Subgroups — C₅₉×#35711 #28447820

Order 15104.

2190 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈²×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅₉×#519	C₂	1	1	yes	maximal, characteristic
3	C₅₉×#2628	C₂	1	3	yes	maximal
4	C₅₉×#2581	C₂	1	3	yes	maximal, complemented
5	C₅₉×#2568	C₂	1	3	yes	maximal, complemented
6	C₅₉×#2451	C₂	1	6	yes	maximal, complemented
7	C₅₉×#2439	C₂	1	6	yes	maximal
8	C₅₉×#2396	C₂	1	3	yes	maximal
9	C₅₉×#2351	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₉×#2351	C₂	1	2	yes	maximal, complemented
11	Q₈×C₂²⋊C₄×C₅₉	C₂	1	2	yes	maximal
12	C₂³×Q₈×C₅₉	C₂²	1	1	yes	characteristic
13	Q₈²×C₅₉	—	2	8	no	—
14	C₂×C₄⋊Q₈×C₅₉	C₂²	1	3	yes	—
15	C₂×C₄⋊Q₈×C₅₉	C₂²	1	6	yes	—
16	C₅₉×#519	—	2	8	no	—
17	C₂×C₄×Q₈×C₅₉	C₂²	1	3	yes	—
18	C₂×C₄×Q₈×C₅₉	C₂²	1	3	yes	—
19	C₂×C₄×Q₈×C₅₉	C₂²	1	2	yes	—
20	C₂×C₄×Q₈×C₅₉	C₂²	1	2	yes	—
21	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
22	C₂×C₄×Q₈×C₅₉	C₂²	1	3	yes	—
23	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
24	C₂×#117×C₅₉	C₂²	1	3	yes	—
25	C₂×#117×C₅₉	C₂²	1	3	yes	—
26	C₅₉×#400	C₂²	1	3	yes	—
27	C₅₉×#400	C₂²	1	6	yes	—
28	C₅₉×#399	C₂²	1	3	yes	—
29	C₅₉×#398	C₂²	1	6	yes	—
30	C₅₉×#396	C₂²	1	6	yes	—
31	C₅₉×#395	C₂²	1	3	yes	—
32	C₅₉×#395	C₂²	1	6	yes	—
33	C₅₉×#393	C₂²	1	6	yes	—
34	C₅₉×#393	C₂²	1	1	yes	characteristic
35	C₅₉×#391	C₂²	1	6	yes	—
36	C₅₉×#391	C₂²	1	12	yes	—
37	C₅₉×#391	C₂²	1	6	yes	—
38	C₅₉×#389	C₂²	1	6	yes	—
39	C₅₉×#389	C₂²	1	6	yes	—
40	C₅₉×#389	C₂²	1	6	yes	—
41	C₅₉×#387	C₂²	1	12	yes	—
42	C₅₉×#382	C₂²	1	6	yes	—
43	C₅₉×#382	C₂²	1	3	yes	—
44	C₅₉×#380	C₂²	1	6	yes	—
45	C₄×C₄⋊C₄×C₅₉	C₂²	1	3	yes	—
46	C₄×C₄⋊C₄×C₅₉	C₂²	1	6	yes	—
47	C₄×C₂²⋊C₄×C₅₉	C₂²	1	6	yes	—
48	C₂²×Q₈×C₅₉	—	2	4	no	—
49	C₂²×Q₈×C₅₉	—	2	4	no	—
50	C₂²×Q₈×C₅₉	Q₈	1	8	yes	complemented
51	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
52	C₂²×Q₈×C₅₉	C₂³	1	3	yes	—
53	C₂²×Q₈×C₅₉	C₂³	1	6	yes	—
54	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
55	C₂³×C₄×C₅₉	C₂³	1	3	yes	—
56	C₄⋊Q₈×C₅₉	—	2	24	no	—
57	C₄⋊Q₈×C₅₉	—	2	12	no	—
58	C₄×Q₈×C₅₉	—	2	4	no	—
59	C₄×Q₈×C₅₉	—	2	8	no	—
60	C₄×Q₈×C₅₉	—	2	8	no	—
61	C₄×Q₈×C₅₉	—	2	12	no	—
62	C₄×Q₈×C₅₉	—	2	12	no	—
63	C₄×Q₈×C₅₉	—	2	12	no	—
64	C₄×Q₈×C₅₉	D₄	1	8	yes	—
65	#117×C₅₉	—	2	12	no	—
66	#117×C₅₉	—	2	12	no	—
67	C₂×C₄⋊C₄×C₅₉	C₂³	1	6	yes	—
68	C₂×C₄⋊C₄×C₅₉	C₂³	1	6	yes	—
69	C₂×C₄⋊C₄×C₅₉	C₂³	1	6	yes	—
70	C₂×C₄⋊C₄×C₅₉	C₂³	1	3	yes	—
71	C₂×C₄⋊C₄×C₅₉	C₂³	1	6	yes	—
72	C₂×C₄⋊C₄×C₅₉	C₂³	1	3	yes	—
73	C₂×C₄⋊C₄×C₅₉	C₂³	1	3	yes	—
74	C₂×C₄⋊C₄×C₅₉	C₂³	1	3	yes	—
75	C₂×C₄⋊C₄×C₅₉	C₂³	1	6	yes	—
76	C₂×C₄⋊C₄×C₅₉	C₂³	1	6	yes	—
77	C₂×C₄⋊C₄×C₅₉	C₂³	1	3	yes	—
78	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
79	C₂×C₂²⋊C₄×C₅₉	C₂³	1	3	yes	—
80	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
81	C₂×C₂²⋊C₄×C₅₉	C₂³	1	6	yes	—
82	C₂×C₄²×C₅₉	C₂³	1	6	yes	—
83	C₂×C₄²×C₅₉	C₂³	1	6	yes	—
84	C₂×C₄²×C₅₉	C₂³	1	3	yes	—
85	C₂×C₄²×C₅₉	C₂³	1	6	yes	—
86	C₂×C₄²×C₅₉	C₂³	1	3	yes	—
87	#95×C₅₉	C₂³	1	6	yes	—
88	#95×C₅₉	C₂³	1	6	yes	—
89	#95×C₅₉	C₂³	1	2	yes	—
90	#95×C₅₉	C₂³	1	1	yes	characteristic
91	#95×C₅₉	C₂³	1	6	yes	—
92	#95×C₅₉	C₂³	1	3	yes	—
93	#95×C₅₉	C₂³	1	12	yes	—
94	#95×C₅₉	C₂³	1	6	yes	—
95	#95×C₅₉	C₂³	1	12	yes	—
96	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
97	C₂×Q₈×C₅₉	—	2	32	no	—
98	C₂×Q₈×C₅₉	—	2	2	no	—
99	C₂×Q₈×C₅₉	—	2	6	no	—
100	C₂×Q₈×C₅₉	—	2	12	no	—
101	C₂×Q₈×C₅₉	—	2	6	no	—
102	C₂×Q₈×C₅₉	—	2	4	no	—
103	C₂×Q₈×C₅₉	—	4	12	no	—
104	C₂×Q₈×C₅₉	C₂×D₄	1	4	yes	—
105	C₂×Q₈×C₅₉	C₂×Q₈	1	12	yes	—
106	C₂×Q₈×C₅₉	C₂×Q₈	1	4	yes	—
107	C₂×Q₈×C₅₉	#41	1	4	yes	—
108	C₂²×C₄×C₅₉	—	2	6	no	—
109	C₂²×C₄×C₅₉	—	2	6	no	—
110	C₂²×C₄×C₅₉	C₂×Q₈	1	12	yes	—
111	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
112	C₂²×C₄×C₅₉	C₂⁴	1	6	yes	—
113	C₂²×C₄×C₅₉	C₂⁴	1	3	yes	—
114	C₂²×C₄×C₅₉	C₂⁴	1	6	yes	—
115	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
116	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
117	C₂²×C₄×C₅₉	C₂⁴	1	3	yes	—
118	C₂²×C₄×C₅₉	C₂⁴	1	3	yes	—
119	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
120	C₂²×C₄×C₅₉	C₂⁴	1	3	yes	—
121	C₄⋊C₄×C₅₉	—	2	6	no	—
122	C₄⋊C₄×C₅₉	—	2	6	no	—
123	C₄⋊C₄×C₅₉	—	2	6	no	—
124	C₄⋊C₄×C₅₉	—	2	12	no	—
125	C₄⋊C₄×C₅₉	—	2	6	no	—
126	C₄⋊C₄×C₅₉	—	2	12	no	—
127	C₄⋊C₄×C₅₉	—	2	12	no	—
128	C₄⋊C₄×C₅₉	—	2	12	no	—
129	C₄⋊C₄×C₅₉	—	4	6	no	—
130	C₄⋊C₄×C₅₉	—	4	6	no	—
131	C₄⋊C₄×C₅₉	C₂×D₄	1	12	yes	—
132	C₂²⋊C₄×C₅₉	—	2	6	no	—
133	C₂²⋊C₄×C₅₉	—	2	2	no	—
134	C₂²⋊C₄×C₅₉	—	2	4	no	—
135	C₂²⋊C₄×C₅₉	—	4	6	no	—
136	C₄²×C₅₉	—	2	12	no	—
137	C₄²×C₅₉	—	2	6	no	—
138	C₄²×C₅₉	—	2	12	no	—
139	C₄²×C₅₉	—	2	12	no	—
140	C₄²×C₅₉	C₂×D₄	1	12	yes	—
141	C₂³×C₅₉	—	2	1	no	—
142	C₂³×C₅₉	—	2	1	no	—
143	C₂³×C₅₉	—	2	2	no	—
144	C₂³×C₅₉	—	2	2	no	—
145	C₂³×C₅₉	C₂²×Q₈	1	2	yes	—
146	C₂³×C₅₉	C₂⁵	1	1	yes	characteristic
147	Q₈×C₅₉	—	2	8	no	—
148	Q₈×C₅₉	—	2	24	no	—
149	Q₈×C₅₉	—	8	12	no	—
150	Q₈×C₅₉	C₂²⋊Q₈	1	16	yes	—
151	C₂×C₄×C₅₉	—	2	2	no	—
152	C₂×C₄×C₅₉	—	2	3	no	—
153	C₂×C₄×C₅₉	—	2	3	no	—
154	C₂×C₄×C₅₉	—	2	2	no	—
155	C₂×C₄×C₅₉	—	2	2	no	—
156	C₂×C₄×C₅₉	—	2	6	no	—
157	C₂×C₄×C₅₉	—	2	24	no	—
158	C₂×C₄×C₅₉	—	2	3	no	—
159	C₂×C₄×C₅₉	—	2	1	no	—
160	C₂×C₄×C₅₉	—	2	6	no	—
161	C₂×C₄×C₅₉	—	2	2	no	—
162	C₂×C₄×C₅₉	—	2	6	no	—
163	C₂×C₄×C₅₉	—	2	2	no	—
164	C₂×C₄×C₅₉	—	2	6	no	—
165	C₂×C₄×C₅₉	—	2	6	no	—
166	C₂×C₄×C₅₉	—	2	6	no	—
167	C₂×C₄×C₅₉	—	2	6	no	—
168	C₂×C₄×C₅₉	—	2	2	no	—
169	C₂×C₄×C₅₉	—	2	2	no	—
170	C₂×C₄×C₅₉	—	2	6	no	—
171	C₂×C₄×C₅₉	C₂²×D₄	1	6	yes	—
172	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
173	C₂×C₄×C₅₉	C₂²×D₄	1	6	yes	—
174	C₂×C₄×C₅₉	C₂²×Q₈	1	6	yes	—
175	C₂×C₄×C₅₉	C₂²×Q₈	1	6	yes	—
176	C₂×C₄×C₅₉	C₂×#41	1	6	yes	—
177	C₂×C₄×C₅₉	2₋¹⁺⁴	1	4	yes	—
178	#35711	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
179	C₂²×C₅₉	—	2	2	no	—
180	C₂²×C₅₉	—	2	4	no	—
181	C₂²×C₅₉	—	4	1	no	—
182	C₂²×C₅₉	—	4	1	no	—
183	C₂²×C₅₉	—	4	2	no	—
184	C₂²×C₅₉	C₂³×D₄	1	1	yes	characteristic
185	C₂²×C₅₉	C₂³×Q₈	1	1	yes	characteristic
186	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
187	C₂²×C₅₉	C₂×2₋¹⁺⁴	1	2	yes	—
188	C₂²×C₅₉	#585	1	2	yes	—
189	C₄×C₅₉	—	2	6	no	—
190	C₄×C₅₉	—	2	2	no	—
191	C₄×C₅₉	—	2	4	no	—
192	C₄×C₅₉	—	2	6	no	—
193	C₄×C₅₉	—	4	3	no	—
194	C₄×C₅₉	—	4	1	no	—
195	C₄×C₅₉	—	4	6	no	—
196	C₄×C₅₉	—	4	2	no	—
197	C₄×C₅₉	—	4	6	no	—
198	C₄×C₅₉	C₂×C₂²⋊Q₈	1	12	yes	—
199	C₂×Q₈²	C₂×C₅₉	1	1	yes	characteristic, complemented
200	C₂×#519	C₂×C₅₉	1	1	yes	characteristic
201	#2628	C₂×C₅₉	1	3	yes	—
202	#2581	C₂×C₅₉	1	3	yes	complemented
203	#2568	C₂×C₅₉	1	3	yes	complemented
204	#2451	C₂×C₅₉	1	6	yes	complemented
205	#2439	C₂×C₅₉	1	6	yes	—
206	#2396	C₂×C₅₉	1	3	yes	—
207	#2351	C₂×C₅₉	1	1	yes	characteristic, complemented
208	#2351	C₂×C₅₉	1	2	yes	complemented
209	Q₈×C₂²⋊C₄	C₂×C₅₉	1	2	yes	—
210	C₂×C₅₉	—	4	2	no	—
211	C₂×C₅₉	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
212	C₂×C₅₉	#3486	1	1	yes	characteristic
213	C₂×C₅₉	#3500	1	1	yes	characteristic
214	C₂×C₅₉	#3502	1	2	yes	—
215	C₂×C₅₉	#3518	1	2	yes	—
216	C₂³×Q₈	C₂²×C₅₉	1	1	yes	characteristic
217	Q₈²	—	2	8	no	—
218	C₂×C₄⋊Q₈	C₂²×C₅₉	1	3	yes	—
219	C₂×C₄⋊Q₈	C₂²×C₅₉	1	6	yes	—
220	#519	—	2	8	no	—
221	C₂×C₄×Q₈	C₂²×C₅₉	1	3	yes	—
222	C₂×C₄×Q₈	C₂²×C₅₉	1	3	yes	—
223	C₂×C₄×Q₈	C₂²×C₅₉	1	2	yes	—
224	C₂×C₄×Q₈	C₂²×C₅₉	1	2	yes	—
225	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
226	C₂×C₄×Q₈	C₂²×C₅₉	1	3	yes	—
227	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
228	C₂×#117	C₂²×C₅₉	1	3	yes	—
229	C₂×#117	C₂²×C₅₉	1	3	yes	—
230	#400	C₂²×C₅₉	1	3	yes	—
231	#400	C₂²×C₅₉	1	6	yes	—
232	#399	C₂²×C₅₉	1	3	yes	—
233	#398	C₂²×C₅₉	1	6	yes	—
234	#396	C₂²×C₅₉	1	6	yes	—
235	#395	C₂²×C₅₉	1	3	yes	—
236	#395	C₂²×C₅₉	1	6	yes	—
237	#393	C₂²×C₅₉	1	6	yes	—
238	#393	C₂²×C₅₉	1	1	yes	characteristic
239	#391	C₂²×C₅₉	1	6	yes	—
240	#391	C₂²×C₅₉	1	12	yes	—
241	#391	C₂²×C₅₉	1	6	yes	—
242	#389	C₂²×C₅₉	1	6	yes	—
243	#389	C₂²×C₅₉	1	6	yes	—
244	#389	C₂²×C₅₉	1	6	yes	—
245	#387	C₂²×C₅₉	1	12	yes	—
246	#382	C₂²×C₅₉	1	6	yes	—
247	#382	C₂²×C₅₉	1	3	yes	—
248	#380	C₂²×C₅₉	1	6	yes	—
249	C₄×C₄⋊C₄	C₂²×C₅₉	1	3	yes	—
250	C₄×C₄⋊C₄	C₂²×C₅₉	1	6	yes	—
251	C₄×C₂²⋊C₄	C₂²×C₅₉	1	6	yes	—
252	C₅₉	#35711	1	1	yes	characteristic, direct product factor, Sylow
253	C₂²×Q₈	—	2	4	no	—
254	C₂²×Q₈	—	2	4	no	—
255	C₂²×Q₈	Q₈×C₅₉	1	8	yes	complemented
256	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
257	C₂²×Q₈	C₂³×C₅₉	1	3	yes	—
258	C₂²×Q₈	C₂³×C₅₉	1	6	yes	—
259	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
260	C₂³×C₄	C₂³×C₅₉	1	3	yes	—
261	C₄⋊Q₈	—	2	24	no	—
262	C₄⋊Q₈	—	2	12	no	—
263	C₄×Q₈	—	2	4	no	—
264	C₄×Q₈	—	2	8	no	—
265	C₄×Q₈	—	2	8	no	—
266	C₄×Q₈	—	2	12	no	—
267	C₄×Q₈	—	2	12	no	—
268	C₄×Q₈	—	2	12	no	—
269	C₄×Q₈	D₄×C₅₉	1	8	yes	—
270	#117	—	2	12	no	—
271	#117	—	2	12	no	—
272	C₂×C₄⋊C₄	C₂³×C₅₉	1	3	yes	—
273	C₂×C₄⋊C₄	C₂³×C₅₉	1	3	yes	—
274	C₂×C₄⋊C₄	C₂³×C₅₉	1	3	yes	—
275	C₂×C₄⋊C₄	C₂³×C₅₉	1	6	yes	—
276	C₂×C₄⋊C₄	C₂³×C₅₉	1	6	yes	—
277	C₂×C₄⋊C₄	C₂³×C₅₉	1	3	yes	—
278	C₂×C₄⋊C₄	C₂³×C₅₉	1	6	yes	—
279	C₂×C₄⋊C₄	C₂³×C₅₉	1	6	yes	—
280	C₂×C₄⋊C₄	C₂³×C₅₉	1	6	yes	—
281	C₂×C₄⋊C₄	C₂³×C₅₉	1	6	yes	—
282	C₂×C₄⋊C₄	C₂³×C₅₉	1	3	yes	—
283	C₂×C₂²⋊C₄	C₂³×C₅₉	1	3	yes	—
284	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
285	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
286	C₂×C₂²⋊C₄	C₂³×C₅₉	1	6	yes	—
287	C₂×C₄²	C₂³×C₅₉	1	3	yes	—
288	C₂×C₄²	C₂³×C₅₉	1	6	yes	—
289	C₂×C₄²	C₂³×C₅₉	1	6	yes	—
290	C₂×C₄²	C₂³×C₅₉	1	6	yes	—
291	C₂×C₄²	C₂³×C₅₉	1	3	yes	—
292	#95	C₂³×C₅₉	1	6	yes	—
293	#95	C₂³×C₅₉	1	6	yes	—
294	#95	C₂³×C₅₉	1	2	yes	—
295	#95	C₂³×C₅₉	1	1	yes	characteristic
296	#95	C₂³×C₅₉	1	6	yes	—
297	#95	C₂³×C₅₉	1	3	yes	—
298	#95	C₂³×C₅₉	1	12	yes	—
299	#95	C₂³×C₅₉	1	6	yes	—
300	#95	C₂³×C₅₉	1	12	yes	—
301	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
302	C₂×Q₈	—	2	32	no	—
303	C₂×Q₈	—	2	2	no	—
304	C₂×Q₈	—	2	6	no	—
305	C₂×Q₈	—	2	12	no	—
306	C₂×Q₈	—	2	6	no	—
307	C₂×Q₈	—	2	4	no	—
308	C₂×Q₈	—	4	12	no	—
309	C₂×Q₈	C₂×D₄×C₅₉	1	4	yes	—
310	C₂×Q₈	C₂×Q₈×C₅₉	1	12	yes	—
311	C₂×Q₈	C₂×Q₈×C₅₉	1	4	yes	—
312	C₂×Q₈	#41×C₅₉	1	4	yes	—
313	C₂²×C₄	—	2	6	no	—
314	C₂²×C₄	—	2	6	no	—
315	C₂²×C₄	C₂×Q₈×C₅₉	1	12	yes	—
316	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
317	C₂²×C₄	C₂⁴×C₅₉	1	6	yes	—
318	C₂²×C₄	C₂⁴×C₅₉	1	3	yes	—
319	C₂²×C₄	C₂⁴×C₅₉	1	6	yes	—
320	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
321	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
322	C₂²×C₄	C₂⁴×C₅₉	1	3	yes	—
323	C₂²×C₄	C₂⁴×C₅₉	1	3	yes	—
324	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
325	C₂²×C₄	C₂⁴×C₅₉	1	3	yes	—
326	C₄⋊C₄	—	2	6	no	—
327	C₄⋊C₄	—	2	6	no	—
328	C₄⋊C₄	—	2	6	no	—
329	C₄⋊C₄	—	2	12	no	—
330	C₄⋊C₄	—	2	6	no	—
331	C₄⋊C₄	—	2	12	no	—
332	C₄⋊C₄	—	2	12	no	—
333	C₄⋊C₄	—	2	12	no	—
334	C₄⋊C₄	—	4	6	no	—
335	C₄⋊C₄	—	4	6	no	—
336	C₄⋊C₄	C₂×D₄×C₅₉	1	12	yes	—
337	C₂²⋊C₄	—	2	6	no	—
338	C₂²⋊C₄	—	2	2	no	—
339	C₂²⋊C₄	—	2	4	no	—
340	C₂²⋊C₄	—	4	6	no	—
341	C₄²	—	2	12	no	—
342	C₄²	—	2	6	no	—
343	C₄²	—	2	12	no	—
344	C₄²	—	2	12	no	—
345	C₄²	C₂×D₄×C₅₉	1	12	yes	—
346	C₂³	—	2	1	no	—
347	C₂³	—	2	1	no	—
348	C₂³	—	2	2	no	—
349	C₂³	—	2	2	no	—
350	C₂³	C₂²×Q₈×C₅₉	1	2	yes	—
351	C₂³	C₂⁵×C₅₉	1	1	yes	characteristic
352	Q₈	—	2	8	no	—
353	Q₈	—	2	24	no	—
354	Q₈	—	8	12	no	—
355	Q₈	C₂²⋊Q₈×C₅₉	1	16	yes	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	3	no	—
358	C₂×C₄	—	2	3	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	6	no	—
362	C₂×C₄	—	2	24	no	—
363	C₂×C₄	—	2	3	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	6	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	6	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	6	no	—
370	C₂×C₄	—	2	6	no	—
371	C₂×C₄	—	2	6	no	—
372	C₂×C₄	—	2	6	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	6	no	—
376	C₂×C₄	C₂²×D₄×C₅₉	1	6	yes	—
377	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
378	C₂×C₄	C₂²×D₄×C₅₉	1	6	yes	—
379	C₂×C₄	C₂²×Q₈×C₅₉	1	6	yes	—
380	C₂×C₄	C₂²×Q₈×C₅₉	1	6	yes	—
381	C₂×C₄	C₂×#41×C₅₉	1	6	yes	—
382	C₂×C₄	2₋¹⁺⁴×C₅₉	1	4	yes	—
383	C₂²	—	2	2	no	—
384	C₂²	—	2	4	no	—
385	C₂²	—	4	2	no	—
386	C₂²	—	4	1	no	—
387	C₂²	—	4	1	no	—
388	C₂²	C₂³×D₄×C₅₉	1	1	yes	characteristic
389	C₂²	C₂³×Q₈×C₅₉	1	1	yes	characteristic
390	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
391	C₂²	C₂×2₋¹⁺⁴×C₅₉	1	2	yes	—
392	C₂²	C₅₉×#585	1	2	yes	—
393	C₄	—	2	6	no	—
394	C₄	—	2	2	no	—
395	C₄	—	2	4	no	—
396	C₄	—	2	6	no	—
397	C₄	—	4	2	no	—
398	C₄	—	4	6	no	—
399	C₄	—	4	3	no	—
400	C₄	—	4	6	no	—
401	C₄	—	4	1	no	—
402	C₄	C₂×C₂²⋊Q₈×C₅₉	1	12	yes	—
403	C₂	—	4	2	no	—
404	C₂	C₂²×C₂²⋊Q₈×C₅₉	1	1	yes	characteristic
405	C₂	C₅₉×#3486	1	1	yes	characteristic
406	C₂	C₅₉×#3500	1	1	yes	characteristic
407	C₂	C₅₉×#3502	1	2	yes	—
408	C₂	C₅₉×#3518	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₅₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₉
prime radical	C₂⁴×C₅₉	C₂⁴
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×Q₈²×C₅₉	C₂	semidirect
4. C₅₉×#2581	C₂	semidirect
5. C₅₉×#2568	C₂	semidirect
6. C₅₉×#2451	C₂	semidirect
9. C₅₉×#2351	C₂	semidirect
10. C₅₉×#2351	C₂	semidirect
50. C₂²×Q₈×C₅₉	Q₈	semidirect
178. #35711	C₅₉	direct (N × H)
199. C₂×Q₈²	C₂×C₅₉	semidirect
202. #2581	C₂×C₅₉	semidirect
203. #2568	C₂×C₅₉	semidirect
204. #2451	C₂×C₅₉	semidirect
207. #2351	C₂×C₅₉	semidirect
208. #2351	C₂×C₅₉	semidirect
252. C₅₉	#35711	direct (N × H)
255. C₂²×Q₈	Q₈×C₅₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×Q₈²×C₅₉	2
C₂×C₅₉×#519	2
C₅₉×#2628	2
C₅₉×#2581	2
C₅₉×#2568	2
C₅₉×#2451	2
C₅₉×#2439	2
C₅₉×#2396	2
C₅₉×#2351	2
Q₈×C₂²⋊C₄×C₅₉	2
#35711	59

Subgroups — C59×#35711 #28447820

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#35711 #28447820