Subgroups — C₁₃×#33580 #15719919

Order 3328.

770 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#509	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3147	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2210	C₂	1	4	yes	maximal, complemented
5	C₁₃×#2208	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2206	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2150	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2139	C₂	1	2	yes	maximal, complemented
9	C₂×C₁₃×#135	—	2	1	no	—
10	C₂×C₁₃×#135	C₂²	1	2	yes	—
11	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
12	C₁₃×#532	—	2	1	no	—
13	C₂×C₄×D₄×C₁₃	—	2	1	no	—
14	C₁₃×#509	—	2	8	no	—
15	C₂×C₁₃×SD₃₂	C₂²	1	4	yes	—
16	C₂×C₁₃×D₁₆	C₂²	1	4	yes	—
17	C₂×C₁₃×M₃₂	C₂²	1	2	yes	—
18	C₁₃×#495	—	2	1	no	—
19	C₁₃×#495	C₂²	1	2	yes	complemented
20	C₁₃×#494	C₂²	1	1	yes	characteristic, complemented
21	C₁₃×#493	C₂²	1	1	yes	characteristic, complemented
22	C₁₃×#492	—	2	1	no	—
23	C₄×C₁₃×D₈	—	2	1	no	—
24	C₄×C₁₃×D₈	—	2	1	no	—
25	C₄×C₁₃×D₈	C₂²	1	2	yes	—
26	C₄×C₁₃×D₈	C₂²	1	2	yes	—
27	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#102	—	2	1	no	—
29	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
30	C₁₃×C₄⋊C₁₆	C₂²	1	2	yes	complemented
31	C₁₃×C₄⋊C₁₆	C₂²	1	2	yes	complemented
32	C₁₃×#358	C₂²	1	4	yes	complemented
33	C₁₃×#357	C₂²	1	4	yes	complemented
34	C₂×C₁₃×#41	—	2	2	no	—
35	C₂²×D₄×C₁₃	—	2	1	no	—
36	C₂³×C₄×C₁₃	—	4	1	no	—
37	C₁₃×#135	—	2	4	no	—
38	C₁₃×#135	—	2	4	no	—
39	C₁₃×#135	—	4	4	no	—
40	C₂×C₁₃×Q₁₆	—	2	1	no	—
41	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
42	C₂×C₁₃×SD₁₆	—	2	2	no	—
43	C₂×C₁₃×SD₁₆	—	2	2	no	—
44	C₂×C₁₃×D₈	—	2	1	no	—
45	C₂×C₁₃×D₈	—	2	1	no	—
46	C₂×C₁₃×D₈	—	2	2	no	—
47	C₂×C₁₃×D₈	D₄	1	4	yes	complemented
48	C₂×C₁₃×D₈	C₂³	1	2	yes	—
49	C₂×C₁₃×D₈	C₂³	1	2	yes	—
50	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
51	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
52	C₁₃×C₄⋊Q₈	—	2	1	no	—
53	C₁₃×#127	—	2	1	no	—
54	C₁₃×#124	—	2	2	no	—
55	C₁₃×#121	—	4	1	no	—
56	C₁₃×#121	—	4	1	no	—
57	C₄×D₄×C₁₃	—	2	2	no	—
58	C₄×D₄×C₁₃	—	2	2	no	—
59	C₄×D₄×C₁₃	—	4	1	no	—
60	C₄×D₄×C₁₃	—	4	1	no	—
61	C₄×D₄×C₁₃	—	4	1	no	—
62	C₄×D₄×C₁₃	—	4	1	no	—
63	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
64	C₂×C₁₃×C₂²⋊C₄	—	4	1	no	—
65	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
66	C₁₃×SD₃₂	—	2	8	no	—
67	C₁₃×D₁₆	—	2	8	no	—
68	C₁₃×M₃₂	—	2	4	no	—
69	C₂×C₁₃×C₁₆	C₂³	1	4	yes	—
70	C₁₃×#107	—	2	1	no	—
71	C₁₃×#107	C₂³	1	2	yes	—
72	C₁₃×#102	—	2	2	no	—
73	C₁₃×#102	—	2	2	no	—
74	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
75	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
76	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
77	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
78	#33580	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
79	C₂⁴×C₁₃	—	4	1	no	—
80	C₁₃×#41	—	4	4	no	—
81	C₁₃×#41	—	4	4	no	—
82	C₂×Q₈×C₁₃	—	2	2	no	—
83	C₂×D₄×C₁₃	—	2	4	no	—
84	C₂×D₄×C₁₃	—	2	2	no	—
85	C₂×D₄×C₁₃	—	2	2	no	—
86	C₂×D₄×C₁₃	—	4	2	no	—
87	C₂×D₄×C₁₃	—	4	1	no	—
88	C₂×D₄×C₁₃	—	4	1	no	—
89	C₂×D₄×C₁₃	—	4	1	no	—
90	C₂×D₄×C₁₃	—	4	2	no	—
91	C₂²×C₄×C₁₃	—	4	1	no	—
92	C₂²×C₄×C₁₃	—	4	2	no	—
93	C₂²×C₄×C₁₃	—	4	2	no	—
94	C₂²×C₄×C₁₃	—	4	2	no	—
95	C₂²×C₄×C₁₃	—	8	4	no	—
96	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
97	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
98	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
99	C₁₃×Q₁₆	—	2	2	no	—
100	C₁₃×Q₁₆	—	2	2	no	—
101	C₁₃×Q₁₆	—	4	2	no	—
102	C₁₃×SD₁₆	—	4	4	no	—
103	C₁₃×SD₁₆	—	4	4	no	—
104	C₁₃×D₈	—	2	4	no	—
105	C₁₃×D₈	—	2	2	no	—
106	C₁₃×D₈	—	2	2	no	—
107	C₁₃×D₈	—	2	2	no	—
108	C₁₃×D₈	—	4	2	no	—
109	C₁₃×D₈	C₂×D₄	1	4	yes	—
110	C₂×C₈×C₁₃	—	2	2	no	—
111	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
112	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
113	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
114	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
115	C₂×C₈×C₁₃	#41	1	2	yes	—
116	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
117	C₁₃×C₄⋊C₄	—	2	2	no	—
118	C₁₃×C₄⋊C₄	—	4	1	no	—
119	C₁₃×C₄⋊C₄	—	4	1	no	—
120	C₁₃×C₄⋊C₄	—	4	1	no	—
121	C₁₃×C₂²⋊C₄	—	4	2	no	—
122	C₁₃×C₂²⋊C₄	—	4	2	no	—
123	C₁₃×C₂²⋊C₄	—	4	2	no	—
124	C₁₃×C₂²⋊C₄	—	4	2	no	—
125	C₄²×C₁₃	D₈	1	1	yes	characteristic
126	C₄²×C₁₃	D₈	1	1	yes	characteristic
127	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
128	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
129	C₁₃×C₁₆	—	2	4	no	—
130	C₂×#509	C₂×C₁₃	1	2	yes	complemented
131	#3147	C₂×C₁₃	1	1	yes	characteristic, complemented
132	C₂×C₄×D₈	C₂×C₁₃	1	1	yes	characteristic, complemented
133	#2210	C₂×C₁₃	1	4	yes	complemented
134	#2208	C₂×C₁₃	1	2	yes	complemented
135	#2206	C₂×C₁₃	1	2	yes	complemented
136	#2150	C₂×C₁₃	1	1	yes	characteristic, complemented
137	#2139	C₂×C₁₃	1	2	yes	complemented
138	C₂³×C₁₃	—	4	2	no	—
139	C₂³×C₁₃	—	4	4	no	—
140	C₂³×C₁₃	—	4	2	no	—
141	C₂³×C₁₃	—	8	2	no	—
142	C₂³×C₁₃	—	8	2	no	—
143	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
144	Q₈×C₁₃	—	4	2	no	—
145	Q₈×C₁₃	—	4	2	no	—
146	D₄×C₁₃	—	2	4	no	—
147	D₄×C₁₃	—	4	2	no	—
148	D₄×C₁₃	—	4	2	no	—
149	D₄×C₁₃	—	4	2	no	—
150	D₄×C₁₃	—	4	4	no	—
151	D₄×C₁₃	—	8	2	no	—
152	D₄×C₁₃	—	8	4	no	—
153	D₄×C₁₃	—	8	2	no	—
154	C₂×C₄×C₁₃	—	2	2	no	—
155	C₂×C₄×C₁₃	—	4	1	no	—
156	C₂×C₄×C₁₃	—	4	2	no	—
157	C₂×C₄×C₁₃	—	4	2	no	—
158	C₂×C₄×C₁₃	—	8	4	no	—
159	C₂×C₄×C₁₃	—	8	2	no	—
160	C₂×C₄×C₁₃	—	8	4	no	—
161	C₂×C₄×C₁₃	—	8	4	no	—
162	C₂×C₄×C₁₃	#121	1	2	yes	—
163	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
164	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
165	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
166	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
167	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
168	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
169	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
170	C₈×C₁₃	—	2	1	no	—
171	C₈×C₁₃	—	2	1	no	—
172	C₈×C₁₃	#121	1	2	yes	—
173	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
174	C₈×C₁₃	C₂×#41	1	1	yes	characteristic
175	C₂×#135	—	2	1	no	—
176	C₂×#135	C₂²×C₁₃	1	2	yes	—
177	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
178	#532	—	2	1	no	—
179	C₂×C₄×D₄	—	2	1	no	—
180	#509	—	2	8	no	—
181	C₂×SD₃₂	C₂²×C₁₃	1	4	yes	—
182	C₂×D₁₆	C₂²×C₁₃	1	4	yes	—
183	C₂×M₃₂	C₂²×C₁₃	1	2	yes	—
184	#495	—	2	1	no	—
185	#495	C₂²×C₁₃	1	2	yes	complemented
186	#494	C₂²×C₁₃	1	1	yes	characteristic, complemented
187	#493	C₂²×C₁₃	1	1	yes	characteristic, complemented
188	#492	—	2	1	no	—
189	C₄×D₈	—	2	1	no	—
190	C₄×D₈	—	2	1	no	—
191	C₄×D₈	C₂²×C₁₃	1	2	yes	—
192	C₄×D₈	C₂²×C₁₃	1	2	yes	—
193	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
194	C₂×#102	—	2	1	no	—
195	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
196	C₄⋊C₁₆	C₂²×C₁₃	1	2	yes	complemented
197	C₄⋊C₁₆	C₂²×C₁₃	1	2	yes	complemented
198	#358	C₂²×C₁₃	1	4	yes	complemented
199	#357	C₂²×C₁₃	1	4	yes	complemented
200	C₂²×C₁₃	—	2	1	no	—
201	C₂²×C₁₃	—	2	1	no	—
202	C₂²×C₁₃	—	4	4	no	—
203	C₂²×C₁₃	—	8	8	no	—
204	C₂²×C₁₃	—	8	2	no	—
205	C₂²×C₁₃	—	8	2	no	—
206	C₂²×C₁₃	—	8	2	no	—
207	C₂²×C₁₃	—	8	2	no	—
208	C₂²×C₁₃	—	8	2	no	—
209	C₂²×C₁₃	#459	1	2	yes	—
210	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
211	C₄×C₁₃	—	2	1	no	—
212	C₄×C₁₃	—	2	1	no	—
213	C₄×C₁₃	—	2	1	no	—
214	C₄×C₁₃	—	8	2	no	—
215	C₄×C₁₃	—	8	2	no	—
216	C₄×C₁₃	#459	1	2	yes	—
217	C₄×C₁₃	#509	1	2	yes	complemented
218	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
219	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
220	C₂×#41	—	2	2	no	—
221	C₂²×D₄	—	2	1	no	—
222	C₂³×C₄	—	4	1	no	—
223	#135	—	2	4	no	—
224	#135	—	2	4	no	—
225	#135	—	4	4	no	—
226	C₂×Q₁₆	—	2	1	no	—
227	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
228	C₂×SD₁₆	—	2	2	no	—
229	C₂×SD₁₆	—	2	2	no	—
230	C₂×D₈	—	2	1	no	—
231	C₂×D₈	—	2	1	no	—
232	C₂×D₈	—	2	2	no	—
233	C₂×D₈	D₄×C₁₃	1	4	yes	complemented
234	C₂×D₈	C₂³×C₁₃	1	2	yes	—
235	C₂×D₈	C₂³×C₁₃	1	2	yes	—
236	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
237	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
238	C₄⋊Q₈	—	2	1	no	—
239	#127	—	2	1	no	—
240	#124	—	2	2	no	—
241	#121	—	4	1	no	—
242	#121	—	4	1	no	—
243	C₄×D₄	—	2	2	no	—
244	C₄×D₄	—	2	2	no	—
245	C₄×D₄	—	4	1	no	—
246	C₄×D₄	—	4	1	no	—
247	C₄×D₄	—	4	1	no	—
248	C₄×D₄	—	4	1	no	—
249	C₂×C₄⋊C₄	—	2	1	no	—
250	C₂×C₂²⋊C₄	—	4	1	no	—
251	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
252	SD₃₂	—	2	8	no	—
253	D₁₆	—	2	8	no	—
254	M₃₂	—	2	4	no	—
255	C₂×C₁₆	C₂³×C₁₃	1	4	yes	—
256	#107	—	2	1	no	—
257	#107	C₂³×C₁₃	1	2	yes	—
258	#102	—	2	2	no	—
259	#102	—	2	2	no	—
260	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
261	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
262	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
263	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
264	C₂×C₁₃	—	2	2	no	—
265	C₂×C₁₃	—	8	4	no	—
266	C₂×C₁₃	—	16	2	no	—
267	C₂×C₁₃	C₂×#459	1	1	yes	characteristic
268	C₂×C₁₃	C₂×#509	1	1	yes	characteristic
269	C₂×C₁₃	#3414	1	1	yes	characteristic
270	C₂⁴	—	4	1	no	—
271	#41	—	4	4	no	—
272	#41	—	4	4	no	—
273	C₂×Q₈	—	2	2	no	—
274	C₂×D₄	—	2	4	no	—
275	C₂×D₄	—	2	2	no	—
276	C₂×D₄	—	2	2	no	—
277	C₂×D₄	—	4	2	no	—
278	C₂×D₄	—	4	1	no	—
279	C₂×D₄	—	4	1	no	—
280	C₂×D₄	—	4	1	no	—
281	C₂×D₄	—	4	2	no	—
282	C₂²×C₄	—	4	1	no	—
283	C₂²×C₄	—	4	2	no	—
284	C₂²×C₄	—	4	2	no	—
285	C₂²×C₄	—	4	2	no	—
286	C₂²×C₄	—	8	4	no	—
287	C₂²×C₄	C₁₃×D₈	1	1	yes	characteristic
288	C₂²×C₄	C₁₃×D₈	1	1	yes	characteristic
289	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
290	Q₁₆	—	2	2	no	—
291	Q₁₆	—	2	2	no	—
292	Q₁₆	—	4	2	no	—
293	SD₁₆	—	4	4	no	—
294	SD₁₆	—	4	4	no	—
295	D₈	—	2	4	no	—
296	D₈	—	2	2	no	—
297	D₈	—	2	2	no	—
298	D₈	—	2	2	no	—
299	D₈	—	4	2	no	—
300	D₈	C₂×D₄×C₁₃	1	4	yes	—
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
303	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
304	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
305	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
306	C₂×C₈	C₁₃×#41	1	2	yes	—
307	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
308	C₄⋊C₄	—	2	2	no	—
309	C₄⋊C₄	—	4	1	no	—
310	C₄⋊C₄	—	4	1	no	—
311	C₄⋊C₄	—	4	1	no	—
312	C₂²⋊C₄	—	4	2	no	—
313	C₂²⋊C₄	—	4	2	no	—
314	C₂²⋊C₄	—	4	2	no	—
315	C₂²⋊C₄	—	4	2	no	—
316	C₄²	C₁₃×D₈	1	1	yes	characteristic
317	C₄²	C₁₃×D₈	1	1	yes	characteristic
318	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
319	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
320	C₁₆	—	2	4	no	—
321	C₁₃	#33580	1	1	yes	characteristic, direct product factor, Sylow
322	C₂³	—	4	4	no	—
323	C₂³	—	4	2	no	—
324	C₂³	—	4	2	no	—
325	C₂³	—	8	2	no	—
326	C₂³	—	8	2	no	—
327	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
328	Q₈	—	4	2	no	—
329	Q₈	—	4	2	no	—
330	D₄	—	2	4	no	—
331	D₄	—	4	4	no	—
332	D₄	—	4	2	no	—
333	D₄	—	4	2	no	—
334	D₄	—	4	2	no	—
335	D₄	—	8	2	no	—
336	D₄	—	8	4	no	—
337	D₄	—	8	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	4	1	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	4	2	no	—
342	C₂×C₄	—	8	4	no	—
343	C₂×C₄	—	8	2	no	—
344	C₂×C₄	—	8	4	no	—
345	C₂×C₄	—	8	4	no	—
346	C₂×C₄	C₁₃×#121	1	2	yes	—
347	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
348	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
349	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
350	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
351	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
352	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
353	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
354	C₈	—	2	1	no	—
355	C₈	—	2	1	no	—
356	C₈	C₁₃×#121	1	2	yes	—
357	C₈	C₂²×D₄×C₁₃	1	1	yes	characteristic
358	C₈	C₂×C₁₃×#41	1	1	yes	characteristic
359	C₂²	—	2	1	no	—
360	C₂²	—	2	1	no	—
361	C₂²	—	4	4	no	—
362	C₂²	—	8	8	no	—
363	C₂²	—	8	2	no	—
364	C₂²	—	8	2	no	—
365	C₂²	—	8	2	no	—
366	C₂²	—	8	2	no	—
367	C₂²	—	8	2	no	—
368	C₂²	C₁₃×#459	1	2	yes	—
369	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
370	C₄	—	2	1	no	—
371	C₄	—	2	1	no	—
372	C₄	—	2	1	no	—
373	C₄	—	8	2	no	—
374	C₄	—	8	2	no	—
375	C₄	C₁₃×#459	1	2	yes	—
376	C₄	C₁₃×#509	1	2	yes	complemented
377	C₄	C₂×C₁₃×#121	1	1	yes	characteristic
378	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
379	C₂	—	2	2	no	—
380	C₂	—	8	4	no	—
381	C₂	—	16	2	no	—
382	C₂	C₂×C₁₃×#459	1	1	yes	characteristic
383	C₂	C₂×C₁₃×#509	1	1	yes	characteristic
384	C₂	C₁₃×#3414	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ C₂×C₄×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#509	C₂	semidirect
2. C₁₃×#3147	C₂	semidirect
3. C₂×C₄×C₁₃×D₈	C₂	semidirect
4. C₁₃×#2210	C₂	semidirect
5. C₁₃×#2208	C₂	semidirect
6. C₁₃×#2206	C₂	semidirect
7. C₁₃×#2150	C₂	semidirect
8. C₁₃×#2139	C₂	semidirect
19. C₁₃×#495	C₂²	semidirect
20. C₁₃×#494	C₂²	semidirect
21. C₁₃×#493	C₂²	semidirect
30. C₁₃×C₄⋊C₁₆	C₂²	semidirect
31. C₁₃×C₄⋊C₁₆	C₂²	semidirect
32. C₁₃×#358	C₂²	semidirect
33. C₁₃×#357	C₂²	semidirect
47. C₂×C₁₃×D₈	D₄	semidirect
78. #33580	C₁₃	direct (N × H)
130. C₂×#509	C₂×C₁₃	semidirect
131. #3147	C₂×C₁₃	semidirect
132. C₂×C₄×D₈	C₂×C₁₃	semidirect
133. #2210	C₂×C₁₃	semidirect
134. #2208	C₂×C₁₃	semidirect
135. #2206	C₂×C₁₃	semidirect
136. #2150	C₂×C₁₃	semidirect
137. #2139	C₂×C₁₃	semidirect
185. #495	C₂²×C₁₃	semidirect
186. #494	C₂²×C₁₃	semidirect
187. #493	C₂²×C₁₃	semidirect
196. C₄⋊C₁₆	C₂²×C₁₃	semidirect
197. C₄⋊C₁₆	C₂²×C₁₃	semidirect
198. #358	C₂²×C₁₃	semidirect
199. #357	C₂²×C₁₃	semidirect
217. C₄×C₁₃	#509	semidirect
233. C₂×D₈	D₄×C₁₃	semidirect
321. C₁₃	#33580	direct (N × H)
376. C₄	C₁₃×#509	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#509	2
C₁₃×#3147	2
C₂×C₄×C₁₃×D₈	2
C₁₃×#2210	2
C₁₃×#2208	2
C₁₃×#2206	2
C₁₃×#2150	2
C₁₃×#2139	2
#33580	13

Subgroups — C13×#33580 #15719919

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#33580 #15719919