Subgroups — #28559627

Order 15104.

602 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21434133	C₂	1	1	yes	maximal, characteristic
2	#21433048	C₂	1	1	yes	maximal, characteristic
3	#21433044	C₂	1	1	yes	maximal, characteristic
4	#21422990	C₂	1	1	yes	maximal, characteristic, complemented
5	#21422947	C₂	1	1	yes	maximal, characteristic, complemented
6	#21422945	C₂	1	1	yes	maximal, characteristic, complemented
7	#21422944	C₂	1	1	yes	maximal, characteristic, complemented
8	#21422944	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈×Dic₂₃₆	C₂	1	1	yes	maximal, characteristic, complemented
10	#21422900	C₂	1	1	yes	maximal, characteristic, complemented
11	#21422869	C₂	1	1	yes	maximal, characteristic
12	#21422549	C₂	1	1	yes	maximal, characteristic
13	Q₈⋊C₈×D₅₉	C₂	1	1	yes	maximal, characteristic
14	C₈×#11745659	C₂	1	1	yes	maximal, characteristic
15	C₅₉×#1591	C₂	1	1	yes	maximal, characteristic, complemented
16	#16837956	C₂²	1	1	yes	characteristic
17	C₄×Q₈×D₅₉	C₂²	1	1	yes	characteristic
18	#16837739	C₄	1	1	yes	characteristic
19	#16837736	C₄	1	1	yes	characteristic
20	#16837696	C₄	1	1	yes	characteristic
21	#16837695	C₄	1	1	yes	characteristic
22	#16837611	C₄	1	1	yes	characteristic
23	#16837610	C₄	1	1	yes	characteristic
24	#16837559	C₄	1	1	yes	characteristic
25	#16837556	C₄	1	1	yes	characteristic
26	#16837533	C₂²	1	1	yes	characteristic
27	#16837531	—	2	1	no	—
28	#16837530	—	2	1	no	—
29	#16837530	—	2	1	no	—
30	#16837529	—	2	1	no	—
31	#16837529	C₂²	1	1	yes	characteristic
32	Q₈×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
33	C₈×Dic₁₁₈	C₂²	1	1	yes	characteristic
34	C₈×Dic₁₁₈	C₂²	1	1	yes	characteristic
35	#16837526	C₂²	1	1	yes	characteristic
36	C₄×Dic₂₃₆	C₂²	1	1	yes	characteristic
37	C₄×#11745672	C₂²	1	1	yes	characteristic
38	C₄×#11745672	C₂²	1	1	yes	characteristic
39	#16837453	C₂²	1	1	yes	characteristic
40	#16837427	—	2	1	no	—
41	#16837424	—	2	1	no	—
42	#16837424	C₂²	1	1	yes	characteristic
43	C₄⋊C₈×D₅₉	C₂²	1	1	yes	characteristic
44	#16837359	—	2	1	no	—
45	#16837354	—	2	1	no	—
46	C₄×#11745659	C₂²	1	1	yes	characteristic
47	C₄×C₈×D₅₉	C₂²	1	1	yes	characteristic
48	#16837155	C₂²	1	1	yes	characteristic
49	#16837154	C₂²	1	1	yes	characteristic
50	#16837154	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	Q₈⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
55	#16837132	C₂²	1	1	yes	characteristic
56	#16837132	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	C₅₉×#446	C₂²	1	1	yes	characteristic
61	C₅₉×#446	C₂²	1	1	yes	characteristic
62	C₄×Q₁₆×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×Q₈⋊C₈	C₂²	1	1	yes	characteristic
66	C₈²×C₅₉	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×#11745672	C₂×C₄	1	1	yes	characteristic
71	C₂×#11745659	—	2	1	no	—
72	C₂×#11745659	D₄	1	1	yes	characteristic
73	C₂×#11745659	D₄	1	1	yes	characteristic
74	C₂×C₈×D₅₉	—	2	1	no	—
75	C₂×C₈×D₅₉	—	2	1	no	—
76	#14273726	C₂×C₄	1	1	yes	characteristic
77	#14273725	C₂×C₄	1	1	yes	characteristic
78	#14273717	—	2	1	no	—
79	#14273707	C₂×C₄	1	1	yes	characteristic
80	#14273705	—	2	1	no	—
81	#14273703	C₂×C₄	1	1	yes	characteristic
82	Q₈×Dic₅₉	C₂×C₄	1	1	yes	characteristic
83	C₄×Dic₁₁₈	—	2	1	no	—
84	C₄×Dic₁₁₈	—	2	1	no	—
85	C₄×Dic₁₁₈	C₂³	1	1	yes	characteristic
86	C₄×Dic₁₁₈	C₂³	1	1	yes	characteristic
87	#14273692	—	2	1	no	—
88	#14273692	C₂×C₄	1	1	yes	characteristic
89	#14273684	—	2	1	no	—
90	C₄⋊C₄×D₅₉	—	2	1	no	—
91	C₄⋊C₄×D₅₉	C₂×C₄	1	1	yes	characteristic
92	C₄²×D₅₉	—	2	1	no	—
93	C₄²×D₅₉	C₂³	1	1	yes	characteristic
94	#14273661	C₂×C₄	1	1	yes	characteristic
95	#14273660	C₂×C₄	1	1	yes	characteristic
96	#14273660	C₂×C₄	1	1	yes	characteristic
97	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
98	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
99	C₄⋊(C₅₉⋊C₈)	C₂³	1	1	yes	characteristic
100	C₄⋊(C₅₉⋊C₈)	C₂³	1	1	yes	characteristic
101	Dic₅₉⋊C₈	—	2	1	no	—
102	Dic₅₉⋊C₈	—	2	1	no	—
103	Dic₅₉⋊C₈	—	2	1	no	—
104	Dic₅₉⋊C₈	—	2	1	no	—
105	Dic₅₉⋊C₈	—	2	1	no	—
106	Dic₅₉⋊C₈	—	2	1	no	—
107	Dic₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
108	Dic₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
109	#14273652	C₂×C₄	1	1	yes	characteristic
110	#14273652	C₂×C₄	1	1	yes	characteristic
111	#14273651	C₂×C₄	1	1	yes	characteristic
112	#14273651	C₂×C₄	1	1	yes	characteristic
113	#14273650	C₂×C₄	1	1	yes	characteristic
114	#14273650	C₂×C₄	1	1	yes	characteristic
115	(C₂×D₅₉)⋊C₈	C₂×C₄	1	1	yes	characteristic
116	(C₂×D₅₉)⋊C₈	C₂×C₄	1	1	yes	characteristic
117	#14273638	—	2	1	no	—
118	#14273637	—	2	1	no	—
119	#14273637	D₄	1	1	yes	characteristic
120	#14273637	D₄	1	1	yes	characteristic
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×Q₁₆×C₅₉	C₂×C₄	1	1	yes	characteristic
130	C₄×Q₈×C₅₉	C₂³	1	1	yes	characteristic
131	C₄×Q₈×C₅₉	C₂³	1	1	yes	characteristic
132	#107×C₅₉	C₂×C₄	1	1	yes	characteristic
133	C₄⋊C₈×C₅₉	—	2	1	no	—
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	#103×C₅₉	C₂×C₄	1	1	yes	characteristic
139	#97×C₅₉	—	2	1	no	—
140	#97×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×Q₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
146	Q₈×D₅₉	—	2	2	no	—
147	Q₈×D₅₉	—	4	1	no	—
148	C₂×C₄×D₅₉	—	2	1	no	—
149	C₂×C₄×D₅₉	—	2	1	no	—
150	C₂×C₄×D₅₉	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₄×D₅₉	C₂×D₄	1	1	yes	characteristic
152	C₂×C₄×D₅₉	#41	1	1	yes	characteristic
153	C₂×Dic₁₁₈	—	2	1	no	—
154	C₂×Dic₁₁₈	—	2	1	no	—
155	C₂×Dic₁₁₈	C₂²×C₄	1	1	yes	characteristic
156	C₂×Dic₁₁₈	C₂²×C₄	1	1	yes	characteristic
157	Q₁₆×C₅₉	—	4	1	no	—
158	C₂×C₈×C₅₉	—	2	1	no	—
159	C₂×C₈×C₅₉	—	2	1	no	—
160	C₂×C₈×C₅₉	—	2	1	no	—
161	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
162	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
163	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
164	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
165	C₄⋊C₄×C₅₉	—	2	1	no	—
166	C₄⋊C₄×C₅₉	—	2	1	no	—
167	C₄⋊C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
168	C₄⋊C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
169	C₄²×C₅₉	—	2	1	no	—
170	C₄²×C₅₉	—	2	1	no	—
171	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
172	#11745672	—	2	2	no	—
173	#11745672	—	4	1	no	—
174	(C₂×D₅₉)⋊C₄	—	2	1	no	—
175	(C₂×D₅₉)⋊C₄	—	2	1	no	—
176	C₄⋊Dic₅₉	—	2	1	no	—
177	C₄⋊Dic₅₉	—	2	1	no	—
178	C₄⋊Dic₅₉	C₂²×C₄	1	1	yes	characteristic
179	C₄⋊Dic₅₉	C₂²×C₄	1	1	yes	characteristic
180	Dic₅₉⋊C₄	—	2	1	no	—
181	Dic₅₉⋊C₄	—	2	1	no	—
182	Dic₅₉⋊C₄	—	2	1	no	—
183	Dic₅₉⋊C₄	—	2	1	no	—
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	C₄×Dic₅₉	—	2	1	no	—
189	C₄×Dic₅₉	—	2	1	no	—
190	C₄×Dic₅₉	—	2	1	no	—
191	C₄×Dic₅₉	—	2	1	no	—
192	C₄×Dic₅₉	C₂²×C₄	1	1	yes	characteristic
193	C₄×Dic₅₉	C₂×D₄	1	1	yes	characteristic
194	C₄×Dic₅₉	#41	1	1	yes	characteristic
195	C₂×C₅₉⋊C₈	—	2	1	no	—
196	C₂×C₅₉⋊C₈	—	2	1	no	—
197	C₂×C₅₉⋊C₈	—	2	1	no	—
198	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
199	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
200	C₂×C₅₉⋊C₈	C₂×D₄	1	1	yes	characteristic
201	C₂×C₅₉⋊C₈	C₂×D₄	1	1	yes	characteristic
202	Dic₂₃₆	—	2	2	no	—
203	#11745659	—	2	2	no	—
204	#11745659	—	4	2	no	—
205	#11745659	Q₁₆	1	4	yes	complemented
206	C₈×D₅₉	—	4	2	no	—
207	C₈×D₅₉	—	4	2	no	—
208	C₂²×D₅₉	C₄×D₄	1	1	yes	characteristic
209	Q₈×C₅₉	—	2	1	no	—
210	Q₈×C₅₉	—	2	1	no	—
211	Q₈×C₅₉	—	2	1	no	—
212	Q₈×C₅₉	—	2	1	no	—
213	C₂×C₄×C₅₉	—	2	1	no	—
214	C₂×C₄×C₅₉	—	2	1	no	—
215	C₂×C₄×C₅₉	—	2	1	no	—
216	C₂×C₄×C₅₉	—	2	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	C₂×Dic₅₉	—	2	1	no	—
221	C₂×Dic₅₉	—	2	1	no	—
222	C₂×Dic₅₉	—	2	1	no	—
223	C₂×Dic₅₉	—	2	1	no	—
224	C₂×Dic₅₉	C₄×D₄	1	1	yes	characteristic
225	C₂×Dic₅₉	C₄×D₄	1	1	yes	characteristic
226	C₂×Dic₅₉	C₄×D₄	1	1	yes	characteristic
227	C₄×D₅₉	—	2	1	no	—
228	C₄×D₅₉	—	2	1	no	—
229	C₄×D₅₉	—	4	1	no	—
230	C₄×D₅₉	—	4	2	no	—
231	C₄×D₅₉	—	8	1	no	—
232	C₄×D₅₉	C₂×Q₁₆	1	2	yes	—
233	C₄×D₅₉	#135	1	2	yes	—
234	Dic₁₁₈	—	2	1	no	—
235	Dic₁₁₈	—	2	1	no	—
236	Dic₁₁₈	—	2	1	no	—
237	Dic₁₁₈	—	4	2	no	—
238	Dic₁₁₈	—	8	1	no	—
239	Dic₁₁₈	#131	1	2	yes	—
240	C₈×C₅₉	—	2	2	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	C₂×Q₁₆	1	2	yes	—
247	C₅₉⋊C₈	—	2	1	no	—
248	C₅₉⋊C₈	—	2	1	no	—
249	C₅₉⋊C₈	—	2	1	no	—
250	C₅₉⋊C₈	—	4	1	no	—
251	C₅₉⋊C₈	—	4	1	no	—
252	C₅₉⋊C₈	—	4	1	no	—
253	C₅₉⋊C₈	C₂×Q₁₆	1	2	yes	—
254	#17998	—	59	1	no	maximal, Sylow
255	C₂²×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
256	C₂×D₅₉	—	2	1	no	—
257	C₂×D₅₉	—	2	1	no	—
258	C₂×D₅₉	C₄×Q₁₆	1	2	yes	—
259	C₄×C₅₉	—	2	1	no	—
260	C₄×C₅₉	—	4	1	no	—
261	C₄×C₅₉	—	4	1	no	—
262	C₄×C₅₉	—	4	1	no	—
263	C₄×C₅₉	—	4	1	no	—
264	C₄×C₅₉	C₂×#131	1	1	yes	characteristic
265	C₄×C₅₉	#568	1	1	yes	characteristic
266	C₄×C₅₉	C₂²×Q₁₆	1	1	yes	characteristic
267	C₄×C₅₉	C₂×#135	1	1	yes	characteristic
268	Dic₅₉	—	2	2	no	—
269	Dic₅₉	—	2	1	no	—
270	Dic₅₉	—	2	1	no	—
271	Dic₅₉	—	4	1	no	—
272	Dic₅₉	—	4	1	no	—
273	Dic₅₉	—	4	1	no	—
274	Dic₅₉	C₄×Q₁₆	1	2	yes	—
275	#3104	—	59	1	no	—
276	Q₈×M₁₆	—	59	1	no	—
277	#2962	—	59	1	no	—
278	#1591	—	59	1	no	—
279	#1591	D₅₉	1	1	yes	characteristic, complemented
280	#1584	—	59	1	no	—
281	#1584	—	59	1	no	—
282	#1584	—	59	1	no	—
283	#1584	—	59	1	no	—
284	C₈×Q₁₆	—	59	1	no	—
285	C₈×Q₁₆	—	59	1	no	—
286	#1571	—	59	1	no	—
287	#1493	—	59	1	no	—
288	C₂×Q₈⋊C₈	—	59	1	no	—
289	C₈×M₁₆	—	59	1	no	—
290	C₂×C₅₉	#2933	1	1	yes	characteristic
291	C₂×C₅₉	C₂×C₄×Q₁₆	1	1	yes	characteristic
292	C₂×C₅₉	#2956	1	1	yes	characteristic
293	D₅₉	—	2	2	no	—
294	#533	—	59	1	no	—
295	C₂×C₄×Q₈	—	59	1	no	—
296	#484	—	59	1	no	—
297	#484	—	59	1	no	—
298	#477	—	59	1	no	—
299	#477	—	59	1	no	—
300	#462	—	59	1	no	—
301	#462	—	59	1	no	—
302	#451	—	59	1	no	—
303	#451	—	59	1	no	—
304	#446	—	59	1	no	—
305	#446	—	59	1	no	—
306	#446	—	118	1	no	—
307	#446	—	118	1	no	—
308	#446	—	118	1	no	—
309	#446	—	118	1	no	—
310	#446	C₂×D₅₉	1	1	yes	characteristic
311	#446	C₂×D₅₉	1	1	yes	characteristic
312	C₈×Q₈	—	59	1	no	—
313	C₈×Q₈	—	59	1	no	—
314	C₈×Q₈	—	59	1	no	—
315	C₈×Q₈	—	59	1	no	—
316	C₄×Q₁₆	—	59	1	no	—
317	C₄×Q₁₆	—	59	1	no	—
318	C₄×Q₁₆	—	59	1	no	—
319	C₄×Q₁₆	C₂×D₅₉	1	1	yes	characteristic
320	#431	—	59	1	no	—
321	#424	—	118	1	no	—
322	#423	—	59	1	no	—
323	#423	—	118	1	no	—
324	C₂×C₄⋊C₈	—	59	1	no	—
325	#405	—	118	1	no	—
326	C₄×M₁₆	—	59	1	no	—
327	C₄×M₁₆	—	118	1	no	—
328	C₂×C₄×C₈	—	59	1	no	—
329	#335	—	59	1	no	—
330	#335	—	59	1	no	—
331	#335	—	59	1	no	—
332	#335	C₂×D₅₉	1	1	yes	characteristic
333	Q₈⋊C₈	—	59	1	no	—
334	Q₈⋊C₈	—	59	1	no	—
335	Q₈⋊C₈	—	59	1	no	—
336	Q₈⋊C₈	—	59	1	no	—
337	Q₈⋊C₈	—	59	1	no	—
338	Q₈⋊C₈	—	59	1	no	—
339	Q₈⋊C₈	C₂×D₅₉	1	1	yes	characteristic
340	Q₈⋊C₈	C₂×D₅₉	1	1	yes	characteristic
341	#322	—	59	1	no	—
342	#322	—	59	1	no	—
343	C₈²	—	59	1	no	—
344	C₈²	C₂×D₅₉	1	1	yes	characteristic
345	C₅₉	#17998	1	1	yes	characteristic, complemented, Sylow
346	C₂²×Q₈	—	59	1	no	—
347	C₂×Q₁₆	—	59	1	no	—
348	C₂×Q₁₆	—	59	1	no	—
349	C₂×Q₁₆	—	59	1	no	—
350	C₂×Q₁₆	C₄×D₅₉	1	1	yes	characteristic
351	C₂×M₁₆	—	59	1	no	—
352	C₂×M₁₆	—	59	1	no	—
353	C₂×M₁₆	—	118	1	no	—
354	C₂²×C₈	—	118	1	no	—
355	C₂²×C₈	—	118	1	no	—
356	C₄⋊Q₈	—	59	1	no	—
357	C₄⋊Q₈	—	59	1	no	—
358	#125	—	118	1	no	—
359	C₂²⋊Q₈	—	59	1	no	—
360	C₂²⋊Q₈	—	59	1	no	—
361	C₂²⋊Q₈	—	118	1	no	—
362	C₄×Q₈	—	59	1	no	—
363	C₄×Q₈	—	59	1	no	—
364	C₄×Q₈	—	59	1	no	—
365	C₄×Q₈	—	59	1	no	—
366	C₄×Q₈	—	118	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×Q₈	C₂²×D₅₉	1	1	yes	characteristic
371	#117	—	118	1	no	—
372	C₂×C₄⋊C₄	—	59	1	no	—
373	C₂×C₄⋊C₄	—	118	1	no	—
374	C₂×C₄²	—	59	1	no	—
375	C₂×C₄²	—	118	1	no	—
376	#107	—	59	1	no	—
377	#107	—	59	1	no	—
378	#107	—	59	1	no	—
379	#107	C₄×D₅₉	1	1	yes	characteristic
380	C₄⋊C₈	—	2	1	no	—
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	—	118	1	no	—
387	C₄⋊C₈	—	118	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	C₂²×D₅₉	1	1	yes	characteristic
395	C₄⋊C₈	C₂²×D₅₉	1	1	yes	characteristic
396	#103	—	59	1	no	—
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	#103	C₄×D₅₉	1	1	yes	characteristic
404	C₂²⋊C₈	—	59	1	no	—
405	C₂²⋊C₈	—	59	1	no	—
406	#97	—	2	1	no	—
407	#97	—	2	1	no	—
408	#97	—	59	1	no	—
409	#97	—	59	1	no	—
410	#97	—	118	1	no	—
411	#97	—	118	1	no	—
412	C₄×C₈	—	59	1	no	—
413	C₄×C₈	—	59	1	no	—
414	C₄×C₈	—	59	1	no	—
415	C₄×C₈	—	118	1	no	—
416	C₄×C₈	—	118	1	no	—
417	C₄×C₈	—	118	1	no	—
418	C₄×C₈	—	118	1	no	—
419	C₄×C₈	—	118	1	no	—
420	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
421	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
422	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
423	C₂×Q₈	—	59	1	no	—
424	C₂×Q₈	—	59	1	no	—
425	C₂×Q₈	—	118	1	no	—
426	C₂×Q₈	—	118	1	no	—
427	C₂×Q₈	—	118	2	no	—
428	C₂×Q₈	—	236	1	no	—
429	C₂×Q₈	C₂×C₄×D₅₉	1	1	yes	characteristic
430	C₂×Q₈	C₂×C₄×D₅₉	1	1	yes	characteristic
431	C₂²×C₄	—	59	1	no	—
432	C₂²×C₄	—	59	1	no	—
433	C₂²×C₄	—	59	1	no	—
434	C₂²×C₄	—	118	1	no	—
435	C₂²×C₄	—	118	1	no	—
436	Q₁₆	—	4	1	no	—
437	Q₁₆	—	118	2	no	—
438	Q₁₆	—	118	2	no	—
439	Q₁₆	—	236	1	no	—
440	M₁₆	—	59	4	no	—
441	M₁₆	—	118	2	no	—
442	M₁₆	—	236	2	no	—
443	C₂×C₈	—	2	1	no	—
444	C₂×C₈	—	2	1	no	—
445	C₂×C₈	—	2	1	no	—
446	C₂×C₈	—	59	1	no	—
447	C₂×C₈	—	59	1	no	—
448	C₂×C₈	—	59	1	no	—
449	C₂×C₈	—	59	1	no	—
450	C₂×C₈	—	118	1	no	—
451	C₂×C₈	—	118	1	no	—
452	C₂×C₈	—	118	1	no	—
453	C₂×C₈	—	236	2	no	—
454	C₂×C₈	—	236	2	no	—
455	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
456	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
457	C₂×C₈	D₄×D₅₉	1	1	yes	characteristic
458	C₂×C₈	D₄×D₅₉	1	1	yes	characteristic
459	C₄⋊C₄	—	2	1	no	—
460	C₄⋊C₄	—	2	1	no	—
461	C₄⋊C₄	—	59	1	no	—
462	C₄⋊C₄	—	59	1	no	—
463	C₄⋊C₄	—	118	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	—	118	1	no	—
473	C₄⋊C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
474	C₄⋊C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
475	C₂²⋊C₄	—	118	1	no	—
476	C₂²⋊C₄	—	118	1	no	—
477	C₄²	—	2	1	no	—
478	C₄²	—	2	1	no	—
479	C₄²	—	59	1	no	—
480	C₄²	—	59	1	no	—
481	C₄²	—	59	1	no	—
482	C₄²	—	118	1	no	—
483	C₄²	—	118	1	no	—
484	C₄²	—	118	1	no	—
485	C₄²	—	118	1	no	—
486	C₄²	C₂³×D₅₉	1	1	yes	characteristic
487	C₂³	—	59	1	no	—
488	Q₈	—	2	1	no	—
489	Q₈	—	2	1	no	—
490	Q₈	—	2	1	no	—
491	Q₈	—	2	1	no	—
492	Q₈	—	59	2	no	—
493	Q₈	—	118	1	no	—
494	Q₈	—	118	1	no	—
495	Q₈	—	118	1	no	—
496	Q₈	—	472	1	no	—
497	Q₈	—	236	2	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	59	1	no	—
503	C₂×C₄	—	59	2	no	—
504	C₂×C₄	—	59	2	no	—
505	C₂×C₄	—	59	1	no	—
506	C₂×C₄	—	59	1	no	—
507	C₂×C₄	—	118	1	no	—
508	C₂×C₄	—	118	1	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	—	472	1	no	—
514	C₂×C₄	—	236	1	no	—
515	C₂×C₄	—	236	2	no	—
516	C₂×C₄	C₂²×C₄×D₅₉	1	1	yes	characteristic
517	C₂×C₄	C₂×D₄×D₅₉	1	1	yes	characteristic
518	C₂×C₄	#41×D₅₉	1	1	yes	characteristic
519	C₈	—	2	2	no	—
520	C₈	—	2	1	no	—
521	C₈	—	2	1	no	—
522	C₈	—	2	1	no	—
523	C₈	—	4	1	no	—
524	C₈	—	4	1	no	—
525	C₈	—	59	2	no	—
526	C₈	—	118	1	no	—
527	C₈	—	118	1	no	—
528	C₈	—	118	1	no	—
529	C₈	—	236	1	no	—
530	C₈	—	236	1	no	—
531	C₈	—	236	1	no	—
532	C₈	Q₁₆×D₅₉	1	2	yes	—
533	C₂²	—	59	2	no	—
534	C₂²	—	118	1	no	—
535	C₂²	—	118	1	no	—
536	C₂²	C₄×D₄×D₅₉	1	1	yes	characteristic
537	C₄	—	2	1	no	—
538	C₄	—	4	1	no	—
539	C₄	—	4	1	no	—
540	C₄	—	4	1	no	—
541	C₄	—	4	1	no	—
542	C₄	—	59	2	no	—
543	C₄	—	118	1	no	—
544	C₄	—	118	1	no	—
545	C₄	—	118	2	no	—
546	C₄	—	236	1	no	—
547	C₄	—	236	1	no	—
548	C₄	—	236	1	no	—
549	C₄	#131×D₅₉	1	1	yes	characteristic
550	C₄	#16838168	1	1	yes	characteristic
551	C₄	C₂×Q₁₆×D₅₉	1	1	yes	characteristic
552	C₄	#135×D₅₉	1	1	yes	characteristic
553	C₂	—	118	2	no	—
554	C₂	#21432825	1	1	yes	characteristic
555	C₂	C₄×Q₁₆×D₅₉	1	1	yes	characteristic
556	C₂	#21433001	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×#1591	C₂
socle	C₂²×C₅₉	C₂×C₄×D₄
prime radical	C₂²×D₅₉	C₄×D₄
cosocle	C₄²×C₅₉	C₂⁴
hypercenter	#1591	D₅₉
hypocenter	C₅₉	#17998
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #1591

Complements

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

N	H ≅ G/N	type
4. #21422990	C₂	semidirect
5. #21422947	C₂	semidirect
6. #21422945	C₂	semidirect
7. #21422944	C₂	semidirect
8. #21422944	C₂	semidirect
9. C₈×Dic₂₃₆	C₂	semidirect
10. #21422900	C₂	semidirect
15. C₅₉×#1591	C₂	semidirect
205. #11745659	Q₁₆	semidirect
279. #1591	D₅₉	semidirect
345. C₅₉	#17998	semidirect

Maximal subgroups

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

subgroup	index
#21434133	2
#21433048	2
#21433044	2
#21422990	2
#21422947	2
#21422945	2
#21422944	2
C₈×Dic₂₃₆	2
#21422900	2
#21422869	2
#21422549	2
Q₈⋊C₈×D₅₉	2
C₈×#11745659	2
C₅₉×#1591	2
#17998	59