Subgroups — #15828556

Order 3328.

742 conjugacy classes of subgroups.

The subgroup lattice has 380 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	#13123469	C₂	1	1	yes	maximal, characteristic
3	#13113136	C₂	1	4	yes	maximal, complemented
4	#13113131	C₂	1	4	yes	maximal, complemented
5	#13113125	C₂	1	2	yes	maximal, complemented
6	C₈×#6099	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₃×#431	C₂	1	1	yes	maximal, characteristic
8	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
9	C₁₃×#431	C₄	1	2	yes	—
10	C₁₃×#431	C₄	1	2	yes	—
11	C₁₃×#431	C₂²	1	2	yes	—
12	C₁₃×#431	C₂²	1	2	yes	—
13	C₂×C₁₃×C₄⋊C₈	C₄	1	2	yes	—
14	C₂×C₁₃×C₂²⋊C₈	C₄	1	2	yes	—
15	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
16	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
17	#11718868	C₄	1	2	yes	—
18	#11718868	C₄	1	2	yes	—
19	#11718587	C₄	1	2	yes	—
20	#11718587	C₄	1	2	yes	—
21	#11718587	C₄	1	2	yes	—
22	#11718587	C₄	1	2	yes	—
23	#11718586	C₂²	1	2	yes	—
24	#11718586	C₂²	1	2	yes	—
25	#11718586	C₂²	1	2	yes	—
26	#11718586	C₂²	1	2	yes	—
27	#11718585	C₄	1	2	yes	—
28	#11718585	C₄	1	2	yes	—
29	C₄×#6099	C₂²	1	2	yes	—
30	C₄×#6099	C₂²	1	2	yes	—
31	#11718047	C₂²	1	4	yes	complemented
32	#11718046	C₂²	1	4	yes	complemented
33	#11718046	C₂²	1	4	yes	complemented
34	C₈×#1055	C₂²	1	4	yes	complemented
35	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
36	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
37	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
38	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
39	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
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	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
50	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
51	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
52	C₂×#6099	C₂×C₄	1	4	yes	—
53	C₂×#6099	C₂×C₄	1	4	yes	—
54	C₁₃×C₄⋊C₈	C₂×C₄	1	4	yes	—
55	C₁₃×C₄⋊C₈	C₂×C₄	1	4	yes	—
56	C₁₃×C₂²⋊C₈	C₂×C₄	1	4	yes	—
57	C₁₃×C₂²⋊C₈	C₂×C₄	1	4	yes	—
58	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
59	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
60	C₄×C₈×C₁₃	C₂³	1	2	yes	—
61	C₄×C₈×C₁₃	C₂³	1	2	yes	—
62	C₂²⋊#1055	C₂×C₄	1	4	yes	—
63	C₂²⋊#1055	C₂×C₄	1	4	yes	—
64	C₂²⋊#1055	C₂×C₄	1	4	yes	—
65	C₂²⋊#1055	C₂×C₄	1	4	yes	—
66	C₄⋊#1055	C₂×C₄	1	4	yes	—
67	C₄⋊#1055	C₂×C₄	1	4	yes	—
68	C₄⋊#1055	C₂×C₄	1	4	yes	—
69	C₄⋊#1055	C₂×C₄	1	4	yes	—
70	#88043	C₂×C₄	1	4	yes	—
71	#88043	C₂×C₄	1	4	yes	—
72	C₄×#1055	C₂³	1	4	yes	—
73	C₄×#1055	C₂³	1	4	yes	—
74	#17324	—	13	1	no	maximal, Sylow
75	C₂⁴×C₁₃	C₄²	1	1	yes	characteristic
76	C₂²×C₄×C₁₃	—	2	4	no	—
77	C₂²×C₄×C₁₃	—	4	2	no	—
78	C₂²×C₄×C₁₃	—	4	2	no	—
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	C₄²	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	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
97	C₂×C₈×C₁₃	—	4	2	no	—
98	C₂×C₈×C₁₃	—	4	2	no	—
99	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
100	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
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	C₄²	1	1	yes	characteristic
105	C₄²×C₁₃	C₄²	1	1	yes	characteristic
106	C₄²×C₁₃	C₄²	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	C₂²×C₄	1	1	yes	characteristic
114	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
115	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
116	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
117	#6099	—	2	8	no	—
118	#6099	—	4	4	no	—
119	C₂×#1055	C₂²×C₄	1	8	yes	—
120	C₂×#1055	C₂²×C₄	1	8	yes	—
121	#2920	—	13	1	no	—
122	#2920	—	13	1	no	—
123	C₂×#431	D₁₃	1	1	yes	characteristic
124	#1454	—	13	4	no	—
125	#1453	—	13	4	no	—
126	#1451	—	13	2	no	—
127	C₈×M₁₆	—	13	2	no	—
128	C₂³×C₁₃	—	2	2	no	—
129	C₂³×C₁₃	—	4	1	no	—
130	C₂³×C₁₃	—	4	1	no	—
131	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
132	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
133	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
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	—	2	2	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	—	4	1	no	—
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	C₂×C₄²	1	1	yes	characteristic
160	C₂×C₄×C₁₃	#131	1	4	yes	—
161	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
162	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
163	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
164	C₈×C₁₃	—	2	4	no	—
165	C₈×C₁₃	—	2	4	no	—
166	#1055	—	2	8	no	—
167	#1055	—	2	8	no	—
168	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
169	#432	—	13	2	no	—
170	#432	—	13	2	no	—
171	#432	—	13	2	no	—
172	#432	—	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	Dic₁₃	1	2	yes	—
178	#431	Dic₁₃	1	2	yes	—
179	#431	C₂×D₁₃	1	2	yes	—
180	#431	C₂×D₁₃	1	2	yes	—
181	#423	—	13	2	no	—
182	#423	—	13	2	no	—
183	C₂×C₄⋊C₈	Dic₁₃	1	2	yes	—
184	#407	—	13	2	no	—
185	#407	—	13	2	no	—
186	C₂×C₂²⋊C₈	Dic₁₃	1	2	yes	—
187	C₄×M₁₆	—	13	2	no	—
188	C₄×M₁₆	—	13	2	no	—
189	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
190	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
191	#322	—	13	4	no	—
192	#322	—	13	4	no	—
193	#322	—	13	4	no	—
194	C₈²	—	13	4	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	—	2	1	no	—
202	C₂²×C₁₃	—	2	1	no	—
203	C₂²×C₁₃	—	4	4	no	—
204	C₂²×C₁₃	#405	1	2	yes	—
205	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
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	—	2	1	no	—
213	C₄×C₁₃	—	2	1	no	—
214	C₄×C₁₃	#405	1	2	yes	—
215	C₄×C₁₃	C₂×#131	1	2	yes	—
216	C₄×C₁₃	#568	1	2	yes	—
217	C₄×C₁₃	#568	1	2	yes	—
218	C₂³×C₄	C₄×D₁₃	1	1	yes	characteristic
219	C₂³×C₄	C₄×D₁₃	1	1	yes	characteristic
220	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
221	C₂×M₁₆	—	13	4	no	—
222	C₂×M₁₆	—	13	4	no	—
223	C₂²×C₈	C₂×Dic₁₃	1	2	yes	—
224	C₂²×C₈	C₂×Dic₁₃	1	2	yes	—
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	C₄×D₁₃	1	1	yes	characteristic
230	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
231	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
232	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
233	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
234	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
235	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
236	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
237	C₄⋊C₈	—	13	4	no	—
238	C₄⋊C₈	—	13	4	no	—
239	C₄⋊C₈	—	13	4	no	—
240	C₄⋊C₈	—	13	4	no	—
241	C₄⋊C₈	C₂×Dic₁₃	1	4	yes	—
242	C₄⋊C₈	C₂×Dic₁₃	1	4	yes	—
243	C₂²⋊C₈	—	13	4	no	—
244	C₂²⋊C₈	—	13	4	no	—
245	C₂²⋊C₈	—	13	4	no	—
246	C₂²⋊C₈	—	13	4	no	—
247	C₂²⋊C₈	C₂×Dic₁₃	1	4	yes	—
248	C₂²⋊C₈	C₂×Dic₁₃	1	4	yes	—
249	#97	—	13	4	no	—
250	#97	—	13	4	no	—
251	C₄×C₈	—	13	4	no	—
252	C₄×C₈	—	13	4	no	—
253	C₄×C₈	C₂×Dic₁₃	1	2	yes	—
254	C₄×C₈	C₂×Dic₁₃	1	2	yes	—
255	C₄×C₈	C₂²×D₁₃	1	2	yes	—
256	C₄×C₈	C₂²×D₁₃	1	2	yes	—
257	C₂×C₁₃	—	2	2	no	—
258	C₂×C₁₃	—	4	1	no	—
259	C₂×C₁₃	—	4	1	no	—
260	C₂×C₁₃	C₂×#405	1	1	yes	characteristic
261	C₂×C₁₃	#2873	1	1	yes	characteristic
262	C₂×C₁₃	#2873	1	1	yes	characteristic
263	C₂⁴	C₄×Dic₁₃	1	1	yes	characteristic
264	C₂²×C₄	—	2	4	no	—
265	C₂²×C₄	—	4	2	no	—
266	C₂²×C₄	—	4	2	no	—
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	C₄×Dic₁₃	1	1	yes	characteristic
275	C₂²×C₄	C₄×Dic₁₃	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	C₂×C₄×D₁₃	1	1	yes	characteristic
281	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
282	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
283	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
284	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
285	M₁₆	—	26	8	no	—
286	M₁₆	—	52	4	no	—
287	C₂×C₈	—	4	2	no	—
288	C₂×C₈	—	4	2	no	—
289	C₂×C₈	—	13	8	no	—
290	C₂×C₈	—	13	8	no	—
291	C₂×C₈	C₂²×Dic₁₃	1	4	yes	—
292	C₂×C₈	C₂²×Dic₁₃	1	4	yes	—
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	C₄×Dic₁₃	1	1	yes	characteristic
298	C₄²	C₄×Dic₁₃	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	C₂×C₄×D₁₃	1	1	yes	characteristic
304	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
305	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
306	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
307	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
308	C₄²	C₂³×D₁₃	1	1	yes	characteristic
309	C₁₃	#17324	1	1	yes	characteristic, complemented, Sylow
310	C₂³	—	2	2	no	—
311	C₂³	—	4	1	no	—
312	C₂³	—	4	1	no	—
313	C₂³	C₂×C₄×Dic₁₃	1	1	yes	characteristic
314	C₂³	C₂×C₄×Dic₁₃	1	1	yes	characteristic
315	C₂³	C₂×C₄×Dic₁₃	1	1	yes	characteristic
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	—	2	2	no	—
326	C₂×C₄	—	2	2	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	—	4	1	no	—
332	C₂×C₄	—	4	1	no	—
333	C₂×C₄	#88155	1	4	yes	—
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	C₂×C₄×Dic₁₃	1	1	yes	characteristic
341	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
342	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
343	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
344	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
345	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
346	C₈	—	2	4	no	—
347	C₈	—	2	4	no	—
348	C₈	—	26	8	no	—
349	C₈	—	26	8	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	—	2	1	no	—
357	C₂²	—	2	1	no	—
358	C₂²	—	4	4	no	—
359	C₂²	#11718762	1	2	yes	—
360	C₂²	C₂²×C₄×Dic₁₃	1	1	yes	characteristic
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	—	2	1	no	—
368	C₄	—	2	1	no	—
369	C₄	#11718762	1	2	yes	—
370	C₄	C₂×#88155	1	2	yes	—
371	C₄	#11719450	1	2	yes	—
372	C₄	#11719524	1	2	yes	—
373	C₂	—	2	2	no	—
374	C₂	—	4	1	no	—
375	C₂	—	4	1	no	—
376	C₂	C₂×#11718762	1	1	yes	characteristic
377	C₂	#13123254	1	1	yes	characteristic
378	C₂	#13123255	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄²	C₂³×D₁₃
commutator, socle	C₂²×C₁₃	C₂²×C₄²
Fitting	C₂×C₁₃×#431	C₂
prime radical	C₂⁴×C₁₃	C₄²
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	C₂×#431	D₁₃
hypocenter	C₁₃	#17324
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄² ◁ C₂×#431

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. #13113125	C₂	semidirect
6. C₈×#6099	C₂	semidirect
31. #11718047	C₂²	semidirect
32. #11718046	C₂²	semidirect
33. #11718046	C₂²	semidirect
34. C₈×#1055	C₂²	semidirect
309. 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
#13113136	2
#13113131	2
#13113125	2
C₈×#6099	2
C₂×C₁₃×#431	2
#17324	13