Subgroups — #15881739

Order 3328.

732 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718685	C₂	1	2	yes	maximal
2	#13115560	C₂	1	2	yes	maximal
3	#13115560	C₂	1	2	yes	maximal
4	#13115555	C₂	1	2	yes	maximal
5	#13114990	C₂	1	2	yes	maximal
6	#13114988	C₂	1	1	yes	maximal, characteristic
7	#13114693	C₂	1	2	yes	maximal
8	#13114689	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#2295	C₂	1	1	yes	maximal, characteristic
10	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
11	C₁₃×#391	C₄	1	1	yes	characteristic
12	C₁₃×#391	C₄	1	1	yes	characteristic
13	C₁₃×#389	C₄	1	1	yes	characteristic
14	C₁₃×#389	C₄	1	1	yes	characteristic
15	C₁₃×#387	C₄	1	2	yes	—
16	C₁₃×#387	C₄	1	2	yes	—
17	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
18	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
19	C₁₃×#376	C₂²	1	2	yes	—
20	C₄³×C₁₃	C₂²	1	1	yes	characteristic
21	#11718685	—	2	8	no	—
22	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊#1055	C₂²	1	2	yes	—
24	C₂×C₄⋊#1055	C₂²	1	2	yes	—
25	C₂×C₄⋊#1055	C₂²	1	2	yes	—
26	C₂×C₄⋊#1055	C₂²	1	2	yes	—
27	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
28	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊#1055	C₂²	1	2	yes	—
30	C₂×C₄⋊#1055	C₂²	1	2	yes	—
31	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
32	C₂×#88043	C₂²	1	2	yes	—
33	C₂×#88043	C₂²	1	2	yes	—
34	C₂×C₄×#1055	C₂²	1	2	yes	—
35	#11718116	C₂²	1	2	yes	—
36	#11718116	C₂²	1	2	yes	—
37	#11718116	C₂²	1	2	yes	—
38	C₂²×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
39	C₄×Q₈×C₁₃	D₄	1	4	yes	—
40	C₄×Q₈×C₁₃	Q₈	1	4	yes	—
41	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
42	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
43	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
44	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
45	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
46	C₂×C₁₃×C₄⋊C₄	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	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
52	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
53	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
54	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
55	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
56	C₂²×#1055	C₂³	1	2	yes	—
57	C₂²×#1055	C₂³	1	2	yes	—
58	C₂²×#1055	C₂³	1	2	yes	—
59	C₂²×#1055	C₂³	1	2	yes	—
60	C₁₃×#95	C₂×C₄	1	2	yes	—
61	C₁₃×#95	C₂×C₄	1	2	yes	—
62	C₁₃×#95	C₂×C₄	1	2	yes	—
63	C₁₃×#95	C₂×C₄	1	2	yes	—
64	C₁₃×#95	C₂×C₄	1	2	yes	—
65	C₁₃×#95	C₂×C₄	1	2	yes	—
66	C₁₃×#95	C₂×C₄	1	2	yes	—
67	C₄⋊#1055	—	2	4	no	—
68	C₄⋊#1055	—	2	4	no	—
69	C₄⋊#1055	—	2	4	no	—
70	C₄⋊#1055	—	2	2	no	—
71	C₄⋊#1055	—	2	4	no	—
72	C₄⋊#1055	—	4	1	no	—
73	C₄⋊#1055	—	4	1	no	—
74	C₄⋊#1055	—	4	2	no	—
75	C₄⋊#1055	—	4	2	no	—
76	C₄⋊#1055	Q₈	1	4	yes	complemented
77	#88043	—	2	4	no	—
78	#88043	—	2	4	no	—
79	C₄×#1055	—	2	4	no	—
80	#22723	—	13	1	no	maximal, Sylow
81	C₂×Q₈×C₁₃	—	4	1	no	—
82	C₂×Q₈×C₁₃	—	4	1	no	—
83	C₂×Q₈×C₁₃	C₄⋊C₄	1	4	yes	—
84	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
85	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
86	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
88	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
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	C₂⁴	1	1	yes	characteristic
95	C₁₃×C₄⋊C₄	—	2	4	no	—
96	C₁₃×C₄⋊C₄	—	4	1	no	—
97	C₁₃×C₄⋊C₄	—	4	1	no	—
98	C₁₃×C₄⋊C₄	—	4	2	no	—
99	C₁₃×C₄⋊C₄	C₄⋊C₄	1	8	yes	—
100	C₁₃×C₄⋊C₄	C₄⋊C₄	1	4	yes	—
101	C₄²×C₁₃	—	2	2	no	—
102	C₄²×C₁₃	—	2	1	no	—
103	C₄²×C₁₃	—	2	2	no	—
104	C₄²×C₁₃	—	2	1	no	—
105	C₄²×C₁₃	—	2	2	no	—
106	C₄²×C₁₃	—	4	1	no	—
107	C₄²×C₁₃	—	4	1	no	—
108	C₄²×C₁₃	—	4	1	no	—
109	C₄²×C₁₃	C₂×D₄	1	4	yes	—
110	C₄²×C₁₃	C₂×D₄	1	2	yes	—
111	C₄²×C₁₃	C₂×Q₈	1	4	yes	—
112	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
113	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
114	C₄²×C₁₃	#41	1	2	yes	—
115	C₂×#1055	—	2	2	no	—
116	C₂×#1055	—	2	2	no	—
117	C₂×#1055	—	2	2	no	—
118	C₂×#1055	—	2	2	no	—
119	C₂×#1055	—	2	2	no	—
120	C₂×#1055	—	2	2	no	—
121	C₂×#1055	—	2	2	no	—
122	C₂×#1055	—	2	2	no	—
123	C₂×#1055	—	2	2	no	—
124	C₂×#1055	—	2	2	no	—
125	C₂×#1055	—	2	2	no	—
126	C₂×#1055	C₂×Q₈	1	4	yes	—
127	C₂×#446	—	13	2	no	—
128	#2295	D₁₃	1	1	yes	characteristic
129	#1940	—	13	2	no	—
130	#1940	—	13	2	no	—
131	#1939	—	13	2	no	—
132	#1843	—	13	2	no	—
133	#1842	—	13	1	no	—
134	#1768	—	13	2	no	—
135	#1767	—	13	1	no	—
136	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
137	Q₈×C₁₃	—	4	4	no	—
138	C₂×C₄×C₁₃	—	2	1	no	—
139	C₂×C₄×C₁₃	—	2	1	no	—
140	C₂×C₄×C₁₃	—	2	1	no	—
141	C₂×C₄×C₁₃	—	2	2	no	—
142	C₂×C₄×C₁₃	—	2	1	no	—
143	C₂×C₄×C₁₃	—	2	1	no	—
144	C₂×C₄×C₁₃	—	2	1	no	—
145	C₂×C₄×C₁₃	—	2	1	no	—
146	C₂×C₄×C₁₃	—	2	1	no	—
147	C₂×C₄×C₁₃	—	2	1	no	—
148	C₂×C₄×C₁₃	—	2	1	no	—
149	C₂×C₄×C₁₃	—	2	2	no	—
150	C₂×C₄×C₁₃	—	2	2	no	—
151	C₂×C₄×C₁₃	—	2	2	no	—
152	C₂×C₄×C₁₃	—	2	2	no	—
153	C₂×C₄×C₁₃	—	2	2	no	—
154	C₂×C₄×C₁₃	—	2	1	no	—
155	C₂×C₄×C₁₃	—	2	2	no	—
156	C₂×C₄×C₁₃	—	2	1	no	—
157	C₂×C₄×C₁₃	—	2	1	no	—
158	C₂×C₄×C₁₃	—	2	2	no	—
159	C₂×C₄×C₁₃	—	2	2	no	—
160	C₂×C₄×C₁₃	—	2	2	no	—
161	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
162	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
163	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
164	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
165	C₂×C₄×C₁₃	C₄×Q₈	1	2	yes	—
166	C₂×C₄×C₁₃	C₄×Q₈	1	2	yes	—
167	C₂×C₄×C₁₃	#131	1	2	yes	—
168	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
170	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
171	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
172	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
173	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
174	#1055	—	2	4	no	—
175	#1055	—	4	2	no	—
176	#1055	—	4	2	no	—
177	#1055	—	4	2	no	—
178	C₂×C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic
179	#446	—	26	8	no	—
180	C₂×C₄⋊C₈	—	13	1	no	—
181	C₂×C₄⋊C₈	—	13	2	no	—
182	C₂×C₄⋊C₈	—	13	2	no	—
183	C₂×C₄⋊C₈	—	13	1	no	—
184	C₂×C₄⋊C₈	—	13	2	no	—
185	C₂×C₄⋊C₈	—	13	2	no	—
186	C₂×C₄⋊C₈	—	13	1	no	—
187	C₂×C₄⋊C₈	—	13	1	no	—
188	C₂×C₄⋊C₈	—	13	2	no	—
189	C₂×C₄⋊C₈	—	13	2	no	—
190	C₂×#97	—	13	2	no	—
191	C₂×#97	—	13	2	no	—
192	C₂×C₄×C₈	—	13	2	no	—
193	#391	Dic₁₃	1	1	yes	characteristic
194	#391	Dic₁₃	1	1	yes	characteristic
195	#389	Dic₁₃	1	1	yes	characteristic
196	#389	Dic₁₃	1	1	yes	characteristic
197	#387	Dic₁₃	1	2	yes	—
198	#387	Dic₁₃	1	2	yes	—
199	C₄×C₄⋊C₄	C₂×D₁₃	1	2	yes	—
200	C₄×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
201	#376	C₂×D₁₃	1	2	yes	—
202	C₄³	C₂×D₁₃	1	1	yes	characteristic
203	#336	—	13	2	no	—
204	#336	—	13	2	no	—
205	#336	—	13	2	no	—
206	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
207	C₂²×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
208	C₂²×C₁₃	#520	1	1	yes	characteristic
209	C₂²×C₁₃	C₂×#131	1	1	yes	characteristic
210	C₂²×C₁₃	#568	1	1	yes	characteristic
211	C₂²×C₁₃	#568	1	1	yes	characteristic
212	C₂²×C₁₃	#568	1	1	yes	characteristic
213	C₄×C₁₃	—	2	2	no	—
214	C₄×C₁₃	—	2	4	no	—
215	C₄×C₁₃	—	2	2	no	—
216	C₄×C₁₃	—	2	4	no	—
217	C₄×C₁₃	—	2	2	no	—
218	C₄×C₁₃	—	2	2	no	—
219	C₄×C₁₃	—	2	2	no	—
220	C₄×C₁₃	—	4	2	no	—
221	C₄×C₁₃	—	4	1	no	—
222	C₄×C₁₃	—	4	2	no	—
223	C₄×C₁₃	D₄×Q₈	1	1	yes	characteristic
224	C₄×C₁₃	#550	1	1	yes	characteristic
225	C₄×C₁₃	#557	1	1	yes	characteristic
226	C₄×C₁₃	Q₈²	1	1	yes	characteristic
227	C₂²×Q₈	C₂×Dic₁₃	1	1	yes	characteristic
228	C₂²×C₈	—	13	2	no	—
229	C₂²×C₈	—	13	2	no	—
230	C₂²×C₈	—	13	2	no	—
231	C₂²×C₈	—	13	2	no	—
232	C₄×Q₈	Dic₂₆	1	4	yes	—
233	C₄×Q₈	D₅₂	1	4	yes	—
234	C₂×C₄⋊C₄	C₂×Dic₁₃	1	2	yes	—
235	C₂×C₄⋊C₄	C₂×Dic₁₃	1	2	yes	—
236	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
237	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
238	C₂×C₄⋊C₄	C₂×Dic₁₃	1	2	yes	—
239	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
240	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
241	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
242	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
243	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
244	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
245	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
246	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
247	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
248	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
249	C₄⋊C₈	—	13	4	no	—
250	C₄⋊C₈	—	26	4	no	—
251	C₄⋊C₈	—	26	4	no	—
252	C₄⋊C₈	—	26	4	no	—
253	C₄⋊C₈	—	26	4	no	—
254	C₄⋊C₈	—	26	2	no	—
255	C₄⋊C₈	—	52	1	no	—
256	C₄⋊C₈	—	52	1	no	—
257	C₄⋊C₈	—	52	2	no	—
258	C₄⋊C₈	—	52	2	no	—
259	#97	—	26	4	no	—
260	#97	—	26	4	no	—
261	C₄×C₈	—	26	4	no	—
262	#95	C₂×Dic₁₃	1	2	yes	—
263	#95	C₂×Dic₁₃	1	2	yes	—
264	#95	C₂×Dic₁₃	1	2	yes	—
265	#95	C₂×Dic₁₃	1	2	yes	—
266	#95	C₂×Dic₁₃	1	2	yes	—
267	#95	C₂×Dic₁₃	1	2	yes	—
268	#95	C₂×Dic₁₃	1	2	yes	—
269	C₂×C₁₃	Q₈×C₄⋊C₄	1	1	yes	characteristic
270	C₂×C₁₃	#2905	1	1	yes	characteristic
271	C₂×C₁₃	#2906	1	1	yes	characteristic
272	C₂×C₁₃	#2961	1	1	yes	characteristic
273	C₂×C₁₃	#2962	1	1	yes	characteristic
274	C₂×C₁₃	#2992	1	1	yes	characteristic
275	C₂×C₁₃	#2995	1	1	yes	characteristic
276	C₂×Q₈	—	4	1	no	—
277	C₂×Q₈	—	4	1	no	—
278	C₂×Q₈	C₄⋊Dic₁₃	1	4	yes	—
279	C₂²×C₄	C₂²×Dic₁₃	1	2	yes	—
280	C₂²×C₄	C₂²×Dic₁₃	1	2	yes	—
281	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
282	C₂²×C₄	C₂²×Dic₁₃	1	2	yes	—
283	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
284	C₂²×C₄	C₂²×Dic₁₃	1	2	yes	—
285	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
286	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
287	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
288	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
289	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
290	C₂×C₈	—	13	4	no	—
291	C₂×C₈	—	26	2	no	—
292	C₂×C₈	—	26	2	no	—
293	C₂×C₈	—	26	2	no	—
294	C₂×C₈	—	26	2	no	—
295	C₂×C₈	—	26	2	no	—
296	C₂×C₈	—	26	2	no	—
297	C₂×C₈	—	26	2	no	—
298	C₂×C₈	—	26	2	no	—
299	C₂×C₈	—	26	2	no	—
300	C₂×C₈	—	26	2	no	—
301	C₂×C₈	—	26	2	no	—
302	C₄⋊C₄	—	2	4	no	—
303	C₄⋊C₄	—	4	1	no	—
304	C₄⋊C₄	—	4	1	no	—
305	C₄⋊C₄	—	4	2	no	—
306	C₄⋊C₄	C₄⋊Dic₁₃	1	8	yes	—
307	C₄⋊C₄	C₄⋊Dic₁₃	1	4	yes	—
308	C₄²	—	2	2	no	—
309	C₄²	—	2	1	no	—
310	C₄²	—	2	2	no	—
311	C₄²	—	2	1	no	—
312	C₄²	—	2	2	no	—
313	C₄²	—	4	1	no	—
314	C₄²	—	4	1	no	—
315	C₄²	—	4	1	no	—
316	C₄²	C₂×Dic₂₆	1	2	yes	—
317	C₄²	C₂×Dic₂₆	1	4	yes	—
318	C₄²	C₂×D₅₂	1	4	yes	—
319	C₄²	C₂×D₅₂	1	2	yes	—
320	C₄²	Q₈×D₁₃	1	2	yes	—
321	C₄²	#6131	1	2	yes	—
322	C₁₃	#22723	1	1	yes	characteristic, complemented, Sylow
323	C₂³	C₂³×Dic₁₃	1	1	yes	characteristic
324	Q₈	—	4	4	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	1	no	—
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	2	1	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	C₂×C₄⋊Dic₁₃	1	4	yes	—
349	C₂×C₄	C₂×C₄⋊Dic₁₃	1	2	yes	—
350	C₂×C₄	C₂×C₄⋊Dic₁₃	1	4	yes	—
351	C₂×C₄	C₂×C₄⋊Dic₁₃	1	2	yes	—
352	C₂×C₄	Q₈×Dic₁₃	1	2	yes	—
353	C₂×C₄	Q₈×Dic₁₃	1	2	yes	—
354	C₂×C₄	#88202	1	2	yes	—
355	C₂×C₄	C₂²×Dic₂₆	1	1	yes	characteristic
356	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
357	C₂×C₄	C₂×Q₈×D₁₃	1	1	yes	characteristic
358	C₂×C₄	C₂×#6131	1	1	yes	characteristic
359	C₂×C₄	#88256	1	1	yes	characteristic
360	C₂×C₄	#88257	1	1	yes	characteristic
361	C₈	—	26	4	no	—
362	C₈	—	52	2	no	—
363	C₈	—	52	2	no	—
364	C₈	—	52	2	no	—
365	C₂²	C₂²×C₄⋊Dic₁₃	1	1	yes	characteristic
366	C₂²	C₂×Q₈×Dic₁₃	1	1	yes	characteristic
367	C₂²	C₂×#88202	1	1	yes	characteristic
368	C₂²	#11719524	1	1	yes	characteristic
369	C₂²	#11719524	1	1	yes	characteristic
370	C₂²	#11719524	1	1	yes	characteristic
371	C₂²	#11719532	1	1	yes	characteristic
372	C₄	—	2	2	no	—
373	C₄	—	2	4	no	—
374	C₄	—	2	2	no	—
375	C₄	—	2	4	no	—
376	C₄	—	2	2	no	—
377	C₄	—	2	2	no	—
378	C₄	—	2	2	no	—
379	C₄	—	4	2	no	—
380	C₄	—	4	1	no	—
381	C₄	—	4	2	no	—
382	C₄	Q₈×Dic₂₆	1	1	yes	characteristic
383	C₄	#11719275	1	1	yes	characteristic
384	C₄	Q₈×D₅₂	1	1	yes	characteristic
385	C₄	#11719282	1	1	yes	characteristic
386	C₂	Q₈×C₄⋊Dic₁₃	1	1	yes	characteristic
387	C₂	#13123400	1	1	yes	characteristic
388	C₂	#13123404	1	1	yes	characteristic
389	C₂	#13123777	1	1	yes	characteristic
390	C₂	#13123785	1	1	yes	characteristic
391	C₂	#13123975	1	1	yes	characteristic
392	C₂	#13124006	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₁₃
commutator, socle, prime radical	C₂³×C₁₃	C₂³×C₄
Fitting	C₁₃×#2295	C₂
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	#2295	D₁₃
hypocenter	C₁₃	#22723
LCS	G ▷ C₂³×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ #2295

Complements

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

N	H ≅ G/N	type
76. C₄⋊#1055	Q₈	semidirect
322. C₁₃	#22723	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718685	2
#13115560	2
#13115555	2
#13114990	2
#13114988	2
#13114693	2
#13114689	2
C₁₃×#2295	2
#22723	13