Subgroups — #15828554

Order 3328.

742 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13123469	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718586	C₂	1	1	yes	maximal, characteristic
3	#13113136	C₂	1	4	yes	maximal, complemented
4	#13113131	C₂	1	4	yes	maximal, complemented
5	#13113123	C₂	1	2	yes	maximal, complemented
6	M₁₆×#1055	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2920	C₂	1	1	yes	maximal, characteristic
8	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
9	C₁₃×#432	C₄	1	2	yes	—
10	C₁₃×#432	C₄	1	2	yes	—
11	C₁₃×#431	C₂²	1	2	yes	—
12	C₁₃×#431	C₂²	1	2	yes	—
13	C₁₃×#423	C₄	1	2	yes	—
14	C₁₃×#407	C₄	1	2	yes	—
15	C₄×C₁₃×M₁₆	C₂²	1	2	yes	—
16	#11718868	C₄	1	2	yes	—
17	C₂×C₂²⋊#1055	C₄	1	2	yes	—
18	#11718587	C₄	1	2	yes	—
19	#11718587	C₄	1	2	yes	—
20	#11718586	C₄	1	2	yes	—
21	#11718586	C₄	1	2	yes	—
22	#11718586	C₂²	1	2	yes	—
23	#11718586	C₂²	1	2	yes	—
24	#11718586	C₂²	1	2	yes	—
25	#11718586	C₂²	1	2	yes	—
26	#11718585	C₄	1	2	yes	—
27	C₂×C₄⋊#1055	C₄	1	2	yes	—
28	C₄×#6099	C₂²	1	2	yes	—
29	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
30	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
31	#11718047	C₂²	1	4	yes	complemented
32	#11718046	C₂²	1	8	yes	complemented
33	C₈×#1055	C₂²	1	4	yes	complemented
34	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
35	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
36	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
37	C₂×C₁₃×M₁₆	C₂×C₄	1	4	yes	—
38	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
48	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
49	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
50	C₂×#6099	C₂×C₄	1	4	yes	—
51	C₂²×#1055	C₂×C₄	1	2	yes	—
52	C₂²×#1055	C₂×C₄	1	2	yes	—
53	C₁₃×C₄⋊C₈	C₂×C₄	1	4	yes	—
54	C₁₃×C₄⋊C₈	C₂×C₄	1	4	yes	—
55	C₁₃×C₂²⋊C₈	C₂×C₄	1	4	yes	—
56	C₁₃×C₂²⋊C₈	C₂×C₄	1	4	yes	—
57	C₁₃×#97	C₂×C₄	1	4	yes	—
58	C₄×C₈×C₁₃	C₂³	1	4	yes	—
59	C₂²⋊#1055	C₂×C₄	1	4	yes	—
60	C₂²⋊#1055	C₂×C₄	1	4	yes	—
61	C₂²⋊#1055	C₂×C₄	1	4	yes	—
62	C₂²⋊#1055	C₂×C₄	1	4	yes	—
63	C₄⋊#1055	C₂×C₄	1	4	yes	—
64	C₄⋊#1055	C₂×C₄	1	4	yes	—
65	C₄⋊#1055	C₂×C₄	1	4	yes	—
66	C₄⋊#1055	C₂×C₄	1	4	yes	—
67	#88043	C₂×C₄	1	4	yes	—
68	C₄×#1055	C₂×C₄	1	2	yes	—
69	C₄×#1055	C₂×C₄	1	2	yes	—
70	C₄×#1055	C₂³	1	2	yes	—
71	C₄×#1055	C₂³	1	4	yes	—
72	C₄×#1055	C₂³	1	2	yes	—
73	#17324	—	13	1	no	maximal, Sylow
74	C₂⁴×C₁₃	C₄²	1	1	yes	characteristic
75	C₂²×C₄×C₁₃	—	2	4	no	—
76	C₂²×C₄×C₁₃	—	4	2	no	—
77	C₂²×C₄×C₁₃	—	4	2	no	—
78	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
79	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
80	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
81	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
82	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
83	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
84	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
85	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
86	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
87	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
96	C₁₃×M₁₆	—	2	8	no	—
97	C₂×C₈×C₁₃	C₂²×C₄	1	8	yes	—
98	C₄²×C₁₃	C₄²	1	1	yes	characteristic
99	C₄²×C₁₃	C₄²	1	1	yes	characteristic
100	C₄²×C₁₃	C₄²	1	1	yes	characteristic
101	C₄²×C₁₃	C₄²	1	1	yes	characteristic
102	C₄²×C₁₃	C₄²	1	1	yes	characteristic
103	C₄²×C₁₃	C₄²	1	1	yes	characteristic
104	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
105	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
106	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
107	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
108	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
109	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
110	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
111	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
112	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
113	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
114	#6099	—	4	4	no	—
115	C₂×#1055	—	4	2	no	—
116	C₂×#1055	—	4	2	no	—
117	C₂×#1055	C₂²×C₄	1	4	yes	—
118	C₂×#1055	C₂²×C₄	1	4	yes	—
119	C₂×#1055	C₂²×C₄	1	8	yes	—
120	#2920	—	13	1	no	—
121	#2920	D₁₃	1	1	yes	characteristic
122	C₂×#431	—	13	1	no	—
123	#1454	—	13	4	no	—
124	#1453	—	13	4	no	—
125	#1451	—	13	2	no	—
126	C₈×M₁₆	—	13	2	no	—
127	C₂³×C₁₃	—	2	2	no	—
128	C₂³×C₁₃	—	4	1	no	—
129	C₂³×C₁₃	—	4	1	no	—
130	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
131	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
132	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
133	C₂×C₄×C₁₃	—	2	2	no	—
134	C₂×C₄×C₁₃	—	2	2	no	—
135	C₂×C₄×C₁₃	—	2	2	no	—
136	C₂×C₄×C₁₃	—	2	2	no	—
137	C₂×C₄×C₁₃	—	2	2	no	—
138	C₂×C₄×C₁₃	—	2	2	no	—
139	C₂×C₄×C₁₃	—	2	2	no	—
140	C₂×C₄×C₁₃	—	2	2	no	—
141	C₂×C₄×C₁₃	—	2	2	no	—
142	C₂×C₄×C₁₃	—	2	2	no	—
143	C₂×C₄×C₁₃	—	2	2	no	—
144	C₂×C₄×C₁₃	—	4	1	no	—
145	C₂×C₄×C₁₃	—	4	1	no	—
146	C₂×C₄×C₁₃	—	4	1	no	—
147	C₂×C₄×C₁₃	—	4	1	no	—
148	C₂×C₄×C₁₃	—	4	1	no	—
149	C₂×C₄×C₁₃	—	4	1	no	—
150	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
151	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
152	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
153	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
154	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
155	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
156	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
157	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
158	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
159	C₂×C₄×C₁₃	#131	1	4	yes	—
160	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
161	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
162	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
163	C₈×C₁₃	—	2	8	no	—
164	#1055	—	2	4	no	—
165	#1055	—	2	4	no	—
166	#1055	—	2	8	no	—
167	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
168	#432	—	13	2	no	—
169	#432	—	13	2	no	—
170	#432	Dic₁₃	1	2	yes	—
171	#432	Dic₁₃	1	2	yes	—
172	#431	—	13	2	no	—
173	#431	—	13	2	no	—
174	#431	—	13	2	no	—
175	#431	—	13	2	no	—
176	#431	—	13	2	no	—
177	#431	—	13	2	no	—
178	#431	C₂×D₁₃	1	2	yes	—
179	#431	C₂×D₁₃	1	2	yes	—
180	#423	—	13	2	no	—
181	#423	Dic₁₃	1	2	yes	—
182	C₂×C₄⋊C₈	—	13	2	no	—
183	#407	—	13	2	no	—
184	#407	Dic₁₃	1	2	yes	—
185	C₂×C₂²⋊C₈	—	13	2	no	—
186	C₄×M₁₆	—	13	2	no	—
187	C₄×M₁₆	C₂×D₁₃	1	2	yes	—
188	C₂×C₄×C₈	—	13	1	no	—
189	C₂×C₄×C₈	—	13	1	no	—
190	#322	—	13	8	no	—
191	#322	—	13	4	no	—
192	C₈²	—	13	4	no	—
193	C₂²×C₁₃	—	2	1	no	—
194	C₂²×C₁₃	—	2	1	no	—
195	C₂²×C₁₃	—	2	1	no	—
196	C₂²×C₁₃	—	2	1	no	—
197	C₂²×C₁₃	—	2	1	no	—
198	C₂²×C₁₃	—	2	1	no	—
199	C₂²×C₁₃	—	2	1	no	—
200	C₂²×C₁₃	—	2	1	no	—
201	C₂²×C₁₃	—	4	4	no	—
202	C₂²×C₁₃	#405	1	2	yes	—
203	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
204	C₄×C₁₃	—	2	1	no	—
205	C₄×C₁₃	—	2	1	no	—
206	C₄×C₁₃	—	2	1	no	—
207	C₄×C₁₃	—	2	1	no	—
208	C₄×C₁₃	—	2	1	no	—
209	C₄×C₁₃	—	2	1	no	—
210	C₄×C₁₃	—	2	1	no	—
211	C₄×C₁₃	—	2	1	no	—
212	C₄×C₁₃	#405	1	2	yes	—
213	C₄×C₁₃	C₂×#131	1	2	yes	—
214	C₄×C₁₃	#568	1	2	yes	—
215	C₄×C₁₃	#568	1	2	yes	—
216	C₂³×C₄	C₄×D₁₃	1	1	yes	characteristic
217	C₂³×C₄	C₄×D₁₃	1	1	yes	characteristic
218	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
219	C₂×M₁₆	—	13	4	no	—
220	C₂×M₁₆	C₂×Dic₁₃	1	4	yes	—
221	C₂²×C₈	—	13	2	no	—
222	C₂²×C₈	—	13	2	no	—
223	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
224	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
225	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
226	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
227	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
228	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
229	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
230	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
231	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
232	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
233	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
234	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
235	C₄⋊C₈	—	13	4	no	—
236	C₄⋊C₈	—	13	4	no	—
237	C₄⋊C₈	—	13	4	no	—
238	C₄⋊C₈	—	13	4	no	—
239	C₄⋊C₈	C₂×Dic₁₃	1	4	yes	—
240	C₄⋊C₈	C₂×Dic₁₃	1	4	yes	—
241	C₂²⋊C₈	—	13	4	no	—
242	C₂²⋊C₈	—	13	4	no	—
243	C₂²⋊C₈	—	13	4	no	—
244	C₂²⋊C₈	—	13	4	no	—
245	C₂²⋊C₈	C₂×Dic₁₃	1	4	yes	—
246	C₂²⋊C₈	C₂×Dic₁₃	1	4	yes	—
247	#97	—	13	4	no	—
248	#97	C₂×Dic₁₃	1	4	yes	—
249	C₄×C₈	—	13	2	no	—
250	C₄×C₈	—	13	2	no	—
251	C₄×C₈	—	13	2	no	—
252	C₄×C₈	—	13	4	no	—
253	C₄×C₈	—	13	2	no	—
254	C₄×C₈	C₂²×D₁₃	1	4	yes	—
255	C₂×C₁₃	—	2	2	no	—
256	C₂×C₁₃	—	4	1	no	—
257	C₂×C₁₃	—	4	1	no	—
258	C₂×C₁₃	C₂×#405	1	1	yes	characteristic
259	C₂×C₁₃	#2873	1	1	yes	characteristic
260	C₂×C₁₃	#2873	1	1	yes	characteristic
261	C₂⁴	C₄×Dic₁₃	1	1	yes	characteristic
262	C₂²×C₄	—	2	4	no	—
263	C₂²×C₄	—	4	2	no	—
264	C₂²×C₄	—	4	2	no	—
265	C₂²×C₄	C₄×Dic₁₃	1	1	yes	characteristic
266	C₂²×C₄	C₄×Dic₁₃	1	1	yes	characteristic
267	C₂²×C₄	C₄×Dic₁₃	1	1	yes	characteristic
268	C₂²×C₄	C₄×Dic₁₃	1	1	yes	characteristic
269	C₂²×C₄	C₄×Dic₁₃	1	1	yes	characteristic
270	C₂²×C₄	C₄×Dic₁₃	1	1	yes	characteristic
271	C₂²×C₄	C₄×Dic₁₃	1	1	yes	characteristic
272	C₂²×C₄	C₄×Dic₁₃	1	1	yes	characteristic
273	C₂²×C₄	C₄×Dic₁₃	1	1	yes	characteristic
274	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
275	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
276	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
277	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
278	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
279	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
280	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
281	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
282	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
283	M₁₆	—	2	8	no	—
284	M₁₆	—	52	4	no	—
285	C₂×C₈	—	13	4	no	—
286	C₂×C₈	—	13	4	no	—
287	C₂×C₈	—	13	8	no	—
288	C₂×C₈	—	52	2	no	—
289	C₂×C₈	—	52	2	no	—
290	C₂×C₈	C₂²×Dic₁₃	1	8	yes	—
291	C₄²	C₄×Dic₁₃	1	1	yes	characteristic
292	C₄²	C₄×Dic₁₃	1	1	yes	characteristic
293	C₄²	C₄×Dic₁₃	1	1	yes	characteristic
294	C₄²	C₄×Dic₁₃	1	1	yes	characteristic
295	C₄²	C₄×Dic₁₃	1	1	yes	characteristic
296	C₄²	C₄×Dic₁₃	1	1	yes	characteristic
297	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
298	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
299	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
300	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
301	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
302	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
303	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
304	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
305	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
306	C₄²	C₂³×D₁₃	1	1	yes	characteristic
307	C₁₃	#17324	1	1	yes	characteristic, complemented, Sylow
308	C₂³	—	2	2	no	—
309	C₂³	—	4	1	no	—
310	C₂³	—	4	1	no	—
311	C₂³	C₂×C₄×Dic₁₃	1	1	yes	characteristic
312	C₂³	C₂×C₄×Dic₁₃	1	1	yes	characteristic
313	C₂³	C₂×C₄×Dic₁₃	1	1	yes	characteristic
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	4	1	no	—
326	C₂×C₄	—	4	1	no	—
327	C₂×C₄	—	4	1	no	—
328	C₂×C₄	—	4	1	no	—
329	C₂×C₄	—	4	1	no	—
330	C₂×C₄	—	4	1	no	—
331	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
332	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
333	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
334	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
335	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
336	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
337	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
338	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
339	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
340	C₂×C₄	#88202	1	4	yes	—
341	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
342	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
343	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
344	C₈	—	2	8	no	—
345	C₈	—	26	4	no	—
346	C₈	—	26	4	no	—
347	C₈	—	26	8	no	—
348	C₂²	—	2	1	no	—
349	C₂²	—	2	1	no	—
350	C₂²	—	2	1	no	—
351	C₂²	—	2	1	no	—
352	C₂²	—	2	1	no	—
353	C₂²	—	2	1	no	—
354	C₂²	—	2	1	no	—
355	C₂²	—	2	1	no	—
356	C₂²	—	4	4	no	—
357	C₂²	#11718658	1	2	yes	—
358	C₂²	C₂²×C₄×Dic₁₃	1	1	yes	characteristic
359	C₄	—	2	1	no	—
360	C₄	—	2	1	no	—
361	C₄	—	2	1	no	—
362	C₄	—	2	1	no	—
363	C₄	—	2	1	no	—
364	C₄	—	2	1	no	—
365	C₄	—	2	1	no	—
366	C₄	—	2	1	no	—
367	C₄	#11718658	1	2	yes	—
368	C₄	#11719450	1	2	yes	—
369	C₄	#11719450	1	2	yes	—
370	C₄	C₂×#88202	1	2	yes	—
371	C₂	—	2	2	no	—
372	C₂	—	4	1	no	—
373	C₂	—	4	1	no	—
374	C₂	C₂×#11718658	1	1	yes	characteristic
375	C₂	#13123254	1	1	yes	characteristic
376	C₂	#13123254	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄²	C₂³×D₁₃
commutator, socle	C₂²×C₁₃	C₂²×C₄²
Fitting	C₁₃×#2920	C₂
prime radical	C₂⁴×C₁₃	C₄²
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	#2920	D₁₃
hypocenter	C₁₃	#17324
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄² ◁ #2920

Complements

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

N	H ≅ G/N	type
3. #13113136	C₂	semidirect
4. #13113131	C₂	semidirect
5. #13113123	C₂	semidirect
6. M₁₆×#1055	C₂	semidirect
31. #11718047	C₂²	semidirect
32. #11718046	C₂²	semidirect
33. C₈×#1055	C₂²	semidirect
307. C₁₃	#17324	semidirect

Maximal subgroups

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

subgroup	index
#13123469	2
C₂×#11718586	2
#13113136	2
#13113131	2
#13113123	2
M₁₆×#1055	2
C₁₃×#2920	2
#17324	13