Subgroups — C₅₉×#35748 #28447857

Order 15104.

2434 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×Q₈²×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅₉×#520	C₂	1	1	yes	maximal, characteristic
3	C₅₉×#2628	C₂	1	3	yes	maximal, complemented
4	C₅₉×#2580	C₂	1	3	yes	maximal, complemented
5	C₅₉×#2542	C₂	1	3	yes	maximal, complemented
6	C₅₉×#2452	C₂	1	6	yes	maximal, complemented
7	C₅₉×#2440	C₂	1	6	yes	maximal, complemented
8	C₅₉×#2396	C₂	1	3	yes	maximal, complemented
9	C₅₉×#2351	C₂	1	1	yes	maximal, characteristic, complemented
10	Q₈×C₄⋊C₄×C₅₉	C₂	1	2	yes	maximal, complemented
11	C₅₉×#2341	C₂	1	2	yes	maximal
12	C₂²×#41×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	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	12	yes	—
17	C₅₉×#520	—	2	8	no	—
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	1	yes	characteristic
23	C₂×C₄×D₄×C₅₉	C₂²	1	3	yes	—
24	C₂×C₄×D₄×C₅₉	C₂²	1	3	yes	—
25	C₂×#117×C₅₉	C₂²	1	3	yes	—
26	C₂²×C₄⋊C₄×C₅₉	C₂²	1	3	yes	—
27	C₅₉×#400	C₂²	1	3	yes	—
28	C₅₉×#399	C₂²	1	3	yes	—
29	C₅₉×#399	C₂²	1	6	yes	—
30	C₅₉×#398	C₂²	1	6	yes	—
31	C₅₉×#396	C₂²	1	6	yes	—
32	C₅₉×#395	C₂²	1	6	yes	—
33	C₅₉×#395	C₂²	1	1	yes	characteristic
34	C₅₉×#393	C₂²	1	3	yes	—
35	C₅₉×#393	C₂²	1	6	yes	—
36	C₅₉×#390	C₂²	1	6	yes	—
37	C₅₉×#390	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×#385	C₂²	1	12	yes	—
42	C₅₉×#384	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	C₂×#41×C₅₉	—	2	4	no	—
49	C₂×#41×C₅₉	—	2	4	no	—
50	C₂×#41×C₅₉	Q₈	1	8	yes	complemented
51	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
52	C₂²×Q₈×C₅₉	C₂³	1	6	yes	—
53	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
54	C₂²×D₄×C₅₉	C₂³	1	3	yes	—
55	C₂³×C₄×C₅₉	C₂³	1	3	yes	—
56	C₂³×C₄×C₅₉	C₂³	1	6	yes	—
57	C₄⋊Q₈×C₅₉	—	2	24	no	—
58	C₄⋊Q₈×C₅₉	—	2	12	no	—
59	C₂²⋊Q₈×C₅₉	—	4	24	no	—
60	C₄×Q₈×C₅₉	—	2	4	no	—
61	C₄×Q₈×C₅₉	—	2	8	no	—
62	C₄×Q₈×C₅₉	—	2	8	no	—
63	C₄×Q₈×C₅₉	—	2	12	no	—
64	C₄×Q₈×C₅₉	D₄	1	8	yes	—
65	C₄×D₄×C₅₉	—	2	12	no	—
66	C₄×D₄×C₅₉	—	2	12	no	—
67	#117×C₅₉	—	2	12	no	—
68	C₂×C₄⋊C₄×C₅₉	—	2	12	no	—
69	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
70	C₂×C₄⋊C₄×C₅₉	C₂³	1	6	yes	—
71	C₂×C₄⋊C₄×C₅₉	C₂³	1	6	yes	—
72	C₂×C₄⋊C₄×C₅₉	C₂³	1	6	yes	—
73	C₂×C₄⋊C₄×C₅₉	C₂³	1	6	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	3	yes	—
77	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
78	C₂×C₄⋊C₄×C₅₉	C₂³	1	3	yes	—
79	C₂×C₄⋊C₄×C₅₉	C₂³	1	12	yes	—
80	C₂×C₄⋊C₄×C₅₉	C₂³	1	3	yes	—
81	C₂×C₂²⋊C₄×C₅₉	C₂³	1	6	yes	—
82	C₂×C₂²⋊C₄×C₅₉	C₂³	1	6	yes	—
83	C₂×C₂²⋊C₄×C₅₉	C₂³	1	3	yes	—
84	C₂×C₂²⋊C₄×C₅₉	C₂³	1	3	yes	—
85	C₂×C₂²⋊C₄×C₅₉	C₂³	1	12	yes	—
86	C₂×C₄²×C₅₉	C₂³	1	6	yes	—
87	C₂×C₄²×C₅₉	C₂³	1	6	yes	—
88	C₂×C₄²×C₅₉	C₂³	1	3	yes	—
89	C₂×C₄²×C₅₉	C₂³	1	3	yes	—
90	#95×C₅₉	C₂³	1	2	yes	—
91	#95×C₅₉	C₂³	1	6	yes	—
92	#95×C₅₉	C₂³	1	1	yes	characteristic
93	#95×C₅₉	C₂³	1	3	yes	—
94	#95×C₅₉	C₂³	1	6	yes	—
95	#95×C₅₉	C₂³	1	6	yes	—
96	#95×C₅₉	C₂³	1	6	yes	—
97	C₂⁴×C₅₉	C₂⁴	1	3	yes	—
98	#41×C₅₉	—	2	32	no	—
99	C₂×Q₈×C₅₉	—	2	2	no	—
100	C₂×Q₈×C₅₉	—	2	12	no	—
101	C₂×Q₈×C₅₉	—	2	4	no	—
102	C₂×Q₈×C₅₉	—	4	12	no	—
103	C₂×Q₈×C₅₉	C₂×D₄	1	4	yes	—
104	C₂×Q₈×C₅₉	C₂×Q₈	1	4	yes	—
105	C₂×Q₈×C₅₉	#41	1	4	yes	—
106	C₂×D₄×C₅₉	—	2	6	no	—
107	C₂×D₄×C₅₉	—	2	6	no	—
108	C₂×D₄×C₅₉	C₂×Q₈	1	12	yes	—
109	C₂²×C₄×C₅₉	—	2	6	no	—
110	C₂²×C₄×C₅₉	—	2	6	no	—
111	C₂²×C₄×C₅₉	—	2	12	no	—
112	C₂²×C₄×C₅₉	—	4	12	no	—
113	C₂²×C₄×C₅₉	C₂×Q₈	1	12	yes	—
114	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
115	C₂²×C₄×C₅₉	C₂⁴	1	6	yes	—
116	C₂²×C₄×C₅₉	C₂⁴	1	6	yes	—
117	C₂²×C₄×C₅₉	C₂⁴	1	3	yes	—
118	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
119	C₂²×C₄×C₅₉	C₂⁴	1	3	yes	—
120	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
121	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
122	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
123	C₂²×C₄×C₅₉	C₂⁴	1	3	yes	—
124	C₄⋊C₄×C₅₉	—	2	6	no	—
125	C₄⋊C₄×C₅₉	—	2	6	no	—
126	C₄⋊C₄×C₅₉	—	2	2	no	—
127	C₄⋊C₄×C₅₉	—	2	12	no	—
128	C₄⋊C₄×C₅₉	—	2	6	no	—
129	C₄⋊C₄×C₅₉	—	2	12	no	—
130	C₄⋊C₄×C₅₉	—	2	12	no	—
131	C₄⋊C₄×C₅₉	—	2	12	no	—
132	C₄⋊C₄×C₅₉	—	2	12	no	—
133	C₄⋊C₄×C₅₉	—	2	4	no	—
134	C₄⋊C₄×C₅₉	—	4	12	no	—
135	C₄⋊C₄×C₅₉	C₂×D₄	1	12	yes	—
136	C₂²⋊C₄×C₅₉	—	2	6	no	—
137	C₂²⋊C₄×C₅₉	—	2	6	no	—
138	C₂²⋊C₄×C₅₉	—	2	12	no	—
139	C₂²⋊C₄×C₅₉	—	2	12	no	—
140	C₂²⋊C₄×C₅₉	—	4	12	no	—
141	C₄²×C₅₉	—	2	6	no	—
142	C₄²×C₅₉	—	2	12	no	—
143	C₄²×C₅₉	—	2	12	no	—
144	C₄²×C₅₉	C₂×D₄	1	12	yes	—
145	C₂³×C₅₉	—	2	3	no	—
146	C₂³×C₅₉	—	2	3	no	—
147	C₂³×C₅₉	—	2	6	no	—
148	C₂³×C₅₉	—	2	6	no	—
149	C₂³×C₅₉	C₂²×Q₈	1	6	yes	—
150	C₂³×C₅₉	C₂⁵	1	1	yes	characteristic
151	Q₈×C₅₉	—	2	8	no	—
152	Q₈×C₅₉	—	8	12	no	—
153	Q₈×C₅₉	C₂²⋊Q₈	1	16	yes	complemented
154	D₄×C₅₉	—	2	24	no	—
155	C₂×C₄×C₅₉	—	2	2	no	—
156	C₂×C₄×C₅₉	—	2	1	no	—
157	C₂×C₄×C₅₉	—	2	2	no	—
158	C₂×C₄×C₅₉	—	2	1	no	—
159	C₂×C₄×C₅₉	—	2	6	no	—
160	C₂×C₄×C₅₉	—	2	2	no	—
161	C₂×C₄×C₅₉	—	2	2	no	—
162	C₂×C₄×C₅₉	—	2	2	no	—
163	C₂×C₄×C₅₉	—	2	24	no	—
164	C₂×C₄×C₅₉	—	2	1	no	—
165	C₂×C₄×C₅₉	—	2	3	no	—
166	C₂×C₄×C₅₉	—	2	6	no	—
167	C₂×C₄×C₅₉	—	2	6	no	—
168	C₂×C₄×C₅₉	—	2	6	no	—
169	C₂×C₄×C₅₉	—	2	6	no	—
170	C₂×C₄×C₅₉	—	2	6	no	—
171	C₂×C₄×C₅₉	—	2	6	no	—
172	C₂×C₄×C₅₉	—	2	6	no	—
173	C₂×C₄×C₅₉	—	2	2	no	—
174	C₂×C₄×C₅₉	—	8	12	no	—
175	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
176	C₂×C₄×C₅₉	C₂²×D₄	1	6	yes	—
177	C₂×C₄×C₅₉	C₂²×D₄	1	6	yes	—
178	C₂×C₄×C₅₉	C₂²×Q₈	1	2	yes	—
179	C₂×C₄×C₅₉	C₂²×Q₈	1	6	yes	—
180	C₂×C₄×C₅₉	C₂×#41	1	6	yes	—
181	C₂×C₄×C₅₉	H(5,𝔽₂)	1	4	yes	—
182	C₂×C₄×C₅₉	2₋¹⁺⁴	1	4	yes	—
183	#35748	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
184	C₂²×C₅₉	—	2	6	no	—
185	C₂²×C₅₉	—	2	12	no	—
186	C₂²×C₅₉	—	4	3	no	—
187	C₂²×C₅₉	—	4	3	no	—
188	C₂²×C₅₉	—	4	6	no	—
189	C₂²×C₅₉	C₂³×D₄	1	1	yes	characteristic
190	C₂²×C₅₉	C₂³×Q₈	1	1	yes	characteristic
191	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
192	C₂²×C₅₉	C₂×H(5,𝔽₂)	1	2	yes	—
193	C₂²×C₅₉	C₂×2₋¹⁺⁴	1	2	yes	—
194	C₄×C₅₉	—	2	2	no	—
195	C₄×C₅₉	—	2	2	no	—
196	C₄×C₅₉	—	2	4	no	—
197	C₄×C₅₉	—	2	6	no	—
198	C₄×C₅₉	—	2	4	no	—
199	C₄×C₅₉	—	4	1	no	—
200	C₄×C₅₉	—	4	3	no	—
201	C₄×C₅₉	—	4	6	no	—
202	C₄×C₅₉	—	4	6	no	—
203	C₄×C₅₉	C₂×C₂²⋊Q₈	1	12	yes	—
204	C₂×Q₈²	C₂×C₅₉	1	1	yes	characteristic, complemented
205	C₂×#520	C₂×C₅₉	1	1	yes	characteristic
206	#2628	C₂×C₅₉	1	3	yes	complemented
207	#2580	C₂×C₅₉	1	3	yes	complemented
208	#2542	C₂×C₅₉	1	3	yes	complemented
209	#2452	C₂×C₅₉	1	6	yes	complemented
210	#2440	C₂×C₅₉	1	6	yes	complemented
211	#2396	C₂×C₅₉	1	3	yes	complemented
212	#2351	C₂×C₅₉	1	1	yes	characteristic, complemented
213	Q₈×C₄⋊C₄	C₂×C₅₉	1	2	yes	complemented
214	#2341	C₂×C₅₉	1	2	yes	—
215	C₂×C₅₉	—	4	6	no	—
216	C₂×C₅₉	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
217	C₂×C₅₉	#3486	1	1	yes	characteristic
218	C₂×C₅₉	#3498	1	1	yes	characteristic
219	C₂×C₅₉	#3503	1	2	yes	—
220	C₂×C₅₉	#3522	1	2	yes	—
221	C₂²×#41	C₂²×C₅₉	1	1	yes	characteristic
222	Q₈²	—	2	8	no	—
223	C₂×C₄⋊Q₈	C₂²×C₅₉	1	3	yes	—
224	C₂×C₄⋊Q₈	C₂²×C₅₉	1	6	yes	—
225	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	12	yes	—
226	#520	—	2	8	no	—
227	C₂×C₄×Q₈	C₂²×C₅₉	1	3	yes	—
228	C₂×C₄×Q₈	C₂²×C₅₉	1	2	yes	—
229	C₂×C₄×Q₈	C₂²×C₅₉	1	2	yes	—
230	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
231	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
232	C₂×C₄×D₄	C₂²×C₅₉	1	3	yes	—
233	C₂×C₄×D₄	C₂²×C₅₉	1	3	yes	—
234	C₂×#117	C₂²×C₅₉	1	3	yes	—
235	C₂²×C₄⋊C₄	C₂²×C₅₉	1	3	yes	—
236	#400	C₂²×C₅₉	1	3	yes	—
237	#399	C₂²×C₅₉	1	6	yes	—
238	#399	C₂²×C₅₉	1	3	yes	—
239	#398	C₂²×C₅₉	1	6	yes	—
240	#396	C₂²×C₅₉	1	6	yes	—
241	#395	C₂²×C₅₉	1	6	yes	—
242	#395	C₂²×C₅₉	1	1	yes	characteristic
243	#393	C₂²×C₅₉	1	3	yes	—
244	#393	C₂²×C₅₉	1	6	yes	—
245	#390	C₂²×C₅₉	1	6	yes	—
246	#390	C₂²×C₅₉	1	6	yes	—
247	#389	C₂²×C₅₉	1	6	yes	—
248	#389	C₂²×C₅₉	1	6	yes	—
249	#389	C₂²×C₅₉	1	6	yes	—
250	#385	C₂²×C₅₉	1	12	yes	—
251	#384	C₂²×C₅₉	1	6	yes	—
252	#382	C₂²×C₅₉	1	3	yes	—
253	#380	C₂²×C₅₉	1	6	yes	—
254	C₄×C₄⋊C₄	C₂²×C₅₉	1	6	yes	—
255	C₄×C₄⋊C₄	C₂²×C₅₉	1	3	yes	—
256	C₄×C₂²⋊C₄	C₂²×C₅₉	1	6	yes	—
257	C₅₉	#35748	1	1	yes	characteristic, direct product factor, Sylow
258	C₂×#41	—	2	4	no	—
259	C₂×#41	—	2	4	no	—
260	C₂×#41	Q₈×C₅₉	1	8	yes	complemented
261	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
262	C₂²×Q₈	C₂³×C₅₉	1	6	yes	—
263	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
264	C₂²×D₄	C₂³×C₅₉	1	3	yes	—
265	C₂³×C₄	C₂³×C₅₉	1	3	yes	—
266	C₂³×C₄	C₂³×C₅₉	1	6	yes	—
267	C₄⋊Q₈	—	2	24	no	—
268	C₄⋊Q₈	—	2	12	no	—
269	C₂²⋊Q₈	—	4	24	no	—
270	C₄×Q₈	—	2	4	no	—
271	C₄×Q₈	—	2	8	no	—
272	C₄×Q₈	—	2	8	no	—
273	C₄×Q₈	—	2	12	no	—
274	C₄×Q₈	D₄×C₅₉	1	8	yes	—
275	C₄×D₄	—	2	12	no	—
276	C₄×D₄	—	2	12	no	—
277	#117	—	2	12	no	—
278	C₂×C₄⋊C₄	—	2	12	no	—
279	C₂×C₄⋊C₄	C₂³×C₅₉	1	3	yes	—
280	C₂×C₄⋊C₄	C₂³×C₅₉	1	3	yes	—
281	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
282	C₂×C₄⋊C₄	C₂³×C₅₉	1	6	yes	—
283	C₂×C₄⋊C₄	C₂³×C₅₉	1	6	yes	—
284	C₂×C₄⋊C₄	C₂³×C₅₉	1	3	yes	—
285	C₂×C₄⋊C₄	C₂³×C₅₉	1	6	yes	—
286	C₂×C₄⋊C₄	C₂³×C₅₉	1	6	yes	—
287	C₂×C₄⋊C₄	C₂³×C₅₉	1	6	yes	—
288	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
289	C₂×C₄⋊C₄	C₂³×C₅₉	1	12	yes	—
290	C₂×C₄⋊C₄	C₂³×C₅₉	1	3	yes	—
291	C₂×C₂²⋊C₄	C₂³×C₅₉	1	3	yes	—
292	C₂×C₂²⋊C₄	C₂³×C₅₉	1	3	yes	—
293	C₂×C₂²⋊C₄	C₂³×C₅₉	1	6	yes	—
294	C₂×C₂²⋊C₄	C₂³×C₅₉	1	6	yes	—
295	C₂×C₂²⋊C₄	C₂³×C₅₉	1	12	yes	—
296	C₂×C₄²	C₂³×C₅₉	1	3	yes	—
297	C₂×C₄²	C₂³×C₅₉	1	6	yes	—
298	C₂×C₄²	C₂³×C₅₉	1	6	yes	—
299	C₂×C₄²	C₂³×C₅₉	1	3	yes	—
300	#95	C₂³×C₅₉	1	2	yes	—
301	#95	C₂³×C₅₉	1	6	yes	—
302	#95	C₂³×C₅₉	1	1	yes	characteristic
303	#95	C₂³×C₅₉	1	3	yes	—
304	#95	C₂³×C₅₉	1	6	yes	—
305	#95	C₂³×C₅₉	1	6	yes	—
306	#95	C₂³×C₅₉	1	6	yes	—
307	C₂⁴	C₂⁴×C₅₉	1	3	yes	—
308	#41	—	2	32	no	—
309	C₂×Q₈	—	2	2	no	—
310	C₂×Q₈	—	2	12	no	—
311	C₂×Q₈	—	2	4	no	—
312	C₂×Q₈	—	4	12	no	—
313	C₂×Q₈	C₂×D₄×C₅₉	1	4	yes	—
314	C₂×Q₈	C₂×Q₈×C₅₉	1	4	yes	—
315	C₂×Q₈	#41×C₅₉	1	4	yes	—
316	C₂×D₄	—	2	6	no	—
317	C₂×D₄	—	2	6	no	—
318	C₂×D₄	C₂×Q₈×C₅₉	1	12	yes	—
319	C₂²×C₄	—	2	6	no	—
320	C₂²×C₄	—	2	6	no	—
321	C₂²×C₄	—	2	12	no	—
322	C₂²×C₄	—	4	12	no	—
323	C₂²×C₄	C₂×Q₈×C₅₉	1	12	yes	—
324	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
325	C₂²×C₄	C₂⁴×C₅₉	1	6	yes	—
326	C₂²×C₄	C₂⁴×C₅₉	1	6	yes	—
327	C₂²×C₄	C₂⁴×C₅₉	1	3	yes	—
328	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
329	C₂²×C₄	C₂⁴×C₅₉	1	3	yes	—
330	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
331	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
332	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
333	C₂²×C₄	C₂⁴×C₅₉	1	3	yes	—
334	C₄⋊C₄	—	2	6	no	—
335	C₄⋊C₄	—	2	6	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	2	12	no	—
338	C₄⋊C₄	—	2	6	no	—
339	C₄⋊C₄	—	2	12	no	—
340	C₄⋊C₄	—	2	12	no	—
341	C₄⋊C₄	—	2	12	no	—
342	C₄⋊C₄	—	2	12	no	—
343	C₄⋊C₄	—	2	4	no	—
344	C₄⋊C₄	—	4	12	no	—
345	C₄⋊C₄	C₂×D₄×C₅₉	1	12	yes	—
346	C₂²⋊C₄	—	2	6	no	—
347	C₂²⋊C₄	—	2	6	no	—
348	C₂²⋊C₄	—	2	12	no	—
349	C₂²⋊C₄	—	2	12	no	—
350	C₂²⋊C₄	—	4	12	no	—
351	C₄²	—	2	6	no	—
352	C₄²	—	2	12	no	—
353	C₄²	—	2	12	no	—
354	C₄²	C₂×D₄×C₅₉	1	12	yes	—
355	C₂³	—	2	3	no	—
356	C₂³	—	2	3	no	—
357	C₂³	—	2	6	no	—
358	C₂³	—	2	6	no	—
359	C₂³	C₂²×Q₈×C₅₉	1	6	yes	—
360	C₂³	C₂⁵×C₅₉	1	1	yes	characteristic
361	Q₈	—	2	8	no	—
362	Q₈	—	8	12	no	—
363	Q₈	C₂²⋊Q₈×C₅₉	1	16	yes	complemented
364	D₄	—	2	24	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	6	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	24	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	3	no	—
376	C₂×C₄	—	2	6	no	—
377	C₂×C₄	—	2	6	no	—
378	C₂×C₄	—	2	6	no	—
379	C₂×C₄	—	2	6	no	—
380	C₂×C₄	—	2	6	no	—
381	C₂×C₄	—	2	6	no	—
382	C₂×C₄	—	2	6	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	8	12	no	—
385	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
386	C₂×C₄	C₂²×D₄×C₅₉	1	6	yes	—
387	C₂×C₄	C₂²×D₄×C₅₉	1	6	yes	—
388	C₂×C₄	C₂²×Q₈×C₅₉	1	2	yes	—
389	C₂×C₄	C₂²×Q₈×C₅₉	1	6	yes	—
390	C₂×C₄	C₂×#41×C₅₉	1	6	yes	—
391	C₂×C₄	H(5,𝔽₂)×C₅₉	1	4	yes	—
392	C₂×C₄	2₋¹⁺⁴×C₅₉	1	4	yes	—
393	C₂²	—	2	6	no	—
394	C₂²	—	2	12	no	—
395	C₂²	—	4	6	no	—
396	C₂²	—	4	3	no	—
397	C₂²	—	4	3	no	—
398	C₂²	C₂³×D₄×C₅₉	1	1	yes	characteristic
399	C₂²	C₂³×Q₈×C₅₉	1	1	yes	characteristic
400	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
401	C₂²	C₂×H(5,𝔽₂)×C₅₉	1	2	yes	—
402	C₂²	C₂×2₋¹⁺⁴×C₅₉	1	2	yes	—
403	C₄	—	2	4	no	—
404	C₄	—	2	2	no	—
405	C₄	—	2	2	no	—
406	C₄	—	2	4	no	—
407	C₄	—	2	6	no	—
408	C₄	—	4	6	no	—
409	C₄	—	4	1	no	—
410	C₄	—	4	3	no	—
411	C₄	—	4	6	no	—
412	C₄	C₂×C₂²⋊Q₈×C₅₉	1	12	yes	—
413	C₂	—	4	6	no	—
414	C₂	C₂²×C₂²⋊Q₈×C₅₉	1	1	yes	characteristic
415	C₂	C₅₉×#3486	1	1	yes	characteristic
416	C₂	C₅₉×#3498	1	1	yes	characteristic
417	C₂	C₅₉×#3503	1	2	yes	—
418	C₂	C₅₉×#3522	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₅₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₉
prime radical	C₂²×#41×C₅₉	C₂²
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
3. C₅₉×#2628	C₂	semidirect
4. C₅₉×#2580	C₂	semidirect
5. C₅₉×#2542	C₂	semidirect
6. C₅₉×#2452	C₂	semidirect
7. C₅₉×#2440	C₂	semidirect
8. C₅₉×#2396	C₂	semidirect
9. C₅₉×#2351	C₂	semidirect
10. Q₈×C₄⋊C₄×C₅₉	C₂	semidirect
50. C₂×#41×C₅₉	Q₈	semidirect
153. Q₈×C₅₉	C₂²⋊Q₈	semidirect
183. #35748	C₅₉	direct (N × H)
204. C₂×Q₈²	C₂×C₅₉	semidirect
206. #2628	C₂×C₅₉	semidirect
207. #2580	C₂×C₅₉	semidirect
208. #2542	C₂×C₅₉	semidirect
209. #2452	C₂×C₅₉	semidirect
210. #2440	C₂×C₅₉	semidirect
211. #2396	C₂×C₅₉	semidirect
212. #2351	C₂×C₅₉	semidirect
213. Q₈×C₄⋊C₄	C₂×C₅₉	semidirect
257. C₅₉	#35748	direct (N × H)
260. C₂×#41	Q₈×C₅₉	semidirect
363. Q₈	C₂²⋊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×#520	2
C₅₉×#2628	2
C₅₉×#2580	2
C₅₉×#2542	2
C₅₉×#2452	2
C₅₉×#2440	2
C₅₉×#2396	2
C₅₉×#2351	2
Q₈×C₄⋊C₄×C₅₉	2
C₅₉×#2341	2
#35748	59

Subgroups — C59×#35748 #28447857

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#35748 #28447857