Subgroups — C₂×C₁₃×#2567 #15721279

Order 3328.

2790 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2567	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#395	C₂	1	4	yes	maximal
5	C₂×C₁₃×#391	C₂	1	2	yes	maximal
6	C₂×C₁₃×#389	C₂	1	4	yes	maximal
7	C₂×C₁₃×#384	C₂	1	2	yes	maximal
8	C₂×C₄×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
9	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
10	C₂³×Q₈×C₁₃	C₂²	1	2	yes	—
11	C₂×C₁₃×C₄⋊Q₈	—	2	8	no	—
12	C₂×C₁₃×C₄⋊Q₈	C₂²	1	8	yes	—
13	C₂×C₄×Q₈×C₁₃	—	2	8	no	—
14	C₂×C₄×Q₈×C₁₃	C₂²	1	8	yes	—
15	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
16	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
17	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
18	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
19	C₂²×C₁₃×C₄⋊C₄	C₂²	1	8	yes	—
20	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
21	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
22	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
23	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
24	C₁₃×#395	C₂²	1	32	yes	—
25	C₁₃×#391	C₂²	1	16	yes	—
26	C₁₃×#389	C₂²	1	32	yes	—
27	C₁₃×#384	C₂²	1	16	yes	—
28	C₄×C₁₃×C₄⋊C₄	C₂²	1	8	yes	—
29	C₂×C₁₃×#95	C₂²	1	2	yes	—
30	C₂×C₁₃×#95	C₂²	1	8	yes	—
31	C₂²×Q₈×C₁₃	—	2	4	no	—
32	C₂²×Q₈×C₁₃	—	2	8	no	—
33	C₂²×Q₈×C₁₃	—	2	4	no	—
34	C₂²×Q₈×C₁₃	—	4	8	no	—
35	C₂²×Q₈×C₁₃	Q₈	1	8	yes	complemented
36	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
37	C₂²×Q₈×C₁₃	C₂³	1	8	yes	—
38	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
39	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
40	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
41	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
42	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
43	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
45	C₁₃×C₄⋊Q₈	—	2	32	no	—
46	C₄×Q₈×C₁₃	—	2	32	no	—
47	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
48	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
49	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
50	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
51	C₂×C₁₃×C₄⋊C₄	—	4	16	no	—
52	C₂×C₁₃×C₄⋊C₄	Q₈	1	16	yes	complemented
53	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
54	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
55	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
56	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
57	C₂×C₁₃×C₄⋊C₄	C₂³	1	32	yes	—
58	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
59	C₂×C₄²×C₁₃	—	2	8	no	—
60	C₂×C₄²×C₁₃	—	2	8	no	—
61	C₂×C₄²×C₁₃	D₄	1	8	yes	—
62	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
63	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
64	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
65	C₁₃×#95	C₂³	1	8	yes	—
66	C₁₃×#95	C₂³	1	32	yes	—
67	C₂×#2567	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
68	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
69	C₂×Q₈×C₁₃	—	2	32	no	—
70	C₂×Q₈×C₁₃	—	2	8	no	—
71	C₂×Q₈×C₁₃	—	2	16	no	—
72	C₂×Q₈×C₁₃	—	2	8	no	—
73	C₂×Q₈×C₁₃	—	4	16	no	—
74	C₂×Q₈×C₁₃	—	4	32	no	—
75	C₂×Q₈×C₁₃	C₂×Q₈	1	16	yes	complemented
76	C₂²×C₄×C₁₃	—	2	4	no	—
77	C₂²×C₄×C₁₃	—	2	8	no	—
78	C₂²×C₄×C₁₃	—	2	4	no	—
79	C₂²×C₄×C₁₃	—	2	8	no	—
80	C₂²×C₄×C₁₃	—	2	4	no	—
81	C₂²×C₄×C₁₃	—	2	4	no	—
82	C₂²×C₄×C₁₃	—	2	8	no	—
83	C₂²×C₄×C₁₃	—	2	8	no	—
84	C₂²×C₄×C₁₃	—	2	16	no	—
85	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
86	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
87	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
88	C₂²×C₄×C₁₃	C₂×Q₈	1	16	yes	—
89	C₂²×C₄×C₁₃	C₂×Q₈	1	8	yes	—
90	C₂²×C₄×C₁₃	C₂×Q₈	1	4	yes	—
91	C₂²×C₄×C₁₃	C₂×Q₈	1	8	yes	—
92	C₂²×C₄×C₁₃	#41	1	4	yes	—
93	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
94	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
95	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
96	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
97	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
98	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
99	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
100	C₁₃×C₄⋊C₄	—	2	16	no	—
101	C₁₃×C₄⋊C₄	—	2	8	no	—
102	C₁₃×C₄⋊C₄	—	2	16	no	—
103	C₁₃×C₄⋊C₄	—	2	16	no	—
104	C₁₃×C₄⋊C₄	—	4	32	no	—
105	C₁₃×C₄⋊C₄	C₂×Q₈	1	32	yes	complemented
106	C₄²×C₁₃	—	2	16	no	—
107	C₄²×C₁₃	—	2	16	no	—
108	C₄²×C₁₃	C₂×D₄	1	16	yes	—
109	C₂²×C₄⋊Q₈	C₂×C₁₃	1	1	yes	characteristic
110	C₂²×C₄×Q₈	C₂×C₁₃	1	1	yes	characteristic
111	#2567	C₂×C₁₃	1	16	yes	direct product factor
112	C₂×#395	C₂×C₁₃	1	4	yes	—
113	C₂×#391	C₂×C₁₃	1	2	yes	—
114	C₂×#389	C₂×C₁₃	1	4	yes	—
115	C₂×#384	C₂×C₁₃	1	2	yes	—
116	C₂×C₄×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic
117	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
118	C₂³×C₁₃	C₂²×Q₈	1	2	yes	—
119	C₂³×C₁₃	C₂²×Q₈	1	4	yes	—
120	C₂³×C₁₃	C₂×#41	1	2	yes	—
121	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
122	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
123	Q₈×C₁₃	—	2	32	no	—
124	Q₈×C₁₃	—	4	32	no	—
125	C₂×C₄×C₁₃	—	2	16	no	—
126	C₂×C₄×C₁₃	—	2	8	no	—
127	C₂×C₄×C₁₃	—	2	32	no	—
128	C₂×C₄×C₁₃	—	2	4	no	—
129	C₂×C₄×C₁₃	—	2	8	no	—
130	C₂×C₄×C₁₃	—	2	4	no	—
131	C₂×C₄×C₁₃	—	2	8	no	—
132	C₂×C₄×C₁₃	—	2	4	no	—
133	C₂×C₄×C₁₃	—	2	4	no	—
134	C₂×C₄×C₁₃	—	2	8	no	—
135	C₂×C₄×C₁₃	—	2	8	no	—
136	C₂×C₄×C₁₃	—	2	16	no	—
137	C₂×C₄×C₁₃	—	4	8	no	—
138	C₂×C₄×C₁₃	—	4	16	no	—
139	C₂×C₄×C₁₃	C₂²⋊Q₈	1	16	yes	—
140	C₂×C₄×C₁₃	C₄⋊Q₈	1	16	yes	—
141	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
142	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
143	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
144	C₂×C₄×C₁₃	C₂²×Q₈	1	16	yes	—
145	C₂×C₄×C₁₃	C₂²×Q₈	1	8	yes	—
146	C₂×C₄×C₁₃	C₂²×Q₈	1	4	yes	—
147	C₂×C₄×C₁₃	C₂²×Q₈	1	8	yes	—
148	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
149	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
150	C₂³×Q₈	C₂²×C₁₃	1	2	yes	—
151	C₂×C₄⋊Q₈	—	2	8	no	—
152	C₂×C₄⋊Q₈	C₂²×C₁₃	1	8	yes	—
153	C₂×C₄×Q₈	—	2	8	no	—
154	C₂×C₄×Q₈	C₂²×C₁₃	1	8	yes	—
155	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
156	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
157	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
158	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
159	C₂²×C₄⋊C₄	C₂²×C₁₃	1	8	yes	—
160	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
161	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
162	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
163	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
164	#395	C₂²×C₁₃	1	32	yes	—
165	#391	C₂²×C₁₃	1	16	yes	—
166	#389	C₂²×C₁₃	1	32	yes	—
167	#384	C₂²×C₁₃	1	16	yes	—
168	C₄×C₄⋊C₄	C₂²×C₁₃	1	8	yes	—
169	C₂×#95	C₂²×C₁₃	1	2	yes	—
170	C₂×#95	C₂²×C₁₃	1	8	yes	—
171	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	4	yes	—
172	C₂²×C₁₃	C₂×C₄⋊Q₈	1	4	yes	—
173	C₂²×C₁₃	#535	1	4	yes	—
174	C₂²×C₁₃	#554	1	8	yes	—
175	C₂²×C₁₃	Q₈²	1	8	yes	—
176	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
177	C₂²×C₁₃	C₂³×Q₈	1	1	yes	characteristic
178	C₂²×C₁₃	C₂³×Q₈	1	2	yes	—
179	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
180	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
181	C₄×C₁₃	—	2	8	no	—
182	C₄×C₁₃	—	2	4	no	—
183	C₄×C₁₃	—	2	16	no	—
184	C₄×C₁₃	—	4	4	no	—
185	C₄×C₁₃	—	4	8	no	—
186	C₄×C₁₃	C₂×C₂²⋊Q₈	1	8	yes	—
187	C₄×C₁₃	C₂×C₄⋊Q₈	1	8	yes	—
188	C₂²×Q₈	—	2	4	no	—
189	C₂²×Q₈	—	2	8	no	—
190	C₂²×Q₈	—	2	4	no	—
191	C₂²×Q₈	—	4	8	no	—
192	C₂²×Q₈	Q₈×C₁₃	1	8	yes	complemented
193	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
194	C₂²×Q₈	C₂³×C₁₃	1	8	yes	—
195	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
196	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
197	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
198	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
199	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
200	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
201	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
202	C₄⋊Q₈	—	2	32	no	—
203	C₄×Q₈	—	2	32	no	—
204	C₂×C₄⋊C₄	—	2	8	no	—
205	C₂×C₄⋊C₄	—	2	4	no	—
206	C₂×C₄⋊C₄	—	2	8	no	—
207	C₂×C₄⋊C₄	—	2	8	no	—
208	C₂×C₄⋊C₄	—	4	16	no	—
209	C₂×C₄⋊C₄	Q₈×C₁₃	1	16	yes	complemented
210	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
211	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
212	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
213	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
214	C₂×C₄⋊C₄	C₂³×C₁₃	1	32	yes	—
215	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
216	C₂×C₄²	—	2	8	no	—
217	C₂×C₄²	—	2	8	no	—
218	C₂×C₄²	D₄×C₁₃	1	8	yes	—
219	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
220	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
221	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
222	#95	C₂³×C₁₃	1	8	yes	—
223	#95	C₂³×C₁₃	1	32	yes	—
224	C₂×C₁₃	#2567	1	8	yes	direct product factor
225	C₂×C₁₃	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
226	C₂×C₁₃	C₂²×C₄⋊Q₈	1	1	yes	characteristic
227	C₂×C₁₃	C₂×#535	1	1	yes	characteristic
228	C₂×C₁₃	C₂×#554	1	2	yes	—
229	C₂×C₁₃	C₂×Q₈²	1	2	yes	—
230	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
231	C₂×Q₈	—	2	32	no	—
232	C₂×Q₈	—	2	8	no	—
233	C₂×Q₈	—	2	16	no	—
234	C₂×Q₈	—	2	8	no	—
235	C₂×Q₈	—	4	16	no	—
236	C₂×Q₈	—	4	32	no	—
237	C₂×Q₈	C₂×Q₈×C₁₃	1	16	yes	complemented
238	C₂²×C₄	—	2	4	no	—
239	C₂²×C₄	—	2	8	no	—
240	C₂²×C₄	—	2	4	no	—
241	C₂²×C₄	—	2	8	no	—
242	C₂²×C₄	—	2	4	no	—
243	C₂²×C₄	—	2	4	no	—
244	C₂²×C₄	—	2	8	no	—
245	C₂²×C₄	—	2	8	no	—
246	C₂²×C₄	—	2	16	no	—
247	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
248	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
249	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
250	C₂²×C₄	C₂×Q₈×C₁₃	1	16	yes	—
251	C₂²×C₄	C₂×Q₈×C₁₃	1	8	yes	—
252	C₂²×C₄	C₂×Q₈×C₁₃	1	4	yes	—
253	C₂²×C₄	C₂×Q₈×C₁₃	1	8	yes	—
254	C₂²×C₄	C₁₃×#41	1	4	yes	—
255	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
256	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
257	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
258	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
259	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
260	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
261	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
262	C₄⋊C₄	—	2	16	no	—
263	C₄⋊C₄	—	2	8	no	—
264	C₄⋊C₄	—	2	16	no	—
265	C₄⋊C₄	—	2	16	no	—
266	C₄⋊C₄	—	4	32	no	—
267	C₄⋊C₄	C₂×Q₈×C₁₃	1	32	yes	complemented
268	C₄²	—	2	16	no	—
269	C₄²	—	2	16	no	—
270	C₄²	C₂×D₄×C₁₃	1	16	yes	—
271	C₁₃	C₂×#2567	1	1	yes	characteristic, direct product factor, Sylow
272	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
273	C₂³	C₂²×Q₈×C₁₃	1	2	yes	—
274	C₂³	C₂²×Q₈×C₁₃	1	4	yes	—
275	C₂³	C₂×C₁₃×#41	1	2	yes	—
276	C₂³	C₁₃×H(5,𝔽₂)	1	4	yes	—
277	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
278	Q₈	—	2	32	no	—
279	Q₈	—	4	32	no	—
280	C₂×C₄	—	2	16	no	—
281	C₂×C₄	—	2	8	no	—
282	C₂×C₄	—	2	32	no	—
283	C₂×C₄	—	2	4	no	—
284	C₂×C₄	—	2	8	no	—
285	C₂×C₄	—	2	4	no	—
286	C₂×C₄	—	2	8	no	—
287	C₂×C₄	—	2	4	no	—
288	C₂×C₄	—	2	4	no	—
289	C₂×C₄	—	2	8	no	—
290	C₂×C₄	—	2	8	no	—
291	C₂×C₄	—	2	16	no	—
292	C₂×C₄	—	4	8	no	—
293	C₂×C₄	—	4	16	no	—
294	C₂×C₄	C₁₃×C₂²⋊Q₈	1	16	yes	—
295	C₂×C₄	C₁₃×C₄⋊Q₈	1	16	yes	—
296	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
297	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
298	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
299	C₂×C₄	C₂²×Q₈×C₁₃	1	16	yes	—
300	C₂×C₄	C₂²×Q₈×C₁₃	1	8	yes	—
301	C₂×C₄	C₂²×Q₈×C₁₃	1	4	yes	—
302	C₂×C₄	C₂²×Q₈×C₁₃	1	8	yes	—
303	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
304	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	4	yes	—
305	C₂²	C₂×C₁₃×C₄⋊Q₈	1	4	yes	—
306	C₂²	C₁₃×#535	1	4	yes	—
307	C₂²	C₁₃×#554	1	8	yes	—
308	C₂²	Q₈²×C₁₃	1	8	yes	—
309	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
310	C₂²	C₂³×Q₈×C₁₃	1	1	yes	characteristic
311	C₂²	C₂³×Q₈×C₁₃	1	2	yes	—
312	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
313	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
314	C₄	—	2	8	no	—
315	C₄	—	2	4	no	—
316	C₄	—	2	16	no	—
317	C₄	—	4	4	no	—
318	C₄	—	4	8	no	—
319	C₄	C₂×C₁₃×C₂²⋊Q₈	1	8	yes	—
320	C₄	C₂×C₁₃×C₄⋊Q₈	1	8	yes	—
321	C₂	C₁₃×#2567	1	8	yes	direct product factor
322	C₂	C₂²×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
323	C₂	C₂²×C₁₃×C₄⋊Q₈	1	1	yes	characteristic
324	C₂	C₂×C₁₃×#535	1	1	yes	characteristic
325	C₂	C₂×C₁₃×#554	1	2	yes	—
326	C₂	C₂×Q₈²×C₁₃	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₃×#2567	C₂	direct (N × H)
35. C₂²×Q₈×C₁₃	Q₈	semidirect
52. C₂×C₁₃×C₄⋊C₄	Q₈	semidirect
67. C₂×#2567	C₁₃	direct (N × H)
75. C₂×Q₈×C₁₃	C₂×Q₈	semidirect
105. C₁₃×C₄⋊C₄	C₂×Q₈	semidirect
111. #2567	C₂×C₁₃	direct (N × H)
192. C₂²×Q₈	Q₈×C₁₃	semidirect
209. C₂×C₄⋊C₄	Q₈×C₁₃	semidirect
224. C₂×C₁₃	#2567	direct (N × H)
237. C₂×Q₈	C₂×Q₈×C₁₃	semidirect
267. C₄⋊C₄	C₂×Q₈×C₁₃	semidirect
271. C₁₃	C₂×#2567	direct (N × H)
321. C₂	C₁₃×#2567	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₃×C₄⋊Q₈	2
C₂²×C₄×Q₈×C₁₃	2
C₁₃×#2567	2
C₂×C₁₃×#395	2
C₂×C₁₃×#391	2
C₂×C₁₃×#389	2
C₂×C₁₃×#384	2
C₂×C₄×C₁₃×C₄⋊C₄	2
C₂×#2567	13

Subgroups — C2×C13×#2567 #15721279

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2567 #15721279