Subgroups — #28559821

Order 15104.

592 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21434172	C₂	1	1	yes	maximal, characteristic
2	#21433101	C₂	1	1	yes	maximal, characteristic
3	#21433047	C₂	1	1	yes	maximal, characteristic, complemented
4	#21423002	C₂	1	1	yes	maximal, characteristic, complemented
5	#21422989	C₂	1	1	yes	maximal, characteristic, complemented
6	#21422970	C₂	1	1	yes	maximal, characteristic, complemented
7	#21422950	C₂	1	1	yes	maximal, characteristic, complemented
8	#21422943	C₂	1	1	yes	maximal, characteristic, complemented
9	#21422942	C₂	1	1	yes	maximal, characteristic, complemented
10	#21422905	C₂	1	1	yes	maximal, characteristic, complemented
11	#21422900	C₂	1	1	yes	maximal, characteristic, complemented
12	#21422887	C₂	1	1	yes	maximal, characteristic, complemented
13	#21422492	C₂	1	1	yes	maximal, characteristic, complemented
14	#21422391	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₉×#1495	C₂	1	1	yes	maximal, characteristic
16	C₂×C₄×Dic₁₁₈	C₂²	1	1	yes	characteristic
17	#16837730	C₄	1	1	yes	characteristic
18	#16837713	C₄	1	1	yes	characteristic
19	#16837706	C₄	1	1	yes	characteristic
20	#16837706	C₄	1	1	yes	characteristic
21	#16837621	C₄	1	1	yes	characteristic
22	#16837621	C₄	1	1	yes	characteristic
23	#16837557	C₄	1	1	yes	characteristic
24	#16837540	C₄	1	1	yes	characteristic
25	#16837533	C₂²	1	1	yes	characteristic
26	#16837531	—	2	1	no	—
27	#16837531	—	2	1	no	—
28	#16837529	C₂²	1	1	yes	characteristic
29	#16837529	C₂²	1	1	yes	characteristic
30	Q₈×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
31	#16837526	C₂²	1	1	yes	characteristic
32	#16837526	C₂²	1	1	yes	characteristic
33	C₄×#11745672	C₂²	1	1	yes	characteristic
34	C₄×#11745672	C₂²	1	1	yes	characteristic
35	C₄×#11745670	C₂²	1	1	yes	characteristic
36	C₄×#11745670	C₂²	1	1	yes	characteristic
37	#16837480	—	2	1	no	—
38	#16837480	C₂²	1	1	yes	characteristic
39	#16837474	—	2	1	no	—
40	D₄×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
41	#16837463	—	2	1	no	—
42	#16837455	C₂²	1	1	yes	characteristic
43	#16837455	C₂²	1	1	yes	characteristic
44	#16837425	—	2	1	no	—
45	#16837358	—	2	1	no	—
46	C₄×#11745664	C₂²	1	1	yes	characteristic
47	M₁₆×Dic₅₉	—	2	1	no	—
48	#16837154	C₂²	1	1	yes	characteristic
49	#16837154	C₂²	1	1	yes	characteristic
50	#16837152	C₂²	1	1	yes	characteristic
51	#16837152	C₂²	1	1	yes	characteristic
52	#16837134	C₂²	1	1	yes	characteristic
53	#16837134	C₂²	1	1	yes	characteristic
54	#16837134	C₂²	1	1	yes	characteristic
55	#16837134	C₂²	1	1	yes	characteristic
56	#16837124	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×#529	C₂²	1	1	yes	characteristic
61	C₅₉×#431	C₂²	1	1	yes	characteristic
62	C₅₉×#423	C₂²	1	1	yes	characteristic
63	C₅₉×Q₈⋊C₈	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×D₄⋊C₈	C₂²	1	1	yes	characteristic
67	C₂²×Dic₁₁₈	C₂×C₄	1	1	yes	characteristic
68	C₂×#11745672	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×#11745670	C₂×C₄	1	1	yes	characteristic
72	C₂×#11745664	—	2	1	no	—
73	C₂×#11745664	D₄	1	1	yes	characteristic
74	C₂×#11745664	D₄	1	1	yes	characteristic
75	C₂²×C₅₉⋊C₈	—	2	1	no	—
76	C₄×Dic₁₁₈	—	2	1	no	—
77	C₄×Dic₁₁₈	—	2	1	no	—
78	C₄×Dic₁₁₈	C₂×C₄	1	1	yes	characteristic
79	C₄×Dic₁₁₈	C₂×C₄	1	1	yes	characteristic
80	C₄×Dic₁₁₈	C₂³	1	1	yes	characteristic
81	C₄×Dic₁₁₈	C₂³	1	1	yes	characteristic
82	C₂×C₄⋊Dic₅₉	C₂×C₄	1	1	yes	characteristic
83	C₂×Dic₅₉⋊C₄	—	2	1	no	—
84	C₂×C₄×Dic₅₉	—	2	1	no	—
85	#14273660	C₂×C₄	1	1	yes	characteristic
86	#14273660	C₂×C₄	1	1	yes	characteristic
87	#14273658	C₂×C₄	1	1	yes	characteristic
88	#14273658	C₂×C₄	1	1	yes	characteristic
89	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
90	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
91	C₄⋊(C₅₉⋊C₈)	C₂×C₄	1	1	yes	characteristic
92	C₄⋊(C₅₉⋊C₈)	C₂×C₄	1	1	yes	characteristic
93	C₄⋊(C₅₉⋊C₈)	C₂³	1	1	yes	characteristic
94	C₄⋊(C₅₉⋊C₈)	C₂³	1	1	yes	characteristic
95	Dic₅₉⋊C₈	—	2	1	no	—
96	Dic₅₉⋊C₈	—	2	1	no	—
97	Dic₅₉⋊C₈	—	2	1	no	—
98	Dic₅₉⋊C₈	—	2	1	no	—
99	#14273651	C₂×C₄	1	1	yes	characteristic
100	#14273651	C₂×C₄	1	1	yes	characteristic
101	#14273650	C₂×C₄	1	1	yes	characteristic
102	#14273650	C₂×C₄	1	1	yes	characteristic
103	#14273650	C₂×C₄	1	1	yes	characteristic
104	#14273650	C₂×C₄	1	1	yes	characteristic
105	#14273648	C₂×C₄	1	1	yes	characteristic
106	#14273648	C₂×C₄	1	1	yes	characteristic
107	C₂²⋊(C₅₉⋊C₈)	—	2	1	no	—
108	C₂²⋊(C₅₉⋊C₈)	—	2	1	no	—
109	C₂²⋊(C₅₉⋊C₈)	—	2	1	no	—
110	C₂²⋊(C₅₉⋊C₈)	C₂×C₄	1	1	yes	characteristic
111	C₂²⋊(C₅₉⋊C₈)	C₂×C₄	1	1	yes	characteristic
112	#14273638	—	2	1	no	—
113	#14273638	D₄	1	1	yes	characteristic
114	#14273638	D₄	1	1	yes	characteristic
115	#14273637	—	2	1	no	—
116	#14273637	—	2	1	no	—
117	C₄×C₅₉⋊C₈	—	2	1	no	—
118	C₄×C₅₉⋊C₈	—	2	1	no	—
119	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
120	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
121	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
122	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
123	C₈×Dic₅₉	—	2	1	no	—
124	C₈×Dic₅₉	—	2	1	no	—
125	C₂×M₁₆×C₅₉	—	2	1	no	—
126	#126×C₅₉	—	2	1	no	—
127	#125×C₅₉	C₂×C₄	1	1	yes	characteristic
128	#124×C₅₉	C₂×C₄	1	1	yes	characteristic
129	#123×C₅₉	—	2	1	no	—
130	C₂²⋊Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
131	#121×C₅₉	C₂×C₄	1	1	yes	characteristic
132	C₄×Q₈×C₅₉	C₂³	1	1	yes	characteristic
133	C₄×D₄×C₅₉	—	2	1	no	—
134	C₄×D₄×C₅₉	C₂³	1	1	yes	characteristic
135	#117×C₅₉	—	2	1	no	—
136	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
137	C₄⋊C₈×C₅₉	—	2	1	no	—
138	C₄⋊C₈×C₅₉	—	2	1	no	—
139	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
140	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
141	C₂²⋊C₈×C₅₉	—	2	1	no	—
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	—	2	1	no	—
146	C₂×D₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
147	C₂²×C₄×C₅₉	—	2	1	no	—
148	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
149	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
151	C₂²×Dic₅₉	—	2	1	no	—
152	C₂²×Dic₅₉	—	2	1	no	—
153	C₂×Dic₁₁₈	—	2	2	no	—
154	C₂×Dic₁₁₈	—	2	1	no	—
155	C₂×Dic₁₁₈	—	4	1	no	—
156	C₂×Dic₁₁₈	C₂²×C₄	1	1	yes	characteristic
157	C₂×Dic₁₁₈	C₂²×C₄	1	1	yes	characteristic
158	M₁₆×C₅₉	—	4	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	—	2	1	no	—
163	C₄⋊C₄×C₅₉	—	2	1	no	—
164	C₄⋊C₄×C₅₉	—	2	1	no	—
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	C₂²⋊C₄×C₅₉	—	2	1	no	—
170	C₂²⋊C₄×C₅₉	—	2	1	no	—
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	C₂²×C₄	1	1	yes	characteristic
176	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
177	C₄²×C₅₉	#41	1	1	yes	characteristic
178	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
179	#11745672	—	2	2	no	—
180	#11745672	—	4	1	no	—
181	#11745670	—	2	2	no	—
182	#11745670	—	4	1	no	—
183	C₄⋊Dic₅₉	—	2	1	no	—
184	C₄⋊Dic₅₉	C₂²×C₄	1	1	yes	characteristic
185	C₄⋊Dic₅₉	C₂²×C₄	1	1	yes	characteristic
186	Dic₅₉⋊C₄	—	2	1	no	—
187	Dic₅₉⋊C₄	—	2	1	no	—
188	Dic₅₉⋊C₄	—	2	1	no	—
189	Dic₅₉⋊C₄	—	2	1	no	—
190	C₄×Dic₅₉	—	2	1	no	—
191	C₄×Dic₅₉	—	2	1	no	—
192	C₄×Dic₅₉	—	2	1	no	—
193	C₄×Dic₅₉	—	2	1	no	—
194	#11745664	—	2	2	no	—
195	#11745664	—	4	1	no	—
196	#11745664	—	4	2	no	—
197	C₂×C₅₉⋊C₈	—	2	1	no	—
198	C₂×C₅₉⋊C₈	—	2	1	no	—
199	C₂×C₅₉⋊C₈	—	4	2	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	C₂²×C₄	1	1	yes	characteristic
203	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
204	C₂×C₅₉⋊C₈	C₂×D₄	1	1	yes	characteristic
205	C₂×C₅₉⋊C₈	C₂×D₄	1	1	yes	characteristic
206	C₂×C₅₉⋊C₈	C₂×D₄	1	1	yes	characteristic
207	C₂×C₅₉⋊C₈	C₂×D₄	1	1	yes	characteristic
208	C₂³×C₅₉	—	2	1	no	—
209	C₂³×C₅₉	C₄×D₄	1	1	yes	characteristic
210	Q₈×C₅₉	—	2	1	no	—
211	Q₈×C₅₉	—	2	1	no	—
212	D₄×C₅₉	—	2	1	no	—
213	D₄×C₅₉	—	2	1	no	—
214	D₄×C₅₉	—	8	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	—	2	1	no	—
222	C₂×C₄×C₅₉	—	4	1	no	—
223	C₂×C₄×C₅₉	—	4	1	no	—
224	C₂×C₄×C₅₉	—	4	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	C₂×Dic₅₉	—	4	2	no	—
236	C₂×Dic₅₉	—	8	1	no	—
237	Dic₁₁₈	—	2	1	no	—
238	Dic₁₁₈	—	2	1	no	—
239	Dic₁₁₈	—	2	1	no	—
240	Dic₁₁₈	—	4	2	no	—
241	Dic₁₁₈	#131	1	2	yes	—
242	C₈×C₅₉	—	4	1	no	—
243	C₈×C₅₉	—	4	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	—	2	1	no	—
251	C₅₉⋊C₈	—	2	1	no	—
252	C₅₉⋊C₈	—	2	1	no	—
253	C₅₉⋊C₈	—	4	1	no	—
254	C₅₉⋊C₈	—	4	1	no	—
255	C₅₉⋊C₈	#137	1	2	yes	—
256	#18012	—	59	1	no	maximal, Sylow
257	C₂²×C₅₉	—	2	1	no	—
258	C₂²×C₅₉	—	2	1	no	—
259	C₂²×C₅₉	—	2	1	no	—
260	C₂²×C₅₉	—	4	1	no	—
261	C₂²×C₅₉	—	4	1	no	—
262	C₂²×C₅₉	—	4	1	no	—
263	C₂²×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
264	C₄×C₅₉	—	2	1	no	—
265	C₄×C₅₉	—	2	1	no	—
266	C₄×C₅₉	—	2	1	no	—
267	C₄×C₅₉	—	2	1	no	—
268	C₄×C₅₉	—	4	1	no	—
269	C₄×C₅₉	—	4	1	no	—
270	C₄×C₅₉	—	4	1	no	—
271	C₄×C₅₉	C₂×#131	1	1	yes	characteristic
272	C₄×C₅₉	#568	1	1	yes	characteristic
273	C₄×C₅₉	C₂×#137	1	1	yes	characteristic
274	C₄×C₅₉	#575	1	1	yes	characteristic
275	Dic₅₉	—	2	2	no	—
276	Dic₅₉	—	4	1	no	—
277	Dic₅₉	—	4	1	no	—
278	Dic₅₉	—	4	1	no	—
279	#3108	—	59	1	no	—
280	#2969	—	59	1	no	—
281	Q₈×M₁₆	—	59	1	no	—
282	#1593	—	59	1	no	—
283	#1590	—	59	1	no	—
284	#1587	—	59	1	no	—
285	#1585	—	59	1	no	—
286	#1584	—	59	1	no	—
287	#1583	—	59	1	no	—
288	SD₁₆⋊C₈	—	59	1	no	—
289	C₈×Q₁₆	—	59	1	no	—
290	#1574	—	59	1	no	—
291	#1495	D₅₉	1	1	yes	characteristic
292	#1479	—	59	1	no	—
293	#1453	—	59	1	no	—
294	C₂×C₅₉	—	4	1	no	—
295	C₂×C₅₉	—	8	1	no	—
296	C₂×C₅₉	#2933	1	1	yes	characteristic
297	C₂×C₅₉	C₄×#137	1	1	yes	characteristic
298	C₂×C₅₉	#2957	1	1	yes	characteristic
299	#529	C₂×D₅₉	1	1	yes	characteristic
300	C₂×C₄×Q₈	—	59	1	no	—
301	#483	—	59	1	no	—
302	#480	—	59	1	no	—
303	#479	—	59	1	no	—
304	#479	—	59	1	no	—
305	#464	—	59	1	no	—
306	#464	—	59	1	no	—
307	#451	—	59	1	no	—
308	#448	—	59	1	no	—
309	#446	—	59	1	no	—
310	#446	—	59	1	no	—
311	#446	—	59	1	no	—
312	#446	—	118	1	no	—
313	#446	—	118	1	no	—
314	C₈×Q₈	—	59	1	no	—
315	C₈×Q₈	—	59	1	no	—
316	C₈×Q₈	—	59	1	no	—
317	C₄×Q₁₆	—	59	1	no	—
318	C₄×Q₁₆	—	59	1	no	—
319	C₄×SD₁₆	—	59	1	no	—
320	C₄×SD₁₆	—	59	1	no	—
321	#436	—	59	1	no	—
322	#436	—	118	1	no	—
323	#435	—	118	1	no	—
324	C₈×D₄	—	59	1	no	—
325	#433	—	118	1	no	—
326	#431	—	59	1	no	—
327	#431	—	59	1	no	—
328	#431	C₂×D₅₉	1	1	yes	characteristic
329	#423	—	118	1	no	—
330	#423	C₂×D₅₉	1	1	yes	characteristic
331	#405	—	118	1	no	—
332	C₄×M₁₆	—	59	1	no	—
333	C₄×M₁₆	—	118	1	no	—
334	#335	—	59	1	no	—
335	#335	—	59	1	no	—
336	#334	—	59	1	no	—
337	#334	—	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	Q₈⋊C₈	C₂×D₅₉	1	1	yes	characteristic
343	Q₈⋊C₈	C₂×D₅₉	1	1	yes	characteristic
344	D₄⋊C₈	C₂×D₅₉	1	1	yes	characteristic
345	D₄⋊C₈	C₂×D₅₉	1	1	yes	characteristic
346	#322	—	59	1	no	—
347	#322	—	59	1	no	—
348	#322	—	59	1	no	—
349	C₈²	—	59	1	no	—
350	C₅₉	#18012	1	1	yes	characteristic, complemented, Sylow
351	C₂²×Q₈	—	59	1	no	—
352	C₂×Q₁₆	—	59	1	no	—
353	C₂×Q₁₆	—	59	1	no	—
354	C₂×SD₁₆	—	59	1	no	—
355	C₂×SD₁₆	—	59	1	no	—
356	C₂×M₁₆	—	2	1	no	—
357	C₂×M₁₆	—	59	1	no	—
358	C₂×M₁₆	—	59	1	no	—
359	C₂×M₁₆	—	118	1	no	—
360	C₂²×C₈	—	118	1	no	—
361	#126	—	2	1	no	—
362	#125	C₄×D₅₉	1	1	yes	characteristic
363	#124	C₄×D₅₉	1	1	yes	characteristic
364	#123	—	2	1	no	—
365	C₂²⋊Q₈	C₄×D₅₉	1	1	yes	characteristic
366	#121	C₄×D₅₉	1	1	yes	characteristic
367	C₄×Q₈	—	59	1	no	—
368	C₄×Q₈	—	59	1	no	—
369	C₄×Q₈	—	59	1	no	—
370	C₄×Q₈	—	59	1	no	—
371	C₄×Q₈	—	118	1	no	—
372	C₄×Q₈	—	118	1	no	—
373	C₄×Q₈	C₂²×D₅₉	1	1	yes	characteristic
374	C₄×D₄	—	2	1	no	—
375	C₄×D₄	C₂²×D₅₉	1	1	yes	characteristic
376	#117	—	2	1	no	—
377	C₂×C₄⋊C₄	—	59	1	no	—
378	C₂×C₄⋊C₄	—	118	1	no	—
379	C₂×C₄²	—	118	1	no	—
380	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
381	#107	—	59	1	no	—
382	#107	—	59	1	no	—
383	#106	—	59	1	no	—
384	#106	—	59	1	no	—
385	C₄⋊C₈	—	2	1	no	—
386	C₄⋊C₈	—	2	1	no	—
387	C₄⋊C₈	—	59	1	no	—
388	C₄⋊C₈	—	59	1	no	—
389	C₄⋊C₈	—	59	1	no	—
390	C₄⋊C₈	—	59	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	—	118	1	no	—
396	C₄⋊C₈	—	118	1	no	—
397	C₄⋊C₈	C₂²×D₅₉	1	1	yes	characteristic
398	C₄⋊C₈	C₂²×D₅₉	1	1	yes	characteristic
399	#103	—	59	1	no	—
400	#103	—	59	1	no	—
401	#103	—	59	1	no	—
402	#103	—	59	1	no	—
403	#103	—	59	1	no	—
404	#103	—	59	1	no	—
405	#102	—	59	1	no	—
406	#102	—	59	1	no	—
407	C₂²⋊C₈	—	2	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	—	59	1	no	—
414	#97	—	59	1	no	—
415	#97	—	118	1	no	—
416	#97	—	118	1	no	—
417	#97	—	118	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	—	118	1	no	—
425	C₄×C₈	—	118	1	no	—
426	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
427	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
428	C₂×Q₈	—	59	1	no	—
429	C₂×Q₈	—	59	1	no	—
430	C₂×Q₈	—	118	2	no	—
431	C₂×Q₈	—	118	1	no	—
432	C₂×Q₈	—	236	1	no	—
433	C₂×Q₈	C₂×C₄×D₅₉	1	1	yes	characteristic
434	C₂×D₄	—	2	1	no	—
435	C₂×D₄	C₂×C₄×D₅₉	1	1	yes	characteristic
436	C₂²×C₄	—	2	1	no	—
437	C₂²×C₄	—	118	1	no	—
438	C₂²×C₄	—	118	1	no	—
439	C₂²×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
440	C₂²×C₄	D₄×D₅₉	1	1	yes	characteristic
441	C₂²×C₄	#11745687	1	1	yes	characteristic
442	Q₁₆	—	118	2	no	—
443	Q₁₆	—	236	1	no	—
444	SD₁₆	—	118	2	no	—
445	SD₁₆	—	236	1	no	—
446	M₁₆	—	4	2	no	—
447	M₁₆	—	118	2	no	—
448	M₁₆	—	236	2	no	—
449	M₁₆	—	236	1	no	—
450	C₂×C₈	—	2	1	no	—
451	C₂×C₈	—	2	1	no	—
452	C₂×C₈	—	2	1	no	—
453	C₂×C₈	—	2	1	no	—
454	C₂×C₈	—	59	1	no	—
455	C₂×C₈	—	59	1	no	—
456	C₂×C₈	—	59	1	no	—
457	C₂×C₈	—	59	1	no	—
458	C₂×C₈	—	59	1	no	—
459	C₂×C₈	—	59	1	no	—
460	C₂×C₈	—	59	1	no	—
461	C₂×C₈	—	59	1	no	—
462	C₂×C₈	—	118	1	no	—
463	C₂×C₈	—	118	1	no	—
464	C₂×C₈	—	236	2	no	—
465	C₄⋊C₄	—	2	1	no	—
466	C₄⋊C₄	—	2	1	no	—
467	C₄⋊C₄	—	2	1	no	—
468	C₄⋊C₄	—	2	1	no	—
469	C₄⋊C₄	—	59	1	no	—
470	C₄⋊C₄	—	59	1	no	—
471	C₄⋊C₄	—	118	1	no	—
472	C₄⋊C₄	—	118	1	no	—
473	C₄⋊C₄	—	118	1	no	—
474	C₄⋊C₄	—	118	1	no	—
475	C₄⋊C₄	—	118	1	no	—
476	C₄⋊C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
477	C₄⋊C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
478	C₂²⋊C₄	—	2	1	no	—
479	C₂²⋊C₄	—	2	1	no	—
480	C₂²⋊C₄	—	2	1	no	—
481	C₂²⋊C₄	—	2	1	no	—
482	C₂²⋊C₄	—	2	1	no	—
483	C₄²	—	2	1	no	—
484	C₄²	—	118	1	no	—
485	C₄²	—	118	1	no	—
486	C₄²	—	118	1	no	—
487	C₄²	—	118	1	no	—
488	C₄²	C₂×C₄×D₅₉	1	1	yes	characteristic
489	C₄²	D₄×D₅₉	1	1	yes	characteristic
490	C₄²	#11745687	1	1	yes	characteristic
491	C₄²	C₂³×D₅₉	1	1	yes	characteristic
492	C₂³	—	2	1	no	—
493	C₂³	(C₂²⋊D₅₉)⋊C₄	1	1	yes	characteristic
494	Q₈	—	2	1	no	—
495	Q₈	—	2	1	no	—
496	Q₈	—	59	2	no	—
497	Q₈	—	118	1	no	—
498	Q₈	—	118	1	no	—
499	Q₈	—	118	1	no	—
500	Q₈	—	236	2	no	—
501	D₄	—	2	1	no	—
502	D₄	—	2	1	no	—
503	D₄	—	8	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	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	4	1	no	—
512	C₂×C₄	—	4	1	no	—
513	C₂×C₄	—	4	1	no	—
514	C₂×C₄	—	118	1	no	—
515	C₂×C₄	—	118	1	no	—
516	C₂×C₄	—	118	1	no	—
517	C₂×C₄	—	118	1	no	—
518	C₂×C₄	—	472	1	no	—
519	C₂×C₄	—	236	2	no	—
520	C₂×C₄	(C₂²⋊D₅₉)⋊C₄	1	1	yes	characteristic
521	C₂×C₄	(C₂²⋊D₅₉)⋊C₄	1	1	yes	characteristic
522	C₂×C₄	(C₂²⋊D₅₉)⋊C₄	1	1	yes	characteristic
523	C₂×C₄	C₂²×C₄×D₅₉	1	1	yes	characteristic
524	C₂×C₄	C₂×D₄×D₅₉	1	1	yes	characteristic
525	C₂×C₄	C₂×#11745687	1	1	yes	characteristic
526	C₈	—	4	1	no	—
527	C₈	—	4	1	no	—
528	C₈	—	4	1	no	—
529	C₈	—	4	1	no	—
530	C₈	—	59	2	no	—
531	C₈	—	118	1	no	—
532	C₈	—	118	1	no	—
533	C₈	—	118	1	no	—
534	C₈	—	118	1	no	—
535	C₈	—	118	1	no	—
536	C₈	—	118	1	no	—
537	C₈	—	118	1	no	—
538	C₈	—	236	1	no	—
539	C₈	—	236	1	no	—
540	C₂²	—	2	1	no	—
541	C₂²	—	2	1	no	—
542	C₂²	—	2	1	no	—
543	C₂²	—	4	1	no	—
544	C₂²	—	4	1	no	—
545	C₂²	—	4	1	no	—
546	C₂²	C₂×(C₂²⋊D₅₉)⋊C₄	1	1	yes	characteristic
547	C₄	—	2	1	no	—
548	C₄	—	2	1	no	—
549	C₄	—	2	1	no	—
550	C₄	—	2	1	no	—
551	C₄	—	4	1	no	—
552	C₄	—	4	1	no	—
553	C₄	—	4	1	no	—
554	C₄	—	118	2	no	—
555	C₄	—	236	1	no	—
556	C₄	—	236	1	no	—
557	C₄	—	236	1	no	—
558	C₄	#131×D₅₉	1	1	yes	characteristic
559	C₄	#16838167	1	1	yes	characteristic
560	C₄	#137×D₅₉	1	1	yes	characteristic
561	C₄	#16838198	1	1	yes	characteristic
562	C₂	—	4	1	no	—
563	C₂	—	8	1	no	—
564	C₂	#21432826	1	1	yes	characteristic
565	C₂	#21432920	1	1	yes	characteristic
566	C₂	#21433009	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×#1495	C₂
socle	C₂²×C₅₉	C₂×C₄×D₄
prime radical	#121×C₅₉	C₂×C₄
cosocle	C₄²×C₅₉	C₂⁴
hypercenter	#1495	D₅₉
hypocenter	C₅₉	#18012
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1495

Complements

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

N	H ≅ G/N	type
3. #21433047	C₂	semidirect
4. #21423002	C₂	semidirect
5. #21422989	C₂	semidirect
6. #21422970	C₂	semidirect
7. #21422950	C₂	semidirect
8. #21422943	C₂	semidirect
9. #21422942	C₂	semidirect
10. #21422905	C₂	semidirect
11. #21422900	C₂	semidirect
12. #21422887	C₂	semidirect
13. #21422492	C₂	semidirect
14. #21422391	C₂	semidirect
350. C₅₉	#18012	semidirect

Maximal subgroups

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

subgroup	index
#21434172	2
#21433101	2
#21433047	2
#21423002	2
#21422989	2
#21422970	2
#21422950	2
#21422943	2
#21422942	2
#21422905	2
#21422900	2
#21422887	2
#21422492	2
#21422391	2
C₅₉×#1495	2
#18012	59