Subgroups — #15881731

Order 3328.

832 conjugacy classes of subgroups.

The subgroup lattice has 376 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	4	yes	maximal
3	#13115555	C₂	1	2	yes	maximal
4	#13114988	C₂	1	2	yes	maximal
5	#13114988	C₂	1	1	yes	maximal, characteristic
6	#13114689	C₂	1	2	yes	maximal
7	C₄×C₄⋊#1055	C₂	1	1	yes	maximal, characteristic
8	C₄²×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic
9	C₂×C₄×Q₈×C₁₃	C₄	1	1	yes	characteristic
10	C₂×C₄×Q₈×C₁₃	C₄	1	1	yes	characteristic
11	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
12	C₄×C₁₃×C₄⋊C₄	C₄	1	2	yes	—
13	C₄×C₁₃×C₄⋊C₄	C₄	1	1	yes	characteristic
14	C₄×C₁₃×C₄⋊C₄	C₄	1	1	yes	characteristic
15	C₄×C₁₃×C₄⋊C₄	C₄	1	2	yes	—
16	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
18	C₄³×C₁₃	C₂²	1	1	yes	characteristic
19	C₄³×C₁₃	C₂²	1	2	yes	—
20	#11718685	—	2	8	no	—
21	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊#1055	C₂²	1	2	yes	—
23	C₂×C₄⋊#1055	C₂²	1	2	yes	—
24	C₂×C₄⋊#1055	C₂²	1	4	yes	—
25	C₂×C₄⋊#1055	C₂²	1	4	yes	—
26	C₂×C₄⋊#1055	C₂²	1	2	yes	—
27	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
28	C₂×#88043	C₂²	1	4	yes	—
29	C₂×C₄×#1055	C₂²	1	2	yes	—
30	#11718116	C₂²	1	2	yes	—
31	#11718116	C₂²	1	4	yes	—
32	C₂²×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
33	C₄×Q₈×C₁₃	—	2	4	no	—
34	C₄×Q₈×C₁₃	—	2	4	no	—
35	C₄×Q₈×C₁₃	D₄	1	4	yes	—
36	C₄×Q₈×C₁₃	Q₈	1	4	yes	—
37	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
38	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
39	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
40	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
41	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
42	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
45	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
46	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
48	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
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	2	yes	—
52	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
53	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
54	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
55	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
56	C₂²×#1055	C₂³	1	2	yes	—
57	C₂²×#1055	C₂³	1	4	yes	—
58	C₂²×#1055	C₂³	1	2	yes	—
59	C₁₃×#95	C₂×C₄	1	2	yes	—
60	C₁₃×#95	C₂×C₄	1	2	yes	—
61	C₁₃×#95	C₂×C₄	1	2	yes	—
62	C₄⋊#1055	—	2	8	no	—
63	C₄⋊#1055	—	2	4	no	—
64	C₄⋊#1055	—	2	2	no	—
65	C₄⋊#1055	—	2	4	no	—
66	C₄⋊#1055	—	4	4	no	—
67	C₄⋊#1055	—	4	2	no	—
68	C₄⋊#1055	Q₈	1	4	yes	complemented
69	#88043	—	2	8	no	—
70	C₄×#1055	—	2	4	no	—
71	#22722	—	13	1	no	maximal, Sylow
72	C₂×Q₈×C₁₃	—	2	2	no	—
73	C₂×Q₈×C₁₃	—	2	2	no	—
74	C₂×Q₈×C₁₃	C₄⋊C₄	1	4	yes	—
75	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
76	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
77	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
79	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
80	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
82	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
86	C₁₃×C₄⋊C₄	—	2	4	no	—
87	C₁₃×C₄⋊C₄	—	2	4	no	—
88	C₁₃×C₄⋊C₄	—	2	2	no	—
89	C₁₃×C₄⋊C₄	C₄⋊C₄	1	8	yes	—
90	C₁₃×C₄⋊C₄	C₄⋊C₄	1	4	yes	—
91	C₁₃×C₄⋊C₄	M₁₆	1	4	yes	—
92	C₄²×C₁₃	—	2	4	no	—
93	C₄²×C₁₃	—	2	2	no	—
94	C₄²×C₁₃	—	2	4	no	—
95	C₄²×C₁₃	—	2	4	no	—
96	C₄²×C₁₃	—	2	2	no	—
97	C₄²×C₁₃	—	2	1	no	—
98	C₄²×C₁₃	—	2	2	no	—
99	C₄²×C₁₃	—	2	1	no	—
100	C₄²×C₁₃	—	2	2	no	—
101	C₄²×C₁₃	—	4	1	no	—
102	C₄²×C₁₃	—	4	2	no	—
103	C₄²×C₁₃	M₁₆	1	4	yes	—
104	C₄²×C₁₃	C₂×D₄	1	2	yes	—
105	C₄²×C₁₃	C₂×D₄	1	4	yes	—
106	C₄²×C₁₃	C₂×Q₈	1	4	yes	—
107	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
108	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
109	C₄²×C₁₃	#41	1	2	yes	—
110	C₂×#1055	—	2	2	no	—
111	C₂×#1055	—	2	2	no	—
112	C₂×#1055	—	2	2	no	—
113	C₂×#1055	—	2	4	no	—
114	C₂×#1055	—	2	2	no	—
115	C₂×#1055	—	2	4	no	—
116	C₂×#1055	—	2	2	no	—
117	C₂×#1055	—	2	4	no	—
118	C₂×#1055	C₂×Q₈	1	4	yes	—
119	C₂×#446	—	13	2	no	—
120	C₄²×Q₈	D₁₃	1	1	yes	characteristic
121	#1940	—	13	4	no	—
122	#1939	—	13	2	no	—
123	#1842	—	13	1	no	—
124	#1842	—	13	2	no	—
125	#1767	—	13	2	no	—
126	C₄×C₄⋊C₈	—	13	1	no	—
127	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
128	Q₈×C₁₃	—	2	8	no	—
129	C₂×C₄×C₁₃	—	2	1	no	—
130	C₂×C₄×C₁₃	—	2	2	no	—
131	C₂×C₄×C₁₃	—	2	1	no	—
132	C₂×C₄×C₁₃	—	2	2	no	—
133	C₂×C₄×C₁₃	—	2	2	no	—
134	C₂×C₄×C₁₃	—	2	2	no	—
135	C₂×C₄×C₁₃	—	2	1	no	—
136	C₂×C₄×C₁₃	—	2	2	no	—
137	C₂×C₄×C₁₃	—	2	1	no	—
138	C₂×C₄×C₁₃	—	2	1	no	—
139	C₂×C₄×C₁₃	—	2	2	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	2	no	—
144	C₂×C₄×C₁₃	—	2	1	no	—
145	C₂×C₄×C₁₃	—	2	1	no	—
146	C₂×C₄×C₁₃	—	2	2	no	—
147	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
148	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
149	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
150	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
151	C₂×C₄×C₁₃	C₄×Q₈	1	2	yes	—
152	C₂×C₄×C₁₃	C₄×Q₈	1	2	yes	—
153	C₂×C₄×C₁₃	C₂×M₁₆	1	4	yes	—
154	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
155	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
156	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
157	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
158	C₂×C₄×C₁₃	#131	1	2	yes	—
159	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
160	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
161	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
162	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
163	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
164	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
165	#1055	—	2	4	no	—
166	#1055	—	4	2	no	—
167	#1055	—	4	4	no	—
168	C₂×C₄×Q₈	Dic₁₃	1	1	yes	characteristic
169	C₂×C₄×Q₈	Dic₁₃	1	1	yes	characteristic
170	C₂×C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic
171	#446	—	26	8	no	—
172	C₂×C₄⋊C₈	—	13	1	no	—
173	C₂×C₄⋊C₈	—	13	1	no	—
174	C₂×C₄⋊C₈	—	13	2	no	—
175	C₂×C₄⋊C₈	—	13	2	no	—
176	C₂×C₄⋊C₈	—	13	4	no	—
177	C₂×C₄⋊C₈	—	13	4	no	—
178	C₂×C₄⋊C₈	—	13	2	no	—
179	C₂×#97	—	13	4	no	—
180	C₂×C₄×C₈	—	13	2	no	—
181	C₄×C₄⋊C₄	Dic₁₃	1	2	yes	—
182	C₄×C₄⋊C₄	Dic₁₃	1	1	yes	characteristic
183	C₄×C₄⋊C₄	Dic₁₃	1	2	yes	—
184	C₄×C₄⋊C₄	Dic₁₃	1	1	yes	characteristic
185	C₄×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
186	C₄×C₄⋊C₄	C₂×D₁₃	1	2	yes	—
187	C₄³	C₂×D₁₃	1	1	yes	characteristic
188	C₄³	C₂×D₁₃	1	2	yes	—
189	#336	—	13	4	no	—
190	#336	—	13	2	no	—
191	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
192	C₂²×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
193	C₂²×C₁₃	#520	1	1	yes	characteristic
194	C₂²×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
195	C₂²×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
196	C₂²×C₁₃	C₂×#131	1	1	yes	characteristic
197	C₂²×C₁₃	#568	1	1	yes	characteristic
198	C₄×C₁₃	—	2	4	no	—
199	C₄×C₁₃	—	2	2	no	—
200	C₄×C₁₃	—	2	4	no	—
201	C₄×C₁₃	—	2	2	no	—
202	C₄×C₁₃	—	2	2	no	—
203	C₄×C₁₃	—	2	4	no	—
204	C₄×C₁₃	—	4	2	no	—
205	C₄×C₁₃	—	4	1	no	—
206	C₄×C₁₃	#423	1	4	yes	—
207	C₄×C₁₃	#446	1	4	yes	complemented
208	C₄×C₁₃	D₄×Q₈	1	1	yes	characteristic
209	C₄×C₁₃	#550	1	1	yes	characteristic
210	C₄×C₁₃	#557	1	1	yes	characteristic
211	C₄×C₁₃	Q₈²	1	1	yes	characteristic
212	C₂²×Q₈	C₂×Dic₁₃	1	1	yes	characteristic
213	C₂²×C₈	—	13	2	no	—
214	C₂²×C₈	—	13	2	no	—
215	C₂²×C₈	—	13	4	no	—
216	C₄×Q₈	—	2	4	no	—
217	C₄×Q₈	—	2	4	no	—
218	C₄×Q₈	Dic₂₆	1	4	yes	—
219	C₄×Q₈	D₅₂	1	4	yes	—
220	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
221	C₂×C₄⋊C₄	C₂×Dic₁₃	1	2	yes	—
222	C₂×C₄⋊C₄	C₂×Dic₁₃	1	2	yes	—
223	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
224	C₂×C₄⋊C₄	C₂×Dic₁₃	1	2	yes	—
225	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
226	C₂×C₄²	C₂×Dic₁₃	1	2	yes	—
227	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
228	C₂×C₄²	C₂×Dic₁₃	1	2	yes	—
229	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
230	C₂×C₄²	C₂×Dic₁₃	1	2	yes	—
231	C₂×C₄²	C₂×Dic₁₃	1	2	yes	—
232	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
233	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
234	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
235	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
236	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
237	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
238	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
239	C₄⋊C₈	—	13	4	no	—
240	C₄⋊C₈	—	26	4	no	—
241	C₄⋊C₈	—	26	8	no	—
242	C₄⋊C₈	—	26	2	no	—
243	C₄⋊C₈	—	26	4	no	—
244	C₄⋊C₈	—	52	4	no	—
245	C₄⋊C₈	—	52	2	no	—
246	#97	—	26	8	no	—
247	C₄×C₈	—	26	4	no	—
248	#95	C₂×Dic₁₃	1	2	yes	—
249	#95	C₂×Dic₁₃	1	2	yes	—
250	#95	C₂×Dic₁₃	1	2	yes	—
251	C₂×C₁₃	Q₈×C₄⋊C₄	1	1	yes	characteristic
252	C₂×C₁₃	C₂×#423	1	1	yes	characteristic
253	C₂×C₁₃	#2906	1	1	yes	characteristic
254	C₂×C₁₃	C₂×#446	1	1	yes	characteristic
255	C₂×C₁₃	Q₈×M₁₆	1	1	yes	characteristic
256	C₂×C₁₃	#2989	1	1	yes	characteristic
257	C₂×C₁₃	#2990	1	1	yes	characteristic
258	C₂×Q₈	—	2	2	no	—
259	C₂×Q₈	—	2	2	no	—
260	C₂×Q₈	C₄⋊Dic₁₃	1	4	yes	—
261	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
262	C₂²×C₄	C₂²×Dic₁₃	1	2	yes	—
263	C₂²×C₄	C₂²×Dic₁₃	1	2	yes	—
264	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
265	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
266	C₂²×C₄	C₂²×Dic₁₃	1	2	yes	—
267	C₂²×C₄	C₂²×Dic₁₃	1	2	yes	—
268	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
269	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
270	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
271	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
272	C₂×C₈	—	13	4	no	—
273	C₂×C₈	—	26	2	no	—
274	C₂×C₈	—	26	2	no	—
275	C₂×C₈	—	26	2	no	—
276	C₂×C₈	—	26	4	no	—
277	C₂×C₈	—	26	2	no	—
278	C₂×C₈	—	26	4	no	—
279	C₂×C₈	—	26	2	no	—
280	C₂×C₈	—	26	4	no	—
281	C₄⋊C₄	—	2	4	no	—
282	C₄⋊C₄	—	2	4	no	—
283	C₄⋊C₄	—	2	2	no	—
284	C₄⋊C₄	#6099	1	4	yes	—
285	C₄⋊C₄	C₄⋊Dic₁₃	1	8	yes	—
286	C₄⋊C₄	C₄⋊Dic₁₃	1	4	yes	—
287	C₄²	—	2	4	no	—
288	C₄²	—	2	2	no	—
289	C₄²	—	2	4	no	—
290	C₄²	—	2	4	no	—
291	C₄²	—	2	2	no	—
292	C₄²	—	2	1	no	—
293	C₄²	—	2	2	no	—
294	C₄²	—	2	1	no	—
295	C₄²	—	2	2	no	—
296	C₄²	—	4	1	no	—
297	C₄²	—	4	2	no	—
298	C₄²	#6099	1	4	yes	—
299	C₄²	C₂×Dic₂₆	1	4	yes	—
300	C₄²	C₂×Dic₂₆	1	2	yes	—
301	C₄²	C₂×D₅₂	1	2	yes	—
302	C₄²	C₂×D₅₂	1	4	yes	—
303	C₄²	Q₈×D₁₃	1	2	yes	—
304	C₄²	#6131	1	2	yes	—
305	C₁₃	#22722	1	1	yes	characteristic, complemented, Sylow
306	C₂³	C₂³×Dic₁₃	1	1	yes	characteristic
307	Q₈	—	2	8	no	—
308	C₂×C₄	—	2	1	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	1	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	1	no	—
315	C₂×C₄	—	2	1	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	1	no	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	1	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	C₂×#6099	1	4	yes	—
327	C₂×C₄	C₂×#6099	1	2	yes	—
328	C₂×C₄	C₂×#6099	1	2	yes	—
329	C₂×C₄	C₂×#6099	1	2	yes	—
330	C₂×C₄	C₂×#6099	1	2	yes	—
331	C₂×C₄	C₂×C₄⋊Dic₁₃	1	2	yes	—
332	C₂×C₄	C₂×C₄⋊Dic₁₃	1	4	yes	—
333	C₂×C₄	C₂×C₄⋊Dic₁₃	1	4	yes	—
334	C₂×C₄	C₂×C₄⋊Dic₁₃	1	2	yes	—
335	C₂×C₄	Q₈×Dic₁₃	1	2	yes	—
336	C₂×C₄	Q₈×Dic₁₃	1	2	yes	—
337	C₂×C₄	#88202	1	2	yes	—
338	C₂×C₄	C₂²×Dic₂₆	1	1	yes	characteristic
339	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
340	C₂×C₄	C₂×Q₈×D₁₃	1	1	yes	characteristic
341	C₂×C₄	C₂×#6131	1	1	yes	characteristic
342	C₂×C₄	#88256	1	1	yes	characteristic
343	C₂×C₄	#88257	1	1	yes	characteristic
344	C₈	—	26	4	no	—
345	C₈	—	52	2	no	—
346	C₈	—	52	4	no	—
347	C₂²	C₂²×#6099	1	1	yes	characteristic
348	C₂²	C₂²×#6099	1	1	yes	characteristic
349	C₂²	C₂²×C₄⋊Dic₁₃	1	1	yes	characteristic
350	C₂²	C₂×Q₈×Dic₁₃	1	1	yes	characteristic
351	C₂²	C₂×#88202	1	1	yes	characteristic
352	C₂²	#11719524	1	1	yes	characteristic
353	C₂²	#11719532	1	1	yes	characteristic
354	C₄	—	2	4	no	—
355	C₄	—	2	2	no	—
356	C₄	—	2	4	no	—
357	C₄	—	2	2	no	—
358	C₄	—	2	4	no	—
359	C₄	—	2	2	no	—
360	C₄	—	4	2	no	—
361	C₄	—	4	1	no	—
362	C₄	#11718585	1	4	yes	—
363	C₄	#11718685	1	4	yes	complemented
364	C₄	Q₈×Dic₂₆	1	1	yes	characteristic
365	C₄	#11719275	1	1	yes	characteristic
366	C₄	Q₈×D₅₂	1	1	yes	characteristic
367	C₄	#11719282	1	1	yes	characteristic
368	C₂	Q₈×C₄⋊Dic₁₃	1	1	yes	characteristic
369	C₂	C₂×#11718585	1	1	yes	characteristic
370	C₂	#13123404	1	1	yes	characteristic
371	C₂	C₂×#11718685	1	1	yes	characteristic
372	C₂	Q₈×#6099	1	1	yes	characteristic
373	C₂	#13123953	1	1	yes	characteristic
374	C₂	#13123961	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₁₃
commutator, socle, prime radical	C₂³×C₁₃	C₂³×C₄
Fitting	C₄²×Q₈×C₁₃	C₂
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	C₄²×Q₈	D₁₃
hypocenter	C₁₃	#22722
LCS	G ▷ C₂³×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₄²×Q₈

Complements

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

N	H ≅ G/N	type
68. C₄⋊#1055	Q₈	semidirect
207. C₄×C₁₃	#446	semidirect
305. C₁₃	#22722	semidirect
363. C₄	#11718685	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
#13114988	2
#13114689	2
C₄×C₄⋊#1055	2
C₄²×Q₈×C₁₃	2
#22722	13