Subgroups — #28558794

Order 15104.

598 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	#21434167	C₂	1	1	yes	maximal, characteristic
2	#21433190	C₂	1	1	yes	maximal, characteristic, complemented
3	#21422967	C₂	1	1	yes	maximal, characteristic, complemented
4	#21422953	C₂	1	1	yes	maximal, characteristic, complemented
5	#21422946	C₂	1	1	yes	maximal, characteristic, complemented
6	#21422932	C₂	1	1	yes	maximal, characteristic, complemented
7	#21422913	C₂	1	1	yes	maximal, characteristic, complemented
8	#21422908	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	#21422879	C₂	1	1	yes	maximal, characteristic, complemented
12	#21422530	C₂	1	1	yes	maximal, characteristic
13	#21422498	C₂	1	1	yes	maximal, characteristic, complemented
14	#21422396	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₉×#2988	C₂	1	1	yes	maximal, characteristic
16	#16837959	C₂²	1	1	yes	characteristic
17	#16837743	C₄	1	1	yes	characteristic
18	#16837743	C₄	1	1	yes	characteristic
19	#16837687	C₄	1	1	yes	characteristic
20	#16837682	C₄	1	1	yes	characteristic
21	#16837612	C₄	1	1	yes	characteristic
22	#16837607	C₄	1	1	yes	characteristic
23	#16837564	C₄	1	1	yes	characteristic
24	#16837564	C₄	1	1	yes	characteristic
25	#16837532	C₂²	1	1	yes	characteristic
26	#16837532	C₂²	1	1	yes	characteristic
27	#16837531	—	2	1	no	—
28	#16837531	—	2	1	no	—
29	C₈×Dic₁₁₈	C₂²	1	1	yes	characteristic
30	C₈×Dic₁₁₈	C₂²	1	1	yes	characteristic
31	C₄×#11745672	C₂²	1	1	yes	characteristic
32	C₄×#11745672	C₂²	1	1	yes	characteristic
33	C₄×#11745670	C₂²	1	1	yes	characteristic
34	C₄×#11745670	C₂²	1	1	yes	characteristic
35	#16837460	—	2	1	no	—
36	#16837460	—	2	1	no	—
37	#16837459	C₂²	1	1	yes	characteristic
38	#16837455	C₂²	1	1	yes	characteristic
39	#16837455	C₂²	1	1	yes	characteristic
40	#16837154	C₂²	1	1	yes	characteristic
41	#16837154	C₂²	1	1	yes	characteristic
42	#16837152	C₂²	1	1	yes	characteristic
43	#16837152	C₂²	1	1	yes	characteristic
44	Q₈⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
45	Q₈⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
46	#16837132	C₂²	1	1	yes	characteristic
47	#16837132	C₂²	1	1	yes	characteristic
48	#16837132	C₂²	1	1	yes	characteristic
49	#16837132	C₂²	1	1	yes	characteristic
50	D₄⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
51	D₄⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
52	#16837124	C₂²	1	1	yes	characteristic
53	#16837124	C₂²	1	1	yes	characteristic
54	#16837123	C₂²	1	1	yes	characteristic
55	C₈×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
56	C₄×#41×C₅₉	C₂²	1	1	yes	characteristic
57	C₈×Q₈×C₅₉	C₂²	1	1	yes	characteristic
58	C₈×Q₈×C₅₉	C₂²	1	1	yes	characteristic
59	C₈×D₄×C₅₉	—	2	1	no	—
60	C₈×D₄×C₅₉	—	2	1	no	—
61	C₈×D₄×C₅₉	C₂²	1	1	yes	characteristic
62	C₈×D₄×C₅₉	C₂²	1	1	yes	characteristic
63	C₅₉×#431	—	2	1	no	—
64	C₅₉×#431	C₂²	1	1	yes	characteristic
65	C₂×C₄⋊C₈×C₅₉	—	2	1	no	—
66	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
67	C₂×#11745672	C₂×C₄	1	1	yes	characteristic
68	C₂×#11745672	C₂×C₄	1	1	yes	characteristic
69	C₂×#11745670	C₂×C₄	1	1	yes	characteristic
70	C₂×#11745670	C₂×C₄	1	1	yes	characteristic
71	#14273727	C₂×C₄	1	1	yes	characteristic
72	#14273727	C₂×C₄	1	1	yes	characteristic
73	#14273719	—	2	1	no	—
74	#14273706	—	2	1	no	—
75	#14273706	C₂×C₄	1	1	yes	characteristic
76	#14273706	C₂×C₄	1	1	yes	characteristic
77	C₄×Dic₁₁₈	—	2	1	no	—
78	C₄×Dic₁₁₈	C₂³	1	1	yes	characteristic
79	C₄×Dic₁₁₈	C₂³	1	1	yes	characteristic
80	#14273686	—	2	1	no	—
81	#14273660	C₂×C₄	1	1	yes	characteristic
82	#14273660	C₂×C₄	1	1	yes	characteristic
83	#14273658	C₂×C₄	1	1	yes	characteristic
84	#14273658	C₂×C₄	1	1	yes	characteristic
85	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
86	C₄⋊(C₅₉⋊C₈)	C₂×C₄	1	1	yes	characteristic
87	C₄⋊(C₅₉⋊C₈)	C₂×C₄	1	1	yes	characteristic
88	C₄⋊(C₅₉⋊C₈)	C₂³	1	1	yes	characteristic
89	C₄⋊(C₅₉⋊C₈)	C₂³	1	1	yes	characteristic
90	Dic₅₉⋊C₈	—	2	1	no	—
91	Dic₅₉⋊C₈	—	2	1	no	—
92	Dic₅₉⋊C₈	—	2	1	no	—
93	Dic₅₉⋊C₈	—	2	1	no	—
94	#14273651	C₂×C₄	1	1	yes	characteristic
95	#14273651	C₂×C₄	1	1	yes	characteristic
96	#14273650	C₂×C₄	1	1	yes	characteristic
97	#14273650	C₂×C₄	1	1	yes	characteristic
98	#14273650	C₂×C₄	1	1	yes	characteristic
99	#14273650	C₂×C₄	1	1	yes	characteristic
100	#14273648	C₂×C₄	1	1	yes	characteristic
101	#14273648	C₂×C₄	1	1	yes	characteristic
102	C₂²⋊(C₅₉⋊C₈)	—	2	1	no	—
103	C₂²⋊(C₅₉⋊C₈)	—	2	1	no	—
104	C₂²⋊(C₅₉⋊C₈)	C₂×C₄	1	1	yes	characteristic
105	C₂²⋊(C₅₉⋊C₈)	C₂×C₄	1	1	yes	characteristic
106	#14273638	—	2	1	no	—
107	#14273637	—	2	1	no	—
108	#14273637	—	2	1	no	—
109	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
110	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
111	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
112	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
113	C₈×Dic₅₉	—	2	1	no	—
114	C₈×Dic₅₉	—	2	1	no	—
115	C₂×#41×C₅₉	C₂×C₄	1	1	yes	characteristic
116	C₂²×C₈×C₅₉	—	2	1	no	—
117	C₂²×C₈×C₅₉	—	2	1	no	—
118	C₂²×C₈×C₅₉	—	2	1	no	—
119	C₄×Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
120	C₄×Q₈×C₅₉	C₂³	1	1	yes	characteristic
121	C₄×D₄×C₅₉	—	2	1	no	—
122	C₄×D₄×C₅₉	—	2	1	no	—
123	C₄×D₄×C₅₉	C₂×C₄	1	1	yes	characteristic
124	C₄×D₄×C₅₉	C₂³	1	1	yes	characteristic
125	#117×C₅₉	—	2	1	no	—
126	#117×C₅₉	C₂×C₄	1	1	yes	characteristic
127	C₂×C₄²×C₅₉	—	2	1	no	—
128	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
129	C₄⋊C₈×C₅₉	—	2	1	no	—
130	C₄⋊C₈×C₅₉	—	2	1	no	—
131	C₄⋊C₈×C₅₉	—	2	1	no	—
132	C₄⋊C₈×C₅₉	D₄	1	1	yes	characteristic
133	C₄⋊C₈×C₅₉	D₄	1	1	yes	characteristic
134	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
135	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
136	C₂²⋊C₈×C₅₉	—	2	1	no	—
137	C₂²⋊C₈×C₅₉	—	2	1	no	—
138	C₂²⋊C₈×C₅₉	D₄	1	1	yes	characteristic
139	C₂²⋊C₈×C₅₉	D₄	1	1	yes	characteristic
140	C₄×C₈×C₅₉	—	2	1	no	—
141	C₄×C₈×C₅₉	—	2	1	no	—
142	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
144	#41×C₅₉	—	2	2	no	—
145	#41×C₅₉	—	2	2	no	—
146	C₂×Q₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
147	C₂×D₄×C₅₉	—	2	1	no	—
148	C₂×D₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
149	C₂²×C₄×C₅₉	—	2	1	no	—
150	C₂²×C₄×C₅₉	—	2	1	no	—
151	C₂²×C₄×C₅₉	—	2	1	no	—
152	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
153	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₅₉	#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	C₂×C₈×C₅₉	—	2	1	no	—
159	C₂×C₈×C₅₉	—	2	1	no	—
160	C₂×C₈×C₅₉	—	8	1	no	—
161	C₂×C₈×C₅₉	—	8	1	no	—
162	C₂×C₈×C₅₉	—	8	1	no	—
163	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
164	C₂×C₈×C₅₉	C₂×D₄	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	—	2	1	no	—
169	C₄⋊C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
170	C₄⋊C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
171	C₂²⋊C₄×C₅₉	—	2	1	no	—
172	C₂²⋊C₄×C₅₉	—	2	1	no	—
173	C₂²⋊C₄×C₅₉	—	2	1	no	—
174	C₄²×C₅₉	—	2	1	no	—
175	C₄²×C₅₉	—	2	1	no	—
176	C₄²×C₅₉	—	2	1	no	—
177	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
178	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
179	C₄²×C₅₉	#41	1	1	yes	characteristic
180	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
181	C₂²⋊Dic₅₉	—	2	1	no	—
182	C₂²⋊Dic₅₉	—	2	1	no	—
183	#11745672	—	2	2	no	—
184	#11745672	—	2	2	no	—
185	#11745670	—	2	2	no	—
186	#11745670	—	2	2	no	—
187	C₄⋊Dic₅₉	—	2	1	no	—
188	C₄⋊Dic₅₉	—	2	1	no	—
189	C₄⋊Dic₅₉	—	2	1	no	—
190	C₄⋊Dic₅₉	C₂²×C₄	1	1	yes	characteristic
191	C₄⋊Dic₅₉	C₂²×C₄	1	1	yes	characteristic
192	Dic₅₉⋊C₄	—	2	1	no	—
193	Dic₅₉⋊C₄	—	2	1	no	—
194	Dic₅₉⋊C₄	—	2	1	no	—
195	Dic₅₉⋊C₄	—	2	1	no	—
196	C₄×Dic₅₉	—	2	1	no	—
197	C₄×Dic₅₉	—	2	1	no	—
198	C₂×C₅₉⋊C₈	—	2	1	no	—
199	C₂×C₅₉⋊C₈	—	2	1	no	—
200	C₂×C₅₉⋊C₈	—	2	1	no	—
201	C₂×C₅₉⋊C₈	—	2	1	no	—
202	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
203	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
204	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
205	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
206	C₂³×C₅₉	—	2	1	no	—
207	C₂³×C₅₉	C₄×D₄	1	1	yes	characteristic
208	Q₈×C₅₉	—	2	1	no	—
209	Q₈×C₅₉	#131	1	2	yes	—
210	D₄×C₅₉	—	2	4	no	—
211	D₄×C₅₉	—	2	1	no	—
212	D₄×C₅₉	#131	1	2	yes	—
213	C₂×C₄×C₅₉	—	2	4	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	—	2	1	no	—
218	C₂×C₄×C₅₉	—	2	1	no	—
219	C₂×C₄×C₅₉	—	2	1	no	—
220	C₂×C₄×C₅₉	—	2	1	no	—
221	C₂×C₄×C₅₉	—	4	1	no	—
222	C₂×C₄×C₅₉	—	4	1	no	—
223	C₂×C₄×C₅₉	—	4	1	no	—
224	C₂×C₄×C₅₉	—	8	1	no	—
225	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
226	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
227	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
228	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
229	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
230	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
231	C₂×Dic₅₉	—	2	1	no	—
232	C₂×Dic₅₉	—	2	1	no	—
233	C₂×Dic₅₉	—	2	1	no	—
234	C₂×Dic₅₉	—	2	1	no	—
235	Dic₁₁₈	—	2	1	no	—
236	Dic₁₁₈	—	2	1	no	—
237	Dic₁₁₈	—	2	1	no	—
238	Dic₁₁₈	—	2	1	no	—
239	Dic₁₁₈	—	8	1	no	—
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	C₅₉⋊C₈	—	2	1	no	—
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	—	4	1	no	—
254	#17921	—	59	1	no	maximal, Sylow
255	C₂²×C₅₉	—	2	1	no	—
256	C₂²×C₅₉	—	2	2	no	—
257	C₂²×C₅₉	—	2	1	no	—
258	C₂²×C₅₉	—	2	1	no	—
259	C₂²×C₅₉	—	4	1	no	—
260	C₂²×C₅₉	—	4	1	no	—
261	C₂²×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
262	C₄×C₅₉	—	2	1	no	—
263	C₄×C₅₉	—	2	2	no	—
264	C₄×C₅₉	—	2	1	no	—
265	C₄×C₅₉	—	2	1	no	—
266	C₄×C₅₉	—	2	1	no	—
267	C₄×C₅₉	—	4	1	no	—
268	C₄×C₅₉	—	4	1	no	—
269	C₄×C₅₉	C₂×#131	1	1	yes	characteristic
270	C₄×C₅₉	C₂×#131	1	1	yes	characteristic
271	C₄×C₅₉	#577	1	1	yes	characteristic
272	C₄×C₅₉	#578	1	1	yes	characteristic
273	Dic₅₉	—	4	1	no	—
274	Dic₅₉	—	4	1	no	—
275	Dic₅₉	—	4	1	no	—
276	Dic₅₉	—	4	1	no	—
277	#3107	—	59	1	no	—
278	#2988	D₅₉	1	1	yes	characteristic
279	#2985	—	59	1	no	—
280	#1587	—	59	1	no	—
281	#1585	—	59	1	no	—
282	#1584	—	59	1	no	—
283	#1582	—	59	1	no	—
284	#1579	—	59	1	no	—
285	SD₁₆⋊C₈	—	59	1	no	—
286	C₈×Q₁₆	—	59	1	no	—
287	C₈×SD₁₆	—	59	1	no	—
288	#1573	—	59	1	no	—
289	#1488	—	59	1	no	—
290	#1481	—	59	1	no	—
291	#1454	—	59	1	no	—
292	C₂×C₅₉	—	4	1	no	—
293	C₂×C₅₉	—	4	2	no	—
294	C₂×C₅₉	#2929	1	1	yes	characteristic
295	C₂×C₅₉	#2947	1	1	yes	characteristic
296	C₂×C₅₉	#2957	1	1	yes	characteristic
297	#533	—	59	1	no	—
298	C₄×#41	C₂×D₅₉	1	1	yes	characteristic
299	#485	—	59	1	no	—
300	#485	—	59	1	no	—
301	#475	—	59	1	no	—
302	#474	—	59	1	no	—
303	#462	—	59	1	no	—
304	#461	—	59	1	no	—
305	#452	—	59	1	no	—
306	#452	—	59	1	no	—
307	#446	—	59	1	no	—
308	#446	—	59	1	no	—
309	#446	—	118	1	no	—
310	#446	—	118	1	no	—
311	C₈×Q₈	—	59	1	no	—
312	C₈×Q₈	—	59	1	no	—
313	C₈×Q₈	C₂×D₅₉	1	1	yes	characteristic
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	—	59	1	no	—
319	C₈×D₄	—	2	1	no	—
320	C₈×D₄	—	2	1	no	—
321	C₈×D₄	C₂×D₅₉	1	1	yes	characteristic
322	C₈×D₄	C₂×D₅₉	1	1	yes	characteristic
323	#433	—	118	1	no	—
324	#433	—	118	1	no	—
325	#432	—	59	1	no	—
326	#431	—	2	1	no	—
327	#431	—	59	1	no	—
328	#431	—	59	1	no	—
329	#431	C₂×D₅₉	1	1	yes	characteristic
330	C₂×C₄⋊C₈	—	2	1	no	—
331	C₂×C₄⋊C₈	C₂×D₅₉	1	1	yes	characteristic
332	#335	—	59	1	no	—
333	#335	—	59	1	no	—
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	—	59	1	no	—
342	D₄⋊C₈	—	59	1	no	—
343	D₄⋊C₈	—	59	1	no	—
344	#322	—	59	1	no	—
345	#322	—	59	1	no	—
346	#322	—	59	1	no	—
347	C₈²	—	59	1	no	—
348	C₅₉	#17921	1	1	yes	characteristic, complemented, Sylow
349	C₂×#41	C₄×D₅₉	1	1	yes	characteristic
350	C₂×Q₁₆	—	59	1	no	—
351	C₂×Q₁₆	—	59	1	no	—
352	C₂×SD₁₆	—	59	1	no	—
353	C₂×SD₁₆	—	59	1	no	—
354	C₂²×C₈	—	2	1	no	—
355	C₂²×C₈	—	2	1	no	—
356	C₂²×C₈	—	2	1	no	—
357	C₄⋊Q₈	—	59	1	no	—
358	C₄⋊Q₈	—	59	1	no	—
359	#125	—	118	1	no	—
360	C₂²⋊Q₈	—	59	1	no	—
361	C₂²⋊Q₈	—	59	1	no	—
362	C₂²⋊Q₈	—	118	1	no	—
363	C₄×Q₈	—	59	1	no	—
364	C₄×Q₈	—	59	1	no	—
365	C₄×Q₈	—	118	1	no	—
366	C₄×Q₈	C₄×D₅₉	1	1	yes	characteristic
367	C₄×Q₈	C₂²×D₅₉	1	1	yes	characteristic
368	C₄×D₄	—	2	1	no	—
369	C₄×D₄	—	2	1	no	—
370	C₄×D₄	C₄×D₅₉	1	1	yes	characteristic
371	C₄×D₄	C₂²×D₅₉	1	1	yes	characteristic
372	#117	—	2	1	no	—
373	#117	—	118	1	no	—
374	#117	C₄×D₅₉	1	1	yes	characteristic
375	C₂×C₄²	—	2	1	no	—
376	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
377	#107	—	59	1	no	—
378	#107	—	59	1	no	—
379	#106	—	59	1	no	—
380	#106	—	59	1	no	—
381	C₄⋊C₈	—	2	1	no	—
382	C₄⋊C₈	—	2	1	no	—
383	C₄⋊C₈	—	2	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	C₂²⋊D₅₉	1	1	yes	characteristic
394	C₄⋊C₈	C₂²⋊D₅₉	1	1	yes	characteristic
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	—	59	1	no	—
403	#102	—	59	1	no	—
404	#102	—	59	1	no	—
405	C₂²⋊C₈	—	2	1	no	—
406	C₂²⋊C₈	—	2	1	no	—
407	C₂²⋊C₈	—	59	1	no	—
408	C₂²⋊C₈	—	59	1	no	—
409	C₂²⋊C₈	—	118	1	no	—
410	C₂²⋊C₈	—	118	1	no	—
411	C₂²⋊C₈	C₂²⋊D₅₉	1	1	yes	characteristic
412	C₂²⋊C₈	C₂²⋊D₅₉	1	1	yes	characteristic
413	#97	—	118	1	no	—
414	#97	—	118	1	no	—
415	#97	—	118	1	no	—
416	C₄×C₈	—	2	1	no	—
417	C₄×C₈	—	2	1	no	—
418	C₄×C₈	—	59	1	no	—
419	C₄×C₈	—	59	1	no	—
420	C₄×C₈	—	59	1	no	—
421	C₄×C₈	—	59	1	no	—
422	C₄×C₈	—	118	1	no	—
423	C₄×C₈	—	118	1	no	—
424	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
425	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
426	#41	—	2	2	no	—
427	#41	—	2	2	no	—
428	C₂×Q₈	—	59	1	no	—
429	C₂×Q₈	—	59	1	no	—
430	C₂×Q₈	—	118	1	no	—
431	C₂×Q₈	C₂×C₄×D₅₉	1	1	yes	characteristic
432	C₂×D₄	—	2	1	no	—
433	C₂×D₄	C₂×C₄×D₅₉	1	1	yes	characteristic
434	C₂²×C₄	—	2	1	no	—
435	C₂²×C₄	—	2	1	no	—
436	C₂²×C₄	—	2	1	no	—
437	C₂²×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
438	C₂²×C₄	#11745685	1	1	yes	characteristic
439	C₂²×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
440	Q₁₆	—	118	2	no	—
441	Q₁₆	—	118	2	no	—
442	SD₁₆	—	118	2	no	—
443	SD₁₆	—	118	2	no	—
444	C₂×C₈	—	2	1	no	—
445	C₂×C₈	—	2	1	no	—
446	C₂×C₈	—	8	1	no	—
447	C₂×C₈	—	8	1	no	—
448	C₂×C₈	—	8	1	no	—
449	C₂×C₈	—	59	1	no	—
450	C₂×C₈	—	59	1	no	—
451	C₂×C₈	—	59	1	no	—
452	C₂×C₈	—	59	1	no	—
453	C₂×C₈	—	118	1	no	—
454	C₂×C₈	—	118	1	no	—
455	C₂×C₈	—	118	1	no	—
456	C₂×C₈	—	118	1	no	—
457	C₂×C₈	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
458	C₂×C₈	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
459	C₂×C₈	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
460	C₂×C₈	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	—	2	1	no	—
463	C₄⋊C₄	—	59	1	no	—
464	C₄⋊C₄	—	59	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	—	2	1	no	—
476	C₂²⋊C₄	—	2	1	no	—
477	C₂²⋊C₄	—	118	1	no	—
478	C₂²⋊C₄	—	118	1	no	—
479	C₄²	—	2	1	no	—
480	C₄²	—	2	1	no	—
481	C₄²	—	2	1	no	—
482	C₄²	—	118	1	no	—
483	C₄²	—	118	1	no	—
484	C₄²	C₂×C₄×D₅₉	1	1	yes	characteristic
485	C₄²	#11745685	1	1	yes	characteristic
486	C₄²	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
487	C₄²	C₂³×D₅₉	1	1	yes	characteristic
488	C₂³	—	2	1	no	—
489	C₂³	C₄×C₂²⋊D₅₉	1	1	yes	characteristic
490	Q₈	—	2	1	no	—
491	Q₈	—	118	1	no	—
492	Q₈	—	118	1	no	—
493	Q₈	—	118	1	no	—
494	Q₈	—	118	1	no	—
495	Q₈	—	472	1	no	—
496	Q₈	#14273733	1	2	yes	—
497	D₄	—	2	4	no	—
498	D₄	—	2	1	no	—
499	D₄	#14273733	1	2	yes	—
500	C₂×C₄	—	2	4	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	4	1	no	—
509	C₂×C₄	—	4	1	no	—
510	C₂×C₄	—	4	1	no	—
511	C₂×C₄	—	8	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	C₄×C₂²⋊D₅₉	1	1	yes	characteristic
517	C₂×C₄	C₄×C₂²⋊D₅₉	1	1	yes	characteristic
518	C₂×C₄	C₄×C₂²⋊D₅₉	1	1	yes	characteristic
519	C₂×C₄	C₂²×C₄×D₅₉	1	1	yes	characteristic
520	C₂×C₄	C₂²×C₂²⋊D₅₉	1	1	yes	characteristic
521	C₂×C₄	C₂×#11745685	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	—	118	1	no	—
529	C₈	—	118	1	no	—
530	C₈	—	118	1	no	—
531	C₈	—	118	1	no	—
532	C₈	—	236	1	no	—
533	C₈	—	236	1	no	—
534	C₈	—	236	1	no	—
535	C₈	—	236	1	no	—
536	C₂²	—	2	1	no	—
537	C₂²	—	2	1	no	—
538	C₂²	—	2	1	no	—
539	C₂²	—	2	2	no	—
540	C₂²	—	4	1	no	—
541	C₂²	—	4	1	no	—
542	C₂²	C₂×C₄×C₂²⋊D₅₉	1	1	yes	characteristic
543	C₄	—	2	1	no	—
544	C₄	—	2	1	no	—
545	C₄	—	2	1	no	—
546	C₄	—	2	1	no	—
547	C₄	—	2	2	no	—
548	C₄	—	4	1	no	—
549	C₄	—	4	1	no	—
550	C₄	—	236	1	no	—
551	C₄	—	236	1	no	—
552	C₄	—	236	1	no	—
553	C₄	—	236	1	no	—
554	C₄	C₂×#14273733	1	1	yes	characteristic
555	C₄	C₂×#14273733	1	1	yes	characteristic
556	C₄	#16838213	1	1	yes	characteristic
557	C₄	#16838217	1	1	yes	characteristic
558	C₂	—	4	1	no	—
559	C₂	—	4	2	no	—
560	C₂	#21432790	1	1	yes	characteristic
561	C₂	#21432935	1	1	yes	characteristic
562	C₂	#21433011	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₅₉
commutator	C₂×C₄×C₅₉	C₂³×C₄
Frattini	C₄²	C₂³×D₅₉
Fitting	C₅₉×#2988	C₂
socle	C₂²×C₅₉	C₂×C₄×D₄
prime radical	C₂×#41×C₅₉	C₂×C₄
cosocle	C₄²×C₅₉	C₂⁴
hypercenter	#2988	D₅₉
hypocenter	C₅₉	#17921
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ #431 ◁ #2988

Complements

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

N	H ≅ G/N	type
2. #21433190	C₂	semidirect
3. #21422967	C₂	semidirect
4. #21422953	C₂	semidirect
5. #21422946	C₂	semidirect
6. #21422932	C₂	semidirect
7. #21422913	C₂	semidirect
8. #21422908	C₂	semidirect
9. C₈×#11745672	C₂	semidirect
10. C₈×#11745670	C₂	semidirect
11. #21422879	C₂	semidirect
13. #21422498	C₂	semidirect
14. #21422396	C₂	semidirect
348. C₅₉	#17921	semidirect

Maximal subgroups

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

subgroup	index
#21434167	2
#21433190	2
#21422967	2
#21422953	2
#21422946	2
#21422932	2
#21422913	2
#21422908	2
C₈×#11745672	2
C₈×#11745670	2
#21422879	2
#21422530	2
#21422498	2
#21422396	2
C₅₉×#2988	2
#17921	59