Subgroups — #28558761

Order 15104.

596 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21434174	C₂	1	1	yes	maximal, characteristic
2	#21433246	C₂	1	1	yes	maximal, characteristic
3	#21433175	C₂	1	1	yes	maximal, characteristic, complemented
4	#21422977	C₂	1	1	yes	maximal, characteristic, complemented
5	#21422964	C₂	1	1	yes	maximal, characteristic, complemented
6	#21422945	C₂	1	1	yes	maximal, characteristic, complemented
7	#21422940	C₂	1	1	yes	maximal, characteristic, complemented
8	#21422916	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈×#11745672	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×#11745670	C₂	1	1	yes	maximal, characteristic, complemented
11	#21422886	C₂	1	1	yes	maximal, characteristic, complemented
12	#21422523	C₂	1	1	yes	maximal, characteristic, complemented
13	#21422501	C₂	1	1	yes	maximal, characteristic
14	#21422397	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₉×SD₁₆⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
16	#16837934	C₂²	1	1	yes	characteristic
17	C₄×Q₈×D₅₉	C₂²	1	1	yes	characteristic
18	#16837734	C₄	1	1	yes	characteristic
19	#16837714	C₄	1	1	yes	characteristic
20	#16837712	C₄	1	1	yes	characteristic
21	#16837711	C₄	1	1	yes	characteristic
22	#16837623	C₄	1	1	yes	characteristic
23	#16837622	C₄	1	1	yes	characteristic
24	#16837559	C₄	1	1	yes	characteristic
25	#16837539	C₄	1	1	yes	characteristic
26	#16837529	C₂²	1	1	yes	characteristic
27	Q₈×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
28	C₈×Dic₁₁₈	—	2	1	no	—
29	C₈×Dic₁₁₈	C₂²	1	1	yes	characteristic
30	C₈×Dic₁₁₈	C₂²	1	1	yes	characteristic
31	#16837526	—	2	1	no	—
32	#16837526	C₂²	1	1	yes	characteristic
33	C₄×Dic₂₃₆	C₂²	1	1	yes	characteristic
34	C₄×#11745672	C₂²	1	1	yes	characteristic
35	C₄×#11745670	C₂²	1	1	yes	characteristic
36	#16837480	C₂²	1	1	yes	characteristic
37	#16837477	—	2	1	no	—
38	#16837473	—	2	1	no	—
39	#16837460	—	2	1	no	—
40	#16837454	—	2	1	no	—
41	#16837454	C₂²	1	1	yes	characteristic
42	#16837453	—	2	1	no	—
43	#16837453	C₂²	1	1	yes	characteristic
44	#16837453	C₂²	1	1	yes	characteristic
45	#16837453	C₂²	1	1	yes	characteristic
46	#16837428	—	2	1	no	—
47	#16837424	C₂²	1	1	yes	characteristic
48	#16837154	C₂²	1	1	yes	characteristic
49	#16837153	C₂²	1	1	yes	characteristic
50	#16837152	C₂²	1	1	yes	characteristic
51	#16837134	C₂²	1	1	yes	characteristic
52	#16837134	C₂²	1	1	yes	characteristic
53	Q₈⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
54	#16837132	C₂²	1	1	yes	characteristic
55	#16837132	C₂²	1	1	yes	characteristic
56	D₄⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
57	#16837124	C₂²	1	1	yes	characteristic
58	#16837123	C₂²	1	1	yes	characteristic
59	C₈×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
60	C₈×Q₈×C₅₉	C₂²	1	1	yes	characteristic
61	C₄×SD₁₆×C₅₉	C₂²	1	1	yes	characteristic
62	C₈×D₄×C₅₉	C₂²	1	1	yes	characteristic
63	C₅₉×#335	C₂²	1	1	yes	characteristic
64	C₅₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
65	C₅₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
66	C₅₉×#322	C₂²	1	1	yes	characteristic
67	C₂×Q₈×D₅₉	C₂×C₄	1	1	yes	characteristic
68	C₂×Dic₂₃₆	C₂×C₄	1	1	yes	characteristic
69	C₂×#11745672	C₂×C₄	1	1	yes	characteristic
70	C₂×#11745670	C₂×C₄	1	1	yes	characteristic
71	C₂×#11745664	—	2	1	no	—
72	C₂×#11745659	—	2	1	no	—
73	#14273720	—	2	1	no	—
74	#14273718	C₂×C₄	1	1	yes	characteristic
75	#14273714	C₂×C₄	1	1	yes	characteristic
76	#14273709	—	2	1	no	—
77	#14273707	C₂×C₄	1	1	yes	characteristic
78	#14273698	C₂×C₄	1	1	yes	characteristic
79	Q₈×Dic₅₉	C₂×C₄	1	1	yes	characteristic
80	C₄×Dic₁₁₈	—	2	1	no	—
81	C₄×Dic₁₁₈	C₂³	1	1	yes	characteristic
82	C₄×Dic₁₁₈	C₂³	1	1	yes	characteristic
83	#14273692	—	2	1	no	—
84	#14273692	C₂×C₄	1	1	yes	characteristic
85	C₄×C₂²⋊D₅₉	—	2	1	no	—
86	#14273686	—	2	1	no	—
87	C₄⋊C₄×D₅₉	—	2	1	no	—
88	C₄⋊C₄×D₅₉	C₂×C₄	1	1	yes	characteristic
89	C₄²×D₅₉	—	2	1	no	—
90	C₄²×D₅₉	C₂³	1	1	yes	characteristic
91	#14273661	C₂×C₄	1	1	yes	characteristic
92	#14273660	C₂×C₄	1	1	yes	characteristic
93	#14273658	C₂×C₄	1	1	yes	characteristic
94	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
95	C₄⋊(C₅₉⋊C₈)	C₂³	1	1	yes	characteristic
96	C₄⋊(C₅₉⋊C₈)	C₂³	1	1	yes	characteristic
97	Dic₅₉⋊C₈	—	2	1	no	—
98	Dic₅₉⋊C₈	—	2	1	no	—
99	Dic₅₉⋊C₈	—	2	1	no	—
100	Dic₅₉⋊C₈	—	2	1	no	—
101	Dic₅₉⋊C₈	—	2	1	no	—
102	Dic₅₉⋊C₈	—	2	1	no	—
103	Dic₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
104	Dic₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
105	Dic₅₉⋊C₈	D₄	1	1	yes	characteristic
106	Dic₅₉⋊C₈	D₄	1	1	yes	characteristic
107	#14273652	C₂×C₄	1	1	yes	characteristic
108	#14273652	C₂×C₄	1	1	yes	characteristic
109	#14273651	C₂×C₄	1	1	yes	characteristic
110	#14273650	C₂×C₄	1	1	yes	characteristic
111	#14273650	C₂×C₄	1	1	yes	characteristic
112	#14273648	C₂×C₄	1	1	yes	characteristic
113	C₂²⋊(C₅₉⋊C₈)	—	2	1	no	—
114	(C₂×D₅₉)⋊C₈	—	2	1	no	—
115	(C₂×D₅₉)⋊C₈	—	2	1	no	—
116	(C₂×D₅₉)⋊C₈	C₂×C₄	1	1	yes	characteristic
117	(C₂×D₅₉)⋊C₈	C₂×C₄	1	1	yes	characteristic
118	(C₂×D₅₉)⋊C₈	D₄	1	1	yes	characteristic
119	(C₂×D₅₉)⋊C₈	D₄	1	1	yes	characteristic
120	#14273637	—	2	1	no	—
121	C₄×C₅₉⋊C₈	—	2	1	no	—
122	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
123	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
124	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
125	C₈×Dic₅₉	—	2	1	no	—
126	C₈×Dic₅₉	—	2	1	no	—
127	C₈×Dic₅₉	—	2	1	no	—
128	C₈×Dic₅₉	—	2	1	no	—
129	C₂×SD₁₆×C₅₉	C₂×C₄	1	1	yes	characteristic
130	C₂²×C₈×C₅₉	—	2	1	no	—
131	C₄×Q₈×C₅₉	C₂³	1	1	yes	characteristic
132	C₄×D₄×C₅₉	C₂³	1	1	yes	characteristic
133	#106×C₅₉	C₂×C₄	1	1	yes	characteristic
134	C₄⋊C₈×C₅₉	—	2	1	no	—
135	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
136	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
137	#103×C₅₉	C₂×C₄	1	1	yes	characteristic
138	#102×C₅₉	C₂×C₄	1	1	yes	characteristic
139	C₂²⋊C₈×C₅₉	—	2	1	no	—
140	C₄×C₈×C₅₉	—	2	1	no	—
141	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
142	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
144	C₂×Q₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
145	C₂×D₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
146	C₂²×C₄×C₅₉	—	2	1	no	—
147	C₂×C₂²⋊D₅₉	—	2	1	no	—
148	Q₈×D₅₉	—	2	2	no	—
149	Q₈×D₅₉	—	2	2	no	—
150	C₂×C₄×D₅₉	—	2	1	no	—
151	C₂×C₄×D₅₉	—	2	1	no	—
152	C₂×C₄×D₅₉	C₂²×C₄	1	1	yes	characteristic
153	C₂×C₄×D₅₉	C₂×D₄	1	1	yes	characteristic
154	C₂×C₄×D₅₉	#41	1	1	yes	characteristic
155	C₂×Dic₁₁₈	—	2	1	no	—
156	C₂×Dic₁₁₈	C₂²×C₄	1	1	yes	characteristic
157	C₂×Dic₁₁₈	C₂²×C₄	1	1	yes	characteristic
158	SD₁₆×C₅₉	—	2	2	no	—
159	C₂×C₈×C₅₉	—	2	1	no	—
160	C₂×C₈×C₅₉	—	2	1	no	—
161	C₂×C₈×C₅₉	—	2	1	no	—
162	C₂×C₈×C₅₉	—	8	1	no	—
163	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
164	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
165	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
166	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
167	C₄⋊C₄×C₅₉	—	2	1	no	—
168	C₄⋊C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
169	C₄⋊C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
170	C₂²⋊C₄×C₅₉	—	2	1	no	—
171	C₄²×C₅₉	—	2	1	no	—
172	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
173	C₂²⋊Dic₅₉	—	2	1	no	—
174	C₂²⋊Dic₅₉	—	2	1	no	—
175	C₂²⋊Dic₅₉	—	2	1	no	—
176	#11745672	—	2	2	no	—
177	#11745670	—	2	2	no	—
178	(C₂×D₅₉)⋊C₄	—	2	1	no	—
179	C₄⋊Dic₅₉	—	2	1	no	—
180	C₄⋊Dic₅₉	—	2	1	no	—
181	C₄⋊Dic₅₉	—	2	1	no	—
182	C₄⋊Dic₅₉	C₂²×C₄	1	1	yes	characteristic
183	C₄⋊Dic₅₉	C₂²×C₄	1	1	yes	characteristic
184	Dic₅₉⋊C₄	—	2	1	no	—
185	Dic₅₉⋊C₄	—	2	1	no	—
186	Dic₅₉⋊C₄	—	2	1	no	—
187	Dic₅₉⋊C₄	—	2	1	no	—
188	Dic₅₉⋊C₄	—	2	1	no	—
189	C₄×Dic₅₉	—	2	1	no	—
190	C₄×Dic₅₉	—	2	1	no	—
191	C₄×Dic₅₉	—	2	1	no	—
192	C₄×Dic₅₉	—	2	1	no	—
193	C₄×Dic₅₉	C₂²×C₄	1	1	yes	characteristic
194	C₄×Dic₅₉	C₂×D₄	1	1	yes	characteristic
195	C₄×Dic₅₉	#41	1	1	yes	characteristic
196	#11745664	—	8	1	no	—
197	C₂×C₅₉⋊C₈	—	2	1	no	—
198	C₂×C₅₉⋊C₈	—	2	1	no	—
199	C₂×C₅₉⋊C₈	—	2	1	no	—
200	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
201	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
202	C₂×C₅₉⋊C₈	C₂×D₄	1	1	yes	characteristic
203	C₂×C₅₉⋊C₈	C₂×D₄	1	1	yes	characteristic
204	Dic₂₃₆	—	2	2	no	—
205	#11745659	—	8	1	no	—
206	C₂³×C₅₉	—	2	1	no	—
207	C₂²×D₅₉	C₄×D₄	1	1	yes	characteristic
208	Q₈×C₅₉	—	2	1	no	—
209	Q₈×C₅₉	#131	1	2	yes	—
210	D₄×C₅₉	—	2	1	no	—
211	D₄×C₅₉	—	2	1	no	—
212	C₂×C₄×C₅₉	—	2	1	no	—
213	C₂×C₄×C₅₉	—	2	1	no	—
214	C₂×C₄×C₅₉	—	2	1	no	—
215	C₂×C₄×C₅₉	—	4	1	no	—
216	C₂×C₄×C₅₉	—	4	1	no	—
217	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
218	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
219	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
220	C₂²⋊D₅₉	—	8	1	no	—
221	C₂×Dic₅₉	—	2	1	no	—
222	C₂×Dic₅₉	—	2	1	no	—
223	C₂×Dic₅₉	—	2	1	no	—
224	C₂×Dic₅₉	—	2	1	no	—
225	C₂×Dic₅₉	C₄×D₄	1	1	yes	characteristic
226	C₂×Dic₅₉	C₄×D₄	1	1	yes	characteristic
227	C₂×Dic₅₉	C₄×D₄	1	1	yes	characteristic
228	C₄×D₅₉	—	2	4	no	—
229	C₄×D₅₉	—	2	1	no	—
230	C₄×D₅₉	—	2	1	no	—
231	C₄×D₅₉	—	2	1	no	—
232	C₄×D₅₉	—	2	1	no	—
233	C₄×D₅₉	—	4	1	no	—
234	C₄×D₅₉	—	8	1	no	—
235	Dic₁₁₈	—	2	4	no	—
236	Dic₁₁₈	—	2	1	no	—
237	Dic₁₁₈	—	2	1	no	—
238	Dic₁₁₈	—	2	1	no	—
239	Dic₁₁₈	#131	1	2	yes	—
240	C₈×C₅₉	—	2	1	no	—
241	C₈×C₅₉	—	2	1	no	—
242	C₈×C₅₉	—	2	1	no	—
243	C₈×C₅₉	—	2	1	no	—
244	C₈×C₅₉	—	4	1	no	—
245	C₈×C₅₉	—	4	1	no	—
246	C₈×C₅₉	—	4	1	no	—
247	C₅₉⋊C₈	—	2	1	no	—
248	C₅₉⋊C₈	—	2	1	no	—
249	C₅₉⋊C₈	—	2	1	no	—
250	C₅₉⋊C₈	—	2	1	no	—
251	C₅₉⋊C₈	—	4	1	no	—
252	C₅₉⋊C₈	—	4	1	no	—
253	C₅₉⋊C₈	—	4	1	no	—
254	#17919	—	59	1	no	maximal, Sylow
255	C₂²×C₅₉	—	4	1	no	—
256	C₂²×C₅₉	—	4	1	no	—
257	C₂²×C₅₉	—	4	1	no	—
258	C₂²×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
259	C₂×D₅₉	—	2	1	no	—
260	C₂×D₅₉	—	2	1	no	—
261	C₂×D₅₉	—	2	1	no	—
262	C₄×C₅₉	—	2	2	no	—
263	C₄×C₅₉	—	2	1	no	—
264	C₄×C₅₉	—	4	1	no	—
265	C₄×C₅₉	—	4	1	no	—
266	C₄×C₅₉	C₂×#131	1	1	yes	characteristic
267	C₄×C₅₉	C₂×#131	1	1	yes	characteristic
268	C₄×C₅₉	#577	1	1	yes	characteristic
269	C₄×C₅₉	#578	1	1	yes	characteristic
270	Dic₅₉	—	2	1	no	—
271	Dic₅₉	—	2	2	no	—
272	Dic₅₉	—	2	1	no	—
273	Dic₅₉	—	2	1	no	—
274	Dic₅₉	—	4	1	no	—
275	Dic₅₉	—	4	1	no	—
276	Dic₅₉	—	4	1	no	—
277	#3108	—	59	1	no	—
278	#2993	—	59	1	no	—
279	#2982	—	59	1	no	—
280	#1588	—	59	1	no	—
281	#1587	—	59	1	no	—
282	#1584	—	59	1	no	—
283	#1583	—	59	1	no	—
284	#1579	—	59	1	no	—
285	SD₁₆⋊C₈	D₅₉	1	1	yes	characteristic, complemented
286	C₈×Q₁₆	—	59	1	no	—
287	C₈×SD₁₆	—	59	1	no	—
288	#1574	—	59	1	no	—
289	#1487	—	59	1	no	—
290	#1482	—	59	1	no	—
291	#1454	—	59	1	no	—
292	C₂×C₅₉	—	8	1	no	—
293	C₂×C₅₉	#2929	1	1	yes	characteristic
294	C₂×C₅₉	#2947	1	1	yes	characteristic
295	C₂×C₅₉	#2957	1	1	yes	characteristic
296	D₅₉	—	4	1	no	—
297	#529	—	59	1	no	—
298	C₂×C₄×Q₈	—	59	1	no	—
299	#483	—	59	1	no	—
300	#480	—	59	1	no	—
301	#479	—	59	1	no	—
302	#479	—	59	1	no	—
303	#464	—	59	1	no	—
304	#464	—	59	1	no	—
305	#451	—	59	1	no	—
306	#448	—	59	1	no	—
307	#446	—	59	1	no	—
308	C₈×Q₈	—	59	1	no	—
309	C₈×Q₈	—	59	1	no	—
310	C₈×Q₈	—	59	1	no	—
311	C₈×Q₈	—	59	1	no	—
312	C₈×Q₈	—	118	1	no	—
313	C₈×Q₈	—	118	1	no	—
314	C₈×Q₈	C₂×D₅₉	1	1	yes	characteristic
315	C₄×Q₁₆	—	59	1	no	—
316	C₄×Q₁₆	—	59	1	no	—
317	C₄×SD₁₆	—	59	1	no	—
318	C₄×SD₁₆	C₂×D₅₉	1	1	yes	characteristic
319	#436	—	59	1	no	—
320	#436	—	118	1	no	—
321	#435	—	118	1	no	—
322	C₈×D₄	C₂×D₅₉	1	1	yes	characteristic
323	#433	—	118	1	no	—
324	#431	—	59	1	no	—
325	#431	—	59	1	no	—
326	#431	—	59	1	no	—
327	#431	—	59	1	no	—
328	#431	—	118	1	no	—
329	#431	—	118	1	no	—
330	#424	—	118	1	no	—
331	#423	—	59	1	no	—
332	#335	—	59	1	no	—
333	#335	C₂×D₅₉	1	1	yes	characteristic
334	#334	—	59	1	no	—
335	#334	—	59	1	no	—
336	Q₈⋊C₈	—	59	1	no	—
337	Q₈⋊C₈	—	59	1	no	—
338	Q₈⋊C₈	—	59	1	no	—
339	Q₈⋊C₈	—	59	1	no	—
340	Q₈⋊C₈	—	59	1	no	—
341	Q₈⋊C₈	C₂×D₅₉	1	1	yes	characteristic
342	D₄⋊C₈	—	59	1	no	—
343	D₄⋊C₈	C₂×D₅₉	1	1	yes	characteristic
344	#322	—	59	1	no	—
345	#322	—	59	1	no	—
346	#322	C₂×D₅₉	1	1	yes	characteristic
347	C₈²	—	59	1	no	—
348	C₅₉	#17919	1	1	yes	characteristic, complemented, Sylow
349	C₂²×Q₈	—	59	1	no	—
350	C₂×Q₁₆	—	59	1	no	—
351	C₂×Q₁₆	—	59	1	no	—
352	C₂×SD₁₆	—	59	1	no	—
353	C₂×SD₁₆	C₄×D₅₉	1	1	yes	characteristic
354	C₂×M₁₆	—	118	1	no	—
355	C₂×M₁₆	—	118	1	no	—
356	C₂²×C₈	—	2	1	no	—
357	#126	—	118	1	no	—
358	#125	—	59	1	no	—
359	#124	—	59	1	no	—
360	#123	—	118	1	no	—
361	C₂²⋊Q₈	—	59	1	no	—
362	#121	—	59	1	no	—
363	C₄×Q₈	—	59	1	no	—
364	C₄×Q₈	—	59	1	no	—
365	C₄×Q₈	—	59	1	no	—
366	C₄×Q₈	—	59	1	no	—
367	C₄×Q₈	—	118	1	no	—
368	C₄×Q₈	—	118	1	no	—
369	C₄×Q₈	C₂²×D₅₉	1	1	yes	characteristic
370	C₄×D₄	—	118	1	no	—
371	C₄×D₄	C₂²×D₅₉	1	1	yes	characteristic
372	#117	—	118	1	no	—
373	C₂×C₄⋊C₄	—	59	1	no	—
374	C₂×C₄⋊C₄	—	118	1	no	—
375	C₂×C₄²	—	59	1	no	—
376	C₂×C₄²	—	118	1	no	—
377	#107	—	59	1	no	—
378	#107	—	59	1	no	—
379	#106	—	59	1	no	—
380	#106	C₄×D₅₉	1	1	yes	characteristic
381	C₄⋊C₈	—	2	1	no	—
382	C₄⋊C₈	—	59	1	no	—
383	C₄⋊C₈	—	59	1	no	—
384	C₄⋊C₈	—	59	1	no	—
385	C₄⋊C₈	—	59	1	no	—
386	C₄⋊C₈	—	59	1	no	—
387	C₄⋊C₈	—	59	1	no	—
388	C₄⋊C₈	—	118	1	no	—
389	C₄⋊C₈	—	118	1	no	—
390	C₄⋊C₈	—	118	1	no	—
391	C₄⋊C₈	—	118	1	no	—
392	C₄⋊C₈	—	118	1	no	—
393	C₄⋊C₈	—	118	1	no	—
394	C₄⋊C₈	—	118	1	no	—
395	C₄⋊C₈	C₂²×D₅₉	1	1	yes	characteristic
396	C₄⋊C₈	C₂²×D₅₉	1	1	yes	characteristic
397	#103	—	59	1	no	—
398	#103	—	59	1	no	—
399	#103	—	59	1	no	—
400	#103	—	59	1	no	—
401	#103	—	59	1	no	—
402	#103	C₄×D₅₉	1	1	yes	characteristic
403	#102	—	59	1	no	—
404	#102	C₄×D₅₉	1	1	yes	characteristic
405	C₂²⋊C₈	—	2	1	no	—
406	C₂²⋊C₈	—	59	1	no	—
407	C₂²⋊C₈	—	59	1	no	—
408	C₂²⋊C₈	—	59	1	no	—
409	C₂²⋊C₈	—	59	1	no	—
410	C₂²⋊C₈	—	118	1	no	—
411	C₂²⋊C₈	—	118	1	no	—
412	C₂²⋊C₈	—	118	1	no	—
413	#97	—	118	1	no	—
414	C₄×C₈	—	2	1	no	—
415	C₄×C₈	—	59	1	no	—
416	C₄×C₈	—	59	1	no	—
417	C₄×C₈	—	59	1	no	—
418	C₄×C₈	—	118	1	no	—
419	C₄×C₈	—	118	1	no	—
420	C₄×C₈	—	118	1	no	—
421	C₄×C₈	—	118	1	no	—
422	C₄×C₈	—	118	1	no	—
423	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
424	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
425	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
426	C₂×Q₈	—	59	1	no	—
427	C₂×Q₈	—	59	1	no	—
428	C₂×Q₈	—	118	1	no	—
429	C₂×Q₈	—	118	2	no	—
430	C₂×Q₈	—	118	2	no	—
431	C₂×Q₈	C₂×C₄×D₅₉	1	1	yes	characteristic
432	C₂×D₄	—	118	1	no	—
433	C₂×D₄	C₂×C₄×D₅₉	1	1	yes	characteristic
434	C₂²×C₄	—	2	1	no	—
435	C₂²×C₄	—	59	1	no	—
436	C₂²×C₄	—	59	1	no	—
437	C₂²×C₄	—	59	1	no	—
438	C₂²×C₄	—	118	1	no	—
439	C₂²×C₄	—	118	1	no	—
440	Q₁₆	—	118	2	no	—
441	Q₁₆	—	118	2	no	—
442	SD₁₆	—	2	2	no	—
443	SD₁₆	—	118	2	no	—
444	M₁₆	—	472	1	no	—
445	M₁₆	—	472	1	no	—
446	C₂×C₈	—	2	1	no	—
447	C₂×C₈	—	2	1	no	—
448	C₂×C₈	—	2	1	no	—
449	C₂×C₈	—	8	1	no	—
450	C₂×C₈	—	59	1	no	—
451	C₂×C₈	—	59	1	no	—
452	C₂×C₈	—	59	1	no	—
453	C₂×C₈	—	59	1	no	—
454	C₂×C₈	—	118	1	no	—
455	C₂×C₈	—	118	1	no	—
456	C₂×C₈	—	118	1	no	—
457	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
458	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
459	C₂×C₈	D₄×D₅₉	1	1	yes	characteristic
460	C₂×C₈	D₄×D₅₉	1	1	yes	characteristic
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	—	59	1	no	—
463	C₄⋊C₄	—	59	1	no	—
464	C₄⋊C₄	—	118	1	no	—
465	C₄⋊C₄	—	118	1	no	—
466	C₄⋊C₄	—	118	1	no	—
467	C₄⋊C₄	—	118	1	no	—
468	C₄⋊C₄	—	118	1	no	—
469	C₄⋊C₄	—	118	1	no	—
470	C₄⋊C₄	—	118	1	no	—
471	C₄⋊C₄	—	118	1	no	—
472	C₄⋊C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
473	C₄⋊C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
474	C₂²⋊C₄	—	2	1	no	—
475	C₂²⋊C₄	—	118	1	no	—
476	C₂²⋊C₄	—	118	1	no	—
477	C₂²⋊C₄	—	118	1	no	—
478	C₂²⋊C₄	—	118	1	no	—
479	C₄²	—	2	1	no	—
480	C₄²	—	59	1	no	—
481	C₄²	—	59	1	no	—
482	C₄²	—	59	1	no	—
483	C₄²	—	118	1	no	—
484	C₄²	—	118	1	no	—
485	C₄²	—	118	1	no	—
486	C₄²	—	118	1	no	—
487	C₄²	C₂³×D₅₉	1	1	yes	characteristic
488	C₂³	—	2	1	no	—
489	C₂³	—	59	1	no	—
490	Q₈	—	2	1	no	—
491	Q₈	—	59	2	no	—
492	Q₈	—	118	4	no	—
493	Q₈	—	118	1	no	—
494	Q₈	—	118	1	no	—
495	Q₈	—	118	1	no	—
496	Q₈	#14273733	1	2	yes	—
497	D₄	—	2	1	no	—
498	D₄	—	2	1	no	—
499	D₄	—	472	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	4	1	no	—
504	C₂×C₄	—	4	1	no	—
505	C₂×C₄	—	59	1	no	—
506	C₂×C₄	—	59	1	no	—
507	C₂×C₄	—	59	1	no	—
508	C₂×C₄	—	118	4	no	—
509	C₂×C₄	—	118	1	no	—
510	C₂×C₄	—	118	1	no	—
511	C₂×C₄	—	118	1	no	—
512	C₂×C₄	—	118	1	no	—
513	C₂×C₄	—	118	1	no	—
514	C₂×C₄	—	118	1	no	—
515	C₂×C₄	—	118	1	no	—
516	C₂×C₄	—	118	1	no	—
517	C₂×C₄	—	472	1	no	—
518	C₂×C₄	—	236	1	no	—
519	C₂×C₄	C₂²×C₄×D₅₉	1	1	yes	characteristic
520	C₂×C₄	C₂×D₄×D₅₉	1	1	yes	characteristic
521	C₂×C₄	#41×D₅₉	1	1	yes	characteristic
522	C₈	—	2	1	no	—
523	C₈	—	2	1	no	—
524	C₈	—	2	1	no	—
525	C₈	—	2	1	no	—
526	C₈	—	4	1	no	—
527	C₈	—	4	1	no	—
528	C₈	—	4	1	no	—
529	C₈	—	118	1	no	—
530	C₈	—	118	1	no	—
531	C₈	—	118	1	no	—
532	C₈	—	118	1	no	—
533	C₈	—	236	1	no	—
534	C₈	—	236	1	no	—
535	C₈	—	236	1	no	—
536	C₂²	—	4	1	no	—
537	C₂²	—	4	1	no	—
538	C₂²	—	4	1	no	—
539	C₂²	—	118	1	no	—
540	C₂²	—	118	1	no	—
541	C₂²	—	118	1	no	—
542	C₂²	C₄×D₄×D₅₉	1	1	yes	characteristic
543	C₄	—	2	1	no	—
544	C₄	—	2	2	no	—
545	C₄	—	4	1	no	—
546	C₄	—	4	1	no	—
547	C₄	—	118	1	no	—
548	C₄	—	118	1	no	—
549	C₄	—	118	1	no	—
550	C₄	—	118	2	no	—
551	C₄	—	236	1	no	—
552	C₄	—	236	1	no	—
553	C₄	—	236	1	no	—
554	C₄	#131×D₅₉	1	1	yes	characteristic
555	C₄	C₂×#14273733	1	1	yes	characteristic
556	C₄	#16838212	1	1	yes	characteristic
557	C₄	#16838218	1	1	yes	characteristic
558	C₂	—	8	1	no	—
559	C₂	—	236	1	no	—
560	C₂	#21432785	1	1	yes	characteristic
561	C₂	#21432936	1	1	yes	characteristic
562	C₂	#21433010	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₅₉
commutator	C₂×C₄×C₅₉	C₂³×C₄
Frattini	C₄²	C₂³×D₅₉
Fitting	C₅₉×SD₁₆⋊C₈	C₂
socle	C₂²×C₅₉	C₂×C₄×D₄
prime radical	#14273698	C₂×C₄
cosocle	C₄²×C₅₉	C₂⁴
hypercenter	SD₁₆⋊C₈	D₅₉
hypocenter	C₅₉	#17919
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ SD₁₆⋊C₈

Complements

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

N	H ≅ G/N	type
3. #21433175	C₂	semidirect
4. #21422977	C₂	semidirect
5. #21422964	C₂	semidirect
6. #21422945	C₂	semidirect
7. #21422940	C₂	semidirect
8. #21422916	C₂	semidirect
9. C₈×#11745672	C₂	semidirect
10. C₈×#11745670	C₂	semidirect
11. #21422886	C₂	semidirect
12. #21422523	C₂	semidirect
14. #21422397	C₂	semidirect
15. C₅₉×SD₁₆⋊C₈	C₂	semidirect
285. SD₁₆⋊C₈	D₅₉	semidirect
348. C₅₉	#17919	semidirect

Maximal subgroups

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

subgroup	index
#21434174	2
#21433246	2
#21433175	2
#21422977	2
#21422964	2
#21422945	2
#21422940	2
#21422916	2
C₈×#11745672	2
C₈×#11745670	2
#21422886	2
#21422523	2
#21422501	2
#21422397	2
C₅₉×SD₁₆⋊C₈	2
#17919	59