Subgroups — C₂×#21421992 #28478913

Order 15104.

666 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16837426	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄⋊(C₅₉⋊C₈)	C₂	1	1	yes	maximal, characteristic
3	#21421992	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₅₉×#431	C₂	1	1	yes	maximal, characteristic
5	C₂²×#11745664	—	2	1	no	—
6	C₂³×C₅₉⋊C₈	—	2	1	no	—
7	#16837426	—	2	1	no	—
8	#16837426	—	2	1	no	—
9	#16837426	C₄	1	2	yes	—
10	#16837426	C₂²	1	2	yes	—
11	C₂×C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
12	C₂×C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
13	C₂×C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
14	C₂×C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
15	C₂×C₄⋊(C₅₉⋊C₈)	C₄	1	2	yes	—
16	C₂×C₄⋊(C₅₉⋊C₈)	C₄	1	2	yes	—
17	C₂×C₄⋊(C₅₉⋊C₈)	C₄	1	2	yes	—
18	C₂×C₄⋊(C₅₉⋊C₈)	C₂²	1	2	yes	—
19	C₂²×C₄²×C₅₉	C₂²	1	1	yes	characteristic
20	C₅₉×#431	—	2	1	no	—
21	C₅₉×#431	—	2	1	no	—
22	C₅₉×#431	C₄	1	2	yes	—
23	C₅₉×#431	C₂²	1	2	yes	—
24	C₂×C₄⋊C₈×C₅₉	—	2	1	no	—
25	C₂×C₂²⋊C₈×C₅₉	C₄	1	2	yes	—
26	C₂×C₄×C₈×C₅₉	—	2	1	no	—
27	C₂×#11745664	—	2	2	no	—
28	C₂×#11745664	—	2	2	no	—
29	C₂×#11745664	—	4	2	no	—
30	C₂×#11745664	—	4	2	no	—
31	C₂²×C₅₉⋊C₈	—	2	2	no	—
32	C₂²×C₅₉⋊C₈	—	2	2	no	—
33	C₂²×C₅₉⋊C₈	—	2	2	no	—
34	C₂²×C₅₉⋊C₈	—	2	2	no	—
35	C₂²×C₅₉⋊C₈	—	4	2	no	—
36	C₂²×C₅₉⋊C₈	—	4	2	no	—
37	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
38	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
39	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
40	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
41	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
42	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
43	C₄⋊(C₅₉⋊C₈)	C₂×C₄	1	4	yes	—
44	C₄⋊(C₅₉⋊C₈)	C₂×C₄	1	4	yes	—
45	C₂³×C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
46	C₂³×C₄×C₅₉	D₄	1	1	yes	characteristic
47	C₂³×C₄×C₅₉	Q₈	1	1	yes	characteristic
48	C₂²×C₈×C₅₉	—	2	2	no	—
49	C₂×C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄²×C₅₉	D₄	1	1	yes	characteristic
55	C₂×C₄²×C₅₉	D₄	1	1	yes	characteristic
56	C₂×C₄²×C₅₉	D₄	1	1	yes	characteristic
57	C₂×C₄²×C₅₉	D₄	1	1	yes	characteristic
58	C₂×C₄²×C₅₉	D₄	1	1	yes	characteristic
59	C₂×C₄²×C₅₉	Q₈	1	1	yes	characteristic
60	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
61	C₄⋊C₈×C₅₉	—	2	2	no	—
62	C₄⋊C₈×C₅₉	—	2	2	no	—
63	C₂²⋊C₈×C₅₉	—	2	2	no	—
64	C₂²⋊C₈×C₅₉	C₂×C₄	1	4	yes	—
65	C₄×C₈×C₅₉	—	2	2	no	—
66	C₄×C₈×C₅₉	—	2	2	no	—
67	C₂⁴×C₅₉	C₄⋊C₄	1	1	yes	characteristic
68	C₂²×C₄×C₅₉	—	2	4	no	—
69	C₂²×C₄×C₅₉	—	4	2	no	—
70	C₂²×C₄×C₅₉	C₄²	1	1	yes	characteristic
71	C₂²×C₄×C₅₉	C₄²	1	1	yes	characteristic
72	C₂²×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
73	C₂²×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
74	C₂²×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
76	C₂²×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
77	C₂²×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₅₉	C₄⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₅₉	C₄⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₅₉	C₄⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₅₉	C₄⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₅₉	C₄⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₅₉	C₄⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₅₉	C₄⋊C₄	1	1	yes	characteristic
85	C₂²×C₄×C₅₉	D₈	1	2	yes	—
86	C₂²×C₄×C₅₉	SD₁₆	1	2	yes	—
87	C₂²×C₄×C₅₉	SD₁₆	1	2	yes	—
88	C₂²×C₄×C₅₉	Q₁₆	1	2	yes	—
89	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₅₉	C₂×Q₈	1	1	yes	characteristic
92	C₂×C₈×C₅₉	—	2	4	no	—
93	C₂×C₈×C₅₉	—	4	4	no	—
94	C₄²×C₅₉	C₄²	1	1	yes	characteristic
95	C₄²×C₅₉	C₄²	1	1	yes	characteristic
96	C₄²×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
97	C₄²×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
98	C₄²×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
99	C₄²×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
100	C₄²×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
101	C₄²×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
102	C₄²×C₅₉	C₄⋊C₄	1	1	yes	characteristic
103	C₄²×C₅₉	C₄⋊C₄	1	1	yes	characteristic
104	C₄²×C₅₉	C₄⋊C₄	1	1	yes	characteristic
105	C₄²×C₅₉	C₄⋊C₄	1	1	yes	characteristic
106	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
107	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
108	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
109	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
110	#11745664	—	4	4	no	—
111	#11745664	—	4	2	no	—
112	#11745664	—	4	2	no	—
113	C₂×C₅₉⋊C₈	—	2	4	no	—
114	C₂×C₅₉⋊C₈	—	2	4	no	—
115	C₂×C₅₉⋊C₈	—	4	4	no	—
116	C₂×C₅₉⋊C₈	—	4	4	no	—
117	C₂×C₅₉⋊C₈	—	4	4	no	—
118	C₂×C₅₉⋊C₈	—	4	2	no	—
119	C₂×C₅₉⋊C₈	—	4	2	no	—
120	C₂³×C₅₉	—	2	2	no	—
121	C₂³×C₅₉	—	2	2	no	—
122	C₂³×C₅₉	#95	1	1	yes	characteristic
123	C₂³×C₅₉	#95	1	1	yes	characteristic
124	C₂³×C₅₉	#106	1	2	yes	—
125	C₂³×C₅₉	#107	1	2	yes	—
126	C₂³×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
127	C₂×C₄×C₅₉	—	2	2	no	—
128	C₂×C₄×C₅₉	—	2	2	no	—
129	C₂×C₄×C₅₉	—	2	2	no	—
130	C₂×C₄×C₅₉	—	2	2	no	—
131	C₂×C₄×C₅₉	—	2	2	no	—
132	C₂×C₄×C₅₉	—	2	2	no	—
133	C₂×C₄×C₅₉	—	2	2	no	—
134	C₂×C₄×C₅₉	—	4	1	no	—
135	C₂×C₄×C₅₉	—	4	1	no	—
136	C₂×C₄×C₅₉	—	4	1	no	—
137	C₂×C₄×C₅₉	—	4	1	no	—
138	C₂×C₄×C₅₉	#95	1	1	yes	characteristic
139	C₂×C₄×C₅₉	#95	1	1	yes	characteristic
140	C₂×C₄×C₅₉	#95	1	1	yes	characteristic
141	C₂×C₄×C₅₉	#95	1	1	yes	characteristic
142	C₂×C₄×C₅₉	#95	1	1	yes	characteristic
143	C₂×C₄×C₅₉	#95	1	1	yes	characteristic
144	C₂×C₄×C₅₉	#102	1	2	yes	—
145	C₂×C₄×C₅₉	#102	1	2	yes	—
146	C₂×C₄×C₅₉	#102	1	2	yes	—
147	C₂×C₄×C₅₉	#102	1	2	yes	—
148	C₂×C₄×C₅₉	#103	1	2	yes	—
149	C₂×C₄×C₅₉	#103	1	2	yes	—
150	C₂×C₄×C₅₉	#103	1	2	yes	—
151	C₂×C₄×C₅₉	#103	1	2	yes	—
152	C₂×C₄×C₅₉	#106	1	2	yes	—
153	C₂×C₄×C₅₉	#107	1	2	yes	—
154	C₂×C₄×C₅₉	#108	1	4	yes	—
155	C₂×C₄×C₅₉	C₂×C₄²	1	1	yes	characteristic
156	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
157	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
158	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
159	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
160	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
161	C₂×C₄×C₅₉	C₂×D₈	1	1	yes	characteristic
162	C₂×C₄×C₅₉	C₂×SD₁₆	1	1	yes	characteristic
163	C₂×C₄×C₅₉	C₂×SD₁₆	1	1	yes	characteristic
164	C₂×C₄×C₅₉	C₂×Q₁₆	1	1	yes	characteristic
165	C₈×C₅₉	—	4	4	no	—
166	C₅₉⋊C₈	—	4	4	no	—
167	C₅₉⋊C₈	—	4	4	no	—
168	C₂×#1301	—	59	1	no	maximal, Sylow
169	C₂²×C₅₉	—	2	4	no	—
170	C₂²×C₅₉	—	2	4	no	—
171	C₂²×C₅₉	—	2	1	no	—
172	C₂²×C₅₉	—	2	1	no	—
173	C₂²×C₅₉	—	2	1	no	—
174	C₂²×C₅₉	—	2	1	no	—
175	C₂²×C₅₉	#340	1	2	yes	—
176	C₂²×C₅₉	#340	1	2	yes	—
177	C₂²×C₅₉	#341	1	2	yes	—
178	C₂²×C₅₉	#344	1	2	yes	—
179	C₂²×C₅₉	C₂×#95	1	1	yes	characteristic
180	C₂²×C₅₉	C₂×#106	1	1	yes	characteristic
181	C₂²×C₅₉	C₂×#107	1	1	yes	characteristic
182	C₄×C₅₉	—	2	1	no	—
183	C₄×C₅₉	—	2	1	no	—
184	C₄×C₅₉	—	2	1	no	—
185	C₄×C₅₉	—	2	1	no	—
186	C₄×C₅₉	—	2	1	no	—
187	C₄×C₅₉	—	2	1	no	—
188	C₄×C₅₉	#340	1	2	yes	—
189	C₄×C₅₉	#340	1	2	yes	—
190	C₄×C₅₉	#341	1	2	yes	—
191	C₄×C₅₉	C₂×#102	1	1	yes	characteristic
192	C₄×C₅₉	C₂×#102	1	1	yes	characteristic
193	C₄×C₅₉	C₂×#103	1	1	yes	characteristic
194	C₄×C₅₉	C₂×#103	1	1	yes	characteristic
195	C₄×C₅₉	C₂×#108	1	2	yes	—
196	C₂×#431	D₅₉	1	1	yes	characteristic
197	C₂×#423	—	59	1	no	—
198	C₂²×C₄⋊C₈	—	59	1	no	—
199	#1301	—	59	4	no	—
200	C₂×C₅₉	—	2	2	no	—
201	C₂×C₅₉	—	2	1	no	—
202	C₂×C₅₉	—	2	1	no	—
203	C₂×C₅₉	#1301	1	4	yes	complemented
204	C₂×C₅₉	C₂×#340	1	1	yes	characteristic
205	C₂×C₅₉	C₂×#341	1	1	yes	characteristic
206	C₂×C₅₉	C₂×#344	1	1	yes	characteristic
207	C₂²×M₁₆	—	118	1	no	—
208	C₂³×C₈	—	118	1	no	—
209	C₂²×C₄²	C₂×D₅₉	1	1	yes	characteristic
210	#431	—	2	1	no	—
211	#431	—	2	1	no	—
212	#431	Dic₅₉	1	2	yes	—
213	#431	C₂×D₅₉	1	2	yes	—
214	#423	—	59	2	no	—
215	#423	—	59	2	no	—
216	#423	—	118	1	no	—
217	#423	—	118	1	no	—
218	C₂×C₄⋊C₈	—	2	1	no	—
219	C₂×C₄⋊C₈	—	59	2	no	—
220	C₂×C₄⋊C₈	—	59	2	no	—
221	C₂×C₄⋊C₈	—	59	2	no	—
222	C₂×C₄⋊C₈	—	59	2	no	—
223	C₂×C₄⋊C₈	—	118	1	no	—
224	C₂×C₄⋊C₈	—	118	1	no	—
225	C₂×C₄⋊C₈	—	118	1	no	—
226	C₂×C₄⋊C₈	—	118	1	no	—
227	C₂×C₂²⋊C₈	Dic₅₉	1	2	yes	—
228	C₂×C₄×C₈	—	2	1	no	—
229	C₅₉	C₂×#1301	1	1	yes	characteristic, complemented, Sylow
230	C₂³×C₄	Dic₁₁₈	1	1	yes	characteristic
231	C₂³×C₄	D₂₃₆	1	1	yes	characteristic
232	C₂³×C₄	C₂×Dic₅₉	1	1	yes	characteristic
233	C₂×M₁₆	—	118	2	no	—
234	C₂×M₁₆	—	118	2	no	—
235	C₂×M₁₆	—	236	2	no	—
236	C₂×M₁₆	—	236	2	no	—
237	C₂²×C₈	—	2	2	no	—
238	C₂²×C₈	—	118	2	no	—
239	C₂²×C₈	—	118	2	no	—
240	C₂²×C₈	—	118	2	no	—
241	C₂²×C₈	—	118	2	no	—
242	C₂²×C₈	—	236	2	no	—
243	C₂²×C₈	—	236	2	no	—
244	C₂×C₄²	Dic₁₁₈	1	1	yes	characteristic
245	C₂×C₄²	C₄×D₅₉	1	1	yes	characteristic
246	C₂×C₄²	C₄×D₅₉	1	1	yes	characteristic
247	C₂×C₄²	C₄×D₅₉	1	1	yes	characteristic
248	C₂×C₄²	C₄×D₅₉	1	1	yes	characteristic
249	C₂×C₄²	D₂₃₆	1	1	yes	characteristic
250	C₂×C₄²	C₂×Dic₅₉	1	1	yes	characteristic
251	C₂×C₄²	C₂²⋊D₅₉	1	1	yes	characteristic
252	C₂×C₄²	C₂²⋊D₅₉	1	1	yes	characteristic
253	C₂×C₄²	C₂²⋊D₅₉	1	1	yes	characteristic
254	C₂×C₄²	C₂²⋊D₅₉	1	1	yes	characteristic
255	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
256	C₄⋊C₈	—	2	2	no	—
257	C₄⋊C₈	—	2	2	no	—
258	C₄⋊C₈	—	59	4	no	—
259	C₄⋊C₈	—	59	4	no	—
260	C₄⋊C₈	—	118	2	no	—
261	C₄⋊C₈	—	118	2	no	—
262	C₄⋊C₈	—	118	2	no	—
263	C₄⋊C₈	—	118	2	no	—
264	C₄⋊C₈	—	118	2	no	—
265	C₄⋊C₈	—	118	2	no	—
266	C₂²⋊C₈	—	2	2	no	—
267	C₂²⋊C₈	C₂×Dic₅₉	1	4	yes	—
268	C₄×C₈	—	2	2	no	—
269	C₄×C₈	—	2	2	no	—
270	C₂⁴	C₄⋊Dic₅₉	1	1	yes	characteristic
271	C₂²×C₄	—	2	4	no	—
272	C₂²×C₄	—	4	2	no	—
273	C₂²×C₄	#11745660	1	2	yes	—
274	C₂²×C₄	#11745660	1	2	yes	—
275	C₂²×C₄	D₄₇₂	1	2	yes	—
276	C₂²×C₄	Dic₂₃₆	1	2	yes	—
277	C₂²×C₄	C₄×Dic₅₉	1	1	yes	characteristic
278	C₂²×C₄	C₄×Dic₅₉	1	1	yes	characteristic
279	C₂²×C₄	Dic₅₉⋊C₄	1	1	yes	characteristic
280	C₂²×C₄	Dic₅₉⋊C₄	1	1	yes	characteristic
281	C₂²×C₄	Dic₅₉⋊C₄	1	1	yes	characteristic
282	C₂²×C₄	Dic₅₉⋊C₄	1	1	yes	characteristic
283	C₂²×C₄	C₄⋊Dic₅₉	1	1	yes	characteristic
284	C₂²×C₄	C₄⋊Dic₅₉	1	1	yes	characteristic
285	C₂²×C₄	C₄⋊Dic₅₉	1	1	yes	characteristic
286	C₂²×C₄	(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
287	C₂²×C₄	(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
288	C₂²×C₄	(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
289	C₂²×C₄	(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
290	C₂²×C₄	C₂²⋊Dic₅₉	1	1	yes	characteristic
291	C₂²×C₄	C₂²⋊Dic₅₉	1	1	yes	characteristic
292	C₂²×C₄	C₂×Dic₁₁₈	1	1	yes	characteristic
293	C₂²×C₄	C₂×D₂₃₆	1	1	yes	characteristic
294	C₂²×C₄	C₂²×Dic₅₉	1	1	yes	characteristic
295	M₁₆	—	236	4	no	—
296	M₁₆	—	236	2	no	—
297	M₁₆	—	236	2	no	—
298	C₂×C₈	—	2	4	no	—
299	C₂×C₈	—	4	4	no	—
300	C₂×C₈	—	118	4	no	—
301	C₂×C₈	—	118	4	no	—
302	C₂×C₈	—	236	4	no	—
303	C₂×C₈	—	236	4	no	—
304	C₂×C₈	—	236	4	no	—
305	C₂×C₈	—	236	2	no	—
306	C₂×C₈	—	236	2	no	—
307	C₄²	C₄×Dic₅₉	1	1	yes	characteristic
308	C₄²	C₄×Dic₅₉	1	1	yes	characteristic
309	C₄²	Dic₅₉⋊C₄	1	1	yes	characteristic
310	C₄²	Dic₅₉⋊C₄	1	1	yes	characteristic
311	C₄²	Dic₅₉⋊C₄	1	1	yes	characteristic
312	C₄²	Dic₅₉⋊C₄	1	1	yes	characteristic
313	C₄²	(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
314	C₄²	(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
315	C₄²	(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
316	C₄²	(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
317	C₄²	C₂²⋊Dic₅₉	1	1	yes	characteristic
318	C₄²	C₂²⋊Dic₅₉	1	1	yes	characteristic
319	C₄²	C₂×C₄×D₅₉	1	1	yes	characteristic
320	C₄²	C₂×C₄×D₅₉	1	1	yes	characteristic
321	C₄²	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
322	C₄²	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
323	C₂³	—	2	2	no	—
324	C₂³	—	2	2	no	—
325	C₂³	C₅₉⋊#95	1	1	yes	characteristic
326	C₂³	C₅₉⋊#95	1	1	yes	characteristic
327	C₂³	#14273659	1	2	yes	—
328	C₂³	#14273661	1	2	yes	—
329	C₂³	C₂×C₄⋊Dic₅₉	1	1	yes	characteristic
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	4	1	no	—
338	C₂×C₄	—	4	1	no	—
339	C₂×C₄	—	4	1	no	—
340	C₂×C₄	—	4	1	no	—
341	C₂×C₄	C₅₉⋊#95	1	1	yes	characteristic
342	C₂×C₄	C₅₉⋊#95	1	1	yes	characteristic
343	C₂×C₄	C₅₉⋊#95	1	1	yes	characteristic
344	C₂×C₄	C₅₉⋊#95	1	1	yes	characteristic
345	C₂×C₄	C₅₉⋊#95	1	1	yes	characteristic
346	C₂×C₄	C₅₉⋊#95	1	1	yes	characteristic
347	C₂×C₄	#14273649	1	2	yes	—
348	C₂×C₄	#14273649	1	2	yes	—
349	C₂×C₄	#14273649	1	2	yes	—
350	C₂×C₄	#14273649	1	2	yes	—
351	C₂×C₄	#14273652	1	2	yes	—
352	C₂×C₄	#14273652	1	2	yes	—
353	C₂×C₄	#14273652	1	2	yes	—
354	C₂×C₄	#14273652	1	2	yes	—
355	C₂×C₄	#14273659	1	2	yes	—
356	C₂×C₄	#14273661	1	2	yes	—
357	C₂×C₄	#14273662	1	4	yes	—
358	C₂×C₄	C₂×C₄×Dic₅₉	1	1	yes	characteristic
359	C₂×C₄	C₂×(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
360	C₂×C₄	C₂×(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
361	C₂×C₄	C₂×C₂²⋊Dic₅₉	1	1	yes	characteristic
362	C₂×C₄	C₂×Dic₅₉⋊C₄	1	1	yes	characteristic
363	C₂×C₄	C₂×Dic₅₉⋊C₄	1	1	yes	characteristic
364	C₂×C₄	C₂×D₄₇₂	1	1	yes	characteristic
365	C₂×C₄	C₂×#11745660	1	1	yes	characteristic
366	C₂×C₄	C₂×#11745660	1	1	yes	characteristic
367	C₂×C₄	C₂×Dic₂₃₆	1	1	yes	characteristic
368	C₈	—	4	4	no	—
369	C₈	—	236	4	no	—
370	C₈	—	236	4	no	—
371	C₂²	—	2	4	no	—
372	C₂²	—	2	4	no	—
373	C₂²	—	2	1	no	—
374	C₂²	—	2	1	no	—
375	C₂²	—	2	1	no	—
376	C₂²	—	2	1	no	—
377	C₂²	#16837165	1	2	yes	—
378	C₂²	#16837165	1	2	yes	—
379	C₂²	#16837166	1	2	yes	—
380	C₂²	#16837172	1	2	yes	—
381	C₂²	C₂×C₅₉⋊#95	1	1	yes	characteristic
382	C₂²	C₂×#14273659	1	1	yes	characteristic
383	C₂²	C₂×#14273661	1	1	yes	characteristic
384	C₄	—	2	1	no	—
385	C₄	—	2	1	no	—
386	C₄	—	2	1	no	—
387	C₄	—	2	1	no	—
388	C₄	—	2	1	no	—
389	C₄	—	2	1	no	—
390	C₄	#16837165	1	2	yes	—
391	C₄	#16837165	1	2	yes	—
392	C₄	#16837166	1	2	yes	—
393	C₄	C₂×#14273649	1	1	yes	characteristic
394	C₄	C₂×#14273649	1	1	yes	characteristic
395	C₄	C₂×#14273652	1	1	yes	characteristic
396	C₄	C₂×#14273652	1	1	yes	characteristic
397	C₄	C₂×#14273662	1	2	yes	—
398	C₂	—	2	2	no	—
399	C₂	—	2	1	no	—
400	C₂	—	2	1	no	—
401	C₂	#21421992	1	4	yes	direct product factor
402	C₂	C₂×#16837165	1	1	yes	characteristic
403	C₂	C₂×#16837166	1	1	yes	characteristic
404	C₂	C₂×#16837172	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	(C₂×D₅₉)⋊C₄
commutator	C₂×C₄×C₅₉	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₅₉
Fitting	C₂×C₅₉×#431	C₂
socle	C₂³×C₅₉	#95
prime radical	C₂⁴×C₅₉	C₄⋊C₄
cosocle	C₂×C₄²×C₅₉	C₂³
hypercenter	C₂×#431	D₅₉
hypocenter	C₅₉	C₂×#1301
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂²×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄² ◁ C₂×#431

Complements

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

N	H ≅ G/N	type
3. #21421992	C₂	direct (N × H)
203. C₂×C₅₉	#1301	semidirect
229. C₅₉	C₂×#1301	semidirect
401. C₂	#21421992	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#16837426	2
C₂²×C₄⋊(C₅₉⋊C₈)	2
#21421992	2
C₂×C₅₉×#431	2
C₂×#1301	59

Subgroups — C2×#21421992 #28478913

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#21421992 #28478913