Subgroups — C₂²×C₁₃×#536 #15749019

Order 3328.

11406 conjugacy classes of subgroups.

The subgroup lattice has 318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₁₃×#41	C₂	1	1	yes	maximal, characteristic
2	C₂⁴×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#536	C₂	1	48	yes	maximal, direct product factor
4	C₂²×C₁₃×C₄⋊Q₈	C₂	1	2	yes	maximal, complemented
5	C₂²×C₁₃×#124	C₂	1	2	yes	maximal, complemented
6	C₂²×C₁₃×#123	C₂	1	4	yes	maximal, complemented
7	C₂²×C₁₃×C₂²⋊Q₈	C₂	1	4	yes	maximal, complemented
8	C₂²×C₁₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₁₃×#41	—	2	16	no	—
10	C₂²×C₁₃×#41	C₂²	1	24	yes	—
11	C₂³×Q₈×C₁₃	—	2	16	no	—
12	C₂³×Q₈×C₁₃	C₂²	1	2	yes	—
13	C₂³×Q₈×C₁₃	C₂²	1	2	yes	—
14	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
15	C₂³×Q₈×C₁₃	C₂²	1	24	yes	complemented
16	C₂³×D₄×C₁₃	C₂²	1	2	yes	—
17	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
18	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	—
19	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	—
20	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
21	C₁₃×#536	C₂²	1	256	yes	direct product factor
22	C₂×C₁₃×C₄⋊Q₈	C₂²	1	48	yes	complemented
23	C₂×C₁₃×#124	C₂²	1	48	yes	complemented
24	C₂×C₁₃×#123	C₂²	1	96	yes	complemented
25	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	96	yes	complemented
26	C₂×C₁₃×#117	C₂²	1	24	yes	complemented
27	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
28	C₂²×C₁₃×C₄⋊C₄	C₂²	1	8	yes	—
29	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
30	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	—
31	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
32	C₂⁵×C₁₃	C₂³	1	2	yes	—
33	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
34	C₂×C₁₃×#41	—	2	192	no	—
35	C₂×C₁₃×#41	C₂³	1	64	yes	—
36	C₂²×Q₈×C₁₃	—	2	16	no	—
37	C₂²×Q₈×C₁₃	—	2	16	no	—
38	C₂²×Q₈×C₁₃	—	2	192	no	—
39	C₂²×Q₈×C₁₃	—	2	8	no	—
40	C₂²×Q₈×C₁₃	C₂³	1	24	yes	—
41	C₂²×Q₈×C₁₃	C₂³	1	24	yes	—
42	C₂²×Q₈×C₁₃	C₂³	1	12	yes	—
43	C₂²×Q₈×C₁₃	C₂³	1	64	yes	complemented
44	C₂²×D₄×C₁₃	—	2	16	no	—
45	C₂²×D₄×C₁₃	—	2	8	no	—
46	C₂²×D₄×C₁₃	C₂³	1	24	yes	—
47	C₂²×D₄×C₁₃	C₂³	1	12	yes	—
48	C₂³×C₄×C₁₃	—	2	16	no	—
49	C₂³×C₄×C₁₃	—	2	16	no	—
50	C₂³×C₄×C₁₃	D₄	1	16	yes	—
51	C₂³×C₄×C₁₃	C₂³	1	24	yes	—
52	C₂³×C₄×C₁₃	C₂³	1	24	yes	—
53	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
54	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
55	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
56	C₂³×C₄×C₁₃	C₂³	1	12	yes	—
57	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
58	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
59	C₁₃×C₄⋊Q₈	C₂³	1	128	yes	complemented
60	C₁₃×#124	C₂³	1	128	yes	complemented
61	C₁₃×#123	C₂³	1	256	yes	complemented
62	C₁₃×C₂²⋊Q₈	C₂³	1	256	yes	complemented
63	C₁₃×#117	C₂³	1	64	yes	complemented
64	C₂×C₁₃×C₄⋊C₄	C₂³	1	24	yes	—
65	C₂×C₁₃×C₄⋊C₄	C₂³	1	96	yes	—
66	C₂×C₁₃×C₂²⋊C₄	C₂³	1	24	yes	—
67	C₂×C₁₃×C₂²⋊C₄	C₂³	1	96	yes	—
68	C₂×C₄²×C₁₃	C₂³	1	24	yes	—
69	C₂²×#536	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
70	C₂⁴×C₁₃	—	2	8	no	—
71	C₂⁴×C₁₃	—	2	8	no	—
72	C₂⁴×C₁₃	—	2	16	no	—
73	C₂⁴×C₁₃	C₂×D₄	1	8	yes	—
74	C₂⁴×C₁₃	C₂⁴	1	12	yes	—
75	C₂⁴×C₁₃	C₂⁴	1	6	yes	—
76	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
77	C₁₃×#41	—	2	256	no	—
78	C₂×Q₈×C₁₃	—	2	96	no	—
79	C₂×Q₈×C₁₃	—	2	96	no	—
80	C₂×Q₈×C₁₃	—	2	256	no	—
81	C₂×Q₈×C₁₃	—	2	48	no	—
82	C₂×Q₈×C₁₃	C₂⁴	1	32	yes	—
83	C₂×Q₈×C₁₃	C₂⁴	1	32	yes	—
84	C₂×Q₈×C₁₃	C₂⁴	1	16	yes	—
85	C₂×D₄×C₁₃	—	2	96	no	—
86	C₂×D₄×C₁₃	—	2	48	no	—
87	C₂×D₄×C₁₃	C₂⁴	1	32	yes	—
88	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
89	C₂²×C₄×C₁₃	—	2	8	no	—
90	C₂²×C₄×C₁₃	—	2	96	no	—
91	C₂²×C₄×C₁₃	—	2	16	no	—
92	C₂²×C₄×C₁₃	—	2	16	no	—
93	C₂²×C₄×C₁₃	—	2	96	no	—
94	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
95	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
96	C₂²×C₄×C₁₃	C₂×D₄	1	96	yes	—
97	C₂²×C₄×C₁₃	C₂⁴	1	24	yes	—
98	C₂²×C₄×C₁₃	C₂⁴	1	24	yes	—
99	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
100	C₂²×C₄×C₁₃	C₂⁴	1	32	yes	—
101	C₂²×C₄×C₁₃	C₂⁴	1	32	yes	—
102	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
103	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
104	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
105	C₁₃×C₄⋊C₄	C₂⁴	1	32	yes	—
106	C₁₃×C₄⋊C₄	C₂⁴	1	128	yes	—
107	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
108	C₁₃×C₂²⋊C₄	C₂⁴	1	128	yes	—
109	C₄²×C₁₃	C₂⁴	1	32	yes	—
110	C₂³×#41	C₂×C₁₃	1	1	yes	characteristic
111	C₂⁴×Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
112	C₂×#536	C₂×C₁₃	1	48	yes	direct product factor
113	C₂²×C₄⋊Q₈	C₂×C₁₃	1	2	yes	complemented
114	C₂²×#124	C₂×C₁₃	1	2	yes	complemented
115	C₂²×#123	C₂×C₁₃	1	4	yes	complemented
116	C₂²×C₂²⋊Q₈	C₂×C₁₃	1	4	yes	complemented
117	C₂²×#117	C₂×C₁₃	1	1	yes	characteristic, complemented
118	C₂³×C₁₃	—	2	32	no	—
119	C₂³×C₁₃	—	2	24	no	—
120	C₂³×C₁₃	—	2	24	no	—
121	C₂³×C₁₃	—	2	48	no	—
122	C₂³×C₁₃	—	4	32	no	—
123	C₂³×C₁₃	C₂²×D₄	1	24	yes	—
124	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
125	C₂³×C₁₃	2₋¹⁺⁴	1	8	yes	—
126	C₂³×C₁₃	C₂⁵	1	8	yes	—
127	C₂³×C₁₃	C₂⁵	1	4	yes	—
128	C₂³×C₁₃	C₂⁵	1	3	yes	—
129	Q₈×C₁₃	—	2	64	no	—
130	Q₈×C₁₃	—	2	64	no	—
131	Q₈×C₁₃	—	2	32	no	—
132	D₄×C₁₃	—	2	64	no	—
133	D₄×C₁₃	—	2	32	no	—
134	C₂×C₄×C₁₃	—	2	24	no	—
135	C₂×C₄×C₁₃	—	2	64	no	—
136	C₂×C₄×C₁₃	—	2	48	no	—
137	C₂×C₄×C₁₃	—	2	48	no	—
138	C₂×C₄×C₁₃	—	2	64	no	—
139	C₂×C₄×C₁₃	C₂²×D₄	1	24	yes	—
140	C₂×C₄×C₁₃	C₂²×D₄	1	24	yes	—
141	C₂×C₄×C₁₃	C₂²×D₄	1	64	yes	—
142	C₂×C₄×C₁₃	C₂⁵	1	16	yes	—
143	C₂×C₄×C₁₃	C₂⁵	1	16	yes	—
144	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
145	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
146	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
147	C₂²×#41	—	2	16	no	—
148	C₂²×#41	C₂²×C₁₃	1	24	yes	—
149	C₂³×Q₈	—	2	16	no	—
150	C₂³×Q₈	C₂²×C₁₃	1	2	yes	—
151	C₂³×Q₈	C₂²×C₁₃	1	2	yes	—
152	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
153	C₂³×Q₈	C₂²×C₁₃	1	24	yes	complemented
154	C₂³×D₄	C₂²×C₁₃	1	2	yes	—
155	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
156	C₂⁴×C₄	C₂²×C₁₃	1	2	yes	—
157	C₂⁴×C₄	C₂²×C₁₃	1	2	yes	—
158	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
159	#536	C₂²×C₁₃	1	256	yes	direct product factor
160	C₂×C₄⋊Q₈	C₂²×C₁₃	1	48	yes	complemented
161	C₂×#124	C₂²×C₁₃	1	48	yes	complemented
162	C₂×#123	C₂²×C₁₃	1	96	yes	complemented
163	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	96	yes	complemented
164	C₂×#117	C₂²×C₁₃	1	24	yes	complemented
165	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
166	C₂²×C₄⋊C₄	C₂²×C₁₃	1	8	yes	—
167	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
168	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	—
169	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
170	C₂²×C₁₃	—	2	8	no	—
171	C₂²×C₁₃	—	2	48	no	—
172	C₂²×C₁₃	—	2	8	no	—
173	C₂²×C₁₃	—	2	16	no	—
174	C₂²×C₁₃	—	4	48	no	—
175	C₂²×C₁₃	#536	1	16	yes	direct product factor
176	C₂²×C₁₃	C₂³×D₄	1	8	yes	—
177	C₂²×C₁₃	C₂³×D₄	1	6	yes	—
178	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	12	yes	—
179	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
180	C₄×C₁₃	—	2	8	no	—
181	C₄×C₁₃	—	2	16	no	—
182	C₄×C₁₃	—	2	16	no	—
183	C₄×C₁₃	C₂³×D₄	1	8	yes	—
184	C₄×C₁₃	C₂³×D₄	1	8	yes	—
185	C₂⁵	C₂³×C₁₃	1	2	yes	—
186	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
187	C₂×#41	—	2	192	no	—
188	C₂×#41	C₂³×C₁₃	1	64	yes	—
189	C₂²×Q₈	—	2	16	no	—
190	C₂²×Q₈	—	2	16	no	—
191	C₂²×Q₈	—	2	192	no	—
192	C₂²×Q₈	—	2	8	no	—
193	C₂²×Q₈	C₂³×C₁₃	1	24	yes	—
194	C₂²×Q₈	C₂³×C₁₃	1	24	yes	—
195	C₂²×Q₈	C₂³×C₁₃	1	12	yes	—
196	C₂²×Q₈	C₂³×C₁₃	1	64	yes	complemented
197	C₂²×D₄	—	2	16	no	—
198	C₂²×D₄	—	2	8	no	—
199	C₂²×D₄	C₂³×C₁₃	1	24	yes	—
200	C₂²×D₄	C₂³×C₁₃	1	12	yes	—
201	C₂³×C₄	—	2	16	no	—
202	C₂³×C₄	—	2	16	no	—
203	C₂³×C₄	D₄×C₁₃	1	16	yes	—
204	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
205	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
206	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
207	C₂³×C₄	C₂³×C₁₃	1	24	yes	—
208	C₂³×C₄	C₂³×C₁₃	1	24	yes	—
209	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
210	C₂³×C₄	C₂³×C₁₃	1	12	yes	—
211	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
212	C₄⋊Q₈	C₂³×C₁₃	1	128	yes	complemented
213	#124	C₂³×C₁₃	1	128	yes	complemented
214	#123	C₂³×C₁₃	1	256	yes	complemented
215	C₂²⋊Q₈	C₂³×C₁₃	1	256	yes	complemented
216	#117	C₂³×C₁₃	1	64	yes	complemented
217	C₂×C₄⋊C₄	C₂³×C₁₃	1	24	yes	—
218	C₂×C₄⋊C₄	C₂³×C₁₃	1	96	yes	—
219	C₂×C₂²⋊C₄	C₂³×C₁₃	1	24	yes	—
220	C₂×C₂²⋊C₄	C₂³×C₁₃	1	96	yes	—
221	C₂×C₄²	C₂³×C₁₃	1	24	yes	—
222	C₂×C₁₃	—	2	8	no	—
223	C₂×C₁₃	—	4	8	no	—
224	C₂×C₁₃	C₂×#536	1	12	yes	direct product factor
225	C₂×C₁₃	C₂⁴×D₄	1	1	yes	characteristic
226	C₂×C₁₃	C₂²×2₋¹⁺⁴	1	2	yes	—
227	C₂⁴	—	2	8	no	—
228	C₂⁴	—	2	8	no	—
229	C₂⁴	—	2	16	no	—
230	C₂⁴	C₂×D₄×C₁₃	1	8	yes	—
231	C₂⁴	C₂⁴×C₁₃	1	12	yes	—
232	C₂⁴	C₂⁴×C₁₃	1	6	yes	—
233	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
234	#41	—	2	256	no	—
235	C₂×Q₈	—	2	96	no	—
236	C₂×Q₈	—	2	96	no	—
237	C₂×Q₈	—	2	256	no	—
238	C₂×Q₈	—	2	48	no	—
239	C₂×Q₈	C₂⁴×C₁₃	1	32	yes	—
240	C₂×Q₈	C₂⁴×C₁₃	1	32	yes	—
241	C₂×Q₈	C₂⁴×C₁₃	1	16	yes	—
242	C₂×D₄	—	2	96	no	—
243	C₂×D₄	—	2	48	no	—
244	C₂×D₄	C₂⁴×C₁₃	1	32	yes	—
245	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
246	C₂²×C₄	—	2	8	no	—
247	C₂²×C₄	—	2	96	no	—
248	C₂²×C₄	—	2	16	no	—
249	C₂²×C₄	—	2	16	no	—
250	C₂²×C₄	—	2	96	no	—
251	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	—
252	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	—
253	C₂²×C₄	C₂×D₄×C₁₃	1	96	yes	—
254	C₂²×C₄	C₂⁴×C₁₃	1	24	yes	—
255	C₂²×C₄	C₂⁴×C₁₃	1	24	yes	—
256	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
257	C₂²×C₄	C₂⁴×C₁₃	1	32	yes	—
258	C₂²×C₄	C₂⁴×C₁₃	1	32	yes	—
259	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
260	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
261	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
262	C₄⋊C₄	C₂⁴×C₁₃	1	32	yes	—
263	C₄⋊C₄	C₂⁴×C₁₃	1	128	yes	—
264	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
265	C₂²⋊C₄	C₂⁴×C₁₃	1	128	yes	—
266	C₄²	C₂⁴×C₁₃	1	32	yes	—
267	C₁₃	C₂²×#536	1	1	yes	characteristic, direct product factor, Sylow
268	C₂³	—	2	32	no	—
269	C₂³	—	2	24	no	—
270	C₂³	—	2	24	no	—
271	C₂³	—	2	48	no	—
272	C₂³	—	4	32	no	—
273	C₂³	C₂²×D₄×C₁₃	1	24	yes	—
274	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
275	C₂³	C₁₃×2₋¹⁺⁴	1	8	yes	—
276	C₂³	C₂⁵×C₁₃	1	8	yes	—
277	C₂³	C₂⁵×C₁₃	1	4	yes	—
278	C₂³	C₂⁵×C₁₃	1	3	yes	—
279	Q₈	—	2	64	no	—
280	Q₈	—	2	64	no	—
281	Q₈	—	2	32	no	—
282	D₄	—	2	64	no	—
283	D₄	—	2	32	no	—
284	C₂×C₄	—	2	24	no	—
285	C₂×C₄	—	2	64	no	—
286	C₂×C₄	—	2	48	no	—
287	C₂×C₄	—	2	48	no	—
288	C₂×C₄	—	2	64	no	—
289	C₂×C₄	C₂²×D₄×C₁₃	1	24	yes	—
290	C₂×C₄	C₂²×D₄×C₁₃	1	24	yes	—
291	C₂×C₄	C₂²×D₄×C₁₃	1	64	yes	—
292	C₂×C₄	C₂⁵×C₁₃	1	16	yes	—
293	C₂×C₄	C₂⁵×C₁₃	1	16	yes	—
294	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
295	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
296	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
297	C₂²	—	2	8	no	—
298	C₂²	—	2	48	no	—
299	C₂²	—	2	8	no	—
300	C₂²	—	2	16	no	—
301	C₂²	—	4	48	no	—
302	C₂²	C₁₃×#536	1	16	yes	direct product factor
303	C₂²	C₂³×D₄×C₁₃	1	8	yes	—
304	C₂²	C₂³×D₄×C₁₃	1	6	yes	—
305	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	12	yes	—
306	C₂²	C₂⁶×C₁₃	1	1	yes	characteristic
307	C₄	—	2	8	no	—
308	C₄	—	2	16	no	—
309	C₄	—	2	16	no	—
310	C₄	C₂³×D₄×C₁₃	1	8	yes	—
311	C₄	C₂³×D₄×C₁₃	1	8	yes	—
312	C₂	—	2	8	no	—
313	C₂	—	4	8	no	—
314	C₂	C₂×C₁₃×#536	1	12	yes	direct product factor
315	C₂	C₂⁴×D₄×C₁₃	1	1	yes	characteristic
316	C₂	C₂²×C₁₃×2₋¹⁺⁴	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁶×C₁₃
prime radical	C₂³×C₁₃×#41	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂⁴×Q₈×C₁₃	C₂	semidirect
3. C₂×C₁₃×#536	C₂	direct (N × H)
4. C₂²×C₁₃×C₄⋊Q₈	C₂	semidirect
5. C₂²×C₁₃×#124	C₂	semidirect
6. C₂²×C₁₃×#123	C₂	semidirect
7. C₂²×C₁₃×C₂²⋊Q₈	C₂	semidirect
8. C₂²×C₁₃×#117	C₂	semidirect
15. C₂³×Q₈×C₁₃	C₂²	semidirect
21. C₁₃×#536	C₂²	direct (N × H)
22. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
23. C₂×C₁₃×#124	C₂²	semidirect
24. C₂×C₁₃×#123	C₂²	semidirect
25. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
26. C₂×C₁₃×#117	C₂²	semidirect
43. C₂²×Q₈×C₁₃	C₂³	semidirect
59. C₁₃×C₄⋊Q₈	C₂³	semidirect
60. C₁₃×#124	C₂³	semidirect
61. C₁₃×#123	C₂³	semidirect
62. C₁₃×C₂²⋊Q₈	C₂³	semidirect
63. C₁₃×#117	C₂³	semidirect
69. C₂²×#536	C₁₃	direct (N × H)
111. C₂⁴×Q₈	C₂×C₁₃	semidirect
112. C₂×#536	C₂×C₁₃	direct (N × H)
113. C₂²×C₄⋊Q₈	C₂×C₁₃	semidirect
114. C₂²×#124	C₂×C₁₃	semidirect
115. C₂²×#123	C₂×C₁₃	semidirect
116. C₂²×C₂²⋊Q₈	C₂×C₁₃	semidirect
117. C₂²×#117	C₂×C₁₃	semidirect
153. C₂³×Q₈	C₂²×C₁₃	semidirect
159. #536	C₂²×C₁₃	direct (N × H)
160. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
161. C₂×#124	C₂²×C₁₃	semidirect
162. C₂×#123	C₂²×C₁₃	semidirect
163. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
164. C₂×#117	C₂²×C₁₃	semidirect
175. C₂²×C₁₃	#536	direct (N × H)
196. C₂²×Q₈	C₂³×C₁₃	semidirect
212. C₄⋊Q₈	C₂³×C₁₃	semidirect
213. #124	C₂³×C₁₃	semidirect
214. #123	C₂³×C₁₃	semidirect
215. C₂²⋊Q₈	C₂³×C₁₃	semidirect
216. #117	C₂³×C₁₃	semidirect
224. C₂×C₁₃	C₂×#536	direct (N × H)
267. C₁₃	C₂²×#536	direct (N × H)
302. C₂²	C₁₃×#536	direct (N × H)
314. C₂	C₂×C₁₃×#536	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₁₃×#41	2
C₂⁴×Q₈×C₁₃	2
C₂×C₁₃×#536	2
C₂²×C₁₃×C₄⋊Q₈	2
C₂²×C₁₃×#124	2
C₂²×C₁₃×#123	2
C₂²×C₁₃×C₂²⋊Q₈	2
C₂²×C₁₃×#117	2
C₂²×#536	13

Subgroups — C22×C13×#536 #15749019

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₁₃×#536 #15749019