Subgroups — C₂²×D₄²×C₁₃ #15749034

Order 3328.

20038 conjugacy classes of subgroups.

The subgroup lattice has 264 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	4	yes	maximal, complemented
2	C₂×D₄²×C₁₃	C₂	1	48	yes	maximal, direct product factor
3	C₂²×C₁₃×#127	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₁₃×#121	C₂	1	4	yes	maximal, complemented
5	C₂²×C₁₃×#120	C₂	1	4	yes	maximal, complemented
6	C₂²×C₄×D₄×C₁₃	C₂	1	2	yes	maximal, complemented
7	C₂⁶×C₁₃	C₂²	1	4	yes	complemented
8	C₂³×D₄×C₁₃	—	2	64	no	—
9	C₂³×D₄×C₁₃	C₂²	1	2	yes	—
10	C₂³×D₄×C₁₃	C₂²	1	8	yes	complemented
11	C₂³×D₄×C₁₃	C₂²	1	4	yes	complemented
12	C₂³×D₄×C₁₃	C₂²	1	2	yes	complemented
13	C₂³×D₄×C₁₃	C₂²	1	96	yes	complemented
14	C₂⁴×C₄×C₁₃	C₂²	1	4	yes	complemented
15	D₄²×C₁₃	C₂²	1	256	yes	direct product factor
16	C₂×C₁₃×#127	C₂²	1	24	yes	complemented
17	C₂×C₁₃×#121	C₂²	1	96	yes	complemented
18	C₂×C₁₃×#120	C₂²	1	96	yes	complemented
19	C₂×C₄×D₄×C₁₃	C₂²	1	48	yes	complemented
20	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
21	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
22	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
23	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic, complemented
24	C₂⁵×C₁₃	—	2	64	no	—
25	C₂⁵×C₁₃	—	4	16	no	—
26	C₂⁵×C₁₃	C₂³	1	4	yes	—
27	C₂⁵×C₁₃	C₂³	1	4	yes	—
28	C₂⁵×C₁₃	C₂³	1	48	yes	complemented
29	C₂²×D₄×C₁₃	—	2	64	no	—
30	C₂²×D₄×C₁₃	—	2	768	no	—
31	C₂²×D₄×C₁₃	—	2	32	no	—
32	C₂²×D₄×C₁₃	—	4	8	no	—
33	C₂²×D₄×C₁₃	D₄	1	32	yes	direct product factor
34	C₂²×D₄×C₁₃	C₂³	1	24	yes	—
35	C₂²×D₄×C₁₃	C₂³	1	96	yes	complemented
36	C₂²×D₄×C₁₃	C₂³	1	48	yes	complemented
37	C₂²×D₄×C₁₃	C₂³	1	24	yes	complemented
38	C₂²×D₄×C₁₃	C₂³	1	256	yes	complemented
39	C₂³×C₄×C₁₃	—	2	32	no	—
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	48	yes	complemented
44	C₁₃×#127	C₂³	1	64	yes	complemented
45	C₁₃×#121	C₂³	1	256	yes	complemented
46	C₁₃×#120	C₂³	1	256	yes	complemented
47	C₄×D₄×C₁₃	C₂³	1	128	yes	complemented
48	C₂×C₁₃×C₄⋊C₄	C₂³	1	24	yes	complemented
49	C₂×C₁₃×C₂²⋊C₄	C₂³	1	48	yes	complemented
50	C₂×C₁₃×C₂²⋊C₄	C₂³	1	48	yes	complemented
51	C₂×C₄²×C₁₃	C₂³	1	12	yes	complemented
52	C₂²×D₄²	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
53	C₂⁴×C₁₃	—	2	16	no	—
54	C₂⁴×C₁₃	—	2	16	no	—
55	C₂⁴×C₁₃	—	2	32	no	—
56	C₂⁴×C₁₃	—	2	384	no	—
57	C₂⁴×C₁₃	—	2	16	no	—
58	C₂⁴×C₁₃	—	4	96	no	—
59	C₂⁴×C₁₃	—	4	256	no	—
60	C₂⁴×C₁₃	C₂×D₄	1	32	yes	complemented
61	C₂⁴×C₁₃	C₂⁴	1	24	yes	—
62	C₂⁴×C₁₃	C₂⁴	1	24	yes	—
63	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
64	C₂⁴×C₁₃	C₂⁴	1	64	yes	complemented
65	C₂×D₄×C₁₃	—	2	384	no	—
66	C₂×D₄×C₁₃	—	2	1024	no	—
67	C₂×D₄×C₁₃	—	2	192	no	—
68	C₂×D₄×C₁₃	—	4	48	no	—
69	C₂×D₄×C₁₃	C₂×D₄	1	192	yes	direct product factor
70	C₂×D₄×C₁₃	C₂⁴	1	32	yes	—
71	C₂×D₄×C₁₃	C₂⁴	1	128	yes	complemented
72	C₂×D₄×C₁₃	C₂⁴	1	64	yes	complemented
73	C₂×D₄×C₁₃	C₂⁴	1	32	yes	complemented
74	C₂²×C₄×C₁₃	—	2	16	no	—
75	C₂²×C₄×C₁₃	—	2	4	no	—
76	C₂²×C₄×C₁₃	—	2	192	no	—
77	C₂²×C₄×C₁₃	C₂×D₄	1	16	yes	complemented
78	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
79	C₂²×C₄×C₁₃	C₂⁴	1	24	yes	—
80	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
81	C₂²×C₄×C₁₃	C₂⁴	1	64	yes	complemented
82	C₁₃×C₄⋊C₄	C₂⁴	1	32	yes	complemented
83	C₁₃×C₂²⋊C₄	C₂⁴	1	64	yes	complemented
84	C₁₃×C₂²⋊C₄	C₂⁴	1	64	yes	complemented
85	C₄²×C₁₃	C₂⁴	1	16	yes	complemented
86	C₂⁴×D₄	C₂×C₁₃	1	4	yes	complemented
87	C₂×D₄²	C₂×C₁₃	1	48	yes	direct product factor
88	C₂²×#127	C₂×C₁₃	1	1	yes	characteristic, complemented
89	C₂²×#121	C₂×C₁₃	1	4	yes	complemented
90	C₂²×#120	C₂×C₁₃	1	4	yes	complemented
91	C₂²×C₄×D₄	C₂×C₁₃	1	2	yes	complemented
92	C₂³×C₁₃	—	2	128	no	—
93	C₂³×C₁₃	—	2	48	no	—
94	C₂³×C₁₃	—	2	48	no	—
95	C₂³×C₁₃	—	2	96	no	—
96	C₂³×C₁₃	—	2	256	no	—
97	C₂³×C₁₃	—	2	48	no	—
98	C₂³×C₁₃	—	4	64	no	—
99	C₂³×C₁₃	—	4	768	no	—
100	C₂³×C₁₃	—	4	64	no	—
101	C₂³×C₁₃	C₂²×D₄	1	8	yes	—
102	C₂³×C₁₃	C₂²×D₄	1	96	yes	complemented
103	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
104	C₂³×C₁₃	C₂⁵	1	16	yes	—
105	C₂³×C₁₃	C₂⁵	1	16	yes	—
106	C₂³×C₁₃	C₂⁵	1	3	yes	—
107	D₄×C₁₃	—	2	256	no	—
108	D₄×C₁₃	—	2	128	no	—
109	D₄×C₁₃	—	4	32	no	—
110	D₄×C₁₃	C₂²×D₄	1	128	yes	direct product factor
111	C₂×C₄×C₁₃	—	2	48	no	—
112	C₂×C₄×C₁₃	—	2	12	no	—
113	C₂×C₄×C₁₃	—	2	128	no	—
114	C₂×C₄×C₁₃	C₂²×D₄	1	48	yes	complemented
115	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
116	C₂×C₄×C₁₃	C₂⁵	1	16	yes	—
117	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
118	C₂⁶	C₂²×C₁₃	1	4	yes	complemented
119	C₂³×D₄	—	2	64	no	—
120	C₂³×D₄	C₂²×C₁₃	1	2	yes	—
121	C₂³×D₄	C₂²×C₁₃	1	8	yes	complemented
122	C₂³×D₄	C₂²×C₁₃	1	4	yes	complemented
123	C₂³×D₄	C₂²×C₁₃	1	2	yes	complemented
124	C₂³×D₄	C₂²×C₁₃	1	96	yes	complemented
125	C₂⁴×C₄	C₂²×C₁₃	1	4	yes	complemented
126	D₄²	C₂²×C₁₃	1	256	yes	direct product factor
127	C₂×#127	C₂²×C₁₃	1	24	yes	complemented
128	C₂×#121	C₂²×C₁₃	1	96	yes	complemented
129	C₂×#120	C₂²×C₁₃	1	96	yes	complemented
130	C₂×C₄×D₄	C₂²×C₁₃	1	48	yes	complemented
131	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
132	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	complemented
133	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	complemented
134	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic, complemented
135	C₂²×C₁₃	—	2	16	no	—
136	C₂²×C₁₃	—	2	16	no	—
137	C₂²×C₁₃	—	2	192	no	—
138	C₂²×C₁₃	—	2	32	no	—
139	C₂²×C₁₃	—	2	16	no	—
140	C₂²×C₁₃	—	4	256	no	—
141	C₂²×C₁₃	—	4	96	no	—
142	C₂²×C₁₃	D₄²	1	16	yes	direct product factor
143	C₂²×C₁₃	C₂³×D₄	1	12	yes	—
144	C₂²×C₁₃	C₂³×D₄	1	32	yes	complemented
145	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	6	yes	—
146	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
147	C₄×C₁₃	—	2	16	no	—
148	C₄×C₁₃	—	2	4	no	—
149	C₄×C₁₃	C₂³×D₄	1	16	yes	complemented
150	C₂⁵	—	2	64	no	—
151	C₂⁵	—	4	16	no	—
152	C₂⁵	C₂³×C₁₃	1	4	yes	—
153	C₂⁵	C₂³×C₁₃	1	4	yes	—
154	C₂⁵	C₂³×C₁₃	1	48	yes	complemented
155	C₂²×D₄	—	2	64	no	—
156	C₂²×D₄	—	2	768	no	—
157	C₂²×D₄	—	2	32	no	—
158	C₂²×D₄	—	4	8	no	—
159	C₂²×D₄	D₄×C₁₃	1	32	yes	direct product factor
160	C₂²×D₄	C₂³×C₁₃	1	24	yes	—
161	C₂²×D₄	C₂³×C₁₃	1	96	yes	complemented
162	C₂²×D₄	C₂³×C₁₃	1	48	yes	complemented
163	C₂²×D₄	C₂³×C₁₃	1	24	yes	complemented
164	C₂²×D₄	C₂³×C₁₃	1	256	yes	complemented
165	C₂³×C₄	—	2	32	no	—
166	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
167	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
168	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
169	C₂³×C₄	C₂³×C₁₃	1	48	yes	complemented
170	#127	C₂³×C₁₃	1	64	yes	complemented
171	#121	C₂³×C₁₃	1	256	yes	complemented
172	#120	C₂³×C₁₃	1	256	yes	complemented
173	C₄×D₄	C₂³×C₁₃	1	128	yes	complemented
174	C₂×C₄⋊C₄	C₂³×C₁₃	1	24	yes	complemented
175	C₂×C₂²⋊C₄	C₂³×C₁₃	1	48	yes	complemented
176	C₂×C₂²⋊C₄	C₂³×C₁₃	1	48	yes	complemented
177	C₂×C₄²	C₂³×C₁₃	1	12	yes	complemented
178	C₂×C₁₃	—	2	32	no	—
179	C₂×C₁₃	—	4	16	no	—
180	C₂×C₁₃	C₂×D₄²	1	12	yes	direct product factor
181	C₂×C₁₃	C₂⁴×D₄	1	2	yes	—
182	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
183	C₂⁴	—	2	16	no	—
184	C₂⁴	—	2	16	no	—
185	C₂⁴	—	2	32	no	—
186	C₂⁴	—	2	384	no	—
187	C₂⁴	—	2	16	no	—
188	C₂⁴	—	4	96	no	—
189	C₂⁴	—	4	256	no	—
190	C₂⁴	C₂×D₄×C₁₃	1	32	yes	complemented
191	C₂⁴	C₂⁴×C₁₃	1	24	yes	—
192	C₂⁴	C₂⁴×C₁₃	1	24	yes	—
193	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
194	C₂⁴	C₂⁴×C₁₃	1	64	yes	complemented
195	C₂×D₄	—	2	384	no	—
196	C₂×D₄	—	2	1024	no	—
197	C₂×D₄	—	2	192	no	—
198	C₂×D₄	—	4	48	no	—
199	C₂×D₄	C₂×D₄×C₁₃	1	192	yes	direct product factor
200	C₂×D₄	C₂⁴×C₁₃	1	32	yes	—
201	C₂×D₄	C₂⁴×C₁₃	1	128	yes	complemented
202	C₂×D₄	C₂⁴×C₁₃	1	64	yes	complemented
203	C₂×D₄	C₂⁴×C₁₃	1	32	yes	complemented
204	C₂²×C₄	—	2	16	no	—
205	C₂²×C₄	—	2	4	no	—
206	C₂²×C₄	—	2	192	no	—
207	C₂²×C₄	C₂×D₄×C₁₃	1	16	yes	complemented
208	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
209	C₂²×C₄	C₂⁴×C₁₃	1	24	yes	—
210	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
211	C₂²×C₄	C₂⁴×C₁₃	1	64	yes	complemented
212	C₄⋊C₄	C₂⁴×C₁₃	1	32	yes	complemented
213	C₂²⋊C₄	C₂⁴×C₁₃	1	64	yes	complemented
214	C₂²⋊C₄	C₂⁴×C₁₃	1	64	yes	complemented
215	C₄²	C₂⁴×C₁₃	1	16	yes	complemented
216	C₁₃	C₂²×D₄²	1	1	yes	characteristic, direct product factor, Sylow
217	C₂³	—	2	128	no	—
218	C₂³	—	2	48	no	—
219	C₂³	—	2	48	no	—
220	C₂³	—	2	96	no	—
221	C₂³	—	2	256	no	—
222	C₂³	—	2	48	no	—
223	C₂³	—	4	64	no	—
224	C₂³	—	4	768	no	—
225	C₂³	—	4	64	no	—
226	C₂³	C₂²×D₄×C₁₃	1	8	yes	—
227	C₂³	C₂²×D₄×C₁₃	1	96	yes	complemented
228	C₂³	C₁₃×H(5,𝔽₂)	1	4	yes	—
229	C₂³	C₂⁵×C₁₃	1	16	yes	—
230	C₂³	C₂⁵×C₁₃	1	16	yes	—
231	C₂³	C₂⁵×C₁₃	1	3	yes	—
232	D₄	—	2	256	no	—
233	D₄	—	2	128	no	—
234	D₄	—	4	32	no	—
235	D₄	C₂²×D₄×C₁₃	1	128	yes	direct product factor
236	C₂×C₄	—	2	48	no	—
237	C₂×C₄	—	2	12	no	—
238	C₂×C₄	—	2	128	no	—
239	C₂×C₄	C₂²×D₄×C₁₃	1	48	yes	complemented
240	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
241	C₂×C₄	C₂⁵×C₁₃	1	16	yes	—
242	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
243	C₂²	—	2	16	no	—
244	C₂²	—	2	16	no	—
245	C₂²	—	2	192	no	—
246	C₂²	—	2	32	no	—
247	C₂²	—	2	16	no	—
248	C₂²	—	4	256	no	—
249	C₂²	—	4	96	no	—
250	C₂²	D₄²×C₁₃	1	16	yes	direct product factor
251	C₂²	C₂³×D₄×C₁₃	1	12	yes	—
252	C₂²	C₂³×D₄×C₁₃	1	32	yes	complemented
253	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	6	yes	—
254	C₂²	C₂⁶×C₁₃	1	1	yes	characteristic
255	C₄	—	2	16	no	—
256	C₄	—	2	4	no	—
257	C₄	C₂³×D₄×C₁₃	1	16	yes	complemented
258	C₂	—	2	32	no	—
259	C₂	—	4	16	no	—
260	C₂	C₂×D₄²×C₁₃	1	12	yes	direct product factor
261	C₂	C₂⁴×D₄×C₁₃	1	2	yes	—
262	C₂	C₂²×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic

	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×D₄²×C₁₃	C₂	direct (N × H)
3. C₂²×C₁₃×#127	C₂	semidirect
4. C₂²×C₁₃×#121	C₂	semidirect
5. C₂²×C₁₃×#120	C₂	semidirect
6. C₂²×C₄×D₄×C₁₃	C₂	semidirect
7. C₂⁶×C₁₃	C₂²	semidirect
10. C₂³×D₄×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. D₄²×C₁₃	C₂²	direct (N × H)
16. C₂×C₁₃×#127	C₂²	semidirect
17. C₂×C₁₃×#121	C₂²	semidirect
18. C₂×C₁₃×#120	C₂²	semidirect
19. C₂×C₄×D₄×C₁₃	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×C₄²×C₁₃	C₂²	semidirect
28. C₂⁵×C₁₃	C₂³	semidirect
33. C₂²×D₄×C₁₃	D₄	direct (N × H)
35. C₂²×D₄×C₁₃	C₂³	semidirect
36. C₂²×D₄×C₁₃	C₂³	semidirect
37. C₂²×D₄×C₁₃	C₂³	semidirect
38. C₂²×D₄×C₁₃	C₂³	semidirect
43. C₂³×C₄×C₁₃	C₂³	semidirect
44. C₁₃×#127	C₂³	semidirect
45. C₁₃×#121	C₂³	semidirect
46. C₁₃×#120	C₂³	semidirect
47. C₄×D₄×C₁₃	C₂³	semidirect
48. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
49. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
50. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
51. C₂×C₄²×C₁₃	C₂³	semidirect
52. C₂²×D₄²	C₁₃	direct (N × H)
60. C₂⁴×C₁₃	C₂×D₄	semidirect
64. C₂⁴×C₁₃	C₂⁴	semidirect
69. C₂×D₄×C₁₃	C₂×D₄	direct (N × H)
71. C₂×D₄×C₁₃	C₂⁴	semidirect
72. C₂×D₄×C₁₃	C₂⁴	semidirect
73. C₂×D₄×C₁₃	C₂⁴	semidirect
77. C₂²×C₄×C₁₃	C₂×D₄	semidirect
81. C₂²×C₄×C₁₃	C₂⁴	semidirect
82. C₁₃×C₄⋊C₄	C₂⁴	semidirect
83. C₁₃×C₂²⋊C₄	C₂⁴	semidirect
84. C₁₃×C₂²⋊C₄	C₂⁴	semidirect
85. C₄²×C₁₃	C₂⁴	semidirect
86. C₂⁴×D₄	C₂×C₁₃	semidirect
87. C₂×D₄²	C₂×C₁₃	direct (N × H)
88. C₂²×#127	C₂×C₁₃	semidirect
89. C₂²×#121	C₂×C₁₃	semidirect
90. C₂²×#120	C₂×C₁₃	semidirect
91. C₂²×C₄×D₄	C₂×C₁₃	semidirect
102. C₂³×C₁₃	C₂²×D₄	semidirect
110. D₄×C₁₃	C₂²×D₄	direct (N × H)
114. C₂×C₄×C₁₃	C₂²×D₄	semidirect
118. C₂⁶	C₂²×C₁₃	semidirect
121. C₂³×D₄	C₂²×C₁₃	semidirect
122. C₂³×D₄	C₂²×C₁₃	semidirect
123. C₂³×D₄	C₂²×C₁₃	semidirect
124. C₂³×D₄	C₂²×C₁₃	semidirect
125. C₂⁴×C₄	C₂²×C₁₃	semidirect
126. D₄²	C₂²×C₁₃	direct (N × H)
127. C₂×#127	C₂²×C₁₃	semidirect
128. C₂×#121	C₂²×C₁₃	semidirect
129. C₂×#120	C₂²×C₁₃	semidirect
130. C₂×C₄×D₄	C₂²×C₁₃	semidirect
131. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
132. C₂²×C₂²⋊C₄	C₂²×C₁₃	semidirect
133. C₂²×C₂²⋊C₄	C₂²×C₁₃	semidirect
134. C₂²×C₄²	C₂²×C₁₃	semidirect
142. C₂²×C₁₃	D₄²	direct (N × H)
144. C₂²×C₁₃	C₂³×D₄	semidirect
149. C₄×C₁₃	C₂³×D₄	semidirect
154. C₂⁵	C₂³×C₁₃	semidirect
159. C₂²×D₄	D₄×C₁₃	direct (N × H)
161. C₂²×D₄	C₂³×C₁₃	semidirect
162. C₂²×D₄	C₂³×C₁₃	semidirect
163. C₂²×D₄	C₂³×C₁₃	semidirect
164. C₂²×D₄	C₂³×C₁₃	semidirect
169. C₂³×C₄	C₂³×C₁₃	semidirect
170. #127	C₂³×C₁₃	semidirect
171. #121	C₂³×C₁₃	semidirect
172. #120	C₂³×C₁₃	semidirect
173. C₄×D₄	C₂³×C₁₃	semidirect
174. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
175. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
176. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
177. C₂×C₄²	C₂³×C₁₃	semidirect
180. C₂×C₁₃	C₂×D₄²	direct (N × H)
190. C₂⁴	C₂×D₄×C₁₃	semidirect
194. C₂⁴	C₂⁴×C₁₃	semidirect
199. C₂×D₄	C₂×D₄×C₁₃	direct (N × H)
201. C₂×D₄	C₂⁴×C₁₃	semidirect
202. C₂×D₄	C₂⁴×C₁₃	semidirect
203. C₂×D₄	C₂⁴×C₁₃	semidirect
207. C₂²×C₄	C₂×D₄×C₁₃	semidirect
211. C₂²×C₄	C₂⁴×C₁₃	semidirect
212. C₄⋊C₄	C₂⁴×C₁₃	semidirect
213. C₂²⋊C₄	C₂⁴×C₁₃	semidirect
214. C₂²⋊C₄	C₂⁴×C₁₃	semidirect
215. C₄²	C₂⁴×C₁₃	semidirect
216. C₁₃	C₂²×D₄²	direct (N × H)
227. C₂³	C₂²×D₄×C₁₃	semidirect
235. D₄	C₂²×D₄×C₁₃	direct (N × H)
239. C₂×C₄	C₂²×D₄×C₁₃	semidirect
250. C₂²	D₄²×C₁₃	direct (N × H)
252. C₂²	C₂³×D₄×C₁₃	semidirect
257. C₄	C₂³×D₄×C₁₃	semidirect
260. C₂	C₂×D₄²×C₁₃	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×D₄²×C₁₃	2
C₂²×C₁₃×#127	2
C₂²×C₁₃×#121	2
C₂²×C₁₃×#120	2
C₂²×C₄×D₄×C₁₃	2
C₂²×D₄²	13

Subgroups — C22×D42×C13 #15749034

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×D₄²×C₁₃ #15749034