1	no	—
433	C₂²×C₄	C₂²×Dic₅₉	1	1	yes	characteristic
434	C₂²×C₄	C₂²×Dic₅₉	1	1	yes	characteristic
435	C₂²×C₄	C₂²×Dic₅₉	1	1	yes	characteristic
436	C₂²×C₄	C₂²×Dic₅₉	1	1	yes	characteristic
437	C₂²×C₄	C₂²×Dic₅₉	1	1	yes	characteristic
438	C₂²×C₄	C₂²×Dic₅₉	1	1	yes	characteristic
439	C₂²×C₄	C₂²×Dic₅₉	1	1	yes	characteristic
440	C₂²×C₄	C₂²×Dic₅₉	1	1	yes	characteristic
441	C₂²×C₄	C₂²×Dic₅₉	1	1	yes	characteristic
442	C₂²×C₄	C₂²×Dic₅₉	1	1	yes	characteristic
443	C₂²×C₄	C₂²×Dic₅₉	1	1	yes	characteristic
444	C₂²×C₄	C₂²×Dic₅₉	1	1	yes	characteristic
445	C₂²×C₄	C₂²×Dic₅₉	1	1	yes	characteristic
446	C₂²×C₄	C₂³×D₅₉	1	1	yes	characteristic
447	C₂×C₈	—	118	1	no	—
448	C₂×C₈	—	118	1	no	—
449	C₂×C₈	—	118	1	no	—
450	C₂×C₈	—	118	1	no	—
451	C₂×C₈	—	118	1	no	—
452	C₂×C₈	—	118	1	no	—
453	C₂×C₈	—	118	1	no	—
454	C₂×C₈	—	118	1	no	—
455	C₂×C₈	—	118	1	no	—
456	C₂×C₈	—	118	1	no	—
457	C₂×C₈	—	118	1	no	—
458	C₂×C₈	—	118	1	no	—
459	C₂×C₈	—	118	1	no	—
460	C₂×C₈	—	118	1	no	—
461	C₂×C₈	—	118	1	no	—
462	C₂×C₈	—	118	1	no	—
463	C₂×C₈	—	118	1	no	—
464	C₂×C₈	—	118	1	no	—
465	C₂×C₈	—	118	1	no	—
466	C₂×C₈	—	118	1	no	—
467	C₂×C₈	—	118	1	no	—
468	C₂×C₈	—	118	1	no	—
469	C₂×C₈	—	118	1	no	—
470	C₂×C₈	—	118	1	no	—
471	C₄⋊C₄	—	2	2	no	—
472	C₄⋊C₄	—	2	2	no	—
473	C₄⋊C₄	—	2	2	no	—
474	C₄⋊C₄	—	2	2	no	—
475	C₄⋊C₄	—	2	2	no	—
476	C₄⋊C₄	—	4	1	no	—
477	C₄⋊C₄	—	4	1	no	—
478	C₄⋊C₄	—	4	1	no	—
479	C₄⋊C₄	—	4	1	no	—
480	C₄⋊C₄	—	4	1	no	—
481	C₄⋊C₄	—	4	1	no	—
482	C₂²⋊C₄	—	2	2	no	—
483	C₂²⋊C₄	—	2	2	no	—
484	C₂²⋊C₄	—	2	2	no	—
485	C₂²⋊C₄	—	4	1	no	—
486	C₂²⋊C₄	—	4	1	no	—
487	C₂²⋊C₄	—	4	1	no	—
488	C₄²	—	2	1	no	—
489	C₄²	—	2	1	no	—
490	C₄²	—	2	1	no	—
491	C₄²	—	2	1	no	—
492	C₄²	—	2	1	no	—
493	C₄²	—	2	1	no	—
494	C₄²	—	2	1	no	—
495	C₄²	—	2	1	no	—
496	C₄²	—	2	1	no	—
497	C₄²	—	2	1	no	—
498	C₄²	—	2	1	no	—
499	C₄²	—	2	1	no	—
500	C₂³	—	2	1	no	—
501	C₂³	—	2	1	no	—
502	C₂³	—	2	1	no	—
503	C₂³	—	2	1	no	—
504	C₂³	—	2	1	no	—
505	C₂³	—	2	1	no	—
506	C₂³	—	2	1	no	—
507	C₂³	C₂³×Dic₅₉	1	1	yes	characteristic
508	Q₈	—	4	4	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	4	1	no	—
549	C₂×C₄	#14273734	1	2	yes	—
550	C₂×C₄	#14273734	1	2	yes	—
551	C₂×C₄	#14273734	1	2	yes	—
552	C₂×C₄	#14273772	1	1	yes	characteristic
553	C₂×C₄	#14273772	1	1	yes	characteristic
554	C₂×C₄	#14273773	1	1	yes	characteristic
555	C₂×C₄	#14273774	1	1	yes	characteristic
556	C₂×C₄	#14273775	1	1	yes	characteristic
557	C₂×C₄	#14273775	1	1	yes	characteristic
558	C₈	—	236	1	no	—
559	C₈	—	236	1	no	—
560	C₈	—	236	1	no	—
561	C₈	—	236	1	no	—
562	C₈	—	236	1	no	—
563	C₈	—	236	1	no	—
564	C₈	—	236	1	no	—
565	C₈	—	236	1	no	—
566	C₂²	—	4	1	no	—
567	C₂²	—	4	1	no	—
568	C₂²	—	4	1	no	—
569	C₂²	—	4	1	no	—
570	C₂²	—	4	1	no	—
571	C₂²	—	4	1	no	—
572	C₂²	—	4	1	no	—
573	C₂²	#16837877	1	1	yes	characteristic
574	C₂²	#16837880	1	1	yes	characteristic
575	C₂²	#16837885	1	1	yes	characteristic
576	C₂²	C₂×#14273734	1	1	yes	characteristic
577	C₂²	C₂×#14273734	1	1	yes	characteristic
578	C₂²	C₂×#14273734	1	1	yes	characteristic
579	C₂²	#16838169	1	1	yes	characteristic
580	C₄	—	2	2	no	—
581	C₄	—	2	2	no	—
582	C₄	—	2	2	no	—
583	C₄	—	4	1	no	—
584	C₄	—	4	1	no	—
585	C₄	—	4	1	no	—
586	C₄	—	4	1	no	—
587	C₄	—	4	1	no	—
588	C₄	—	4	1	no	—
589	C₄	—	4	1	no	—
590	C₄	—	4	1	no	—
591	C₄	—	4	1	no	—
592	C₄	—	4	1	no	—
593	C₄	#16838148	1	1	yes	characteristic
594	C₄	#16838148	1	1	yes	characteristic
595	C₄	#16838153	1	1	yes	characteristic
596	C₄	#16838153	1	1	yes	characteristic
597	C₂	—	8	1	no	—
598	C₂	#21427262	1	1	yes	characteristic
599	C₂	#21433144	1	1	yes	characteristic
600	C₂	#21433163	1	1	yes	characteristic
601	C₂	#21433191	1	1	yes	characteristic
602	C₂	#21433198	1	1	yes	characteristic
603	C₂	#21433235	1	1	yes	characteristic
604	C₂	#21433256	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₅₉
commutator, socle	C₂³×C₅₉	C₂³×C₄
Fitting	C₅₉×#2396	C₂
prime radical	C₂⁴×C₅₉	C₂²×C₄
cosocle	C₂²×C₄×C₅₉	C₂⁴
hypercenter	#2396	D₅₉
hypocenter	C₅₉	#23338
LCS	G ▷ C₂³×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂²×C₄ ◁ #2396

Complements

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

N	H ≅ G/N	type
1. #21425037	C₂	semidirect
2. #21425033	C₂	semidirect
3. #21424815	C₂	semidirect
4. #21424815	C₂	semidirect
9. #21424662	C₂	semidirect
10. #21424655	C₂	semidirect
11. #21424655	C₂	semidirect
12. #21424655	C₂	semidirect
361. C₅₉	#23338	semidirect

Maximal subgroups

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

subgroup	index
#21425037	2
#21425033	2
#21424815	2
#21424711	2
#21424704	2
#21424662	2
#21424655	2
#21424167	2
#21424080	2
C₅₉×#2396	2
#23338	59