Subgroups — C₁₃×#19905 #15706244

Order 3328.

604 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3341	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3329	C₂	1	2	yes	maximal, complemented
4	C₁₃×#1710	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1703	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1676	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1673	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1646	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1637	C₂	1	2	yes	maximal, complemented
10	C₁₃×#1589	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×C₁₃×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#555	C₂²	1	2	yes	—
13	D₄×Q₈×C₁₃	C₂²	1	2	yes	—
14	C₁₃×#500	—	2	1	no	—
15	C₁₃×#500	C₂²	1	1	yes	characteristic
16	C₁₃×#500	C₂²	1	1	yes	characteristic
17	C₁₃×#487	C₂²	1	2	yes	—
18	C₁₃×#487	C₂²	1	2	yes	—
19	C₁₃×#485	—	2	2	no	—
20	C₁₃×#482	—	2	2	no	—
21	C₁₃×#477	C₂²	1	2	yes	—
22	C₁₃×#476	C₂²	1	2	yes	—
23	C₁₃×#474	—	2	2	no	—
24	C₁₃×#474	C₂²	1	2	yes	—
25	C₁₃×#468	—	2	2	no	—
26	C₁₃×#466	—	2	1	no	—
27	C₁₃×#461	C₂²	1	2	yes	—
28	C₁₃×#448	—	2	2	no	—
29	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
30	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
31	C₄×C₁₃×D₈	—	2	1	no	—
32	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
33	C₁₃×#436	C₂²	1	2	yes	—
34	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
35	C₁₃×#427	—	2	1	no	—
36	C₁₃×#419	—	2	2	no	—
37	C₁₃×#335	C₂²	1	1	yes	characteristic
38	C₁₃×#334	C₂²	1	1	yes	characteristic
39	C₁₃×#333	C₂²	1	2	yes	—
40	C₁₃×#332	C₂²	1	2	yes	—
41	C₁₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
42	C₁₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
43	C₁₃×D₄⋊C₈	C₂²	1	2	yes	—
44	C₈²×C₁₃	C₂²	1	1	yes	characteristic
45	C₂²×Q₈×C₁₃	—	2	2	no	—
46	C₂×C₁₃×SD₁₆	—	2	2	no	—
47	C₂×C₁₃×SD₁₆	D₄	1	1	yes	characteristic
48	C₂×C₁₃×D₈	D₄	1	1	yes	characteristic
49	C₂×C₁₃×M₁₆	—	2	2	no	—
50	C₂²×C₈×C₁₃	—	2	1	no	—
51	C₁₃×C₄⋊Q₈	—	2	2	no	—
52	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
53	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
54	C₁₃×#124	—	4	2	no	—
55	C₁₃×C₂²⋊Q₈	—	2	2	no	—
56	C₁₃×C₂²⋊Q₈	—	4	2	no	—
57	C₁₃×#121	—	2	2	no	—
58	C₁₃×#121	—	2	2	no	—
59	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
60	C₄×D₄×C₁₃	—	2	2	no	—
61	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
62	C₄×D₄×C₁₃	C₂³	1	2	yes	—
63	C₁₃×#117	—	2	2	no	—
64	C₁₃×#117	—	2	2	no	—
65	C₁₃×#107	—	2	1	no	—
66	C₁₃×#107	—	2	1	no	—
67	C₁₃×#107	—	2	1	no	—
68	C₁₃×#107	—	2	1	no	—
69	C₁₃×#107	—	2	2	no	—
70	C₁₃×#107	—	2	2	no	—
71	C₁₃×#107	D₄	1	1	yes	characteristic
72	C₁₃×#106	—	2	2	no	—
73	C₁₃×#106	D₄	1	1	yes	characteristic
74	C₁₃×C₄⋊C₈	—	2	1	no	—
75	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
76	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
77	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
78	C₁₃×#103	—	2	2	no	—
79	C₁₃×#103	—	2	2	no	—
80	C₁₃×#103	—	2	2	no	—
81	C₁₃×#103	—	2	2	no	—
82	C₁₃×#103	—	4	2	no	—
83	C₁₃×#103	D₄	1	1	yes	characteristic
84	C₁₃×#102	—	2	2	no	—
85	C₁₃×#102	—	2	2	no	—
86	C₁₃×#102	D₄	1	2	yes	—
87	C₁₃×#102	D₄	1	1	yes	characteristic
88	C₁₃×C₂²⋊C₈	—	2	1	no	—
89	C₁₃×C₂²⋊C₈	—	2	2	no	—
90	C₄×C₈×C₁₃	—	2	1	no	—
91	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
92	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
94	#19905	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
95	C₂×Q₈×C₁₃	—	2	2	no	—
96	C₂×Q₈×C₁₃	—	2	2	no	—
97	C₂×Q₈×C₁₃	—	4	2	no	—
98	C₂×Q₈×C₁₃	—	4	4	no	—
99	C₂×Q₈×C₁₃	—	8	2	no	—
100	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
101	C₂×D₄×C₁₃	—	4	2	no	—
102	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
103	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₃	—	2	1	no	—
105	C₂²×C₄×C₁₃	—	2	2	no	—
106	C₂²×C₄×C₁₃	—	4	2	no	—
107	C₁₃×SD₁₆	—	2	2	no	—
108	C₁₃×SD₁₆	—	8	2	no	—
109	C₁₃×D₈	—	2	2	no	—
110	C₁₃×M₁₆	—	8	2	no	—
111	C₂×C₈×C₁₃	—	2	1	no	—
112	C₂×C₈×C₁₃	—	2	1	no	—
113	C₂×C₈×C₁₃	—	2	2	no	—
114	C₂×C₈×C₁₃	—	2	1	no	—
115	C₂×C₈×C₁₃	—	4	2	no	—
116	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
117	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
118	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
119	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
120	C₁₃×C₄⋊C₄	—	2	1	no	—
121	C₁₃×C₄⋊C₄	—	2	2	no	—
122	C₁₃×C₄⋊C₄	—	2	2	no	—
123	C₁₃×C₄⋊C₄	—	2	2	no	—
124	C₁₃×C₄⋊C₄	—	2	2	no	—
125	C₁₃×C₄⋊C₄	—	4	2	no	—
126	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
127	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
128	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
129	C₁₃×C₂²⋊C₄	—	2	2	no	—
130	C₁₃×C₂²⋊C₄	—	2	1	no	—
131	C₁₃×C₂²⋊C₄	—	4	2	no	—
132	C₁₃×C₂²⋊C₄	—	4	2	no	—
133	C₁₃×C₂²⋊C₄	—	4	2	no	—
134	C₄²×C₁₃	—	2	1	no	—
135	C₄²×C₁₃	—	4	2	no	—
136	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
137	Q₈×D₈	C₂×C₁₃	1	1	yes	characteristic, complemented
138	#3341	C₂×C₁₃	1	1	yes	characteristic
139	#3329	C₂×C₁₃	1	2	yes	complemented
140	#1710	C₂×C₁₃	1	1	yes	characteristic, complemented
141	#1703	C₂×C₁₃	1	2	yes	complemented
142	#1676	C₂×C₁₃	1	1	yes	characteristic, complemented
143	#1673	C₂×C₁₃	1	1	yes	characteristic, complemented
144	#1646	C₂×C₁₃	1	2	yes	complemented
145	#1637	C₂×C₁₃	1	2	yes	complemented
146	#1589	C₂×C₁₃	1	1	yes	characteristic, complemented
147	C₈×SD₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
148	C₂³×C₁₃	—	2	2	no	—
149	C₂³×C₁₃	—	2	1	no	—
150	Q₈×C₁₃	—	2	1	no	—
151	Q₈×C₁₃	—	4	2	no	—
152	Q₈×C₁₃	—	4	2	no	—
153	Q₈×C₁₃	—	8	4	no	—
154	Q₈×C₁₃	—	8	2	no	—
155	Q₈×C₁₃	#135	1	2	yes	—
156	D₄×C₁₃	—	2	1	no	—
157	D₄×C₁₃	—	2	2	no	—
158	D₄×C₁₃	—	2	1	no	—
159	D₄×C₁₃	—	2	2	no	—
160	D₄×C₁₃	—	16	2	no	—
161	C₂×C₄×C₁₃	—	2	1	no	—
162	C₂×C₄×C₁₃	—	2	1	no	—
163	C₂×C₄×C₁₃	—	2	1	no	—
164	C₂×C₄×C₁₃	—	2	2	no	—
165	C₂×C₄×C₁₃	—	4	2	no	—
166	C₂×C₄×C₁₃	—	4	1	no	—
167	C₂×C₄×C₁₃	—	4	2	no	—
168	C₂×C₄×C₁₃	—	4	1	no	—
169	C₂×C₄×C₁₃	—	4	2	no	—
170	C₂×C₄×C₁₃	—	4	2	no	—
171	C₂×C₄×C₁₃	—	8	4	no	—
172	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
173	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
174	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
175	C₈×C₁₃	—	2	1	no	—
176	C₈×C₁₃	—	2	1	no	—
177	C₈×C₁₃	—	2	1	no	—
178	C₈×C₁₃	—	4	1	no	—
179	C₈×C₁₃	—	4	1	no	—
180	C₈×C₁₃	—	4	2	no	—
181	C₈×C₁₃	—	4	1	no	—
182	C₈×C₁₃	#137	1	2	yes	—
183	#555	C₂²×C₁₃	1	2	yes	—
184	D₄×Q₈	C₂²×C₁₃	1	2	yes	—
185	#500	—	2	1	no	—
186	#500	C₂²×C₁₃	1	1	yes	characteristic
187	#500	C₂²×C₁₃	1	1	yes	characteristic
188	#487	C₂²×C₁₃	1	2	yes	—
189	#487	C₂²×C₁₃	1	2	yes	—
190	#485	—	2	2	no	—
191	#482	—	2	2	no	—
192	#477	C₂²×C₁₃	1	2	yes	—
193	#476	C₂²×C₁₃	1	2	yes	—
194	#474	—	2	2	no	—
195	#474	C₂²×C₁₃	1	2	yes	—
196	#468	—	2	2	no	—
197	#466	—	2	1	no	—
198	#461	C₂²×C₁₃	1	2	yes	—
199	#448	—	2	2	no	—
200	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
201	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
202	C₄×D₈	—	2	1	no	—
203	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
204	#436	C₂²×C₁₃	1	2	yes	—
205	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
206	#427	—	2	1	no	—
207	#419	—	2	2	no	—
208	#335	C₂²×C₁₃	1	1	yes	characteristic
209	#334	C₂²×C₁₃	1	1	yes	characteristic
210	#333	C₂²×C₁₃	1	2	yes	—
211	#332	C₂²×C₁₃	1	2	yes	—
212	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
213	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
214	D₄⋊C₈	C₂²×C₁₃	1	2	yes	—
215	C₈²	C₂²×C₁₃	1	1	yes	characteristic
216	C₂²×C₁₃	—	4	1	no	—
217	C₂²×C₁₃	—	4	2	no	—
218	C₂²×C₁₃	—	4	2	no	—
219	C₂²×C₁₃	—	4	1	no	—
220	C₂²×C₁₃	—	4	1	no	—
221	C₂²×C₁₃	—	4	2	no	—
222	C₂²×C₁₃	D₄²	1	1	yes	characteristic
223	C₄×C₁₃	—	2	2	no	—
224	C₄×C₁₃	—	2	1	no	—
225	C₄×C₁₃	—	4	1	no	—
226	C₄×C₁₃	—	4	2	no	—
227	C₄×C₁₃	—	4	1	no	—
228	C₄×C₁₃	—	8	2	no	—
229	C₄×C₁₃	—	8	2	no	—
230	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
231	C₄×C₁₃	C₂×#137	1	1	yes	characteristic
232	C₄×C₁₃	#576	1	1	yes	characteristic
233	C₄×C₁₃	#578	1	1	yes	characteristic
234	C₂²×Q₈	—	2	2	no	—
235	C₂×SD₁₆	—	2	2	no	—
236	C₂×SD₁₆	D₄×C₁₃	1	1	yes	characteristic
237	C₂×D₈	D₄×C₁₃	1	1	yes	characteristic
238	C₂×M₁₆	—	2	2	no	—
239	C₂²×C₈	—	2	1	no	—
240	C₄⋊Q₈	—	2	2	no	—
241	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
242	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
243	#124	—	4	2	no	—
244	C₂²⋊Q₈	—	2	2	no	—
245	C₂²⋊Q₈	—	4	2	no	—
246	#121	—	2	2	no	—
247	#121	—	2	2	no	—
248	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
249	C₄×D₄	—	2	2	no	—
250	C₄×D₄	C₂³×C₁₃	1	2	yes	—
251	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
252	#117	—	2	2	no	—
253	#117	—	2	2	no	—
254	#107	—	2	1	no	—
255	#107	—	2	1	no	—
256	#107	—	2	1	no	—
257	#107	—	2	1	no	—
258	#107	—	2	2	no	—
259	#107	—	2	2	no	—
260	#107	D₄×C₁₃	1	1	yes	characteristic
261	#106	—	2	2	no	—
262	#106	D₄×C₁₃	1	1	yes	characteristic
263	C₄⋊C₈	—	2	1	no	—
264	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
265	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
266	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
267	#103	—	2	2	no	—
268	#103	—	2	2	no	—
269	#103	—	2	2	no	—
270	#103	—	2	2	no	—
271	#103	—	4	2	no	—
272	#103	D₄×C₁₃	1	1	yes	characteristic
273	#102	—	2	2	no	—
274	#102	—	2	2	no	—
275	#102	D₄×C₁₃	1	2	yes	—
276	#102	D₄×C₁₃	1	1	yes	characteristic
277	C₂²⋊C₈	—	2	1	no	—
278	C₂²⋊C₈	—	2	2	no	—
279	C₄×C₈	—	2	1	no	—
280	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
281	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
282	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
283	C₂×C₁₃	—	8	1	no	—
284	C₂×C₁₃	—	8	2	no	—
285	C₂×C₁₃	#3276	1	1	yes	characteristic
286	C₂×C₁₃	#3280	1	1	yes	characteristic
287	C₂×C₁₃	#3290	1	1	yes	characteristic
288	C₂×Q₈	—	2	2	no	—
289	C₂×Q₈	—	2	2	no	—
290	C₂×Q₈	—	4	2	no	—
291	C₂×Q₈	—	4	4	no	—
292	C₂×Q₈	—	8	2	no	—
293	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
294	C₂×D₄	—	4	2	no	—
295	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
296	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
297	C₂²×C₄	—	2	1	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	4	2	no	—
300	SD₁₆	—	2	2	no	—
301	SD₁₆	—	8	2	no	—
302	D₈	—	2	2	no	—
303	M₁₆	—	8	2	no	—
304	C₂×C₈	—	2	1	no	—
305	C₂×C₈	—	2	1	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	—	2	1	no	—
308	C₂×C₈	—	4	2	no	—
309	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
310	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
311	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
312	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
313	C₄⋊C₄	—	2	1	no	—
314	C₄⋊C₄	—	2	2	no	—
315	C₄⋊C₄	—	2	2	no	—
316	C₄⋊C₄	—	2	2	no	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	—	4	2	no	—
319	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
320	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
321	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
322	C₂²⋊C₄	—	2	2	no	—
323	C₂²⋊C₄	—	2	1	no	—
324	C₂²⋊C₄	—	4	2	no	—
325	C₂²⋊C₄	—	4	2	no	—
326	C₂²⋊C₄	—	4	2	no	—
327	C₄²	—	2	1	no	—
328	C₄²	—	4	2	no	—
329	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
330	C₁₃	#19905	1	1	yes	characteristic, direct product factor, Sylow
331	C₂³	—	2	2	no	—
332	C₂³	—	2	1	no	—
333	Q₈	—	2	1	no	—
334	Q₈	—	4	2	no	—
335	Q₈	—	4	2	no	—
336	Q₈	—	8	4	no	—
337	Q₈	—	8	2	no	—
338	Q₈	C₁₃×#135	1	2	yes	—
339	D₄	—	2	1	no	—
340	D₄	—	2	2	no	—
341	D₄	—	2	1	no	—
342	D₄	—	2	2	no	—
343	D₄	—	16	2	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	4	1	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	4	1	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	8	4	no	—
355	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
356	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
357	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
358	C₈	—	2	1	no	—
359	C₈	—	2	1	no	—
360	C₈	—	2	1	no	—
361	C₈	—	4	1	no	—
362	C₈	—	4	1	no	—
363	C₈	—	4	2	no	—
364	C₈	—	4	1	no	—
365	C₈	C₁₃×#137	1	2	yes	—
366	C₂²	—	4	1	no	—
367	C₂²	—	4	2	no	—
368	C₂²	—	4	2	no	—
369	C₂²	—	4	1	no	—
370	C₂²	—	4	1	no	—
371	C₂²	—	4	2	no	—
372	C₂²	D₄²×C₁₃	1	1	yes	characteristic
373	C₄	—	2	2	no	—
374	C₄	—	2	1	no	—
375	C₄	—	4	1	no	—
376	C₄	—	4	2	no	—
377	C₄	—	4	1	no	—
378	C₄	—	8	2	no	—
379	C₄	—	8	2	no	—
380	C₄	C₂×C₁₃×#135	1	1	yes	characteristic
381	C₄	C₂×C₁₃×#137	1	1	yes	characteristic
382	C₄	C₁₃×#576	1	1	yes	characteristic
383	C₄	C₁₃×#578	1	1	yes	characteristic
384	C₂	—	8	1	no	—
385	C₂	—	8	2	no	—
386	C₂	C₁₃×#3276	1	1	yes	characteristic
387	C₂	C₁₃×#3280	1	1	yes	characteristic
388	C₂	C₁₃×#3290	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃
prime radical	C₁₃×#3341	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. Q₈×C₁₃×D₈	C₂	semidirect
3. C₁₃×#3329	C₂	semidirect
4. C₁₃×#1710	C₂	semidirect
5. C₁₃×#1703	C₂	semidirect
6. C₁₃×#1676	C₂	semidirect
7. C₁₃×#1673	C₂	semidirect
8. C₁₃×#1646	C₂	semidirect
9. C₁₃×#1637	C₂	semidirect
10. C₁₃×#1589	C₂	semidirect
11. C₈×C₁₃×SD₁₆	C₂	semidirect
94. #19905	C₁₃	direct (N × H)
137. Q₈×D₈	C₂×C₁₃	semidirect
139. #3329	C₂×C₁₃	semidirect
140. #1710	C₂×C₁₃	semidirect
141. #1703	C₂×C₁₃	semidirect
142. #1676	C₂×C₁₃	semidirect
143. #1673	C₂×C₁₃	semidirect
144. #1646	C₂×C₁₃	semidirect
145. #1637	C₂×C₁₃	semidirect
146. #1589	C₂×C₁₃	semidirect
147. C₈×SD₁₆	C₂×C₁₃	semidirect
330. C₁₃	#19905	direct (N × H)

Maximal subgroups

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

subgroup	index
Q₈×C₁₃×D₈	2
C₁₃×#3341	2
C₁₃×#3329	2
C₁₃×#1710	2
C₁₃×#1703	2
C₁₃×#1676	2
C₁₃×#1673	2
C₁₃×#1646	2
C₁₃×#1637	2
C₁₃×#1589	2
C₈×C₁₃×SD₁₆	2
#19905	13

Subgroups — C13×#19905 #15706244

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#19905 #15706244