Subgroups — C₂²×C₁₃×#556 #15749045

Order 3328.

7846 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	C₂×C₁₃×#556	C₂	1	48	yes	maximal, direct product factor
2	C₂²×C₁₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₁₃×#126	C₂	1	4	yes	maximal, complemented
4	C₂²×C₁₃×#124	C₂	1	2	yes	maximal
5	C₂²×C₁₃×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
6	C₂²×C₄×Q₈×C₁₃	C₂	1	2	yes	maximal, complemented
7	C₂²×C₄×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₄×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic
9	C₂²×C₁₃×#117	C₂	1	2	yes	maximal, complemented
10	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
11	C₂³×Q₈×C₁₃	C₂²	1	2	yes	—
12	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
13	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	—
14	C₁₃×#556	C₂²	1	256	yes	direct product factor
15	C₂×C₁₃×C₄⋊Q₈	C₂²	1	24	yes	complemented
16	C₂×C₁₃×#126	C₂²	1	96	yes	complemented
17	C₂×C₁₃×#124	C₂²	1	48	yes	—
18	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	48	yes	complemented
19	C₂×C₄×Q₈×C₁₃	C₂²	1	48	yes	complemented
20	C₂×C₄×Q₈×C₁₃	C₂²	1	24	yes	complemented
21	C₂×C₄×D₄×C₁₃	C₂²	1	24	yes	—
22	C₂×C₁₃×#117	C₂²	1	48	yes	complemented
23	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
25	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
26	C₂²×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
27	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
28	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
29	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
30	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
31	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
32	C₂²×C₄²×C₁₃	C₂²	1	4	yes	—
33	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
34	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
35	C₂⁵×C₁₃	C₂³	1	2	yes	—
36	C₂²×Q₈×C₁₃	—	2	8	no	—
37	C₂²×Q₈×C₁₃	—	2	16	no	—
38	C₂²×Q₈×C₁₃	C₂³	1	12	yes	—
39	C₂²×Q₈×C₁₃	C₂³	1	24	yes	—
40	C₂²×D₄×C₁₃	—	2	8	no	—
41	C₂²×D₄×C₁₃	C₂³	1	12	yes	—
42	C₂³×C₄×C₁₃	—	2	16	no	—
43	C₂³×C₄×C₁₃	C₂³	1	24	yes	—
44	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
45	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
46	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
47	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
48	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
49	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
50	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
51	C₁₃×C₄⋊Q₈	C₂³	1	64	yes	complemented
52	C₁₃×#126	C₂³	1	256	yes	complemented
53	C₁₃×#124	C₂³	1	128	yes	—
54	C₁₃×C₂²⋊Q₈	C₂³	1	128	yes	complemented
55	C₄×Q₈×C₁₃	C₂³	1	128	yes	complemented
56	C₄×Q₈×C₁₃	C₂³	1	64	yes	complemented
57	C₄×D₄×C₁₃	C₂³	1	64	yes	—
58	C₁₃×#117	C₂³	1	128	yes	complemented
59	C₂×C₁₃×C₄⋊C₄	C₂³	1	12	yes	—
60	C₂×C₁₃×C₄⋊C₄	C₂³	1	24	yes	—
61	C₂×C₁₃×C₄⋊C₄	C₂³	1	12	yes	—
62	C₂×C₁₃×C₄⋊C₄	C₂³	1	48	yes	—
63	C₂×C₁₃×C₄⋊C₄	C₂³	1	24	yes	—
64	C₂×C₁₃×C₄⋊C₄	C₂³	1	24	yes	—
65	C₂×C₁₃×C₂²⋊C₄	C₂³	1	48	yes	—
66	C₂×C₁₃×C₂²⋊C₄	C₂³	1	24	yes	—
67	C₂×C₁₃×C₂²⋊C₄	C₂³	1	48	yes	—
68	C₂×C₄²×C₁₃	C₂³	1	48	yes	—
69	C₂×C₄²×C₁₃	C₂³	1	12	yes	—
70	C₂×C₄²×C₁₃	C₂³	1	24	yes	—
71	C₂²×#556	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
72	C₂⁴×C₁₃	—	2	8	no	—
73	C₂⁴×C₁₃	—	2	8	no	—
74	C₂⁴×C₁₃	—	2	8	no	—
75	C₂⁴×C₁₃	C₂⁴	1	12	yes	—
76	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
77	C₂×Q₈×C₁₃	—	2	48	no	—
78	C₂×Q₈×C₁₃	—	2	96	no	—
79	C₂×Q₈×C₁₃	C₂⁴	1	16	yes	—
80	C₂×Q₈×C₁₃	C₂⁴	1	32	yes	—
81	C₂×D₄×C₁₃	—	2	48	no	—
82	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
83	C₂²×C₄×C₁₃	—	2	8	no	—
84	C₂²×C₄×C₁₃	—	2	8	no	—
85	C₂²×C₄×C₁₃	—	2	16	no	—
86	C₂²×C₄×C₁₃	—	2	8	no	—
87	C₂²×C₄×C₁₃	—	2	4	no	—
88	C₂²×C₄×C₁₃	—	2	96	no	—
89	C₂²×C₄×C₁₃	#41	1	8	yes	—
90	C₂²×C₄×C₁₃	#41	1	8	yes	—
91	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
92	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
93	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
94	C₂²×C₄×C₁₃	C₂⁴	1	24	yes	—
95	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
96	C₂²×C₄×C₁₃	C₂⁴	1	32	yes	—
97	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
98	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
99	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
100	C₁₃×C₄⋊C₄	C₂⁴	1	32	yes	—
101	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
102	C₁₃×C₄⋊C₄	C₂⁴	1	64	yes	—
103	C₁₃×C₄⋊C₄	C₂⁴	1	32	yes	—
104	C₁₃×C₄⋊C₄	C₂⁴	1	32	yes	—
105	C₁₃×C₂²⋊C₄	C₂⁴	1	64	yes	—
106	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
107	C₁₃×C₂²⋊C₄	C₂⁴	1	64	yes	—
108	C₄²×C₁₃	C₂⁴	1	64	yes	—
109	C₄²×C₁₃	C₂⁴	1	16	yes	—
110	C₄²×C₁₃	C₂⁴	1	32	yes	—
111	C₂×#556	C₂×C₁₃	1	48	yes	direct product factor
112	C₂²×C₄⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
113	C₂²×#126	C₂×C₁₃	1	4	yes	complemented
114	C₂²×#124	C₂×C₁₃	1	2	yes	—
115	C₂²×C₂²⋊Q₈	C₂×C₁₃	1	2	yes	complemented
116	C₂²×C₄×Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
117	C₂²×C₄×Q₈	C₂×C₁₃	1	2	yes	complemented
118	C₂²×C₄×D₄	C₂×C₁₃	1	1	yes	characteristic
119	C₂²×#117	C₂×C₁₃	1	2	yes	complemented
120	C₂³×C₁₃	—	2	24	no	—
121	C₂³×C₁₃	—	2	24	no	—
122	C₂³×C₁₃	—	2	24	no	—
123	C₂³×C₁₃	—	4	32	no	—
124	C₂³×C₁₃	C₂×#41	1	4	yes	—
125	C₂³×C₁₃	C₂×#41	1	4	yes	—
126	C₂³×C₁₃	2₋¹⁺⁴	1	4	yes	—
127	C₂³×C₁₃	C₂⁵	1	8	yes	—
128	C₂³×C₁₃	C₂⁵	1	3	yes	—
129	Q₈×C₁₃	—	2	32	no	—
130	Q₈×C₁₃	—	2	64	no	—
131	D₄×C₁₃	—	2	32	no	—
132	C₂×C₄×C₁₃	—	2	24	no	—
133	C₂×C₄×C₁₃	—	2	24	no	—
134	C₂×C₄×C₁₃	—	2	48	no	—
135	C₂×C₄×C₁₃	—	2	24	no	—
136	C₂×C₄×C₁₃	—	2	12	no	—
137	C₂×C₄×C₁₃	—	2	64	no	—
138	C₂×C₄×C₁₃	C₂×#41	1	24	yes	—
139	C₂×C₄×C₁₃	C₂×#41	1	24	yes	—
140	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
141	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
142	C₂×C₄×C₁₃	C₂⁵	1	4	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	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
148	C₂³×Q₈	C₂²×C₁₃	1	2	yes	—
149	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
150	C₂⁴×C₄	C₂²×C₁₃	1	2	yes	—
151	#556	C₂²×C₁₃	1	256	yes	direct product factor
152	C₂×C₄⋊Q₈	C₂²×C₁₃	1	24	yes	complemented
153	C₂×#126	C₂²×C₁₃	1	96	yes	complemented
154	C₂×#124	C₂²×C₁₃	1	48	yes	—
155	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	48	yes	complemented
156	C₂×C₄×Q₈	C₂²×C₁₃	1	48	yes	complemented
157	C₂×C₄×Q₈	C₂²×C₁₃	1	24	yes	complemented
158	C₂×C₄×D₄	C₂²×C₁₃	1	24	yes	—
159	C₂×#117	C₂²×C₁₃	1	48	yes	complemented
160	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
161	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
162	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
163	C₂²×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
164	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
165	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
166	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
167	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
168	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
169	C₂²×C₄²	C₂²×C₁₃	1	4	yes	—
170	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
171	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
172	C₂²×C₁₃	—	2	8	no	—
173	C₂²×C₁₃	—	2	8	no	—
174	C₂²×C₁₃	—	2	8	no	—
175	C₂²×C₁₃	—	4	48	no	—
176	C₂²×C₁₃	#556	1	16	yes	direct product factor
177	C₂²×C₁₃	C₂²×#41	1	6	yes	—
178	C₂²×C₁₃	C₂²×#41	1	6	yes	—
179	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	6	yes	—
180	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
181	C₄×C₁₃	—	2	8	no	—
182	C₄×C₁₃	—	2	8	no	—
183	C₄×C₁₃	—	2	16	no	—
184	C₄×C₁₃	—	2	8	no	—
185	C₄×C₁₃	—	2	4	no	—
186	C₄×C₁₃	C₂²×#41	1	8	yes	—
187	C₄×C₁₃	C₂²×#41	1	8	yes	—
188	C₂⁵	C₂³×C₁₃	1	2	yes	—
189	C₂²×Q₈	—	2	8	no	—
190	C₂²×Q₈	—	2	16	no	—
191	C₂²×Q₈	C₂³×C₁₃	1	12	yes	—
192	C₂²×Q₈	C₂³×C₁₃	1	24	yes	—
193	C₂²×D₄	—	2	8	no	—
194	C₂²×D₄	C₂³×C₁₃	1	12	yes	—
195	C₂³×C₄	—	2	16	no	—
196	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
197	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
198	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
199	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
200	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
201	C₂³×C₄	C₂³×C₁₃	1	24	yes	—
202	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
203	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
204	C₄⋊Q₈	C₂³×C₁₃	1	64	yes	complemented
205	#126	C₂³×C₁₃	1	256	yes	complemented
206	#124	C₂³×C₁₃	1	128	yes	—
207	C₂²⋊Q₈	C₂³×C₁₃	1	128	yes	complemented
208	C₄×Q₈	C₂³×C₁₃	1	128	yes	complemented
209	C₄×Q₈	C₂³×C₁₃	1	64	yes	complemented
210	C₄×D₄	C₂³×C₁₃	1	64	yes	—
211	#117	C₂³×C₁₃	1	128	yes	complemented
212	C₂×C₄⋊C₄	C₂³×C₁₃	1	12	yes	—
213	C₂×C₄⋊C₄	C₂³×C₁₃	1	24	yes	—
214	C₂×C₄⋊C₄	C₂³×C₁₃	1	12	yes	—
215	C₂×C₄⋊C₄	C₂³×C₁₃	1	48	yes	—
216	C₂×C₄⋊C₄	C₂³×C₁₃	1	24	yes	—
217	C₂×C₄⋊C₄	C₂³×C₁₃	1	24	yes	—
218	C₂×C₂²⋊C₄	C₂³×C₁₃	1	48	yes	—
219	C₂×C₂²⋊C₄	C₂³×C₁₃	1	24	yes	—
220	C₂×C₂²⋊C₄	C₂³×C₁₃	1	48	yes	—
221	C₂×C₄²	C₂³×C₁₃	1	48	yes	—
222	C₂×C₄²	C₂³×C₁₃	1	12	yes	—
223	C₂×C₄²	C₂³×C₁₃	1	24	yes	—
224	C₂×C₁₃	—	4	8	no	—
225	C₂×C₁₃	C₂×#556	1	12	yes	direct product factor
226	C₂×C₁₃	C₂³×#41	1	1	yes	characteristic
227	C₂×C₁₃	C₂³×#41	1	1	yes	characteristic
228	C₂×C₁₃	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
229	C₂⁴	—	2	8	no	—
230	C₂⁴	—	2	8	no	—
231	C₂⁴	—	2	8	no	—
232	C₂⁴	C₂⁴×C₁₃	1	12	yes	—
233	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
234	C₂×Q₈	—	2	48	no	—
235	C₂×Q₈	—	2	96	no	—
236	C₂×Q₈	C₂⁴×C₁₃	1	16	yes	—
237	C₂×Q₈	C₂⁴×C₁₃	1	32	yes	—
238	C₂×D₄	—	2	48	no	—
239	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
240	C₂²×C₄	—	2	8	no	—
241	C₂²×C₄	—	2	8	no	—
242	C₂²×C₄	—	2	16	no	—
243	C₂²×C₄	—	2	4	no	—
244	C₂²×C₄	—	2	8	no	—
245	C₂²×C₄	—	2	96	no	—
246	C₂²×C₄	C₁₃×#41	1	8	yes	—
247	C₂²×C₄	C₁₃×#41	1	8	yes	—
248	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
249	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
250	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
251	C₂²×C₄	C₂⁴×C₁₃	1	24	yes	—
252	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
253	C₂²×C₄	C₂⁴×C₁₃	1	32	yes	—
254	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
255	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
256	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
257	C₄⋊C₄	C₂⁴×C₁₃	1	32	yes	—
258	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
259	C₄⋊C₄	C₂⁴×C₁₃	1	64	yes	—
260	C₄⋊C₄	C₂⁴×C₁₃	1	32	yes	—
261	C₄⋊C₄	C₂⁴×C₁₃	1	32	yes	—
262	C₂²⋊C₄	C₂⁴×C₁₃	1	64	yes	—
263	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
264	C₂²⋊C₄	C₂⁴×C₁₃	1	64	yes	—
265	C₄²	C₂⁴×C₁₃	1	64	yes	—
266	C₄²	C₂⁴×C₁₃	1	16	yes	—
267	C₄²	C₂⁴×C₁₃	1	32	yes	—
268	C₁₃	C₂²×#556	1	1	yes	characteristic, direct product factor, Sylow
269	C₂³	—	2	24	no	—
270	C₂³	—	2	24	no	—
271	C₂³	—	2	24	no	—
272	C₂³	—	4	32	no	—
273	C₂³	C₂×C₁₃×#41	1	4	yes	—
274	C₂³	C₂×C₁₃×#41	1	4	yes	—
275	C₂³	C₁₃×2₋¹⁺⁴	1	4	yes	—
276	C₂³	C₂⁵×C₁₃	1	8	yes	—
277	C₂³	C₂⁵×C₁₃	1	3	yes	—
278	Q₈	—	2	32	no	—
279	Q₈	—	2	64	no	—
280	D₄	—	2	32	no	—
281	C₂×C₄	—	2	24	no	—
282	C₂×C₄	—	2	24	no	—
283	C₂×C₄	—	2	48	no	—
284	C₂×C₄	—	2	24	no	—
285	C₂×C₄	—	2	12	no	—
286	C₂×C₄	—	2	64	no	—
287	C₂×C₄	C₂×C₁₃×#41	1	24	yes	—
288	C₂×C₄	C₂×C₁₃×#41	1	24	yes	—
289	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
290	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
291	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
292	C₂×C₄	C₂⁵×C₁₃	1	16	yes	—
293	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
294	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
295	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
296	C₂²	—	2	8	no	—
297	C₂²	—	2	8	no	—
298	C₂²	—	2	8	no	—
299	C₂²	—	4	48	no	—
300	C₂²	C₁₃×#556	1	16	yes	direct product factor
301	C₂²	C₂²×C₁₃×#41	1	6	yes	—
302	C₂²	C₂²×C₁₃×#41	1	6	yes	—
303	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	6	yes	—
304	C₂²	C₂⁶×C₁₃	1	1	yes	characteristic
305	C₄	—	2	8	no	—
306	C₄	—	2	8	no	—
307	C₄	—	2	16	no	—
308	C₄	—	2	8	no	—
309	C₄	—	2	4	no	—
310	C₄	C₂²×C₁₃×#41	1	8	yes	—
311	C₄	C₂²×C₁₃×#41	1	8	yes	—
312	C₂	—	4	8	no	—
313	C₂	C₂×C₁₃×#556	1	12	yes	direct product factor
314	C₂	C₂³×C₁₃×#41	1	1	yes	characteristic
315	C₂	C₂³×C₁₃×#41	1	1	yes	characteristic
316	C₂	C₂²×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁶×C₁₃
prime radical	C₂³×D₄×C₁₃	C₂²
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
1. C₂×C₁₃×#556	C₂	direct (N × H)
2. C₂²×C₁₃×C₄⋊Q₈	C₂	semidirect
3. C₂²×C₁₃×#126	C₂	semidirect
5. C₂²×C₁₃×C₂²⋊Q₈	C₂	semidirect
6. C₂²×C₄×Q₈×C₁₃	C₂	semidirect
7. C₂²×C₄×Q₈×C₁₃	C₂	semidirect
9. C₂²×C₁₃×#117	C₂	semidirect
14. C₁₃×#556	C₂²	direct (N × H)
15. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
16. C₂×C₁₃×#126	C₂²	semidirect
18. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
19. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
20. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
22. C₂×C₁₃×#117	C₂²	semidirect
51. C₁₃×C₄⋊Q₈	C₂³	semidirect
52. C₁₃×#126	C₂³	semidirect
54. C₁₃×C₂²⋊Q₈	C₂³	semidirect
55. C₄×Q₈×C₁₃	C₂³	semidirect
56. C₄×Q₈×C₁₃	C₂³	semidirect
58. C₁₃×#117	C₂³	semidirect
71. C₂²×#556	C₁₃	direct (N × H)
111. C₂×#556	C₂×C₁₃	direct (N × H)
112. C₂²×C₄⋊Q₈	C₂×C₁₃	semidirect
113. C₂²×#126	C₂×C₁₃	semidirect
115. C₂²×C₂²⋊Q₈	C₂×C₁₃	semidirect
116. C₂²×C₄×Q₈	C₂×C₁₃	semidirect
117. C₂²×C₄×Q₈	C₂×C₁₃	semidirect
119. C₂²×#117	C₂×C₁₃	semidirect
151. #556	C₂²×C₁₃	direct (N × H)
152. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
153. C₂×#126	C₂²×C₁₃	semidirect
155. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
156. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
157. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
159. C₂×#117	C₂²×C₁₃	semidirect
176. C₂²×C₁₃	#556	direct (N × H)
204. C₄⋊Q₈	C₂³×C₁₃	semidirect
205. #126	C₂³×C₁₃	semidirect
207. C₂²⋊Q₈	C₂³×C₁₃	semidirect
208. C₄×Q₈	C₂³×C₁₃	semidirect
209. C₄×Q₈	C₂³×C₁₃	semidirect
211. #117	C₂³×C₁₃	semidirect
225. C₂×C₁₃	C₂×#556	direct (N × H)
268. C₁₃	C₂²×#556	direct (N × H)
300. C₂²	C₁₃×#556	direct (N × H)
313. C₂	C₂×C₁₃×#556	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#556	2
C₂²×C₁₃×C₄⋊Q₈	2
C₂²×C₁₃×#126	2
C₂²×C₁₃×#124	2
C₂²×C₁₃×C₂²⋊Q₈	2
C₂²×C₄×Q₈×C₁₃	2
C₂²×C₄×D₄×C₁₃	2
C₂²×C₁₃×#117	2
C₂²×#556	13

Subgroups — C22×C13×#556 #15749045

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₁₃×#556 #15749045