Subgroups — C₂²×C₁₃×#534 #15749008

Order 3328.

15230 conjugacy classes of subgroups.

The subgroup lattice has 288 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×D₄×C₁₃	C₂	1	2	yes	maximal, complemented
2	C₂×C₁₃×#534	C₂	1	48	yes	maximal, direct product factor
3	C₂²×C₁₃×#123	C₂	1	4	yes	maximal, complemented
4	C₂²×C₁₃×#121	C₂	1	4	yes	maximal, complemented
5	C₂²×C₁₃×#120	C₂	1	4	yes	maximal, complemented
6	C₂³×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂⁶×C₁₃	C₂²	1	1	yes	characteristic
8	C₂⁶×C₁₃	C₂²	1	2	yes	complemented
9	C₂³×D₄×C₁₃	—	2	32	no	—
10	C₂³×D₄×C₁₃	C₂²	1	4	yes	—
11	C₂³×D₄×C₁₃	C₂²	1	4	yes	complemented
12	C₂³×D₄×C₁₃	C₂²	1	4	yes	complemented
13	C₂³×D₄×C₁₃	C₂²	1	48	yes	complemented
14	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	complemented
15	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	complemented
16	C₁₃×#534	C₂²	1	256	yes	direct product factor
17	C₂×C₁₃×#123	C₂²	1	96	yes	complemented
18	C₂×C₁₃×#121	C₂²	1	96	yes	complemented
19	C₂×C₁₃×#120	C₂²	1	96	yes	complemented
20	C₂²×C₁₃×C₄⋊C₄	C₂²	1	4	yes	complemented
21	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
22	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	complemented
23	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	24	yes	complemented
24	C₂⁵×C₁₃	—	2	16	no	—
25	C₂⁵×C₁₃	—	4	8	no	—
26	C₂⁵×C₁₃	—	4	16	no	—
27	C₂⁵×C₁₃	D₄	1	16	yes	complemented
28	C₂⁵×C₁₃	C₂³	1	4	yes	—
29	C₂⁵×C₁₃	C₂³	1	2	yes	—
30	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
31	C₂⁵×C₁₃	C₂³	1	12	yes	—
32	C₂⁵×C₁₃	C₂³	1	24	yes	complemented
33	C₂²×D₄×C₁₃	—	2	32	no	—
34	C₂²×D₄×C₁₃	—	2	32	no	—
35	C₂²×D₄×C₁₃	—	2	384	no	—
36	C₂²×D₄×C₁₃	—	4	16	no	—
37	C₂²×D₄×C₁₃	C₂³	1	48	yes	—
38	C₂²×D₄×C₁₃	C₂³	1	48	yes	complemented
39	C₂²×D₄×C₁₃	C₂³	1	48	yes	complemented
40	C₂²×D₄×C₁₃	C₂³	1	128	yes	complemented
41	C₂³×C₄×C₁₃	—	2	16	no	—
42	C₂³×C₄×C₁₃	—	4	8	no	—
43	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
44	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
45	C₂³×C₄×C₁₃	C₂³	1	24	yes	complemented
46	C₂³×C₄×C₁₃	C₂³	1	24	yes	complemented
47	C₁₃×#123	C₂³	1	256	yes	complemented
48	C₁₃×#121	C₂³	1	256	yes	complemented
49	C₁₃×#120	C₂³	1	256	yes	complemented
50	C₂×C₁₃×C₄⋊C₄	C₂³	1	48	yes	complemented
51	C₂×C₁₃×C₂²⋊C₄	C₂³	1	48	yes	complemented
52	C₂×C₁₃×C₂²⋊C₄	C₂³	1	96	yes	complemented
53	C₂×C₁₃×C₂²⋊C₄	C₂³	1	64	yes	complemented
54	C₂²×#534	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
55	C₂⁴×C₁₃	—	2	8	no	—
56	C₂⁴×C₁₃	—	2	16	no	—
57	C₂⁴×C₁₃	—	2	16	no	—
58	C₂⁴×C₁₃	—	2	96	no	—
59	C₂⁴×C₁₃	—	2	32	no	—
60	C₂⁴×C₁₃	—	4	64	no	—
61	C₂⁴×C₁₃	—	4	48	no	—
62	C₂⁴×C₁₃	—	4	96	no	—
63	C₂⁴×C₁₃	—	4	128	no	—
64	C₂⁴×C₁₃	C₂×D₄	1	16	yes	—
65	C₂⁴×C₁₃	C₂×D₄	1	8	yes	—
66	C₂⁴×C₁₃	C₂×D₄	1	96	yes	complemented
67	C₂⁴×C₁₃	C₂⁴	1	24	yes	—
68	C₂⁴×C₁₃	C₂⁴	1	12	yes	—
69	C₂⁴×C₁₃	C₂⁴	1	6	yes	—
70	C₂⁴×C₁₃	C₂⁴	1	16	yes	—
71	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
72	C₂⁴×C₁₃	C₂⁴	1	32	yes	complemented
73	C₂×D₄×C₁₃	—	2	192	no	—
74	C₂×D₄×C₁₃	—	2	192	no	—
75	C₂×D₄×C₁₃	—	2	512	no	—
76	C₂×D₄×C₁₃	—	4	96	no	—
77	C₂×D₄×C₁₃	C₂⁴	1	64	yes	—
78	C₂×D₄×C₁₃	C₂⁴	1	64	yes	complemented
79	C₂×D₄×C₁₃	C₂⁴	1	64	yes	complemented
80	C₂²×C₄×C₁₃	—	2	16	no	—
81	C₂²×C₄×C₁₃	—	2	96	no	—
82	C₂²×C₄×C₁₃	—	2	16	no	—
83	C₂²×C₄×C₁₃	—	4	48	no	—
84	C₂²×C₄×C₁₃	C₂⁴	1	24	yes	—
85	C₂²×C₄×C₁₃	C₂⁴	1	24	yes	—
86	C₂²×C₄×C₁₃	C₂⁴	1	32	yes	complemented
87	C₂²×C₄×C₁₃	C₂⁴	1	32	yes	complemented
88	C₁₃×C₄⋊C₄	C₂⁴	1	64	yes	complemented
89	C₁₃×C₂²⋊C₄	C₂⁴	1	64	yes	complemented
90	C₁₃×C₂²⋊C₄	C₂⁴	1	128	yes	complemented
91	C₂⁴×D₄	C₂×C₁₃	1	2	yes	complemented
92	C₂×#534	C₂×C₁₃	1	48	yes	direct product factor
93	C₂²×#123	C₂×C₁₃	1	4	yes	complemented
94	C₂²×#121	C₂×C₁₃	1	4	yes	complemented
95	C₂²×#120	C₂×C₁₃	1	4	yes	complemented
96	C₂³×C₂²⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
97	C₂³×C₁₃	—	2	64	no	—
98	C₂³×C₁₃	—	2	32	no	—
99	C₂³×C₁₃	—	2	24	no	—
100	C₂³×C₁₃	—	2	48	no	—
101	C₂³×C₁₃	—	2	48	no	—
102	C₂³×C₁₃	—	2	64	no	—
103	C₂³×C₁₃	—	2	96	no	—
104	C₂³×C₁₃	—	4	192	no	—
105	C₂³×C₁₃	—	4	32	no	—
106	C₂³×C₁₃	—	4	64	no	—
107	C₂³×C₁₃	—	4	384	no	—
108	C₂³×C₁₃	—	4	64	no	—
109	C₂³×C₁₃	C₂²×D₄	1	48	yes	—
110	C₂³×C₁₃	C₂²×D₄	1	24	yes	—
111	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
112	C₂³×C₁₃	C₂²×D₄	1	64	yes	complemented
113	C₂³×C₁₃	H(5,𝔽₂)	1	8	yes	—
114	C₂³×C₁₃	C₂⁵	1	16	yes	—
115	C₂³×C₁₃	C₂⁵	1	8	yes	—
116	C₂³×C₁₃	C₂⁵	1	4	yes	—
117	C₂³×C₁₃	C₂⁵	1	3	yes	—
118	D₄×C₁₃	—	2	128	no	—
119	D₄×C₁₃	—	2	128	no	—
120	D₄×C₁₃	—	4	64	no	—
121	C₂×C₄×C₁₃	—	2	48	no	—
122	C₂×C₄×C₁₃	—	2	64	no	—
123	C₂×C₄×C₁₃	—	2	48	no	—
124	C₂×C₄×C₁₃	—	4	32	no	—
125	C₂×C₄×C₁₃	C₂⁵	1	16	yes	—
126	C₂×C₄×C₁₃	C₂⁵	1	16	yes	—
127	C₂⁶	C₂²×C₁₃	1	1	yes	characteristic
128	C₂⁶	C₂²×C₁₃	1	2	yes	complemented
129	C₂³×D₄	—	2	32	no	—
130	C₂³×D₄	C₂²×C₁₃	1	4	yes	—
131	C₂³×D₄	C₂²×C₁₃	1	4	yes	complemented
132	C₂³×D₄	C₂²×C₁₃	1	4	yes	complemented
133	C₂³×D₄	C₂²×C₁₃	1	48	yes	complemented
134	C₂⁴×C₄	C₂²×C₁₃	1	2	yes	complemented
135	C₂⁴×C₄	C₂²×C₁₃	1	2	yes	complemented
136	#534	C₂²×C₁₃	1	256	yes	direct product factor
137	C₂×#123	C₂²×C₁₃	1	96	yes	complemented
138	C₂×#121	C₂²×C₁₃	1	96	yes	complemented
139	C₂×#120	C₂²×C₁₃	1	96	yes	complemented
140	C₂²×C₄⋊C₄	C₂²×C₁₃	1	4	yes	complemented
141	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	complemented
142	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	complemented
143	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	24	yes	complemented
144	C₂²×C₁₃	—	2	8	no	—
145	C₂²×C₁₃	—	2	16	no	—
146	C₂²×C₁₃	—	2	96	no	—
147	C₂²×C₁₃	—	2	48	no	—
148	C₂²×C₁₃	—	2	16	no	—
149	C₂²×C₁₃	—	2	32	no	—
150	C₂²×C₁₃	—	4	64	no	—
151	C₂²×C₁₃	—	4	128	no	—
152	C₂²×C₁₃	—	4	96	no	—
153	C₂²×C₁₃	#534	1	16	yes	direct product factor
154	C₂²×C₁₃	C₂³×D₄	1	16	yes	—
155	C₂²×C₁₃	C₂³×D₄	1	8	yes	—
156	C₂²×C₁₃	C₂³×D₄	1	6	yes	—
157	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	12	yes	—
158	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
159	C₄×C₁₃	—	2	16	no	—
160	C₄×C₁₃	—	2	16	no	—
161	C₂⁵	—	2	16	no	—
162	C₂⁵	—	4	8	no	—
163	C₂⁵	—	4	16	no	—
164	C₂⁵	D₄×C₁₃	1	16	yes	complemented
165	C₂⁵	C₂³×C₁₃	1	4	yes	—
166	C₂⁵	C₂³×C₁₃	1	2	yes	—
167	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
168	C₂⁵	C₂³×C₁₃	1	12	yes	—
169	C₂⁵	C₂³×C₁₃	1	24	yes	complemented
170	C₂²×D₄	—	2	32	no	—
171	C₂²×D₄	—	2	32	no	—
172	C₂²×D₄	—	2	384	no	—
173	C₂²×D₄	—	4	16	no	—
174	C₂²×D₄	C₂³×C₁₃	1	48	yes	—
175	C₂²×D₄	C₂³×C₁₃	1	48	yes	complemented
176	C₂²×D₄	C₂³×C₁₃	1	48	yes	complemented
177	C₂²×D₄	C₂³×C₁₃	1	128	yes	complemented
178	C₂³×C₄	—	2	16	no	—
179	C₂³×C₄	—	4	8	no	—
180	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
181	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
182	C₂³×C₄	C₂³×C₁₃	1	24	yes	complemented
183	C₂³×C₄	C₂³×C₁₃	1	24	yes	complemented
184	#123	C₂³×C₁₃	1	256	yes	complemented
185	#121	C₂³×C₁₃	1	256	yes	complemented
186	#120	C₂³×C₁₃	1	256	yes	complemented
187	C₂×C₄⋊C₄	C₂³×C₁₃	1	48	yes	complemented
188	C₂×C₂²⋊C₄	C₂³×C₁₃	1	48	yes	complemented
189	C₂×C₂²⋊C₄	C₂³×C₁₃	1	96	yes	complemented
190	C₂×C₂²⋊C₄	C₂³×C₁₃	1	64	yes	complemented
191	C₂×C₁₃	—	2	16	no	—
192	C₂×C₁₃	—	2	8	no	—
193	C₂×C₁₃	—	4	16	no	—
194	C₂×C₁₃	C₂×#534	1	12	yes	direct product factor
195	C₂×C₁₃	C₂⁴×D₄	1	1	yes	characteristic
196	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	2	yes	—
197	C₂⁴	—	2	8	no	—
198	C₂⁴	—	2	16	no	—
199	C₂⁴	—	2	16	no	—
200	C₂⁴	—	2	96	no	—
201	C₂⁴	—	2	32	no	—
202	C₂⁴	—	4	64	no	—
203	C₂⁴	—	4	48	no	—
204	C₂⁴	—	4	96	no	—
205	C₂⁴	—	4	128	no	—
206	C₂⁴	C₂×D₄×C₁₃	1	16	yes	—
207	C₂⁴	C₂×D₄×C₁₃	1	8	yes	—
208	C₂⁴	C₂×D₄×C₁₃	1	96	yes	complemented
209	C₂⁴	C₂⁴×C₁₃	1	24	yes	—
210	C₂⁴	C₂⁴×C₁₃	1	12	yes	—
211	C₂⁴	C₂⁴×C₁₃	1	6	yes	—
212	C₂⁴	C₂⁴×C₁₃	1	16	yes	—
213	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
214	C₂⁴	C₂⁴×C₁₃	1	32	yes	complemented
215	C₂×D₄	—	2	192	no	—
216	C₂×D₄	—	2	192	no	—
217	C₂×D₄	—	2	512	no	—
218	C₂×D₄	—	4	96	no	—
219	C₂×D₄	C₂⁴×C₁₃	1	64	yes	—
220	C₂×D₄	C₂⁴×C₁₃	1	64	yes	complemented
221	C₂×D₄	C₂⁴×C₁₃	1	64	yes	complemented
222	C₂²×C₄	—	2	16	no	—
223	C₂²×C₄	—	2	96	no	—
224	C₂²×C₄	—	2	16	no	—
225	C₂²×C₄	—	4	48	no	—
226	C₂²×C₄	C₂⁴×C₁₃	1	24	yes	—
227	C₂²×C₄	C₂⁴×C₁₃	1	24	yes	—
228	C₂²×C₄	C₂⁴×C₁₃	1	32	yes	complemented
229	C₂²×C₄	C₂⁴×C₁₃	1	32	yes	complemented
230	C₄⋊C₄	C₂⁴×C₁₃	1	64	yes	complemented
231	C₂²⋊C₄	C₂⁴×C₁₃	1	64	yes	complemented
232	C₂²⋊C₄	C₂⁴×C₁₃	1	128	yes	complemented
233	C₁₃	C₂²×#534	1	1	yes	characteristic, direct product factor, Sylow
234	C₂³	—	2	64	no	—
235	C₂³	—	2	32	no	—
236	C₂³	—	2	24	no	—
237	C₂³	—	2	48	no	—
238	C₂³	—	2	48	no	—
239	C₂³	—	2	64	no	—
240	C₂³	—	2	96	no	—
241	C₂³	—	4	192	no	—
242	C₂³	—	4	32	no	—
243	C₂³	—	4	64	no	—
244	C₂³	—	4	384	no	—
245	C₂³	—	4	64	no	—
246	C₂³	C₂²×D₄×C₁₃	1	48	yes	—
247	C₂³	C₂²×D₄×C₁₃	1	24	yes	—
248	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
249	C₂³	C₂²×D₄×C₁₃	1	64	yes	complemented
250	C₂³	C₁₃×H(5,𝔽₂)	1	8	yes	—
251	C₂³	C₂⁵×C₁₃	1	16	yes	—
252	C₂³	C₂⁵×C₁₃	1	8	yes	—
253	C₂³	C₂⁵×C₁₃	1	4	yes	—
254	C₂³	C₂⁵×C₁₃	1	3	yes	—
255	D₄	—	2	128	no	—
256	D₄	—	2	128	no	—
257	D₄	—	4	64	no	—
258	C₂×C₄	—	2	48	no	—
259	C₂×C₄	—	2	64	no	—
260	C₂×C₄	—	2	48	no	—
261	C₂×C₄	—	4	32	no	—
262	C₂×C₄	C₂⁵×C₁₃	1	16	yes	—
263	C₂×C₄	C₂⁵×C₁₃	1	16	yes	—
264	C₂²	—	2	8	no	—
265	C₂²	—	2	16	no	—
266	C₂²	—	2	96	no	—
267	C₂²	—	2	48	no	—
268	C₂²	—	2	16	no	—
269	C₂²	—	2	32	no	—
270	C₂²	—	4	64	no	—
271	C₂²	—	4	128	no	—
272	C₂²	—	4	96	no	—
273	C₂²	C₁₃×#534	1	16	yes	direct product factor
274	C₂²	C₂³×D₄×C₁₃	1	16	yes	—
275	C₂²	C₂³×D₄×C₁₃	1	8	yes	—
276	C₂²	C₂³×D₄×C₁₃	1	6	yes	—
277	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	12	yes	—
278	C₂²	C₂⁶×C₁₃	1	1	yes	characteristic
279	C₄	—	2	16	no	—
280	C₄	—	2	16	no	—
281	C₂	—	2	16	no	—
282	C₂	—	2	8	no	—
283	C₂	—	4	16	no	—
284	C₂	C₂×C₁₃×#534	1	12	yes	direct product factor
285	C₂	C₂⁴×D₄×C₁₃	1	1	yes	characteristic
286	C₂	C₂²×C₁₃×H(5,𝔽₂)	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁶×C₁₃
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. C₂⁴×D₄×C₁₃	C₂	semidirect
2. C₂×C₁₃×#534	C₂	direct (N × H)
3. C₂²×C₁₃×#123	C₂	semidirect
4. C₂²×C₁₃×#121	C₂	semidirect
5. C₂²×C₁₃×#120	C₂	semidirect
6. C₂³×C₁₃×C₂²⋊C₄	C₂	semidirect
8. C₂⁶×C₁₃	C₂²	semidirect
11. C₂³×D₄×C₁₃	C₂²	semidirect
12. C₂³×D₄×C₁₃	C₂²	semidirect
13. C₂³×D₄×C₁₃	C₂²	semidirect
14. C₂⁴×C₄×C₁₃	C₂²	semidirect
15. C₂⁴×C₄×C₁₃	C₂²	semidirect
16. C₁₃×#534	C₂²	direct (N × H)
17. C₂×C₁₃×#123	C₂²	semidirect
18. C₂×C₁₃×#121	C₂²	semidirect
19. C₂×C₁₃×#120	C₂²	semidirect
20. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
21. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
22. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
23. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
27. C₂⁵×C₁₃	D₄	semidirect
32. C₂⁵×C₁₃	C₂³	semidirect
38. C₂²×D₄×C₁₃	C₂³	semidirect
39. C₂²×D₄×C₁₃	C₂³	semidirect
40. C₂²×D₄×C₁₃	C₂³	semidirect
45. C₂³×C₄×C₁₃	C₂³	semidirect
46. C₂³×C₄×C₁₃	C₂³	semidirect
47. C₁₃×#123	C₂³	semidirect
48. C₁₃×#121	C₂³	semidirect
49. C₁₃×#120	C₂³	semidirect
50. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
51. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
52. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
53. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
54. C₂²×#534	C₁₃	direct (N × H)
66. C₂⁴×C₁₃	C₂×D₄	semidirect
72. C₂⁴×C₁₃	C₂⁴	semidirect
78. C₂×D₄×C₁₃	C₂⁴	semidirect
79. C₂×D₄×C₁₃	C₂⁴	semidirect
86. C₂²×C₄×C₁₃	C₂⁴	semidirect
87. C₂²×C₄×C₁₃	C₂⁴	semidirect
88. C₁₃×C₄⋊C₄	C₂⁴	semidirect
89. C₁₃×C₂²⋊C₄	C₂⁴	semidirect
90. C₁₃×C₂²⋊C₄	C₂⁴	semidirect
91. C₂⁴×D₄	C₂×C₁₃	semidirect
92. C₂×#534	C₂×C₁₃	direct (N × H)
93. C₂²×#123	C₂×C₁₃	semidirect
94. C₂²×#121	C₂×C₁₃	semidirect
95. C₂²×#120	C₂×C₁₃	semidirect
96. C₂³×C₂²⋊C₄	C₂×C₁₃	semidirect
112. C₂³×C₁₃	C₂²×D₄	semidirect
128. C₂⁶	C₂²×C₁₃	semidirect
131. C₂³×D₄	C₂²×C₁₃	semidirect
132. C₂³×D₄	C₂²×C₁₃	semidirect
133. C₂³×D₄	C₂²×C₁₃	semidirect
134. C₂⁴×C₄	C₂²×C₁₃	semidirect
135. C₂⁴×C₄	C₂²×C₁₃	semidirect
136. #534	C₂²×C₁₃	direct (N × H)
137. C₂×#123	C₂²×C₁₃	semidirect
138. C₂×#121	C₂²×C₁₃	semidirect
139. C₂×#120	C₂²×C₁₃	semidirect
140. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
141. C₂²×C₂²⋊C₄	C₂²×C₁₃	semidirect
142. C₂²×C₂²⋊C₄	C₂²×C₁₃	semidirect
143. C₂²×C₂²⋊C₄	C₂²×C₁₃	semidirect
153. C₂²×C₁₃	#534	direct (N × H)
164. C₂⁵	D₄×C₁₃	semidirect
169. C₂⁵	C₂³×C₁₃	semidirect
175. C₂²×D₄	C₂³×C₁₃	semidirect
176. C₂²×D₄	C₂³×C₁₃	semidirect
177. C₂²×D₄	C₂³×C₁₃	semidirect
182. C₂³×C₄	C₂³×C₁₃	semidirect
183. C₂³×C₄	C₂³×C₁₃	semidirect
184. #123	C₂³×C₁₃	semidirect
185. #121	C₂³×C₁₃	semidirect
186. #120	C₂³×C₁₃	semidirect
187. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
188. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
189. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
190. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
194. C₂×C₁₃	C₂×#534	direct (N × H)
208. C₂⁴	C₂×D₄×C₁₃	semidirect
214. C₂⁴	C₂⁴×C₁₃	semidirect
220. C₂×D₄	C₂⁴×C₁₃	semidirect
221. C₂×D₄	C₂⁴×C₁₃	semidirect
228. C₂²×C₄	C₂⁴×C₁₃	semidirect
229. C₂²×C₄	C₂⁴×C₁₃	semidirect
230. C₄⋊C₄	C₂⁴×C₁₃	semidirect
231. C₂²⋊C₄	C₂⁴×C₁₃	semidirect
232. C₂²⋊C₄	C₂⁴×C₁₃	semidirect
233. C₁₃	C₂²×#534	direct (N × H)
249. C₂³	C₂²×D₄×C₁₃	semidirect
273. C₂²	C₁₃×#534	direct (N × H)
284. C₂	C₂×C₁₃×#534	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×D₄×C₁₃	2
C₂×C₁₃×#534	2
C₂²×C₁₃×#123	2
C₂²×C₁₃×#121	2
C₂²×C₁₃×#120	2
C₂³×C₁₃×C₂²⋊C₄	2
C₂²×#534	13

Subgroups — C22×C13×#534 #15749008

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₁₃×#534 #15749008