Subgroups — C₁₃×#61406 #15747745

Order 3328.

1986 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3506	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3403	C₂	1	4	yes	maximal, complemented
3	C₁₃×#3397	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3396	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3393	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3391	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3155	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3147	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3045	C₂	1	4	yes	maximal, complemented
10	C₁₃×#3036	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2960	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#2951	C₂	1	2	yes	maximal, complemented
13	C₂×C₄×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	4	yes	—
15	C₂×C₁₃×#135	C₂²	1	2	yes	—
16	C₂×C₁₃×#135	C₂²	1	2	yes	—
17	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
18	C₁₃×#559	C₂²	1	8	yes	complemented
19	C₁₃×#556	C₂²	1	4	yes	complemented
20	C₁₃×#555	—	2	2	no	—
21	C₁₃×#553	—	2	4	no	—
22	C₁₃×#550	C₂²	1	4	yes	complemented
23	C₁₃×#547	—	2	2	no	—
24	C₁₃×#538	—	2	4	no	—
25	C₁₃×#535	C₂²	1	4	yes	—
26	C₁₃×#533	C₂²	1	1	yes	characteristic
27	C₁₃×#532	C₂²	1	2	yes	—
28	C₁₃×#525	—	2	4	no	—
29	C₁₃×#520	C₂²	1	4	yes	—
30	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
31	C₁₃×#496	C₂²	1	8	yes	—
32	C₁₃×#495	C₂²	1	4	yes	—
33	C₁₃×#495	C₂²	1	2	yes	complemented
34	C₁₃×#495	C₂²	1	2	yes	complemented
35	C₁₃×#494	C₂²	1	1	yes	characteristic, complemented
36	C₁₃×#493	C₂²	1	4	yes	—
37	C₁₃×#493	C₂²	1	1	yes	characteristic, complemented
38	C₁₃×#492	C₂²	1	2	yes	complemented
39	C₁₃×#464	C₂²	1	8	yes	complemented
40	C₁₃×#463	C₂²	1	8	yes	complemented
41	C₁₃×#463	C₂²	1	8	yes	complemented
42	C₁₃×#461	C₂²	1	4	yes	complemented
43	C₁₃×#460	C₂²	1	8	yes	complemented
44	C₁₃×#459	C₂²	1	4	yes	complemented
45	C₁₃×#459	C₂²	1	8	yes	complemented
46	C₁₃×#446	C₂²	1	2	yes	complemented
47	C₁₃×#446	C₂²	1	2	yes	complemented
48	C₈×Q₈×C₁₃	C₂²	1	2	yes	complemented
49	C₈×Q₈×C₁₃	C₂²	1	2	yes	complemented
50	C₁₃×#440	C₂²	1	8	yes	complemented
51	C₄×C₁₃×Q₁₆	C₂²	1	4	yes	complemented
52	C₄×C₁₃×D₈	C₂²	1	2	yes	—
53	C₄×C₁₃×D₈	C₂²	1	2	yes	—
54	C₄×C₁₃×D₈	C₂²	1	2	yes	—
55	C₄×C₁₃×D₈	C₂²	1	2	yes	—
56	C₄×C₁₃×D₈	C₂²	1	4	yes	complemented
57	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
58	C₁₃×#424	C₂²	1	2	yes	—
59	C₁₃×#423	C₂²	1	1	yes	characteristic
60	C₁₃×#417	C₂²	1	4	yes	—
61	C₂×C₁₃×#102	C₂²	1	2	yes	—
62	C₁₃×#405	C₂²	1	2	yes	—
63	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
64	C₂×C₁₃×#41	—	2	4	no	—
65	C₂×C₁₃×#41	C₂³	1	4	yes	—
66	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
67	C₂³×C₄×C₁₃	—	2	2	no	—
68	C₁₃×AGL(1,ℤ/8)	—	4	8	no	—
69	C₁₃×#135	—	2	8	no	—
70	C₁₃×#135	—	4	4	no	—
71	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
72	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
73	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
74	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
75	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
76	C₂×C₁₃×D₈	—	2	4	no	—
77	C₂×C₁₃×D₈	C₂³	1	2	yes	—
78	C₂×C₁₃×D₈	C₂³	1	2	yes	—
79	C₂×C₁₃×D₈	C₂³	1	2	yes	—
80	C₂×C₁₃×D₈	C₂³	1	2	yes	—
81	C₂×C₁₃×D₈	C₂³	1	8	yes	—
82	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
83	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
84	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
85	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
86	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
87	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
88	C₁₃×#127	C₂³	1	2	yes	—
89	C₁₃×#127	C₂³	1	8	yes	—
90	C₁₃×#126	—	2	8	no	—
91	C₁₃×#125	D₄	1	2	yes	—
92	C₁₃×#124	—	2	8	no	—
93	C₁₃×#124	C₂³	1	4	yes	—
94	C₁₃×#124	C₂³	1	8	yes	—
95	C₁₃×#123	—	2	8	no	—
96	C₁₃×#123	—	2	8	no	—
97	C₁₃×C₂²⋊Q₈	—	2	4	no	—
98	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
99	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
100	C₁₃×#121	—	2	2	no	—
101	C₁₃×#121	—	2	2	no	—
102	C₁₃×#121	—	2	4	no	—
103	C₁₃×#121	—	2	4	no	—
104	C₁₃×#121	—	2	4	no	—
105	C₁₃×#121	—	2	8	no	—
106	C₁₃×#120	—	2	8	no	—
107	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
108	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
109	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
110	C₄×D₄×C₁₃	—	2	8	no	—
111	C₄×D₄×C₁₃	—	2	8	no	—
112	C₄×D₄×C₁₃	—	2	2	no	—
113	C₄×D₄×C₁₃	—	2	2	no	—
114	C₄×D₄×C₁₃	—	2	2	no	—
115	C₄×D₄×C₁₃	—	2	2	no	—
116	C₄×D₄×C₁₃	C₂³	1	4	yes	—
117	C₄×D₄×C₁₃	C₂³	1	4	yes	—
118	C₄×D₄×C₁₃	C₂³	1	8	yes	—
119	C₁₃×#117	—	2	4	no	—
120	C₁₃×#117	—	2	4	no	—
121	C₁₃×#117	C₂³	1	2	yes	—
122	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
123	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
124	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
125	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
126	C₁₃×#107	C₂³	1	2	yes	—
127	C₁₃×#107	C₂³	1	2	yes	—
128	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
129	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
130	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
131	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
132	C₁₃×#103	C₂³	1	8	yes	—
133	C₁₃×#102	C₂³	1	4	yes	—
134	C₁₃×#102	C₂³	1	4	yes	—
135	C₁₃×#102	C₂³	1	8	yes	—
136	C₁₃×#97	C₂³	1	4	yes	—
137	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
138	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
139	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
140	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
141	C₄×C₈×C₁₃	C₂³	1	4	yes	—
142	#61406	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
143	C₂⁴×C₁₃	—	2	2	no	—
144	C₁₃×#41	—	2	8	no	—
145	C₁₃×#41	—	2	8	no	—
146	C₁₃×#41	—	8	8	no	—
147	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
148	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
149	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
150	C₂×D₄×C₁₃	—	2	4	no	—
151	C₂×D₄×C₁₃	—	2	2	no	—
152	C₂×D₄×C₁₃	—	2	2	no	—
153	C₂×D₄×C₁₃	—	2	8	no	—
154	C₂×D₄×C₁₃	—	2	2	no	—
155	C₂×D₄×C₁₃	—	2	8	no	—
156	C₂×D₄×C₁₃	—	2	4	no	—
157	C₂×D₄×C₁₃	—	2	4	no	—
158	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
159	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
160	C₂²×C₄×C₁₃	—	2	2	no	—
161	C₂²×C₄×C₁₃	—	2	4	no	—
162	C₂²×C₄×C₁₃	—	2	4	no	—
163	C₂²×C₄×C₁₃	—	2	8	no	—
164	C₂²×C₄×C₁₃	—	2	4	no	—
165	C₂²×C₄×C₁₃	—	8	4	no	—
166	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
169	C₁₃×Q₁₆	—	2	4	no	—
170	C₁₃×Q₁₆	—	4	2	no	—
171	C₁₃×SD₁₆	—	2	8	no	—
172	C₁₃×SD₁₆	—	4	4	no	—
173	C₁₃×SD₁₆	—	4	8	no	—
174	C₁₃×D₈	—	2	4	no	—
175	C₁₃×D₈	—	2	4	no	—
176	C₁₃×D₈	—	2	4	no	—
177	C₁₃×D₈	—	4	2	no	—
178	C₁₃×D₈	—	4	8	no	—
179	C₁₃×M₁₆	—	2	4	no	—
180	C₂×C₈×C₁₃	—	2	2	no	—
181	C₂×C₈×C₁₃	#41	1	4	yes	complemented
182	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
183	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
184	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
185	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
186	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
187	C₁₃×C₄⋊C₄	—	2	2	no	—
188	C₁₃×C₄⋊C₄	—	2	8	no	—
189	C₁₃×C₄⋊C₄	—	2	2	no	—
190	C₁₃×C₄⋊C₄	—	2	2	no	—
191	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
192	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
193	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
194	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
195	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
196	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
197	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
198	C₁₃×C₂²⋊C₄	—	2	4	no	—
199	C₁₃×C₂²⋊C₄	—	2	4	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	4	no	—
205	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
206	C₄²×C₁₃	—	2	8	no	—
207	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
208	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
209	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
210	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
211	C₄²×C₁₃	C₂⁴	1	4	yes	—
212	#3506	C₂×C₁₃	1	2	yes	complemented
213	#3403	C₂×C₁₃	1	4	yes	complemented
214	#3397	C₂×C₁₃	1	4	yes	complemented
215	#3396	C₂×C₁₃	1	4	yes	complemented
216	#3393	C₂×C₁₃	1	2	yes	complemented
217	#3391	C₂×C₁₃	1	2	yes	complemented
218	#3155	C₂×C₁₃	1	2	yes	complemented
219	#3147	C₂×C₁₃	1	1	yes	characteristic, complemented
220	#3045	C₂×C₁₃	1	4	yes	complemented
221	#3036	C₂×C₁₃	1	2	yes	complemented
222	#2960	C₂×C₁₃	1	1	yes	characteristic, complemented
223	#2951	C₂×C₁₃	1	2	yes	complemented
224	C₂×C₄×D₈	C₂×C₁₃	1	1	yes	characteristic, complemented
225	C₂³×C₁₃	—	2	4	no	—
226	C₂³×C₁₃	—	2	4	no	—
227	C₂³×C₁₃	—	4	4	no	—
228	C₂³×C₁₃	—	8	2	no	—
229	C₂³×C₁₃	—	8	2	no	—
230	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
231	Q₈×C₁₃	—	2	4	no	—
232	Q₈×C₁₃	—	2	4	no	—
233	Q₈×C₁₃	—	2	4	no	—
234	Q₈×C₁₃	—	4	2	no	—
235	D₄×C₁₃	—	2	4	no	—
236	D₄×C₁₃	—	2	4	no	—
237	D₄×C₁₃	—	2	4	no	—
238	D₄×C₁₃	—	2	4	no	—
239	D₄×C₁₃	—	4	8	no	—
240	D₄×C₁₃	—	4	4	no	—
241	D₄×C₁₃	—	4	4	no	—
242	D₄×C₁₃	—	8	2	no	—
243	D₄×C₁₃	—	8	8	no	—
244	D₄×C₁₃	—	8	8	no	—
245	C₂×C₄×C₁₃	—	2	2	no	—
246	C₂×C₄×C₁₃	—	2	4	no	—
247	C₂×C₄×C₁₃	—	2	4	no	—
248	C₂×C₄×C₁₃	—	4	1	no	—
249	C₂×C₄×C₁₃	—	4	8	no	—
250	C₂×C₄×C₁₃	—	4	8	no	—
251	C₂×C₄×C₁₃	—	8	4	no	—
252	C₂×C₄×C₁₃	—	8	8	no	—
253	C₂×C₄×C₁₃	—	8	2	no	—
254	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
255	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
256	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
257	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
258	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
259	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
260	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
261	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
262	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
263	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
264	C₈×C₁₃	—	2	1	no	—
265	C₈×C₁₃	—	2	1	no	—
266	C₈×C₁₃	—	2	4	no	—
267	C₈×C₁₃	C₂×#41	1	2	yes	—
268	C₈×C₁₃	C₂×#41	1	2	yes	—
269	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	4	yes	—
270	C₂×#135	C₂²×C₁₃	1	2	yes	—
271	C₂×#135	C₂²×C₁₃	1	2	yes	—
272	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
273	#559	C₂²×C₁₃	1	8	yes	complemented
274	#556	C₂²×C₁₃	1	4	yes	complemented
275	#555	—	2	2	no	—
276	#553	—	2	4	no	—
277	#550	C₂²×C₁₃	1	4	yes	complemented
278	#547	—	2	2	no	—
279	#538	—	2	4	no	—
280	#535	C₂²×C₁₃	1	4	yes	—
281	#533	C₂²×C₁₃	1	1	yes	characteristic
282	#532	C₂²×C₁₃	1	2	yes	—
283	#525	—	2	4	no	—
284	#520	C₂²×C₁₃	1	4	yes	—
285	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
286	#496	C₂²×C₁₃	1	8	yes	—
287	#495	C₂²×C₁₃	1	4	yes	—
288	#495	C₂²×C₁₃	1	2	yes	complemented
289	#495	C₂²×C₁₃	1	2	yes	complemented
290	#494	C₂²×C₁₃	1	1	yes	characteristic, complemented
291	#493	C₂²×C₁₃	1	4	yes	—
292	#493	C₂²×C₁₃	1	1	yes	characteristic, complemented
293	#492	C₂²×C₁₃	1	2	yes	complemented
294	#464	C₂²×C₁₃	1	8	yes	complemented
295	#463	C₂²×C₁₃	1	8	yes	complemented
296	#463	C₂²×C₁₃	1	8	yes	complemented
297	#461	C₂²×C₁₃	1	4	yes	complemented
298	#460	C₂²×C₁₃	1	8	yes	complemented
299	#459	C₂²×C₁₃	1	4	yes	complemented
300	#459	C₂²×C₁₃	1	8	yes	complemented
301	#446	C₂²×C₁₃	1	2	yes	complemented
302	#446	C₂²×C₁₃	1	2	yes	complemented
303	C₈×Q₈	C₂²×C₁₃	1	2	yes	complemented
304	C₈×Q₈	C₂²×C₁₃	1	2	yes	complemented
305	#440	C₂²×C₁₃	1	8	yes	complemented
306	C₄×Q₁₆	C₂²×C₁₃	1	4	yes	complemented
307	C₄×D₈	C₂²×C₁₃	1	2	yes	—
308	C₄×D₈	C₂²×C₁₃	1	2	yes	—
309	C₄×D₈	C₂²×C₁₃	1	2	yes	—
310	C₄×D₈	C₂²×C₁₃	1	2	yes	—
311	C₄×D₈	C₂²×C₁₃	1	4	yes	complemented
312	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
313	#424	C₂²×C₁₃	1	2	yes	—
314	#423	C₂²×C₁₃	1	1	yes	characteristic
315	#417	C₂²×C₁₃	1	4	yes	—
316	C₂×#102	C₂²×C₁₃	1	2	yes	—
317	#405	C₂²×C₁₃	1	2	yes	—
318	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
319	C₂²×C₁₃	—	2	1	no	—
320	C₂²×C₁₃	—	2	1	no	—
321	C₂²×C₁₃	—	4	4	no	—
322	C₂²×C₁₃	—	4	4	no	—
323	C₂²×C₁₃	—	4	4	no	—
324	C₂²×C₁₃	—	4	4	no	—
325	C₂²×C₁₃	—	4	4	no	—
326	C₂²×C₁₃	—	4	4	no	—
327	C₂²×C₁₃	—	8	8	no	—
328	C₂²×C₁₃	#550	1	2	yes	—
329	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
330	C₄×C₁₃	—	2	1	no	—
331	C₄×C₁₃	—	2	1	no	—
332	C₄×C₁₃	—	2	4	no	—
333	C₄×C₁₃	—	2	1	no	—
334	C₄×C₁₃	—	2	4	no	—
335	C₄×C₁₃	—	4	4	no	—
336	C₄×C₁₃	—	4	4	no	—
337	C₄×C₁₃	#550	1	2	yes	—
338	C₄×C₁₃	#576	1	2	yes	—
339	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
340	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
341	C₂×#41	—	2	4	no	—
342	C₂×#41	C₂³×C₁₃	1	4	yes	—
343	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
344	C₂³×C₄	—	2	2	no	—
345	AGL(1,ℤ/8)	—	4	8	no	—
346	#135	—	2	8	no	—
347	#135	—	4	4	no	—
348	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
349	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
350	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
351	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
352	C₂×SD₁₆	C₂³×C₁₃	1	8	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	2	yes	—
357	C₂×D₈	C₂³×C₁₃	1	2	yes	—
358	C₂×D₈	C₂³×C₁₃	1	8	yes	—
359	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
360	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
361	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
362	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
363	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
364	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
365	#127	C₂³×C₁₃	1	2	yes	—
366	#127	C₂³×C₁₃	1	8	yes	—
367	#126	—	2	8	no	—
368	#125	D₄×C₁₃	1	2	yes	—
369	#124	—	2	8	no	—
370	#124	C₂³×C₁₃	1	4	yes	—
371	#124	C₂³×C₁₃	1	8	yes	—
372	#123	—	2	8	no	—
373	#123	—	2	8	no	—
374	C₂²⋊Q₈	—	2	4	no	—
375	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
376	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
377	#121	—	2	2	no	—
378	#121	—	2	2	no	—
379	#121	—	2	4	no	—
380	#121	—	2	4	no	—
381	#121	—	2	4	no	—
382	#121	—	2	8	no	—
383	#120	—	2	8	no	—
384	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
385	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
386	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
387	C₄×D₄	—	2	8	no	—
388	C₄×D₄	—	2	8	no	—
389	C₄×D₄	—	2	2	no	—
390	C₄×D₄	—	2	2	no	—
391	C₄×D₄	—	2	2	no	—
392	C₄×D₄	—	2	2	no	—
393	C₄×D₄	C₂³×C₁₃	1	4	yes	—
394	C₄×D₄	C₂³×C₁₃	1	4	yes	—
395	C₄×D₄	C₂³×C₁₃	1	8	yes	—
396	#117	—	2	4	no	—
397	#117	—	2	4	no	—
398	#117	C₂³×C₁₃	1	2	yes	—
399	C₂×C₄⋊C₄	—	2	4	no	—
400	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
401	C₂×C₂²⋊C₄	—	2	2	no	—
402	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
403	#107	C₂³×C₁₃	1	2	yes	—
404	#107	C₂³×C₁₃	1	2	yes	—
405	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
406	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
407	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
408	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
409	#103	C₂³×C₁₃	1	8	yes	—
410	#102	C₂³×C₁₃	1	4	yes	—
411	#102	C₂³×C₁₃	1	4	yes	—
412	#102	C₂³×C₁₃	1	8	yes	—
413	#97	C₂³×C₁₃	1	4	yes	—
414	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
415	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
416	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
417	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
418	C₄×C₈	C₂³×C₁₃	1	4	yes	—
419	C₂×C₁₃	—	2	2	no	—
420	C₂×C₁₃	—	8	4	no	—
421	C₂×C₁₃	—	8	4	no	—
422	C₂×C₁₃	C₂×#550	1	1	yes	characteristic
423	C₂×C₁₃	C₂×#576	1	1	yes	characteristic
424	C₂×C₁₃	#3584	1	1	yes	characteristic
425	C₂⁴	—	2	2	no	—
426	#41	—	2	8	no	—
427	#41	—	2	8	no	—
428	#41	—	8	8	no	—
429	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
430	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
431	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
432	C₂×D₄	—	2	4	no	—
433	C₂×D₄	—	2	2	no	—
434	C₂×D₄	—	2	2	no	—
435	C₂×D₄	—	2	8	no	—
436	C₂×D₄	—	2	2	no	—
437	C₂×D₄	—	2	8	no	—
438	C₂×D₄	—	2	4	no	—
439	C₂×D₄	—	2	4	no	—
440	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
441	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
442	C₂²×C₄	—	2	2	no	—
443	C₂²×C₄	—	2	4	no	—
444	C₂²×C₄	—	2	4	no	—
445	C₂²×C₄	—	2	8	no	—
446	C₂²×C₄	—	2	4	no	—
447	C₂²×C₄	—	8	4	no	—
448	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
449	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
450	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
451	Q₁₆	—	2	4	no	—
452	Q₁₆	—	4	2	no	—
453	SD₁₆	—	2	8	no	—
454	SD₁₆	—	4	4	no	—
455	SD₁₆	—	4	8	no	—
456	D₈	—	2	4	no	—
457	D₈	—	2	4	no	—
458	D₈	—	2	4	no	—
459	D₈	—	4	2	no	—
460	D₈	—	4	8	no	—
461	M₁₆	—	2	4	no	—
462	C₂×C₈	—	2	2	no	—
463	C₂×C₈	C₁₃×#41	1	4	yes	complemented
464	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
465	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
466	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
467	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
468	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
469	C₄⋊C₄	—	2	2	no	—
470	C₄⋊C₄	—	2	8	no	—
471	C₄⋊C₄	—	2	2	no	—
472	C₄⋊C₄	—	2	2	no	—
473	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
474	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
475	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
476	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
477	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
478	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
479	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
480	C₂²⋊C₄	—	2	4	no	—
481	C₂²⋊C₄	—	2	4	no	—
482	C₂²⋊C₄	—	2	8	no	—
483	C₂²⋊C₄	—	2	8	no	—
484	C₂²⋊C₄	—	2	4	no	—
485	C₂²⋊C₄	—	2	8	no	—
486	C₂²⋊C₄	—	2	4	no	—
487	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
488	C₄²	—	2	8	no	—
489	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
490	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
491	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
492	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
493	C₄²	C₂⁴×C₁₃	1	4	yes	—
494	C₁₃	#61406	1	1	yes	characteristic, direct product factor, Sylow
495	C₂³	—	2	4	no	—
496	C₂³	—	2	4	no	—
497	C₂³	—	4	4	no	—
498	C₂³	—	8	2	no	—
499	C₂³	—	8	2	no	—
500	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
501	Q₈	—	2	4	no	—
502	Q₈	—	2	4	no	—
503	Q₈	—	2	4	no	—
504	Q₈	—	4	2	no	—
505	D₄	—	2	4	no	—
506	D₄	—	2	4	no	—
507	D₄	—	2	4	no	—
508	D₄	—	2	4	no	—
509	D₄	—	4	8	no	—
510	D₄	—	4	4	no	—
511	D₄	—	4	4	no	—
512	D₄	—	8	2	no	—
513	D₄	—	8	8	no	—
514	D₄	—	8	8	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	4	no	—
517	C₂×C₄	—	2	4	no	—
518	C₂×C₄	—	4	1	no	—
519	C₂×C₄	—	4	8	no	—
520	C₂×C₄	—	4	8	no	—
521	C₂×C₄	—	8	4	no	—
522	C₂×C₄	—	8	8	no	—
523	C₂×C₄	—	8	2	no	—
524	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
525	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
526	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
527	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
528	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
529	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
530	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
531	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
532	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
533	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
534	C₈	—	2	1	no	—
535	C₈	—	2	1	no	—
536	C₈	—	2	4	no	—
537	C₈	C₂×C₁₃×#41	1	2	yes	—
538	C₈	C₂×C₁₃×#41	1	2	yes	—
539	C₂²	—	2	1	no	—
540	C₂²	—	2	1	no	—
541	C₂²	—	4	4	no	—
542	C₂²	—	4	4	no	—
543	C₂²	—	4	4	no	—
544	C₂²	—	4	4	no	—
545	C₂²	—	4	4	no	—
546	C₂²	—	4	4	no	—
547	C₂²	—	8	8	no	—
548	C₂²	C₁₃×#550	1	2	yes	—
549	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
550	C₄	—	2	1	no	—
551	C₄	—	2	4	no	—
552	C₄	—	2	1	no	—
553	C₄	—	2	1	no	—
554	C₄	—	2	4	no	—
555	C₄	—	4	4	no	—
556	C₄	—	4	4	no	—
557	C₄	C₁₃×#550	1	2	yes	—
558	C₄	C₁₃×#576	1	2	yes	—
559	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
560	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
561	C₂	—	2	2	no	—
562	C₂	—	8	4	no	—
563	C₂	—	8	4	no	—
564	C₂	C₂×C₁₃×#550	1	1	yes	characteristic
565	C₂	C₂×C₁₃×#576	1	1	yes	characteristic
566	C₂	C₁₃×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
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×#3506	C₂	semidirect
2. C₁₃×#3403	C₂	semidirect
3. C₁₃×#3397	C₂	semidirect
4. C₁₃×#3396	C₂	semidirect
5. C₁₃×#3393	C₂	semidirect
6. C₁₃×#3391	C₂	semidirect
7. C₁₃×#3155	C₂	semidirect
8. C₁₃×#3147	C₂	semidirect
9. C₁₃×#3045	C₂	semidirect
10. C₁₃×#3036	C₂	semidirect
11. C₁₃×#2960	C₂	semidirect
12. C₁₃×#2951	C₂	semidirect
13. C₂×C₄×C₁₃×D₈	C₂	semidirect
18. C₁₃×#559	C₂²	semidirect
19. C₁₃×#556	C₂²	semidirect
22. C₁₃×#550	C₂²	semidirect
33. C₁₃×#495	C₂²	semidirect
34. C₁₃×#495	C₂²	semidirect
35. C₁₃×#494	C₂²	semidirect
37. C₁₃×#493	C₂²	semidirect
38. C₁₃×#492	C₂²	semidirect
39. C₁₃×#464	C₂²	semidirect
40. C₁₃×#463	C₂²	semidirect
41. C₁₃×#463	C₂²	semidirect
42. C₁₃×#461	C₂²	semidirect
43. C₁₃×#460	C₂²	semidirect
44. C₁₃×#459	C₂²	semidirect
45. C₁₃×#459	C₂²	semidirect
46. C₁₃×#446	C₂²	semidirect
47. C₁₃×#446	C₂²	semidirect
48. C₈×Q₈×C₁₃	C₂²	semidirect
49. C₈×Q₈×C₁₃	C₂²	semidirect
50. C₁₃×#440	C₂²	semidirect
51. C₄×C₁₃×Q₁₆	C₂²	semidirect
56. C₄×C₁₃×D₈	C₂²	semidirect
142. #61406	C₁₃	direct (N × H)
181. C₂×C₈×C₁₃	#41	semidirect
212. #3506	C₂×C₁₃	semidirect
213. #3403	C₂×C₁₃	semidirect
214. #3397	C₂×C₁₃	semidirect
215. #3396	C₂×C₁₃	semidirect
216. #3393	C₂×C₁₃	semidirect
217. #3391	C₂×C₁₃	semidirect
218. #3155	C₂×C₁₃	semidirect
219. #3147	C₂×C₁₃	semidirect
220. #3045	C₂×C₁₃	semidirect
221. #3036	C₂×C₁₃	semidirect
222. #2960	C₂×C₁₃	semidirect
223. #2951	C₂×C₁₃	semidirect
224. C₂×C₄×D₈	C₂×C₁₃	semidirect
273. #559	C₂²×C₁₃	semidirect
274. #556	C₂²×C₁₃	semidirect
277. #550	C₂²×C₁₃	semidirect
288. #495	C₂²×C₁₃	semidirect
289. #495	C₂²×C₁₃	semidirect
290. #494	C₂²×C₁₃	semidirect
292. #493	C₂²×C₁₃	semidirect
293. #492	C₂²×C₁₃	semidirect
294. #464	C₂²×C₁₃	semidirect
295. #463	C₂²×C₁₃	semidirect
296. #463	C₂²×C₁₃	semidirect
297. #461	C₂²×C₁₃	semidirect
298. #460	C₂²×C₁₃	semidirect
299. #459	C₂²×C₁₃	semidirect
300. #459	C₂²×C₁₃	semidirect
301. #446	C₂²×C₁₃	semidirect
302. #446	C₂²×C₁₃	semidirect
303. C₈×Q₈	C₂²×C₁₃	semidirect
304. C₈×Q₈	C₂²×C₁₃	semidirect
305. #440	C₂²×C₁₃	semidirect
306. C₄×Q₁₆	C₂²×C₁₃	semidirect
311. C₄×D₈	C₂²×C₁₃	semidirect
463. C₂×C₈	C₁₃×#41	semidirect
494. C₁₃	#61406	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×#3506	2
C₁₃×#3403	2
C₁₃×#3397	2
C₁₃×#3396	2
C₁₃×#3393	2
C₁₃×#3391	2
C₁₃×#3155	2
C₁₃×#3147	2
C₁₃×#3045	2
C₁₃×#3036	2
C₁₃×#2960	2
C₁₃×#2951	2
C₂×C₄×C₁₃×D₈	2
#61406	13

Subgroups — C13×#61406 #15747745

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61406 #15747745