Subgroups — #28610397

Order 15104.

840 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16837533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#16837426	C₂	1	1	yes	maximal, characteristic
3	#21425037	C₂	1	1	yes	maximal, characteristic, complemented
4	#21424820	C₂	1	1	yes	maximal, characteristic, complemented
5	#21424820	C₂	1	1	yes	maximal, characteristic, complemented
6	#21424815	C₂	1	1	yes	maximal, characteristic, complemented
7	#21424662	C₂	1	1	yes	maximal, characteristic, complemented
8	#21424655	C₂	1	1	yes	maximal, characteristic, complemented
9	#21424281	C₂	1	1	yes	maximal, characteristic
10	#21424281	C₂	1	1	yes	maximal, characteristic
11	#21423971	C₂	1	1	yes	maximal, characteristic, complemented
12	#21423880	C₂	1	1	yes	maximal, characteristic
13	#21423880	C₂	1	1	yes	maximal, characteristic
14	#21423858	C₂	1	1	yes	maximal, characteristic
15	C₄×C₂²⋊Q₈×C₅₉	C₂	1	1	yes	maximal, characteristic
16	C₂²×#11745664	C₂²	1	1	yes	characteristic
17	C₂²×#11745664	C₂²	1	1	yes	characteristic
18	#16837533	—	2	4	no	—
19	#16837426	—	2	4	no	—
20	C₂×C₄⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
27	C₂×C₄⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
29	C₂×C₂²⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
30	C₂×#14273638	C₂²	1	1	yes	characteristic
31	C₂×#14273638	C₂²	1	1	yes	characteristic
32	C₂×#14273638	C₂²	1	1	yes	characteristic
33	C₂×#14273638	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
35	C₂×C₄×C₅₉⋊C₈	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	#16837157	C₂²	1	1	yes	characteristic
45	#16837157	C₂²	1	1	yes	characteristic
46	C₂×C₂²⋊Q₈×C₅₉	C₄	1	1	yes	characteristic
47	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
48	C₂²×C₄²×C₅₉	C₂²	1	1	yes	characteristic
49	C₅₉×#391	C₄	1	1	yes	characteristic
50	C₅₉×#389	C₄	1	1	yes	characteristic
51	C₅₉×#387	C₄	1	1	yes	characteristic
52	C₅₉×#387	C₄	1	1	yes	characteristic
53	C₅₉×#385	C₄	1	1	yes	characteristic
54	C₅₉×#385	C₄	1	1	yes	characteristic
55	C₅₉×#380	C₄	1	1	yes	characteristic
56	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
57	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
58	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
59	C₄×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
60	C₄×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
61	C₂×#11745664	—	2	2	no	—
62	C₂×#11745664	—	2	2	no	—
63	C₂×#11745664	—	2	2	no	—
64	C₂×#11745664	—	2	2	no	—
65	C₂×#11745664	—	4	1	no	—
66	C₂×#11745664	—	4	1	no	—
67	C₂²×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
68	C₂²×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
69	C₂²×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
70	C₂²×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
71	C₂²×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
72	C₂²×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
73	C₂²×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
74	C₂²×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
75	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
76	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
77	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
78	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
79	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
80	C₄⋊(C₅₉⋊C₈)	—	4	1	no	—
81	C₄⋊(C₅₉⋊C₈)	—	4	1	no	—
82	C₄⋊(C₅₉⋊C₈)	D₄	1	4	yes	—
83	C₂²⋊(C₅₉⋊C₈)	—	2	2	no	—
84	C₂²⋊(C₅₉⋊C₈)	Q₈	1	4	yes	complemented
85	#14273638	—	2	2	no	—
86	#14273638	—	2	2	no	—
87	#14273638	—	2	2	no	—
88	#14273638	—	4	1	no	—
89	C₄×C₅₉⋊C₈	—	2	2	no	—
90	C₄×C₅₉⋊C₈	—	4	1	no	—
91	C₂²×Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
92	C₂³×C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
93	C₂³×C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
94	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
95	C₂²⋊Q₈×C₅₉	—	2	4	no	—
96	C₄×Q₈×C₅₉	—	2	2	no	—
97	C₄×Q₈×C₅₉	—	2	2	no	—
98	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
99	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
100	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
101	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
102	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
103	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
104	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
105	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
106	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
107	C₂×C₂²⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
108	C₂×C₂²⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
109	C₂×C₂²⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
110	C₂×C₂²⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
111	C₂×C₄²×C₅₉	—	2	2	no	—
112	C₂×C₄²×C₅₉	—	2	2	no	—
113	C₂×C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
114	C₂×C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
115	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
116	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
117	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
118	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
119	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
120	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
121	#95×C₅₉	C₂×C₄	1	1	yes	characteristic
122	#95×C₅₉	C₂×C₄	1	1	yes	characteristic
123	#95×C₅₉	C₂×C₄	1	1	yes	characteristic
124	#95×C₅₉	C₂×C₄	1	1	yes	characteristic
125	#95×C₅₉	C₂×C₄	1	1	yes	characteristic
126	#95×C₅₉	C₂×C₄	1	1	yes	characteristic
127	#95×C₅₉	C₂×C₄	1	1	yes	characteristic
128	#95×C₅₉	C₂×C₄	1	1	yes	characteristic
129	#95×C₅₉	C₂×C₄	1	1	yes	characteristic
130	#95×C₅₉	C₂×C₄	1	1	yes	characteristic
131	C₂⁴×C₅₉	C₂²×C₄	1	1	yes	characteristic
132	C₂×Q₈×C₅₉	—	2	2	no	—
133	C₂×Q₈×C₅₉	—	2	2	no	—
134	C₂×Q₈×C₅₉	—	4	1	no	—
135	C₂²×C₄×C₅₉	—	2	1	no	—
136	C₂²×C₄×C₅₉	—	2	1	no	—
137	C₂²×C₄×C₅₉	—	2	1	no	—
138	C₂²×C₄×C₅₉	—	2	1	no	—
139	C₂²×C₄×C₅₉	—	2	2	no	—
140	C₂²×C₄×C₅₉	—	2	2	no	—
141	C₂²×C₄×C₅₉	—	2	2	no	—
142	C₂²×C₄×C₅₉	—	4	1	no	—
143	C₂²×C₄×C₅₉	—	4	1	no	—
144	C₂²×C₄×C₅₉	—	4	1	no	—
145	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
146	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
147	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
148	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
149	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
150	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
151	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
152	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
153	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
154	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
155	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
156	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
157	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
158	C₂²×C₄×C₅₉	C₂×Q₈	1	2	yes	—
159	C₂²×C₄×C₅₉	#41	1	2	yes	—
160	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
161	C₄⋊C₄×C₅₉	—	2	2	no	—
162	C₄⋊C₄×C₅₉	—	2	2	no	—
163	C₄⋊C₄×C₅₉	—	2	2	no	—
164	C₄⋊C₄×C₅₉	—	2	2	no	—
165	C₄⋊C₄×C₅₉	—	2	2	no	—
166	C₄⋊C₄×C₅₉	—	4	1	no	—
167	C₄⋊C₄×C₅₉	—	4	1	no	—
168	C₄⋊C₄×C₅₉	—	4	1	no	—
169	C₄⋊C₄×C₅₉	M₁₆	1	4	yes	complemented
170	C₂²⋊C₄×C₅₉	—	2	2	no	—
171	C₂²⋊C₄×C₅₉	—	2	2	no	—
172	C₂²⋊C₄×C₅₉	—	4	1	no	—
173	C₂²⋊C₄×C₅₉	—	4	1	no	—
174	C₄²×C₅₉	—	2	2	no	—
175	C₄²×C₅₉	—	2	2	no	—
176	C₄²×C₅₉	—	2	1	no	—
177	C₄²×C₅₉	—	2	1	no	—
178	C₄²×C₅₉	—	2	1	no	—
179	C₄²×C₅₉	—	2	1	no	—
180	C₄²×C₅₉	—	2	1	no	—
181	C₄²×C₅₉	—	2	1	no	—
182	C₄²×C₅₉	—	2	1	no	—
183	C₄²×C₅₉	—	2	1	no	—
184	C₄²×C₅₉	—	2	1	no	—
185	C₄²×C₅₉	—	2	1	no	—
186	C₄²×C₅₉	C₂×D₄	1	2	yes	—
187	C₄²×C₅₉	#41	1	2	yes	—
188	#11745664	—	4	4	no	—
189	#11745664	—	4	4	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	C₂×C₅₉⋊C₈	—	2	1	no	—
198	C₂×C₅₉⋊C₈	—	2	1	no	—
199	C₂×C₅₉⋊C₈	—	2	1	no	—
200	C₂×C₅₉⋊C₈	—	2	1	no	—
201	C₂×C₅₉⋊C₈	—	2	1	no	—
202	C₂×C₅₉⋊C₈	—	2	1	no	—
203	C₂×C₅₉⋊C₈	—	2	1	no	—
204	C₂×C₅₉⋊C₈	—	2	1	no	—
205	C₂×C₅₉⋊C₈	—	2	1	no	—
206	C₂×C₅₉⋊C₈	—	2	1	no	—
207	C₂×C₅₉⋊C₈	—	2	1	no	—
208	C₂×C₅₉⋊C₈	—	2	1	no	—
209	C₂×C₅₉⋊C₈	—	2	1	no	—
210	C₂×C₅₉⋊C₈	C₂×D₄	1	2	yes	—
211	C₂×C₅₉⋊C₈	C₂×D₄	1	2	yes	—
212	C₂×C₅₉⋊C₈	C₂×Q₈	1	2	yes	—
213	C₂×C₅₉⋊C₈	C₂×Q₈	1	2	yes	—
214	C₂³×C₅₉	—	2	1	no	—
215	C₂³×C₅₉	—	2	1	no	—
216	C₂³×C₅₉	—	2	1	no	—
217	C₂³×C₅₉	—	2	1	no	—
218	C₂³×C₅₉	—	2	1	no	—
219	C₂³×C₅₉	—	2	1	no	—
220	C₂³×C₅₉	C₄×Q₈	1	2	yes	—
221	C₂³×C₅₉	C₂³×C₄	1	1	yes	characteristic
222	Q₈×C₅₉	—	4	4	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	2	no	—
236	C₂×C₄×C₅₉	—	2	2	no	—
237	C₂×C₄×C₅₉	—	2	2	no	—
238	C₂×C₄×C₅₉	—	2	2	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	—	2	1	no	—
243	C₂×C₄×C₅₉	—	2	1	no	—
244	C₂×C₄×C₅₉	—	2	1	no	—
245	C₂×C₄×C₅₉	—	2	1	no	—
246	C₂×C₄×C₅₉	—	2	1	no	—
247	C₂×C₄×C₅₉	—	2	1	no	—
248	C₂×C₄×C₅₉	—	2	1	no	—
249	C₂×C₄×C₅₉	—	2	1	no	—
250	C₂×C₄×C₅₉	—	2	1	no	—
251	C₂×C₄×C₅₉	—	2	1	no	—
252	C₂×C₄×C₅₉	—	2	1	no	—
253	C₂×C₄×C₅₉	—	2	1	no	—
254	C₂×C₄×C₅₉	—	2	1	no	—
255	C₂×C₄×C₅₉	—	2	1	no	—
256	C₂×C₄×C₅₉	—	2	1	no	—
257	C₂×C₄×C₅₉	—	2	1	no	—
258	C₂×C₄×C₅₉	—	2	1	no	—
259	C₂×C₄×C₅₉	—	2	1	no	—
260	C₂×C₄×C₅₉	—	4	4	no	—
261	C₂×C₄×C₅₉	—	4	4	no	—
262	C₂×C₄×C₅₉	C₄×D₄	1	2	yes	—
263	C₂×C₄×C₅₉	C₄×D₄	1	2	yes	—
264	C₂×C₄×C₅₉	C₄×Q₈	1	2	yes	—
265	C₂×C₄×C₅₉	C₂×M₁₆	1	2	yes	—
266	C₂×C₄×C₅₉	C₂×M₁₆	1	2	yes	—
267	C₂×C₄×C₅₉	C₂×M₁₆	1	2	yes	—
268	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
269	C₂×C₄×C₅₉	C₂²×Q₈	1	1	yes	characteristic
270	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
271	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
272	C₂×C₄×C₅₉	H(5,𝔽₂)	1	1	yes	characteristic
273	C₂×C₄×C₅₉	2₋¹⁺⁴	1	1	yes	characteristic
274	C₅₉⋊C₈	—	2	2	no	—
275	C₅₉⋊C₈	—	2	2	no	—
276	C₅₉⋊C₈	—	2	2	no	—
277	C₅₉⋊C₈	—	2	2	no	—
278	C₅₉⋊C₈	—	4	1	no	—
279	C₅₉⋊C₈	—	4	1	no	—
280	C₅₉⋊C₈	—	4	1	no	—
281	C₅₉⋊C₈	—	4	1	no	—
282	#22955	—	59	1	no	maximal, Sylow
283	C₂²×C₅₉	—	2	2	no	—
284	C₂²×C₅₉	—	2	2	no	—
285	C₂²×C₅₉	—	2	2	no	—
286	C₂²×C₅₉	—	4	1	no	—
287	C₂²×C₅₉	—	4	1	no	—
288	C₂²×C₅₉	—	4	1	no	—
289	C₂²×C₅₉	—	4	1	no	—
290	C₂²×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
291	C₂²×C₅₉	C₂×C₄×Q₈	1	1	yes	characteristic
292	C₂²×C₅₉	#520	1	1	yes	characteristic
293	C₂²×C₅₉	C₂²×M₁₆	1	1	yes	characteristic
294	C₂²×C₅₉	#568	1	1	yes	characteristic
295	C₂²×C₅₉	#568	1	1	yes	characteristic
296	C₂²×C₅₉	#568	1	1	yes	characteristic
297	C₄×C₅₉	—	2	2	no	—
298	C₄×C₅₉	—	2	2	no	—
299	C₄×C₅₉	—	2	2	no	—
300	C₄×C₅₉	—	2	2	no	—
301	C₄×C₅₉	—	2	2	no	—
302	C₄×C₅₉	—	2	2	no	—
303	C₄×C₅₉	—	4	1	no	—
304	C₄×C₅₉	—	4	1	no	—
305	C₄×C₅₉	—	4	1	no	—
306	C₄×C₅₉	—	4	1	no	—
307	C₄×C₅₉	—	4	1	no	—
308	C₄×C₅₉	—	4	1	no	—
309	C₄×C₅₉	—	4	1	no	—
310	C₄×C₅₉	#546	1	1	yes	characteristic
311	C₄×C₅₉	D₄×Q₈	1	1	yes	characteristic
312	C₄×C₅₉	#552	1	1	yes	characteristic
313	C₄×C₅₉	#554	1	1	yes	characteristic
314	C₂×#446	—	59	1	no	—
315	C₂×#423	—	59	1	no	—
316	C₄×C₂²⋊Q₈	D₅₉	1	1	yes	characteristic
317	#1985	—	59	1	no	—
318	#1940	—	59	1	no	—
319	#1940	—	59	1	no	—
320	#1939	—	59	1	no	—
321	#1917	—	59	1	no	—
322	#1916	—	59	1	no	—
323	#1851	—	59	1	no	—
324	#1851	—	59	1	no	—
325	#1771	—	59	1	no	—
326	#1753	—	59	1	no	—
327	#1753	—	59	1	no	—
328	#1749	—	59	1	no	—
329	C₂×C₅₉	—	4	2	no	—
330	C₂×C₅₉	#2360	1	1	yes	characteristic
331	C₂×C₅₉	#2930	1	1	yes	characteristic
332	C₂×C₅₉	D₄×M₁₆	1	1	yes	characteristic
333	C₂×C₅₉	#2961	1	1	yes	characteristic
334	C₂×C₅₉	Q₈×M₁₆	1	1	yes	characteristic
335	C₂×C₅₉	#2989	1	1	yes	characteristic
336	C₂×C₅₉	#2995	1	1	yes	characteristic
337	C₂²×M₁₆	—	59	1	no	—
338	C₂²×M₁₆	—	59	1	no	—
339	C₂×C₂²⋊Q₈	Dic₅₉	1	1	yes	characteristic
340	C₂×C₄×Q₈	C₂×D₅₉	1	1	yes	characteristic
341	C₂²×C₄²	C₂×D₅₉	1	1	yes	characteristic
342	#446	—	118	4	no	—
343	#423	—	118	4	no	—
344	C₂×C₄⋊C₈	—	59	1	no	—
345	C₂×C₄⋊C₈	—	59	1	no	—
346	C₂×C₄⋊C₈	—	59	1	no	—
347	C₂×C₄⋊C₈	—	59	1	no	—
348	C₂×C₄⋊C₈	—	59	1	no	—
349	C₂×C₄⋊C₈	—	59	1	no	—
350	C₂×C₄⋊C₈	—	59	1	no	—
351	C₂×C₄⋊C₈	—	59	1	no	—
352	C₂×C₂²⋊C₈	—	59	1	no	—
353	C₂×C₂²⋊C₈	—	59	1	no	—
354	C₂×#97	—	59	1	no	—
355	C₂×#97	—	59	1	no	—
356	C₂×#97	—	59	1	no	—
357	C₂×#97	—	59	1	no	—
358	C₂×C₄×C₈	—	59	1	no	—
359	C₂×C₄×C₈	—	59	1	no	—
360	#391	Dic₅₉	1	1	yes	characteristic
361	#389	Dic₅₉	1	1	yes	characteristic
362	#387	Dic₅₉	1	1	yes	characteristic
363	#387	Dic₅₉	1	1	yes	characteristic
364	#385	Dic₅₉	1	1	yes	characteristic
365	#385	Dic₅₉	1	1	yes	characteristic
366	#380	Dic₅₉	1	1	yes	characteristic
367	C₄×C₄⋊C₄	C₂×D₅₉	1	1	yes	characteristic
368	C₄×C₄⋊C₄	C₂×D₅₉	1	1	yes	characteristic
369	C₄×C₄⋊C₄	C₂×D₅₉	1	1	yes	characteristic
370	C₄×C₂²⋊C₄	C₂×D₅₉	1	1	yes	characteristic
371	C₄×C₂²⋊C₄	C₂×D₅₉	1	1	yes	characteristic
372	#336	—	59	1	no	—
373	#336	—	59	1	no	—
374	#336	—	59	1	no	—
375	#336	—	59	1	no	—
376	#336	—	59	1	no	—
377	#336	—	59	1	no	—
378	#336	—	59	1	no	—
379	#336	—	59	1	no	—
380	#336	—	59	1	no	—
381	#336	—	59	1	no	—
382	C₅₉	#22955	1	1	yes	characteristic, complemented, Sylow
383	C₂²×Q₈	C₂×Dic₅₉	1	1	yes	characteristic
384	C₂³×C₄	C₂×Dic₅₉	1	1	yes	characteristic
385	C₂³×C₄	C₂×Dic₅₉	1	1	yes	characteristic
386	C₂³×C₄	C₂²×D₅₉	1	1	yes	characteristic
387	C₂×M₁₆	—	118	2	no	—
388	C₂×M₁₆	—	118	2	no	—
389	C₂×M₁₆	—	118	2	no	—
390	C₂×M₁₆	—	118	2	no	—
391	C₂×M₁₆	—	236	1	no	—
392	C₂×M₁₆	—	236	1	no	—
393	C₂²×C₈	—	59	1	no	—
394	C₂²×C₈	—	59	1	no	—
395	C₂²×C₈	—	59	1	no	—
396	C₂²×C₈	—	59	1	no	—
397	C₂²×C₈	—	59	1	no	—
398	C₂²×C₈	—	59	1	no	—
399	C₂²×C₈	—	59	1	no	—
400	C₂²×C₈	—	59	1	no	—
401	C₂²⋊Q₈	—	2	4	no	—
402	C₄×Q₈	—	2	2	no	—
403	C₄×Q₈	—	2	2	no	—
404	C₂×C₄⋊C₄	C₂×Dic₅₉	1	1	yes	characteristic
405	C₂×C₄⋊C₄	C₂×Dic₅₉	1	1	yes	characteristic
406	C₂×C₄⋊C₄	C₂×Dic₅₉	1	1	yes	characteristic
407	C₂×C₄⋊C₄	C₂×Dic₅₉	1	1	yes	characteristic
408	C₂×C₄⋊C₄	C₂×Dic₅₉	1	1	yes	characteristic
409	C₂×C₄⋊C₄	C₂×Dic₅₉	1	1	yes	characteristic
410	C₂×C₄⋊C₄	C₂×Dic₅₉	1	1	yes	characteristic
411	C₂×C₄⋊C₄	C₂×Dic₅₉	1	1	yes	characteristic
412	C₂×C₄⋊C₄	C₂×Dic₅₉	1	1	yes	characteristic
413	C₂×C₂²⋊C₄	C₂×Dic₅₉	1	1	yes	characteristic
414	C₂×C₂²⋊C₄	C₂×Dic₅₉	1	1	yes	characteristic
415	C₂×C₂²⋊C₄	C₂×Dic₅₉	1	1	yes	characteristic
416	C₂×C₂²⋊C₄	C₂×Dic₅₉	1	1	yes	characteristic
417	C₂×C₄²	—	2	2	no	—
418	C₂×C₄²	—	2	2	no	—
419	C₂×C₄²	C₂×Dic₅₉	1	1	yes	characteristic
420	C₂×C₄²	C₂×Dic₅₉	1	1	yes	characteristic
421	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
422	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
423	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
424	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
425	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
426	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
427	C₄⋊C₈	—	59	4	no	—
428	C₄⋊C₈	—	118	2	no	—
429	C₄⋊C₈	—	118	2	no	—
430	C₄⋊C₈	—	118	2	no	—
431	C₄⋊C₈	—	118	2	no	—
432	C₄⋊C₈	—	118	2	no	—
433	C₄⋊C₈	—	236	1	no	—
434	C₄⋊C₈	—	236	1	no	—
435	C₂²⋊C₈	—	59	4	no	—
436	C₂²⋊C₈	—	118	2	no	—
437	#97	—	118	2	no	—
438	#97	—	118	2	no	—
439	#97	—	118	2	no	—
440	#97	—	236	1	no	—
441	C₄×C₈	—	118	2	no	—
442	C₄×C₈	—	236	1	no	—
443	#95	C₂×Dic₅₉	1	1	yes	characteristic
444	#95	C₂×Dic₅₉	1	1	yes	characteristic
445	#95	C₂×Dic₅₉	1	1	yes	characteristic
446	#95	C₂×Dic₅₉	1	1	yes	characteristic
447	#95	C₂×Dic₅₉	1	1	yes	characteristic
448	#95	C₂×Dic₅₉	1	1	yes	characteristic
449	#95	C₂×Dic₅₉	1	1	yes	characteristic
450	#95	C₂×Dic₅₉	1	1	yes	characteristic
451	#95	C₂×Dic₅₉	1	1	yes	characteristic
452	#95	C₂×Dic₅₉	1	1	yes	characteristic
453	C₂⁴	C₂²×Dic₅₉	1	1	yes	characteristic
454	C₂×Q₈	—	2	2	no	—
455	C₂×Q₈	—	2	2	no	—
456	C₂×Q₈	—	4	1	no	—
457	C₂²×C₄	—	2	1	no	—
458	C₂²×C₄	—	2	1	no	—
459	C₂²×C₄	—	2	1	no	—
460	C₂²×C₄	—	2	1	no	—
461	C₂²×C₄	—	2	2	no	—
462	C₂²×C₄	—	2	2	no	—
463	C₂²×C₄	—	2	2	no	—
464	C₂²×C₄	—	4	1	no	—
465	C₂²×C₄	—	4	1	no	—
466	C₂²×C₄	—	4	1	no	—
467	C₂²×C₄	Q₈×D₅₉	1	2	yes	—
468	C₂²×C₄	#11745689	1	2	yes	—
469	C₂²×C₄	C₂²×Dic₅₉	1	1	yes	characteristic
470	C₂²×C₄	C₂²×Dic₅₉	1	1	yes	characteristic
471	C₂²×C₄	C₂²×Dic₅₉	1	1	yes	characteristic
472	C₂²×C₄	C₂²×Dic₅₉	1	1	yes	characteristic
473	C₂²×C₄	C₂²×Dic₅₉	1	1	yes	characteristic
474	C₂²×C₄	C₂²×Dic₅₉	1	1	yes	characteristic
475	C₂²×C₄	C₂²×Dic₅₉	1	1	yes	characteristic
476	C₂²×C₄	C₂²×Dic₅₉	1	1	yes	characteristic
477	C₂²×C₄	C₂²×Dic₅₉	1	1	yes	characteristic
478	C₂²×C₄	C₂²×Dic₅₉	1	1	yes	characteristic
479	C₂²×C₄	C₂²×Dic₅₉	1	1	yes	characteristic
480	C₂²×C₄	C₂²×Dic₅₉	1	1	yes	characteristic
481	C₂²×C₄	C₂²×Dic₅₉	1	1	yes	characteristic
482	C₂²×C₄	C₂³×D₅₉	1	1	yes	characteristic
483	M₁₆	—	236	4	no	—
484	M₁₆	—	236	4	no	—
485	C₂×C₈	—	59	2	no	—
486	C₂×C₈	—	59	2	no	—
487	C₂×C₈	—	59	2	no	—
488	C₂×C₈	—	59	2	no	—
489	C₂×C₈	—	118	1	no	—
490	C₂×C₈	—	118	1	no	—
491	C₂×C₈	—	118	1	no	—
492	C₂×C₈	—	118	1	no	—
493	C₂×C₈	—	118	1	no	—
494	C₂×C₈	—	118	1	no	—
495	C₂×C₈	—	118	1	no	—
496	C₂×C₈	—	118	1	no	—
497	C₂×C₈	—	118	1	no	—
498	C₂×C₈	—	118	1	no	—
499	C₂×C₈	—	118	1	no	—
500	C₂×C₈	—	118	1	no	—
501	C₂×C₈	—	118	1	no	—
502	C₂×C₈	—	118	1	no	—
503	C₂×C₈	—	118	1	no	—
504	C₂×C₈	—	118	1	no	—
505	C₂×C₈	—	118	1	no	—
506	C₂×C₈	—	118	1	no	—
507	C₂×C₈	—	118	1	no	—
508	C₂×C₈	—	118	1	no	—
509	C₄⋊C₄	—	2	2	no	—
510	C₄⋊C₄	—	2	2	no	—
511	C₄⋊C₄	—	2	2	no	—
512	C₄⋊C₄	—	2	2	no	—
513	C₄⋊C₄	—	2	2	no	—
514	C₄⋊C₄	—	4	1	no	—
515	C₄⋊C₄	—	4	1	no	—
516	C₄⋊C₄	—	4	1	no	—
517	C₄⋊C₄	#11745664	1	4	yes	complemented
518	C₂²⋊C₄	—	2	2	no	—
519	C₂²⋊C₄	—	2	2	no	—
520	C₂²⋊C₄	—	4	1	no	—
521	C₂²⋊C₄	—	4	1	no	—
522	C₄²	—	2	2	no	—
523	C₄²	—	2	2	no	—
524	C₄²	—	2	1	no	—
525	C₄²	—	2	1	no	—
526	C₄²	—	2	1	no	—
527	C₄²	—	2	1	no	—
528	C₄²	—	2	1	no	—
529	C₄²	—	2	1	no	—
530	C₄²	—	2	1	no	—
531	C₄²	—	2	1	no	—
532	C₄²	—	2	1	no	—
533	C₄²	—	2	1	no	—
534	C₄²	D₄×D₅₉	1	2	yes	—
535	C₄²	#11745687	1	2	yes	—
536	C₂³	—	2	1	no	—
537	C₂³	—	2	1	no	—
538	C₂³	—	2	1	no	—
539	C₂³	—	2	1	no	—
540	C₂³	—	2	1	no	—
541	C₂³	—	2	1	no	—
542	C₂³	Q₈×Dic₅₉	1	2	yes	—
543	C₂³	C₂³×Dic₅₉	1	1	yes	characteristic
544	Q₈	—	4	4	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	2	1	no	—
552	C₂×C₄	—	2	1	no	—
553	C₂×C₄	—	2	1	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	2	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	2	2	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	2	1	no	—
564	C₂×C₄	—	2	1	no	—
565	C₂×C₄	—	2	1	no	—
566	C₂×C₄	—	2	1	no	—
567	C₂×C₄	—	2	1	no	—
568	C₂×C₄	—	2	1	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	1	no	—
571	C₂×C₄	—	2	1	no	—
572	C₂×C₄	—	2	1	no	—
573	C₂×C₄	—	2	1	no	—
574	C₂×C₄	—	2	1	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	2	1	no	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	2	1	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	4	4	no	—
583	C₂×C₄	—	4	4	no	—
584	C₂×C₄	D₄×Dic₅₉	1	2	yes	—
585	C₂×C₄	D₄×Dic₅₉	1	2	yes	—
586	C₂×C₄	Q₈×Dic₅₉	1	2	yes	—
587	C₂×C₄	C₂×#11745664	1	2	yes	—
588	C₂×C₄	C₂×#11745664	1	2	yes	—
589	C₂×C₄	C₂×#11745664	1	2	yes	—
590	C₂×C₄	C₂×D₄×D₅₉	1	1	yes	characteristic
591	C₂×C₄	C₂×Q₈×D₅₉	1	1	yes	characteristic
592	C₂×C₄	C₂×#11745687	1	1	yes	characteristic
593	C₂×C₄	C₂×#11745689	1	1	yes	characteristic
594	C₂×C₄	#14273773	1	1	yes	characteristic
595	C₂×C₄	#14273774	1	1	yes	characteristic
596	C₈	—	118	2	no	—
597	C₈	—	118	2	no	—
598	C₈	—	118	2	no	—
599	C₈	—	118	2	no	—
600	C₈	—	236	1	no	—
601	C₈	—	236	1	no	—
602	C₈	—	236	1	no	—
603	C₈	—	236	1	no	—
604	C₂²	—	2	2	no	—
605	C₂²	—	2	2	no	—
606	C₂²	—	2	2	no	—
607	C₂²	—	4	1	no	—
608	C₂²	—	4	1	no	—
609	C₂²	—	4	1	no	—
610	C₂²	—	4	1	no	—
611	C₂²	C₂×D₄×Dic₅₉	1	1	yes	characteristic
612	C₂²	C₂×Q₈×Dic₅₉	1	1	yes	characteristic
613	C₂²	#16837885	1	1	yes	characteristic
614	C₂²	C₂²×#11745664	1	1	yes	characteristic
615	C₂²	#16838169	1	1	yes	characteristic
616	C₂²	#16838169	1	1	yes	characteristic
617	C₂²	#16838169	1	1	yes	characteristic
618	C₄	—	2	2	no	—
619	C₄	—	2	2	no	—
620	C₄	—	2	2	no	—
621	C₄	—	2	2	no	—
622	C₄	—	2	2	no	—
623	C₄	—	2	2	no	—
624	C₄	—	4	1	no	—
625	C₄	—	4	1	no	—
626	C₄	—	4	1	no	—
627	C₄	—	4	1	no	—
628	C₄	—	4	1	no	—
629	C₄	—	4	1	no	—
630	C₄	—	4	1	no	—
631	C₄	#16838043	1	1	yes	characteristic
632	C₄	#16838065	1	1	yes	characteristic
633	C₄	#16838094	1	1	yes	characteristic
634	C₄	#16838110	1	1	yes	characteristic
635	C₂	—	4	2	no	—
636	C₂	#21427105	1	1	yes	characteristic
637	C₂	#21432800	1	1	yes	characteristic
638	C₂	D₄×#11745664	1	1	yes	characteristic
639	C₂	#21433037	1	1	yes	characteristic
640	C₂	Q₈×#11745664	1	1	yes	characteristic
641	C₂	#21433213	1	1	yes	characteristic
642	C₂	#21433266	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₅₉
commutator, socle	C₂³×C₅₉	C₂³×C₄
Fitting	C₄×C₂²⋊Q₈×C₅₉	C₂
prime radical	C₂⁴×C₅₉	C₂²×C₄
cosocle	C₂²×C₄×C₅₉	C₂⁴
hypercenter	C₄×C₂²⋊Q₈	D₅₉
hypocenter	C₅₉	#22955
LCS	G ▷ C₂³×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₄×C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
1. C₂×#16837533	C₂	semidirect
3. #21425037	C₂	semidirect
4. #21424820	C₂	semidirect
5. #21424820	C₂	semidirect
6. #21424815	C₂	semidirect
7. #21424662	C₂	semidirect
8. #21424655	C₂	semidirect
11. #21423971	C₂	semidirect
84. C₂²⋊(C₅₉⋊C₈)	Q₈	semidirect
169. C₄⋊C₄×C₅₉	M₁₆	semidirect
382. C₅₉	#22955	semidirect
517. C₄⋊C₄	#11745664	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16837533	2
C₂×#16837426	2
#21425037	2
#21424820	2
#21424815	2
#21424662	2
#21424655	2
#21424281	2
#21423971	2
#21423880	2
#21423858	2
C₄×C₂²⋊Q₈×C₅₉	2
#22955	59