Subgroups — C₁₃×#25924 #15712263

Order 3328.

1138 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3503	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3138	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3038	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2858	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2027	C₂	1	4	yes	maximal, complemented
6	C₁₃×#1997	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1994	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1883	C₂	1	4	yes	maximal, complemented
9	C₄×C₁₃×#104	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
11	Q₈²×C₁₃	—	2	1	no	—
12	C₁₃×#557	—	2	1	no	—
13	C₁₃×#554	—	2	1	no	—
14	C₁₃×#554	—	2	2	no	—
15	D₄×Q₈×C₁₃	—	2	2	no	—
16	D₄×Q₈×C₁₃	—	2	1	no	—
17	C₁₃×#544	—	2	2	no	—
18	C₁₃×#544	C₂²	1	2	yes	—
19	C₁₃×#533	—	2	1	no	—
20	C₁₃×#533	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
22	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#124	—	2	2	no	—
25	C₁₃×#520	C₂²	1	2	yes	—
26	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
27	C₁₃×#490	—	2	2	no	—
28	C₁₃×#486	—	2	1	no	—
29	C₁₃×#486	—	2	1	no	—
30	C₁₃×#460	—	2	1	no	—
31	C₁₃×#460	—	2	1	no	—
32	C₁₃×#459	—	2	1	no	—
33	C₁₃×#459	—	2	1	no	—
34	C₁₃×#423	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×#104	C₂²	1	2	yes	—
36	C₁₃×#418	C₂²	1	2	yes	—
37	C₁₃×#418	C₂²	1	4	yes	—
38	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
39	C₁₃×#390	—	2	2	no	—
40	C₁₃×#390	C₂²	1	4	yes	—
41	C₄³×C₁₃	C₂²	1	1	yes	characteristic
42	C₁₃×#343	C₂²	1	4	yes	—
43	C₁₃×#339	C₂²	1	4	yes	—
44	C₁₃×#339	C₂²	1	2	yes	—
45	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
46	C₂²×Q₈×C₁₃	—	2	2	no	—
47	C₂²×Q₈×C₁₃	D₄	1	2	yes	—
48	C₂²×D₄×C₁₃	—	2	1	no	—
49	C₂²×D₄×C₁₃	—	2	1	no	—
50	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
51	C₁₃×AGL(1,ℤ/8)	—	2	8	no	—
52	C₂×C₁₃×SD₁₆	—	2	2	no	—
53	C₂×C₁₃×D₈	—	2	2	no	—
54	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
55	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
56	C₁₃×C₄⋊Q₈	—	2	2	no	—
57	C₁₃×C₄⋊Q₈	—	2	2	no	—
58	C₁₃×C₄⋊Q₈	—	2	4	no	—
59	C₁₃×C₄⋊Q₈	—	2	2	no	—
60	C₁₃×C₄⋊Q₈	—	2	2	no	—
61	C₁₃×C₄⋊Q₈	—	2	1	no	—
62	C₁₃×C₄⋊Q₈	—	2	1	no	—
63	C₁₃×C₄⋊Q₈	—	2	1	no	—
64	C₁₃×C₄⋊Q₈	—	2	1	no	—
65	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
66	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
67	C₁₃×#127	—	2	1	no	—
68	C₁₃×#127	—	2	1	no	—
69	C₁₃×#127	—	2	1	no	—
70	C₁₃×#127	—	2	1	no	—
71	C₁₃×#125	—	2	4	no	—
72	C₁₃×#125	—	2	2	no	—
73	C₁₃×#125	—	2	2	no	—
74	C₁₃×#125	D₄	1	2	yes	—
75	C₁₃×#124	—	4	8	no	—
76	C₁₃×C₂²⋊Q₈	—	2	2	no	—
77	C₁₃×C₂²⋊Q₈	—	2	2	no	—
78	C₁₃×C₂²⋊Q₈	—	2	4	no	—
79	C₁₃×C₂²⋊Q₈	—	2	4	no	—
80	C₁₃×C₂²⋊Q₈	—	2	1	no	—
81	C₁₃×C₂²⋊Q₈	—	2	1	no	—
82	C₁₃×C₂²⋊Q₈	—	2	4	no	—
83	C₄×Q₈×C₁₃	—	2	2	no	—
84	C₄×Q₈×C₁₃	—	2	2	no	—
85	C₄×Q₈×C₁₃	—	2	2	no	—
86	C₄×Q₈×C₁₃	—	2	1	no	—
87	C₄×Q₈×C₁₃	—	2	1	no	—
88	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
89	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
90	C₄×D₄×C₁₃	—	2	2	no	—
91	C₄×D₄×C₁₃	—	2	1	no	—
92	C₄×D₄×C₁₃	—	2	1	no	—
93	C₄×D₄×C₁₃	—	2	4	no	—
94	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
95	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
96	C₁₃×#117	—	2	2	no	—
97	C₁₃×#117	—	2	1	no	—
98	C₁₃×#117	C₂³	1	1	yes	characteristic
99	C₁₃×#117	C₂³	1	2	yes	—
100	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
101	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
102	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
103	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
104	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
105	C₂×C₄²×C₁₃	—	2	1	no	—
106	C₂×C₄²×C₁₃	—	2	1	no	—
107	C₂×C₄²×C₁₃	—	2	1	no	—
108	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
109	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
110	C₁₃×C₄⋊C₈	—	2	1	no	—
111	C₁₃×C₄⋊C₈	—	2	1	no	—
112	C₁₃×#104	—	2	4	no	—
113	C₁₃×#102	—	2	2	no	—
114	C₁₃×#102	—	2	2	no	—
115	C₁₃×#102	—	2	4	no	—
116	C₁₃×#102	—	2	4	no	—
117	C₁₃×#97	—	2	1	no	—
118	C₄×C₈×C₁₃	—	2	1	no	—
119	#25924	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
120	C₂⁴×C₁₃	—	2	2	no	—
121	C₁₃×#41	—	2	2	no	—
122	C₁₃×#41	#41	1	4	yes	—
123	C₂×Q₈×C₁₃	—	2	4	no	—
124	C₂×Q₈×C₁₃	—	2	1	no	—
125	C₂×Q₈×C₁₃	—	2	2	no	—
126	C₂×Q₈×C₁₃	—	2	1	no	—
127	C₂×Q₈×C₁₃	—	2	2	no	—
128	C₂×Q₈×C₁₃	—	4	4	no	—
129	C₂×Q₈×C₁₃	—	8	4	no	—
130	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
131	C₂×D₄×C₁₃	—	2	1	no	—
132	C₂×D₄×C₁₃	—	2	2	no	—
133	C₂×D₄×C₁₃	—	2	2	no	—
134	C₂×D₄×C₁₃	—	2	4	no	—
135	C₂×D₄×C₁₃	—	2	4	no	—
136	C₂×D₄×C₁₃	—	4	4	no	—
137	C₂×D₄×C₁₃	—	4	4	no	—
138	C₂×D₄×C₁₃	—	4	1	no	—
139	C₂×D₄×C₁₃	—	4	1	no	—
140	C₂×D₄×C₁₃	—	4	1	no	—
141	C₂×D₄×C₁₃	—	4	1	no	—
142	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₁₃	—	2	1	no	—
144	C₂²×C₄×C₁₃	—	2	2	no	—
145	C₂²×C₄×C₁₃	—	2	4	no	—
146	C₂²×C₄×C₁₃	—	2	1	no	—
147	C₂²×C₄×C₁₃	—	2	1	no	—
148	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
151	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
152	C₁₃×SD₁₆	—	4	4	no	—
153	C₁₃×D₈	—	4	4	no	—
154	C₁₃×M₁₆	—	2	2	no	—
155	C₁₃×M₁₆	—	2	4	no	—
156	C₁₃×M₁₆	—	2	2	no	—
157	C₂×C₈×C₁₃	—	2	2	no	—
158	C₂×C₈×C₁₃	—	2	2	no	—
159	C₁₃×C₄⋊C₄	—	2	4	no	—
160	C₁₃×C₄⋊C₄	—	2	4	no	—
161	C₁₃×C₄⋊C₄	—	2	4	no	—
162	C₁₃×C₄⋊C₄	—	2	4	no	—
163	C₁₃×C₄⋊C₄	—	2	1	no	—
164	C₁₃×C₄⋊C₄	—	2	2	no	—
165	C₁₃×C₄⋊C₄	—	2	2	no	—
166	C₁₃×C₄⋊C₄	—	2	1	no	—
167	C₁₃×C₄⋊C₄	—	2	1	no	—
168	C₁₃×C₄⋊C₄	—	2	1	no	—
169	C₁₃×C₄⋊C₄	—	2	2	no	—
170	C₁₃×C₄⋊C₄	—	2	2	no	—
171	C₁₃×C₄⋊C₄	—	2	2	no	—
172	C₁₃×C₄⋊C₄	—	2	2	no	—
173	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
174	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
175	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
176	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
177	C₁₃×C₂²⋊C₄	—	2	4	no	—
178	C₁₃×C₂²⋊C₄	—	2	2	no	—
179	C₁₃×C₂²⋊C₄	—	2	1	no	—
180	C₁₃×C₂²⋊C₄	—	2	1	no	—
181	C₁₃×C₂²⋊C₄	—	2	1	no	—
182	C₁₃×C₂²⋊C₄	—	4	16	no	—
183	C₄²×C₁₃	—	2	4	no	—
184	C₄²×C₁₃	—	2	4	no	—
185	C₄²×C₁₃	—	2	1	no	—
186	C₄²×C₁₃	—	2	1	no	—
187	C₄²×C₁₃	—	2	1	no	—
188	C₄²×C₁₃	—	2	2	no	—
189	C₄²×C₁₃	—	2	2	no	—
190	C₄²×C₁₃	—	2	2	no	—
191	C₄²×C₁₃	—	4	2	no	—
192	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
193	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
194	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
195	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
196	#3503	C₂×C₁₃	1	1	yes	characteristic, complemented
197	#3138	C₂×C₁₃	1	1	yes	characteristic, complemented
198	#3038	C₂×C₁₃	1	1	yes	characteristic
199	#2858	C₂×C₁₃	1	1	yes	characteristic, complemented
200	#2027	C₂×C₁₃	1	4	yes	complemented
201	#1997	C₂×C₁₃	1	1	yes	characteristic, complemented
202	#1994	C₂×C₁₃	1	1	yes	characteristic, complemented
203	#1883	C₂×C₁₃	1	4	yes	complemented
204	C₄×#104	C₂×C₁₃	1	1	yes	characteristic, complemented
205	C₂³×C₁₃	—	2	1	no	—
206	C₂³×C₁₃	—	4	4	no	—
207	C₂³×C₁₃	—	4	4	no	—
208	C₂³×C₁₃	—	4	2	no	—
209	C₂³×C₁₃	—	4	4	no	—
210	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
211	Q₈×C₁₃	—	2	1	no	—
212	Q₈×C₁₃	—	4	4	no	—
213	Q₈×C₁₃	—	4	2	no	—
214	Q₈×C₁₃	—	4	2	no	—
215	Q₈×C₁₃	—	8	2	no	—
216	Q₈×C₁₃	—	8	4	no	—
217	Q₈×C₁₃	#124	1	2	yes	complemented
218	D₄×C₁₃	—	2	4	no	—
219	D₄×C₁₃	—	2	1	no	—
220	D₄×C₁₃	—	4	2	no	—
221	D₄×C₁₃	—	4	2	no	—
222	D₄×C₁₃	—	4	4	no	—
223	D₄×C₁₃	—	8	2	no	—
224	D₄×C₁₃	—	8	2	no	—
225	D₄×C₁₃	—	8	2	no	—
226	D₄×C₁₃	—	8	2	no	—
227	D₄×C₁₃	#124	1	2	yes	complemented
228	C₂×C₄×C₁₃	—	2	1	no	—
229	C₂×C₄×C₁₃	—	2	4	no	—
230	C₂×C₄×C₁₃	—	2	2	no	—
231	C₂×C₄×C₁₃	—	2	2	no	—
232	C₂×C₄×C₁₃	—	2	4	no	—
233	C₂×C₄×C₁₃	—	2	2	no	—
234	C₂×C₄×C₁₃	—	2	1	no	—
235	C₂×C₄×C₁₃	—	2	1	no	—
236	C₂×C₄×C₁₃	—	2	4	no	—
237	C₂×C₄×C₁₃	—	2	2	no	—
238	C₂×C₄×C₁₃	—	4	2	no	—
239	C₂×C₄×C₁₃	—	4	2	no	—
240	C₂×C₄×C₁₃	—	4	2	no	—
241	C₂×C₄×C₁₃	—	4	2	no	—
242	C₂×C₄×C₁₃	—	4	4	no	—
243	C₂×C₄×C₁₃	—	8	4	no	—
244	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
245	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
246	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
247	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
248	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
249	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
250	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
251	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
252	C₈×C₁₃	—	4	2	no	—
253	C₈×C₁₃	—	4	2	no	—
254	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	—
255	Q₈²	—	2	1	no	—
256	#557	—	2	1	no	—
257	#554	—	2	1	no	—
258	#554	—	2	2	no	—
259	D₄×Q₈	—	2	2	no	—
260	D₄×Q₈	—	2	1	no	—
261	#544	—	2	2	no	—
262	#544	C₂²×C₁₃	1	2	yes	—
263	#533	—	2	1	no	—
264	#533	C₂²×C₁₃	1	1	yes	characteristic
265	C₂×C₄⋊Q₈	—	2	1	no	—
266	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
267	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
268	C₂×#124	—	2	2	no	—
269	#520	C₂²×C₁₃	1	2	yes	—
270	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
271	#490	—	2	2	no	—
272	#486	—	2	1	no	—
273	#486	—	2	1	no	—
274	#460	—	2	1	no	—
275	#460	—	2	1	no	—
276	#459	—	2	1	no	—
277	#459	—	2	1	no	—
278	#423	C₂²×C₁₃	1	1	yes	characteristic
279	C₂×#104	C₂²×C₁₃	1	2	yes	—
280	#418	C₂²×C₁₃	1	4	yes	—
281	#418	C₂²×C₁₃	1	2	yes	—
282	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
283	#390	—	2	2	no	—
284	#390	C₂²×C₁₃	1	4	yes	—
285	C₄³	C₂²×C₁₃	1	1	yes	characteristic
286	#343	C₂²×C₁₃	1	4	yes	—
287	#339	C₂²×C₁₃	1	4	yes	—
288	#339	C₂²×C₁₃	1	2	yes	—
289	C₂²×C₁₃	—	2	1	no	—
290	C₂²×C₁₃	—	2	1	no	—
291	C₂²×C₁₃	—	2	2	no	—
292	C₂²×C₁₃	—	4	1	no	—
293	C₂²×C₁₃	—	4	1	no	—
294	C₂²×C₁₃	—	8	8	no	—
295	C₂²×C₁₃	—	8	2	no	—
296	C₂²×C₁₃	—	8	2	no	—
297	C₂²×C₁₃	—	8	2	no	—
298	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
299	C₂²×C₁₃	#548	1	2	yes	—
300	C₄×C₁₃	—	2	2	no	—
301	C₄×C₁₃	—	2	1	no	—
302	C₄×C₁₃	—	2	1	no	—
303	C₄×C₁₃	—	4	4	no	—
304	C₄×C₁₃	—	4	1	no	—
305	C₄×C₁₃	—	4	4	no	—
306	C₄×C₁₃	—	4	2	no	—
307	C₄×C₁₃	—	4	1	no	—
308	C₄×C₁₃	—	4	2	no	—
309	C₄×C₁₃	#453	1	2	yes	—
310	C₄×C₁₃	#454	1	2	yes	—
311	C₄×C₁₃	C₂×#124	1	1	yes	characteristic
312	C₄×C₁₃	#536	1	1	yes	characteristic
313	C₄×C₁₃	#548	1	2	yes	—
314	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
315	C₂²×Q₈	—	2	2	no	—
316	C₂²×Q₈	D₄×C₁₃	1	2	yes	—
317	C₂²×D₄	—	2	1	no	—
318	C₂²×D₄	—	2	1	no	—
319	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
320	AGL(1,ℤ/8)	—	2	8	no	—
321	C₂×SD₁₆	—	2	2	no	—
322	C₂×D₈	—	2	2	no	—
323	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
324	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
325	C₄⋊Q₈	—	2	2	no	—
326	C₄⋊Q₈	—	2	2	no	—
327	C₄⋊Q₈	—	2	4	no	—
328	C₄⋊Q₈	—	2	2	no	—
329	C₄⋊Q₈	—	2	2	no	—
330	C₄⋊Q₈	—	2	1	no	—
331	C₄⋊Q₈	—	2	1	no	—
332	C₄⋊Q₈	—	2	1	no	—
333	C₄⋊Q₈	—	2	1	no	—
334	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
335	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
336	#127	—	2	1	no	—
337	#127	—	2	1	no	—
338	#127	—	2	1	no	—
339	#127	—	2	1	no	—
340	#125	—	2	4	no	—
341	#125	—	2	2	no	—
342	#125	—	2	2	no	—
343	#125	D₄×C₁₃	1	2	yes	—
344	#124	—	4	8	no	—
345	C₂²⋊Q₈	—	2	2	no	—
346	C₂²⋊Q₈	—	2	2	no	—
347	C₂²⋊Q₈	—	2	4	no	—
348	C₂²⋊Q₈	—	2	4	no	—
349	C₂²⋊Q₈	—	2	1	no	—
350	C₂²⋊Q₈	—	2	1	no	—
351	C₂²⋊Q₈	—	2	4	no	—
352	C₄×Q₈	—	2	2	no	—
353	C₄×Q₈	—	2	2	no	—
354	C₄×Q₈	—	2	2	no	—
355	C₄×Q₈	—	2	1	no	—
356	C₄×Q₈	—	2	1	no	—
357	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
358	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
359	C₄×D₄	—	2	2	no	—
360	C₄×D₄	—	2	1	no	—
361	C₄×D₄	—	2	1	no	—
362	C₄×D₄	—	2	4	no	—
363	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
364	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
365	#117	—	2	2	no	—
366	#117	—	2	1	no	—
367	#117	C₂³×C₁₃	1	1	yes	characteristic
368	#117	C₂³×C₁₃	1	2	yes	—
369	C₂×C₄⋊C₄	—	2	2	no	—
370	C₂×C₄⋊C₄	—	2	2	no	—
371	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
372	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
373	C₂×C₂²⋊C₄	—	2	8	no	—
374	C₂×C₄²	—	2	1	no	—
375	C₂×C₄²	—	2	1	no	—
376	C₂×C₄²	—	2	1	no	—
377	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
378	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
379	C₄⋊C₈	—	2	1	no	—
380	C₄⋊C₈	—	2	1	no	—
381	#104	—	2	4	no	—
382	#102	—	2	2	no	—
383	#102	—	2	2	no	—
384	#102	—	2	4	no	—
385	#102	—	2	4	no	—
386	#97	—	2	1	no	—
387	C₄×C₈	—	2	1	no	—
388	C₂×C₁₃	—	2	2	no	—
389	C₂×C₁₃	—	4	2	no	—
390	C₂×C₁₃	—	16	2	no	—
391	C₂×C₁₃	#2436	1	1	yes	characteristic
392	C₂×C₁₃	C₂×#453	1	1	yes	characteristic
393	C₂×C₁₃	C₂×#454	1	1	yes	characteristic
394	C₂⁴	—	2	2	no	—
395	#41	—	2	2	no	—
396	#41	C₁₃×#41	1	4	yes	—
397	C₂×Q₈	—	2	4	no	—
398	C₂×Q₈	—	2	1	no	—
399	C₂×Q₈	—	2	2	no	—
400	C₂×Q₈	—	2	1	no	—
401	C₂×Q₈	—	2	2	no	—
402	C₂×Q₈	—	4	4	no	—
403	C₂×Q₈	—	8	4	no	—
404	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
405	C₂×D₄	—	2	1	no	—
406	C₂×D₄	—	2	2	no	—
407	C₂×D₄	—	2	2	no	—
408	C₂×D₄	—	2	4	no	—
409	C₂×D₄	—	2	4	no	—
410	C₂×D₄	—	4	4	no	—
411	C₂×D₄	—	4	4	no	—
412	C₂×D₄	—	4	1	no	—
413	C₂×D₄	—	4	1	no	—
414	C₂×D₄	—	4	1	no	—
415	C₂×D₄	—	4	1	no	—
416	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
417	C₂²×C₄	—	2	1	no	—
418	C₂²×C₄	—	2	2	no	—
419	C₂²×C₄	—	2	4	no	—
420	C₂²×C₄	—	2	1	no	—
421	C₂²×C₄	—	2	1	no	—
422	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
423	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
424	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
425	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
426	SD₁₆	—	4	4	no	—
427	D₈	—	4	4	no	—
428	M₁₆	—	2	2	no	—
429	M₁₆	—	2	4	no	—
430	M₁₆	—	2	2	no	—
431	C₂×C₈	—	2	2	no	—
432	C₂×C₈	—	2	2	no	—
433	C₄⋊C₄	—	2	4	no	—
434	C₄⋊C₄	—	2	4	no	—
435	C₄⋊C₄	—	2	4	no	—
436	C₄⋊C₄	—	2	4	no	—
437	C₄⋊C₄	—	2	1	no	—
438	C₄⋊C₄	—	2	2	no	—
439	C₄⋊C₄	—	2	2	no	—
440	C₄⋊C₄	—	2	1	no	—
441	C₄⋊C₄	—	2	1	no	—
442	C₄⋊C₄	—	2	1	no	—
443	C₄⋊C₄	—	2	2	no	—
444	C₄⋊C₄	—	2	2	no	—
445	C₄⋊C₄	—	2	2	no	—
446	C₄⋊C₄	—	2	2	no	—
447	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
448	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
449	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
450	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
451	C₂²⋊C₄	—	2	4	no	—
452	C₂²⋊C₄	—	2	2	no	—
453	C₂²⋊C₄	—	2	1	no	—
454	C₂²⋊C₄	—	2	1	no	—
455	C₂²⋊C₄	—	2	1	no	—
456	C₂²⋊C₄	—	4	16	no	—
457	C₄²	—	2	4	no	—
458	C₄²	—	2	4	no	—
459	C₄²	—	2	1	no	—
460	C₄²	—	2	1	no	—
461	C₄²	—	2	1	no	—
462	C₄²	—	2	2	no	—
463	C₄²	—	2	2	no	—
464	C₄²	—	2	2	no	—
465	C₄²	—	4	2	no	—
466	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
467	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
468	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
469	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
470	C₁₃	#25924	1	1	yes	characteristic, direct product factor, Sylow
471	C₂³	—	2	1	no	—
472	C₂³	—	4	4	no	—
473	C₂³	—	4	4	no	—
474	C₂³	—	4	2	no	—
475	C₂³	—	4	4	no	—
476	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
477	Q₈	—	2	1	no	—
478	Q₈	—	4	4	no	—
479	Q₈	—	4	2	no	—
480	Q₈	—	4	2	no	—
481	Q₈	—	8	2	no	—
482	Q₈	—	8	4	no	—
483	Q₈	C₁₃×#124	1	2	yes	complemented
484	D₄	—	2	4	no	—
485	D₄	—	2	1	no	—
486	D₄	—	4	2	no	—
487	D₄	—	4	2	no	—
488	D₄	—	4	4	no	—
489	D₄	—	8	2	no	—
490	D₄	—	8	2	no	—
491	D₄	—	8	2	no	—
492	D₄	—	8	2	no	—
493	D₄	C₁₃×#124	1	2	yes	complemented
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	4	no	—
498	C₂×C₄	—	2	4	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	4	no	—
503	C₂×C₄	—	2	2	no	—
504	C₂×C₄	—	4	2	no	—
505	C₂×C₄	—	4	2	no	—
506	C₂×C₄	—	4	2	no	—
507	C₂×C₄	—	4	2	no	—
508	C₂×C₄	—	4	4	no	—
509	C₂×C₄	—	8	4	no	—
510	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
511	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
512	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
513	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
514	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
515	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
516	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
517	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
518	C₈	—	4	2	no	—
519	C₈	—	4	2	no	—
520	C₂²	—	2	1	no	—
521	C₂²	—	2	1	no	—
522	C₂²	—	2	2	no	—
523	C₂²	—	4	1	no	—
524	C₂²	—	4	1	no	—
525	C₂²	—	8	8	no	—
526	C₂²	—	8	2	no	—
527	C₂²	—	8	2	no	—
528	C₂²	—	8	2	no	—
529	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
530	C₂²	C₁₃×#548	1	2	yes	—
531	C₄	—	2	1	no	—
532	C₄	—	2	1	no	—
533	C₄	—	2	2	no	—
534	C₄	—	4	4	no	—
535	C₄	—	4	1	no	—
536	C₄	—	4	4	no	—
537	C₄	—	4	2	no	—
538	C₄	—	4	1	no	—
539	C₄	—	4	2	no	—
540	C₄	C₁₃×#453	1	2	yes	—
541	C₄	C₁₃×#454	1	2	yes	—
542	C₄	C₂×C₁₃×#124	1	1	yes	characteristic
543	C₄	C₁₃×#536	1	1	yes	characteristic
544	C₄	C₁₃×#548	1	2	yes	—
545	C₂	—	2	2	no	—
546	C₂	—	4	2	no	—
547	C₂	—	16	2	no	—
548	C₂	C₁₃×#2436	1	1	yes	characteristic
549	C₂	C₂×C₁₃×#453	1	1	yes	characteristic
550	C₂	C₂×C₁₃×#454	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₁₃×#3038	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3503	C₂	semidirect
2. C₁₃×#3138	C₂	semidirect
4. C₁₃×#2858	C₂	semidirect
5. C₁₃×#2027	C₂	semidirect
6. C₁₃×#1997	C₂	semidirect
7. C₁₃×#1994	C₂	semidirect
8. C₁₃×#1883	C₂	semidirect
9. C₄×C₁₃×#104	C₂	semidirect
119. #25924	C₁₃	direct (N × H)
196. #3503	C₂×C₁₃	semidirect
197. #3138	C₂×C₁₃	semidirect
199. #2858	C₂×C₁₃	semidirect
200. #2027	C₂×C₁₃	semidirect
201. #1997	C₂×C₁₃	semidirect
202. #1994	C₂×C₁₃	semidirect
203. #1883	C₂×C₁₃	semidirect
204. C₄×#104	C₂×C₁₃	semidirect
217. Q₈×C₁₃	#124	semidirect
227. D₄×C₁₃	#124	semidirect
470. C₁₃	#25924	direct (N × H)
483. Q₈	C₁₃×#124	semidirect
493. D₄	C₁₃×#124	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#3503	2
C₁₃×#3138	2
C₁₃×#3038	2
C₁₃×#2858	2
C₁₃×#2027	2
C₁₃×#1997	2
C₁₃×#1994	2
C₁₃×#1883	2
C₄×C₁₃×#104	2
#25924	13

Subgroups — C13×#25924 #15712263

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#25924 #15712263