Subgroups — C₁₃×#33839 #15720178

Order 3328.

712 conjugacy classes of subgroups.

The subgroup lattice has 344 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×#3280	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2249	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2220	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2210	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2189	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2184	C₂	1	2	yes	maximal, complemented
8	C₄×C₁₃×D₁₆	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2169	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×#135	C₂²	1	2	yes	—
11	C₂²×C₁₃×D₈	C₂²	1	2	yes	complemented
12	C₁₃×#546	—	2	2	no	—
13	C₁₃×#509	—	2	8	no	—
14	C₂×C₁₃×Q₃₂	C₂²	1	1	yes	characteristic, complemented
15	C₂×C₁₃×SD₃₂	C₂²	1	2	yes	complemented
16	C₂×C₁₃×SD₃₂	C₂²	1	2	yes	complemented
17	C₂×C₁₃×D₁₆	C₂²	1	2	yes	—
18	C₂×C₁₃×D₁₆	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×D₁₆	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×M₃₂	C₂²	1	2	yes	complemented
21	C₁₃×#495	C₂²	1	2	yes	complemented
22	C₁₃×#467	C₂²	1	2	yes	complemented
23	C₁₃×#466	C₂²	1	2	yes	—
24	C₁₃×#463	—	2	2	no	—
25	C₁₃×#450	—	2	2	no	—
26	C₁₃×#449	—	2	2	no	—
27	C₄×C₁₃×D₈	C₂²	1	2	yes	complemented
28	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
29	C₁₃×#366	C₂²	1	1	yes	characteristic, complemented
30	C₁₃×C₄⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
31	C₁₃×#358	C₂²	1	2	yes	complemented
32	C₁₃×#357	C₂²	1	2	yes	complemented
33	C₁₃×#357	C₂²	1	2	yes	complemented
34	C₁₃×C₂²⋊C₁₆	C₂²	1	2	yes	complemented
35	C₄×C₁₃×C₁₆	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₁₃×#41	—	2	2	no	—
37	C₂²×D₄×C₁₃	—	2	2	no	—
38	C₁₃×#135	—	2	4	no	—
39	C₁₃×#135	—	4	2	no	—
40	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
41	C₂×C₁₃×SD₁₆	—	2	2	no	—
42	C₂×C₁₃×SD₁₆	—	2	2	no	—
43	C₂×C₁₃×D₈	—	2	4	no	—
44	C₂×C₁₃×D₈	—	2	2	no	—
45	C₂×C₁₃×D₈	—	4	2	no	—
46	C₂×C₁₃×D₈	C₂³	1	2	yes	—
47	C₂×C₁₃×D₈	C₂³	1	2	yes	—
48	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
49	C₁₃×#124	—	2	2	no	—
50	C₁₃×#123	—	4	2	no	—
51	C₁₃×C₂²⋊Q₈	—	2	2	no	—
52	C₁₃×#121	—	2	2	no	—
53	C₁₃×#121	—	4	2	no	—
54	C₁₃×#120	—	4	2	no	—
55	C₄×D₄×C₁₃	—	2	2	no	—
56	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
57	C₂×C₁₃×C₂²⋊C₄	—	4	2	no	—
58	C₁₃×Q₃₂	—	4	1	no	—
59	C₁₃×SD₃₂	—	2	4	no	—
60	C₁₃×SD₃₂	—	2	4	no	—
61	C₁₃×D₁₆	—	2	4	no	—
62	C₁₃×D₁₆	—	4	1	no	—
63	C₁₃×D₁₆	D₄	1	4	yes	complemented
64	C₁₃×M₃₂	—	2	4	no	—
65	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
66	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
67	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
68	C₁₃×#107	C₂³	1	2	yes	—
69	C₁₃×C₄⋊C₈	D₄	1	1	yes	characteristic
70	C₁₃×#103	—	2	2	no	—
71	C₁₃×#102	—	2	2	no	—
72	C₁₃×#102	—	2	2	no	—
73	C₁₃×C₂²⋊C₈	D₄	1	2	yes	—
74	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
75	#33839	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
76	C₂⁴×C₁₃	—	4	2	no	—
77	C₁₃×#41	—	4	4	no	—
78	C₁₃×#41	—	8	2	no	—
79	C₂×Q₈×C₁₃	—	2	2	no	—
80	C₂×D₄×C₁₃	—	2	2	no	—
81	C₂×D₄×C₁₃	—	2	2	no	—
82	C₂×D₄×C₁₃	—	4	4	no	—
83	C₂×D₄×C₁₃	—	4	2	no	—
84	C₂×D₄×C₁₃	—	4	2	no	—
85	C₂×D₄×C₁₃	—	4	2	no	—
86	C₂×D₄×C₁₃	—	8	2	no	—
87	C₂×D₄×C₁₃	D₈	1	1	yes	characteristic
88	C₂²×C₄×C₁₃	—	4	2	no	—
89	C₂²×C₄×C₁₃	—	4	2	no	—
90	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
91	C₁₃×Q₁₆	—	2	2	no	—
92	C₁₃×Q₁₆	—	2	2	no	—
93	C₁₃×SD₁₆	—	4	4	no	—
94	C₁₃×SD₁₆	—	8	2	no	—
95	C₁₃×D₈	—	2	2	no	—
96	C₁₃×D₈	—	2	2	no	—
97	C₁₃×D₈	—	2	2	no	—
98	C₁₃×D₈	—	4	4	no	—
99	C₁₃×D₈	C₂×D₄	1	4	yes	—
100	C₂×C₈×C₁₃	—	2	2	no	—
101	C₂×C₈×C₁₃	—	2	2	no	—
102	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
103	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
104	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
105	C₁₃×C₄⋊C₄	—	2	2	no	—
106	C₁₃×C₄⋊C₄	—	4	2	no	—
107	C₁₃×C₄⋊C₄	D₈	1	1	yes	characteristic
108	C₁₃×C₂²⋊C₄	—	4	2	no	—
109	C₁₃×C₂²⋊C₄	—	4	2	no	—
110	C₁₃×C₂²⋊C₄	—	4	2	no	—
111	C₁₃×C₂²⋊C₄	—	4	2	no	—
112	C₁₃×C₂²⋊C₄	—	4	2	no	—
113	C₁₃×C₂²⋊C₄	D₈	1	2	yes	—
114	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
115	C₁₃×C₁₆	—	2	2	no	—
116	C₁₃×C₁₆	—	2	1	no	—
117	C₁₃×C₁₆	C₂×D₄	1	2	yes	—
118	C₂×#509	C₂×C₁₃	1	2	yes	complemented
119	#3280	C₂×C₁₃	1	2	yes	complemented
120	#2249	C₂×C₁₃	1	1	yes	characteristic, complemented
121	#2220	C₂×C₁₃	1	2	yes	complemented
122	#2210	C₂×C₁₃	1	2	yes	complemented
123	#2189	C₂×C₁₃	1	2	yes	complemented
124	#2184	C₂×C₁₃	1	2	yes	complemented
125	C₄×D₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
126	#2169	C₂×C₁₃	1	1	yes	characteristic, complemented
127	C₂³×C₁₃	—	4	2	no	—
128	C₂³×C₁₃	—	4	2	no	—
129	C₂³×C₁₃	—	8	4	no	—
130	C₂³×C₁₃	—	8	4	no	—
131	C₂³×C₁₃	—	16	2	no	—
132	C₂³×C₁₃	C₂×D₈	1	2	yes	—
133	Q₈×C₁₃	—	4	2	no	—
134	Q₈×C₁₃	—	4	2	no	—
135	D₄×C₁₃	—	2	4	no	—
136	D₄×C₁₃	—	4	1	no	—
137	D₄×C₁₃	—	4	2	no	—
138	D₄×C₁₃	—	4	2	no	—
139	D₄×C₁₃	—	4	2	no	—
140	D₄×C₁₃	—	8	4	no	—
141	D₄×C₁₃	—	8	4	no	—
142	D₄×C₁₃	—	16	2	no	—
143	C₂×C₄×C₁₃	—	2	2	no	—
144	C₂×C₄×C₁₃	—	2	2	no	—
145	C₂×C₄×C₁₃	—	4	2	no	—
146	C₂×C₄×C₁₃	—	4	2	no	—
147	C₂×C₄×C₁₃	—	8	4	no	—
148	C₂×C₄×C₁₃	—	16	2	no	—
149	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
150	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
151	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
152	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
153	C₈×C₁₃	—	2	2	no	—
154	C₈×C₁₃	—	2	1	no	—
155	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
156	C₈×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
157	C₂×#135	C₂²×C₁₃	1	2	yes	—
158	C₂²×D₈	C₂²×C₁₃	1	2	yes	complemented
159	#546	—	2	2	no	—
160	#509	—	2	8	no	—
161	C₂×Q₃₂	C₂²×C₁₃	1	1	yes	characteristic, complemented
162	C₂×SD₃₂	C₂²×C₁₃	1	2	yes	complemented
163	C₂×SD₃₂	C₂²×C₁₃	1	2	yes	complemented
164	C₂×D₁₆	C₂²×C₁₃	1	2	yes	—
165	C₂×D₁₆	C₂²×C₁₃	1	1	yes	characteristic
166	C₂×D₁₆	C₂²×C₁₃	1	1	yes	characteristic
167	C₂×M₃₂	C₂²×C₁₃	1	2	yes	complemented
168	#495	C₂²×C₁₃	1	2	yes	complemented
169	#467	C₂²×C₁₃	1	2	yes	complemented
170	#466	C₂²×C₁₃	1	2	yes	—
171	#463	—	2	2	no	—
172	#450	—	2	2	no	—
173	#449	—	2	2	no	—
174	C₄×D₈	C₂²×C₁₃	1	2	yes	complemented
175	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
176	#366	C₂²×C₁₃	1	1	yes	characteristic, complemented
177	C₄⋊C₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
178	#358	C₂²×C₁₃	1	2	yes	complemented
179	#357	C₂²×C₁₃	1	2	yes	complemented
180	#357	C₂²×C₁₃	1	2	yes	complemented
181	C₂²⋊C₁₆	C₂²×C₁₃	1	2	yes	complemented
182	C₄×C₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
183	C₂²×C₁₃	—	2	2	no	—
184	C₂²×C₁₃	—	2	2	no	—
185	C₂²×C₁₃	—	2	2	no	—
186	C₂²×C₁₃	—	4	4	no	—
187	C₂²×C₁₃	—	8	2	no	—
188	C₂²×C₁₃	—	8	2	no	—
189	C₂²×C₁₃	—	8	2	no	—
190	C₂²×C₁₃	—	8	2	no	—
191	C₂²×C₁₃	—	8	2	no	—
192	C₂²×C₁₃	—	16	8	no	—
193	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
194	C₄×C₁₃	—	2	1	no	—
195	C₄×C₁₃	—	2	1	no	—
196	C₄×C₁₃	—	2	2	no	—
197	C₄×C₁₃	—	8	2	no	—
198	C₄×C₁₃	—	8	2	no	—
199	C₄×C₁₃	D₄²	1	1	yes	characteristic
200	C₄×C₁₃	#576	1	1	yes	characteristic
201	C₂×#41	—	2	2	no	—
202	C₂²×D₄	—	2	2	no	—
203	#135	—	2	4	no	—
204	#135	—	4	2	no	—
205	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
206	C₂×SD₁₆	—	2	2	no	—
207	C₂×SD₁₆	—	2	2	no	—
208	C₂×D₈	—	2	4	no	—
209	C₂×D₈	—	2	2	no	—
210	C₂×D₈	—	4	2	no	—
211	C₂×D₈	C₂³×C₁₃	1	2	yes	—
212	C₂×D₈	C₂³×C₁₃	1	2	yes	—
213	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
214	#124	—	2	2	no	—
215	#123	—	4	2	no	—
216	C₂²⋊Q₈	—	2	2	no	—
217	#121	—	2	2	no	—
218	#121	—	4	2	no	—
219	#120	—	4	2	no	—
220	C₄×D₄	—	2	2	no	—
221	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
222	C₂×C₂²⋊C₄	—	4	2	no	—
223	Q₃₂	—	4	1	no	—
224	SD₃₂	—	2	4	no	—
225	SD₃₂	—	2	4	no	—
226	D₁₆	—	2	4	no	—
227	D₁₆	—	4	1	no	—
228	D₁₆	D₄×C₁₃	1	4	yes	complemented
229	M₃₂	—	2	4	no	—
230	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
231	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
232	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
233	#107	C₂³×C₁₃	1	2	yes	—
234	C₄⋊C₈	D₄×C₁₃	1	1	yes	characteristic
235	#103	—	2	2	no	—
236	#102	—	2	2	no	—
237	#102	—	2	2	no	—
238	C₂²⋊C₈	D₄×C₁₃	1	2	yes	—
239	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
240	C₂×C₁₃	—	4	2	no	—
241	C₂×C₁₃	—	8	4	no	—
242	C₂×C₁₃	—	16	2	no	—
243	C₂×C₁₃	D₄×D₈	1	1	yes	characteristic
244	C₂×C₁₃	#3414	1	1	yes	characteristic
245	C₂×C₁₃	#3415	1	1	yes	characteristic
246	C₂⁴	—	4	2	no	—
247	#41	—	4	4	no	—
248	#41	—	8	2	no	—
249	C₂×Q₈	—	2	2	no	—
250	C₂×D₄	—	2	2	no	—
251	C₂×D₄	—	2	2	no	—
252	C₂×D₄	—	4	4	no	—
253	C₂×D₄	—	4	2	no	—
254	C₂×D₄	—	4	2	no	—
255	C₂×D₄	—	4	2	no	—
256	C₂×D₄	—	8	2	no	—
257	C₂×D₄	C₁₃×D₈	1	1	yes	characteristic
258	C₂²×C₄	—	4	2	no	—
259	C₂²×C₄	—	4	2	no	—
260	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
261	Q₁₆	—	2	2	no	—
262	Q₁₆	—	2	2	no	—
263	SD₁₆	—	4	4	no	—
264	SD₁₆	—	8	2	no	—
265	D₈	—	2	2	no	—
266	D₈	—	2	2	no	—
267	D₈	—	2	2	no	—
268	D₈	—	4	4	no	—
269	D₈	C₂×D₄×C₁₃	1	4	yes	—
270	C₂×C₈	—	2	2	no	—
271	C₂×C₈	—	2	2	no	—
272	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
273	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
274	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
275	C₄⋊C₄	—	2	2	no	—
276	C₄⋊C₄	—	4	2	no	—
277	C₄⋊C₄	C₁₃×D₈	1	1	yes	characteristic
278	C₂²⋊C₄	—	4	2	no	—
279	C₂²⋊C₄	—	4	2	no	—
280	C₂²⋊C₄	—	4	2	no	—
281	C₂²⋊C₄	—	4	2	no	—
282	C₂²⋊C₄	—	4	2	no	—
283	C₂²⋊C₄	C₁₃×D₈	1	2	yes	—
284	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
285	C₁₆	—	2	2	no	—
286	C₁₆	—	2	1	no	—
287	C₁₆	C₂×D₄×C₁₃	1	2	yes	—
288	C₁₃	#33839	1	1	yes	characteristic, direct product factor, Sylow
289	C₂³	—	4	2	no	—
290	C₂³	—	4	2	no	—
291	C₂³	—	8	4	no	—
292	C₂³	—	8	4	no	—
293	C₂³	—	16	2	no	—
294	C₂³	C₂×C₁₃×D₈	1	2	yes	—
295	Q₈	—	4	2	no	—
296	Q₈	—	4	2	no	—
297	D₄	—	2	4	no	—
298	D₄	—	4	1	no	—
299	D₄	—	4	2	no	—
300	D₄	—	4	2	no	—
301	D₄	—	4	2	no	—
302	D₄	—	8	4	no	—
303	D₄	—	8	4	no	—
304	D₄	—	16	2	no	—
305	C₂×C₄	—	2	2	no	—
306	C₂×C₄	—	2	2	no	—
307	C₂×C₄	—	4	2	no	—
308	C₂×C₄	—	4	2	no	—
309	C₂×C₄	—	8	4	no	—
310	C₂×C₄	—	16	2	no	—
311	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
312	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
313	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
314	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
315	C₈	—	2	2	no	—
316	C₈	—	2	1	no	—
317	C₈	C₂²×D₄×C₁₃	1	1	yes	characteristic
318	C₈	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
319	C₂²	—	2	2	no	—
320	C₂²	—	2	2	no	—
321	C₂²	—	2	2	no	—
322	C₂²	—	4	4	no	—
323	C₂²	—	8	2	no	—
324	C₂²	—	8	2	no	—
325	C₂²	—	8	2	no	—
326	C₂²	—	8	2	no	—
327	C₂²	—	8	2	no	—
328	C₂²	—	16	8	no	—
329	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
330	C₄	—	2	2	no	—
331	C₄	—	2	1	no	—
332	C₄	—	2	1	no	—
333	C₄	—	8	2	no	—
334	C₄	—	8	2	no	—
335	C₄	D₄²×C₁₃	1	1	yes	characteristic
336	C₄	C₁₃×#576	1	1	yes	characteristic
337	C₂	—	4	2	no	—
338	C₂	—	8	4	no	—
339	C₂	—	16	2	no	—
340	C₂	D₄×C₁₃×D₈	1	1	yes	characteristic
341	C₂	C₁₃×#3414	1	1	yes	characteristic
342	C₂	C₁₃×#3415	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 ◁ C₄×D₄×C₁₃ ◁ C₈×D₄×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×#3280	C₂	semidirect
3. C₁₃×#2249	C₂	semidirect
4. C₁₃×#2220	C₂	semidirect
5. C₁₃×#2210	C₂	semidirect
6. C₁₃×#2189	C₂	semidirect
7. C₁₃×#2184	C₂	semidirect
8. C₄×C₁₃×D₁₆	C₂	semidirect
9. C₁₃×#2169	C₂	semidirect
11. C₂²×C₁₃×D₈	C₂²	semidirect
14. C₂×C₁₃×Q₃₂	C₂²	semidirect
15. C₂×C₁₃×SD₃₂	C₂²	semidirect
16. C₂×C₁₃×SD₃₂	C₂²	semidirect
20. C₂×C₁₃×M₃₂	C₂²	semidirect
21. C₁₃×#495	C₂²	semidirect
22. C₁₃×#467	C₂²	semidirect
27. C₄×C₁₃×D₈	C₂²	semidirect
29. C₁₃×#366	C₂²	semidirect
30. C₁₃×C₄⋊C₁₆	C₂²	semidirect
31. C₁₃×#358	C₂²	semidirect
32. C₁₃×#357	C₂²	semidirect
33. C₁₃×#357	C₂²	semidirect
34. C₁₃×C₂²⋊C₁₆	C₂²	semidirect
35. C₄×C₁₃×C₁₆	C₂²	semidirect
63. C₁₃×D₁₆	D₄	semidirect
75. #33839	C₁₃	direct (N × H)
118. C₂×#509	C₂×C₁₃	semidirect
119. #3280	C₂×C₁₃	semidirect
120. #2249	C₂×C₁₃	semidirect
121. #2220	C₂×C₁₃	semidirect
122. #2210	C₂×C₁₃	semidirect
123. #2189	C₂×C₁₃	semidirect
124. #2184	C₂×C₁₃	semidirect
125. C₄×D₁₆	C₂×C₁₃	semidirect
126. #2169	C₂×C₁₃	semidirect
158. C₂²×D₈	C₂²×C₁₃	semidirect
161. C₂×Q₃₂	C₂²×C₁₃	semidirect
162. C₂×SD₃₂	C₂²×C₁₃	semidirect
163. C₂×SD₃₂	C₂²×C₁₃	semidirect
167. C₂×M₃₂	C₂²×C₁₃	semidirect
168. #495	C₂²×C₁₃	semidirect
169. #467	C₂²×C₁₃	semidirect
174. C₄×D₈	C₂²×C₁₃	semidirect
176. #366	C₂²×C₁₃	semidirect
177. C₄⋊C₁₆	C₂²×C₁₃	semidirect
178. #358	C₂²×C₁₃	semidirect
179. #357	C₂²×C₁₃	semidirect
180. #357	C₂²×C₁₃	semidirect
181. C₂²⋊C₁₆	C₂²×C₁₃	semidirect
182. C₄×C₁₆	C₂²×C₁₃	semidirect
228. D₁₆	D₄×C₁₃	semidirect
288. C₁₃	#33839	direct (N × H)

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×#3280	2
C₁₃×#2249	2
C₁₃×#2220	2
C₁₃×#2210	2
C₁₃×#2189	2
C₁₃×#2184	2
C₄×C₁₃×D₁₆	2
C₁₃×#2169	2
#33839	13

Subgroups — C13×#33839 #15720178

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#33839 #15720178