Subgroups — C₂×C₁₃×#3416 #15748972

Order 3328.

2074 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#578	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#576	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3416	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#510	C₂	1	3	yes	maximal, complemented
5	C₂×C₁₃×#509	C₂	1	3	yes	maximal, complemented
6	C₂×C₁₃×#508	C₂	1	3	yes	maximal, complemented
7	C₂²×C₁₃×SD₃₂	C₂	1	3	yes	maximal, complemented
8	C₂×C₁₃×#504	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×2₋¹⁺⁴	—	2	1	no	—
10	C₂×C₁₃×H(5,𝔽₂)	—	2	1	no	—
11	C₁₃×#578	—	2	4	no	—
12	C₁₃×#578	C₂²	1	8	yes	complemented
13	C₁₃×#576	—	2	4	no	—
14	C₁₃×#576	C₂²	1	8	yes	complemented
15	C₂×C₁₃×#137	—	2	3	no	—
16	C₂×C₁₃×AGL(1,ℤ/8)	—	2	3	no	—
17	C₂×C₁₃×#135	C₂²	1	3	yes	—
18	C₂×C₁₃×#135	C₂²	1	3	yes	complemented
19	C₂²×C₁₃×Q₁₆	C₂²	1	3	yes	complemented
20	C₂²×C₁₃×D₈	C₂²	1	3	yes	—
21	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
22	C₁₃×#510	C₂²	1	24	yes	complemented
23	C₁₃×#509	C₂²	1	24	yes	complemented
24	C₁₃×#508	C₂²	1	24	yes	complemented
25	C₂×C₁₃×Q₃₂	C₂²	1	3	yes	complemented
26	C₂×C₁₃×SD₃₂	C₂²	1	3	yes	complemented
27	C₂×C₁₃×SD₃₂	C₂²	1	6	yes	complemented
28	C₂×C₁₃×SD₃₂	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₁₃×SD₃₂	C₂²	1	24	yes	complemented
30	C₂×C₁₃×D₁₆	C₂²	1	3	yes	complemented
31	C₁₃×#504	C₂²	1	8	yes	complemented
32	C₂×C₁₃×M₃₂	C₂²	1	3	yes	complemented
33	C₂²×C₁₃×C₁₆	C₂²	1	3	yes	complemented
34	C₁₃×2₋¹⁺⁴	—	2	8	no	—
35	C₁₃×2₋¹⁺⁴	—	4	4	no	—
36	C₁₃×H(5,𝔽₂)	—	2	8	no	—
37	C₁₃×H(5,𝔽₂)	—	4	4	no	—
38	C₂×C₁₃×#41	—	2	3	no	—
39	C₂×C₁₃×#41	—	2	3	no	—
40	C₂×C₁₃×#41	—	4	1	no	—
41	C₂×C₁₃×#41	—	4	3	no	—
42	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
43	C₂²×Q₈×C₁₃	—	2	3	no	—
44	C₂²×Q₈×C₁₃	—	4	1	no	—
45	C₂²×D₄×C₁₃	—	2	3	no	—
46	C₂²×D₄×C₁₃	—	4	3	no	—
47	C₁₃×#137	—	2	24	no	—
48	C₁₃×AGL(1,ℤ/8)	—	2	24	no	—
49	C₁₃×#135	—	2	6	no	—
50	C₁₃×#135	—	2	6	no	—
51	C₁₃×#135	C₂³	1	12	yes	—
52	C₁₃×#135	C₂³	1	12	yes	complemented
53	C₂×C₁₃×Q₁₆	—	2	3	no	—
54	C₂×C₁₃×Q₁₆	—	2	6	no	—
55	C₂×C₁₃×Q₁₆	C₂³	1	3	yes	—
56	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
57	C₂×C₁₃×Q₁₆	C₂³	1	12	yes	complemented
58	C₂×C₁₃×SD₁₆	—	2	3	no	—
59	C₂×C₁₃×SD₁₆	—	2	3	no	—
60	C₂×C₁₃×D₈	—	2	3	no	—
61	C₂×C₁₃×D₈	—	2	6	no	—
62	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
63	C₂×C₁₃×D₈	C₂³	1	3	yes	—
64	C₂×C₁₃×D₈	C₂³	1	12	yes	—
65	C₁₃×#131	D₄	1	4	yes	—
66	C₁₃×#131	C₂³	1	4	yes	—
67	C₂×C₁₃×M₁₆	D₄	1	3	yes	—
68	C₂²×C₈×C₁₃	C₂³	1	3	yes	—
69	C₁₃×Q₃₂	C₂³	1	12	yes	complemented
70	C₁₃×SD₃₂	C₂³	1	12	yes	complemented
71	C₁₃×SD₃₂	C₂³	1	24	yes	complemented
72	C₁₃×SD₃₂	C₂³	1	4	yes	complemented
73	C₁₃×D₁₆	C₂³	1	12	yes	complemented
74	C₁₃×M₃₂	C₂³	1	12	yes	complemented
75	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
76	C₂×C₁₃×C₁₆	C₂³	1	3	yes	—
77	C₂×C₁₃×C₁₆	C₂³	1	12	yes	complemented
78	C₂×#3416	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
79	C₂⁴×C₁₃	—	4	3	no	—
80	C₁₃×#41	—	2	12	no	—
81	C₁₃×#41	—	2	12	no	—
82	C₁₃×#41	—	4	8	no	—
83	C₁₃×#41	—	4	24	no	—
84	C₁₃×#41	—	4	6	no	—
85	C₁₃×#41	—	4	6	no	—
86	C₁₃×#41	D₈	1	4	yes	—
87	C₁₃×#41	C₂×D₄	1	4	yes	—
88	C₂×Q₈×C₁₃	—	2	1	no	—
89	C₂×Q₈×C₁₃	—	2	3	no	—
90	C₂×Q₈×C₁₃	—	2	12	no	—
91	C₂×Q₈×C₁₃	—	4	8	no	—
92	C₂×Q₈×C₁₃	—	4	3	no	—
93	C₂×Q₈×C₁₃	—	4	6	no	—
94	C₂×Q₈×C₁₃	D₈	1	1	yes	characteristic
95	C₂×D₄×C₁₃	—	2	3	no	—
96	C₂×D₄×C₁₃	—	2	12	no	—
97	C₂×D₄×C₁₃	—	2	1	no	—
98	C₂×D₄×C₁₃	—	4	3	no	—
99	C₂×D₄×C₁₃	—	4	3	no	—
100	C₂×D₄×C₁₃	—	4	24	no	—
101	C₂×D₄×C₁₃	—	4	3	no	—
102	C₂×D₄×C₁₃	—	4	6	no	—
103	C₂×D₄×C₁₃	D₈	1	3	yes	—
104	C₂²×C₄×C₁₃	—	4	3	no	—
105	C₂²×C₄×C₁₃	—	4	3	no	—
106	C₂²×C₄×C₁₃	—	4	3	no	—
107	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
108	C₁₃×Q₁₆	—	2	3	no	—
109	C₁₃×Q₁₆	—	2	12	no	—
110	C₁₃×Q₁₆	—	2	1	no	—
111	C₁₃×Q₁₆	C₂⁴	1	6	yes	—
112	C₁₃×Q₁₆	C₂⁴	1	2	yes	—
113	C₁₃×SD₁₆	—	2	12	no	—
114	C₁₃×SD₁₆	—	2	12	no	—
115	C₁₃×D₈	—	2	3	no	—
116	C₁₃×D₈	—	2	12	no	—
117	C₁₃×D₈	—	2	1	no	—
118	C₁₃×D₈	C₂⁴	1	2	yes	—
119	C₁₃×D₈	C₂⁴	1	6	yes	—
120	C₁₃×M₁₆	C₂×D₄	1	12	yes	—
121	C₂×C₈×C₁₃	C₂×D₄	1	3	yes	—
122	C₂×C₈×C₁₃	C₂×D₄	1	6	yes	—
123	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
124	C₂×C₈×C₁₃	C₂⁴	1	6	yes	—
125	C₁₃×C₁₆	C₂⁴	1	2	yes	—
126	C₁₃×C₁₆	C₂⁴	1	6	yes	—
127	C₂×#578	C₂×C₁₃	1	1	yes	characteristic, complemented
128	C₂×#576	C₂×C₁₃	1	1	yes	characteristic, complemented
129	#3416	C₂×C₁₃	1	16	yes	direct product factor
130	C₂×#510	C₂×C₁₃	1	3	yes	complemented
131	C₂×#509	C₂×C₁₃	1	3	yes	complemented
132	C₂×#508	C₂×C₁₃	1	3	yes	complemented
133	C₂²×SD₃₂	C₂×C₁₃	1	3	yes	complemented
134	C₂×#504	C₂×C₁₃	1	1	yes	characteristic, complemented
135	C₂³×C₁₃	—	4	1	no	—
136	C₂³×C₁₃	—	4	3	no	—
137	C₂³×C₁₃	—	4	12	no	—
138	C₂³×C₁₃	—	16	6	no	—
139	C₂³×C₁₃	C₂×D₈	1	3	yes	—
140	Q₈×C₁₃	—	2	2	no	—
141	Q₈×C₁₃	—	2	6	no	—
142	Q₈×C₁₃	—	4	12	no	—
143	Q₈×C₁₃	—	4	3	no	—
144	Q₈×C₁₃	—	4	1	no	—
145	Q₈×C₁₃	C₂×D₈	1	4	yes	—
146	D₄×C₁₃	—	2	6	no	—
147	D₄×C₁₃	—	2	2	no	—
148	D₄×C₁₃	—	4	12	no	—
149	D₄×C₁₃	—	4	12	no	—
150	D₄×C₁₃	—	4	12	no	—
151	D₄×C₁₃	—	4	3	no	—
152	D₄×C₁₃	—	4	1	no	—
153	D₄×C₁₃	C₂×D₈	1	12	yes	—
154	C₂×C₄×C₁₃	—	4	12	no	—
155	C₂×C₄×C₁₃	—	4	1	no	—
156	C₂×C₄×C₁₃	—	4	3	no	—
157	C₂×C₄×C₁₃	—	4	12	no	—
158	C₂×C₄×C₁₃	—	4	12	no	—
159	C₂×C₄×C₁₃	C₂×D₈	1	6	yes	—
160	C₂×C₄×C₁₃	C₂×D₈	1	3	yes	—
161	C₂×C₄×C₁₃	C₂²×D₄	1	6	yes	—
162	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
163	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
164	C₈×C₁₃	C₂²×D₄	1	6	yes	—
165	C₈×C₁₃	C₂⁵	1	1	yes	characteristic
166	C₂×2₋¹⁺⁴	—	2	1	no	—
167	C₂×H(5,𝔽₂)	—	2	1	no	—
168	#578	—	2	4	no	—
169	#578	C₂²×C₁₃	1	8	yes	complemented
170	#576	—	2	4	no	—
171	#576	C₂²×C₁₃	1	8	yes	complemented
172	C₂×#137	—	2	3	no	—
173	C₂×AGL(1,ℤ/8)	—	2	3	no	—
174	C₂×#135	C₂²×C₁₃	1	3	yes	—
175	C₂×#135	C₂²×C₁₃	1	3	yes	complemented
176	C₂²×Q₁₆	C₂²×C₁₃	1	3	yes	complemented
177	C₂²×D₈	C₂²×C₁₃	1	3	yes	—
178	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
179	#510	C₂²×C₁₃	1	24	yes	complemented
180	#509	C₂²×C₁₃	1	24	yes	complemented
181	#508	C₂²×C₁₃	1	24	yes	complemented
182	C₂×Q₃₂	C₂²×C₁₃	1	3	yes	complemented
183	C₂×SD₃₂	C₂²×C₁₃	1	3	yes	complemented
184	C₂×SD₃₂	C₂²×C₁₃	1	6	yes	complemented
185	C₂×SD₃₂	C₂²×C₁₃	1	1	yes	characteristic, complemented
186	C₂×SD₃₂	C₂²×C₁₃	1	24	yes	complemented
187	C₂×D₁₆	C₂²×C₁₃	1	3	yes	complemented
188	#504	C₂²×C₁₃	1	8	yes	complemented
189	C₂×M₃₂	C₂²×C₁₃	1	3	yes	complemented
190	C₂²×C₁₆	C₂²×C₁₃	1	3	yes	complemented
191	C₂²×C₁₃	—	2	6	no	—
192	C₂²×C₁₃	—	4	2	no	—
193	C₂²×C₁₃	—	4	6	no	—
194	C₂²×C₁₃	—	8	2	no	—
195	C₂²×C₁₃	—	8	6	no	—
196	C₂²×C₁₃	—	16	12	no	—
197	C₂²×C₁₃	C₂²×D₈	1	6	yes	—
198	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
199	C₄×C₁₃	—	4	2	no	—
200	C₄×C₁₃	—	4	6	no	—
201	C₄×C₁₃	C₂²×D₈	1	6	yes	—
202	C₄×C₁₃	C₂²×D₈	1	1	yes	characteristic
203	C₄×C₁₃	C₂³×D₄	1	1	yes	characteristic
204	2₋¹⁺⁴	—	2	8	no	—
205	2₋¹⁺⁴	—	4	4	no	—
206	H(5,𝔽₂)	—	2	8	no	—
207	H(5,𝔽₂)	—	4	4	no	—
208	C₂×#41	—	2	3	no	—
209	C₂×#41	—	2	3	no	—
210	C₂×#41	—	4	1	no	—
211	C₂×#41	—	4	3	no	—
212	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
213	C₂²×Q₈	—	2	3	no	—
214	C₂²×Q₈	—	4	1	no	—
215	C₂²×D₄	—	2	3	no	—
216	C₂²×D₄	—	4	3	no	—
217	#137	—	2	24	no	—
218	AGL(1,ℤ/8)	—	2	24	no	—
219	#135	—	2	6	no	—
220	#135	—	2	6	no	—
221	#135	C₂³×C₁₃	1	12	yes	—
222	#135	C₂³×C₁₃	1	12	yes	complemented
223	C₂×Q₁₆	—	2	3	no	—
224	C₂×Q₁₆	—	2	6	no	—
225	C₂×Q₁₆	C₂³×C₁₃	1	3	yes	—
226	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
227	C₂×Q₁₆	C₂³×C₁₃	1	12	yes	complemented
228	C₂×SD₁₆	—	2	3	no	—
229	C₂×SD₁₆	—	2	3	no	—
230	C₂×D₈	—	2	3	no	—
231	C₂×D₈	—	2	6	no	—
232	C₂×D₈	C₂³×C₁₃	1	3	yes	—
233	C₂×D₈	C₂³×C₁₃	1	12	yes	—
234	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
235	#131	D₄×C₁₃	1	4	yes	—
236	#131	C₂³×C₁₃	1	4	yes	—
237	C₂×M₁₆	D₄×C₁₃	1	3	yes	—
238	C₂²×C₈	C₂³×C₁₃	1	3	yes	—
239	Q₃₂	C₂³×C₁₃	1	12	yes	complemented
240	SD₃₂	C₂³×C₁₃	1	12	yes	complemented
241	SD₃₂	C₂³×C₁₃	1	24	yes	complemented
242	SD₃₂	C₂³×C₁₃	1	4	yes	complemented
243	D₁₆	C₂³×C₁₃	1	12	yes	complemented
244	M₃₂	C₂³×C₁₃	1	12	yes	complemented
245	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
246	C₂×C₁₆	C₂³×C₁₃	1	3	yes	—
247	C₂×C₁₆	C₂³×C₁₃	1	12	yes	complemented
248	C₂×C₁₃	—	2	6	no	—
249	C₂×C₁₃	—	8	2	no	—
250	C₂×C₁₃	—	8	6	no	—
251	C₂×C₁₃	#3416	1	2	yes	direct product factor
252	C₂×C₁₃	C₂³×D₈	1	1	yes	characteristic
253	C₂⁴	—	4	3	no	—
254	#41	—	2	12	no	—
255	#41	—	2	12	no	—
256	#41	—	4	8	no	—
257	#41	—	4	24	no	—
258	#41	—	4	6	no	—
259	#41	—	4	6	no	—
260	#41	C₁₃×D₈	1	4	yes	—
261	#41	C₂×D₄×C₁₃	1	4	yes	—
262	C₂×Q₈	—	2	1	no	—
263	C₂×Q₈	—	2	3	no	—
264	C₂×Q₈	—	2	12	no	—
265	C₂×Q₈	—	4	8	no	—
266	C₂×Q₈	—	4	3	no	—
267	C₂×Q₈	—	4	6	no	—
268	C₂×Q₈	C₁₃×D₈	1	1	yes	characteristic
269	C₂×D₄	—	2	3	no	—
270	C₂×D₄	—	2	12	no	—
271	C₂×D₄	—	2	1	no	—
272	C₂×D₄	—	4	3	no	—
273	C₂×D₄	—	4	3	no	—
274	C₂×D₄	—	4	24	no	—
275	C₂×D₄	—	4	3	no	—
276	C₂×D₄	—	4	6	no	—
277	C₂×D₄	C₁₃×D₈	1	3	yes	—
278	C₂²×C₄	—	4	3	no	—
279	C₂²×C₄	—	4	3	no	—
280	C₂²×C₄	—	4	3	no	—
281	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
282	Q₁₆	—	2	3	no	—
283	Q₁₆	—	2	12	no	—
284	Q₁₆	—	2	1	no	—
285	Q₁₆	C₂⁴×C₁₃	1	6	yes	—
286	Q₁₆	C₂⁴×C₁₃	1	2	yes	—
287	SD₁₆	—	2	12	no	—
288	SD₁₆	—	2	12	no	—
289	D₈	—	2	3	no	—
290	D₈	—	2	12	no	—
291	D₈	—	2	1	no	—
292	D₈	C₂⁴×C₁₃	1	2	yes	—
293	D₈	C₂⁴×C₁₃	1	6	yes	—
294	M₁₆	C₂×D₄×C₁₃	1	12	yes	—
295	C₂×C₈	C₂×D₄×C₁₃	1	3	yes	—
296	C₂×C₈	C₂×D₄×C₁₃	1	6	yes	—
297	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
298	C₂×C₈	C₂⁴×C₁₃	1	6	yes	—
299	C₁₆	C₂⁴×C₁₃	1	2	yes	—
300	C₁₆	C₂⁴×C₁₃	1	6	yes	—
301	C₁₃	C₂×#3416	1	1	yes	characteristic, direct product factor, Sylow
302	C₂³	—	4	1	no	—
303	C₂³	—	4	3	no	—
304	C₂³	—	4	12	no	—
305	C₂³	—	16	6	no	—
306	C₂³	C₂×C₁₃×D₈	1	3	yes	—
307	Q₈	—	2	2	no	—
308	Q₈	—	2	6	no	—
309	Q₈	—	4	12	no	—
310	Q₈	—	4	3	no	—
311	Q₈	—	4	1	no	—
312	Q₈	C₂×C₁₃×D₈	1	4	yes	—
313	D₄	—	2	6	no	—
314	D₄	—	2	2	no	—
315	D₄	—	4	12	no	—
316	D₄	—	4	12	no	—
317	D₄	—	4	12	no	—
318	D₄	—	4	3	no	—
319	D₄	—	4	1	no	—
320	D₄	C₂×C₁₃×D₈	1	12	yes	—
321	C₂×C₄	—	4	1	no	—
322	C₂×C₄	—	4	3	no	—
323	C₂×C₄	—	4	12	no	—
324	C₂×C₄	—	4	12	no	—
325	C₂×C₄	—	4	12	no	—
326	C₂×C₄	C₂×C₁₃×D₈	1	3	yes	—
327	C₂×C₄	C₂×C₁₃×D₈	1	6	yes	—
328	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
329	C₂×C₄	C₂²×D₄×C₁₃	1	6	yes	—
330	C₈	C₂²×D₄×C₁₃	1	1	yes	characteristic
331	C₈	C₂²×D₄×C₁₃	1	6	yes	—
332	C₈	C₂⁵×C₁₃	1	1	yes	characteristic
333	C₂²	—	2	6	no	—
334	C₂²	—	4	2	no	—
335	C₂²	—	4	6	no	—
336	C₂²	—	8	2	no	—
337	C₂²	—	8	6	no	—
338	C₂²	—	16	12	no	—
339	C₂²	C₂²×C₁₃×D₈	1	6	yes	—
340	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
341	C₄	—	4	2	no	—
342	C₄	—	4	6	no	—
343	C₄	C₂²×C₁₃×D₈	1	6	yes	—
344	C₄	C₂²×C₁₃×D₈	1	1	yes	characteristic
345	C₄	C₂³×D₄×C₁₃	1	1	yes	characteristic
346	C₂	—	2	6	no	—
347	C₂	—	8	6	no	—
348	C₂	—	8	2	no	—
349	C₂	C₁₃×#3416	1	2	yes	direct product factor
350	C₂	C₂³×C₁₃×D₈	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂²×D₈
commutator, Frattini, cosocle	C₈	C₂⁵×C₁₃
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₁₃×#41 ◁ C₂×C₁₃×#131 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#578	C₂	semidirect
2. C₂×C₁₃×#576	C₂	semidirect
3. C₁₃×#3416	C₂	direct (N × H)
4. C₂×C₁₃×#510	C₂	semidirect
5. C₂×C₁₃×#509	C₂	semidirect
6. C₂×C₁₃×#508	C₂	semidirect
7. C₂²×C₁₃×SD₃₂	C₂	semidirect
8. C₂×C₁₃×#504	C₂	semidirect
12. C₁₃×#578	C₂²	semidirect
14. C₁₃×#576	C₂²	semidirect
18. C₂×C₁₃×#135	C₂²	semidirect
19. C₂²×C₁₃×Q₁₆	C₂²	semidirect
22. C₁₃×#510	C₂²	semidirect
23. C₁₃×#509	C₂²	semidirect
24. C₁₃×#508	C₂²	semidirect
25. C₂×C₁₃×Q₃₂	C₂²	semidirect
26. C₂×C₁₃×SD₃₂	C₂²	semidirect
27. C₂×C₁₃×SD₃₂	C₂²	semidirect
28. C₂×C₁₃×SD₃₂	C₂²	semidirect
29. C₂×C₁₃×SD₃₂	C₂²	semidirect
30. C₂×C₁₃×D₁₆	C₂²	semidirect
31. C₁₃×#504	C₂²	semidirect
32. C₂×C₁₃×M₃₂	C₂²	semidirect
33. C₂²×C₁₃×C₁₆	C₂²	semidirect
52. C₁₃×#135	C₂³	semidirect
57. C₂×C₁₃×Q₁₆	C₂³	semidirect
69. C₁₃×Q₃₂	C₂³	semidirect
70. C₁₃×SD₃₂	C₂³	semidirect
71. C₁₃×SD₃₂	C₂³	semidirect
72. C₁₃×SD₃₂	C₂³	semidirect
73. C₁₃×D₁₆	C₂³	semidirect
74. C₁₃×M₃₂	C₂³	semidirect
77. C₂×C₁₃×C₁₆	C₂³	semidirect
78. C₂×#3416	C₁₃	direct (N × H)
127. C₂×#578	C₂×C₁₃	semidirect
128. C₂×#576	C₂×C₁₃	semidirect
129. #3416	C₂×C₁₃	direct (N × H)
130. C₂×#510	C₂×C₁₃	semidirect
131. C₂×#509	C₂×C₁₃	semidirect
132. C₂×#508	C₂×C₁₃	semidirect
133. C₂²×SD₃₂	C₂×C₁₃	semidirect
134. C₂×#504	C₂×C₁₃	semidirect
169. #578	C₂²×C₁₃	semidirect
171. #576	C₂²×C₁₃	semidirect
175. C₂×#135	C₂²×C₁₃	semidirect
176. C₂²×Q₁₆	C₂²×C₁₃	semidirect
179. #510	C₂²×C₁₃	semidirect
180. #509	C₂²×C₁₃	semidirect
181. #508	C₂²×C₁₃	semidirect
182. C₂×Q₃₂	C₂²×C₁₃	semidirect
183. C₂×SD₃₂	C₂²×C₁₃	semidirect
184. C₂×SD₃₂	C₂²×C₁₃	semidirect
185. C₂×SD₃₂	C₂²×C₁₃	semidirect
186. C₂×SD₃₂	C₂²×C₁₃	semidirect
187. C₂×D₁₆	C₂²×C₁₃	semidirect
188. #504	C₂²×C₁₃	semidirect
189. C₂×M₃₂	C₂²×C₁₃	semidirect
190. C₂²×C₁₆	C₂²×C₁₃	semidirect
222. #135	C₂³×C₁₃	semidirect
227. C₂×Q₁₆	C₂³×C₁₃	semidirect
239. Q₃₂	C₂³×C₁₃	semidirect
240. SD₃₂	C₂³×C₁₃	semidirect
241. SD₃₂	C₂³×C₁₃	semidirect
242. SD₃₂	C₂³×C₁₃	semidirect
243. D₁₆	C₂³×C₁₃	semidirect
244. M₃₂	C₂³×C₁₃	semidirect
247. C₂×C₁₆	C₂³×C₁₃	semidirect
251. C₂×C₁₃	#3416	direct (N × H)
301. C₁₃	C₂×#3416	direct (N × H)
349. C₂	C₁₃×#3416	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×#578	2
C₂×C₁₃×#576	2
C₁₃×#3416	2
C₂×C₁₃×#510	2
C₂×C₁₃×#509	2
C₂×C₁₃×#508	2
C₂²×C₁₃×SD₃₂	2
C₂×C₁₃×#504	2
C₂×#3416	13

Subgroups — C2×C13×#3416 #15748972

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3416 #15748972