Subgroups — C₁₃×#25909 #15712248

Order 3328.

1092 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#489	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2850	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2026	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2025	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1993	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1875	C₂	1	2	yes	maximal
8	C₁₃×#1873	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1749	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#533	—	2	8	no	—
11	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
12	C₂×C₁₃×#125	C₂²	1	2	yes	—
13	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
15	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
17	C₂×C₄×Q₈×C₁₃	—	2	2	no	—
18	C₂×C₁₃×#117	C₂²	1	2	yes	—
19	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
20	C₁₃×#489	—	2	8	no	—
21	C₂×C₁₃×#103	C₂²	1	4	yes	—
22	C₂×C₁₃×#102	C₂²	1	4	yes	—
23	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
24	C₂×C₁₃×#97	C₂²	1	2	yes	—
25	C₁₃×#391	C₂²	1	1	yes	characteristic
26	C₁₃×#390	C₂²	1	1	yes	characteristic
27	C₁₃×#388	—	2	2	no	—
28	C₁₃×#386	—	2	2	no	—
29	C₁₃×#382	C₂²	1	1	yes	characteristic
30	C₁₃×#340	C₂²	1	4	yes	—
31	C₁₃×#340	C₂²	1	4	yes	—
32	C₁₃×#336	C₂²	1	2	yes	—
33	C₂²×Q₈×C₁₃	—	2	2	no	—
34	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
35	C₂²×D₄×C₁₃	—	2	1	no	—
36	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
37	C₂³×C₄×C₁₃	D₄	1	2	yes	—
38	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
39	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
40	C₁₃×C₄⋊Q₈	—	2	4	no	—
41	C₁₃×C₄⋊Q₈	D₄	1	8	yes	complemented
42	C₁₃×#125	—	2	8	no	—
43	C₁₃×#124	—	2	4	no	—
44	C₁₃×C₂²⋊Q₈	—	2	16	no	—
45	C₁₃×C₂²⋊Q₈	—	2	4	no	—
46	C₁₃×#121	—	2	4	no	—
47	C₄×Q₈×C₁₃	—	2	16	no	—
48	C₁₃×#117	—	2	8	no	—
49	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
50	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
51	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
52	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
53	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
54	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
55	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
56	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
57	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
58	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
59	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
60	C₂×C₄²×C₁₃	—	2	2	no	—
61	C₂×C₄²×C₁₃	—	2	4	no	—
62	C₂×C₄²×C₁₃	D₄	1	2	yes	—
63	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
64	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
65	C₁₃×#103	—	2	8	no	—
66	C₁₃×#102	—	2	8	no	—
67	C₁₃×C₂²⋊C₈	—	2	4	no	—
68	C₁₃×#97	—	2	4	no	—
69	C₁₃×#95	—	2	2	no	—
70	C₁₃×#95	—	2	2	no	—
71	#25909	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
72	C₂⁴×C₁₃	—	2	1	no	—
73	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
74	C₂×Q₈×C₁₃	—	2	8	no	—
75	C₂×Q₈×C₁₃	—	2	2	no	—
76	C₂×Q₈×C₁₃	—	2	2	no	—
77	C₂×Q₈×C₁₃	—	2	2	no	—
78	C₂×Q₈×C₁₃	—	4	4	no	—
79	C₂×Q₈×C₁₃	—	4	4	no	—
80	C₂×D₄×C₁₃	—	2	2	no	—
81	C₂×D₄×C₁₃	—	2	2	no	—
82	C₂×D₄×C₁₃	—	2	2	no	—
83	C₂×D₄×C₁₃	—	4	4	no	—
84	C₂×D₄×C₁₃	—	4	2	no	—
85	C₂²×C₄×C₁₃	—	2	2	no	—
86	C₂²×C₄×C₁₃	—	2	2	no	—
87	C₂²×C₄×C₁₃	—	2	4	no	—
88	C₂²×C₄×C₁₃	—	2	4	no	—
89	C₂²×C₄×C₁₃	—	2	1	no	—
90	C₂²×C₄×C₁₃	—	2	1	no	—
91	C₂²×C₄×C₁₃	—	2	1	no	—
92	C₂²×C₄×C₁₃	—	4	2	no	—
93	C₂²×C₄×C₁₃	—	4	2	no	—
94	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
95	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
96	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₃	#41	1	4	yes	—
98	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
99	C₂×C₈×C₁₃	—	2	4	no	—
100	C₂×C₈×C₁₃	—	2	4	no	—
101	C₂×C₈×C₁₃	—	2	4	no	—
102	C₁₃×C₄⋊C₄	—	2	16	no	—
103	C₁₃×C₄⋊C₄	—	2	8	no	—
104	C₁₃×C₄⋊C₄	—	2	4	no	—
105	C₁₃×C₄⋊C₄	—	2	2	no	—
106	C₁₃×C₄⋊C₄	—	2	2	no	—
107	C₁₃×C₄⋊C₄	—	4	2	no	—
108	C₁₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
109	C₁₃×C₂²⋊C₄	—	2	8	no	—
110	C₁₃×C₂²⋊C₄	—	4	4	no	—
111	C₁₃×C₂²⋊C₄	—	4	2	no	—
112	C₁₃×C₂²⋊C₄	—	4	4	no	—
113	C₁₃×C₂²⋊C₄	—	4	2	no	—
114	C₄²×C₁₃	—	2	8	no	—
115	C₄²×C₁₃	—	2	4	no	—
116	C₄²×C₁₃	—	2	2	no	—
117	C₄²×C₁₃	C₂×D₄	1	4	yes	—
118	C₂×#533	C₂×C₁₃	1	1	yes	characteristic, complemented
119	C₂×#489	C₂×C₁₃	1	2	yes	complemented
120	#2850	C₂×C₁₃	1	1	yes	characteristic
121	#2026	C₂×C₁₃	1	2	yes	complemented
122	#2025	C₂×C₁₃	1	2	yes	complemented
123	#1993	C₂×C₁₃	1	2	yes	complemented
124	#1875	C₂×C₁₃	1	2	yes	—
125	#1873	C₂×C₁₃	1	2	yes	complemented
126	#1749	C₂×C₁₃	1	1	yes	characteristic, complemented
127	C₂³×C₁₃	—	2	1	no	—
128	C₂³×C₁₃	—	2	1	no	—
129	C₂³×C₁₃	—	2	2	no	—
130	C₂³×C₁₃	—	2	2	no	—
131	C₂³×C₁₃	—	4	1	no	—
132	C₂³×C₁₃	—	4	1	no	—
133	C₂³×C₁₃	—	4	1	no	—
134	C₂³×C₁₃	—	4	2	no	—
135	C₂³×C₁₃	—	4	2	no	—
136	C₂³×C₁₃	#124	1	2	yes	—
137	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
138	Q₈×C₁₃	—	4	16	no	—
139	Q₈×C₁₃	—	4	4	no	—
140	D₄×C₁₃	—	4	4	no	—
141	D₄×C₁₃	—	8	4	no	—
142	C₂×C₄×C₁₃	—	2	1	no	—
143	C₂×C₄×C₁₃	—	2	1	no	—
144	C₂×C₄×C₁₃	—	2	2	no	—
145	C₂×C₄×C₁₃	—	2	2	no	—
146	C₂×C₄×C₁₃	—	2	8	no	—
147	C₂×C₄×C₁₃	—	2	2	no	—
148	C₂×C₄×C₁₃	—	2	8	no	—
149	C₂×C₄×C₁₃	—	2	2	no	—
150	C₂×C₄×C₁₃	—	2	2	no	—
151	C₂×C₄×C₁₃	—	4	8	no	—
152	C₂×C₄×C₁₃	—	4	4	no	—
153	C₂×C₄×C₁₃	—	4	4	no	—
154	C₂×C₄×C₁₃	—	4	1	no	—
155	C₂×C₄×C₁₃	—	4	1	no	—
156	C₂×C₄×C₁₃	—	4	1	no	—
157	C₂×C₄×C₁₃	—	4	1	no	—
158	C₂×C₄×C₁₃	—	4	1	no	—
159	C₂×C₄×C₁₃	—	4	2	no	—
160	C₂×C₄×C₁₃	—	4	2	no	—
161	C₂×C₄×C₁₃	#120	1	4	yes	—
162	C₂×C₄×C₁₃	#124	1	2	yes	—
163	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
164	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
165	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
166	C₈×C₁₃	—	4	4	no	—
167	#533	—	2	8	no	—
168	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
169	C₂×#125	C₂²×C₁₃	1	2	yes	—
170	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
171	C₂×C₂²⋊Q₈	—	2	2	no	—
172	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
173	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
174	C₂×C₄×Q₈	—	2	2	no	—
175	C₂×#117	C₂²×C₁₃	1	2	yes	—
176	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
177	#489	—	2	8	no	—
178	C₂×#103	C₂²×C₁₃	1	4	yes	—
179	C₂×#102	C₂²×C₁₃	1	4	yes	—
180	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
181	C₂×#97	C₂²×C₁₃	1	2	yes	—
182	#391	C₂²×C₁₃	1	1	yes	characteristic
183	#390	C₂²×C₁₃	1	1	yes	characteristic
184	#388	—	2	2	no	—
185	#386	—	2	2	no	—
186	#382	C₂²×C₁₃	1	1	yes	characteristic
187	#340	C₂²×C₁₃	1	4	yes	—
188	#340	C₂²×C₁₃	1	4	yes	—
189	#336	C₂²×C₁₃	1	2	yes	—
190	C₂²×C₁₃	—	2	2	no	—
191	C₂²×C₁₃	—	2	2	no	—
192	C₂²×C₁₃	—	2	2	no	—
193	C₂²×C₁₃	—	4	2	no	—
194	C₂²×C₁₃	—	4	2	no	—
195	C₂²×C₁₃	—	8	1	no	—
196	C₂²×C₁₃	—	8	1	no	—
197	C₂²×C₁₃	—	8	1	no	—
198	C₂²×C₁₃	—	8	2	no	—
199	C₂²×C₁₃	—	8	2	no	—
200	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
201	C₂²×C₁₃	C₂×#124	1	1	yes	characteristic
202	C₂²×C₁₃	#536	1	1	yes	characteristic
203	C₂²×C₁₃	#575	1	2	yes	—
204	C₂²×C₁₃	#575	1	2	yes	—
205	C₄×C₁₃	—	2	2	no	—
206	C₄×C₁₃	—	2	4	no	—
207	C₄×C₁₃	—	4	2	no	—
208	C₄×C₁₃	—	4	8	no	—
209	C₄×C₁₃	—	8	1	no	—
210	C₄×C₁₃	—	8	1	no	—
211	C₄×C₁₃	—	8	1	no	—
212	C₄×C₁₃	#548	1	4	yes	—
213	C₂²×Q₈	—	2	2	no	—
214	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
215	C₂²×D₄	—	2	1	no	—
216	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
217	C₂³×C₄	D₄×C₁₃	1	2	yes	—
218	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
219	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
220	C₄⋊Q₈	—	2	4	no	—
221	C₄⋊Q₈	D₄×C₁₃	1	8	yes	complemented
222	#125	—	2	8	no	—
223	#124	—	2	4	no	—
224	C₂²⋊Q₈	—	2	16	no	—
225	C₂²⋊Q₈	—	2	4	no	—
226	#121	—	2	4	no	—
227	C₄×Q₈	—	2	16	no	—
228	#117	—	2	8	no	—
229	C₂×C₄⋊C₄	—	2	4	no	—
230	C₂×C₄⋊C₄	—	2	2	no	—
231	C₂×C₄⋊C₄	—	2	1	no	—
232	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
233	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
234	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
235	C₂×C₂²⋊C₄	—	2	2	no	—
236	C₂×C₂²⋊C₄	—	2	1	no	—
237	C₂×C₂²⋊C₄	—	2	1	no	—
238	C₂×C₂²⋊C₄	—	2	2	no	—
239	C₂×C₂²⋊C₄	—	2	2	no	—
240	C₂×C₄²	—	2	2	no	—
241	C₂×C₄²	—	2	4	no	—
242	C₂×C₄²	D₄×C₁₃	1	2	yes	—
243	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
244	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
245	#103	—	2	8	no	—
246	#102	—	2	8	no	—
247	C₂²⋊C₈	—	2	4	no	—
248	#97	—	2	4	no	—
249	#95	—	2	2	no	—
250	#95	—	2	2	no	—
251	C₂×C₁₃	—	4	2	no	—
252	C₂×C₁₃	—	16	1	no	—
253	C₂×C₁₃	#2436	1	1	yes	characteristic
254	C₂×C₁₃	#3005	1	2	yes	—
255	C₂×C₁₃	#3135	1	1	yes	characteristic
256	C₂×C₁₃	#3140	1	1	yes	characteristic
257	C₂×C₁₃	#3240	1	2	yes	—
258	C₂⁴	—	2	1	no	—
259	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
260	C₂×Q₈	—	2	8	no	—
261	C₂×Q₈	—	2	2	no	—
262	C₂×Q₈	—	2	2	no	—
263	C₂×Q₈	—	2	2	no	—
264	C₂×Q₈	—	4	4	no	—
265	C₂×Q₈	—	4	4	no	—
266	C₂×D₄	—	2	2	no	—
267	C₂×D₄	—	2	2	no	—
268	C₂×D₄	—	2	2	no	—
269	C₂×D₄	—	4	4	no	—
270	C₂×D₄	—	4	2	no	—
271	C₂²×C₄	—	2	2	no	—
272	C₂²×C₄	—	2	2	no	—
273	C₂²×C₄	—	2	4	no	—
274	C₂²×C₄	—	2	4	no	—
275	C₂²×C₄	—	2	1	no	—
276	C₂²×C₄	—	2	1	no	—
277	C₂²×C₄	—	2	1	no	—
278	C₂²×C₄	—	4	2	no	—
279	C₂²×C₄	—	4	2	no	—
280	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
281	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
282	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
283	C₂²×C₄	C₁₃×#41	1	4	yes	—
284	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
285	C₂×C₈	—	2	4	no	—
286	C₂×C₈	—	2	4	no	—
287	C₂×C₈	—	2	4	no	—
288	C₄⋊C₄	—	2	16	no	—
289	C₄⋊C₄	—	2	8	no	—
290	C₄⋊C₄	—	2	4	no	—
291	C₄⋊C₄	—	2	2	no	—
292	C₄⋊C₄	—	2	2	no	—
293	C₄⋊C₄	—	4	2	no	—
294	C₄⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
295	C₂²⋊C₄	—	2	8	no	—
296	C₂²⋊C₄	—	4	4	no	—
297	C₂²⋊C₄	—	4	2	no	—
298	C₂²⋊C₄	—	4	4	no	—
299	C₂²⋊C₄	—	4	2	no	—
300	C₄²	—	2	8	no	—
301	C₄²	—	2	4	no	—
302	C₄²	—	2	2	no	—
303	C₄²	C₂×D₄×C₁₃	1	4	yes	—
304	C₁₃	#25909	1	1	yes	characteristic, direct product factor, Sylow
305	C₂³	—	2	1	no	—
306	C₂³	—	2	1	no	—
307	C₂³	—	2	2	no	—
308	C₂³	—	2	2	no	—
309	C₂³	—	4	1	no	—
310	C₂³	—	4	1	no	—
311	C₂³	—	4	1	no	—
312	C₂³	—	4	2	no	—
313	C₂³	—	4	2	no	—
314	C₂³	C₁₃×#124	1	2	yes	—
315	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
316	Q₈	—	4	16	no	—
317	Q₈	—	4	4	no	—
318	D₄	—	4	4	no	—
319	D₄	—	8	4	no	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	2	1	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	8	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	8	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	4	8	no	—
330	C₂×C₄	—	4	4	no	—
331	C₂×C₄	—	4	4	no	—
332	C₂×C₄	—	4	1	no	—
333	C₂×C₄	—	4	1	no	—
334	C₂×C₄	—	4	1	no	—
335	C₂×C₄	—	4	1	no	—
336	C₂×C₄	—	4	1	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	—	4	2	no	—
339	C₂×C₄	C₁₃×#120	1	4	yes	—
340	C₂×C₄	C₁₃×#124	1	2	yes	—
341	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
342	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
343	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
344	C₈	—	4	4	no	—
345	C₂²	—	2	2	no	—
346	C₂²	—	2	2	no	—
347	C₂²	—	2	2	no	—
348	C₂²	—	4	2	no	—
349	C₂²	—	4	2	no	—
350	C₂²	—	8	1	no	—
351	C₂²	—	8	1	no	—
352	C₂²	—	8	1	no	—
353	C₂²	—	8	2	no	—
354	C₂²	—	8	2	no	—
355	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
356	C₂²	C₂×C₁₃×#124	1	1	yes	characteristic
357	C₂²	C₁₃×#536	1	1	yes	characteristic
358	C₂²	C₁₃×#575	1	2	yes	—
359	C₂²	C₁₃×#575	1	2	yes	—
360	C₄	—	2	2	no	—
361	C₄	—	2	4	no	—
362	C₄	—	4	2	no	—
363	C₄	—	4	8	no	—
364	C₄	—	8	1	no	—
365	C₄	—	8	1	no	—
366	C₄	—	8	1	no	—
367	C₄	C₁₃×#548	1	4	yes	—
368	C₂	—	4	2	no	—
369	C₂	—	16	1	no	—
370	C₂	C₁₃×#2436	1	1	yes	characteristic
371	C₂	C₁₃×#3005	1	2	yes	—
372	C₂	C₁₃×#3135	1	1	yes	characteristic
373	C₂	C₁₃×#3140	1	1	yes	characteristic
374	C₂	C₁₃×#3240	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#121	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#533	C₂	semidirect
2. C₂×C₁₃×#489	C₂	semidirect
4. C₁₃×#2026	C₂	semidirect
5. C₁₃×#2025	C₂	semidirect
6. C₁₃×#1993	C₂	semidirect
8. C₁₃×#1873	C₂	semidirect
9. C₁₃×#1749	C₂	semidirect
41. C₁₃×C₄⋊Q₈	D₄	semidirect
71. #25909	C₁₃	direct (N × H)
118. C₂×#533	C₂×C₁₃	semidirect
119. C₂×#489	C₂×C₁₃	semidirect
121. #2026	C₂×C₁₃	semidirect
122. #2025	C₂×C₁₃	semidirect
123. #1993	C₂×C₁₃	semidirect
125. #1873	C₂×C₁₃	semidirect
126. #1749	C₂×C₁₃	semidirect
221. C₄⋊Q₈	D₄×C₁₃	semidirect
304. C₁₃	#25909	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×#533	2
C₂×C₁₃×#489	2
C₁₃×#2850	2
C₁₃×#2026	2
C₁₃×#2025	2
C₁₃×#1993	2
C₁₃×#1875	2
C₁₃×#1873	2
C₁₃×#1749	2
#25909	13

Subgroups — C13×#25909 #15712248

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#25909 #15712248