Subgroups — #29495307

Order 15104.

11674 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#14273773	C₂	1	1	yes	maximal, characteristic
2	C₄×#14273773	C₂	1	16	yes	maximal, complemented
3	#21437302	C₂	1	16	yes	maximal, complemented
4	#21437299	C₂	1	1	yes	maximal, characteristic, complemented
5	#21437298	C₂	1	4	yes	maximal, complemented
6	#21437297	C₂	1	6	yes	maximal, complemented
7	C₂×#16837876	C₂	1	6	yes	maximal, complemented
8	#518×D₅₉	C₂	1	12	yes	maximal, complemented
9	C₅₉×#3428	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#14273773	C₄	1	32	yes	complemented
11	C₂×#14273773	C₂²	1	8	yes	—
12	C₂×#14273773	C₂²	1	8	yes	—
13	C₂²×#11745689	C₂²	1	2	yes	—
14	C₂²×#11745685	C₂²	1	3	yes	—
15	C₂³×D₂₃₆	C₂²	1	3	yes	—
16	C₂²×D₄×D₅₉	C₂²	1	6	yes	—
17	#16837885	C₂²	1	8	yes	complemented
18	#16837884	C₂²	1	32	yes	complemented
19	#16837883	C₂²	1	24	yes	complemented
20	#16837882	C₂²	1	24	yes	complemented
21	#16837880	C₂²	1	2	yes	complemented
22	#16837879	C₂²	1	4	yes	complemented
23	#16837877	C₂²	1	6	yes	complemented
24	#16837876	C₂²	1	24	yes	complemented
25	#16837876	C₂²	1	12	yes	complemented
26	#16837876	C₂²	1	24	yes	complemented
27	#16837876	C₂²	1	24	yes	complemented
28	#16837875	C₂²	1	24	yes	complemented
29	#16837874	C₂²	1	96	yes	complemented
30	#41×Dic₅₉	C₂²	1	8	yes	complemented
31	C₄×#11745689	C₂²	1	32	yes	complemented
32	C₄×#11745685	C₂²	1	24	yes	complemented
33	#16837870	C₂²	1	24	yes	complemented
34	C₂×C₄×D₂₃₆	C₂²	1	24	yes	complemented
35	C₂×#14273689	C₂²	1	24	yes	complemented
36	C₄×D₄×D₅₉	C₂²	1	96	yes	complemented
37	C₂×#14273686	C₂²	1	6	yes	complemented
38	#117×D₅₉	C₂²	1	24	yes	complemented
39	C₂×C₂²⋊C₄×D₅₉	C₂²	1	24	yes	complemented
40	C₂²×#41×C₅₉	C₂²	1	1	yes	characteristic
41	C₅₉×#520	C₂²	1	8	yes	complemented
42	C₅₉×#519	C₂²	1	2	yes	complemented
43	C₅₉×#518	C₂²	1	6	yes	complemented
44	C₄×#41×C₅₉	C₂²	1	8	yes	complemented
45	C₂×#117×C₅₉	C₂²	1	6	yes	complemented
46	C₂⁴×D₅₉	C₂³	1	6	yes	—
47	#14273773	C₂×C₄	1	128	yes	complemented
48	#14273773	C₂×C₄	1	128	yes	complemented
49	C₂×#11745689	C₂×C₄	1	32	yes	complemented
50	C₂×#11745689	C₂³	1	16	yes	—
51	C₂×#11745685	C₂×C₄	1	48	yes	complemented
52	C₂×#11745685	C₂³	1	12	yes	—
53	C₂×#11745685	C₂³	1	12	yes	—
54	C₂²×Dic₁₁₈	C₂³	1	1	yes	characteristic
55	C₂²×D₂₃₆	C₂×C₄	1	48	yes	complemented
56	C₂²×D₂₃₆	C₂³	1	6	yes	—
57	C₂²×D₂₃₆	C₂³	1	3	yes	—
58	C₂²×D₂₃₆	C₂³	1	12	yes	—
59	C₂²×D₂₃₆	C₂³	1	12	yes	—
60	C₂²×C₂²⋊D₅₉	C₂³	1	6	yes	—
61	C₂×D₄×D₅₉	C₂×C₄	1	96	yes	complemented
62	C₂×D₄×D₅₉	C₂³	1	48	yes	—
63	C₂²×C₄×D₅₉	C₂³	1	6	yes	—
64	C₂²×C₄×D₅₉	C₂³	1	48	yes	complemented
65	Q₈×Dic₅₉	C₂³	1	16	yes	complemented
66	C₄×Dic₁₁₈	C₂³	1	16	yes	complemented
67	#14273692	C₂³	1	16	yes	complemented
68	C₄×D₂₃₆	C₂³	1	96	yes	complemented
69	C₄×D₂₃₆	C₂³	1	48	yes	complemented
70	D₄×Dic₅₉	C₂³	1	48	yes	complemented
71	#14273689	C₂³	1	96	yes	complemented
72	#14273689	C₂³	1	48	yes	complemented
73	C₄×C₂²⋊D₅₉	C₂³	1	96	yes	complemented
74	(C₂²⋊D₅₉)⋊C₄	C₂³	1	96	yes	complemented
75	#14273686	C₂³	1	12	yes	—
76	#14273686	C₂³	1	4	yes	—
77	#14273686	C₂³	1	12	yes	complemented
78	#14273686	C₂³	1	12	yes	complemented
79	#14273685	C₂³	1	48	yes	complemented
80	#14273684	C₂³	1	48	yes	complemented
81	#14273683	C₂³	1	16	yes	—
82	C₂×C₄⋊Dic₅₉	C₂³	1	12	yes	complemented
83	C₄⋊C₄×D₅₉	C₂³	1	48	yes	complemented
84	C₂×C₂²⋊Dic₅₉	C₂³	1	12	yes	—
85	C₂×(C₂×D₅₉)⋊C₄	C₂³	1	48	yes	complemented
86	C₂²⋊C₄×D₅₉	C₂³	1	48	yes	—
87	C₂²⋊C₄×D₅₉	C₂³	1	96	yes	complemented
88	C₂×C₄×Dic₅₉	C₂³	1	12	yes	complemented
89	C₄²×D₅₉	C₂³	1	48	yes	complemented
90	C₂×#41×C₅₉	C₂×C₄	1	16	yes	complemented
91	C₂×#41×C₅₉	C₂³	1	4	yes	—
92	C₂×#41×C₅₉	C₂³	1	4	yes	—
93	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
94	C₂²×D₄×C₅₉	C₂³	1	3	yes	—
95	C₂³×C₄×C₅₉	C₂³	1	3	yes	—
96	C₄×Q₈×C₅₉	C₂³	1	16	yes	complemented
97	C₄×D₄×C₅₉	C₂³	1	48	yes	complemented
98	#117×C₅₉	C₂³	1	4	yes	—
99	#117×C₅₉	C₂³	1	12	yes	—
100	#117×C₅₉	C₂³	1	12	yes	complemented
101	#117×C₅₉	C₂³	1	12	yes	complemented
102	C₂×C₄⋊C₄×C₅₉	C₂³	1	12	yes	complemented
103	C₂×C₂²⋊C₄×C₅₉	C₂³	1	12	yes	—
104	C₂×C₄²×C₅₉	C₂³	1	12	yes	complemented
105	C₂⁴×C₅₉	C₂⁴	1	3	yes	—
106	C₂³×D₅₉	—	8	12	no	—
107	C₂³×D₅₉	C₂²×C₄	1	48	yes	complemented
108	C₂³×D₅₉	C₂⁴	1	6	yes	—
109	C₂³×D₅₉	C₂⁴	1	24	yes	—
110	#41×C₅₉	C₂²×C₄	1	32	yes	complemented
111	#41×C₅₉	C₂²×C₄	1	32	yes	complemented
112	C₂×Q₈×C₅₉	C₂²×C₄	1	8	yes	complemented
113	C₂×Q₈×C₅₉	C₂⁴	1	4	yes	—
114	C₂×D₄×C₅₉	C₂²×C₄	1	24	yes	complemented
115	C₂×D₄×C₅₉	C₂⁴	1	12	yes	—
116	C₂²×C₄×C₅₉	C₂²×C₄	1	24	yes	complemented
117	C₂²×C₄×C₅₉	C₂⁴	1	24	yes	—
118	C₂²×C₄×C₅₉	C₂⁴	1	6	yes	—
119	C₂²×C₄×C₅₉	C₂⁴	1	6	yes	—
120	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
121	C₂²×C₄×C₅₉	C₂⁴	1	3	yes	—
122	C₂×C₂²⋊D₅₉	C₂²×C₄	1	48	yes	complemented
123	C₂×C₂²⋊D₅₉	C₂⁴	1	24	yes	—
124	C₂²×Dic₅₉	C₂⁴	1	24	yes	—
125	C₂²×Dic₅₉	C₂⁴	1	2	yes	—
126	#11745689	C₂²×C₄	1	128	yes	complemented
127	D₄×D₅₉	C₂²×C₄	1	384	yes	complemented
128	#11745685	C₂²×C₄	1	96	yes	complemented
129	#11745685	C₂²×C₄	1	96	yes	complemented
130	C₂×D₂₃₆	C₂²×C₄	1	48	yes	complemented
131	C₂×D₂₃₆	C₂²×C₄	1	24	yes	complemented
132	C₂×D₂₃₆	C₂²×C₄	1	96	yes	complemented
133	C₂×D₂₃₆	C₂²×C₄	1	96	yes	complemented
134	C₂×D₂₃₆	C₂⁴	1	6	yes	—
135	C₂×D₂₃₆	C₂⁴	1	24	yes	—
136	C₂×D₂₃₆	C₂⁴	1	6	yes	—
137	C₂×C₄×D₅₉	—	8	48	no	—
138	C₂×C₄×D₅₉	C₂²×C₄	1	48	yes	complemented
139	C₂×C₄×D₅₉	C₂⁴	1	96	yes	—
140	C₂×C₄×D₅₉	C₂⁴	1	24	yes	—
141	C₂×Dic₁₁₈	C₂²×C₄	1	8	yes	complemented
142	C₂×Dic₁₁₈	C₂⁴	1	2	yes	—
143	C₂×Dic₁₁₈	C₂⁴	1	2	yes	—
144	C₄⋊C₄×C₅₉	C₂⁴	1	8	yes	—
145	C₄⋊C₄×C₅₉	C₂⁴	1	24	yes	—
146	C₂²⋊C₄×C₅₉	C₂⁴	1	8	yes	—
147	C₂²⋊C₄×C₅₉	C₂⁴	1	24	yes	—
148	C₄²×C₅₉	C₂⁴	1	8	yes	—
149	C₄²×C₅₉	C₂⁴	1	24	yes	—
150	C₂²⋊Dic₅₉	C₂⁴	1	8	yes	—
151	C₂²⋊Dic₅₉	C₂⁴	1	24	yes	—
152	(C₂×D₅₉)⋊C₄	C₂⁴	1	96	yes	—
153	C₄⋊Dic₅₉	C₂⁴	1	24	yes	—
154	C₄⋊Dic₅₉	C₂⁴	1	8	yes	—
155	Dic₅₉⋊C₄	C₂⁴	1	32	yes	—
156	C₄×Dic₅₉	C₂⁴	1	32	yes	—
157	C₄×Dic₅₉	C₂⁴	1	24	yes	—
158	C₄×Dic₅₉	C₂⁴	1	8	yes	—
159	C₂³×C₅₉	—	4	6	no	—
160	C₂³×C₅₉	C₂³×C₄	1	12	yes	—
161	C₂³×C₅₉	C₂⁵	1	1	yes	characteristic
162	C₂³×C₅₉	C₂⁵	1	6	yes	—
163	C₂²×D₅₉	—	4	48	no	—
164	C₂²×D₅₉	—	4	12	no	—
165	C₂²×D₅₉	—	8	48	no	—
166	C₂²×D₅₉	C₂³×C₄	1	24	yes	—
167	C₂²×D₅₉	C₂³×C₄	1	96	yes	—
168	C₂²×D₅₉	C₂⁵	1	12	yes	—
169	Q₈×C₅₉	C₂³×C₄	1	16	yes	—
170	D₄×C₅₉	C₂³×C₄	1	48	yes	—
171	C₂×C₄×C₅₉	—	4	24	no	—
172	C₂×C₄×C₅₉	C₂³×C₄	1	4	yes	—
173	C₂×C₄×C₅₉	C₂³×C₄	1	12	yes	—
174	C₂×C₄×C₅₉	C₂³×C₄	1	24	yes	—
175	C₂×C₄×C₅₉	C₂³×C₄	1	24	yes	—
176	C₂×C₄×C₅₉	C₂⁵	1	16	yes	—
177	C₂×C₄×C₅₉	C₂⁵	1	1	yes	characteristic
178	C₂×C₄×C₅₉	C₂⁵	1	6	yes	—
179	C₂×C₄×C₅₉	C₂⁵	1	1	yes	characteristic
180	C₂²⋊D₅₉	C₂³×C₄	1	96	yes	—
181	C₂×Dic₅₉	—	4	24	no	—
182	C₂×Dic₅₉	C₂³×C₄	1	8	yes	—
183	C₂×Dic₅₉	C₂⁵	1	16	yes	—
184	C₂×Dic₅₉	C₂⁵	1	4	yes	—
185	D₂₃₆	C₂³×C₄	1	24	yes	—
186	D₂₃₆	C₂³×C₄	1	24	yes	—
187	D₂₃₆	C₂³×C₄	1	96	yes	—
188	C₄×D₅₉	—	4	96	no	—
189	C₄×D₅₉	C₂³×C₄	1	96	yes	—
190	Dic₁₁₈	C₂³×C₄	1	8	yes	—
191	Dic₁₁₈	C₂³×C₄	1	8	yes	—
192	#62652	—	59	1	no	maximal, Sylow
193	C₂²×C₅₉	—	2	12	no	—
194	C₂²×C₅₉	—	2	2	no	—
195	C₂²×C₅₉	—	4	12	no	—
196	C₂²×C₅₉	C₂⁴×C₄	1	2	yes	—
197	C₂²×C₅₉	C₂⁴×C₄	1	12	yes	—
198	C₂²×C₅₉	C₂⁶	1	1	yes	characteristic
199	C₂×D₅₉	—	2	24	no	—
200	C₂×D₅₉	—	4	24	no	—
201	C₂×D₅₉	—	4	96	no	—
202	C₂×D₅₉	C₂⁴×C₄	1	24	yes	—
203	C₄×C₅₉	—	2	16	no	—
204	C₄×C₅₉	C₂⁴×C₄	1	2	yes	—
205	C₄×C₅₉	C₂⁴×C₄	1	2	yes	—
206	C₄×C₅₉	C₂⁴×C₄	1	12	yes	—
207	Dic₅₉	—	2	16	no	—
208	Dic₅₉	C₂⁴×C₄	1	8	yes	—
209	C₂²×H(5,𝔽₂)	—	59	1	no	—
210	C₄×H(5,𝔽₂)	—	59	16	no	—
211	C₄×H(5,𝔽₂)	—	59	16	no	—
212	#3428	—	59	1	no	—
213	#3428	—	59	4	no	—
214	#3428	—	59	6	no	—
215	#3428	D₅₉	1	1	yes	characteristic, complemented
216	C₂×#518	—	59	12	no	—
217	C₂×#518	—	59	6	no	—
218	C₂×C₅₉	—	2	2	no	—
219	C₂×C₅₉	—	2	12	no	—
220	C₂×C₅₉	C₂⁵×C₄	1	1	yes	characteristic
221	C₂×C₅₉	H(7,𝔽₂)	1	2	yes	—
222	D₅₉	—	2	24	no	—
223	C₂×H(5,𝔽₂)	—	59	32	no	—
224	C₂×H(5,𝔽₂)	—	59	8	no	—
225	C₂×H(5,𝔽₂)	—	59	8	no	—
226	C₂²×#41	—	59	2	no	—
227	C₂²×#41	—	59	3	no	—
228	C₂²×#41	C₂×D₅₉	1	1	yes	characteristic
229	C₂³×D₄	—	59	6	no	—
230	C₂³×D₄	—	59	3	no	—
231	#520	—	59	8	no	—
232	#520	—	59	32	no	—
233	#520	—	59	24	no	—
234	#520	—	59	24	no	—
235	#520	C₂×D₅₉	1	8	yes	complemented
236	#519	—	59	2	no	—
237	#519	—	59	4	no	—
238	#519	C₂×D₅₉	1	2	yes	complemented
239	#518	—	59	6	no	—
240	#518	—	59	96	no	—
241	#518	—	59	24	no	—
242	#518	—	59	12	no	—
243	#518	—	59	24	no	—
244	#518	—	59	24	no	—
245	#518	—	59	24	no	—
246	#518	C₂×D₅₉	1	6	yes	complemented
247	C₄×#41	—	59	8	no	—
248	C₄×#41	—	59	32	no	—
249	C₄×#41	—	59	24	no	—
250	C₄×#41	—	59	24	no	—
251	C₄×#41	C₂×D₅₉	1	8	yes	complemented
252	C₂×C₄×D₄	—	59	96	no	—
253	C₂×C₄×D₄	—	59	24	no	—
254	C₂×C₄×D₄	—	59	24	no	—
255	C₂×#117	—	59	6	no	—
256	C₂×#117	—	59	24	no	—
257	C₂×#117	C₂×D₅₉	1	6	yes	complemented
258	C₂²×C₂²⋊C₄	—	59	24	no	—
259	C₅₉	#62652	1	1	yes	characteristic, complemented, Sylow
260	C₂⁵	—	59	6	no	—
261	H(5,𝔽₂)	—	59	128	no	—
262	H(5,𝔽₂)	—	59	128	no	—
263	C₂×#41	—	59	32	no	—
264	C₂×#41	—	59	16	no	—
265	C₂×#41	—	59	48	no	—
266	C₂×#41	—	59	12	no	—
267	C₂×#41	—	59	12	no	—
268	C₂×#41	C₄×D₅₉	1	16	yes	complemented
269	C₂×#41	C₂²×D₅₉	1	4	yes	—
270	C₂×#41	C₂²×D₅₉	1	4	yes	—
271	C₂²×Q₈	—	59	1	no	—
272	C₂²×Q₈	C₂²×D₅₉	1	1	yes	characteristic
273	C₂²×D₄	—	59	6	no	—
274	C₂²×D₄	—	59	96	no	—
275	C₂²×D₄	—	59	48	no	—
276	C₂²×D₄	—	59	48	no	—
277	C₂²×D₄	—	59	12	no	—
278	C₂²×D₄	—	59	12	no	—
279	C₂²×D₄	—	59	6	no	—
280	C₂²×D₄	—	59	3	no	—
281	C₂²×D₄	C₂²×D₅₉	1	3	yes	—
282	C₂³×C₄	—	59	6	no	—
283	C₂³×C₄	—	59	48	no	—
284	C₂³×C₄	C₂²×D₅₉	1	3	yes	—
285	C₄×Q₈	—	59	16	no	—
286	C₄×Q₈	—	59	16	no	—
287	C₄×Q₈	—	59	16	no	—
288	C₄×Q₈	C₂²×D₅₉	1	16	yes	complemented
289	C₄×D₄	—	59	48	no	—
290	C₄×D₄	—	59	96	no	—
291	C₄×D₄	—	59	96	no	—
292	C₄×D₄	—	59	48	no	—
293	C₄×D₄	—	59	96	no	—
294	C₄×D₄	—	59	96	no	—
295	C₄×D₄	—	59	48	no	—
296	C₄×D₄	C₂²×D₅₉	1	48	yes	complemented
297	#117	—	59	12	no	—
298	#117	—	59	4	no	—
299	#117	—	59	12	no	—
300	#117	—	59	12	no	—
301	#117	—	59	48	no	—
302	#117	—	59	16	no	—
303	#117	—	59	48	no	—
304	#117	C₂²×D₅₉	1	12	yes	—
305	#117	C₂²×D₅₉	1	4	yes	—
306	#117	C₂²×D₅₉	1	12	yes	complemented
307	#117	C₂²×D₅₉	1	12	yes	complemented
308	C₂×C₄⋊C₄	—	59	12	no	—
309	C₂×C₄⋊C₄	—	59	48	no	—
310	C₂×C₄⋊C₄	C₂²×D₅₉	1	12	yes	complemented
311	C₂×C₂²⋊C₄	—	59	12	no	—
312	C₂×C₂²⋊C₄	—	59	48	no	—
313	C₂×C₂²⋊C₄	—	59	48	no	—
314	C₂×C₂²⋊C₄	—	59	96	no	—
315	C₂×C₂²⋊C₄	C₂²×D₅₉	1	12	yes	—
316	C₂×C₄²	—	59	12	no	—
317	C₂×C₄²	—	59	48	no	—
318	C₂×C₄²	C₂²×D₅₉	1	12	yes	complemented
319	C₂⁴	—	59	48	no	—
320	C₂⁴	—	59	6	no	—
321	C₂⁴	—	59	24	no	—
322	C₂⁴	—	472	12	no	—
323	C₂⁴	C₂³×D₅₉	1	3	yes	—
324	#41	—	59	128	no	—
325	#41	—	59	96	no	—
326	#41	—	59	96	no	—
327	#41	C₂×C₄×D₅₉	1	32	yes	complemented
328	#41	C₂×C₄×D₅₉	1	32	yes	complemented
329	C₂×Q₈	—	59	8	no	—
330	C₂×Q₈	—	59	2	no	—
331	C₂×Q₈	—	59	2	no	—
332	C₂×Q₈	C₂×C₄×D₅₉	1	8	yes	complemented
333	C₂×Q₈	C₂³×D₅₉	1	4	yes	—
334	C₂×D₄	—	59	48	no	—
335	C₂×D₄	—	59	24	no	—
336	C₂×D₄	—	59	384	no	—
337	C₂×D₄	—	59	48	no	—
338	C₂×D₄	—	59	24	no	—
339	C₂×D₄	—	59	96	no	—
340	C₂×D₄	—	59	96	no	—
341	C₂×D₄	—	59	6	no	—
342	C₂×D₄	—	59	24	no	—
343	C₂×D₄	—	59	6	no	—
344	C₂×D₄	C₂×C₄×D₅₉	1	24	yes	complemented
345	C₂×D₄	C₂³×D₅₉	1	12	yes	—
346	C₂²×C₄	—	59	2	no	—
347	C₂²×C₄	—	59	48	no	—
348	C₂²×C₄	—	59	24	no	—
349	C₂²×C₄	—	59	24	no	—
350	C₂²×C₄	—	59	96	no	—
351	C₂²×C₄	—	472	48	no	—
352	C₂²×C₄	C₂×C₄×D₅₉	1	24	yes	complemented
353	C₂²×C₄	C₂³×D₅₉	1	24	yes	—
354	C₂²×C₄	C₂³×D₅₉	1	6	yes	—
355	C₂²×C₄	C₂³×D₅₉	1	6	yes	—
356	C₂²×C₄	C₂³×D₅₉	1	3	yes	—
357	C₂²×C₄	C₂³×D₅₉	1	1	yes	characteristic
358	C₄⋊C₄	—	59	32	no	—
359	C₄⋊C₄	—	59	24	no	—
360	C₄⋊C₄	—	59	8	no	—
361	C₄⋊C₄	C₂³×D₅₉	1	24	yes	—
362	C₄⋊C₄	C₂³×D₅₉	1	8	yes	—
363	C₂²⋊C₄	—	59	8	no	—
364	C₂²⋊C₄	—	59	24	no	—
365	C₂²⋊C₄	—	59	96	no	—
366	C₂²⋊C₄	C₂³×D₅₉	1	8	yes	—
367	C₂²⋊C₄	C₂³×D₅₉	1	24	yes	—
368	C₄²	—	59	32	no	—
369	C₄²	—	59	8	no	—
370	C₄²	—	59	24	no	—
371	C₄²	C₂³×D₅₉	1	24	yes	—
372	C₄²	C₂³×D₅₉	1	8	yes	—
373	C₂³	—	4	6	no	—
374	C₂³	—	59	12	no	—
375	C₂³	—	59	24	no	—
376	C₂³	—	59	96	no	—
377	C₂³	—	472	48	no	—
378	C₂³	—	236	48	no	—
379	C₂³	—	236	12	no	—
380	C₂³	C₂²×C₄×D₅₉	1	12	yes	—
381	C₂³	C₂⁴×D₅₉	1	1	yes	characteristic
382	C₂³	C₂⁴×D₅₉	1	6	yes	—
383	Q₈	—	59	8	no	—
384	Q₈	—	59	8	no	—
385	Q₈	C₂²×C₄×D₅₉	1	16	yes	—
386	D₄	—	59	96	no	—
387	D₄	—	59	96	no	—
388	D₄	—	59	24	no	—
389	D₄	—	59	24	no	—
390	D₄	C₂²×C₄×D₅₉	1	48	yes	—
391	C₂×C₄	—	4	24	no	—
392	C₂×C₄	—	59	8	no	—
393	C₂×C₄	—	59	4	no	—
394	C₂×C₄	—	59	96	no	—
395	C₂×C₄	—	59	16	no	—
396	C₂×C₄	—	236	96	no	—
397	C₂×C₄	—	236	24	no	—
398	C₂×C₄	C₂²×C₄×D₅₉	1	12	yes	—
399	C₂×C₄	C₂²×C₄×D₅₉	1	4	yes	—
400	C₂×C₄	C₂²×C₄×D₅₉	1	24	yes	—
401	C₂×C₄	C₂²×C₄×D₅₉	1	24	yes	—
402	C₂×C₄	C₂⁴×D₅₉	1	16	yes	—
403	C₂×C₄	C₂⁴×D₅₉	1	1	yes	characteristic
404	C₂×C₄	C₂⁴×D₅₉	1	6	yes	—
405	C₂×C₄	C₂⁴×D₅₉	1	1	yes	characteristic
406	C₂²	—	2	12	no	—
407	C₂²	—	2	2	no	—
408	C₂²	—	4	12	no	—
409	C₂²	—	59	24	no	—
410	C₂²	—	118	24	no	—
411	C₂²	—	236	24	no	—
412	C₂²	—	236	96	no	—
413	C₂²	C₂³×C₄×D₅₉	1	2	yes	—
414	C₂²	C₂³×C₄×D₅₉	1	12	yes	—
415	C₂²	C₂⁵×D₅₉	1	1	yes	characteristic
416	C₄	—	2	16	no	—
417	C₄	—	59	8	no	—
418	C₄	—	118	16	no	—
419	C₄	C₂³×C₄×D₅₉	1	12	yes	—
420	C₄	C₂³×C₄×D₅₉	1	2	yes	—
421	C₄	C₂³×C₄×D₅₉	1	2	yes	—
422	C₂	—	2	2	no	—
423	C₂	—	2	12	no	—
424	C₂	—	118	24	no	—
425	C₂	C₂⁴×C₄×D₅₉	1	1	yes	characteristic
426	C₂	#21438907	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₅₉
commutator	C₂×C₅₉	C₂⁵×C₄
Fitting	C₅₉×#3428	C₂
socle, cosocle	C₂²×C₅₉	C₂⁶
prime radical	C₂²×#14273773	C₂
hypercenter	#3428	D₅₉
hypocenter	C₅₉	#62652
LCS	G ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂² ◁ #3428

Complements

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

N	H ≅ G/N	type
2. C₄×#14273773	C₂	semidirect
3. #21437302	C₂	semidirect
4. #21437299	C₂	semidirect
5. #21437298	C₂	semidirect
6. #21437297	C₂	semidirect
7. C₂×#16837876	C₂	semidirect
8. #518×D₅₉	C₂	semidirect
9. C₅₉×#3428	C₂	semidirect
10. C₂×#14273773	C₄	semidirect
17. #16837885	C₂²	semidirect
18. #16837884	C₂²	semidirect
19. #16837883	C₂²	semidirect
20. #16837882	C₂²	semidirect
21. #16837880	C₂²	semidirect
22. #16837879	C₂²	semidirect
23. #16837877	C₂²	semidirect
24. #16837876	C₂²	semidirect
25. #16837876	C₂²	semidirect
26. #16837876	C₂²	semidirect
27. #16837876	C₂²	semidirect
28. #16837875	C₂²	semidirect
29. #16837874	C₂²	semidirect
30. #41×Dic₅₉	C₂²	semidirect
31. C₄×#11745689	C₂²	semidirect
32. C₄×#11745685	C₂²	semidirect
33. #16837870	C₂²	semidirect
34. C₂×C₄×D₂₃₆	C₂²	semidirect
35. C₂×#14273689	C₂²	semidirect
36. C₄×D₄×D₅₉	C₂²	semidirect
37. C₂×#14273686	C₂²	semidirect
38. #117×D₅₉	C₂²	semidirect
39. C₂×C₂²⋊C₄×D₅₉	C₂²	semidirect
41. C₅₉×#520	C₂²	semidirect
42. C₅₉×#519	C₂²	semidirect
43. C₅₉×#518	C₂²	semidirect
44. C₄×#41×C₅₉	C₂²	semidirect
45. C₂×#117×C₅₉	C₂²	semidirect
47. #14273773	C₂×C₄	semidirect
48. #14273773	C₂×C₄	semidirect
49. C₂×#11745689	C₂×C₄	semidirect
51. C₂×#11745685	C₂×C₄	semidirect
55. C₂²×D₂₃₆	C₂×C₄	semidirect
61. C₂×D₄×D₅₉	C₂×C₄	semidirect
64. C₂²×C₄×D₅₉	C₂³	semidirect
65. Q₈×Dic₅₉	C₂³	semidirect
66. C₄×Dic₁₁₈	C₂³	semidirect
67. #14273692	C₂³	semidirect
68. C₄×D₂₃₆	C₂³	semidirect
69. C₄×D₂₃₆	C₂³	semidirect
70. D₄×Dic₅₉	C₂³	semidirect
71. #14273689	C₂³	semidirect
72. #14273689	C₂³	semidirect
73. C₄×C₂²⋊D₅₉	C₂³	semidirect
74. (C₂²⋊D₅₉)⋊C₄	C₂³	semidirect
77. #14273686	C₂³	semidirect
78. #14273686	C₂³	semidirect
79. #14273685	C₂³	semidirect
80. #14273684	C₂³	semidirect
82. C₂×C₄⋊Dic₅₉	C₂³	semidirect
83. C₄⋊C₄×D₅₉	C₂³	semidirect
85. C₂×(C₂×D₅₉)⋊C₄	C₂³	semidirect
87. C₂²⋊C₄×D₅₉	C₂³	semidirect
88. C₂×C₄×Dic₅₉	C₂³	semidirect
89. C₄²×D₅₉	C₂³	semidirect
90. C₂×#41×C₅₉	C₂×C₄	semidirect
96. C₄×Q₈×C₅₉	C₂³	semidirect
97. C₄×D₄×C₅₉	C₂³	semidirect
100. #117×C₅₉	C₂³	semidirect
101. #117×C₅₉	C₂³	semidirect
102. C₂×C₄⋊C₄×C₅₉	C₂³	semidirect
104. C₂×C₄²×C₅₉	C₂³	semidirect
107. C₂³×D₅₉	C₂²×C₄	semidirect
110. #41×C₅₉	C₂²×C₄	semidirect
111. #41×C₅₉	C₂²×C₄	semidirect
112. C₂×Q₈×C₅₉	C₂²×C₄	semidirect
114. C₂×D₄×C₅₉	C₂²×C₄	semidirect
116. C₂²×C₄×C₅₉	C₂²×C₄	semidirect
122. C₂×C₂²⋊D₅₉	C₂²×C₄	semidirect
126. #11745689	C₂²×C₄	semidirect
127. D₄×D₅₉	C₂²×C₄	semidirect
128. #11745685	C₂²×C₄	semidirect
129. #11745685	C₂²×C₄	semidirect
130. C₂×D₂₃₆	C₂²×C₄	semidirect
131. C₂×D₂₃₆	C₂²×C₄	semidirect
132. C₂×D₂₃₆	C₂²×C₄	semidirect
133. C₂×D₂₃₆	C₂²×C₄	semidirect
138. C₂×C₄×D₅₉	C₂²×C₄	semidirect
141. C₂×Dic₁₁₈	C₂²×C₄	semidirect
215. #3428	D₅₉	semidirect
235. #520	C₂×D₅₉	semidirect
238. #519	C₂×D₅₉	semidirect
246. #518	C₂×D₅₉	semidirect
251. C₄×#41	C₂×D₅₉	semidirect
257. C₂×#117	C₂×D₅₉	semidirect
259. C₅₉	#62652	semidirect
268. C₂×#41	C₄×D₅₉	semidirect
288. C₄×Q₈	C₂²×D₅₉	semidirect
296. C₄×D₄	C₂²×D₅₉	semidirect
306. #117	C₂²×D₅₉	semidirect
307. #117	C₂²×D₅₉	semidirect
310. C₂×C₄⋊C₄	C₂²×D₅₉	semidirect
318. C₂×C₄²	C₂²×D₅₉	semidirect
327. #41	C₂×C₄×D₅₉	semidirect
328. #41	C₂×C₄×D₅₉	semidirect
332. C₂×Q₈	C₂×C₄×D₅₉	semidirect
344. C₂×D₄	C₂×C₄×D₅₉	semidirect
352. C₂²×C₄	C₂×C₄×D₅₉	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#14273773	2
C₄×#14273773	2
#21437302	2
#21437299	2
#21437298	2
#21437297	2
C₂×#16837876	2
#518×D₅₉	2
C₅₉×#3428	2
#62652	59