Subgroups — C₁₃×#3537 #13112595

Order 1664.

1270 conjugacy classes of subgroups.

The subgroup lattice has 302 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#560	C₂	1	4	yes	maximal, complemented
2	C₁₃×#553	C₂	1	4	yes	maximal, complemented
3	D₄²×C₁₃	C₂	1	4	yes	maximal, complemented
4	D₄²×C₁₃	C₂	1	4	yes	maximal, complemented
5	C₁₃×#540	C₂	1	2	yes	maximal, complemented
6	C₁₃×#538	C₂	1	4	yes	maximal, complemented
7	C₁₃×#535	C₂	1	2	yes	maximal, complemented
8	C₁₃×#534	C₂	1	4	yes	maximal, complemented
9	C₁₃×#525	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×#121	C₂	1	2	yes	maximal, complemented
11	C₂×C₁₃×#41	C₂²	1	1	yes	characteristic, complemented
12	C₂²×D₄×C₁₃	C₂²	1	2	yes	complemented
13	C₂²×D₄×C₁₃	C₂²	1	4	yes	complemented
14	C₂²×D₄×C₁₃	C₂²	1	8	yes	complemented
15	C₂²×D₄×C₁₃	C₂²	1	2	yes	complemented
16	C₂³×C₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
17	C₁₃×#127	C₂²	1	4	yes	complemented
18	C₁₃×#127	C₂²	1	2	yes	complemented
19	C₁₃×#126	C₂²	1	8	yes	complemented
20	C₁₃×#125	C₂²	1	2	yes	complemented
21	C₁₃×#124	C₂²	1	4	yes	complemented
22	C₁₃×#123	C₂²	1	2	yes	complemented
23	C₁₃×#123	C₂²	1	8	yes	complemented
24	C₁₃×#123	C₂²	1	8	yes	complemented
25	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
26	C₁₃×#121	C₂²	1	4	yes	complemented
27	C₁₃×#121	C₂²	1	4	yes	complemented
28	C₁₃×#121	C₂²	1	4	yes	complemented
29	C₁₃×#121	C₂²	1	4	yes	complemented
30	C₁₃×#121	C₂²	1	2	yes	complemented
31	C₁₃×#121	C₂²	1	8	yes	complemented
32	C₁₃×#121	C₂²	1	4	yes	complemented
33	C₁₃×#121	C₂²	1	8	yes	complemented
34	C₁₃×#121	C₂²	1	8	yes	complemented
35	C₁₃×#120	C₂²	1	2	yes	complemented
36	C₁₃×#120	C₂²	1	4	yes	complemented
37	C₁₃×#120	C₂²	1	8	yes	complemented
38	C₁₃×#120	C₂²	1	4	yes	complemented
39	C₁₃×#120	C₂²	1	8	yes	complemented
40	C₄×D₄×C₁₃	C₂²	1	4	yes	complemented
41	C₄×D₄×C₁₃	C₂²	1	8	yes	complemented
42	C₄×D₄×C₁₃	C₂²	1	4	yes	complemented
43	C₁₃×#117	C₂²	1	1	yes	characteristic, complemented
44	C₁₃×#117	C₂²	1	2	yes	complemented
45	C₂×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
46	C₂×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
47	C₂⁴×C₁₃	C₂³	1	1	yes	characteristic
48	C₂⁴×C₁₃	C₂³	1	4	yes	—
49	C₂⁴×C₁₃	C₂³	1	4	yes	—
50	C₁₃×#41	—	4	2	no	—
51	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
52	C₂×D₄×C₁₃	—	4	4	no	—
53	C₂×D₄×C₁₃	—	4	4	no	—
54	C₂×D₄×C₁₃	—	4	8	no	—
55	C₂×D₄×C₁₃	—	4	16	no	—
56	C₂×D₄×C₁₃	C₂³	1	4	yes	—
57	C₂×D₄×C₁₃	C₂³	1	8	yes	—
58	C₂×D₄×C₁₃	C₂³	1	4	yes	—
59	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
60	C₂×D₄×C₁₃	C₂³	1	2	yes	—
61	C₂×D₄×C₁₃	C₂³	1	4	yes	—
62	C₂×D₄×C₁₃	C₂³	1	8	yes	—
63	C₂×D₄×C₁₃	C₂³	1	8	yes	—
64	C₂×D₄×C₁₃	C₂³	1	4	yes	—
65	C₂×D₄×C₁₃	C₂³	1	8	yes	—
66	C₂²×C₄×C₁₃	—	4	2	no	—
67	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
68	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
69	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
70	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
71	C₂²×C₄×C₁₃	C₂³	1	4	yes	—
72	C₂²×C₄×C₁₃	C₂³	1	8	yes	—
73	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
74	C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
75	C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
76	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
77	C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
78	C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
79	C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
80	C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
81	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
82	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
83	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
84	C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
85	C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
86	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
87	C₄²×C₁₃	C₂³	1	2	yes	—
88	C₄²×C₁₃	C₂³	1	4	yes	—
89	#3537	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
90	C₂³×C₁₃	—	2	4	no	—
91	C₂³×C₁₃	—	2	8	no	—
92	C₂³×C₁₃	—	4	1	no	—
93	C₂³×C₁₃	—	4	4	no	—
94	C₂³×C₁₃	—	4	4	no	—
95	C₂³×C₁₃	—	4	4	no	—
96	C₂³×C₁₃	—	4	8	no	—
97	C₂³×C₁₃	C₂⁴	1	2	yes	—
98	C₂³×C₁₃	C₂⁴	1	8	yes	—
99	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
100	C₂³×C₁₃	C₂⁴	1	2	yes	—
101	Q₈×C₁₃	—	4	1	no	—
102	D₄×C₁₃	—	2	16	no	—
103	D₄×C₁₃	—	2	8	no	—
104	D₄×C₁₃	—	2	8	no	—
105	D₄×C₁₃	—	4	4	no	—
106	D₄×C₁₃	—	4	4	no	—
107	D₄×C₁₃	—	4	8	no	—
108	D₄×C₁₃	—	4	8	no	—
109	D₄×C₁₃	—	4	8	no	—
110	D₄×C₁₃	—	4	1	no	—
111	D₄×C₁₃	—	4	2	no	—
112	C₂×C₄×C₁₃	—	2	4	no	—
113	C₂×C₄×C₁₃	—	2	2	no	—
114	C₂×C₄×C₁₃	—	2	4	no	—
115	C₂×C₄×C₁₃	—	4	1	no	—
116	C₂×C₄×C₁₃	—	4	2	no	—
117	C₂×C₄×C₁₃	—	4	4	no	—
118	C₂×C₄×C₁₃	—	4	8	no	—
119	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
120	C₂×C₄×C₁₃	C₂⁴	1	4	yes	—
121	C₂×C₄×C₁₃	C₂⁴	1	8	yes	—
122	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
123	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
124	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
125	#560	C₂×C₁₃	1	4	yes	complemented
126	#553	C₂×C₁₃	1	4	yes	complemented
127	D₄²	C₂×C₁₃	1	4	yes	complemented
128	D₄²	C₂×C₁₃	1	4	yes	complemented
129	#540	C₂×C₁₃	1	2	yes	complemented
130	#538	C₂×C₁₃	1	4	yes	complemented
131	#535	C₂×C₁₃	1	2	yes	complemented
132	#534	C₂×C₁₃	1	4	yes	complemented
133	#525	C₂×C₁₃	1	1	yes	characteristic, complemented
134	C₂×#121	C₂×C₁₃	1	2	yes	complemented
135	C₂²×C₁₃	—	2	2	no	—
136	C₂²×C₁₃	—	2	2	no	—
137	C₂²×C₁₃	—	2	1	no	—
138	C₂²×C₁₃	—	2	2	no	—
139	C₂²×C₁₃	—	2	8	no	—
140	C₂²×C₁₃	—	2	4	no	—
141	C₂²×C₁₃	—	2	8	no	—
142	C₂²×C₁₃	—	2	8	no	—
143	C₂²×C₁₃	—	2	2	no	—
144	C₂²×C₁₃	—	4	4	no	—
145	C₂²×C₁₃	—	8	8	no	—
146	C₂²×C₁₃	—	8	8	no	—
147	C₂²×C₁₃	H(5,𝔽₂)	1	4	yes	—
148	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
149	C₄×C₁₃	—	2	2	no	—
150	C₄×C₁₃	—	2	1	no	—
151	C₄×C₁₃	—	2	2	no	—
152	C₄×C₁₃	—	2	8	no	—
153	C₄×C₁₃	—	2	4	no	—
154	C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
155	C₂×#41	C₂²×C₁₃	1	1	yes	characteristic, complemented
156	C₂²×D₄	C₂²×C₁₃	1	2	yes	complemented
157	C₂²×D₄	C₂²×C₁₃	1	4	yes	complemented
158	C₂²×D₄	C₂²×C₁₃	1	8	yes	complemented
159	C₂²×D₄	C₂²×C₁₃	1	2	yes	complemented
160	C₂³×C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
161	#127	C₂²×C₁₃	1	4	yes	complemented
162	#127	C₂²×C₁₃	1	2	yes	complemented
163	#126	C₂²×C₁₃	1	8	yes	complemented
164	#125	C₂²×C₁₃	1	2	yes	complemented
165	#124	C₂²×C₁₃	1	4	yes	complemented
166	#123	C₂²×C₁₃	1	2	yes	complemented
167	#123	C₂²×C₁₃	1	8	yes	complemented
168	#123	C₂²×C₁₃	1	8	yes	complemented
169	C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
170	#121	C₂²×C₁₃	1	4	yes	complemented
171	#121	C₂²×C₁₃	1	4	yes	complemented
172	#121	C₂²×C₁₃	1	4	yes	complemented
173	#121	C₂²×C₁₃	1	4	yes	complemented
174	#121	C₂²×C₁₃	1	2	yes	complemented
175	#121	C₂²×C₁₃	1	8	yes	complemented
176	#121	C₂²×C₁₃	1	4	yes	complemented
177	#121	C₂²×C₁₃	1	8	yes	complemented
178	#121	C₂²×C₁₃	1	8	yes	complemented
179	#120	C₂²×C₁₃	1	2	yes	complemented
180	#120	C₂²×C₁₃	1	4	yes	complemented
181	#120	C₂²×C₁₃	1	8	yes	complemented
182	#120	C₂²×C₁₃	1	4	yes	complemented
183	#120	C₂²×C₁₃	1	8	yes	complemented
184	C₄×D₄	C₂²×C₁₃	1	4	yes	complemented
185	C₄×D₄	C₂²×C₁₃	1	8	yes	complemented
186	C₄×D₄	C₂²×C₁₃	1	4	yes	complemented
187	#117	C₂²×C₁₃	1	1	yes	characteristic, complemented
188	#117	C₂²×C₁₃	1	2	yes	complemented
189	C₂×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
190	C₂×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	complemented
191	C₂×C₁₃	—	2	4	no	—
192	C₂×C₁₃	—	4	1	no	—
193	C₂×C₁₃	—	4	2	no	—
194	C₂×C₁₃	—	4	8	no	—
195	C₂×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
196	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
197	C₂⁴	C₂³×C₁₃	1	1	yes	characteristic
198	C₂⁴	C₂³×C₁₃	1	4	yes	—
199	C₂⁴	C₂³×C₁₃	1	4	yes	—
200	#41	—	4	2	no	—
201	C₂×Q₈	C₂³×C₁₃	1	1	yes	characteristic
202	C₂×D₄	—	4	4	no	—
203	C₂×D₄	—	4	4	no	—
204	C₂×D₄	—	4	8	no	—
205	C₂×D₄	—	4	16	no	—
206	C₂×D₄	C₂³×C₁₃	1	4	yes	—
207	C₂×D₄	C₂³×C₁₃	1	8	yes	—
208	C₂×D₄	C₂³×C₁₃	1	4	yes	—
209	C₂×D₄	C₂³×C₁₃	1	1	yes	characteristic
210	C₂×D₄	C₂³×C₁₃	1	2	yes	—
211	C₂×D₄	C₂³×C₁₃	1	4	yes	—
212	C₂×D₄	C₂³×C₁₃	1	8	yes	—
213	C₂×D₄	C₂³×C₁₃	1	8	yes	—
214	C₂×D₄	C₂³×C₁₃	1	4	yes	—
215	C₂×D₄	C₂³×C₁₃	1	8	yes	—
216	C₂²×C₄	—	4	2	no	—
217	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
218	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
219	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
220	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
221	C₂²×C₄	C₂³×C₁₃	1	4	yes	—
222	C₂²×C₄	C₂³×C₁₃	1	8	yes	—
223	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
224	C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
225	C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
226	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
227	C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
228	C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
229	C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
230	C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
231	C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
232	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
233	C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
234	C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
235	C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
236	C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
237	C₄²	C₂³×C₁₃	1	2	yes	—
238	C₄²	C₂³×C₁₃	1	4	yes	—
239	C₁₃	#3537	1	1	yes	characteristic, direct product factor, Sylow
240	C₂³	—	2	4	no	—
241	C₂³	—	2	8	no	—
242	C₂³	—	4	1	no	—
243	C₂³	—	4	4	no	—
244	C₂³	—	4	4	no	—
245	C₂³	—	4	4	no	—
246	C₂³	—	4	8	no	—
247	C₂³	C₂⁴×C₁₃	1	2	yes	—
248	C₂³	C₂⁴×C₁₃	1	8	yes	—
249	C₂³	C₂⁴×C₁₃	1	1	yes	characteristic
250	C₂³	C₂⁴×C₁₃	1	2	yes	—
251	Q₈	—	4	1	no	—
252	D₄	—	2	16	no	—
253	D₄	—	2	8	no	—
254	D₄	—	2	8	no	—
255	D₄	—	4	4	no	—
256	D₄	—	4	4	no	—
257	D₄	—	4	8	no	—
258	D₄	—	4	8	no	—
259	D₄	—	4	8	no	—
260	D₄	—	4	1	no	—
261	D₄	—	4	2	no	—
262	C₂×C₄	—	2	4	no	—
263	C₂×C₄	—	2	2	no	—
264	C₂×C₄	—	2	4	no	—
265	C₂×C₄	—	4	1	no	—
266	C₂×C₄	—	4	2	no	—
267	C₂×C₄	—	4	4	no	—
268	C₂×C₄	—	4	8	no	—
269	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
270	C₂×C₄	C₂⁴×C₁₃	1	4	yes	—
271	C₂×C₄	C₂⁴×C₁₃	1	8	yes	—
272	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
273	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
274	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
275	C₂²	—	2	2	no	—
276	C₂²	—	2	2	no	—
277	C₂²	—	2	1	no	—
278	C₂²	—	2	2	no	—
279	C₂²	—	2	8	no	—
280	C₂²	—	2	4	no	—
281	C₂²	—	2	8	no	—
282	C₂²	—	2	8	no	—
283	C₂²	—	2	2	no	—
284	C₂²	—	4	4	no	—
285	C₂²	—	8	8	no	—
286	C₂²	—	8	8	no	—
287	C₂²	C₁₃×H(5,𝔽₂)	1	4	yes	—
288	C₂²	C₂⁵×C₁₃	1	1	yes	characteristic
289	C₄	—	2	2	no	—
290	C₄	—	2	1	no	—
291	C₄	—	2	2	no	—
292	C₄	—	2	8	no	—
293	C₄	—	2	4	no	—
294	C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
295	C₂	—	2	4	no	—
296	C₂	—	4	1	no	—
297	C₂	—	4	2	no	—
298	C₂	—	4	8	no	—
299	C₂	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
300	C₂	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₁₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#560	C₂	semidirect
2. C₁₃×#553	C₂	semidirect
3. D₄²×C₁₃	C₂	semidirect
4. D₄²×C₁₃	C₂	semidirect
5. C₁₃×#540	C₂	semidirect
6. C₁₃×#538	C₂	semidirect
7. C₁₃×#535	C₂	semidirect
8. C₁₃×#534	C₂	semidirect
9. C₁₃×#525	C₂	semidirect
10. C₂×C₁₃×#121	C₂	semidirect
11. C₂×C₁₃×#41	C₂²	semidirect
12. C₂²×D₄×C₁₃	C₂²	semidirect
13. C₂²×D₄×C₁₃	C₂²	semidirect
14. C₂²×D₄×C₁₃	C₂²	semidirect
15. C₂²×D₄×C₁₃	C₂²	semidirect
16. C₂³×C₄×C₁₃	C₂²	semidirect
17. C₁₃×#127	C₂²	semidirect
18. C₁₃×#127	C₂²	semidirect
19. C₁₃×#126	C₂²	semidirect
20. C₁₃×#125	C₂²	semidirect
21. C₁₃×#124	C₂²	semidirect
22. C₁₃×#123	C₂²	semidirect
23. C₁₃×#123	C₂²	semidirect
24. C₁₃×#123	C₂²	semidirect
25. C₁₃×C₂²⋊Q₈	C₂²	semidirect
26. C₁₃×#121	C₂²	semidirect
27. C₁₃×#121	C₂²	semidirect
28. C₁₃×#121	C₂²	semidirect
29. C₁₃×#121	C₂²	semidirect
30. C₁₃×#121	C₂²	semidirect
31. C₁₃×#121	C₂²	semidirect
32. C₁₃×#121	C₂²	semidirect
33. C₁₃×#121	C₂²	semidirect
34. C₁₃×#121	C₂²	semidirect
35. C₁₃×#120	C₂²	semidirect
36. C₁₃×#120	C₂²	semidirect
37. C₁₃×#120	C₂²	semidirect
38. C₁₃×#120	C₂²	semidirect
39. C₁₃×#120	C₂²	semidirect
40. C₄×D₄×C₁₃	C₂²	semidirect
41. C₄×D₄×C₁₃	C₂²	semidirect
42. C₄×D₄×C₁₃	C₂²	semidirect
43. C₁₃×#117	C₂²	semidirect
44. C₁₃×#117	C₂²	semidirect
45. C₂×C₁₃×C₄⋊C₄	C₂²	semidirect
46. C₂×C₁₃×C₂²⋊C₄	C₂²	semidirect
89. #3537	C₁₃	direct (N × H)
125. #560	C₂×C₁₃	semidirect
126. #553	C₂×C₁₃	semidirect
127. D₄²	C₂×C₁₃	semidirect
128. D₄²	C₂×C₁₃	semidirect
129. #540	C₂×C₁₃	semidirect
130. #538	C₂×C₁₃	semidirect
131. #535	C₂×C₁₃	semidirect
132. #534	C₂×C₁₃	semidirect
133. #525	C₂×C₁₃	semidirect
134. C₂×#121	C₂×C₁₃	semidirect
155. C₂×#41	C₂²×C₁₃	semidirect
156. C₂²×D₄	C₂²×C₁₃	semidirect
157. C₂²×D₄	C₂²×C₁₃	semidirect
158. C₂²×D₄	C₂²×C₁₃	semidirect
159. C₂²×D₄	C₂²×C₁₃	semidirect
160. C₂³×C₄	C₂²×C₁₃	semidirect
161. #127	C₂²×C₁₃	semidirect
162. #127	C₂²×C₁₃	semidirect
163. #126	C₂²×C₁₃	semidirect
164. #125	C₂²×C₁₃	semidirect
165. #124	C₂²×C₁₃	semidirect
166. #123	C₂²×C₁₃	semidirect
167. #123	C₂²×C₁₃	semidirect
168. #123	C₂²×C₁₃	semidirect
169. C₂²⋊Q₈	C₂²×C₁₃	semidirect
170. #121	C₂²×C₁₃	semidirect
171. #121	C₂²×C₁₃	semidirect
172. #121	C₂²×C₁₃	semidirect
173. #121	C₂²×C₁₃	semidirect
174. #121	C₂²×C₁₃	semidirect
175. #121	C₂²×C₁₃	semidirect
176. #121	C₂²×C₁₃	semidirect
177. #121	C₂²×C₁₃	semidirect
178. #121	C₂²×C₁₃	semidirect
179. #120	C₂²×C₁₃	semidirect
180. #120	C₂²×C₁₃	semidirect
181. #120	C₂²×C₁₃	semidirect
182. #120	C₂²×C₁₃	semidirect
183. #120	C₂²×C₁₃	semidirect
184. C₄×D₄	C₂²×C₁₃	semidirect
185. C₄×D₄	C₂²×C₁₃	semidirect
186. C₄×D₄	C₂²×C₁₃	semidirect
187. #117	C₂²×C₁₃	semidirect
188. #117	C₂²×C₁₃	semidirect
189. C₂×C₄⋊C₄	C₂²×C₁₃	semidirect
190. C₂×C₂²⋊C₄	C₂²×C₁₃	semidirect
239. C₁₃	#3537	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#560	2
C₁₃×#553	2
D₄²×C₁₃	2
C₁₃×#540	2
C₁₃×#538	2
C₁₃×#535	2
C₁₃×#534	2
C₁₃×#525	2
C₂×C₁₃×#121	2
#3537	13

Subgroups — C13×#3537 #13112595

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#3537 #13112595