Subgroups — D₄×C₁₃×#106 #15708992

Order 3328.

1126 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₃×#106	C₂	1	2	yes	maximal, complemented
3	D₄×C₁₃×C₄⋊C₄	C₂	1	2	yes	maximal
4	C₁₃×#1948	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1853	C₂	1	4	yes	maximal, complemented
6	C₁₃×#1844	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1807	C₂	1	2	yes	maximal, complemented
8	C₄×C₁₃×#106	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×C₈×C₁₃	C₂²	1	2	yes	—
10	C₂×C₄×D₄×C₁₃	—	2	2	no	—
11	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
12	C₂²×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
13	C₈×D₄×C₁₃	C₄	1	8	yes	complemented
14	C₂×C₁₃×#106	—	2	8	no	—
15	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×#106	C₂²	1	2	yes	—
17	C₂×C₁₃×#106	C₂²	1	4	yes	—
18	C₂×C₁₃×#106	C₂²	1	2	yes	—
19	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
22	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
23	C₁₃×#389	—	2	2	no	—
24	C₁₃×#385	—	2	4	no	—
25	C₁₃×#384	C₂²	1	2	yes	—
26	C₁₃×#380	C₂²	1	4	yes	—
27	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
28	C₁₃×#340	C₂²	1	2	yes	—
29	C₁₃×#340	C₂²	1	4	yes	—
30	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
31	C₂³×C₄×C₁₃	—	2	4	no	—
32	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
33	C₂²×C₈×C₁₃	—	2	4	no	—
34	C₂²×C₈×C₁₃	—	2	4	no	—
35	C₂²×C₈×C₁₃	C₂×C₄	1	8	yes	complemented
36	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
37	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
38	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
39	C₄×D₄×C₁₃	—	4	8	no	—
40	C₄×D₄×C₁₃	C₂×C₄	1	4	yes	—
41	C₄×D₄×C₁₃	Q₈	1	4	yes	—
42	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
43	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
44	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
45	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
46	C₂×C₁₃×C₄⋊C₄	—	4	4	no	—
47	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
48	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
49	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
50	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
51	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
52	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
53	C₂×C₄²×C₁₃	—	2	2	no	—
54	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
55	C₁₃×#106	—	2	4	no	—
56	C₁₃×#106	—	2	2	no	—
57	C₁₃×#106	—	2	8	no	—
58	C₁₃×#106	—	4	2	no	—
59	C₁₃×#106	D₄	1	4	yes	direct product factor
60	C₁₃×C₄⋊C₈	C₂×C₄	1	4	yes	complemented
61	C₁₃×C₂²⋊C₈	C₂×C₄	1	8	yes	complemented
62	C₄×C₈×C₁₃	C₂×C₄	1	4	yes	complemented
63	C₁₃×#95	—	2	2	no	—
64	C₁₃×#95	—	2	4	no	—
65	D₄×#106	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
66	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
67	C₂×D₄×C₁₃	C₄⋊C₄	1	4	yes	—
68	C₂×D₄×C₁₃	SD₁₆	1	8	yes	—
69	C₂²×C₄×C₁₃	—	2	2	no	—
70	C₂²×C₄×C₁₃	—	2	2	no	—
71	C₂²×C₄×C₁₃	—	2	2	no	—
72	C₂²×C₄×C₁₃	—	2	2	no	—
73	C₂²×C₄×C₁₃	—	2	2	no	—
74	C₂²×C₄×C₁₃	—	2	2	no	—
75	C₂²×C₄×C₁₃	—	2	4	no	—
76	C₂²×C₄×C₁₃	—	4	8	no	—
77	C₂²×C₄×C₁₃	—	4	8	no	—
78	C₂²×C₄×C₁₃	—	8	4	no	—
79	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
80	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
82	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₃	C₂×Q₈	1	4	yes	—
84	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
85	C₂×C₈×C₁₃	—	2	2	no	—
86	C₂×C₈×C₁₃	—	2	2	no	—
87	C₂×C₈×C₁₃	—	2	1	no	—
88	C₂×C₈×C₁₃	—	2	1	no	—
89	C₂×C₈×C₁₃	—	2	16	no	—
90	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
91	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
92	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
93	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
94	C₂×C₈×C₁₃	#41	1	2	yes	—
95	C₁₃×C₄⋊C₄	—	2	2	no	—
96	C₁₃×C₄⋊C₄	—	2	4	no	—
97	C₁₃×C₄⋊C₄	—	2	2	no	—
98	C₁₃×C₄⋊C₄	—	2	4	no	—
99	C₁₃×C₄⋊C₄	—	2	2	no	—
100	C₁₃×C₄⋊C₄	—	4	8	no	—
101	C₁₃×C₄⋊C₄	—	4	4	no	—
102	C₁₃×C₄⋊C₄	—	8	2	no	—
103	C₁₃×C₄⋊C₄	C₄⋊C₄	1	4	yes	—
104	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
105	C₁₃×C₂²⋊C₄	—	4	8	no	—
106	C₁₃×C₂²⋊C₄	C₄⋊C₄	1	8	yes	—
107	C₄²×C₁₃	—	4	4	no	—
108	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
109	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
110	C₂×C₈×D₄	C₂×C₁₃	1	1	yes	characteristic
111	C₂²×#106	C₂×C₁₃	1	2	yes	complemented
112	D₄×C₄⋊C₄	C₂×C₁₃	1	2	yes	—
113	#1948	C₂×C₁₃	1	2	yes	complemented
114	#1853	C₂×C₁₃	1	4	yes	complemented
115	#1844	C₂×C₁₃	1	1	yes	characteristic, complemented
116	#1807	C₂×C₁₃	1	2	yes	complemented
117	C₄×#106	C₂×C₁₃	1	1	yes	characteristic, complemented
118	C₂³×C₁₃	—	2	2	no	—
119	C₂³×C₁₃	—	2	2	no	—
120	C₂³×C₁₃	—	2	4	no	—
121	C₂³×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
122	C₂³×C₁₃	C₂×SD₁₆	1	8	yes	—
123	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
124	D₄×C₁₃	#106	1	16	yes	direct product factor
125	C₂×C₄×C₁₃	—	2	2	no	—
126	C₂×C₄×C₁₃	—	2	2	no	—
127	C₂×C₄×C₁₃	—	2	2	no	—
128	C₂×C₄×C₁₃	—	2	4	no	—
129	C₂×C₄×C₁₃	—	2	4	no	—
130	C₂×C₄×C₁₃	—	2	4	no	—
131	C₂×C₄×C₁₃	—	2	4	no	—
132	C₂×C₄×C₁₃	—	2	4	no	—
133	C₂×C₄×C₁₃	—	4	2	no	—
134	C₂×C₄×C₁₃	—	4	2	no	—
135	C₂×C₄×C₁₃	—	4	4	no	—
136	C₂×C₄×C₁₃	—	4	2	no	—
137	C₂×C₄×C₁₃	—	4	2	no	—
138	C₂×C₄×C₁₃	—	4	4	no	—
139	C₂×C₄×C₁₃	—	4	4	no	—
140	C₂×C₄×C₁₃	—	4	2	no	—
141	C₂×C₄×C₁₃	—	8	16	no	—
142	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
143	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
144	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
145	C₂×C₄×C₁₃	C₂×SD₁₆	1	4	yes	—
146	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
147	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
148	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
149	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
150	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
151	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
152	C₈×C₁₃	—	2	4	no	—
153	C₈×C₁₃	—	2	2	no	—
154	C₈×C₁₃	C₄×D₄	1	4	yes	complemented
155	C₂³×C₈	C₂²×C₁₃	1	2	yes	—
156	C₂×C₄×D₄	—	2	2	no	—
157	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
158	C₂²×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
159	C₈×D₄	C₄×C₁₃	1	8	yes	complemented
160	C₂×#106	—	2	8	no	—
161	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
162	C₂×#106	C₂²×C₁₃	1	2	yes	—
163	C₂×#106	C₂²×C₁₃	1	4	yes	—
164	C₂×#106	C₂²×C₁₃	1	2	yes	—
165	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
166	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
167	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
168	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
169	#389	—	2	2	no	—
170	#385	—	2	4	no	—
171	#384	C₂²×C₁₃	1	2	yes	—
172	#380	C₂²×C₁₃	1	4	yes	—
173	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
174	#340	C₂²×C₁₃	1	4	yes	—
175	#340	C₂²×C₁₃	1	2	yes	—
176	C₂²×C₁₃	—	2	8	no	—
177	C₂²×C₁₃	—	2	4	no	—
178	C₂²×C₁₃	—	2	4	no	—
179	C₂²×C₁₃	—	2	8	no	—
180	C₂²×C₁₃	C₂×#106	1	8	yes	complemented
181	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
182	C₂²×C₁₃	D₄²	1	1	yes	characteristic
183	C₂²×C₁₃	#547	1	1	yes	characteristic
184	C₂²×C₁₃	C₂²×SD₁₆	1	2	yes	—
185	C₂²×C₁₃	#577	1	2	yes	—
186	C₄×C₁₃	—	2	4	no	—
187	C₄×C₁₃	—	2	2	no	—
188	C₄×C₁₃	—	4	4	no	—
189	C₄×C₁₃	—	8	2	no	—
190	C₄×C₁₃	—	8	4	no	—
191	C₄×C₁₃	C₂×#106	1	4	yes	complemented
192	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
193	C₄×C₁₃	#520	1	1	yes	characteristic
194	C₄×C₁₃	D₄×Q₈	1	1	yes	characteristic
195	C₄×C₁₃	#554	1	1	yes	characteristic
196	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
197	C₂³×C₄	—	2	4	no	—
198	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
199	C₂²×C₈	—	2	4	no	—
200	C₂²×C₈	—	2	4	no	—
201	C₂²×C₈	C₂×C₄×C₁₃	1	8	yes	complemented
202	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
203	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
204	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
205	C₄×D₄	—	4	8	no	—
206	C₄×D₄	C₂×C₄×C₁₃	1	4	yes	—
207	C₄×D₄	Q₈×C₁₃	1	4	yes	—
208	C₂×C₄⋊C₄	—	2	8	no	—
209	C₂×C₄⋊C₄	—	2	4	no	—
210	C₂×C₄⋊C₄	—	2	2	no	—
211	C₂×C₄⋊C₄	—	2	2	no	—
212	C₂×C₄⋊C₄	—	4	4	no	—
213	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
214	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
215	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
216	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
217	C₂×C₂²⋊C₄	—	2	4	no	—
218	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
219	C₂×C₄²	—	2	2	no	—
220	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
221	#106	—	2	4	no	—
222	#106	—	2	2	no	—
223	#106	—	2	8	no	—
224	#106	—	4	2	no	—
225	#106	D₄×C₁₃	1	4	yes	direct product factor
226	C₄⋊C₈	C₂×C₄×C₁₃	1	4	yes	complemented
227	C₂²⋊C₈	C₂×C₄×C₁₃	1	8	yes	complemented
228	C₄×C₈	C₂×C₄×C₁₃	1	4	yes	complemented
229	#95	—	2	2	no	—
230	#95	—	2	4	no	—
231	C₂×C₁₃	—	2	8	no	—
232	C₂×C₁₃	D₄×C₄⋊C₄	1	1	yes	characteristic
233	C₂×C₁₃	C₂²×#106	1	1	yes	characteristic
234	C₂×C₁₃	#2912	1	1	yes	characteristic
235	C₂×C₁₃	D₄×SD₁₆	1	2	yes	—
236	C₂×C₁₃	#3335	1	2	yes	—
237	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
238	C₂×D₄	C₁₃×C₄⋊C₄	1	4	yes	—
239	C₂×D₄	C₁₃×SD₁₆	1	8	yes	—
240	C₂²×C₄	—	2	2	no	—
241	C₂²×C₄	—	2	2	no	—
242	C₂²×C₄	—	2	2	no	—
243	C₂²×C₄	—	2	2	no	—
244	C₂²×C₄	—	2	2	no	—
245	C₂²×C₄	—	2	2	no	—
246	C₂²×C₄	—	2	4	no	—
247	C₂²×C₄	—	4	8	no	—
248	C₂²×C₄	—	4	8	no	—
249	C₂²×C₄	—	8	4	no	—
250	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
251	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
252	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
253	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
254	C₂²×C₄	C₂×Q₈×C₁₃	1	4	yes	—
255	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
256	C₂×C₈	—	2	2	no	—
257	C₂×C₈	—	2	2	no	—
258	C₂×C₈	—	2	1	no	—
259	C₂×C₈	—	2	1	no	—
260	C₂×C₈	—	2	16	no	—
261	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
262	C₂×C₈	C₂²×C₄×C₁₃	1	4	yes	—
263	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
264	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
265	C₂×C₈	C₁₃×#41	1	2	yes	—
266	C₄⋊C₄	—	2	2	no	—
267	C₄⋊C₄	—	2	4	no	—
268	C₄⋊C₄	—	2	2	no	—
269	C₄⋊C₄	—	2	4	no	—
270	C₄⋊C₄	—	2	2	no	—
271	C₄⋊C₄	—	4	8	no	—
272	C₄⋊C₄	—	4	4	no	—
273	C₄⋊C₄	—	8	2	no	—
274	C₄⋊C₄	C₁₃×C₄⋊C₄	1	4	yes	—
275	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
276	C₂²⋊C₄	—	4	8	no	—
277	C₂²⋊C₄	C₁₃×C₄⋊C₄	1	8	yes	—
278	C₄²	—	4	4	no	—
279	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
280	C₄²	C₂×Q₈×C₁₃	1	2	yes	—
281	C₁₃	D₄×#106	1	1	yes	characteristic, direct product factor, Sylow
282	C₂³	—	2	2	no	—
283	C₂³	—	2	2	no	—
284	C₂³	—	2	4	no	—
285	C₂³	C₂×C₁₃×C₄⋊C₄	1	4	yes	—
286	C₂³	C₂×C₁₃×SD₁₆	1	8	yes	—
287	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
288	D₄	C₁₃×#106	1	16	yes	direct product factor
289	C₂×C₄	—	2	2	no	—
290	C₂×C₄	—	2	2	no	—
291	C₂×C₄	—	2	2	no	—
292	C₂×C₄	—	2	4	no	—
293	C₂×C₄	—	2	4	no	—
294	C₂×C₄	—	2	4	no	—
295	C₂×C₄	—	2	4	no	—
296	C₂×C₄	—	2	4	no	—
297	C₂×C₄	—	4	2	no	—
298	C₂×C₄	—	4	2	no	—
299	C₂×C₄	—	4	4	no	—
300	C₂×C₄	—	4	2	no	—
301	C₂×C₄	—	4	2	no	—
302	C₂×C₄	—	4	4	no	—
303	C₂×C₄	—	4	4	no	—
304	C₂×C₄	—	4	2	no	—
305	C₂×C₄	—	8	16	no	—
306	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	2	yes	—
307	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	4	yes	—
308	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	2	yes	—
309	C₂×C₄	C₂×C₁₃×SD₁₆	1	4	yes	—
310	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
311	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
312	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
313	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
314	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
315	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
316	C₈	—	2	4	no	—
317	C₈	—	2	2	no	—
318	C₈	C₄×D₄×C₁₃	1	4	yes	complemented
319	C₂²	—	2	8	no	—
320	C₂²	—	2	8	no	—
321	C₂²	—	2	4	no	—
322	C₂²	—	2	4	no	—
323	C₂²	C₂×C₁₃×#106	1	8	yes	complemented
324	C₂²	C₂²×C₁₃×C₄⋊C₄	1	1	yes	characteristic
325	C₂²	D₄²×C₁₃	1	1	yes	characteristic
326	C₂²	C₁₃×#547	1	1	yes	characteristic
327	C₂²	C₂²×C₁₃×SD₁₆	1	2	yes	—
328	C₂²	C₁₃×#577	1	2	yes	—
329	C₄	—	2	4	no	—
330	C₄	—	2	2	no	—
331	C₄	—	4	4	no	—
332	C₄	—	8	4	no	—
333	C₄	—	8	2	no	—
334	C₄	C₂×C₁₃×#106	1	4	yes	complemented
335	C₄	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
336	C₄	C₁₃×#520	1	1	yes	characteristic
337	C₄	D₄×Q₈×C₁₃	1	1	yes	characteristic
338	C₄	C₁₃×#554	1	1	yes	characteristic
339	C₂	—	2	8	no	—
340	C₂	D₄×C₁₃×C₄⋊C₄	1	1	yes	characteristic
341	C₂	C₂²×C₁₃×#106	1	1	yes	characteristic
342	C₂	C₁₃×#2912	1	1	yes	characteristic
343	C₂	D₄×C₁₃×SD₁₆	1	2	yes	—
344	C₂	C₁₃×#3335	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×D₄×C₁₃	D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄×D₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₁₃×#106	C₂	semidirect
4. C₁₃×#1948	C₂	semidirect
5. C₁₃×#1853	C₂	semidirect
6. C₁₃×#1844	C₂	semidirect
7. C₁₃×#1807	C₂	semidirect
8. C₄×C₁₃×#106	C₂	semidirect
13. C₈×D₄×C₁₃	C₄	semidirect
35. C₂²×C₈×C₁₃	C₂×C₄	semidirect
59. C₁₃×#106	D₄	direct (N × H)
60. C₁₃×C₄⋊C₈	C₂×C₄	semidirect
61. C₁₃×C₂²⋊C₈	C₂×C₄	semidirect
62. C₄×C₈×C₁₃	C₂×C₄	semidirect
65. D₄×#106	C₁₃	direct (N × H)
111. C₂²×#106	C₂×C₁₃	semidirect
113. #1948	C₂×C₁₃	semidirect
114. #1853	C₂×C₁₃	semidirect
115. #1844	C₂×C₁₃	semidirect
116. #1807	C₂×C₁₃	semidirect
117. C₄×#106	C₂×C₁₃	semidirect
124. D₄×C₁₃	#106	direct (N × H)
154. C₈×C₁₃	C₄×D₄	semidirect
159. C₈×D₄	C₄×C₁₃	semidirect
180. C₂²×C₁₃	C₂×#106	semidirect
191. C₄×C₁₃	C₂×#106	semidirect
201. C₂²×C₈	C₂×C₄×C₁₃	semidirect
225. #106	D₄×C₁₃	direct (N × H)
226. C₄⋊C₈	C₂×C₄×C₁₃	semidirect
227. C₂²⋊C₈	C₂×C₄×C₁₃	semidirect
228. C₄×C₈	C₂×C₄×C₁₃	semidirect
281. C₁₃	D₄×#106	direct (N × H)
288. D₄	C₁₃×#106	direct (N × H)
318. C₈	C₄×D₄×C₁₃	semidirect
323. C₂²	C₂×C₁₃×#106	semidirect
334. C₄	C₂×C₁₃×#106	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₈×D₄×C₁₃	2
C₂²×C₁₃×#106	2
D₄×C₁₃×C₄⋊C₄	2
C₁₃×#1948	2
C₁₃×#1853	2
C₁₃×#1844	2
C₁₃×#1807	2
C₄×C₁₃×#106	2
D₄×#106	13

Subgroups — D4×C13×#106 #15708992

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄×C₁₃×#106 #15708992