Subgroups — #28558581

Order 15104.

618 conjugacy classes of subgroups.

The subgroup lattice has 556 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	#21433027	C₂	1	1	yes	maximal, characteristic
3	C₈×Q₈×D₅₉	C₂	1	1	yes	maximal, characteristic
4	#21422948	C₂	1	1	yes	maximal, characteristic, complemented
5	#21422946	C₂	1	1	yes	maximal, characteristic, complemented
6	#21422944	C₂	1	1	yes	maximal, characteristic, complemented
7	Q₁₆×C₅₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	#21422902	C₂	1	1	yes	maximal, characteristic, complemented
9	#21422900	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	#21422523	C₂	1	1	yes	maximal, characteristic
13	#21422497	C₂	1	1	yes	maximal, characteristic
14	#21422381	C₂	1	1	yes	maximal, characteristic
15	C₅₉×#1584	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	#16837532	C₂²	1	1	yes	characteristic
27	#16837530	—	2	1	no	—
28	Q₈×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
29	Q₈×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
30	C₈×Dic₁₁₈	—	2	1	no	—
31	C₈×Dic₁₁₈	C₂²	1	1	yes	characteristic
32	#16837526	—	2	1	no	—
33	#16837526	—	2	1	no	—
34	#16837526	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	#16837453	C₂²	1	1	yes	characteristic
41	#16837427	—	2	1	no	—
42	#16837424	C₂²	1	1	yes	characteristic
43	C₄⋊C₈×D₅₉	—	2	1	no	—
44	C₄⋊C₈×D₅₉	C₂²	1	1	yes	characteristic
45	#16837359	—	2	1	no	—
46	C₄×C₈×D₅₉	—	2	1	no	—
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	#16837123	C₂²	1	1	yes	characteristic
58	C₈×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
59	C₈×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
60	C₅₉×#446	C₂²	1	1	yes	characteristic
61	C₈×Q₈×C₅₉	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	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×#11745672	C₂×C₄	1	1	yes	characteristic
71	C₂×#11745659	—	2	1	no	—
72	C₂×C₈×D₅₉	—	2	1	no	—
73	C₂×C₈×D₅₉	D₄	1	1	yes	characteristic
74	C₂×C₈×D₅₉	D₄	1	1	yes	characteristic
75	#14273726	C₂×C₄	1	1	yes	characteristic
76	#14273725	C₂×C₄	1	1	yes	characteristic
77	#14273717	—	2	1	no	—
78	#14273707	C₂×C₄	1	1	yes	characteristic
79	#14273705	—	2	1	no	—
80	#14273703	C₂×C₄	1	1	yes	characteristic
81	Q₈×Dic₅₉	C₂×C₄	1	1	yes	characteristic
82	C₄×Dic₁₁₈	—	2	1	no	—
83	C₄×Dic₁₁₈	—	2	1	no	—
84	C₄×Dic₁₁₈	C₂³	1	1	yes	characteristic
85	C₄×Dic₁₁₈	C₂³	1	1	yes	characteristic
86	#14273692	—	2	1	no	—
87	#14273692	C₂×C₄	1	1	yes	characteristic
88	#14273684	—	2	1	no	—
89	C₄⋊C₄×D₅₉	—	2	1	no	—
90	C₄⋊C₄×D₅₉	C₂×C₄	1	1	yes	characteristic
91	C₄²×D₅₉	—	2	1	no	—
92	C₄²×D₅₉	C₂³	1	1	yes	characteristic
93	#14273661	C₂×C₄	1	1	yes	characteristic
94	#14273660	C₂×C₄	1	1	yes	characteristic
95	#14273660	C₂×C₄	1	1	yes	characteristic
96	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
97	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
98	C₄⋊(C₅₉⋊C₈)	C₂³	1	1	yes	characteristic
99	C₄⋊(C₅₉⋊C₈)	C₂³	1	1	yes	characteristic
100	Dic₅₉⋊C₈	—	2	1	no	—
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	—	2	1	no	—
116	(C₂×D₅₉)⋊C₈	C₂×C₄	1	1	yes	characteristic
117	(C₂×D₅₉)⋊C₈	C₂×C₄	1	1	yes	characteristic
118	#14273637	—	2	1	no	—
119	C₄×C₅₉⋊C₈	—	2	1	no	—
120	C₄×C₅₉⋊C₈	—	2	1	no	—
121	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
122	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
123	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
124	C₈×Dic₅₉	—	2	1	no	—
125	C₈×Dic₅₉	—	2	1	no	—
126	C₈×Dic₅₉	—	2	1	no	—
127	C₈×Dic₅₉	D₄	1	1	yes	characteristic
128	C₈×Dic₅₉	D₄	1	1	yes	characteristic
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	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×Q₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
146	Q₈×D₅₉	—	2	2	no	—
147	Q₈×D₅₉	—	2	2	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	—	2	2	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	—	2	2	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	—	4	2	no	—
204	C₈×D₅₉	—	2	2	no	—
205	C₈×D₅₉	—	4	2	no	—
206	C₈×D₅₉	Q₁₆	1	4	yes	complemented
207	C₂²×D₅₉	C₄×D₄	1	1	yes	characteristic
208	Q₈×C₅₉	—	2	1	no	—
209	Q₈×C₅₉	—	2	1	no	—
210	Q₈×C₅₉	—	2	1	no	—
211	Q₈×C₅₉	#131	1	2	yes	—
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	—	2	1	no	—
216	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
217	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
218	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
219	C₂×Dic₅₉	—	2	1	no	—
220	C₂×Dic₅₉	—	2	1	no	—
221	C₂×Dic₅₉	—	2	1	no	—
222	C₂×Dic₅₉	—	2	1	no	—
223	C₂×Dic₅₉	C₄×D₄	1	1	yes	characteristic
224	C₂×Dic₅₉	C₄×D₄	1	1	yes	characteristic
225	C₂×Dic₅₉	C₄×D₄	1	1	yes	characteristic
226	C₄×D₅₉	—	2	4	no	—
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	C₂×Q₁₆	1	2	yes	—
232	C₄×D₅₉	#135	1	2	yes	—
233	Dic₁₁₈	—	2	4	no	—
234	Dic₁₁₈	—	2	1	no	—
235	Dic₁₁₈	—	2	1	no	—
236	Dic₁₁₈	—	2	1	no	—
237	Dic₁₁₈	—	4	2	no	—
238	Dic₁₁₈	#131	1	2	yes	—
239	C₈×C₅₉	—	2	1	no	—
240	C₈×C₅₉	—	2	1	no	—
241	C₈×C₅₉	—	2	1	no	—
242	C₈×C₅₉	—	4	1	no	—
243	C₈×C₅₉	—	4	1	no	—
244	C₈×C₅₉	—	4	1	no	—
245	C₈×C₅₉	C₂×Q₁₆	1	2	yes	—
246	C₅₉⋊C₈	—	2	1	no	—
247	C₅₉⋊C₈	—	2	1	no	—
248	C₅₉⋊C₈	—	2	1	no	—
249	C₅₉⋊C₈	—	4	1	no	—
250	C₅₉⋊C₈	—	4	1	no	—
251	C₅₉⋊C₈	—	4	1	no	—
252	C₅₉⋊C₈	C₂×Q₁₆	1	2	yes	—
253	#17903	—	59	1	no	maximal, Sylow
254	C₂²×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
255	C₂×D₅₉	—	2	1	no	—
256	C₂×D₅₉	—	2	1	no	—
257	C₂×D₅₉	C₄×Q₁₆	1	2	yes	—
258	C₄×C₅₉	—	2	2	no	—
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	C₂×#131	1	1	yes	characteristic
264	C₄×C₅₉	C₂×#131	1	1	yes	characteristic
265	C₄×C₅₉	C₂²×Q₁₆	1	1	yes	characteristic
266	C₄×C₅₉	C₂×#135	1	1	yes	characteristic
267	Dic₅₉	—	2	1	no	—
268	Dic₅₉	—	2	2	no	—
269	Dic₅₉	—	2	1	no	—
270	Dic₅₉	—	4	1	no	—
271	Dic₅₉	—	4	1	no	—
272	Dic₅₉	—	4	1	no	—
273	Dic₅₉	C₄×Q₁₆	1	2	yes	—
274	#3104	—	59	1	no	—
275	#2960	—	59	1	no	—
276	C₂×C₈×Q₈	—	59	1	no	—
277	#1584	—	59	1	no	—
278	#1584	—	59	1	no	—
279	#1584	—	59	1	no	—
280	#1584	D₅₉	1	1	yes	characteristic, complemented
281	C₈×Q₁₆	—	59	1	no	—
282	C₈×Q₁₆	—	59	1	no	—
283	C₈×Q₁₆	—	59	1	no	—
284	C₈×Q₁₆	—	59	1	no	—
285	#1571	—	59	1	no	—
286	#1487	—	59	1	no	—
287	#1481	—	59	1	no	—
288	#1450	—	59	1	no	—
289	C₂×C₅₉	#2929	1	1	yes	characteristic
290	C₂×C₅₉	C₂×C₄×Q₁₆	1	1	yes	characteristic
291	C₂×C₅₉	#2955	1	1	yes	characteristic
292	D₅₉	—	2	2	no	—
293	#533	—	59	1	no	—
294	C₂×C₄×Q₈	—	59	1	no	—
295	#484	—	59	1	no	—
296	#484	—	59	1	no	—
297	#477	—	59	1	no	—
298	#477	—	59	1	no	—
299	#462	—	59	1	no	—
300	#462	—	59	1	no	—
301	#451	—	59	1	no	—
302	#451	—	59	1	no	—
303	#446	—	59	1	no	—
304	#446	—	118	1	no	—
305	#446	C₂×D₅₉	1	1	yes	characteristic
306	C₈×Q₈	—	59	1	no	—
307	C₈×Q₈	—	59	1	no	—
308	C₈×Q₈	—	59	1	no	—
309	C₈×Q₈	—	59	1	no	—
310	C₈×Q₈	—	59	1	no	—
311	C₈×Q₈	—	118	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×Q₁₆	—	59	1	no	—
318	C₄×Q₁₆	C₂×D₅₉	1	1	yes	characteristic
319	#431	—	59	1	no	—
320	#431	—	59	1	no	—
321	#424	—	118	1	no	—
322	#423	—	59	1	no	—
323	C₂×C₄⋊C₈	—	59	1	no	—
324	C₂×C₄⋊C₈	—	118	1	no	—
325	#405	—	118	1	no	—
326	C₂×C₄×C₈	—	59	1	no	—
327	C₂×C₄×C₈	—	118	1	no	—
328	#335	—	59	1	no	—
329	#335	—	59	1	no	—
330	#335	—	59	1	no	—
331	#335	C₂×D₅₉	1	1	yes	characteristic
332	Q₈⋊C₈	—	59	1	no	—
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	C₂×D₅₉	1	1	yes	characteristic
339	Q₈⋊C₈	C₂×D₅₉	1	1	yes	characteristic
340	#322	—	59	1	no	—
341	#322	C₂×D₅₉	1	1	yes	characteristic
342	C₈²	—	59	1	no	—
343	C₈²	—	59	1	no	—
344	C₅₉	#17903	1	1	yes	characteristic, complemented, Sylow
345	C₂²×Q₈	—	59	1	no	—
346	C₂×Q₁₆	—	59	1	no	—
347	C₂×Q₁₆	—	59	1	no	—
348	C₂×Q₁₆	—	59	1	no	—
349	C₂×Q₁₆	C₄×D₅₉	1	1	yes	characteristic
350	C₂×M₁₆	—	118	1	no	—
351	C₂²×C₈	—	59	1	no	—
352	C₂²×C₈	—	59	1	no	—
353	C₂²×C₈	—	118	1	no	—
354	C₄⋊Q₈	—	59	1	no	—
355	C₄⋊Q₈	—	59	1	no	—
356	#125	—	118	1	no	—
357	C₂²⋊Q₈	—	59	1	no	—
358	C₂²⋊Q₈	—	59	1	no	—
359	C₂²⋊Q₈	—	118	1	no	—
360	C₄×Q₈	—	59	1	no	—
361	C₄×Q₈	—	59	1	no	—
362	C₄×Q₈	—	59	1	no	—
363	C₄×Q₈	—	59	1	no	—
364	C₄×Q₈	—	118	1	no	—
365	C₄×Q₈	—	118	1	no	—
366	C₄×Q₈	—	118	1	no	—
367	C₄×Q₈	C₂²×D₅₉	1	1	yes	characteristic
368	C₄×Q₈	C₂²×D₅₉	1	1	yes	characteristic
369	#117	—	118	1	no	—
370	C₂×C₄⋊C₄	—	59	1	no	—
371	C₂×C₄⋊C₄	—	118	1	no	—
372	C₂×C₄²	—	59	1	no	—
373	C₂×C₄²	—	118	1	no	—
374	#107	—	59	1	no	—
375	#107	—	59	1	no	—
376	#107	—	59	1	no	—
377	#107	C₄×D₅₉	1	1	yes	characteristic
378	C₄⋊C₈	—	2	1	no	—
379	C₄⋊C₈	—	2	1	no	—
380	C₄⋊C₈	—	59	1	no	—
381	C₄⋊C₈	—	59	1	no	—
382	C₄⋊C₈	—	59	1	no	—
383	C₄⋊C₈	—	59	1	no	—
384	C₄⋊C₈	—	118	1	no	—
385	C₄⋊C₈	—	118	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	C₂²×D₅₉	1	1	yes	characteristic
394	C₄⋊C₈	C₂²×D₅₉	1	1	yes	characteristic
395	#103	—	59	1	no	—
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	C₄×D₅₉	1	1	yes	characteristic
402	#103	C₄×D₅₉	1	1	yes	characteristic
403	C₂²⋊C₈	—	59	1	no	—
404	C₂²⋊C₈	—	59	1	no	—
405	C₂²⋊C₈	—	118	1	no	—
406	#97	—	2	1	no	—
407	#97	—	118	1	no	—
408	C₄×C₈	—	2	1	no	—
409	C₄×C₈	—	59	1	no	—
410	C₄×C₈	—	59	1	no	—
411	C₄×C₈	—	59	1	no	—
412	C₄×C₈	—	59	1	no	—
413	C₄×C₈	—	59	1	no	—
414	C₄×C₈	—	118	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	C₂²×D₅₉	1	1	yes	characteristic
420	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
421	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
422	C₂×Q₈	—	59	1	no	—
423	C₂×Q₈	—	59	1	no	—
424	C₂×Q₈	—	118	1	no	—
425	C₂×Q₈	—	118	1	no	—
426	C₂×Q₈	—	118	2	no	—
427	C₂×Q₈	—	118	2	no	—
428	C₂×Q₈	C₂×C₄×D₅₉	1	1	yes	characteristic
429	C₂×Q₈	C₂×C₄×D₅₉	1	1	yes	characteristic
430	C₂²×C₄	—	59	1	no	—
431	C₂²×C₄	—	59	1	no	—
432	C₂²×C₄	—	59	1	no	—
433	C₂²×C₄	—	118	1	no	—
434	C₂²×C₄	—	118	1	no	—
435	Q₁₆	—	2	2	no	—
436	Q₁₆	—	118	2	no	—
437	Q₁₆	—	118	2	no	—
438	Q₁₆	—	118	2	no	—
439	M₁₆	—	236	2	no	—
440	C₂×C₈	—	2	1	no	—
441	C₂×C₈	—	2	1	no	—
442	C₂×C₈	—	2	1	no	—
443	C₂×C₈	—	59	1	no	—
444	C₂×C₈	—	59	4	no	—
445	C₂×C₈	—	59	1	no	—
446	C₂×C₈	—	59	1	no	—
447	C₂×C₈	—	59	1	no	—
448	C₂×C₈	—	118	2	no	—
449	C₂×C₈	—	118	1	no	—
450	C₂×C₈	—	118	1	no	—
451	C₂×C₈	—	118	1	no	—
452	C₂×C₈	—	236	2	no	—
453	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
454	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
455	C₂×C₈	D₄×D₅₉	1	1	yes	characteristic
456	C₂×C₈	D₄×D₅₉	1	1	yes	characteristic
457	C₄⋊C₄	—	2	1	no	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	59	1	no	—
460	C₄⋊C₄	—	59	1	no	—
461	C₄⋊C₄	—	118	1	no	—
462	C₄⋊C₄	—	118	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	C₂×C₄×D₅₉	1	1	yes	characteristic
472	C₄⋊C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
473	C₂²⋊C₄	—	118	1	no	—
474	C₂²⋊C₄	—	118	1	no	—
475	C₄²	—	2	1	no	—
476	C₄²	—	2	1	no	—
477	C₄²	—	59	1	no	—
478	C₄²	—	59	1	no	—
479	C₄²	—	59	1	no	—
480	C₄²	—	118	1	no	—
481	C₄²	—	118	1	no	—
482	C₄²	—	118	1	no	—
483	C₄²	—	118	1	no	—
484	C₄²	C₂³×D₅₉	1	1	yes	characteristic
485	C₂³	—	59	1	no	—
486	Q₈	—	2	1	no	—
487	Q₈	—	2	1	no	—
488	Q₈	—	2	1	no	—
489	Q₈	—	59	2	no	—
490	Q₈	—	118	4	no	—
491	Q₈	—	118	1	no	—
492	Q₈	—	118	1	no	—
493	Q₈	—	118	1	no	—
494	Q₈	—	236	2	no	—
495	Q₈	#14273735	1	2	yes	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	59	1	no	—
501	C₂×C₄	—	59	2	no	—
502	C₂×C₄	—	59	2	no	—
503	C₂×C₄	—	59	1	no	—
504	C₂×C₄	—	59	1	no	—
505	C₂×C₄	—	118	4	no	—
506	C₂×C₄	—	118	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	—	236	1	no	—
513	C₂×C₄	—	236	2	no	—
514	C₂×C₄	C₂²×C₄×D₅₉	1	1	yes	characteristic
515	C₂×C₄	C₂×D₄×D₅₉	1	1	yes	characteristic
516	C₂×C₄	#41×D₅₉	1	1	yes	characteristic
517	C₈	—	2	1	no	—
518	C₈	—	2	1	no	—
519	C₈	—	2	1	no	—
520	C₈	—	4	1	no	—
521	C₈	—	4	1	no	—
522	C₈	—	4	1	no	—
523	C₈	—	59	2	no	—
524	C₈	—	118	1	no	—
525	C₈	—	118	1	no	—
526	C₈	—	118	1	no	—
527	C₈	—	236	1	no	—
528	C₈	—	236	1	no	—
529	C₈	—	236	1	no	—
530	C₈	Q₁₆×D₅₉	1	2	yes	—
531	C₂²	—	59	2	no	—
532	C₂²	—	118	1	no	—
533	C₂²	—	118	1	no	—
534	C₂²	C₄×D₄×D₅₉	1	1	yes	characteristic
535	C₄	—	2	1	no	—
536	C₄	—	2	2	no	—
537	C₄	—	4	1	no	—
538	C₄	—	4	1	no	—
539	C₄	—	4	1	no	—
540	C₄	—	59	2	no	—
541	C₄	—	118	1	no	—
542	C₄	—	118	1	no	—
543	C₄	—	118	2	no	—
544	C₄	—	236	1	no	—
545	C₄	—	236	1	no	—
546	C₄	—	236	1	no	—
547	C₄	#131×D₅₉	1	1	yes	characteristic
548	C₄	C₂×#14273735	1	1	yes	characteristic
549	C₄	C₂×Q₁₆×D₅₉	1	1	yes	characteristic
550	C₄	#135×D₅₉	1	1	yes	characteristic
551	C₂	—	118	2	no	—
552	C₂	#21432787	1	1	yes	characteristic
553	C₂	C₄×Q₁₆×D₅₉	1	1	yes	characteristic
554	C₂	#21432996	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×#1584	C₂
socle	C₂²×C₅₉	C₂×C₄×D₄
prime radical	C₂²×D₅₉	C₄×D₄
cosocle	C₄²×C₅₉	C₂⁴
hypercenter	#1584	D₅₉
hypocenter	C₅₉	#17903
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #1584

Complements

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

N	H ≅ G/N	type
4. #21422948	C₂	semidirect
5. #21422946	C₂	semidirect
6. #21422944	C₂	semidirect
7. Q₁₆×C₅₉⋊C₈	C₂	semidirect
8. #21422902	C₂	semidirect
9. #21422900	C₂	semidirect
10. #21422900	C₂	semidirect
15. C₅₉×#1584	C₂	semidirect
206. C₈×D₅₉	Q₁₆	semidirect
280. #1584	D₅₉	semidirect
344. C₅₉	#17903	semidirect

Maximal subgroups

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

subgroup	index
#21434133	2
#21433027	2
C₈×Q₈×D₅₉	2
#21422948	2
#21422946	2
#21422944	2
Q₁₆×C₅₉⋊C₈	2
#21422902	2
#21422900	2
#21422869	2
#21422523	2
#21422497	2
#21422381	2
C₅₉×#1584	2
#17903	59