Subgroups — C₁₃×#61413 #15747752

Order 3328.

1886 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3510	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3401	C₂	1	8	yes	maximal, complemented
3	C₁₃×#3396	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3393	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3156	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#3155	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₃×#495	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#3043	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3042	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3040	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2960	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#2950	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#2948	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₁₃×#135	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₁₃×#137	C₂²	1	2	yes	—
16	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
17	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
18	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
19	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
20	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
21	C₁₃×#559	C₂²	1	8	yes	complemented
22	C₁₃×#556	C₂²	1	8	yes	complemented
23	C₁₃×#551	—	2	8	no	—
24	C₁₃×#542	—	2	4	no	—
25	C₁₃×#536	C₂²	1	2	yes	—
26	C₁₃×#535	C₂²	1	2	yes	—
27	C₁₃×#533	C₂²	1	1	yes	characteristic
28	C₁₃×#529	—	2	4	no	—
29	C₂×C₁₃×#124	C₂²	1	2	yes	—
30	C₁₃×#519	C₂²	1	2	yes	—
31	C₁₃×#518	C₂²	1	2	yes	—
32	C₄×C₁₃×#41	C₂²	1	2	yes	—
33	C₁₃×#497	C₂²	1	4	yes	complemented
34	C₁₃×#496	C₂²	1	4	yes	—
35	C₁₃×#495	C₂²	1	2	yes	—
36	C₁₃×#495	C₂²	1	4	yes	—
37	C₁₃×#495	C₂²	1	4	yes	—
38	C₁₃×#495	C₂²	1	2	yes	complemented
39	C₁₃×#494	C₂²	1	2	yes	complemented
40	C₁₃×#493	C₂²	1	2	yes	—
41	C₁₃×#464	C₂²	1	8	yes	complemented
42	C₁₃×#464	C₂²	1	8	yes	complemented
43	C₁₃×#463	C₂²	1	8	yes	complemented
44	C₁₃×#463	C₂²	1	8	yes	complemented
45	C₁₃×#461	C₂²	1	8	yes	complemented
46	C₁₃×#460	C₂²	1	8	yes	complemented
47	C₁₃×#446	C₂²	1	4	yes	complemented
48	C₈×Q₈×C₁₃	C₂²	1	4	yes	complemented
49	C₁₃×#442	C₂²	1	4	yes	—
50	C₁₃×#441	C₂²	1	4	yes	complemented
51	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
52	C₄×C₁₃×Q₁₆	C₂²	1	4	yes	complemented
53	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
54	C₄×C₁₃×D₈	C₂²	1	4	yes	—
55	C₄×C₁₃×D₈	C₂²	1	2	yes	complemented
56	C₁₃×#427	C₂²	1	1	yes	characteristic
57	C₁₃×#424	C₂²	1	1	yes	characteristic
58	C₁₃×#424	C₂²	1	1	yes	characteristic
59	C₁₃×#423	C₂²	1	1	yes	characteristic
60	C₁₃×#419	C₂²	1	2	yes	—
61	C₁₃×#418	C₂²	1	2	yes	—
62	C₁₃×#416	C₂²	1	2	yes	—
63	C₁₃×#405	C₂²	1	1	yes	characteristic
64	C₁₃×#405	C₂²	1	1	yes	characteristic
65	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
66	C₂×C₁₃×#41	C₂³	1	2	yes	—
67	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
68	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
69	C₁₃×#137	—	4	4	no	—
70	C₁₃×AGL(1,ℤ/8)	—	4	4	no	—
71	C₁₃×#135	—	2	4	no	—
72	C₂×C₁₃×Q₁₆	—	2	4	no	—
73	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
74	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
75	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
76	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
77	C₂×C₁₃×SD₁₆	—	4	4	no	—
78	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
79	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
80	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
81	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
82	C₂×C₁₃×D₈	—	2	4	no	—
83	C₂×C₁₃×D₈	C₂³	1	2	yes	—
84	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
85	C₂×C₁₃×D₈	C₂³	1	2	yes	—
86	C₂×C₁₃×D₈	C₂³	1	4	yes	—
87	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
88	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
89	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
90	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
91	C₁₃×C₄⋊Q₈	D₄	1	2	yes	—
92	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
93	C₁₃×#127	C₂³	1	4	yes	—
94	C₁₃×#126	—	2	8	no	—
95	C₁₃×#126	—	2	8	no	—
96	C₁₃×#125	D₄	1	2	yes	—
97	C₁₃×#124	—	2	8	no	—
98	C₁₃×#124	—	2	2	no	—
99	C₁₃×#124	—	2	2	no	—
100	C₁₃×#124	C₂³	1	4	yes	—
101	C₁₃×#124	C₂³	1	8	yes	—
102	C₁₃×#124	C₂³	1	4	yes	—
103	C₁₃×#123	—	2	8	no	—
104	C₁₃×#123	—	2	8	no	—
105	C₁₃×#123	—	2	4	no	—
106	C₁₃×C₂²⋊Q₈	—	2	8	no	—
107	C₁₃×C₂²⋊Q₈	—	2	4	no	—
108	C₁₃×C₂²⋊Q₈	D₄	1	4	yes	—
109	C₁₃×#121	—	2	4	no	—
110	C₁₃×#120	—	2	4	no	—
111	C₄×Q₈×C₁₃	—	2	4	no	—
112	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
113	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
114	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
115	C₄×D₄×C₁₃	—	2	4	no	—
116	C₄×D₄×C₁₃	—	2	4	no	—
117	C₄×D₄×C₁₃	—	2	8	no	—
118	C₄×D₄×C₁₃	C₂³	1	8	yes	—
119	C₄×D₄×C₁₃	C₂³	1	4	yes	—
120	C₁₃×#117	—	2	8	no	—
121	C₁₃×#117	—	2	4	no	—
122	C₁₃×#117	—	2	2	no	—
123	C₁₃×#117	C₂³	1	2	yes	—
124	C₁₃×#117	C₂³	1	1	yes	characteristic
125	C₁₃×#117	C₂³	1	1	yes	characteristic
126	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
127	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
128	C₂×C₄²×C₁₃	—	2	2	no	—
129	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
130	C₁₃×#107	C₂³	1	2	yes	—
131	C₁₃×#106	C₂³	1	2	yes	—
132	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
133	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
134	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
135	C₁₃×#103	C₂³	1	4	yes	—
136	C₁₃×#103	C₂³	1	8	yes	—
137	C₁₃×#102	C₂³	1	4	yes	—
138	C₁₃×#102	C₂³	1	8	yes	—
139	C₁₃×#97	C₂³	1	2	yes	—
140	C₁₃×#97	C₂³	1	2	yes	—
141	C₄×C₈×C₁₃	C₂³	1	2	yes	—
142	C₄×C₈×C₁₃	C₂³	1	2	yes	—
143	C₄×C₈×C₁₃	C₂³	1	2	yes	—
144	C₄×C₈×C₁₃	C₂³	1	2	yes	—
145	#61413	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
146	C₂⁴×C₁₃	—	2	2	no	—
147	C₁₃×#41	—	2	4	no	—
148	C₁₃×#41	—	2	4	no	—
149	C₂×Q₈×C₁₃	—	2	2	no	—
150	C₂×Q₈×C₁₃	—	2	4	no	—
151	C₂×Q₈×C₁₃	—	2	4	no	—
152	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
153	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
154	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
155	C₂×D₄×C₁₃	—	2	2	no	—
156	C₂×D₄×C₁₃	—	2	2	no	—
157	C₂×D₄×C₁₃	—	2	8	no	—
158	C₂×D₄×C₁₃	—	2	4	no	—
159	C₂×D₄×C₁₃	—	2	4	no	—
160	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
161	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
162	C₂²×C₄×C₁₃	—	2	2	no	—
163	C₂²×C₄×C₁₃	—	2	2	no	—
164	C₂²×C₄×C₁₃	—	2	4	no	—
165	C₂²×C₄×C₁₃	—	2	8	no	—
166	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
167	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
168	C₁₃×Q₁₆	—	2	4	no	—
169	C₁₃×Q₁₆	—	2	4	no	—
170	C₁₃×Q₁₆	—	2	2	no	—
171	C₁₃×Q₁₆	—	4	4	no	—
172	C₁₃×SD₁₆	—	2	4	no	—
173	C₁₃×SD₁₆	—	4	8	no	—
174	C₁₃×SD₁₆	—	4	4	no	—
175	C₁₃×SD₁₆	—	4	4	no	—
176	C₁₃×D₈	—	2	4	no	—
177	C₁₃×D₈	—	2	4	no	—
178	C₁₃×D₈	—	2	2	no	—
179	C₁₃×D₈	—	4	4	no	—
180	C₁₃×M₁₆	—	2	2	no	—
181	C₁₃×M₁₆	—	2	2	no	—
182	C₂×C₈×C₁₃	—	2	2	no	—
183	C₂×C₈×C₁₃	#41	1	4	yes	—
184	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
185	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
186	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
187	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
188	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
189	C₁₃×C₄⋊C₄	—	2	4	no	—
190	C₁₃×C₄⋊C₄	—	2	8	no	—
191	C₁₃×C₄⋊C₄	—	2	8	no	—
192	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
193	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
194	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
195	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
196	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
197	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
198	C₁₃×C₂²⋊C₄	—	2	2	no	—
199	C₁₃×C₂²⋊C₄	—	2	8	no	—
200	C₁₃×C₂²⋊C₄	—	2	8	no	—
201	C₁₃×C₂²⋊C₄	—	2	8	no	—
202	C₁₃×C₂²⋊C₄	—	2	4	no	—
203	C₁₃×C₂²⋊C₄	—	2	8	no	—
204	C₁₃×C₂²⋊C₄	—	2	8	no	—
205	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
206	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
207	C₄²×C₁₃	—	2	4	no	—
208	C₄²×C₁₃	—	2	2	no	—
209	C₄²×C₁₃	—	2	8	no	—
210	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
211	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
212	C₄²×C₁₃	C₂⁴	1	2	yes	—
213	C₄²×C₁₃	C₂⁴	1	2	yes	—
214	C₄²×C₁₃	C₂⁴	1	2	yes	—
215	#3510	C₂×C₁₃	1	2	yes	complemented
216	#3401	C₂×C₁₃	1	8	yes	complemented
217	#3396	C₂×C₁₃	1	4	yes	complemented
218	#3393	C₂×C₁₃	1	4	yes	complemented
219	#3156	C₂×C₁₃	1	1	yes	characteristic, complemented
220	#3155	C₂×C₁₃	1	1	yes	characteristic
221	C₂×#495	C₂×C₁₃	1	1	yes	characteristic, complemented
222	#3043	C₂×C₁₃	1	2	yes	complemented
223	#3042	C₂×C₁₃	1	2	yes	complemented
224	#3040	C₂×C₁₃	1	2	yes	complemented
225	#2960	C₂×C₁₃	1	1	yes	characteristic, complemented
226	#2950	C₂×C₁₃	1	1	yes	characteristic, complemented
227	#2948	C₂×C₁₃	1	1	yes	characteristic, complemented
228	C₄×#135	C₂×C₁₃	1	1	yes	characteristic, complemented
229	C₂³×C₁₃	—	2	4	no	—
230	C₂³×C₁₃	—	2	2	no	—
231	C₂³×C₁₃	—	4	4	no	—
232	C₂³×C₁₃	—	8	4	no	—
233	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
234	Q₈×C₁₃	—	2	2	no	—
235	Q₈×C₁₃	—	2	4	no	—
236	Q₈×C₁₃	—	2	4	no	—
237	Q₈×C₁₃	—	2	2	no	—
238	Q₈×C₁₃	—	4	4	no	—
239	Q₈×C₁₃	—	4	4	no	—
240	D₄×C₁₃	—	2	4	no	—
241	D₄×C₁₃	—	2	2	no	—
242	D₄×C₁₃	—	2	2	no	—
243	D₄×C₁₃	—	2	4	no	—
244	D₄×C₁₃	—	4	4	no	—
245	D₄×C₁₃	—	4	4	no	—
246	D₄×C₁₃	—	8	8	no	—
247	C₂×C₄×C₁₃	—	2	4	no	—
248	C₂×C₄×C₁₃	—	2	4	no	—
249	C₂×C₄×C₁₃	—	2	2	no	—
250	C₂×C₄×C₁₃	—	4	2	no	—
251	C₂×C₄×C₁₃	—	4	4	no	—
252	C₂×C₄×C₁₃	—	4	4	no	—
253	C₂×C₄×C₁₃	—	8	4	no	—
254	C₂×C₄×C₁₃	—	8	8	no	—
255	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
256	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
257	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
258	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
259	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
260	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
261	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
262	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
263	C₈×C₁₃	—	2	2	no	—
264	C₈×C₁₃	—	2	2	no	—
265	C₈×C₁₃	—	2	2	no	—
266	C₈×C₁₃	C₂×#41	1	2	yes	—
267	C₈×C₁₃	C₂×#41	1	2	yes	—
268	C₂×#137	C₂²×C₁₃	1	2	yes	—
269	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	—
270	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
271	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
272	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
273	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
274	#559	C₂²×C₁₃	1	8	yes	complemented
275	#556	C₂²×C₁₃	1	8	yes	complemented
276	#551	—	2	8	no	—
277	#542	—	2	4	no	—
278	#536	C₂²×C₁₃	1	2	yes	—
279	#535	C₂²×C₁₃	1	2	yes	—
280	#533	C₂²×C₁₃	1	1	yes	characteristic
281	#529	—	2	4	no	—
282	C₂×#124	C₂²×C₁₃	1	2	yes	—
283	#519	C₂²×C₁₃	1	2	yes	—
284	#518	C₂²×C₁₃	1	2	yes	—
285	C₄×#41	C₂²×C₁₃	1	2	yes	—
286	#497	C₂²×C₁₃	1	4	yes	complemented
287	#496	C₂²×C₁₃	1	4	yes	—
288	#495	C₂²×C₁₃	1	2	yes	—
289	#495	C₂²×C₁₃	1	4	yes	—
290	#495	C₂²×C₁₃	1	4	yes	—
291	#495	C₂²×C₁₃	1	2	yes	complemented
292	#494	C₂²×C₁₃	1	2	yes	complemented
293	#493	C₂²×C₁₃	1	2	yes	—
294	#464	C₂²×C₁₃	1	8	yes	complemented
295	#464	C₂²×C₁₃	1	8	yes	complemented
296	#463	C₂²×C₁₃	1	8	yes	complemented
297	#463	C₂²×C₁₃	1	8	yes	complemented
298	#461	C₂²×C₁₃	1	8	yes	complemented
299	#460	C₂²×C₁₃	1	8	yes	complemented
300	#446	C₂²×C₁₃	1	4	yes	complemented
301	C₈×Q₈	C₂²×C₁₃	1	4	yes	complemented
302	#442	C₂²×C₁₃	1	4	yes	—
303	#441	C₂²×C₁₃	1	4	yes	complemented
304	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
305	C₄×Q₁₆	C₂²×C₁₃	1	4	yes	complemented
306	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
307	C₄×D₈	C₂²×C₁₃	1	4	yes	—
308	C₄×D₈	C₂²×C₁₃	1	2	yes	complemented
309	#427	C₂²×C₁₃	1	1	yes	characteristic
310	#424	C₂²×C₁₃	1	1	yes	characteristic
311	#424	C₂²×C₁₃	1	1	yes	characteristic
312	#423	C₂²×C₁₃	1	1	yes	characteristic
313	#419	C₂²×C₁₃	1	2	yes	—
314	#418	C₂²×C₁₃	1	2	yes	—
315	#416	C₂²×C₁₃	1	2	yes	—
316	#405	C₂²×C₁₃	1	1	yes	characteristic
317	#405	C₂²×C₁₃	1	1	yes	characteristic
318	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
319	C₂²×C₁₃	—	2	2	no	—
320	C₂²×C₁₃	—	4	4	no	—
321	C₂²×C₁₃	—	4	8	no	—
322	C₂²×C₁₃	—	4	2	no	—
323	C₂²×C₁₃	—	4	4	no	—
324	C₂²×C₁₃	—	16	4	no	—
325	C₂²×C₁₃	#550	1	2	yes	—
326	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
327	C₄×C₁₃	—	2	2	no	—
328	C₄×C₁₃	—	2	2	no	—
329	C₄×C₁₃	—	2	4	no	—
330	C₄×C₁₃	—	2	4	no	—
331	C₄×C₁₃	—	4	4	no	—
332	C₄×C₁₃	—	4	2	no	—
333	C₄×C₁₃	—	4	4	no	—
334	C₄×C₁₃	#550	1	2	yes	—
335	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
336	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
337	C₂×#41	C₂³×C₁₃	1	2	yes	—
338	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
339	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
340	#137	—	4	4	no	—
341	AGL(1,ℤ/8)	—	4	4	no	—
342	#135	—	2	4	no	—
343	C₂×Q₁₆	—	2	4	no	—
344	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
345	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
346	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
347	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
348	C₂×SD₁₆	—	4	4	no	—
349	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
350	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
351	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
352	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
353	C₂×D₈	—	2	4	no	—
354	C₂×D₈	C₂³×C₁₃	1	2	yes	—
355	C₂×D₈	C₂³×C₁₃	1	2	yes	—
356	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
357	C₂×D₈	C₂³×C₁₃	1	4	yes	—
358	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
359	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
360	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
361	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
362	C₄⋊Q₈	D₄×C₁₃	1	2	yes	—
363	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
364	#127	C₂³×C₁₃	1	4	yes	—
365	#126	—	2	8	no	—
366	#126	—	2	8	no	—
367	#125	D₄×C₁₃	1	2	yes	—
368	#124	—	2	8	no	—
369	#124	—	2	2	no	—
370	#124	—	2	2	no	—
371	#124	C₂³×C₁₃	1	8	yes	—
372	#124	C₂³×C₁₃	1	4	yes	—
373	#124	C₂³×C₁₃	1	4	yes	—
374	#123	—	2	8	no	—
375	#123	—	2	8	no	—
376	#123	—	2	4	no	—
377	C₂²⋊Q₈	—	2	8	no	—
378	C₂²⋊Q₈	—	2	4	no	—
379	C₂²⋊Q₈	D₄×C₁₃	1	4	yes	—
380	#121	—	2	4	no	—
381	#120	—	2	4	no	—
382	C₄×Q₈	—	2	4	no	—
383	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
384	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
385	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
386	C₄×D₄	—	2	4	no	—
387	C₄×D₄	—	2	4	no	—
388	C₄×D₄	—	2	8	no	—
389	C₄×D₄	C₂³×C₁₃	1	4	yes	—
390	C₄×D₄	C₂³×C₁₃	1	8	yes	—
391	#117	—	2	8	no	—
392	#117	—	2	4	no	—
393	#117	—	2	2	no	—
394	#117	C₂³×C₁₃	1	2	yes	—
395	#117	C₂³×C₁₃	1	1	yes	characteristic
396	#117	C₂³×C₁₃	1	1	yes	characteristic
397	C₂×C₂²⋊C₄	—	2	4	no	—
398	C₂×C₂²⋊C₄	—	2	4	no	—
399	C₂×C₄²	—	2	2	no	—
400	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
401	#107	C₂³×C₁₃	1	2	yes	—
402	#106	C₂³×C₁₃	1	2	yes	—
403	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
404	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
405	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
406	#103	C₂³×C₁₃	1	4	yes	—
407	#103	C₂³×C₁₃	1	8	yes	—
408	#102	C₂³×C₁₃	1	4	yes	—
409	#102	C₂³×C₁₃	1	8	yes	—
410	#97	C₂³×C₁₃	1	2	yes	—
411	#97	C₂³×C₁₃	1	2	yes	—
412	C₄×C₈	C₂³×C₁₃	1	2	yes	—
413	C₄×C₈	C₂³×C₁₃	1	2	yes	—
414	C₄×C₈	C₂³×C₁₃	1	2	yes	—
415	C₄×C₈	C₂³×C₁₃	1	2	yes	—
416	C₂×C₁₃	—	2	2	no	—
417	C₂×C₁₃	—	8	2	no	—
418	C₂×C₁₃	—	8	4	no	—
419	C₂×C₁₃	C₂×#550	1	1	yes	characteristic
420	C₂×C₁₃	#3584	1	2	yes	—
421	C₂⁴	—	2	2	no	—
422	#41	—	2	4	no	—
423	#41	—	2	4	no	—
424	C₂×Q₈	—	2	2	no	—
425	C₂×Q₈	—	2	4	no	—
426	C₂×Q₈	—	2	4	no	—
427	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
428	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
429	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
430	C₂×D₄	—	2	2	no	—
431	C₂×D₄	—	2	2	no	—
432	C₂×D₄	—	2	8	no	—
433	C₂×D₄	—	2	4	no	—
434	C₂×D₄	—	2	4	no	—
435	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
436	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
437	C₂²×C₄	—	2	2	no	—
438	C₂²×C₄	—	2	2	no	—
439	C₂²×C₄	—	2	4	no	—
440	C₂²×C₄	—	2	8	no	—
441	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
442	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
443	Q₁₆	—	2	4	no	—
444	Q₁₆	—	2	4	no	—
445	Q₁₆	—	2	2	no	—
446	Q₁₆	—	4	4	no	—
447	SD₁₆	—	2	4	no	—
448	SD₁₆	—	4	8	no	—
449	SD₁₆	—	4	4	no	—
450	SD₁₆	—	4	4	no	—
451	D₈	—	2	4	no	—
452	D₈	—	2	4	no	—
453	D₈	—	2	2	no	—
454	D₈	—	4	4	no	—
455	M₁₆	—	2	2	no	—
456	M₁₆	—	2	2	no	—
457	C₂×C₈	—	2	2	no	—
458	C₂×C₈	C₁₃×#41	1	4	yes	—
459	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
460	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
461	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
462	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
463	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
464	C₄⋊C₄	—	2	4	no	—
465	C₄⋊C₄	—	2	8	no	—
466	C₄⋊C₄	—	2	8	no	—
467	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
468	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
469	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
470	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
471	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
472	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
473	C₂²⋊C₄	—	2	2	no	—
474	C₂²⋊C₄	—	2	8	no	—
475	C₂²⋊C₄	—	2	8	no	—
476	C₂²⋊C₄	—	2	8	no	—
477	C₂²⋊C₄	—	2	4	no	—
478	C₂²⋊C₄	—	2	8	no	—
479	C₂²⋊C₄	—	2	8	no	—
480	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
481	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
482	C₄²	—	2	4	no	—
483	C₄²	—	2	2	no	—
484	C₄²	—	2	8	no	—
485	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
486	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
487	C₄²	C₂⁴×C₁₃	1	2	yes	—
488	C₄²	C₂⁴×C₁₃	1	2	yes	—
489	C₄²	C₂⁴×C₁₃	1	2	yes	—
490	C₁₃	#61413	1	1	yes	characteristic, direct product factor, Sylow
491	C₂³	—	2	4	no	—
492	C₂³	—	2	2	no	—
493	C₂³	—	4	4	no	—
494	C₂³	—	8	4	no	—
495	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
496	Q₈	—	2	2	no	—
497	Q₈	—	2	4	no	—
498	Q₈	—	2	4	no	—
499	Q₈	—	2	2	no	—
500	Q₈	—	4	4	no	—
501	Q₈	—	4	4	no	—
502	D₄	—	2	4	no	—
503	D₄	—	2	2	no	—
504	D₄	—	2	2	no	—
505	D₄	—	2	4	no	—
506	D₄	—	4	4	no	—
507	D₄	—	4	4	no	—
508	D₄	—	8	8	no	—
509	C₂×C₄	—	2	4	no	—
510	C₂×C₄	—	2	4	no	—
511	C₂×C₄	—	2	2	no	—
512	C₂×C₄	—	4	2	no	—
513	C₂×C₄	—	4	4	no	—
514	C₂×C₄	—	4	4	no	—
515	C₂×C₄	—	8	4	no	—
516	C₂×C₄	—	8	8	no	—
517	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
518	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
519	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
520	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
521	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
522	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
523	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
524	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
525	C₈	—	2	2	no	—
526	C₈	—	2	2	no	—
527	C₈	—	2	2	no	—
528	C₈	C₂×C₁₃×#41	1	2	yes	—
529	C₈	C₂×C₁₃×#41	1	2	yes	—
530	C₂²	—	2	2	no	—
531	C₂²	—	4	4	no	—
532	C₂²	—	4	8	no	—
533	C₂²	—	4	2	no	—
534	C₂²	—	4	4	no	—
535	C₂²	—	16	4	no	—
536	C₂²	C₁₃×#550	1	2	yes	—
537	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
538	C₄	—	2	2	no	—
539	C₄	—	2	2	no	—
540	C₄	—	2	4	no	—
541	C₄	—	2	4	no	—
542	C₄	—	4	4	no	—
543	C₄	—	4	2	no	—
544	C₄	—	4	4	no	—
545	C₄	C₁₃×#550	1	2	yes	—
546	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
547	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
548	C₂	—	2	2	no	—
549	C₂	—	8	4	no	—
550	C₂	—	8	2	no	—
551	C₂	C₂×C₁₃×#550	1	1	yes	characteristic
552	C₂	C₁₃×#3584	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3155	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₁₃×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3510	C₂	semidirect
2. C₁₃×#3401	C₂	semidirect
3. C₁₃×#3396	C₂	semidirect
4. C₁₃×#3393	C₂	semidirect
5. C₁₃×#3156	C₂	semidirect
7. C₂×C₁₃×#495	C₂	semidirect
8. C₁₃×#3043	C₂	semidirect
9. C₁₃×#3042	C₂	semidirect
10. C₁₃×#3040	C₂	semidirect
11. C₁₃×#2960	C₂	semidirect
12. C₁₃×#2950	C₂	semidirect
13. C₁₃×#2948	C₂	semidirect
14. C₄×C₁₃×#135	C₂	semidirect
21. C₁₃×#559	C₂²	semidirect
22. C₁₃×#556	C₂²	semidirect
33. C₁₃×#497	C₂²	semidirect
38. C₁₃×#495	C₂²	semidirect
39. C₁₃×#494	C₂²	semidirect
41. C₁₃×#464	C₂²	semidirect
42. C₁₃×#464	C₂²	semidirect
43. C₁₃×#463	C₂²	semidirect
44. C₁₃×#463	C₂²	semidirect
45. C₁₃×#461	C₂²	semidirect
46. C₁₃×#460	C₂²	semidirect
47. C₁₃×#446	C₂²	semidirect
48. C₈×Q₈×C₁₃	C₂²	semidirect
50. C₁₃×#441	C₂²	semidirect
51. C₄×C₁₃×Q₁₆	C₂²	semidirect
52. C₄×C₁₃×Q₁₆	C₂²	semidirect
53. C₄×C₁₃×SD₁₆	C₂²	semidirect
55. C₄×C₁₃×D₈	C₂²	semidirect
145. #61413	C₁₃	direct (N × H)
215. #3510	C₂×C₁₃	semidirect
216. #3401	C₂×C₁₃	semidirect
217. #3396	C₂×C₁₃	semidirect
218. #3393	C₂×C₁₃	semidirect
219. #3156	C₂×C₁₃	semidirect
221. C₂×#495	C₂×C₁₃	semidirect
222. #3043	C₂×C₁₃	semidirect
223. #3042	C₂×C₁₃	semidirect
224. #3040	C₂×C₁₃	semidirect
225. #2960	C₂×C₁₃	semidirect
226. #2950	C₂×C₁₃	semidirect
227. #2948	C₂×C₁₃	semidirect
228. C₄×#135	C₂×C₁₃	semidirect
274. #559	C₂²×C₁₃	semidirect
275. #556	C₂²×C₁₃	semidirect
286. #497	C₂²×C₁₃	semidirect
291. #495	C₂²×C₁₃	semidirect
292. #494	C₂²×C₁₃	semidirect
294. #464	C₂²×C₁₃	semidirect
295. #464	C₂²×C₁₃	semidirect
296. #463	C₂²×C₁₃	semidirect
297. #463	C₂²×C₁₃	semidirect
298. #461	C₂²×C₁₃	semidirect
299. #460	C₂²×C₁₃	semidirect
300. #446	C₂²×C₁₃	semidirect
301. C₈×Q₈	C₂²×C₁₃	semidirect
303. #441	C₂²×C₁₃	semidirect
304. C₄×Q₁₆	C₂²×C₁₃	semidirect
305. C₄×Q₁₆	C₂²×C₁₃	semidirect
306. C₄×SD₁₆	C₂²×C₁₃	semidirect
308. C₄×D₈	C₂²×C₁₃	semidirect
490. C₁₃	#61413	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#3510	2
C₁₃×#3401	2
C₁₃×#3396	2
C₁₃×#3393	2
C₁₃×#3156	2
C₁₃×#3155	2
C₂×C₁₃×#495	2
C₁₃×#3043	2
C₁₃×#3042	2
C₁₃×#3040	2
C₁₃×#2960	2
C₁₃×#2950	2
C₁₃×#2948	2
C₄×C₁₃×#135	2
#61413	13

Subgroups — C13×#61413 #15747752

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61413 #15747752