Subgroups — C₁₃×#33517 #15719856

Order 3328.

1380 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#509	C₂	1	2	yes	maximal, complemented
3	C₁₃×#3050	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2187	C₂	1	4	yes	maximal, complemented
5	C₁₃×#2184	C₂	1	4	yes	maximal, complemented
6	C₁₃×#2140	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2112	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂³×D₄×C₁₃	—	2	1	no	—
9	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic, complemented
10	C₂²×C₁₃×D₈	—	2	8	no	—
11	C₂²×C₁₃×D₈	—	2	1	no	—
12	C₂²×C₁₃×D₈	—	2	2	no	—
13	C₂²×C₁₃×D₈	C₂²	1	4	yes	—
14	C₂²×C₁₃×D₈	C₂²	1	2	yes	—
15	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
16	C₁₃×#525	—	2	1	no	—
17	C₁₃×#509	—	2	8	no	—
18	C₂×C₁₃×SD₃₂	C₂²	1	4	yes	complemented
19	C₂×C₁₃×D₁₆	C₂²	1	4	yes	complemented
20	C₂×C₁₃×M₃₂	C₂²	1	2	yes	complemented
21	C₁₃×#467	C₂²	1	2	yes	complemented
22	C₁₃×#466	C₂²	1	2	yes	complemented
23	C₁₃×#465	—	2	2	no	—
24	C₁₃×#427	C₂²	1	1	yes	characteristic, complemented
25	C₁₃×#416	—	2	1	no	—
26	C₁₃×#357	C₂²	1	8	yes	complemented
27	C₁₃×C₂²⋊C₁₆	C₂²	1	4	yes	complemented
28	C₂⁵×C₁₃	—	4	1	no	—
29	C₂×C₁₃×#41	—	2	1	no	—
30	C₂²×D₄×C₁₃	—	2	8	no	—
31	C₂²×D₄×C₁₃	—	2	4	no	—
32	C₂²×D₄×C₁₃	—	2	2	no	—
33	C₂²×D₄×C₁₃	—	4	4	no	—
34	C₂²×D₄×C₁₃	—	4	2	no	—
35	C₂²×D₄×C₁₃	—	4	1	no	—
36	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
37	C₁₃×#135	—	2	4	no	—
38	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic, complemented
39	C₂×C₁₃×SD₁₆	—	2	1	no	—
40	C₂×C₁₃×D₈	—	2	8	no	—
41	C₂×C₁₃×D₈	—	2	16	no	—
42	C₂×C₁₃×D₈	—	2	16	no	—
43	C₂×C₁₃×D₈	—	2	4	no	—
44	C₂×C₁₃×D₈	—	2	2	no	—
45	C₂×C₁₃×D₈	—	2	4	no	—
46	C₂×C₁₃×D₈	D₄	1	8	yes	complemented
47	C₂×C₁₃×D₈	C₂³	1	4	yes	—
48	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic, complemented
49	C₂²×C₈×C₁₃	—	2	4	no	—
50	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
51	C₂²×C₈×C₁₃	D₄	1	2	yes	—
52	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
53	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
54	C₁₃×#123	—	4	1	no	—
55	C₁₃×C₂²⋊Q₈	—	2	2	no	—
56	C₁₃×#121	—	2	2	no	—
57	C₁₃×#120	—	4	1	no	—
58	C₄×D₄×C₁₃	—	4	2	no	—
59	C₁₃×#117	—	2	1	no	—
60	C₁₃×SD₃₂	—	2	8	no	—
61	C₁₃×D₁₆	—	2	8	no	—
62	C₁₃×M₃₂	—	2	4	no	—
63	C₂×C₁₃×C₁₆	C₂³	1	4	yes	complemented
64	C₁₃×#107	C₂³	1	2	yes	complemented
65	C₁₃×#106	—	2	1	no	—
66	C₁₃×#103	—	2	2	no	—
67	C₁₃×#102	—	2	2	no	—
68	#33517	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
69	C₂⁴×C₁₃	—	4	8	no	—
70	C₂⁴×C₁₃	—	4	4	no	—
71	C₂⁴×C₁₃	—	4	2	no	—
72	C₂⁴×C₁₃	—	8	8	no	—
73	C₂⁴×C₁₃	D₈	1	1	yes	characteristic
74	C₁₃×#41	—	4	2	no	—
75	C₁₃×#41	—	4	2	no	—
76	C₂×Q₈×C₁₃	—	2	1	no	—
77	C₂×D₄×C₁₃	—	2	16	no	—
78	C₂×D₄×C₁₃	—	2	8	no	—
79	C₂×D₄×C₁₃	—	2	4	no	—
80	C₂×D₄×C₁₃	—	2	1	no	—
81	C₂×D₄×C₁₃	—	4	8	no	—
82	C₂×D₄×C₁₃	—	4	8	no	—
83	C₂×D₄×C₁₃	—	4	16	no	—
84	C₂×D₄×C₁₃	—	4	2	no	—
85	C₂×D₄×C₁₃	—	4	1	no	—
86	C₂×D₄×C₁₃	—	4	4	no	—
87	C₂×D₄×C₁₃	—	4	2	no	—
88	C₂×D₄×C₁₃	—	4	4	no	—
89	C₂²×C₄×C₁₃	—	2	2	no	—
90	C₂²×C₄×C₁₃	—	2	2	no	—
91	C₂²×C₄×C₁₃	—	4	1	no	—
92	C₂²×C₄×C₁₃	D₈	1	2	yes	—
93	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
94	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
95	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
96	C₁₃×Q₁₆	—	2	2	no	—
97	C₁₃×SD₁₆	—	4	2	no	—
98	C₁₃×D₈	—	2	16	no	—
99	C₁₃×D₈	—	2	8	no	—
100	C₁₃×D₈	—	2	4	no	—
101	C₁₃×D₈	—	2	2	no	—
102	C₁₃×D₈	C₂×D₄	1	8	yes	—
103	C₂×C₈×C₁₃	—	2	2	no	—
104	C₂×C₈×C₁₃	—	2	4	no	—
105	C₂×C₈×C₁₃	—	2	4	no	—
106	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
107	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
108	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
109	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
110	C₁₃×C₄⋊C₄	—	2	2	no	—
111	C₁₃×C₄⋊C₄	—	4	2	no	—
112	C₁₃×C₂²⋊C₄	—	4	1	no	—
113	C₁₃×C₂²⋊C₄	—	4	2	no	—
114	C₁₃×C₂²⋊C₄	—	4	2	no	—
115	C₄²×C₁₃	—	4	1	no	—
116	C₁₃×C₁₆	—	2	4	no	—
117	C₂³×D₈	C₂×C₁₃	1	1	yes	characteristic, complemented
118	C₂×#509	C₂×C₁₃	1	2	yes	complemented
119	#3050	C₂×C₁₃	1	1	yes	characteristic, complemented
120	#2187	C₂×C₁₃	1	4	yes	complemented
121	#2184	C₂×C₁₃	1	4	yes	complemented
122	#2140	C₂×C₁₃	1	2	yes	complemented
123	#2112	C₂×C₁₃	1	1	yes	characteristic, complemented
124	C₂³×C₁₃	—	2	2	no	—
125	C₂³×C₁₃	—	2	4	no	—
126	C₂³×C₁₃	—	4	16	no	—
127	C₂³×C₁₃	—	4	4	no	—
128	C₂³×C₁₃	—	4	8	no	—
129	C₂³×C₁₃	—	4	1	no	—
130	C₂³×C₁₃	—	8	32	no	—
131	C₂³×C₁₃	—	8	8	no	—
132	C₂³×C₁₃	—	8	8	no	—
133	C₂³×C₁₃	—	8	8	no	—
134	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
135	C₂³×C₁₃	C₂×D₈	1	2	yes	—
136	Q₈×C₁₃	—	4	1	no	—
137	Q₈×C₁₃	—	4	1	no	—
138	D₄×C₁₃	—	2	8	no	—
139	D₄×C₁₃	—	4	16	no	—
140	D₄×C₁₃	—	4	1	no	—
141	D₄×C₁₃	—	4	4	no	—
142	D₄×C₁₃	—	4	1	no	—
143	D₄×C₁₃	—	4	8	no	—
144	D₄×C₁₃	—	8	2	no	—
145	D₄×C₁₃	—	8	4	no	—
146	C₂×C₄×C₁₃	—	2	2	no	—
147	C₂×C₄×C₁₃	—	2	2	no	—
148	C₂×C₄×C₁₃	—	2	2	no	—
149	C₂×C₄×C₁₃	—	2	4	no	—
150	C₂×C₄×C₁₃	—	4	2	no	—
151	C₂×C₄×C₁₃	—	4	1	no	—
152	C₂×C₄×C₁₃	—	8	2	no	—
153	C₂×C₄×C₁₃	#120	1	2	yes	—
154	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
155	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
156	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
157	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
158	C₈×C₁₃	—	2	2	no	—
159	C₈×C₁₃	#120	1	2	yes	—
160	C₈×C₁₃	C₂²×D₄	1	2	yes	—
161	C₂³×D₄	—	2	1	no	—
162	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic, complemented
163	C₂²×D₈	—	2	8	no	—
164	C₂²×D₈	—	2	1	no	—
165	C₂²×D₈	—	2	2	no	—
166	C₂²×D₈	C₂²×C₁₃	1	4	yes	—
167	C₂²×D₈	C₂²×C₁₃	1	2	yes	—
168	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
169	#525	—	2	1	no	—
170	#509	—	2	8	no	—
171	C₂×SD₃₂	C₂²×C₁₃	1	4	yes	complemented
172	C₂×D₁₆	C₂²×C₁₃	1	4	yes	complemented
173	C₂×M₃₂	C₂²×C₁₃	1	2	yes	complemented
174	#467	C₂²×C₁₃	1	2	yes	complemented
175	#466	C₂²×C₁₃	1	2	yes	complemented
176	#465	—	2	2	no	—
177	#427	C₂²×C₁₃	1	1	yes	characteristic, complemented
178	#416	—	2	1	no	—
179	#357	C₂²×C₁₃	1	8	yes	complemented
180	C₂²⋊C₁₆	C₂²×C₁₃	1	4	yes	complemented
181	C₂²×C₁₃	—	2	8	no	—
182	C₂²×C₁₃	—	2	2	no	—
183	C₂²×C₁₃	—	2	2	no	—
184	C₂²×C₁₃	—	2	2	no	—
185	C₂²×C₁₃	—	4	8	no	—
186	C₂²×C₁₃	—	8	16	no	—
187	C₂²×C₁₃	—	8	32	no	—
188	C₂²×C₁₃	—	8	8	no	—
189	C₂²×C₁₃	—	8	2	no	—
190	C₂²×C₁₃	—	8	1	no	—
191	C₂²×C₁₃	#447	1	2	yes	—
192	C₂²×C₁₃	#509	1	4	yes	complemented
193	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
194	C₄×C₁₃	—	2	2	no	—
195	C₄×C₁₃	—	8	2	no	—
196	C₄×C₁₃	—	8	1	no	—
197	C₄×C₁₃	#447	1	2	yes	—
198	C₄×C₁₃	C₂×#120	1	1	yes	characteristic
199	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
200	C₂⁵	—	4	1	no	—
201	C₂×#41	—	2	1	no	—
202	C₂²×D₄	—	2	8	no	—
203	C₂²×D₄	—	2	4	no	—
204	C₂²×D₄	—	2	2	no	—
205	C₂²×D₄	—	4	4	no	—
206	C₂²×D₄	—	4	2	no	—
207	C₂²×D₄	—	4	1	no	—
208	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
209	#135	—	2	4	no	—
210	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic, complemented
211	C₂×SD₁₆	—	2	1	no	—
212	C₂×D₈	—	2	8	no	—
213	C₂×D₈	—	2	16	no	—
214	C₂×D₈	—	2	16	no	—
215	C₂×D₈	—	2	4	no	—
216	C₂×D₈	—	2	2	no	—
217	C₂×D₈	—	2	4	no	—
218	C₂×D₈	D₄×C₁₃	1	8	yes	complemented
219	C₂×D₈	C₂³×C₁₃	1	4	yes	—
220	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic, complemented
221	C₂²×C₈	—	2	4	no	—
222	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
223	C₂²×C₈	D₄×C₁₃	1	2	yes	—
224	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
225	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
226	#123	—	4	1	no	—
227	C₂²⋊Q₈	—	2	2	no	—
228	#121	—	2	2	no	—
229	#120	—	4	1	no	—
230	C₄×D₄	—	4	2	no	—
231	#117	—	2	1	no	—
232	SD₃₂	—	2	8	no	—
233	D₁₆	—	2	8	no	—
234	M₃₂	—	2	4	no	—
235	C₂×C₁₆	C₂³×C₁₃	1	4	yes	complemented
236	#107	C₂³×C₁₃	1	2	yes	complemented
237	#106	—	2	1	no	—
238	#103	—	2	2	no	—
239	#102	—	2	2	no	—
240	C₂×C₁₃	—	2	2	no	—
241	C₂×C₁₃	—	2	4	no	—
242	C₂×C₁₃	—	8	8	no	—
243	C₂×C₁₃	—	16	1	no	—
244	C₂×C₁₃	C₂×#447	1	1	yes	characteristic
245	C₂×C₁₃	C₂×#509	1	2	yes	—
246	C₂⁴	—	4	8	no	—
247	C₂⁴	—	4	4	no	—
248	C₂⁴	—	4	2	no	—
249	C₂⁴	—	8	8	no	—
250	C₂⁴	C₁₃×D₈	1	1	yes	characteristic
251	#41	—	4	2	no	—
252	#41	—	4	2	no	—
253	C₂×Q₈	—	2	1	no	—
254	C₂×D₄	—	2	16	no	—
255	C₂×D₄	—	2	8	no	—
256	C₂×D₄	—	2	4	no	—
257	C₂×D₄	—	2	1	no	—
258	C₂×D₄	—	4	8	no	—
259	C₂×D₄	—	4	16	no	—
260	C₂×D₄	—	4	8	no	—
261	C₂×D₄	—	4	2	no	—
262	C₂×D₄	—	4	1	no	—
263	C₂×D₄	—	4	4	no	—
264	C₂×D₄	—	4	2	no	—
265	C₂×D₄	—	4	4	no	—
266	C₂²×C₄	—	2	2	no	—
267	C₂²×C₄	—	2	2	no	—
268	C₂²×C₄	—	4	1	no	—
269	C₂²×C₄	C₁₃×D₈	1	2	yes	—
270	C₂²×C₄	C₁₃×D₈	1	1	yes	characteristic
271	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
272	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
273	Q₁₆	—	2	2	no	—
274	SD₁₆	—	4	2	no	—
275	D₈	—	2	16	no	—
276	D₈	—	2	8	no	—
277	D₈	—	2	4	no	—
278	D₈	—	2	2	no	—
279	D₈	C₂×D₄×C₁₃	1	8	yes	—
280	C₂×C₈	—	2	2	no	—
281	C₂×C₈	—	2	4	no	—
282	C₂×C₈	—	2	4	no	—
283	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
284	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
285	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
286	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
287	C₄⋊C₄	—	2	2	no	—
288	C₄⋊C₄	—	4	2	no	—
289	C₂²⋊C₄	—	4	1	no	—
290	C₂²⋊C₄	—	4	2	no	—
291	C₂²⋊C₄	—	4	2	no	—
292	C₄²	—	4	1	no	—
293	C₁₆	—	2	4	no	—
294	C₁₃	#33517	1	1	yes	characteristic, direct product factor, Sylow
295	C₂³	—	2	2	no	—
296	C₂³	—	2	4	no	—
297	C₂³	—	4	16	no	—
298	C₂³	—	4	8	no	—
299	C₂³	—	4	4	no	—
300	C₂³	—	4	1	no	—
301	C₂³	—	8	32	no	—
302	C₂³	—	8	8	no	—
303	C₂³	—	8	8	no	—
304	C₂³	—	8	8	no	—
305	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
306	C₂³	C₂×C₁₃×D₈	1	2	yes	—
307	Q₈	—	4	1	no	—
308	Q₈	—	4	1	no	—
309	D₄	—	2	8	no	—
310	D₄	—	4	16	no	—
311	D₄	—	4	8	no	—
312	D₄	—	4	1	no	—
313	D₄	—	4	4	no	—
314	D₄	—	4	1	no	—
315	D₄	—	8	2	no	—
316	D₄	—	8	4	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	4	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	4	2	no	—
322	C₂×C₄	—	4	1	no	—
323	C₂×C₄	—	8	2	no	—
324	C₂×C₄	C₁₃×#120	1	2	yes	—
325	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
326	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
327	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
328	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
329	C₈	—	2	2	no	—
330	C₈	C₁₃×#120	1	2	yes	—
331	C₈	C₂²×D₄×C₁₃	1	2	yes	—
332	C₂²	—	2	8	no	—
333	C₂²	—	2	2	no	—
334	C₂²	—	2	2	no	—
335	C₂²	—	2	2	no	—
336	C₂²	—	4	8	no	—
337	C₂²	—	8	16	no	—
338	C₂²	—	8	32	no	—
339	C₂²	—	8	8	no	—
340	C₂²	—	8	2	no	—
341	C₂²	—	8	1	no	—
342	C₂²	C₁₃×#447	1	2	yes	—
343	C₂²	C₁₃×#509	1	4	yes	complemented
344	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
345	C₄	—	2	2	no	—
346	C₄	—	8	2	no	—
347	C₄	—	8	1	no	—
348	C₄	C₁₃×#447	1	2	yes	—
349	C₄	C₂×C₁₃×#120	1	1	yes	characteristic
350	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
351	C₂	—	2	2	no	—
352	C₂	—	2	4	no	—
353	C₂	—	8	8	no	—
354	C₂	—	16	1	no	—
355	C₂	C₂×C₁₃×#447	1	1	yes	characteristic
356	C₂	C₂×C₁₃×#509	1	2	yes	—

	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 ◁ C₂³×C₄×C₁₃ ◁ C₂³×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂³×C₁₃×D₈	C₂	semidirect
2. C₂×C₁₃×#509	C₂	semidirect
3. C₁₃×#3050	C₂	semidirect
4. C₁₃×#2187	C₂	semidirect
5. C₁₃×#2184	C₂	semidirect
6. C₁₃×#2140	C₂	semidirect
7. C₁₃×#2112	C₂	semidirect
9. C₂×C₁₃×#135	C₂²	semidirect
18. C₂×C₁₃×SD₃₂	C₂²	semidirect
19. C₂×C₁₃×D₁₆	C₂²	semidirect
20. C₂×C₁₃×M₃₂	C₂²	semidirect
21. C₁₃×#467	C₂²	semidirect
22. C₁₃×#466	C₂²	semidirect
24. C₁₃×#427	C₂²	semidirect
26. C₁₃×#357	C₂²	semidirect
27. C₁₃×C₂²⋊C₁₆	C₂²	semidirect
38. C₂×C₁₃×Q₁₆	C₂³	semidirect
46. C₂×C₁₃×D₈	D₄	semidirect
48. C₂×C₁₃×D₈	C₂³	semidirect
63. C₂×C₁₃×C₁₆	C₂³	semidirect
64. C₁₃×#107	C₂³	semidirect
68. #33517	C₁₃	direct (N × H)
117. C₂³×D₈	C₂×C₁₃	semidirect
118. C₂×#509	C₂×C₁₃	semidirect
119. #3050	C₂×C₁₃	semidirect
120. #2187	C₂×C₁₃	semidirect
121. #2184	C₂×C₁₃	semidirect
122. #2140	C₂×C₁₃	semidirect
123. #2112	C₂×C₁₃	semidirect
162. C₂×#135	C₂²×C₁₃	semidirect
171. C₂×SD₃₂	C₂²×C₁₃	semidirect
172. C₂×D₁₆	C₂²×C₁₃	semidirect
173. C₂×M₃₂	C₂²×C₁₃	semidirect
174. #467	C₂²×C₁₃	semidirect
175. #466	C₂²×C₁₃	semidirect
177. #427	C₂²×C₁₃	semidirect
179. #357	C₂²×C₁₃	semidirect
180. C₂²⋊C₁₆	C₂²×C₁₃	semidirect
192. C₂²×C₁₃	#509	semidirect
210. C₂×Q₁₆	C₂³×C₁₃	semidirect
218. C₂×D₈	D₄×C₁₃	semidirect
220. C₂×D₈	C₂³×C₁₃	semidirect
235. C₂×C₁₆	C₂³×C₁₃	semidirect
236. #107	C₂³×C₁₃	semidirect
294. C₁₃	#33517	direct (N × H)
343. C₂²	C₁₃×#509	semidirect

Maximal subgroups

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

subgroup	index
C₂³×C₁₃×D₈	2
C₂×C₁₃×#509	2
C₁₃×#3050	2
C₁₃×#2187	2
C₁₃×#2184	2
C₁₃×#2140	2
C₁₃×#2112	2
#33517	13

Subgroups — C13×#33517 #15719856

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#33517 #15719856