Subgroups — #28607153

Order 15104.

870 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16837517	C₂	1	2	yes	maximal
2	C₄×#14273747	C₂	1	1	yes	maximal, characteristic
3	#21432661	C₂	1	1	yes	maximal, characteristic, complemented
4	#21424841	C₂	1	2	yes	maximal, complemented
5	#21424371	C₂	1	2	yes	maximal, complemented
6	#21424370	C₂	1	2	yes	maximal, complemented
7	#21424267	C₂	1	1	yes	maximal, characteristic, complemented
8	#21424116	C₂	1	1	yes	maximal, characteristic, complemented
9	#21424113	C₂	1	1	yes	maximal, characteristic, complemented
10	#21423961	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#2906	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14273747	C₂²	1	1	yes	characteristic
13	C₂×#14273733	C₂²	1	2	yes	—
14	C₄×#11745685	C₂²	1	1	yes	characteristic
15	#16837517	—	2	8	no	—
16	C₄×#11745672	C₄	1	1	yes	characteristic, complemented
17	C₄×#11745672	C₄	1	1	yes	characteristic, complemented
18	C₄×#11745671	C₄	1	1	yes	characteristic, complemented
19	C₄×#11745671	C₄	1	1	yes	characteristic, complemented
20	C₄×#11745670	C₄	1	1	yes	characteristic, complemented
21	C₄×#11745670	C₄	1	1	yes	characteristic, complemented
22	C₄×#11745669	C₄	1	1	yes	characteristic, complemented
23	C₄×#11745669	C₄	1	1	yes	characteristic, complemented
24	C₂×#14273662	C₂²	1	2	yes	—
25	C₂×#14273662	C₂²	1	2	yes	—
26	#16837438	C₂²	1	1	yes	characteristic
27	#16837428	C₂²	1	2	yes	—
28	#16837427	—	2	2	no	—
29	#16837426	C₂²	1	1	yes	characteristic
30	#16837424	—	2	1	no	—
31	C₄⋊C₈×D₅₉	—	2	1	no	—
32	C₂×#14273654	C₂²	1	2	yes	—
33	C₂×#14273653	C₂²	1	2	yes	—
34	#16837398	C₂²	1	1	yes	characteristic
35	#16837396	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
37	C₂×C₈×Dic₅₉	C₂²	1	2	yes	—
38	C₄×C₄⋊Dic₅₉	C₂²	1	1	yes	characteristic
39	#16837163	C₂²	1	2	yes	—
40	#16837161	C₂²	1	2	yes	—
41	#16837156	C₂²	1	2	yes	—
42	C₂×#131×C₅₉	C₂²	1	2	yes	—
43	C₄×#41×C₅₉	C₂²	1	1	yes	characteristic
44	C₅₉×#424	—	2	2	no	—
45	C₅₉×#424	C₂²	1	2	yes	—
46	C₅₉×#423	—	2	1	no	—
47	C₅₉×#423	C₂²	1	1	yes	characteristic
48	C₂×C₄⋊C₈×C₅₉	—	2	1	no	—
49	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
50	C₂×#11745685	C₂³	1	1	yes	characteristic
51	#14273747	D₄	1	4	yes	—
52	#14273747	Q₈	1	4	yes	—
53	C₂×#11745672	C₂×C₄	1	1	yes	characteristic
54	C₂×#11745670	C₂×C₄	1	1	yes	characteristic
55	C₂×#11745671	C₂×C₄	1	1	yes	characteristic
56	C₂×#11745669	C₂×C₄	1	1	yes	characteristic
57	#14273733	—	2	4	no	—
58	#14273733	—	4	2	no	—
59	C₂×#11745664	C₂³	1	2	yes	—
60	C₂×#11745659	—	2	2	no	—
61	C₂²×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
62	C₂²×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
63	C₂×C₈×D₅₉	—	2	2	no	—
64	C₄×Dic₁₁₈	C₂×C₄	1	1	yes	characteristic
65	C₄×Dic₁₁₈	C₂×C₄	1	1	yes	characteristic
66	C₄×D₂₃₆	C₂×C₄	1	1	yes	characteristic
67	C₄×D₂₃₆	C₂×C₄	1	1	yes	characteristic
68	C₄×C₂²⋊D₅₉	—	2	1	no	—
69	C₄×C₂²⋊D₅₉	—	2	1	no	—
70	#14273686	C₂³	1	1	yes	characteristic
71	#14273684	—	2	1	no	—
72	C₂×C₄⋊Dic₅₉	—	2	1	no	—
73	C₂×C₄×Dic₅₉	C₂³	1	2	yes	—
74	C₄²×D₅₉	—	2	1	no	—
75	#14273662	—	2	4	no	—
76	#14273662	—	4	2	no	—
77	#14273660	C₂×C₄	1	1	yes	characteristic
78	#14273660	C₂×C₄	1	1	yes	characteristic
79	#14273658	C₂×C₄	1	1	yes	characteristic
80	#14273658	C₂×C₄	1	1	yes	characteristic
81	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
82	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
83	Dic₅₉⋊C₈	—	2	2	no	—
84	Dic₅₉⋊C₈	—	2	2	no	—
85	#14273654	—	2	4	no	—
86	#14273653	—	2	4	no	—
87	#14273651	C₂×C₄	1	1	yes	characteristic
88	#14273651	C₂×C₄	1	1	yes	characteristic
89	#14273650	C₂×C₄	1	1	yes	characteristic
90	#14273650	C₂×C₄	1	1	yes	characteristic
91	#14273648	C₂×C₄	1	1	yes	characteristic
92	#14273648	C₂×C₄	1	1	yes	characteristic
93	#14273647	C₂×C₄	1	1	yes	characteristic
94	#14273647	C₂×C₄	1	1	yes	characteristic
95	C₄×C₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
96	C₄×C₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
97	C₄×C₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
98	C₄×C₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
99	C₈×Dic₅₉	—	2	4	no	—
100	C₅₉⋊#95	—	2	1	no	—
101	C₂×#41×C₅₉	C₂³	1	1	yes	characteristic
102	#131×C₅₉	—	2	4	no	—
103	#131×C₅₉	—	4	2	no	—
104	C₂×M₁₆×C₅₉	—	2	2	no	—
105	C₂×M₁₆×C₅₉	C₂³	1	2	yes	—
106	C₂²×C₈×C₅₉	—	2	2	no	—
107	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
108	C₄×Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
109	C₄×Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
110	C₄×D₄×C₅₉	—	2	1	no	—
111	C₄×D₄×C₅₉	—	2	1	no	—
112	C₄×D₄×C₅₉	C₂×C₄	1	1	yes	characteristic
113	C₄×D₄×C₅₉	C₂×C₄	1	1	yes	characteristic
114	#117×C₅₉	—	2	1	no	—
115	#117×C₅₉	C₂³	1	1	yes	characteristic
116	C₂×C₄²×C₅₉	—	2	1	no	—
117	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
118	C₄⋊C₈×C₅₉	—	2	2	no	—
119	C₄⋊C₈×C₅₉	—	2	2	no	—
120	C₄⋊C₈×C₅₉	—	2	1	no	—
121	C₄⋊C₈×C₅₉	—	2	1	no	—
122	C₄⋊C₈×C₅₉	D₄	1	1	yes	characteristic
123	C₄⋊C₈×C₅₉	D₄	1	1	yes	characteristic
124	C₄⋊C₈×C₅₉	D₄	1	2	yes	—
125	#41×C₅₉	—	2	1	no	—
126	#41×C₅₉	—	2	1	no	—
127	#41×C₅₉	C₂×D₄	1	2	yes	—
128	#41×C₅₉	C₂×Q₈	1	2	yes	—
129	C₂×Q₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
130	C₂×D₄×C₅₉	—	2	1	no	—
131	C₂×D₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
132	C₂²×C₄×C₅₉	—	2	1	no	—
133	C₂²×C₄×C₅₉	—	2	1	no	—
134	C₂²×C₄×C₅₉	—	2	1	no	—
135	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
136	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
137	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
138	C₂×C₂²⋊D₅₉	—	2	1	no	—
139	C₂²×Dic₅₉	—	2	2	no	—
140	#11745685	—	2	1	no	—
141	#11745685	—	2	1	no	—
142	#11745685	C₂×D₄	1	2	yes	—
143	#11745685	C₂×Q₈	1	2	yes	—
144	C₂×D₂₃₆	C₂²×C₄	1	1	yes	characteristic
145	C₂×C₄×D₅₉	—	2	1	no	—
146	C₂×C₄×D₅₉	—	2	1	no	—
147	C₂×C₄×D₅₉	—	2	1	no	—
148	C₂×Dic₁₁₈	C₂²×C₄	1	1	yes	characteristic
149	M₁₆×C₅₉	—	2	2	no	—
150	M₁₆×C₅₉	—	2	2	no	—
151	M₁₆×C₅₉	—	4	4	no	—
152	C₂×C₈×C₅₉	—	2	2	no	—
153	C₂×C₈×C₅₉	—	2	2	no	—
154	C₂×C₈×C₅₉	—	2	2	no	—
155	C₂×C₈×C₅₉	—	4	4	no	—
156	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
157	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
158	C₄⋊C₄×C₅₉	—	2	1	no	—
159	C₄⋊C₄×C₅₉	—	2	1	no	—
160	C₄⋊C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
161	C₄⋊C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
162	C₂²⋊C₄×C₅₉	—	2	1	no	—
163	C₂²⋊C₄×C₅₉	—	2	1	no	—
164	C₂²⋊C₄×C₅₉	—	2	1	no	—
165	C₄²×C₅₉	—	2	1	no	—
166	C₄²×C₅₉	—	2	1	no	—
167	C₄²×C₅₉	—	2	1	no	—
168	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
169	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
170	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
171	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
172	C₂²⋊Dic₅₉	—	2	1	no	—
173	#11745672	C₄⋊C₄	1	4	yes	complemented
174	#11745671	C₄⋊C₄	1	4	yes	complemented
175	#11745670	C₄⋊C₄	1	4	yes	complemented
176	#11745669	C₄⋊C₄	1	4	yes	complemented
177	(C₂×D₅₉)⋊C₄	—	2	1	no	—
178	(C₂×D₅₉)⋊C₄	—	2	1	no	—
179	C₄⋊Dic₅₉	—	2	4	no	—
180	C₄⋊Dic₅₉	C₂²×C₄	1	1	yes	characteristic
181	C₄⋊Dic₅₉	C₂²×C₄	1	1	yes	characteristic
182	Dic₅₉⋊C₄	—	2	1	no	—
183	Dic₅₉⋊C₄	—	2	1	no	—
184	C₄×Dic₅₉	—	2	1	no	—
185	C₄×Dic₅₉	—	2	1	no	—
186	C₄×Dic₅₉	—	2	1	no	—
187	C₄×Dic₅₉	—	2	2	no	—
188	C₄×Dic₅₉	—	2	2	no	—
189	#11745664	—	2	2	no	—
190	#11745664	—	2	2	no	—
191	C₂×C₅₉⋊C₈	—	2	1	no	—
192	C₂×C₅₉⋊C₈	—	2	1	no	—
193	C₂×C₅₉⋊C₈	—	2	2	no	—
194	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
195	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
196	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
197	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
198	C₂×C₅₉⋊C₈	C₂×D₄	1	2	yes	—
199	C₂×C₅₉⋊C₈	C₂×Q₈	1	2	yes	—
200	#11745659	—	4	4	no	—
201	C₈×D₅₉	—	4	4	no	—
202	C₂³×C₅₉	—	2	1	no	—
203	C₂³×C₅₉	C₂×#41	1	1	yes	characteristic
204	C₂²×D₅₉	—	2	1	no	—
205	Q₈×C₅₉	—	2	1	no	—
206	Q₈×C₅₉	C₂×C₄⋊C₄	1	2	yes	—
207	D₄×C₅₉	—	2	2	no	—
208	D₄×C₅₉	—	2	2	no	—
209	D₄×C₅₉	—	2	1	no	—
210	D₄×C₅₉	C₂×C₄⋊C₄	1	2	yes	—
211	C₂×C₄×C₅₉	—	2	1	no	—
212	C₂×C₄×C₅₉	—	2	2	no	—
213	C₂×C₄×C₅₉	—	2	2	no	—
214	C₂×C₄×C₅₉	—	2	2	no	—
215	C₂×C₄×C₅₉	—	2	1	no	—
216	C₂×C₄×C₅₉	—	2	1	no	—
217	C₂×C₄×C₅₉	—	4	1	no	—
218	C₂×C₄×C₅₉	—	4	2	no	—
219	C₂×C₄×C₅₉	—	8	1	no	—
220	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
221	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
222	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
223	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
224	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
225	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
226	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
227	C₂×C₄×C₅₉	C₂²×Q₈	1	1	yes	characteristic
228	C₂×C₄×C₅₉	H(5,𝔽₂)	1	1	yes	characteristic
229	C₂×C₄×C₅₉	2₋¹⁺⁴	1	1	yes	characteristic
230	C₂²⋊D₅₉	—	2	2	no	—
231	C₂²⋊D₅₉	—	2	2	no	—
232	C₂×Dic₅₉	—	2	1	no	—
233	C₂×Dic₅₉	—	2	4	no	—
234	C₂×Dic₅₉	—	2	1	no	—
235	C₂×Dic₅₉	—	2	1	no	—
236	C₂×Dic₅₉	—	4	2	no	—
237	C₂×Dic₅₉	—	4	2	no	—
238	D₂₃₆	—	2	1	no	—
239	D₂₃₆	C₂×C₄⋊C₄	1	2	yes	—
240	C₄×D₅₉	—	2	2	no	—
241	C₄×D₅₉	—	2	2	no	—
242	C₄×D₅₉	—	4	2	no	—
243	C₄×D₅₉	—	8	1	no	—
244	Dic₁₁₈	—	2	1	no	—
245	Dic₁₁₈	C₂×C₄⋊C₄	1	2	yes	—
246	C₈×C₅₉	—	2	2	no	—
247	C₈×C₅₉	—	2	2	no	—
248	C₈×C₅₉	—	4	2	no	—
249	C₅₉⋊C₈	—	2	1	no	—
250	C₅₉⋊C₈	—	2	1	no	—
251	C₅₉⋊C₈	—	4	2	no	—
252	C₅₉⋊C₈	C₂×C₄⋊C₄	1	2	yes	—
253	C₅₉⋊C₈	C₂×C₄⋊C₄	1	2	yes	—
254	#22688	—	59	1	no	maximal, Sylow
255	C₂²×C₅₉	—	2	1	no	—
256	C₂²×C₅₉	—	2	1	no	—
257	C₂²×C₅₉	—	2	2	no	—
258	C₂²×C₅₉	—	4	1	no	—
259	C₂²×C₅₉	—	4	1	no	—
260	C₂²×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
261	C₂²×C₅₉	#547	1	1	yes	characteristic
262	C₂²×C₅₉	#554	1	1	yes	characteristic
263	C₂×D₅₉	—	2	2	no	—
264	C₂×D₅₉	—	4	1	no	—
265	C₂×D₅₉	—	4	1	no	—
266	C₄×C₅₉	—	2	2	no	—
267	C₄×C₅₉	—	2	1	no	—
268	C₄×C₅₉	—	2	1	no	—
269	C₄×C₅₉	—	2	1	no	—
270	C₄×C₅₉	—	4	1	no	—
271	C₄×C₅₉	—	4	1	no	—
272	C₄×C₅₉	#443	1	2	yes	complemented
273	C₄×C₅₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
274	C₄×C₅₉	#520	1	1	yes	characteristic
275	C₄×C₅₉	D₄²	1	1	yes	characteristic
276	C₄×C₅₉	D₄×Q₈	1	1	yes	characteristic
277	Dic₅₉	—	2	2	no	—
278	Dic₅₉	—	4	4	no	—
279	Dic₅₉	—	4	1	no	—
280	Dic₅₉	—	4	1	no	—
281	C₂×#443	—	59	2	no	—
282	C₄×#135	—	59	1	no	—
283	#2906	—	59	1	no	—
284	#2906	D₅₉	1	1	yes	characteristic, complemented
285	#1945	—	59	2	no	—
286	#1866	—	59	2	no	—
287	#1866	—	59	2	no	—
288	#1848	—	59	1	no	—
289	#1806	—	59	1	no	—
290	#1806	—	59	1	no	—
291	C₈×C₄⋊C₄	—	59	1	no	—
292	C₂×C₅₉	—	2	1	no	—
293	C₂×C₅₉	—	2	1	no	—
294	C₂×C₅₉	—	4	2	no	—
295	C₂×C₅₉	D₄×C₄⋊C₄	1	1	yes	characteristic
296	C₂×C₅₉	C₂×#443	1	1	yes	characteristic
297	C₂×C₅₉	#2957	1	1	yes	characteristic
298	D₅₉	—	4	2	no	—
299	C₂×#135	—	59	1	no	—
300	C₂×#131	—	59	2	no	—
301	C₂×#131	C₂×D₅₉	1	2	yes	—
302	C₄×#41	—	59	1	no	—
303	C₄×#41	C₂×D₅₉	1	1	yes	characteristic
304	#443	—	118	8	no	—
305	C₄×Q₁₆	—	59	1	no	—
306	C₄×Q₁₆	—	59	1	no	—
307	C₄×SD₁₆	—	59	1	no	—
308	C₄×SD₁₆	—	59	1	no	—
309	C₄×SD₁₆	—	59	1	no	—
310	C₄×SD₁₆	—	59	1	no	—
311	C₄×D₈	—	59	1	no	—
312	C₄×D₈	—	59	1	no	—
313	C₂×#108	—	59	2	no	—
314	C₂×#108	—	59	2	no	—
315	#427	—	59	1	no	—
316	#424	—	2	2	no	—
317	#424	—	59	2	no	—
318	#424	—	118	2	no	—
319	#424	C₂×D₅₉	1	2	yes	—
320	#423	—	2	1	no	—
321	#423	—	59	1	no	—
322	#423	—	118	1	no	—
323	#423	C₂×D₅₉	1	1	yes	characteristic
324	C₂×C₄⋊C₈	—	2	1	no	—
325	C₂×C₄⋊C₈	—	118	1	no	—
326	C₂×C₄⋊C₈	C₂×D₅₉	1	1	yes	characteristic
327	C₂×#104	—	59	2	no	—
328	C₂×#104	—	59	2	no	—
329	#416	—	59	1	no	—
330	#416	—	59	1	no	—
331	C₂×C₄×C₈	—	59	1	no	—
332	C₂×C₄×C₈	—	59	2	no	—
333	C₄×C₄⋊C₄	—	59	1	no	—
334	#339	—	59	2	no	—
335	#339	—	59	2	no	—
336	#336	—	59	2	no	—
337	C₅₉	#22688	1	1	yes	characteristic, complemented, Sylow
338	C₂×#41	—	59	1	no	—
339	C₂×#41	C₂²×D₅₉	1	1	yes	characteristic
340	#135	—	59	4	no	—
341	#135	—	59	4	no	—
342	C₂×Q₁₆	—	59	1	no	—
343	C₂×SD₁₆	—	59	1	no	—
344	C₂×SD₁₆	—	59	1	no	—
345	C₂×D₈	—	59	1	no	—
346	#131	—	2	4	no	—
347	#131	—	4	2	no	—
348	#131	—	118	4	no	—
349	#131	—	236	2	no	—
350	C₂×M₁₆	—	2	2	no	—
351	C₂×M₁₆	—	59	2	no	—
352	C₂×M₁₆	—	118	2	no	—
353	C₂×M₁₆	C₂²×D₅₉	1	2	yes	—
354	C₂²×C₈	—	2	2	no	—
355	C₂²×C₈	—	59	1	no	—
356	C₂²×C₈	—	59	1	no	—
357	C₂²×C₈	—	118	2	no	—
358	C₂²×C₈	C₂²×D₅₉	1	2	yes	—
359	C₄×Q₈	—	59	1	no	—
360	C₄×Q₈	—	59	1	no	—
361	C₄×Q₈	C₄×D₅₉	1	1	yes	characteristic
362	C₄×Q₈	C₄×D₅₉	1	1	yes	characteristic
363	C₄×D₄	—	2	1	no	—
364	C₄×D₄	—	2	1	no	—
365	C₄×D₄	—	59	1	no	—
366	C₄×D₄	—	59	1	no	—
367	C₄×D₄	—	118	1	no	—
368	C₄×D₄	—	118	1	no	—
369	C₄×D₄	C₄×D₅₉	1	1	yes	characteristic
370	C₄×D₄	C₄×D₅₉	1	1	yes	characteristic
371	#117	—	2	1	no	—
372	#117	—	59	1	no	—
373	#117	—	118	1	no	—
374	#117	C₂²×D₅₉	1	1	yes	characteristic
375	C₂×C₄⋊C₄	—	118	1	no	—
376	C₂×C₄²	—	2	1	no	—
377	C₂×C₄²	—	59	2	no	—
378	C₂×C₄²	—	118	1	no	—
379	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
380	#108	—	118	4	no	—
381	#108	—	236	2	no	—
382	#107	—	59	1	no	—
383	#107	—	59	1	no	—
384	#106	—	59	1	no	—
385	#106	—	59	1	no	—
386	C₄⋊C₈	—	2	2	no	—
387	C₄⋊C₈	—	2	2	no	—
388	C₄⋊C₈	—	2	1	no	—
389	C₄⋊C₈	—	2	1	no	—
390	C₄⋊C₈	—	118	2	no	—
391	C₄⋊C₈	—	118	2	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	C₄⋊C₈	C₂²⋊D₅₉	1	2	yes	—
397	#104	—	118	4	no	—
398	#104	—	118	4	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	#102	—	59	1	no	—
406	#102	—	59	1	no	—
407	C₄×C₈	—	59	1	no	—
408	C₄×C₈	—	59	1	no	—
409	C₄×C₈	—	59	1	no	—
410	C₄×C₈	—	59	1	no	—
411	C₄×C₈	—	118	4	no	—
412	#95	—	118	1	no	—
413	#41	—	2	1	no	—
414	#41	—	2	1	no	—
415	#41	—	59	2	no	—
416	#41	—	59	2	no	—
417	#41	—	118	1	no	—
418	#41	—	118	1	no	—
419	#41	D₄×D₅₉	1	2	yes	—
420	#41	Q₈×D₅₉	1	2	yes	—
421	C₂×Q₈	—	59	1	no	—
422	C₂×Q₈	C₂×C₄×D₅₉	1	1	yes	characteristic
423	C₂×D₄	—	2	1	no	—
424	C₂×D₄	—	59	1	no	—
425	C₂×D₄	—	118	1	no	—
426	C₂×D₄	C₂×C₄×D₅₉	1	1	yes	characteristic
427	C₂²×C₄	—	2	1	no	—
428	C₂²×C₄	—	2	1	no	—
429	C₂²×C₄	—	2	1	no	—
430	C₂²×C₄	—	118	1	no	—
431	C₂²×C₄	—	118	2	no	—
432	C₂²×C₄	—	118	1	no	—
433	C₂²×C₄	—	118	1	no	—
434	C₂²×C₄	#11745685	1	1	yes	characteristic
435	C₂²×C₄	#11745685	1	1	yes	characteristic
436	C₂²×C₄	C₂³×D₅₉	1	1	yes	characteristic
437	Q₁₆	—	59	4	no	—
438	SD₁₆	—	59	4	no	—
439	SD₁₆	—	59	4	no	—
440	D₈	—	59	4	no	—
441	M₁₆	—	2	2	no	—
442	M₁₆	—	2	2	no	—
443	M₁₆	—	4	4	no	—
444	M₁₆	—	118	2	no	—
445	M₁₆	—	118	2	no	—
446	M₁₆	—	236	4	no	—
447	C₂×C₈	—	2	2	no	—
448	C₂×C₈	—	2	2	no	—
449	C₂×C₈	—	2	2	no	—
450	C₂×C₈	—	4	4	no	—
451	C₂×C₈	—	59	1	no	—
452	C₂×C₈	—	59	1	no	—
453	C₂×C₈	—	59	2	no	—
454	C₂×C₈	—	59	2	no	—
455	C₂×C₈	—	59	1	no	—
456	C₂×C₈	—	59	1	no	—
457	C₂×C₈	—	118	1	no	—
458	C₂×C₈	—	118	1	no	—
459	C₂×C₈	—	118	2	no	—
460	C₂×C₈	—	236	4	no	—
461	C₂×C₈	C₂×C₂²⋊D₅₉	1	2	yes	—
462	C₂×C₈	C₂×C₂²⋊D₅₉	1	2	yes	—
463	C₄⋊C₄	—	2	1	no	—
464	C₄⋊C₄	—	2	1	no	—
465	C₄⋊C₄	—	59	1	no	—
466	C₄⋊C₄	—	59	1	no	—
467	C₄⋊C₄	—	118	4	no	—
468	C₄⋊C₄	—	118	1	no	—
469	C₄⋊C₄	—	118	1	no	—
470	C₄⋊C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
471	C₄⋊C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
472	C₂²⋊C₄	—	2	1	no	—
473	C₂²⋊C₄	—	2	1	no	—
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	C₄²	—	2	1	no	—
479	C₄²	—	2	1	no	—
480	C₄²	—	2	1	no	—
481	C₄²	—	118	1	no	—
482	C₄²	—	118	1	no	—
483	C₄²	—	118	1	no	—
484	C₄²	—	118	2	no	—
485	C₄²	—	118	2	no	—
486	C₄²	C₂×C₄×D₅₉	1	1	yes	characteristic
487	C₄²	C₂×C₄×D₅₉	1	1	yes	characteristic
488	C₄²	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
489	C₄²	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
490	C₂³	—	2	1	no	—
491	C₂³	—	118	1	no	—
492	C₂³	C₂×#11745685	1	1	yes	characteristic
493	Q₈	—	2	1	no	—
494	Q₈	—	59	2	no	—
495	Q₈	—	118	1	no	—
496	Q₈	C₄⋊C₄×D₅₉	1	2	yes	—
497	D₄	—	2	2	no	—
498	D₄	—	2	2	no	—
499	D₄	—	2	1	no	—
500	D₄	—	59	2	no	—
501	D₄	—	118	2	no	—
502	D₄	—	118	2	no	—
503	D₄	—	118	1	no	—
504	D₄	C₄⋊C₄×D₅₉	1	2	yes	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	4	1	no	—
512	C₂×C₄	—	4	2	no	—
513	C₂×C₄	—	8	1	no	—
514	C₂×C₄	—	118	1	no	—
515	C₂×C₄	—	118	2	no	—
516	C₂×C₄	—	118	2	no	—
517	C₂×C₄	—	118	4	no	—
518	C₂×C₄	—	118	1	no	—
519	C₂×C₄	—	118	1	no	—
520	C₂×C₄	—	472	1	no	—
521	C₂×C₄	—	236	2	no	—
522	C₂×C₄	—	236	2	no	—
523	C₂×C₄	—	236	2	no	—
524	C₂×C₄	C₄×C₂²⋊D₅₉	1	1	yes	characteristic
525	C₂×C₄	C₄×C₂²⋊D₅₉	1	1	yes	characteristic
526	C₂×C₄	C₄×C₂²⋊D₅₉	1	1	yes	characteristic
527	C₂×C₄	C₄×C₂²⋊D₅₉	1	1	yes	characteristic
528	C₂×C₄	C₂²×C₄×D₅₉	1	1	yes	characteristic
529	C₂×C₄	C₂×D₄×D₅₉	1	1	yes	characteristic
530	C₂×C₄	C₂²×C₂²⋊D₅₉	1	1	yes	characteristic
531	C₂×C₄	C₂×Q₈×D₅₉	1	1	yes	characteristic
532	C₂×C₄	#14273772	1	1	yes	characteristic
533	C₂×C₄	#14273775	1	1	yes	characteristic
534	C₈	—	2	2	no	—
535	C₈	—	2	2	no	—
536	C₈	—	4	2	no	—
537	C₈	—	59	2	no	—
538	C₈	—	59	2	no	—
539	C₈	—	118	1	no	—
540	C₈	—	118	1	no	—
541	C₈	—	236	2	no	—
542	C₂²	—	2	1	no	—
543	C₂²	—	2	1	no	—
544	C₂²	—	2	2	no	—
545	C₂²	—	4	1	no	—
546	C₂²	—	4	1	no	—
547	C₂²	—	118	2	no	—
548	C₂²	—	236	1	no	—
549	C₂²	—	236	1	no	—
550	C₂²	C₂×C₄×C₂²⋊D₅₉	1	1	yes	characteristic
551	C₂²	#16838053	1	1	yes	characteristic
552	C₂²	#16838107	1	1	yes	characteristic
553	C₄	—	2	2	no	—
554	C₄	—	2	1	no	—
555	C₄	—	2	1	no	—
556	C₄	—	2	1	no	—
557	C₄	—	4	1	no	—
558	C₄	—	4	1	no	—
559	C₄	—	118	2	no	—
560	C₄	—	236	4	no	—
561	C₄	—	236	1	no	—
562	C₄	—	236	1	no	—
563	C₄	#16837517	1	2	yes	complemented
564	C₄	C₂×C₄⋊C₄×D₅₉	1	1	yes	characteristic
565	C₄	#16837883	1	1	yes	characteristic
566	C₄	D₄×C₂²⋊D₅₉	1	1	yes	characteristic
567	C₄	Q₈×C₂²⋊D₅₉	1	1	yes	characteristic
568	C₂	—	2	1	no	—
569	C₂	—	2	1	no	—
570	C₂	—	4	2	no	—
571	C₂	—	236	2	no	—
572	C₂	C₄⋊C₄×C₂²⋊D₅₉	1	1	yes	characteristic
573	C₂	C₂×#16837517	1	1	yes	characteristic
574	C₂	#21433011	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₅₉
commutator	C₂×C₄×C₅₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₅₉
Fitting	C₅₉×#2906	C₂
socle	C₂²×C₅₉	C₂×C₄×D₄
prime radical	C₂×#14273747	C₂²
cosocle	C₂²×C₄×C₅₉	C₂⁴
hypercenter	#2906	D₅₉
hypocenter	C₅₉	#22688
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄⋊C₈ ◁ #2906

Complements

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

N	H ≅ G/N	type
3. #21432661	C₂	semidirect
4. #21424841	C₂	semidirect
5. #21424371	C₂	semidirect
6. #21424370	C₂	semidirect
7. #21424267	C₂	semidirect
8. #21424116	C₂	semidirect
9. #21424113	C₂	semidirect
10. #21423961	C₂	semidirect
11. C₅₉×#2906	C₂	semidirect
16. C₄×#11745672	C₄	semidirect
17. C₄×#11745672	C₄	semidirect
18. C₄×#11745671	C₄	semidirect
19. C₄×#11745671	C₄	semidirect
20. C₄×#11745670	C₄	semidirect
21. C₄×#11745670	C₄	semidirect
22. C₄×#11745669	C₄	semidirect
23. C₄×#11745669	C₄	semidirect
173. #11745672	C₄⋊C₄	semidirect
174. #11745671	C₄⋊C₄	semidirect
175. #11745670	C₄⋊C₄	semidirect
176. #11745669	C₄⋊C₄	semidirect
272. C₄×C₅₉	#443	semidirect
284. #2906	D₅₉	semidirect
337. C₅₉	#22688	semidirect
563. C₄	#16837517	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16837517	2
C₄×#14273747	2
#21432661	2
#21424841	2
#21424371	2
#21424370	2
#21424267	2
#21424116	2
#21424113	2
#21423961	2
C₅₉×#2906	2
#22688	59