Subgroups — #28557937

Order 15104.

634 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21433062	C₂	1	1	yes	maximal, characteristic
2	#21432761	C₂	1	1	yes	maximal, characteristic
3	#21432661	C₂	1	1	yes	maximal, characteristic
4	#21422883	C₂	1	2	yes	maximal, complemented
5	#21422878	C₂	1	2	yes	maximal, complemented
6	#21422870	C₂	1	1	yes	maximal, characteristic, complemented
7	#21422866	C₂	1	1	yes	maximal, characteristic, complemented
8	#21422860	C₂	1	2	yes	maximal, complemented
9	#21422855	C₂	1	1	yes	maximal, characteristic, complemented
10	#21422845	C₂	1	2	yes	maximal, complemented
11	C₂×C₅₉×#334	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14273733	—	2	1	no	—
13	C₄×#11745685	C₂²	1	1	yes	characteristic
14	#16837532	C₄	1	1	yes	characteristic
15	#16837532	C₄	1	1	yes	characteristic
16	#16837481	C₄	1	1	yes	characteristic
17	#16837481	C₄	1	1	yes	characteristic
18	#16837473	C₄	1	2	yes	—
19	#16837473	C₄	1	2	yes	—
20	#16837462	—	2	2	no	—
21	#16837458	C₂²	1	2	yes	—
22	#16837455	C₂²	1	1	yes	characteristic
23	#16837454	C₂²	1	2	yes	—
24	#16837453	C₂²	1	2	yes	—
25	#16837428	—	2	1	no	—
26	#16837427	—	2	2	no	—
27	#16837426	C₂²	1	1	yes	characteristic
28	#16837426	C₂²	1	1	yes	characteristic
29	#16837424	C₂²	1	2	yes	—
30	C₄⋊C₈×D₅₉	C₂²	1	2	yes	—
31	#16837368	—	2	1	no	—
32	#16837357	—	2	1	no	—
33	C₄×#11745659	C₂²	1	2	yes	—
34	#16837155	C₂²	1	2	yes	—
35	#16837155	C₂²	1	2	yes	—
36	#16837154	C₂²	1	2	yes	—
37	#16837154	C₂²	1	2	yes	—
38	#16837152	C₂²	1	2	yes	—
39	#16837152	C₂²	1	2	yes	—
40	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
41	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
42	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
43	C₅₉×#334	C₂²	1	1	yes	characteristic
44	C₅₉×#334	C₂²	1	1	yes	characteristic
45	C₅₉×#334	C₂²	1	1	yes	characteristic
46	C₅₉×#334	C₂²	1	1	yes	characteristic
47	C₂×#11745685	D₄	1	1	yes	characteristic
48	#14273733	—	4	4	no	—
49	C₂×#11745664	—	2	1	no	—
50	C₂×#11745664	—	2	1	no	—
51	C₂×#11745659	—	2	2	no	—
52	C₂×#11745659	C₂×C₄	1	2	yes	—
53	C₂×#11745659	C₂×C₄	1	2	yes	—
54	C₂×C₈×D₅₉	—	2	2	no	—
55	C₄×Dic₁₁₈	C₂×C₄	1	1	yes	characteristic
56	C₄×Dic₁₁₈	Q₈	1	1	yes	characteristic
57	C₄×D₂₃₆	C₂×C₄	1	1	yes	characteristic
58	C₄×D₂₃₆	Q₈	1	1	yes	characteristic
59	C₄×C₂²⋊D₅₉	C₂×C₄	1	2	yes	—
60	C₄×C₂²⋊D₅₉	Q₈	1	2	yes	—
61	#14273686	D₄	1	1	yes	characteristic
62	#14273684	D₄	1	2	yes	—
63	C₄²×D₅₉	C₂³	1	2	yes	—
64	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
65	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
66	C₄⋊(C₅₉⋊C₈)	C₂×C₄	1	1	yes	characteristic
67	C₄⋊(C₅₉⋊C₈)	C₂×C₄	1	1	yes	characteristic
68	C₄⋊(C₅₉⋊C₈)	C₂³	1	2	yes	—
69	C₄⋊(C₅₉⋊C₈)	C₂³	1	2	yes	—
70	Dic₅₉⋊C₈	—	2	2	no	—
71	Dic₅₉⋊C₈	—	2	2	no	—
72	Dic₅₉⋊C₈	C₂×C₄	1	2	yes	—
73	Dic₅₉⋊C₈	C₂×C₄	1	2	yes	—
74	C₂²⋊(C₅₉⋊C₈)	C₂×C₄	1	2	yes	—
75	(C₂×D₅₉)⋊C₈	—	2	2	no	—
76	(C₂×D₅₉)⋊C₈	—	2	2	no	—
77	(C₂×D₅₉)⋊C₈	C₂×C₄	1	2	yes	—
78	(C₂×D₅₉)⋊C₈	C₂×C₄	1	2	yes	—
79	#14273637	—	2	2	no	—
80	#14273637	C₂×C₄	1	2	yes	—
81	#14273637	C₂×C₄	1	2	yes	—
82	C₄×C₅₉⋊C₈	C₂³	1	2	yes	—
83	C₈×Dic₅₉	—	2	2	no	—
84	C₂²×C₈×C₅₉	—	2	1	no	—
85	C₂²×C₈×C₅₉	—	2	1	no	—
86	C₂²×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
87	C₂²×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
88	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
89	C₄⋊C₈×C₅₉	—	2	1	no	—
90	C₄⋊C₈×C₅₉	—	2	1	no	—
91	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
92	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
93	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
94	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
95	C₄×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
96	C₄×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
97	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
98	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
99	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₅₉	C₂×Q₈	1	1	yes	characteristic
102	C₂×C₂²⋊D₅₉	C₄⋊C₄	1	2	yes	—
103	#11745685	—	2	2	no	—
104	#11745685	—	2	2	no	—
105	C₂×D₂₃₆	C₄⋊C₄	1	1	yes	characteristic
106	C₂×C₄×D₅₉	C₂²×C₄	1	2	yes	—
107	C₂×C₄×D₅₉	C₂×D₄	1	2	yes	—
108	C₂×C₄×D₅₉	C₂×Q₈	1	2	yes	—
109	C₂×Dic₁₁₈	C₄⋊C₄	1	1	yes	characteristic
110	C₂×C₈×C₅₉	—	2	2	no	—
111	C₂×C₈×C₅₉	—	2	1	no	—
112	C₂×C₈×C₅₉	—	2	1	no	—
113	C₂×C₈×C₅₉	—	2	1	no	—
114	C₂×C₈×C₅₉	—	2	1	no	—
115	C₂×C₈×C₅₉	—	4	1	no	—
116	C₂×C₈×C₅₉	—	4	2	no	—
117	C₂×C₈×C₅₉	—	4	2	no	—
118	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
119	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
120	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
122	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
123	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
124	C₄²×C₅₉	C₂×Q₈	1	1	yes	characteristic
125	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
126	C₂²⋊Dic₅₉	C₄⋊C₄	1	2	yes	—
127	(C₂×D₅₉)⋊C₄	C₄⋊C₄	1	2	yes	—
128	(C₂×D₅₉)⋊C₄	C₄⋊C₄	1	2	yes	—
129	C₄⋊Dic₅₉	C₄⋊C₄	1	1	yes	characteristic
130	C₄⋊Dic₅₉	C₄⋊C₄	1	1	yes	characteristic
131	Dic₅₉⋊C₄	C₄⋊C₄	1	2	yes	—
132	Dic₅₉⋊C₄	C₄⋊C₄	1	2	yes	—
133	C₄×Dic₅₉	C₂²×C₄	1	2	yes	—
134	C₄×Dic₅₉	C₂×D₄	1	2	yes	—
135	C₄×Dic₅₉	C₂×Q₈	1	2	yes	—
136	#11745664	—	4	2	no	—
137	#11745664	—	4	2	no	—
138	C₂×C₅₉⋊C₈	—	2	2	no	—
139	C₂×C₅₉⋊C₈	—	2	2	no	—
140	C₂×C₅₉⋊C₈	C₂²×C₄	1	2	yes	—
141	C₂×C₅₉⋊C₈	C₂²×C₄	1	2	yes	—
142	#11745659	—	2	4	no	—
143	#11745659	—	4	2	no	—
144	#11745659	—	4	4	no	—
145	C₈×D₅₉	—	4	4	no	—
146	C₂³×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
147	C₂²×D₅₉	C₂×C₄⋊C₄	1	2	yes	—
148	C₂×C₄×C₅₉	—	2	1	no	—
149	C₂×C₄×C₅₉	—	2	1	no	—
150	C₂×C₄×C₅₉	—	4	1	no	—
151	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
152	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
153	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
154	C₂×C₄×C₅₉	AGL(1,ℤ/8)	1	2	yes	—
155	C₂×C₄×C₅₉	#137	1	2	yes	—
156	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
157	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
158	C₂×C₄×C₅₉	C₂²×Q₈	1	1	yes	characteristic
159	C₂²⋊D₅₉	—	2	4	no	—
160	C₂×Dic₅₉	C₂×C₄⋊C₄	1	2	yes	—
161	C₂×Dic₅₉	C₂×C₄⋊C₄	1	2	yes	—
162	C₂×Dic₅₉	C₂×C₄⋊C₄	1	2	yes	—
163	D₂₃₆	—	2	2	no	—
164	C₄×D₅₉	—	2	2	no	—
165	C₄×D₅₉	—	2	2	no	—
166	C₄×D₅₉	—	2	2	no	—
167	C₄×D₅₉	—	2	2	no	—
168	C₄×D₅₉	—	4	2	no	—
169	Dic₁₁₈	—	2	2	no	—
170	C₈×C₅₉	—	2	1	no	—
171	C₈×C₅₉	—	2	1	no	—
172	C₈×C₅₉	—	2	1	no	—
173	C₈×C₅₉	—	4	1	no	—
174	C₈×C₅₉	—	4	1	no	—
175	C₈×C₅₉	—	4	1	no	—
176	C₈×C₅₉	—	4	1	no	—
177	C₈×C₅₉	#131	1	2	yes	complemented
178	C₅₉⋊C₈	—	2	2	no	—
179	C₅₉⋊C₈	—	2	2	no	—
180	C₅₉⋊C₈	—	4	2	no	—
181	C₅₉⋊C₈	—	4	2	no	—
182	#17830	—	59	1	no	maximal, Sylow
183	C₂²×C₅₉	—	2	1	no	—
184	C₂²×C₅₉	—	2	1	no	—
185	C₂²×C₅₉	#428	1	2	yes	—
186	C₂²×C₅₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
187	C₂×D₅₉	—	2	2	no	—
188	C₂×D₅₉	—	2	2	no	—
189	C₂×D₅₉	—	2	2	no	—
190	C₄×C₅₉	—	2	1	no	—
191	C₄×C₅₉	—	2	1	no	—
192	C₄×C₅₉	—	2	1	no	—
193	C₄×C₅₉	#428	1	2	yes	—
194	C₄×C₅₉	C₂×#131	1	1	yes	characteristic
195	C₄×C₅₉	#568	1	1	yes	characteristic
196	C₄×C₅₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
197	C₄×C₅₉	C₂×#137	1	1	yes	characteristic
198	Dic₅₉	—	2	2	no	—
199	Dic₅₉	—	2	2	no	—
200	Dic₅₉	—	2	2	no	—
201	#2965	—	59	1	no	—
202	#2925	—	59	1	no	—
203	#2906	—	59	1	no	—
204	#1574	—	59	2	no	—
205	#1573	—	59	2	no	—
206	#1571	—	59	1	no	—
207	#1570	—	59	1	no	—
208	#1569	—	59	2	no	—
209	#1567	—	59	1	no	—
210	#1565	—	59	2	no	—
211	C₂×#334	D₅₉	1	1	yes	characteristic, complemented
212	C₂×C₅₉	—	2	2	no	—
213	C₂×C₅₉	#2906	1	1	yes	characteristic
214	C₂×C₅₉	C₂×#428	1	1	yes	characteristic
215	C₂×C₅₉	#2916	1	1	yes	characteristic
216	D₅₉	—	4	2	no	—
217	C₂×#131	—	118	1	no	—
218	C₄×#41	—	59	1	no	—
219	#446	—	59	1	no	—
220	#446	—	59	1	no	—
221	#436	—	59	1	no	—
222	#436	—	59	1	no	—
223	#435	—	59	2	no	—
224	#435	—	59	2	no	—
225	#433	—	118	2	no	—
226	#432	—	59	2	no	—
227	#431	—	59	1	no	—
228	#431	—	59	2	no	—
229	#431	—	59	2	no	—
230	#424	—	118	2	no	—
231	#424	—	118	1	no	—
232	#423	—	59	1	no	—
233	#423	—	59	1	no	—
234	#423	—	59	2	no	—
235	C₂×C₄⋊C₈	—	59	2	no	—
236	C₂×C₄⋊C₈	C₂×D₅₉	1	1	yes	characteristic
237	C₂×C₄⋊C₈	C₂×D₅₉	1	1	yes	characteristic
238	#408	—	118	1	no	—
239	#405	—	118	1	no	—
240	C₄×M₁₆	—	59	2	no	—
241	C₂×C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
242	#335	—	59	2	no	—
243	#335	—	59	2	no	—
244	#335	—	59	2	no	—
245	#335	—	59	2	no	—
246	#334	—	59	2	no	—
247	#334	—	59	2	no	—
248	#334	C₂×D₅₉	1	1	yes	characteristic
249	#334	C₂×D₅₉	1	1	yes	characteristic
250	#334	C₂×D₅₉	1	1	yes	characteristic
251	#334	C₂×D₅₉	1	1	yes	characteristic
252	C₅₉	#17830	1	1	yes	characteristic, complemented, Sylow
253	C₂×#41	—	59	1	no	—
254	#131	—	236	4	no	—
255	C₂×M₁₆	—	59	2	no	—
256	C₂×M₁₆	—	59	2	no	—
257	C₂×M₁₆	—	118	2	no	—
258	C₂×M₁₆	—	118	1	no	—
259	C₂×M₁₆	—	118	1	no	—
260	C₂²×C₈	—	2	1	no	—
261	C₂²×C₈	—	2	1	no	—
262	C₂²×C₈	—	118	2	no	—
263	C₂²×C₈	C₄×D₅₉	1	1	yes	characteristic
264	C₂²×C₈	C₄×D₅₉	1	1	yes	characteristic
265	C₄×Q₈	—	59	1	no	—
266	C₄×Q₈	—	59	1	no	—
267	C₄×D₄	—	59	2	no	—
268	C₄×D₄	—	59	2	no	—
269	C₄×D₄	—	59	1	no	—
270	C₄×D₄	—	59	1	no	—
271	#117	—	59	1	no	—
272	#117	—	59	2	no	—
273	C₂×C₄²	—	59	2	no	—
274	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
275	C₄⋊C₈	—	2	1	no	—
276	C₄⋊C₈	—	2	1	no	—
277	C₄⋊C₈	—	59	2	no	—
278	C₄⋊C₈	—	59	2	no	—
279	C₄⋊C₈	—	59	1	no	—
280	C₄⋊C₈	—	59	1	no	—
281	C₄⋊C₈	—	59	2	no	—
282	C₄⋊C₈	—	59	2	no	—
283	C₄⋊C₈	—	118	2	no	—
284	C₄⋊C₈	—	118	2	no	—
285	C₄⋊C₈	—	118	1	no	—
286	C₄⋊C₈	—	118	1	no	—
287	C₄⋊C₈	C₂²×D₅₉	1	1	yes	characteristic
288	C₄⋊C₈	C₂²×D₅₉	1	1	yes	characteristic
289	C₄⋊C₈	C₂²×D₅₉	1	1	yes	characteristic
290	C₄⋊C₈	C₂²×D₅₉	1	1	yes	characteristic
291	C₂²⋊C₈	—	59	2	no	—
292	C₂²⋊C₈	—	59	2	no	—
293	C₂²⋊C₈	—	59	2	no	—
294	C₂²⋊C₈	—	118	2	no	—
295	C₂²⋊C₈	—	118	2	no	—
296	#97	—	59	2	no	—
297	#97	—	59	2	no	—
298	#97	—	118	2	no	—
299	C₄×C₈	—	59	2	no	—
300	C₄×C₈	—	118	2	no	—
301	C₄×C₈	C₄×D₅₉	1	1	yes	characteristic
302	C₄×C₈	C₄×D₅₉	1	1	yes	characteristic
303	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
304	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
305	#41	—	118	2	no	—
306	#41	—	118	2	no	—
307	C₂×Q₈	—	59	1	no	—
308	C₂×D₄	—	59	2	no	—
309	C₂×D₄	—	59	1	no	—
310	C₂²×C₄	—	59	2	no	—
311	C₂²×C₄	—	59	2	no	—
312	C₂²×C₄	—	59	2	no	—
313	C₂²×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
314	C₂²×C₄	D₄×D₅₉	1	1	yes	characteristic
315	C₂²×C₄	Q₈×D₅₉	1	1	yes	characteristic
316	M₁₆	—	118	4	no	—
317	M₁₆	—	236	2	no	—
318	M₁₆	—	236	4	no	—
319	M₁₆	—	236	2	no	—
320	M₁₆	—	236	2	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	1	no	—
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	2	1	no	—
325	C₂×C₈	—	2	1	no	—
326	C₂×C₈	—	4	1	no	—
327	C₂×C₈	—	4	2	no	—
328	C₂×C₈	—	4	2	no	—
329	C₂×C₈	—	59	2	no	—
330	C₂×C₈	—	59	2	no	—
331	C₂×C₈	—	118	2	no	—
332	C₂×C₈	—	118	2	no	—
333	C₂×C₈	—	236	4	no	—
334	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
335	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
336	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
337	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
338	C₄⋊C₄	—	59	2	no	—
339	C₄⋊C₄	—	59	2	no	—
340	C₄⋊C₄	—	59	1	no	—
341	C₄⋊C₄	—	59	1	no	—
342	C₂²⋊C₄	—	59	2	no	—
343	C₂²⋊C₄	—	59	2	no	—
344	C₂²⋊C₄	—	59	2	no	—
345	C₄²	—	59	2	no	—
346	C₄²	—	59	2	no	—
347	C₄²	—	59	2	no	—
348	C₄²	C₂×C₄×D₅₉	1	1	yes	characteristic
349	C₄²	D₄×D₅₉	1	1	yes	characteristic
350	C₄²	Q₈×D₅₉	1	1	yes	characteristic
351	C₄²	C₂³×D₅₉	1	1	yes	characteristic
352	C₂³	—	59	2	no	—
353	C₂³	C₄⋊C₄×D₅₉	1	1	yes	characteristic
354	Q₈	—	118	2	no	—
355	D₄	—	118	4	no	—
356	D₄	—	118	2	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	4	1	no	—
360	C₂×C₄	—	59	2	no	—
361	C₂×C₄	—	59	2	no	—
362	C₂×C₄	—	59	2	no	—
363	C₂×C₄	—	118	2	no	—
364	C₂×C₄	—	118	2	no	—
365	C₂×C₄	—	118	2	no	—
366	C₂×C₄	—	118	2	no	—
367	C₂×C₄	—	236	2	no	—
368	C₂×C₄	C₄⋊C₄×D₅₉	1	1	yes	characteristic
369	C₂×C₄	C₄⋊C₄×D₅₉	1	1	yes	characteristic
370	C₂×C₄	C₄⋊C₄×D₅₉	1	1	yes	characteristic
371	C₂×C₄	#14273754	1	2	yes	—
372	C₂×C₄	#14273756	1	2	yes	—
373	C₂×C₄	C₂²×C₄×D₅₉	1	1	yes	characteristic
374	C₂×C₄	C₂×D₄×D₅₉	1	1	yes	characteristic
375	C₂×C₄	C₂×Q₈×D₅₉	1	1	yes	characteristic
376	C₈	—	2	1	no	—
377	C₈	—	2	1	no	—
378	C₈	—	2	1	no	—
379	C₈	—	4	1	no	—
380	C₈	—	4	1	no	—
381	C₈	—	4	1	no	—
382	C₈	—	4	1	no	—
383	C₈	—	118	2	no	—
384	C₈	—	118	2	no	—
385	C₈	—	236	2	no	—
386	C₈	—	236	2	no	—
387	C₈	#14273733	1	2	yes	complemented
388	C₂²	—	2	1	no	—
389	C₂²	—	2	1	no	—
390	C₂²	—	118	2	no	—
391	C₂²	—	118	2	no	—
392	C₂²	—	118	2	no	—
393	C₂²	#16837441	1	2	yes	—
394	C₂²	C₂×C₄⋊C₄×D₅₉	1	1	yes	characteristic
395	C₄	—	2	1	no	—
396	C₄	—	2	1	no	—
397	C₄	—	2	1	no	—
398	C₄	—	118	2	no	—
399	C₄	—	118	2	no	—
400	C₄	—	118	2	no	—
401	C₄	#16837441	1	2	yes	—
402	C₄	C₂×#14273733	1	1	yes	characteristic
403	C₄	#16838168	1	1	yes	characteristic
404	C₄	C₂×#14273754	1	1	yes	characteristic
405	C₄	C₂×#14273756	1	1	yes	characteristic
406	C₂	—	2	2	no	—
407	C₂	—	236	2	no	—
408	C₂	#21432661	1	1	yes	characteristic
409	C₂	C₂×#16837441	1	1	yes	characteristic
410	C₂	#21432704	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₅₉
commutator	C₂×C₄×C₅₉	C₂³×C₄
Frattini	C₄²	C₂³×D₅₉
Fitting	C₂×C₅₉×#334	C₂
socle	C₂²×C₅₉	C₂²×C₄⋊C₄
prime radical	C₂×#11745685	D₄
cosocle	C₄²×C₅₉	C₂⁴
hypercenter	C₂×#334	D₅₉
hypocenter	C₅₉	#17830
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×#334

Complements

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

N	H ≅ G/N	type
4. #21422883	C₂	semidirect
5. #21422878	C₂	semidirect
6. #21422870	C₂	semidirect
7. #21422866	C₂	semidirect
8. #21422860	C₂	semidirect
9. #21422855	C₂	semidirect
10. #21422845	C₂	semidirect
11. C₂×C₅₉×#334	C₂	semidirect
177. C₈×C₅₉	#131	semidirect
211. C₂×#334	D₅₉	semidirect
252. C₅₉	#17830	semidirect
387. C₈	#14273733	semidirect

Maximal subgroups

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

subgroup	index
#21433062	2
#21432761	2
#21432661	2
#21422883	2
#21422878	2
#21422870	2
#21422866	2
#21422860	2
#21422855	2
#21422845	2
C₂×C₅₉×#334	2
#17830	59