Subgroups — #21438053

Order 7552.

1142 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16838135	C₂	1	1	yes	maximal, characteristic, complemented
2	#16838120	C₂	1	1	yes	maximal, characteristic, complemented
3	#16838115	C₂	1	1	yes	maximal, characteristic, complemented
4	#16838082	C₂	1	2	yes	maximal, complemented
5	#16838076	C₂	1	2	yes	maximal, complemented
6	#16838067	C₂	1	1	yes	maximal, characteristic, complemented
7	#16838060	C₂	1	2	yes	maximal, complemented
8	#16838049	C₂	1	1	yes	maximal, characteristic, complemented
9	#16838048	C₂	1	1	yes	maximal, characteristic, complemented
10	#16838041	C₂	1	2	yes	maximal, complemented
11	#16838036	C₂	1	1	yes	maximal, characteristic, complemented
12	#16838026	C₂	1	1	yes	maximal, characteristic, complemented
13	#16838019	C₂	1	1	yes	maximal, characteristic, complemented
14	#16837986	C₂	1	2	yes	maximal, complemented
15	#16837984	C₂	1	2	yes	maximal, complemented
16	#16837947	C₂	1	1	yes	maximal, characteristic, complemented
17	#16837932	C₂	1	1	yes	maximal, characteristic, complemented
18	#16837930	C₂	1	2	yes	maximal, complemented
19	#124×D₅₉	C₂	1	2	yes	maximal, complemented
20	#16837876	C₂	1	1	yes	maximal, characteristic, complemented
21	#16837874	C₂	1	1	yes	maximal, characteristic, complemented
22	#16837870	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₉×#555	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#11745685	C₂²	1	1	yes	characteristic
25	C₂×#11745687	C₂²	1	2	yes	complemented
26	C₂×Q₈×D₅₉	C₂²	1	2	yes	complemented
27	C₂²×D₂₃₆	C₂²	1	1	yes	characteristic
28	C₂×D₄×D₅₉	C₂²	1	1	yes	characteristic
29	C₂×D₄×D₅₉	C₂²	1	2	yes	—
30	#14273726	C₂²	1	1	yes	characteristic, complemented
31	#14273726	C₂²	1	1	yes	characteristic, complemented
32	#14273723	C₂²	1	1	yes	characteristic
33	#14273722	C₂²	1	2	yes	complemented
34	#14273722	C₂²	1	1	yes	characteristic, complemented
35	#14273721	C₂²	1	2	yes	complemented
36	#14273720	C₂²	1	2	yes	complemented
37	#14273720	C₂²	1	1	yes	characteristic, complemented
38	#14273720	C₂²	1	2	yes	complemented
39	#14273717	C₂²	1	1	yes	characteristic, complemented
40	#14273716	C₂²	1	2	yes	complemented
41	#14273715	C₂²	1	2	yes	complemented
42	#14273715	C₂²	1	1	yes	characteristic, complemented
43	#14273714	C₂²	1	2	yes	complemented
44	#14273714	C₂²	1	1	yes	characteristic, complemented
45	#14273713	C₂²	1	1	yes	characteristic
46	#14273713	C₂²	1	2	yes	—
47	#14273713	C₂²	1	2	yes	complemented
48	#14273713	C₂²	1	2	yes	complemented
49	#14273713	C₂²	1	2	yes	complemented
50	#14273712	C₂²	1	2	yes	complemented
51	#14273712	C₂²	1	2	yes	complemented
52	#14273711	C₂²	1	1	yes	characteristic, complemented
53	#14273710	C₂²	1	2	yes	complemented
54	#14273709	C₂²	1	2	yes	complemented
55	#14273709	C₂²	1	2	yes	complemented
56	#14273708	C₂²	1	1	yes	characteristic, complemented
57	#14273708	C₂²	1	2	yes	complemented
58	#14273707	C₂²	1	1	yes	characteristic, complemented
59	#14273706	C₂²	1	1	yes	characteristic, complemented
60	#14273705	C₂²	1	2	yes	complemented
61	#14273705	C₂²	1	2	yes	complemented
62	#14273704	C₂²	1	1	yes	characteristic, complemented
63	#14273704	C₂²	1	2	yes	complemented
64	#14273703	C₂²	1	2	yes	complemented
65	#14273703	C₂²	1	2	yes	complemented
66	#14273702	C₂²	1	1	yes	characteristic
67	#14273701	C₂²	1	1	yes	characteristic, complemented
68	#14273700	C₂²	1	2	yes	—
69	#14273700	C₂²	1	2	yes	complemented
70	#14273700	C₂²	1	2	yes	complemented
71	#14273699	C₂²	1	1	yes	characteristic
72	#14273699	C₂²	1	2	yes	complemented
73	#14273698	C₂²	1	2	yes	complemented
74	#14273697	C₂²	1	2	yes	—
75	#14273695	C₂²	1	2	yes	—
76	#14273695	C₂²	1	2	yes	complemented
77	#14273695	C₂²	1	2	yes	complemented
78	C₄×Dic₁₁₈	C₂²	1	2	yes	complemented
79	C₄×Dic₁₁₈	C₂²	1	1	yes	characteristic, complemented
80	#14273692	C₂²	1	1	yes	characteristic, complemented
81	#14273692	C₂²	1	1	yes	characteristic, complemented
82	C₄×D₂₃₆	C₂²	1	1	yes	characteristic
83	C₄×D₂₃₆	C₂²	1	2	yes	complemented
84	C₄×D₂₃₆	C₂²	1	2	yes	complemented
85	D₄×Dic₅₉	C₂²	1	1	yes	characteristic, complemented
86	#14273689	C₂²	1	1	yes	characteristic
87	#14273689	C₂²	1	1	yes	characteristic
88	#14273689	C₂²	1	1	yes	characteristic
89	#14273689	C₂²	1	1	yes	characteristic, complemented
90	#14273689	C₂²	1	1	yes	characteristic, complemented
91	C₄×C₂²⋊D₅₉	C₂²	1	1	yes	characteristic
92	C₄×C₂²⋊D₅₉	C₂²	1	2	yes	complemented
93	C₄×C₂²⋊D₅₉	C₂²	1	2	yes	complemented
94	C₄×C₂²⋊D₅₉	C₂²	1	1	yes	characteristic, complemented
95	(C₂²⋊D₅₉)⋊C₄	C₂²	1	2	yes	complemented
96	(C₂²⋊D₅₉)⋊C₄	C₂²	1	2	yes	complemented
97	(C₂²⋊D₅₉)⋊C₄	C₂²	1	2	yes	complemented
98	(C₂²⋊D₅₉)⋊C₄	C₂²	1	2	yes	complemented
99	#14273686	C₂²	1	1	yes	characteristic, complemented
100	#14273685	C₂²	1	1	yes	characteristic, complemented
101	#14273684	C₂²	1	2	yes	complemented
102	#14273684	C₂²	1	1	yes	characteristic, complemented
103	#14273684	C₂²	1	2	yes	complemented
104	C₂×(C₂×D₅₉)⋊C₄	C₂²	1	2	yes	complemented
105	C₂²⋊C₄×D₅₉	C₂²	1	2	yes	complemented
106	C₂²⋊C₄×D₅₉	C₂²	1	2	yes	complemented
107	C₂²⋊C₄×D₅₉	C₂²	1	2	yes	complemented
108	C₂²⋊C₄×D₅₉	C₂²	1	2	yes	complemented
109	C₂²⋊C₄×D₅₉	C₂²	1	2	yes	complemented
110	C₂×C₄×Dic₅₉	C₂²	1	1	yes	characteristic, complemented
111	C₄²×D₅₉	C₂²	1	2	yes	complemented
112	C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic, complemented
113	#124×C₅₉	C₂²	1	2	yes	complemented
114	#124×C₅₉	C₂²	1	2	yes	complemented
115	#121×C₅₉	C₂²	1	1	yes	characteristic
116	#121×C₅₉	C₂²	1	1	yes	characteristic, complemented
117	#121×C₅₉	C₂²	1	2	yes	complemented
118	C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic, complemented
120	#117×C₅₉	C₂²	1	2	yes	complemented
121	#117×C₅₉	C₂²	1	1	yes	characteristic, complemented
122	#117×C₅₉	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₅₉	C₂³	1	2	yes	—
124	C₂³×D₅₉	C₂³	1	2	yes	—
125	C₂×Q₈×C₅₉	C₂³	1	2	yes	—
126	C₂×D₄×C₅₉	C₂³	1	1	yes	characteristic
127	C₂×D₄×C₅₉	C₂³	1	1	yes	characteristic
128	C₂×D₄×C₅₉	C₂³	1	2	yes	—
129	C₂×D₄×C₅₉	C₂³	1	2	yes	—
130	C₂²×C₄×C₅₉	C₂³	1	1	yes	characteristic
131	C₂²×C₄×C₅₉	C₂³	1	1	yes	characteristic
132	C₂²×C₄×C₅₉	C₂³	1	2	yes	—
133	C₂×C₂²⋊D₅₉	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₅₉	C₂³	1	2	yes	—
135	C₂×C₂²⋊D₅₉	C₂³	1	1	yes	characteristic
136	C₂×C₂²⋊D₅₉	C₂³	1	2	yes	—
137	C₂×C₂²⋊D₅₉	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₅₉	C₂³	1	1	yes	characteristic
139	C₂×C₂²⋊D₅₉	C₂³	1	2	yes	—
140	C₂²×Dic₅₉	C₂³	1	1	yes	characteristic
141	C₂²×Dic₅₉	C₂³	1	1	yes	characteristic
142	C₂²×Dic₅₉	C₂³	1	2	yes	—
143	Q₈×D₅₉	—	4	4	no	—
144	#11745687	—	4	4	no	—
145	D₄×D₅₉	—	2	4	no	—
146	D₄×D₅₉	—	4	4	no	—
147	#11745685	—	2	4	no	—
148	C₂×D₂₃₆	—	2	4	no	—
149	C₂×D₂₃₆	C₂³	1	1	yes	characteristic
150	C₂×D₂₃₆	C₂³	1	2	yes	—
151	C₂×D₂₃₆	C₂³	1	2	yes	—
152	C₂×D₂₃₆	C₂³	1	1	yes	characteristic
153	C₂×C₄×D₅₉	C₂³	1	2	yes	—
154	C₂×C₄×D₅₉	C₂³	1	2	yes	—
155	C₂×C₄×D₅₉	C₂³	1	1	yes	characteristic
156	C₂×C₄×D₅₉	C₂³	1	2	yes	—
157	C₂×C₄×D₅₉	C₂³	1	2	yes	—
158	C₂×C₄×D₅₉	C₂³	1	2	yes	—
159	C₂×C₄×D₅₉	C₂³	1	2	yes	—
160	C₂×C₄×D₅₉	C₂³	1	2	yes	—
161	C₂×Dic₁₁₈	C₂³	1	1	yes	characteristic
162	C₂×Dic₁₁₈	C₂³	1	1	yes	characteristic
163	C₂×Dic₁₁₈	C₂³	1	2	yes	—
164	C₂×Dic₁₁₈	C₂³	1	2	yes	—
165	C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
166	C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
167	C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
168	C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
169	C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
170	C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
171	C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
172	C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
173	C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
174	C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
175	C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
176	C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
177	C₄²×C₅₉	C₂³	1	2	yes	—
178	C₄²×C₅₉	C₂³	1	2	yes	—
179	C₄²×C₅₉	C₂³	1	1	yes	characteristic
180	C₂²⋊Dic₅₉	C₂³	1	1	yes	characteristic
181	C₂²⋊Dic₅₉	C₂³	1	1	yes	characteristic
182	C₂²⋊Dic₅₉	C₂³	1	2	yes	—
183	C₂²⋊Dic₅₉	C₂³	1	2	yes	—
184	C₂²⋊Dic₅₉	C₂³	1	2	yes	—
185	C₂²⋊Dic₅₉	C₂³	1	1	yes	characteristic
186	C₂²⋊Dic₅₉	C₂³	1	2	yes	—
187	C₂²⋊Dic₅₉	C₂³	1	1	yes	characteristic
188	(C₂×D₅₉)⋊C₄	C₂³	1	1	yes	characteristic
189	(C₂×D₅₉)⋊C₄	C₂³	1	1	yes	characteristic
190	(C₂×D₅₉)⋊C₄	C₂³	1	2	yes	—
191	(C₂×D₅₉)⋊C₄	C₂³	1	2	yes	—
192	(C₂×D₅₉)⋊C₄	C₂³	1	2	yes	—
193	(C₂×D₅₉)⋊C₄	C₂³	1	2	yes	—
194	(C₂×D₅₉)⋊C₄	C₂³	1	2	yes	—
195	(C₂×D₅₉)⋊C₄	C₂³	1	2	yes	—
196	(C₂×D₅₉)⋊C₄	C₂³	1	2	yes	—
197	(C₂×D₅₉)⋊C₄	C₂³	1	2	yes	—
198	(C₂×D₅₉)⋊C₄	C₂³	1	1	yes	characteristic
199	(C₂×D₅₉)⋊C₄	C₂³	1	2	yes	—
200	(C₂×D₅₉)⋊C₄	C₂³	1	2	yes	—
201	(C₂×D₅₉)⋊C₄	C₂³	1	2	yes	—
202	(C₂×D₅₉)⋊C₄	C₂³	1	1	yes	characteristic
203	(C₂×D₅₉)⋊C₄	C₂³	1	2	yes	—
204	C₄⋊Dic₅₉	C₂³	1	1	yes	characteristic
205	C₄⋊Dic₅₉	C₂³	1	1	yes	characteristic
206	C₄⋊Dic₅₉	C₂³	1	1	yes	characteristic
207	C₄⋊Dic₅₉	C₂³	1	2	yes	—
208	C₄⋊Dic₅₉	C₂³	1	1	yes	characteristic
209	Dic₅₉⋊C₄	C₂³	1	1	yes	characteristic
210	Dic₅₉⋊C₄	C₂³	1	1	yes	characteristic
211	Dic₅₉⋊C₄	C₂³	1	2	yes	—
212	Dic₅₉⋊C₄	C₂³	1	2	yes	—
213	Dic₅₉⋊C₄	C₂³	1	1	yes	characteristic
214	Dic₅₉⋊C₄	C₂³	1	2	yes	—
215	Dic₅₉⋊C₄	C₂³	1	2	yes	—
216	Dic₅₉⋊C₄	C₂³	1	1	yes	characteristic
217	Dic₅₉⋊C₄	C₂³	1	1	yes	characteristic
218	Dic₅₉⋊C₄	C₂³	1	2	yes	—
219	Dic₅₉⋊C₄	C₂³	1	1	yes	characteristic
220	C₄×Dic₅₉	C₂³	1	1	yes	characteristic
221	C₄×Dic₅₉	C₂³	1	2	yes	—
222	C₄×Dic₅₉	C₂³	1	2	yes	—
223	C₄×Dic₅₉	C₂³	1	1	yes	characteristic
224	C₄×Dic₅₉	C₂³	1	1	yes	characteristic
225	C₄×Dic₅₉	C₂³	1	1	yes	characteristic
226	C₄×Dic₅₉	C₂³	1	2	yes	—
227	C₄×Dic₅₉	C₂³	1	1	yes	characteristic
228	C₂³×C₅₉	C₂⁴	1	1	yes	characteristic
229	C₂³×C₅₉	C₂⁴	1	2	yes	—
230	C₂³×C₅₉	C₂⁴	1	1	yes	characteristic
231	C₂²×D₅₉	—	2	4	no	—
232	C₂²×D₅₉	—	2	4	no	—
233	C₂²×D₅₉	—	4	2	no	—
234	C₂²×D₅₉	—	4	2	no	—
235	C₂²×D₅₉	—	4	2	no	—
236	C₂²×D₅₉	—	4	2	no	—
237	C₂²×D₅₉	C₂⁴	1	1	yes	characteristic
238	C₂²×D₅₉	C₂⁴	1	2	yes	—
239	C₂²×D₅₉	C₂⁴	1	2	yes	—
240	Q₈×C₅₉	—	4	2	no	—
241	D₄×C₅₉	—	2	2	no	—
242	D₄×C₅₉	—	4	2	no	—
243	D₄×C₅₉	—	4	2	no	—
244	D₄×C₅₉	—	4	1	no	—
245	C₂×C₄×C₅₉	—	2	2	no	—
246	C₂×C₄×C₅₉	—	2	2	no	—
247	C₂×C₄×C₅₉	—	4	2	no	—
248	C₂×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
249	C₂×C₄×C₅₉	C₂⁴	1	2	yes	—
250	C₂×C₄×C₅₉	C₂⁴	1	2	yes	—
251	C₂×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
252	C₂×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
253	C₂×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
254	C₂×C₄×C₅₉	C₂⁴	1	2	yes	—
255	C₂×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
256	C₂²⋊D₅₉	—	2	4	no	—
257	C₂²⋊D₅₉	—	2	4	no	—
258	C₂²⋊D₅₉	—	2	2	no	—
259	C₂²⋊D₅₉	—	2	4	no	—
260	C₂²⋊D₅₉	—	4	2	no	—
261	C₂²⋊D₅₉	—	4	1	no	—
262	C₂²⋊D₅₉	—	4	2	no	—
263	C₂×Dic₅₉	—	2	2	no	—
264	C₂×Dic₅₉	—	4	2	no	—
265	C₂×Dic₅₉	—	4	1	no	—
266	C₂×Dic₅₉	C₂⁴	1	1	yes	characteristic
267	C₂×Dic₅₉	C₂⁴	1	1	yes	characteristic
268	C₂×Dic₅₉	C₂⁴	1	1	yes	characteristic
269	C₂×Dic₅₉	C₂⁴	1	2	yes	—
270	C₂×Dic₅₉	C₂⁴	1	1	yes	characteristic
271	C₂×Dic₅₉	C₂⁴	1	1	yes	characteristic
272	C₂×Dic₅₉	C₂⁴	1	2	yes	—
273	C₂×Dic₅₉	C₂⁴	1	1	yes	characteristic
274	C₂×Dic₅₉	C₂⁴	1	1	yes	characteristic
275	D₂₃₆	—	2	4	no	—
276	D₂₃₆	—	2	2	no	—
277	D₂₃₆	—	4	2	no	—
278	D₂₃₆	#41	1	4	yes	complemented
279	C₄×D₅₉	—	2	4	no	—
280	C₄×D₅₉	—	2	2	no	—
281	C₄×D₅₉	—	2	4	no	—
282	C₄×D₅₉	—	4	2	no	—
283	C₄×D₅₉	—	4	2	no	—
284	C₄×D₅₉	—	4	2	no	—
285	C₄×D₅₉	—	4	2	no	—
286	C₄×D₅₉	—	4	2	no	—
287	Dic₁₁₈	—	2	2	no	—
288	Dic₁₁₈	—	2	4	no	—
289	Dic₁₁₈	—	2	2	no	—
290	Dic₁₁₈	—	4	2	no	—
291	C₂²×C₅₉	—	2	1	no	—
292	C₂²×C₅₉	—	2	2	no	—
293	C₂²×C₅₉	—	2	1	no	—
294	C₂²×C₅₉	—	2	1	no	—
295	C₂²×C₅₉	—	2	2	no	—
296	C₂²×C₅₉	—	2	1	no	—
297	C₂²×C₅₉	—	2	1	no	—
298	C₂²×C₅₉	—	2	2	no	—
299	C₂²×C₅₉	—	2	1	no	—
300	C₂²×C₅₉	C₂⁵	1	1	yes	characteristic
301	C₂×D₅₉	—	2	2	no	—
302	C₂×D₅₉	—	2	2	no	—
303	C₂×D₅₉	—	2	1	no	—
304	C₂×D₅₉	—	2	2	no	—
305	C₂×D₅₉	—	2	2	no	—
306	C₂×D₅₉	—	2	1	no	—
307	C₂×D₅₉	—	2	2	no	—
308	C₂×D₅₉	—	2	1	no	—
309	C₂×D₅₉	—	8	4	no	—
310	C₂×D₅₉	—	8	4	no	—
311	C₂×D₅₉	C₂×#41	1	4	yes	—
312	C₄×C₅₉	—	2	1	no	—
313	C₄×C₅₉	—	2	1	no	—
314	C₄×C₅₉	—	2	2	no	—
315	C₄×C₅₉	—	2	1	no	—
316	C₄×C₅₉	—	2	2	no	—
317	C₄×C₅₉	—	2	2	no	—
318	C₄×C₅₉	—	2	1	no	—
319	C₄×C₅₉	C₂×#41	1	2	yes	—
320	Dic₅₉	—	2	2	no	—
321	Dic₅₉	—	2	1	no	—
322	Dic₅₉	—	2	1	no	—
323	Dic₅₉	—	2	2	no	—
324	Dic₅₉	—	2	1	no	—
325	Dic₅₉	—	2	1	no	—
326	Dic₅₉	—	2	1	no	—
327	Dic₅₉	—	2	1	no	—
328	Dic₅₉	H(5,𝔽₂)	1	2	yes	—
329	#3514	—	59	1	no	maximal, Sylow
330	C₂×C₅₉	—	4	1	no	—
331	C₂×C₅₉	—	4	2	no	—
332	C₂×C₅₉	—	4	1	no	—
333	C₂×C₅₉	C₂²×#41	1	1	yes	characteristic
334	C₂×C₅₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
335	C₂×C₅₉	#585	1	1	yes	characteristic
336	D₅₉	—	2	4	no	—
337	D₅₉	—	4	2	no	—
338	D₅₉	—	4	1	no	—
339	#559	—	59	1	no	—
340	#556	—	59	1	no	—
341	#555	—	59	1	no	—
342	#555	D₅₉	1	1	yes	characteristic, complemented
343	#551	—	59	2	no	—
344	#551	—	59	2	no	—
345	D₄×Q₈	—	59	1	no	—
346	#548	—	59	2	no	—
347	#546	—	59	2	no	—
348	#546	—	59	1	no	—
349	#546	—	59	1	no	—
350	D₄²	—	59	1	no	—
351	#542	—	59	1	no	—
352	#542	—	59	1	no	—
353	#538	—	59	2	no	—
354	#538	—	59	2	no	—
355	#532	—	59	1	no	—
356	#529	—	59	1	no	—
357	#529	—	59	2	no	—
358	C₂×#124	—	59	2	no	—
359	#518	—	59	1	no	—
360	#518	—	59	1	no	—
361	C₄×#41	—	59	1	no	—
362	C₅₉	#3514	1	1	yes	characteristic, complemented, Sylow
363	C₂×#41	—	59	2	no	—
364	C₂×#41	—	59	1	no	—
365	C₂²×Q₈	—	59	2	no	—
366	C₂²×D₄	—	59	1	no	—
367	C₂²×D₄	—	59	2	no	—
368	C₂²×D₄	—	59	1	no	—
369	C₄⋊Q₈	—	59	1	no	—
370	C₄⋊Q₈	—	59	1	no	—
371	C₄⋊Q₈	C₂×D₅₉	1	1	yes	characteristic, complemented
372	#127	—	59	1	no	—
373	#126	—	59	2	no	—
374	#126	—	59	1	no	—
375	#126	—	59	2	no	—
376	#126	—	59	1	no	—
377	#126	—	59	2	no	—
378	#126	—	59	2	no	—
379	#125	—	59	1	no	—
380	#124	—	59	2	no	—
381	#124	—	59	2	no	—
382	#124	—	59	1	no	—
383	#124	—	59	1	no	—
384	#124	—	59	2	no	—
385	#124	—	59	2	no	—
386	#124	—	59	2	no	—
387	#124	—	59	2	no	—
388	#124	—	59	2	no	—
389	#124	—	59	1	no	—
390	#124	C₂×D₅₉	1	2	yes	complemented
391	#124	C₂×D₅₉	1	2	yes	complemented
392	#123	—	59	1	no	—
393	#123	—	59	2	no	—
394	#123	—	59	2	no	—
395	#123	—	59	2	no	—
396	#123	—	59	2	no	—
397	#123	—	59	1	no	—
398	#123	—	59	2	no	—
399	#123	—	59	2	no	—
400	C₂²⋊Q₈	—	59	2	no	—
401	C₂²⋊Q₈	—	59	2	no	—
402	C₂²⋊Q₈	—	59	1	no	—
403	C₂²⋊Q₈	—	59	2	no	—
404	C₂²⋊Q₈	—	59	2	no	—
405	C₂²⋊Q₈	—	59	1	no	—
406	C₂²⋊Q₈	—	59	1	no	—
407	C₂²⋊Q₈	—	59	2	no	—
408	#121	—	59	1	no	—
409	#121	—	59	2	no	—
410	#121	—	59	2	no	—
411	#121	—	59	1	no	—
412	#121	—	59	1	no	—
413	#121	—	59	2	no	—
414	#121	—	59	2	no	—
415	#121	—	59	2	no	—
416	#121	C₂×D₅₉	1	1	yes	characteristic
417	#121	C₂×D₅₉	1	1	yes	characteristic, complemented
418	#121	C₂×D₅₉	1	2	yes	complemented
419	#120	—	59	2	no	—
420	#120	—	59	2	no	—
421	#120	—	59	2	no	—
422	#120	—	59	2	no	—
423	C₄×Q₈	—	59	1	no	—
424	C₄×Q₈	—	59	1	no	—
425	C₄×Q₈	—	59	2	no	—
426	C₄×Q₈	—	59	1	no	—
427	C₄×D₄	—	59	1	no	—
428	C₄×D₄	—	59	2	no	—
429	C₄×D₄	—	59	1	no	—
430	C₄×D₄	—	59	1	no	—
431	C₄×D₄	—	59	2	no	—
432	C₄×D₄	—	59	1	no	—
433	C₄×D₄	—	59	1	no	—
434	C₄×D₄	—	59	1	no	—
435	C₄×D₄	—	59	1	no	—
436	C₄×D₄	—	59	1	no	—
437	C₄×D₄	—	59	2	no	—
438	C₄×D₄	—	59	2	no	—
439	C₄×D₄	—	59	2	no	—
440	C₄×D₄	—	59	2	no	—
441	C₄×D₄	—	59	2	no	—
442	C₄×D₄	—	59	1	no	—
443	C₄×D₄	—	59	2	no	—
444	C₄×D₄	C₂×D₅₉	1	1	yes	characteristic, complemented
445	C₄×D₄	C₂×D₅₉	1	1	yes	characteristic, complemented
446	#117	—	59	1	no	—
447	#117	—	59	1	no	—
448	#117	—	59	2	no	—
449	#117	—	59	1	no	—
450	#117	—	59	2	no	—
451	#117	C₂×D₅₉	1	1	yes	characteristic, complemented
452	#117	C₂×D₅₉	1	1	yes	characteristic, complemented
453	#117	C₂×D₅₉	1	2	yes	complemented
454	C₂×C₂²⋊C₄	—	59	2	no	—
455	C₂×C₂²⋊C₄	—	59	2	no	—
456	C₂×C₂²⋊C₄	—	59	2	no	—
457	C₂×C₂²⋊C₄	—	59	2	no	—
458	C₂×C₂²⋊C₄	—	59	2	no	—
459	C₂×C₂²⋊C₄	—	59	2	no	—
460	C₂×C₄²	—	59	1	no	—
461	C₂×C₄²	—	59	2	no	—
462	C₂⁴	—	59	2	no	—
463	C₂⁴	—	59	2	no	—
464	#41	—	118	4	no	—
465	#41	—	236	4	no	—
466	C₂×Q₈	—	59	1	no	—
467	C₂×Q₈	—	59	1	no	—
468	C₂×Q₈	—	59	2	no	—
469	C₂×Q₈	—	59	2	no	—
470	C₂×Q₈	—	236	4	no	—
471	C₂×Q₈	C₂²×D₅₉	1	2	yes	—
472	C₂×D₄	—	59	2	no	—
473	C₂×D₄	—	59	2	no	—
474	C₂×D₄	—	59	1	no	—
475	C₂×D₄	—	59	2	no	—
476	C₂×D₄	—	59	1	no	—
477	C₂×D₄	—	59	2	no	—
478	C₂×D₄	—	59	2	no	—
479	C₂×D₄	—	59	1	no	—
480	C₂×D₄	—	59	2	no	—
481	C₂×D₄	—	59	1	no	—
482	C₂×D₄	—	59	2	no	—
483	C₂×D₄	—	118	4	no	—
484	C₂×D₄	—	118	4	no	—
485	C₂×D₄	—	236	4	no	—
486	C₂×D₄	C₂²×D₅₉	1	1	yes	characteristic
487	C₂×D₄	C₂²×D₅₉	1	1	yes	characteristic
488	C₂×D₄	C₂²×D₅₉	1	2	yes	—
489	C₂×D₄	C₂²×D₅₉	1	2	yes	—
490	C₂²×C₄	—	59	1	no	—
491	C₂²×C₄	—	59	1	no	—
492	C₂²×C₄	—	59	2	no	—
493	C₂²×C₄	—	59	2	no	—
494	C₂²×C₄	—	59	2	no	—
495	C₂²×C₄	—	59	1	no	—
496	C₂²×C₄	—	59	2	no	—
497	C₂²×C₄	—	59	2	no	—
498	C₂²×C₄	—	59	2	no	—
499	C₂²×C₄	—	59	2	no	—
500	C₂²×C₄	—	59	2	no	—
501	C₂²×C₄	C₂²×D₅₉	1	1	yes	characteristic
502	C₂²×C₄	C₂²×D₅₉	1	1	yes	characteristic
503	C₂²×C₄	C₂²×D₅₉	1	2	yes	—
504	C₄⋊C₄	—	59	1	no	—
505	C₄⋊C₄	—	59	1	no	—
506	C₄⋊C₄	—	59	1	no	—
507	C₄⋊C₄	—	59	1	no	—
508	C₄⋊C₄	—	59	1	no	—
509	C₄⋊C₄	—	59	1	no	—
510	C₄⋊C₄	—	59	2	no	—
511	C₄⋊C₄	—	59	2	no	—
512	C₄⋊C₄	—	59	2	no	—
513	C₄⋊C₄	—	59	1	no	—
514	C₄⋊C₄	—	59	1	no	—
515	C₄⋊C₄	—	59	2	no	—
516	C₄⋊C₄	—	59	2	no	—
517	C₄⋊C₄	—	59	2	no	—
518	C₄⋊C₄	—	59	1	no	—
519	C₄⋊C₄	—	59	1	no	—
520	C₄⋊C₄	C₂²×D₅₉	1	1	yes	characteristic
521	C₄⋊C₄	C₂²×D₅₉	1	1	yes	characteristic
522	C₄⋊C₄	C₂²×D₅₉	1	1	yes	characteristic
523	C₄⋊C₄	C₂²×D₅₉	1	1	yes	characteristic
524	C₄⋊C₄	C₂²×D₅₉	1	2	yes	—
525	C₂²⋊C₄	—	59	1	no	—
526	C₂²⋊C₄	—	59	1	no	—
527	C₂²⋊C₄	—	59	2	no	—
528	C₂²⋊C₄	—	59	2	no	—
529	C₂²⋊C₄	—	59	2	no	—
530	C₂²⋊C₄	—	59	1	no	—
531	C₂²⋊C₄	—	59	2	no	—
532	C₂²⋊C₄	—	59	1	no	—
533	C₂²⋊C₄	—	59	2	no	—
534	C₂²⋊C₄	—	59	1	no	—
535	C₂²⋊C₄	—	59	2	no	—
536	C₂²⋊C₄	—	59	1	no	—
537	C₂²⋊C₄	—	59	1	no	—
538	C₂²⋊C₄	—	59	2	no	—
539	C₂²⋊C₄	—	59	2	no	—
540	C₂²⋊C₄	—	59	2	no	—
541	C₂²⋊C₄	—	59	2	no	—
542	C₂²⋊C₄	—	59	2	no	—
543	C₂²⋊C₄	—	59	2	no	—
544	C₂²⋊C₄	—	59	2	no	—
545	C₂²⋊C₄	—	59	2	no	—
546	C₂²⋊C₄	—	59	2	no	—
547	C₂²⋊C₄	—	59	1	no	—
548	C₂²⋊C₄	—	59	2	no	—
549	C₂²⋊C₄	C₂²×D₅₉	1	2	yes	—
550	C₂²⋊C₄	C₂²×D₅₉	1	1	yes	characteristic
551	C₂²⋊C₄	C₂²×D₅₉	1	2	yes	—
552	C₂²⋊C₄	C₂²×D₅₉	1	2	yes	—
553	C₂²⋊C₄	C₂²×D₅₉	1	2	yes	—
554	C₂²⋊C₄	C₂²×D₅₉	1	2	yes	—
555	C₂²⋊C₄	C₂²×D₅₉	1	1	yes	characteristic
556	C₄²	—	59	1	no	—
557	C₄²	—	59	1	no	—
558	C₄²	—	59	1	no	—
559	C₄²	—	59	2	no	—
560	C₄²	—	59	1	no	—
561	C₄²	—	59	2	no	—
562	C₄²	—	59	2	no	—
563	C₄²	—	59	1	no	—
564	C₄²	C₂²×D₅₉	1	2	yes	—
565	C₄²	C₂²×D₅₉	1	1	yes	characteristic
566	C₄²	C₂²×D₅₉	1	2	yes	—
567	C₂³	—	59	2	no	—
568	C₂³	—	59	1	no	—
569	C₂³	—	59	2	no	—
570	C₂³	—	118	4	no	—
571	C₂³	—	118	4	no	—
572	C₂³	—	236	2	no	—
573	C₂³	—	236	2	no	—
574	C₂³	—	236	2	no	—
575	C₂³	—	236	2	no	—
576	C₂³	C₂³×D₅₉	1	1	yes	characteristic
577	C₂³	C₂³×D₅₉	1	2	yes	—
578	C₂³	C₂³×D₅₉	1	1	yes	characteristic
579	Q₈	—	4	2	no	—
580	Q₈	—	118	2	no	—
581	Q₈	—	118	4	no	—
582	Q₈	—	118	2	no	—
583	Q₈	—	236	2	no	—
584	D₄	—	2	2	no	—
585	D₄	—	4	2	no	—
586	D₄	—	4	1	no	—
587	D₄	—	4	2	no	—
588	D₄	—	59	4	no	—
589	D₄	—	118	4	no	—
590	D₄	—	118	2	no	—
591	D₄	—	118	4	no	—
592	D₄	—	118	4	no	—
593	D₄	—	118	4	no	—
594	D₄	—	118	2	no	—
595	D₄	—	236	2	no	—
596	D₄	—	236	1	no	—
597	D₄	—	236	2	no	—
598	D₄	—	236	2	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	2	2	no	—
601	C₂×C₄	—	4	2	no	—
602	C₂×C₄	—	59	1	no	—
603	C₂×C₄	—	59	1	no	—
604	C₂×C₄	—	59	2	no	—
605	C₂×C₄	—	59	1	no	—
606	C₂×C₄	—	59	1	no	—
607	C₂×C₄	—	59	1	no	—
608	C₂×C₄	—	59	1	no	—
609	C₂×C₄	—	59	1	no	—
610	C₂×C₄	—	59	2	no	—
611	C₂×C₄	—	118	4	no	—
612	C₂×C₄	—	118	4	no	—
613	C₂×C₄	—	118	2	no	—
614	C₂×C₄	—	118	2	no	—
615	C₂×C₄	—	236	2	no	—
616	C₂×C₄	—	236	2	no	—
617	C₂×C₄	—	236	2	no	—
618	C₂×C₄	—	236	2	no	—
619	C₂×C₄	—	236	2	no	—
620	C₂×C₄	—	236	1	no	—
621	C₂×C₄	—	236	2	no	—
622	C₂×C₄	C₂³×D₅₉	1	1	yes	characteristic
623	C₂×C₄	C₂³×D₅₉	1	2	yes	—
624	C₂×C₄	C₂³×D₅₉	1	2	yes	—
625	C₂×C₄	C₂³×D₅₉	1	1	yes	characteristic
626	C₂×C₄	C₂³×D₅₉	1	1	yes	characteristic
627	C₂×C₄	C₂³×D₅₉	1	1	yes	characteristic
628	C₂×C₄	C₂³×D₅₉	1	2	yes	—
629	C₂×C₄	C₂³×D₅₉	1	1	yes	characteristic
630	C₂²	—	2	1	no	—
631	C₂²	—	2	1	no	—
632	C₂²	—	2	2	no	—
633	C₂²	—	2	1	no	—
634	C₂²	—	2	2	no	—
635	C₂²	—	2	1	no	—
636	C₂²	—	2	2	no	—
637	C₂²	—	2	1	no	—
638	C₂²	—	2	1	no	—
639	C₂²	—	59	4	no	—
640	C₂²	—	118	2	no	—
641	C₂²	—	118	2	no	—
642	C₂²	—	118	1	no	—
643	C₂²	—	118	2	no	—
644	C₂²	—	118	2	no	—
645	C₂²	—	118	1	no	—
646	C₂²	—	118	2	no	—
647	C₂²	—	118	1	no	—
648	C₂²	—	472	4	no	—
649	C₂²	—	472	4	no	—
650	C₂²	C₂⁴×D₅₉	1	1	yes	characteristic
651	C₄	—	2	1	no	—
652	C₄	—	2	1	no	—
653	C₄	—	2	2	no	—
654	C₄	—	2	2	no	—
655	C₄	—	2	1	no	—
656	C₄	—	2	1	no	—
657	C₄	—	2	2	no	—
658	C₄	—	59	2	no	—
659	C₄	—	118	1	no	—
660	C₄	—	118	2	no	—
661	C₄	—	118	1	no	—
662	C₄	—	118	2	no	—
663	C₄	—	118	1	no	—
664	C₄	—	118	1	no	—
665	C₄	—	118	1	no	—
666	C₄	—	118	1	no	—
667	C₄	#41×D₅₉	1	2	yes	—
668	C₂	—	4	1	no	—
669	C₂	—	4	2	no	—
670	C₂	—	4	1	no	—
671	C₂	—	118	4	no	—
672	C₂	—	236	1	no	—
673	C₂	—	236	2	no	—
674	C₂	C₂×#41×D₅₉	1	1	yes	characteristic
675	C₂	H(5,𝔽₂)×D₅₉	1	1	yes	characteristic
676	C₂	#16838238	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₅₉
commutator, socle	C₂²×C₅₉	C₂⁵
Fitting	C₅₉×#555	C₂
hypercenter	#555	D₅₉
hypocenter	C₅₉	#3514
LCS	G ▷ C₂²×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂² ◁ #555

Complements

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

N	H ≅ G/N	type
1. #16838135	C₂	semidirect
2. #16838120	C₂	semidirect
3. #16838115	C₂	semidirect
4. #16838082	C₂	semidirect
5. #16838076	C₂	semidirect
6. #16838067	C₂	semidirect
7. #16838060	C₂	semidirect
8. #16838049	C₂	semidirect
9. #16838048	C₂	semidirect
10. #16838041	C₂	semidirect
11. #16838036	C₂	semidirect
12. #16838026	C₂	semidirect
13. #16838019	C₂	semidirect
14. #16837986	C₂	semidirect
15. #16837984	C₂	semidirect
16. #16837947	C₂	semidirect
17. #16837932	C₂	semidirect
18. #16837930	C₂	semidirect
19. #124×D₅₉	C₂	semidirect
20. #16837876	C₂	semidirect
21. #16837874	C₂	semidirect
22. #16837870	C₂	semidirect
23. C₅₉×#555	C₂	semidirect
25. C₂×#11745687	C₂²	semidirect
26. C₂×Q₈×D₅₉	C₂²	semidirect
30. #14273726	C₂²	semidirect
31. #14273726	C₂²	semidirect
33. #14273722	C₂²	semidirect
34. #14273722	C₂²	semidirect
35. #14273721	C₂²	semidirect
36. #14273720	C₂²	semidirect
37. #14273720	C₂²	semidirect
38. #14273720	C₂²	semidirect
39. #14273717	C₂²	semidirect
40. #14273716	C₂²	semidirect
41. #14273715	C₂²	semidirect
42. #14273715	C₂²	semidirect
43. #14273714	C₂²	semidirect
44. #14273714	C₂²	semidirect
47. #14273713	C₂²	semidirect
48. #14273713	C₂²	semidirect
49. #14273713	C₂²	semidirect
50. #14273712	C₂²	semidirect
51. #14273712	C₂²	semidirect
52. #14273711	C₂²	semidirect
53. #14273710	C₂²	semidirect
54. #14273709	C₂²	semidirect
55. #14273709	C₂²	semidirect
56. #14273708	C₂²	semidirect
57. #14273708	C₂²	semidirect
58. #14273707	C₂²	semidirect
59. #14273706	C₂²	semidirect
60. #14273705	C₂²	semidirect
61. #14273705	C₂²	semidirect
62. #14273704	C₂²	semidirect
63. #14273704	C₂²	semidirect
64. #14273703	C₂²	semidirect
65. #14273703	C₂²	semidirect
67. #14273701	C₂²	semidirect
69. #14273700	C₂²	semidirect
70. #14273700	C₂²	semidirect
72. #14273699	C₂²	semidirect
73. #14273698	C₂²	semidirect
76. #14273695	C₂²	semidirect
77. #14273695	C₂²	semidirect
78. C₄×Dic₁₁₈	C₂²	semidirect
79. C₄×Dic₁₁₈	C₂²	semidirect
80. #14273692	C₂²	semidirect
81. #14273692	C₂²	semidirect
83. C₄×D₂₃₆	C₂²	semidirect
84. C₄×D₂₃₆	C₂²	semidirect
85. D₄×Dic₅₉	C₂²	semidirect
89. #14273689	C₂²	semidirect
90. #14273689	C₂²	semidirect
92. C₄×C₂²⋊D₅₉	C₂²	semidirect
93. C₄×C₂²⋊D₅₉	C₂²	semidirect
94. C₄×C₂²⋊D₅₉	C₂²	semidirect
95. (C₂²⋊D₅₉)⋊C₄	C₂²	semidirect
96. (C₂²⋊D₅₉)⋊C₄	C₂²	semidirect
97. (C₂²⋊D₅₉)⋊C₄	C₂²	semidirect
98. (C₂²⋊D₅₉)⋊C₄	C₂²	semidirect
99. #14273686	C₂²	semidirect
100. #14273685	C₂²	semidirect
101. #14273684	C₂²	semidirect
102. #14273684	C₂²	semidirect
103. #14273684	C₂²	semidirect
104. C₂×(C₂×D₅₉)⋊C₄	C₂²	semidirect
105. C₂²⋊C₄×D₅₉	C₂²	semidirect
106. C₂²⋊C₄×D₅₉	C₂²	semidirect
107. C₂²⋊C₄×D₅₉	C₂²	semidirect
108. C₂²⋊C₄×D₅₉	C₂²	semidirect
109. C₂²⋊C₄×D₅₉	C₂²	semidirect
110. C₂×C₄×Dic₅₉	C₂²	semidirect
111. C₄²×D₅₉	C₂²	semidirect
112. C₄⋊Q₈×C₅₉	C₂²	semidirect
113. #124×C₅₉	C₂²	semidirect
114. #124×C₅₉	C₂²	semidirect
116. #121×C₅₉	C₂²	semidirect
117. #121×C₅₉	C₂²	semidirect
118. C₄×D₄×C₅₉	C₂²	semidirect
119. C₄×D₄×C₅₉	C₂²	semidirect
120. #117×C₅₉	C₂²	semidirect
121. #117×C₅₉	C₂²	semidirect
122. #117×C₅₉	C₂²	semidirect
278. D₂₃₆	#41	semidirect
342. #555	D₅₉	semidirect
362. C₅₉	#3514	semidirect
371. C₄⋊Q₈	C₂×D₅₉	semidirect
390. #124	C₂×D₅₉	semidirect
391. #124	C₂×D₅₉	semidirect
417. #121	C₂×D₅₉	semidirect
418. #121	C₂×D₅₉	semidirect
444. C₄×D₄	C₂×D₅₉	semidirect
445. C₄×D₄	C₂×D₅₉	semidirect
451. #117	C₂×D₅₉	semidirect
452. #117	C₂×D₅₉	semidirect
453. #117	C₂×D₅₉	semidirect