Subgroups — #28557917

Order 15104.

610 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#41×C₅₉⋊C₈	C₂	1	1	yes	maximal, characteristic
2	#21432762	C₂	1	1	yes	maximal, characteristic
3	#21422877	C₂	1	2	yes	maximal, complemented
4	#21422874	C₂	1	2	yes	maximal, complemented
5	#21422872	C₂	1	1	yes	maximal, characteristic, complemented
6	#21422870	C₂	1	1	yes	maximal, characteristic, complemented
7	#21422857	C₂	1	2	yes	maximal, complemented
8	#21422851	C₂	1	1	yes	maximal, characteristic, complemented
9	#21422842	C₂	1	2	yes	maximal, complemented
10	C₂×#16837152	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#2925	C₂	1	1	yes	maximal, characteristic
12	Q₈×C₅₉⋊C₈	C₄	1	1	yes	characteristic
13	Q₈×C₅₉⋊C₈	C₄	1	1	yes	characteristic
14	D₄×C₅₉⋊C₈	C₄	1	1	yes	characteristic
15	D₄×C₅₉⋊C₈	C₄	1	2	yes	—
16	D₄×C₅₉⋊C₈	C₄	1	1	yes	characteristic
17	D₄×C₅₉⋊C₈	C₄	1	2	yes	—
18	#16837463	—	2	2	no	—
19	#16837459	C₂²	1	2	yes	—
20	#16837455	C₂²	1	2	yes	—
21	#16837455	C₂²	1	1	yes	characteristic
22	#16837455	C₂²	1	2	yes	—
23	#16837426	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
25	#16837369	—	2	1	no	—
26	#16837358	—	2	1	no	—
27	C₂×C₄×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₅₉⋊C₈	C₂²	1	2	yes	—
29	#16837154	C₂²	1	2	yes	—
30	#16837154	C₂²	1	2	yes	—
31	#16837154	C₂²	1	2	yes	—
32	#16837154	C₂²	1	2	yes	—
33	#16837152	C₂²	1	2	yes	—
34	#16837152	C₂²	1	2	yes	—
35	#16837152	C₂²	1	1	yes	characteristic
36	#16837152	C₂²	1	1	yes	characteristic
37	#16837152	C₂²	1	1	yes	characteristic
38	#16837152	C₂²	1	1	yes	characteristic
39	C₄×#41×C₅₉	C₂²	1	1	yes	characteristic
40	C₅₉×#433	—	2	2	no	—
41	C₅₉×#432	C₂²	1	2	yes	—
42	C₅₉×#431	C₂²	1	2	yes	—
43	C₅₉×#423	C₂²	1	1	yes	characteristic
44	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
45	C₅₉×#408	—	2	1	no	—
46	C₅₉×#405	—	2	1	no	—
47	C₂×#11745664	—	2	1	no	—
48	C₂²×C₅₉⋊C₈	—	2	1	no	—
49	C₂²×C₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
50	C₂²×C₅₉⋊C₈	C₂×C₄	1	2	yes	—
51	C₂²×C₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
52	C₂²×C₅₉⋊C₈	C₂×C₄	1	2	yes	—
53	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
54	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
55	C₄⋊(C₅₉⋊C₈)	C₂×C₄	1	1	yes	characteristic
56	C₄⋊(C₅₉⋊C₈)	C₂×C₄	1	1	yes	characteristic
57	C₄⋊(C₅₉⋊C₈)	C₂×C₄	1	2	yes	—
58	C₄⋊(C₅₉⋊C₈)	C₂×C₄	1	2	yes	—
59	C₄⋊(C₅₉⋊C₈)	C₂³	1	1	yes	characteristic
60	C₄⋊(C₅₉⋊C₈)	C₂³	1	1	yes	characteristic
61	C₄⋊(C₅₉⋊C₈)	C₂³	1	2	yes	—
62	C₂²⋊(C₅₉⋊C₈)	—	2	2	no	—
63	C₂²⋊(C₅₉⋊C₈)	—	2	2	no	—
64	C₂²⋊(C₅₉⋊C₈)	C₂×C₄	1	2	yes	—
65	C₂²⋊(C₅₉⋊C₈)	C₂×C₄	1	2	yes	—
66	C₂²⋊(C₅₉⋊C₈)	C₂×C₄	1	2	yes	—
67	#14273638	—	2	2	no	—
68	C₄×C₅₉⋊C₈	—	2	2	no	—
69	C₄×C₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
70	C₄×C₅₉⋊C₈	C₂×C₄	1	2	yes	—
71	C₄×C₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
72	C₄×C₅₉⋊C₈	C₂×C₄	1	2	yes	—
73	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
74	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
75	C₄×C₅₉⋊C₈	C₂³	1	2	yes	—
76	C₂×#41×C₅₉	D₄	1	1	yes	characteristic
77	C₂×M₁₆×C₅₉	—	2	1	no	—
78	C₂²×C₈×C₅₉	—	2	1	no	—
79	C₄×Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
80	C₄×Q₈×C₅₉	Q₈	1	1	yes	characteristic
81	C₄×D₄×C₅₉	C₂×C₄	1	2	yes	—
82	C₄×D₄×C₅₉	C₂×C₄	1	1	yes	characteristic
83	C₄×D₄×C₅₉	Q₈	1	2	yes	—
84	C₄×D₄×C₅₉	Q₈	1	1	yes	characteristic
85	#117×C₅₉	D₄	1	1	yes	characteristic
86	#117×C₅₉	D₄	1	2	yes	—
87	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
88	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
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	2	yes	—
94	C₂²⋊C₈×C₅₉	—	2	2	no	—
95	C₂²⋊C₈×C₅₉	—	2	2	no	—
96	#97×C₅₉	—	2	2	no	—
97	C₄×C₈×C₅₉	—	2	2	no	—
98	#41×C₅₉	—	2	2	no	—
99	#41×C₅₉	—	2	2	no	—
100	C₂×Q₈×C₅₉	C₄⋊C₄	1	1	yes	characteristic
101	C₂×D₄×C₅₉	C₄⋊C₄	1	2	yes	—
102	C₂×D₄×C₅₉	C₄⋊C₄	1	1	yes	characteristic
103	C₂²×C₄×C₅₉	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₅₉	C₂×Q₈	1	2	yes	—
108	C₂²×C₄×C₅₉	C₂×Q₈	1	1	yes	characteristic
109	M₁₆×C₅₉	—	4	2	no	—
110	C₂×C₈×C₅₉	—	2	1	no	—
111	C₂×C₈×C₅₉	—	2	2	no	—
112	C₂×C₈×C₅₉	—	2	1	no	—
113	C₂×C₈×C₅₉	—	4	2	no	—
114	C₄⋊C₄×C₅₉	C₄⋊C₄	1	2	yes	—
115	C₄⋊C₄×C₅₉	C₄⋊C₄	1	1	yes	characteristic
116	C₄⋊C₄×C₅₉	C₄⋊C₄	1	2	yes	—
117	C₄⋊C₄×C₅₉	C₄⋊C₄	1	1	yes	characteristic
118	C₂²⋊C₄×C₅₉	C₄⋊C₄	1	2	yes	—
119	C₂²⋊C₄×C₅₉	C₄⋊C₄	1	2	yes	—
120	C₂²⋊C₄×C₅₉	C₄⋊C₄	1	2	yes	—
121	C₄²×C₅₉	C₂²×C₄	1	2	yes	—
122	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
123	C₄²×C₅₉	C₂×D₄	1	2	yes	—
124	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
125	C₄²×C₅₉	C₂×Q₈	1	2	yes	—
126	C₄²×C₅₉	C₂×Q₈	1	1	yes	characteristic
127	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
128	#11745664	—	4	2	no	—
129	C₂×C₅₉⋊C₈	—	2	2	no	—
130	C₂×C₅₉⋊C₈	—	2	4	no	—
131	C₂×C₅₉⋊C₈	—	2	1	no	—
132	C₂×C₅₉⋊C₈	—	2	2	no	—
133	C₂×C₅₉⋊C₈	—	2	1	no	—
134	C₂×C₅₉⋊C₈	—	4	1	no	—
135	C₂×C₅₉⋊C₈	—	4	2	no	—
136	C₂×C₅₉⋊C₈	—	4	2	no	—
137	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₅₉⋊C₈	C₂²×C₄	1	2	yes	—
140	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
141	C₂×C₅₉⋊C₈	C₂²×C₄	1	2	yes	—
142	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
143	C₂³×C₅₉	C₂×C₄⋊C₄	1	2	yes	—
144	C₂³×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
145	Q₈×C₅₉	—	2	2	no	—
146	D₄×C₅₉	—	2	4	no	—
147	D₄×C₅₉	—	2	2	no	—
148	C₂×C₄×C₅₉	—	2	1	no	—
149	C₂×C₄×C₅₉	—	2	2	no	—
150	C₂×C₄×C₅₉	—	2	1	no	—
151	C₂×C₄×C₅₉	—	2	2	no	—
152	C₂×C₄×C₅₉	—	2	2	no	—
153	C₂×C₄×C₅₉	—	2	2	no	—
154	C₂×C₄×C₅₉	—	4	1	no	—
155	C₂×C₄×C₅₉	—	4	2	no	—
156	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	2	yes	—
157	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
158	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	2	yes	—
159	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	2	yes	—
160	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
161	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
162	C₂×C₄×C₅₉	#135	1	2	yes	—
163	C₂×C₄×C₅₉	#135	1	2	yes	—
164	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
165	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
166	C₂×C₄×C₅₉	C₂²×Q₈	1	1	yes	characteristic
167	C₈×C₅₉	—	4	1	no	—
168	C₈×C₅₉	—	4	1	no	—
169	C₈×C₅₉	—	4	2	no	—
170	C₅₉⋊C₈	—	2	1	no	—
171	C₅₉⋊C₈	—	2	2	no	—
172	C₅₉⋊C₈	—	2	1	no	—
173	C₅₉⋊C₈	—	2	1	no	—
174	C₅₉⋊C₈	—	2	2	no	—
175	C₅₉⋊C₈	—	4	1	no	—
176	C₅₉⋊C₈	—	4	1	no	—
177	C₅₉⋊C₈	—	4	2	no	—
178	C₅₉⋊C₈	#131	1	2	yes	—
179	#17827	—	59	1	no	maximal, Sylow
180	C₂²×C₅₉	—	2	1	no	—
181	C₂²×C₅₉	—	2	1	no	—
182	C₂²×C₅₉	—	2	2	no	—
183	C₂²×C₅₉	—	2	2	no	—
184	C₂²×C₅₉	—	2	2	no	—
185	C₂²×C₅₉	#427	1	2	yes	—
186	C₂²×C₅₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
187	C₄×C₅₉	—	2	1	no	—
188	C₄×C₅₉	—	2	2	no	—
189	C₄×C₅₉	—	2	2	no	—
190	C₄×C₅₉	—	2	1	no	—
191	C₄×C₅₉	—	2	1	no	—
192	C₄×C₅₉	—	2	2	no	—
193	C₄×C₅₉	#427	1	2	yes	—
194	C₄×C₅₉	C₂×#131	1	1	yes	characteristic
195	C₄×C₅₉	#568	1	1	yes	characteristic
196	C₄×C₅₉	C₂×#135	1	1	yes	characteristic
197	C₄×C₅₉	C₂×#135	1	1	yes	characteristic
198	C₈×#41	—	59	1	no	—
199	#2925	—	59	1	no	—
200	#2925	D₅₉	1	1	yes	characteristic
201	#1572	—	59	2	no	—
202	#1572	—	59	2	no	—
203	#1571	—	59	1	no	—
204	#1571	—	59	1	no	—
205	#1568	—	59	2	no	—
206	#1566	—	59	1	no	—
207	#1564	—	59	2	no	—
208	C₂×#334	—	59	1	no	—
209	C₂×C₅₉	—	2	2	no	—
210	C₂×C₅₉	—	4	2	no	—
211	C₂×C₅₉	#2906	1	1	yes	characteristic
212	C₂×C₅₉	C₂×#427	1	1	yes	characteristic
213	C₂×C₅₉	#2916	1	1	yes	characteristic
214	C₄×#41	C₂×D₅₉	1	1	yes	characteristic
215	C₈×Q₈	—	59	1	no	—
216	C₈×Q₈	—	59	1	no	—
217	C₈×D₄	—	59	1	no	—
218	C₈×D₄	—	59	2	no	—
219	C₈×D₄	—	59	1	no	—
220	C₈×D₄	—	59	2	no	—
221	#433	—	2	2	no	—
222	#433	—	118	2	no	—
223	#432	—	59	2	no	—
224	#432	C₂×D₅₉	1	2	yes	—
225	#431	—	59	1	no	—
226	#431	—	59	2	no	—
227	#431	—	59	2	no	—
228	#431	C₂×D₅₉	1	2	yes	—
229	#423	—	59	1	no	—
230	#423	C₂×D₅₉	1	1	yes	characteristic
231	C₂×C₄⋊C₈	—	59	1	no	—
232	C₂×C₄⋊C₈	C₂×D₅₉	1	1	yes	characteristic
233	#408	—	2	1	no	—
234	#408	—	118	1	no	—
235	#405	—	2	1	no	—
236	#405	—	118	1	no	—
237	C₂×C₄×C₈	—	59	1	no	—
238	C₂×C₄×C₈	—	59	2	no	—
239	#335	—	59	2	no	—
240	#335	—	59	2	no	—
241	#335	—	59	2	no	—
242	#335	—	59	2	no	—
243	#334	—	59	1	no	—
244	#334	—	59	1	no	—
245	#334	—	59	1	no	—
246	#334	—	59	1	no	—
247	#334	—	59	2	no	—
248	#334	—	59	2	no	—
249	C₅₉	#17827	1	1	yes	characteristic, complemented, Sylow
250	C₂×#41	C₂²⋊D₅₉	1	1	yes	characteristic
251	C₂×M₁₆	—	2	1	no	—
252	C₂×M₁₆	—	118	1	no	—
253	C₂²×C₈	—	2	1	no	—
254	C₂²×C₈	—	59	1	no	—
255	C₂²×C₈	—	59	2	no	—
256	C₂²×C₈	—	59	1	no	—
257	C₂²×C₈	—	59	2	no	—
258	C₂²×C₈	—	118	1	no	—
259	C₄×Q₈	Dic₁₁₈	1	1	yes	characteristic
260	C₄×Q₈	C₄×D₅₉	1	1	yes	characteristic
261	C₄×D₄	Dic₁₁₈	1	2	yes	—
262	C₄×D₄	Dic₁₁₈	1	1	yes	characteristic
263	C₄×D₄	C₄×D₅₉	1	2	yes	—
264	C₄×D₄	C₄×D₅₉	1	1	yes	characteristic
265	#117	C₂²⋊D₅₉	1	1	yes	characteristic
266	#117	C₂²⋊D₅₉	1	2	yes	—
267	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
268	C₂×C₄²	C₂²×D₅₉	1	2	yes	—
269	C₄⋊C₈	—	2	1	no	—
270	C₄⋊C₈	—	2	1	no	—
271	C₄⋊C₈	—	59	1	no	—
272	C₄⋊C₈	—	59	1	no	—
273	C₄⋊C₈	—	59	2	no	—
274	C₄⋊C₈	—	59	2	no	—
275	C₄⋊C₈	—	59	1	no	—
276	C₄⋊C₈	—	59	1	no	—
277	C₄⋊C₈	—	59	2	no	—
278	C₄⋊C₈	—	118	1	no	—
279	C₄⋊C₈	—	118	1	no	—
280	C₄⋊C₈	C₂²×D₅₉	1	1	yes	characteristic
281	C₄⋊C₈	C₂²×D₅₉	1	1	yes	characteristic
282	C₄⋊C₈	C₂²×D₅₉	1	2	yes	—
283	C₂²⋊C₈	—	2	2	no	—
284	C₂²⋊C₈	—	2	2	no	—
285	C₂²⋊C₈	—	59	2	no	—
286	C₂²⋊C₈	—	59	2	no	—
287	C₂²⋊C₈	—	59	2	no	—
288	C₂²⋊C₈	—	118	2	no	—
289	C₂²⋊C₈	—	118	2	no	—
290	#97	—	2	2	no	—
291	#97	—	118	2	no	—
292	C₄×C₈	—	2	2	no	—
293	C₄×C₈	—	59	1	no	—
294	C₄×C₈	—	59	2	no	—
295	C₄×C₈	—	59	1	no	—
296	C₄×C₈	—	59	2	no	—
297	C₄×C₈	—	59	1	no	—
298	C₄×C₈	—	59	1	no	—
299	C₄×C₈	—	59	2	no	—
300	C₄×C₈	—	118	2	no	—
301	#41	—	2	2	no	—
302	#41	—	2	2	no	—
303	C₂×Q₈	Dic₅₉⋊C₄	1	1	yes	characteristic
304	C₂×D₄	Dic₅₉⋊C₄	1	2	yes	—
305	C₂×D₄	Dic₅₉⋊C₄	1	1	yes	characteristic
306	C₂²×C₄	C₂×Dic₁₁₈	1	2	yes	—
307	C₂²×C₄	C₂×Dic₁₁₈	1	1	yes	characteristic
308	C₂²×C₄	C₂×C₄×D₅₉	1	2	yes	—
309	C₂²×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
310	C₂²×C₄	C₂×C₂²⋊D₅₉	1	2	yes	—
311	C₂²×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
312	M₁₆	—	4	2	no	—
313	M₁₆	—	236	2	no	—
314	C₂×C₈	—	2	1	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	2	1	no	—
317	C₂×C₈	—	4	2	no	—
318	C₂×C₈	—	59	1	no	—
319	C₂×C₈	—	59	1	no	—
320	C₂×C₈	—	59	1	no	—
321	C₂×C₈	—	59	2	no	—
322	C₂×C₈	—	59	1	no	—
323	C₂×C₈	—	59	2	no	—
324	C₂×C₈	—	118	2	no	—
325	C₂×C₈	—	118	4	no	—
326	C₂×C₈	—	118	1	no	—
327	C₂×C₈	—	118	2	no	—
328	C₂×C₈	—	118	1	no	—
329	C₂×C₈	—	236	1	no	—
330	C₂×C₈	—	236	2	no	—
331	C₂×C₈	—	236	2	no	—
332	C₄⋊C₄	Dic₅₉⋊C₄	1	2	yes	—
333	C₄⋊C₄	Dic₅₉⋊C₄	1	1	yes	characteristic
334	C₄⋊C₄	Dic₅₉⋊C₄	1	2	yes	—
335	C₄⋊C₄	Dic₅₉⋊C₄	1	1	yes	characteristic
336	C₂²⋊C₄	Dic₅₉⋊C₄	1	2	yes	—
337	C₂²⋊C₄	Dic₅₉⋊C₄	1	2	yes	—
338	C₂²⋊C₄	Dic₅₉⋊C₄	1	2	yes	—
339	C₄²	C₂×Dic₁₁₈	1	2	yes	—
340	C₄²	C₂×Dic₁₁₈	1	1	yes	characteristic
341	C₄²	C₂×C₄×D₅₉	1	2	yes	—
342	C₄²	C₂×C₄×D₅₉	1	1	yes	characteristic
343	C₄²	C₂×C₂²⋊D₅₉	1	2	yes	—
344	C₄²	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
345	C₄²	C₂³×D₅₉	1	1	yes	characteristic
346	C₂³	C₂×Dic₅₉⋊C₄	1	2	yes	—
347	C₂³	C₂×Dic₅₉⋊C₄	1	1	yes	characteristic
348	Q₈	—	2	2	no	—
349	D₄	—	2	4	no	—
350	D₄	—	2	2	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	4	1	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	C₂×Dic₅₉⋊C₄	1	2	yes	—
360	C₂×C₄	C₂×Dic₅₉⋊C₄	1	2	yes	—
361	C₂×C₄	C₂×Dic₅₉⋊C₄	1	1	yes	characteristic
362	C₂×C₄	C₂×Dic₅₉⋊C₄	1	2	yes	—
363	C₂×C₄	C₂×Dic₅₉⋊C₄	1	1	yes	characteristic
364	C₂×C₄	C₂×Dic₅₉⋊C₄	1	1	yes	characteristic
365	C₂×C₄	#14273747	1	2	yes	—
366	C₂×C₄	#14273747	1	2	yes	—
367	C₂×C₄	C₂²×C₄×D₅₉	1	1	yes	characteristic
368	C₂×C₄	C₂²×C₂²⋊D₅₉	1	1	yes	characteristic
369	C₂×C₄	C₂²×Dic₁₁₈	1	1	yes	characteristic
370	C₈	—	4	1	no	—
371	C₈	—	4	1	no	—
372	C₈	—	4	2	no	—
373	C₈	—	59	2	no	—
374	C₈	—	118	1	no	—
375	C₈	—	118	2	no	—
376	C₈	—	118	1	no	—
377	C₈	—	118	2	no	—
378	C₈	—	118	1	no	—
379	C₈	—	236	1	no	—
380	C₈	—	236	1	no	—
381	C₈	—	236	2	no	—
382	C₂²	—	2	1	no	—
383	C₂²	—	2	1	no	—
384	C₂²	—	2	2	no	—
385	C₂²	—	2	2	no	—
386	C₂²	—	2	2	no	—
387	C₂²	#16837438	1	2	yes	—
388	C₂²	C₂²×Dic₅₉⋊C₄	1	1	yes	characteristic
389	C₄	—	2	1	no	—
390	C₄	—	2	2	no	—
391	C₄	—	2	2	no	—
392	C₄	—	2	1	no	—
393	C₄	—	2	1	no	—
394	C₄	—	2	2	no	—
395	C₄	#16837438	1	2	yes	—
396	C₄	#131×D₅₉	1	1	yes	characteristic
397	C₄	#16838167	1	1	yes	characteristic
398	C₄	C₂×#14273747	1	1	yes	characteristic
399	C₄	C₂×#14273747	1	1	yes	characteristic
400	C₂	—	2	2	no	—
401	C₂	—	4	2	no	—
402	C₂	#21432662	1	1	yes	characteristic
403	C₂	C₂×#16837438	1	1	yes	characteristic
404	C₂	#21432705	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×#2925	C₂
socle	C₂²×C₅₉	C₂²×C₄⋊C₄
prime radical	C₂×#41×C₅₉	D₄
cosocle	C₄²×C₅₉	C₂⁴
hypercenter	#2925	D₅₉
hypocenter	C₅₉	#17827
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×#41 ◁ #2925

Complements

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

N	H ≅ G/N	type
3. #21422877	C₂	semidirect
4. #21422874	C₂	semidirect
5. #21422872	C₂	semidirect
6. #21422870	C₂	semidirect
7. #21422857	C₂	semidirect
8. #21422851	C₂	semidirect
9. #21422842	C₂	semidirect
10. C₂×#16837152	C₂	semidirect
249. C₅₉	#17827	semidirect

Maximal subgroups

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

subgroup	index
#41×C₅₉⋊C₈	2
#21432762	2
#21422877	2
#21422874	2
#21422872	2
#21422870	2
#21422857	2
#21422851	2
#21422842	2
C₂×#16837152	2
C₅₉×#2925	2
#17827	59