Subgroups — C₁₃×#62003 #15748342

Order 3328.

2126 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3517	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3392	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3391	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#3359	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#3358	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#3332	C₂	1	3	yes	maximal, complemented
8	C₁₃×#3330	C₂	1	3	yes	maximal, complemented
9	C₁₃×#3274	C₂	1	3	yes	maximal, complemented
10	C₁₃×#3272	C₂	1	3	yes	maximal, complemented
11	C₁₃×#3251	C₂	1	3	yes	maximal, complemented
12	C₁₃×#3207	C₂	1	3	yes	maximal, complemented
13	C₁₃×#3105	C₂	1	3	yes	maximal, complemented
14	C₁₃×#3036	C₂	1	3	yes	maximal, complemented
15	C₁₃×#2991	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×#41	—	2	1	no	—
17	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	6	yes	—
18	C₁₃×#557	C₂²	1	1	yes	characteristic, complemented
19	C₁₃×#553	—	2	3	no	—
20	C₁₃×#550	—	2	1	no	—
21	C₁₃×#550	C₂²	1	1	yes	characteristic
22	C₁₃×#550	C₂²	1	3	yes	complemented
23	C₁₃×#550	C₂²	1	1	yes	characteristic, complemented
24	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
25	C₁₃×#548	—	2	1	no	—
26	C₁₃×#547	C₂²	1	3	yes	—
27	C₁₃×#547	C₂²	1	3	yes	complemented
28	C₁₃×#546	—	2	3	no	—
29	D₄²×C₁₃	C₂²	1	3	yes	—
30	C₁₃×#540	—	2	3	no	—
31	C₁₃×#532	C₂²	1	3	yes	—
32	C₁₃×#532	C₂²	1	3	yes	complemented
33	C₁₃×#529	C₂²	1	3	yes	complemented
34	C₁₃×#525	—	2	3	no	—
35	C₁₃×#520	—	2	1	no	—
36	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₁₃	C₂²	1	3	yes	—
38	C₁₃×#493	C₂²	1	3	yes	complemented
39	C₁₃×#492	C₂²	1	3	yes	complemented
40	C₁₃×#487	C₂²	1	3	yes	complemented
41	C₁₃×#486	C₂²	1	3	yes	complemented
42	C₁₃×#484	C₂²	1	3	yes	complemented
43	C₁₃×#481	C₂²	1	3	yes	complemented
44	C₁₃×#478	C₂²	1	1	yes	characteristic
45	C₁₃×#478	C₂²	1	3	yes	complemented
46	C₁₃×#475	C₂²	1	3	yes	complemented
47	C₁₃×#474	C₂²	1	3	yes	complemented
48	C₁₃×#469	C₂²	1	6	yes	complemented
49	C₁₃×#468	C₂²	1	6	yes	complemented
50	C₁₃×#463	C₂²	1	3	yes	—
51	C₁₃×#463	C₂²	1	6	yes	complemented
52	C₁₃×#463	C₂²	1	3	yes	complemented
53	C₁₃×#461	C₂²	1	3	yes	—
54	C₁₃×#461	C₂²	1	3	yes	complemented
55	C₁₃×#460	C₂²	1	3	yes	complemented
56	C₁₃×#459	C₂²	1	3	yes	—
57	C₁₃×#459	C₂²	1	3	yes	complemented
58	C₁₃×#459	C₂²	1	3	yes	complemented
59	C₁₃×#450	C₂²	1	3	yes	—
60	C₁₃×#449	C₂²	1	6	yes	complemented
61	C₁₃×#449	C₂²	1	6	yes	complemented
62	C₁₃×#447	C₂²	1	3	yes	—
63	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
64	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
65	C₄×C₁₃×SD₁₆	C₂²	1	3	yes	—
66	C₄×C₁₃×SD₁₆	C₂²	1	3	yes	complemented
67	C₄×C₁₃×D₈	C₂²	1	3	yes	—
68	C₄×C₁₃×D₈	C₂²	1	3	yes	complemented
69	C₁₃×#436	C₂²	1	3	yes	complemented
70	C₁₃×#436	C₂²	1	3	yes	complemented
71	C₁₃×#431	C₂²	1	3	yes	complemented
72	C₁₃×#423	C₂²	1	3	yes	complemented
73	C₁₃×#417	C₂²	1	6	yes	complemented
74	C₂×C₁₃×#41	—	2	1	no	—
75	C₂×C₁₃×#41	—	2	1	no	—
76	C₂×C₁₃×#41	—	2	3	no	—
77	C₂×C₁₃×#41	—	2	3	no	—
78	C₂×C₁₃×#41	—	4	8	no	—
79	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
80	C₂×C₁₃×#41	C₂³	1	6	yes	—
81	C₂²×Q₈×C₁₃	—	2	1	no	—
82	C₂²×D₄×C₁₃	—	2	3	no	—
83	C₂²×D₄×C₁₃	C₂³	1	3	yes	—
84	C₂³×C₄×C₁₃	—	2	3	no	—
85	C₁₃×AGL(1,ℤ/8)	—	4	12	no	—
86	C₂×C₁₃×SD₁₆	C₂³	1	3	yes	—
87	C₂×C₁₃×SD₁₆	C₂³	1	3	yes	—
88	C₂×C₁₃×SD₁₆	C₂³	1	6	yes	—
89	C₂×C₁₃×D₈	C₂³	1	3	yes	—
90	C₂×C₁₃×D₈	C₂³	1	3	yes	—
91	C₂×C₁₃×D₈	C₂³	1	6	yes	—
92	C₂×C₁₃×M₁₆	C₂³	1	6	yes	—
93	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
94	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
95	C₁₃×#127	—	2	3	no	—
96	C₁₃×#127	C₂³	1	3	yes	—
97	C₁₃×#127	C₂³	1	3	yes	—
98	C₁₃×#126	—	2	3	no	—
99	C₁₃×#125	—	2	3	no	—
100	C₁₃×#125	C₂³	1	1	yes	characteristic
101	C₁₃×#124	—	2	3	no	—
102	C₁₃×#124	C₂³	1	3	yes	—
103	C₁₃×#123	—	2	3	no	—
104	C₁₃×#123	—	2	6	no	—
105	C₁₃×#123	—	2	6	no	—
106	C₁₃×C₂²⋊Q₈	—	2	3	no	—
107	C₁₃×C₂²⋊Q₈	—	2	3	no	—
108	C₁₃×C₂²⋊Q₈	C₂³	1	3	yes	—
109	C₁₃×#121	—	2	3	no	—
110	C₁₃×#121	—	2	3	no	—
111	C₁₃×#121	—	2	3	no	—
112	C₁₃×#121	—	2	3	no	—
113	C₁₃×#121	—	2	3	no	—
114	C₁₃×#121	—	2	3	no	—
115	C₁₃×#121	—	2	3	no	—
116	C₁₃×#121	—	2	6	no	—
117	C₁₃×#121	C₂³	1	3	yes	—
118	C₁₃×#121	C₂³	1	6	yes	—
119	C₁₃×#120	—	2	6	no	—
120	C₄×Q₈×C₁₃	—	2	1	no	—
121	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
122	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
123	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
124	C₄×D₄×C₁₃	—	2	3	no	—
125	C₄×D₄×C₁₃	—	2	3	no	—
126	C₄×D₄×C₁₃	—	2	3	no	—
127	C₄×D₄×C₁₃	—	2	3	no	—
128	C₄×D₄×C₁₃	—	2	3	no	—
129	C₄×D₄×C₁₃	—	2	3	no	—
130	C₄×D₄×C₁₃	—	2	3	no	—
131	C₄×D₄×C₁₃	D₄	1	3	yes	—
132	C₄×D₄×C₁₃	C₂³	1	3	yes	—
133	C₄×D₄×C₁₃	C₂³	1	3	yes	—
134	C₄×D₄×C₁₃	C₂³	1	3	yes	—
135	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
136	C₄×D₄×C₁₃	C₂³	1	3	yes	—
137	C₄×D₄×C₁₃	C₂³	1	3	yes	—
138	C₁₃×#117	—	2	3	no	—
139	C₁₃×#117	D₄	1	3	yes	—
140	C₂×C₁₃×C₄⋊C₄	—	2	3	no	—
141	C₂×C₁₃×C₄⋊C₄	C₂³	1	3	yes	—
142	C₂×C₁₃×C₂²⋊C₄	—	2	3	no	—
143	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
144	C₁₃×#107	C₂³	1	3	yes	—
145	C₁₃×#107	C₂³	1	1	yes	characteristic
146	C₁₃×#106	C₂³	1	3	yes	—
147	C₁₃×#106	C₂³	1	1	yes	characteristic
148	C₁₃×C₄⋊C₈	C₂³	1	3	yes	—
149	C₁₃×C₄⋊C₈	C₂³	1	3	yes	—
150	C₁₃×C₄⋊C₈	C₂³	1	3	yes	—
151	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
152	C₁₃×#103	C₂³	1	3	yes	—
153	C₁₃×#103	C₂³	1	6	yes	—
154	C₁₃×#103	C₂³	1	3	yes	—
155	C₁₃×#102	C₂³	1	3	yes	—
156	C₁₃×#102	C₂³	1	6	yes	—
157	C₁₃×#102	C₂³	1	1	yes	characteristic
158	C₁₃×#102	C₂³	1	3	yes	—
159	C₁₃×#102	C₂³	1	3	yes	—
160	C₁₃×#102	C₂³	1	1	yes	characteristic
161	C₁₃×#102	C₂³	1	3	yes	—
162	C₁₃×C₂²⋊C₈	C₂³	1	3	yes	—
163	C₁₃×C₂²⋊C₈	C₂³	1	3	yes	—
164	C₄×C₈×C₁₃	C₂³	1	3	yes	—
165	C₄×C₈×C₁₃	C₂³	1	3	yes	—
166	#62003	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
167	C₂⁴×C₁₃	—	2	3	no	—
168	C₁₃×#41	—	2	4	no	—
169	C₁₃×#41	—	4	12	no	—
170	C₁₃×#41	—	4	6	no	—
171	C₁₃×#41	—	4	6	no	—
172	C₁₃×#41	—	4	12	no	—
173	C₁₃×#41	—	4	4	no	—
174	C₁₃×#41	—	4	4	no	—
175	C₂×Q₈×C₁₃	—	2	3	no	—
176	C₂×Q₈×C₁₃	—	4	4	no	—
177	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
178	C₂×Q₈×C₁₃	C₂⁴	1	3	yes	—
179	C₂×D₄×C₁₃	—	2	6	no	—
180	C₂×D₄×C₁₃	—	2	6	no	—
181	C₂×D₄×C₁₃	—	2	3	no	—
182	C₂×D₄×C₁₃	—	2	6	no	—
183	C₂×D₄×C₁₃	—	2	3	no	—
184	C₂×D₄×C₁₃	—	2	3	no	—
185	C₂×D₄×C₁₃	—	2	3	no	—
186	C₂×D₄×C₁₃	—	2	3	no	—
187	C₂×D₄×C₁₃	—	2	3	no	—
188	C₂×D₄×C₁₃	—	4	3	no	—
189	C₂×D₄×C₁₃	—	4	12	no	—
190	C₂×D₄×C₁₃	C₂×D₄	1	3	yes	—
191	C₂×D₄×C₁₃	C₂⁴	1	3	yes	—
192	C₂×D₄×C₁₃	C₂⁴	1	3	yes	—
193	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
194	C₂²×C₄×C₁₃	—	2	3	no	—
195	C₂²×C₄×C₁₃	—	2	3	no	—
196	C₂²×C₄×C₁₃	—	2	1	no	—
197	C₂²×C₄×C₁₃	—	2	3	no	—
198	C₂²×C₄×C₁₃	—	2	3	no	—
199	C₂²×C₄×C₁₃	—	2	3	no	—
200	C₂²×C₄×C₁₃	—	2	6	no	—
201	C₂²×C₄×C₁₃	—	4	12	no	—
202	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
203	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
204	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
205	C₁₃×SD₁₆	—	2	6	no	—
206	C₁₃×SD₁₆	—	4	3	no	—
207	C₁₃×SD₁₆	—	4	6	no	—
208	C₁₃×D₈	—	2	6	no	—
209	C₁₃×D₈	—	4	3	no	—
210	C₁₃×D₈	—	4	6	no	—
211	C₁₃×M₁₆	—	4	6	no	—
212	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
213	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
214	C₂×C₈×C₁₃	C₂⁴	1	3	yes	—
215	C₂×C₈×C₁₃	C₂⁴	1	3	yes	—
216	C₁₃×C₄⋊C₄	—	2	3	no	—
217	C₁₃×C₄⋊C₄	—	2	3	no	—
218	C₁₃×C₄⋊C₄	—	2	3	no	—
219	C₁₃×C₄⋊C₄	—	2	1	no	—
220	C₁₃×C₄⋊C₄	—	2	1	no	—
221	C₁₃×C₄⋊C₄	—	2	3	no	—
222	C₁₃×C₄⋊C₄	—	2	3	no	—
223	C₁₃×C₄⋊C₄	—	2	3	no	—
224	C₁₃×C₄⋊C₄	C₂×D₄	1	3	yes	—
225	C₁₃×C₄⋊C₄	C₂×D₄	1	3	yes	—
226	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
227	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
228	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
229	C₁₃×C₄⋊C₄	C₂⁴	1	3	yes	—
230	C₁₃×C₂²⋊C₄	—	2	3	no	—
231	C₁₃×C₂²⋊C₄	—	2	1	no	—
232	C₁₃×C₂²⋊C₄	—	2	3	no	—
233	C₁₃×C₂²⋊C₄	—	2	3	no	—
234	C₁₃×C₂²⋊C₄	—	2	3	no	—
235	C₁₃×C₂²⋊C₄	—	2	3	no	—
236	C₁₃×C₂²⋊C₄	—	2	3	no	—
237	C₁₃×C₂²⋊C₄	—	2	3	no	—
238	C₁₃×C₂²⋊C₄	—	2	6	no	—
239	C₁₃×C₂²⋊C₄	—	2	3	no	—
240	C₁₃×C₂²⋊C₄	C₂×D₄	1	6	yes	—
241	C₄²×C₁₃	—	2	3	no	—
242	C₄²×C₁₃	C₂×D₄	1	3	yes	—
243	C₄²×C₁₃	C₂×D₄	1	3	yes	—
244	C₄²×C₁₃	C₂⁴	1	3	yes	—
245	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
246	#3517	C₂×C₁₃	1	1	yes	characteristic, complemented
247	D₄×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
248	#3392	C₂×C₁₃	1	1	yes	characteristic, complemented
249	#3391	C₂×C₁₃	1	1	yes	characteristic, complemented
250	#3359	C₂×C₁₃	1	1	yes	characteristic, complemented
251	#3358	C₂×C₁₃	1	1	yes	characteristic, complemented
252	#3332	C₂×C₁₃	1	3	yes	complemented
253	#3330	C₂×C₁₃	1	3	yes	complemented
254	#3274	C₂×C₁₃	1	3	yes	complemented
255	#3272	C₂×C₁₃	1	3	yes	complemented
256	#3251	C₂×C₁₃	1	3	yes	complemented
257	#3207	C₂×C₁₃	1	3	yes	complemented
258	#3105	C₂×C₁₃	1	3	yes	complemented
259	#3036	C₂×C₁₃	1	3	yes	complemented
260	#2991	C₂×C₁₃	1	1	yes	characteristic, complemented
261	C₂³×C₁₃	—	2	1	no	—
262	C₂³×C₁₃	—	2	3	no	—
263	C₂³×C₁₃	—	2	3	no	—
264	C₂³×C₁₃	—	4	6	no	—
265	C₂³×C₁₃	—	4	6	no	—
266	C₂³×C₁₃	—	8	3	no	—
267	C₂³×C₁₃	C₂²×D₄	1	3	yes	—
268	Q₈×C₁₃	—	2	3	no	—
269	Q₈×C₁₃	—	2	3	no	—
270	Q₈×C₁₃	—	4	6	no	—
271	Q₈×C₁₃	AGL(1,ℤ/8)	1	4	yes	complemented
272	D₄×C₁₃	—	2	6	no	—
273	D₄×C₁₃	—	2	3	no	—
274	D₄×C₁₃	—	2	3	no	—
275	D₄×C₁₃	—	2	1	no	—
276	D₄×C₁₃	—	2	3	no	—
277	D₄×C₁₃	—	2	3	no	—
278	D₄×C₁₃	—	4	6	no	—
279	D₄×C₁₃	—	4	12	no	—
280	D₄×C₁₃	—	4	6	no	—
281	D₄×C₁₃	—	4	6	no	—
282	D₄×C₁₃	—	8	3	no	—
283	D₄×C₁₃	—	8	3	no	—
284	D₄×C₁₃	—	8	3	no	—
285	D₄×C₁₃	—	8	6	no	—
286	D₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
287	C₂×C₄×C₁₃	—	2	6	no	—
288	C₂×C₄×C₁₃	—	2	3	no	—
289	C₂×C₄×C₁₃	—	2	3	no	—
290	C₂×C₄×C₁₃	—	2	1	no	—
291	C₂×C₄×C₁₃	—	2	3	no	—
292	C₂×C₄×C₁₃	—	2	1	no	—
293	C₂×C₄×C₁₃	—	2	1	no	—
294	C₂×C₄×C₁₃	—	2	3	no	—
295	C₂×C₄×C₁₃	—	4	3	no	—
296	C₂×C₄×C₁₃	—	4	2	no	—
297	C₂×C₄×C₁₃	—	4	6	no	—
298	C₂×C₄×C₁₃	—	4	6	no	—
299	C₂×C₄×C₁₃	—	4	6	no	—
300	C₂×C₄×C₁₃	—	4	6	no	—
301	C₂×C₄×C₁₃	—	4	6	no	—
302	C₂×C₄×C₁₃	—	8	6	no	—
303	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
304	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
305	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
306	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
307	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
308	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
309	C₈×C₁₃	—	2	3	no	—
310	C₈×C₁₃	—	2	3	no	—
311	C₈×C₁₃	—	2	1	no	—
312	C₈×C₁₃	—	2	1	no	—
313	C₂²×#41	—	2	1	no	—
314	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	6	yes	—
315	#557	C₂²×C₁₃	1	1	yes	characteristic, complemented
316	#553	—	2	3	no	—
317	#550	—	2	1	no	—
318	#550	C₂²×C₁₃	1	1	yes	characteristic
319	#550	C₂²×C₁₃	1	3	yes	complemented
320	#550	C₂²×C₁₃	1	1	yes	characteristic, complemented
321	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
322	#548	—	2	1	no	—
323	#547	C₂²×C₁₃	1	3	yes	—
324	#547	C₂²×C₁₃	1	3	yes	complemented
325	#546	—	2	3	no	—
326	D₄²	C₂²×C₁₃	1	3	yes	—
327	#540	—	2	3	no	—
328	#532	C₂²×C₁₃	1	3	yes	—
329	#532	C₂²×C₁₃	1	3	yes	complemented
330	#529	C₂²×C₁₃	1	3	yes	complemented
331	#525	—	2	3	no	—
332	#520	—	2	1	no	—
333	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
334	C₂×C₄×D₄	C₂²×C₁₃	1	3	yes	—
335	#493	C₂²×C₁₃	1	3	yes	complemented
336	#492	C₂²×C₁₃	1	3	yes	complemented
337	#487	C₂²×C₁₃	1	3	yes	complemented
338	#486	C₂²×C₁₃	1	3	yes	complemented
339	#484	C₂²×C₁₃	1	3	yes	complemented
340	#481	C₂²×C₁₃	1	3	yes	complemented
341	#478	C₂²×C₁₃	1	1	yes	characteristic
342	#478	C₂²×C₁₃	1	3	yes	complemented
343	#475	C₂²×C₁₃	1	3	yes	complemented
344	#474	C₂²×C₁₃	1	3	yes	complemented
345	#469	C₂²×C₁₃	1	6	yes	complemented
346	#468	C₂²×C₁₃	1	6	yes	complemented
347	#463	C₂²×C₁₃	1	3	yes	—
348	#463	C₂²×C₁₃	1	3	yes	complemented
349	#463	C₂²×C₁₃	1	6	yes	complemented
350	#461	C₂²×C₁₃	1	3	yes	—
351	#461	C₂²×C₁₃	1	3	yes	complemented
352	#460	C₂²×C₁₃	1	3	yes	complemented
353	#459	C₂²×C₁₃	1	3	yes	—
354	#459	C₂²×C₁₃	1	3	yes	complemented
355	#459	C₂²×C₁₃	1	3	yes	complemented
356	#450	C₂²×C₁₃	1	3	yes	—
357	#449	C₂²×C₁₃	1	6	yes	complemented
358	#449	C₂²×C₁₃	1	6	yes	complemented
359	#447	C₂²×C₁₃	1	3	yes	—
360	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
361	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
362	C₄×SD₁₆	C₂²×C₁₃	1	3	yes	—
363	C₄×SD₁₆	C₂²×C₁₃	1	3	yes	complemented
364	C₄×D₈	C₂²×C₁₃	1	3	yes	—
365	C₄×D₈	C₂²×C₁₃	1	3	yes	complemented
366	#436	C₂²×C₁₃	1	3	yes	complemented
367	#436	C₂²×C₁₃	1	3	yes	complemented
368	#431	C₂²×C₁₃	1	3	yes	complemented
369	#423	C₂²×C₁₃	1	3	yes	complemented
370	#417	C₂²×C₁₃	1	6	yes	complemented
371	C₂²×C₁₃	—	2	3	no	—
372	C₂²×C₁₃	—	2	3	no	—
373	C₂²×C₁₃	—	2	2	no	—
374	C₂²×C₁₃	—	2	3	no	—
375	C₂²×C₁₃	—	4	1	no	—
376	C₂²×C₁₃	—	4	1	no	—
377	C₂²×C₁₃	—	4	3	no	—
378	C₂²×C₁₃	—	4	3	no	—
379	C₂²×C₁₃	—	4	3	no	—
380	C₂²×C₁₃	—	4	3	no	—
381	C₂²×C₁₃	—	4	3	no	—
382	C₂²×C₁₃	—	4	3	no	—
383	C₂²×C₁₃	—	8	12	no	—
384	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
385	C₄×C₁₃	—	2	1	no	—
386	C₄×C₁₃	—	2	3	no	—
387	C₄×C₁₃	—	2	3	no	—
388	C₄×C₁₃	—	2	1	no	—
389	C₄×C₁₃	—	4	1	no	—
390	C₄×C₁₃	—	4	3	no	—
391	C₄×C₁₃	—	4	1	no	—
392	C₄×C₁₃	—	4	1	no	—
393	C₄×C₁₃	—	4	3	no	—
394	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	6	yes	—
395	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
396	C₄×C₁₃	#585	1	1	yes	characteristic
397	C₂×#41	—	2	1	no	—
398	C₂×#41	—	2	1	no	—
399	C₂×#41	—	2	3	no	—
400	C₂×#41	—	2	3	no	—
401	C₂×#41	—	4	8	no	—
402	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
403	C₂×#41	C₂³×C₁₃	1	6	yes	—
404	C₂²×Q₈	—	2	1	no	—
405	C₂²×D₄	—	2	3	no	—
406	C₂²×D₄	C₂³×C₁₃	1	3	yes	—
407	C₂³×C₄	—	2	3	no	—
408	AGL(1,ℤ/8)	—	4	12	no	—
409	C₂×SD₁₆	C₂³×C₁₃	1	3	yes	—
410	C₂×SD₁₆	C₂³×C₁₃	1	6	yes	—
411	C₂×SD₁₆	C₂³×C₁₃	1	3	yes	—
412	C₂×D₈	C₂³×C₁₃	1	3	yes	—
413	C₂×D₈	C₂³×C₁₃	1	6	yes	—
414	C₂×D₈	C₂³×C₁₃	1	3	yes	—
415	C₂×M₁₆	C₂³×C₁₃	1	6	yes	—
416	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
417	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
418	#127	—	2	3	no	—
419	#127	C₂³×C₁₃	1	3	yes	—
420	#127	C₂³×C₁₃	1	3	yes	—
421	#126	—	2	3	no	—
422	#125	—	2	3	no	—
423	#125	C₂³×C₁₃	1	1	yes	characteristic
424	#124	—	2	3	no	—
425	#124	C₂³×C₁₃	1	3	yes	—
426	#123	—	2	3	no	—
427	#123	—	2	6	no	—
428	#123	—	2	6	no	—
429	C₂²⋊Q₈	—	2	3	no	—
430	C₂²⋊Q₈	—	2	3	no	—
431	C₂²⋊Q₈	C₂³×C₁₃	1	3	yes	—
432	#121	—	2	3	no	—
433	#121	—	2	3	no	—
434	#121	—	2	3	no	—
435	#121	—	2	3	no	—
436	#121	—	2	3	no	—
437	#121	—	2	3	no	—
438	#121	—	2	3	no	—
439	#121	—	2	6	no	—
440	#121	C₂³×C₁₃	1	3	yes	—
441	#121	C₂³×C₁₃	1	6	yes	—
442	#120	—	2	6	no	—
443	C₄×Q₈	—	2	1	no	—
444	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
445	C₄×Q₈	C₂³×C₁₃	1	3	yes	—
446	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
447	C₄×D₄	—	2	3	no	—
448	C₄×D₄	—	2	3	no	—
449	C₄×D₄	—	2	3	no	—
450	C₄×D₄	—	2	3	no	—
451	C₄×D₄	—	2	3	no	—
452	C₄×D₄	—	2	3	no	—
453	C₄×D₄	—	2	3	no	—
454	C₄×D₄	D₄×C₁₃	1	3	yes	—
455	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
456	C₄×D₄	C₂³×C₁₃	1	3	yes	—
457	C₄×D₄	C₂³×C₁₃	1	3	yes	—
458	C₄×D₄	C₂³×C₁₃	1	3	yes	—
459	C₄×D₄	C₂³×C₁₃	1	3	yes	—
460	C₄×D₄	C₂³×C₁₃	1	3	yes	—
461	#117	—	2	3	no	—
462	#117	D₄×C₁₃	1	3	yes	—
463	C₂×C₄⋊C₄	—	2	3	no	—
464	C₂×C₄⋊C₄	C₂³×C₁₃	1	3	yes	—
465	C₂×C₂²⋊C₄	—	2	3	no	—
466	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
467	#107	C₂³×C₁₃	1	3	yes	—
468	#107	C₂³×C₁₃	1	1	yes	characteristic
469	#106	C₂³×C₁₃	1	3	yes	—
470	#106	C₂³×C₁₃	1	1	yes	characteristic
471	C₄⋊C₈	C₂³×C₁₃	1	3	yes	—
472	C₄⋊C₈	C₂³×C₁₃	1	3	yes	—
473	C₄⋊C₈	C₂³×C₁₃	1	3	yes	—
474	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
475	#103	C₂³×C₁₃	1	3	yes	—
476	#103	C₂³×C₁₃	1	6	yes	—
477	#103	C₂³×C₁₃	1	3	yes	—
478	#102	C₂³×C₁₃	1	3	yes	—
479	#102	C₂³×C₁₃	1	6	yes	—
480	#102	C₂³×C₁₃	1	1	yes	characteristic
481	#102	C₂³×C₁₃	1	3	yes	—
482	#102	C₂³×C₁₃	1	3	yes	—
483	#102	C₂³×C₁₃	1	1	yes	characteristic
484	#102	C₂³×C₁₃	1	3	yes	—
485	C₂²⋊C₈	C₂³×C₁₃	1	3	yes	—
486	C₂²⋊C₈	C₂³×C₁₃	1	3	yes	—
487	C₄×C₈	C₂³×C₁₃	1	3	yes	—
488	C₄×C₈	C₂³×C₁₃	1	3	yes	—
489	C₂×C₁₃	—	4	3	no	—
490	C₂×C₁₃	—	4	2	no	—
491	C₂×C₁₃	—	8	3	no	—
492	C₂×C₁₃	—	8	3	no	—
493	C₂×C₁₃	#3488	1	1	yes	characteristic
494	C₂×C₁₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
495	C₂×C₁₃	#3584	1	1	yes	characteristic
496	C₂⁴	—	2	3	no	—
497	#41	—	2	4	no	—
498	#41	—	4	12	no	—
499	#41	—	4	6	no	—
500	#41	—	4	6	no	—
501	#41	—	4	12	no	—
502	#41	—	4	4	no	—
503	#41	—	4	4	no	—
504	C₂×Q₈	—	2	3	no	—
505	C₂×Q₈	—	4	4	no	—
506	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
507	C₂×Q₈	C₂⁴×C₁₃	1	3	yes	—
508	C₂×D₄	—	2	6	no	—
509	C₂×D₄	—	2	6	no	—
510	C₂×D₄	—	2	3	no	—
511	C₂×D₄	—	2	6	no	—
512	C₂×D₄	—	2	3	no	—
513	C₂×D₄	—	2	3	no	—
514	C₂×D₄	—	2	3	no	—
515	C₂×D₄	—	2	3	no	—
516	C₂×D₄	—	2	3	no	—
517	C₂×D₄	—	4	3	no	—
518	C₂×D₄	—	4	12	no	—
519	C₂×D₄	C₂×D₄×C₁₃	1	3	yes	—
520	C₂×D₄	C₂⁴×C₁₃	1	3	yes	—
521	C₂×D₄	C₂⁴×C₁₃	1	3	yes	—
522	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
523	C₂²×C₄	—	2	3	no	—
524	C₂²×C₄	—	2	3	no	—
525	C₂²×C₄	—	2	1	no	—
526	C₂²×C₄	—	2	3	no	—
527	C₂²×C₄	—	2	3	no	—
528	C₂²×C₄	—	2	3	no	—
529	C₂²×C₄	—	2	6	no	—
530	C₂²×C₄	—	4	12	no	—
531	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
532	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
533	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
534	SD₁₆	—	2	6	no	—
535	SD₁₆	—	4	6	no	—
536	SD₁₆	—	4	3	no	—
537	D₈	—	2	6	no	—
538	D₈	—	4	6	no	—
539	D₈	—	4	3	no	—
540	M₁₆	—	4	6	no	—
541	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
542	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
543	C₂×C₈	C₂⁴×C₁₃	1	3	yes	—
544	C₂×C₈	C₂⁴×C₁₃	1	3	yes	—
545	C₄⋊C₄	—	2	3	no	—
546	C₄⋊C₄	—	2	3	no	—
547	C₄⋊C₄	—	2	3	no	—
548	C₄⋊C₄	—	2	1	no	—
549	C₄⋊C₄	—	2	1	no	—
550	C₄⋊C₄	—	2	3	no	—
551	C₄⋊C₄	—	2	3	no	—
552	C₄⋊C₄	—	2	3	no	—
553	C₄⋊C₄	C₂×D₄×C₁₃	1	3	yes	—
554	C₄⋊C₄	C₂×D₄×C₁₃	1	3	yes	—
555	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
556	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
557	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
558	C₄⋊C₄	C₂⁴×C₁₃	1	3	yes	—
559	C₂²⋊C₄	—	2	3	no	—
560	C₂²⋊C₄	—	2	1	no	—
561	C₂²⋊C₄	—	2	3	no	—
562	C₂²⋊C₄	—	2	3	no	—
563	C₂²⋊C₄	—	2	3	no	—
564	C₂²⋊C₄	—	2	3	no	—
565	C₂²⋊C₄	—	2	3	no	—
566	C₂²⋊C₄	—	2	3	no	—
567	C₂²⋊C₄	—	2	6	no	—
568	C₂²⋊C₄	—	2	3	no	—
569	C₂²⋊C₄	C₂×D₄×C₁₃	1	6	yes	—
570	C₄²	—	2	3	no	—
571	C₄²	C₂×D₄×C₁₃	1	3	yes	—
572	C₄²	C₂×D₄×C₁₃	1	3	yes	—
573	C₄²	C₂⁴×C₁₃	1	3	yes	—
574	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
575	C₁₃	#62003	1	1	yes	characteristic, direct product factor, Sylow
576	C₂³	—	2	1	no	—
577	C₂³	—	2	3	no	—
578	C₂³	—	2	3	no	—
579	C₂³	—	4	6	no	—
580	C₂³	—	4	6	no	—
581	C₂³	—	8	3	no	—
582	C₂³	C₂²×D₄×C₁₃	1	3	yes	—
583	Q₈	—	2	3	no	—
584	Q₈	—	2	3	no	—
585	Q₈	—	4	6	no	—
586	Q₈	C₁₃×AGL(1,ℤ/8)	1	4	yes	complemented
587	D₄	—	2	6	no	—
588	D₄	—	2	3	no	—
589	D₄	—	2	3	no	—
590	D₄	—	2	1	no	—
591	D₄	—	2	3	no	—
592	D₄	—	2	3	no	—
593	D₄	—	4	6	no	—
594	D₄	—	4	12	no	—
595	D₄	—	4	6	no	—
596	D₄	—	4	6	no	—
597	D₄	—	8	3	no	—
598	D₄	—	8	3	no	—
599	D₄	—	8	3	no	—
600	D₄	—	8	6	no	—
601	D₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
602	C₂×C₄	—	2	6	no	—
603	C₂×C₄	—	2	3	no	—
604	C₂×C₄	—	2	3	no	—
605	C₂×C₄	—	2	1	no	—
606	C₂×C₄	—	2	3	no	—
607	C₂×C₄	—	2	1	no	—
608	C₂×C₄	—	2	1	no	—
609	C₂×C₄	—	2	3	no	—
610	C₂×C₄	—	4	3	no	—
611	C₂×C₄	—	4	2	no	—
612	C₂×C₄	—	4	6	no	—
613	C₂×C₄	—	4	6	no	—
614	C₂×C₄	—	4	6	no	—
615	C₂×C₄	—	4	6	no	—
616	C₂×C₄	—	4	6	no	—
617	C₂×C₄	—	8	6	no	—
618	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
619	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
620	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
621	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
622	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
623	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
624	C₈	—	2	3	no	—
625	C₈	—	2	3	no	—
626	C₈	—	2	1	no	—
627	C₈	—	2	1	no	—
628	C₂²	—	2	3	no	—
629	C₂²	—	2	3	no	—
630	C₂²	—	2	3	no	—
631	C₂²	—	2	2	no	—
632	C₂²	—	4	1	no	—
633	C₂²	—	4	1	no	—
634	C₂²	—	4	3	no	—
635	C₂²	—	4	3	no	—
636	C₂²	—	4	3	no	—
637	C₂²	—	4	3	no	—
638	C₂²	—	4	3	no	—
639	C₂²	—	4	3	no	—
640	C₂²	—	8	12	no	—
641	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
642	C₄	—	2	1	no	—
643	C₄	—	2	1	no	—
644	C₄	—	2	3	no	—
645	C₄	—	2	3	no	—
646	C₄	—	4	1	no	—
647	C₄	—	4	1	no	—
648	C₄	—	4	3	no	—
649	C₄	—	4	1	no	—
650	C₄	—	4	3	no	—
651	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	6	yes	—
652	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
653	C₄	C₁₃×#585	1	1	yes	characteristic
654	C₂	—	4	3	no	—
655	C₂	—	4	2	no	—
656	C₂	—	8	3	no	—
657	C₂	—	8	3	no	—
658	C₂	C₁₃×#3488	1	1	yes	characteristic
659	C₂	C₂²×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
660	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 ◁ C₄×C₁₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3517	C₂	semidirect
2. D₄×C₁₃×#41	C₂	semidirect
3. C₁₃×#3392	C₂	semidirect
4. C₁₃×#3391	C₂	semidirect
5. C₁₃×#3359	C₂	semidirect
6. C₁₃×#3358	C₂	semidirect
7. C₁₃×#3332	C₂	semidirect
8. C₁₃×#3330	C₂	semidirect
9. C₁₃×#3274	C₂	semidirect
10. C₁₃×#3272	C₂	semidirect
11. C₁₃×#3251	C₂	semidirect
12. C₁₃×#3207	C₂	semidirect
13. C₁₃×#3105	C₂	semidirect
14. C₁₃×#3036	C₂	semidirect
15. C₁₃×#2991	C₂	semidirect
18. C₁₃×#557	C₂²	semidirect
22. C₁₃×#550	C₂²	semidirect
23. C₁₃×#550	C₂²	semidirect
27. C₁₃×#547	C₂²	semidirect
32. C₁₃×#532	C₂²	semidirect
33. C₁₃×#529	C₂²	semidirect
38. C₁₃×#493	C₂²	semidirect
39. C₁₃×#492	C₂²	semidirect
40. C₁₃×#487	C₂²	semidirect
41. C₁₃×#486	C₂²	semidirect
42. C₁₃×#484	C₂²	semidirect
43. C₁₃×#481	C₂²	semidirect
45. C₁₃×#478	C₂²	semidirect
46. C₁₃×#475	C₂²	semidirect
47. C₁₃×#474	C₂²	semidirect
48. C₁₃×#469	C₂²	semidirect
49. C₁₃×#468	C₂²	semidirect
51. C₁₃×#463	C₂²	semidirect
52. C₁₃×#463	C₂²	semidirect
54. C₁₃×#461	C₂²	semidirect
55. C₁₃×#460	C₂²	semidirect
57. C₁₃×#459	C₂²	semidirect
58. C₁₃×#459	C₂²	semidirect
60. C₁₃×#449	C₂²	semidirect
61. C₁₃×#449	C₂²	semidirect
63. C₈×Q₈×C₁₃	C₂²	semidirect
64. C₈×Q₈×C₁₃	C₂²	semidirect
66. C₄×C₁₃×SD₁₆	C₂²	semidirect
68. C₄×C₁₃×D₈	C₂²	semidirect
69. C₁₃×#436	C₂²	semidirect
70. C₁₃×#436	C₂²	semidirect
71. C₁₃×#431	C₂²	semidirect
72. C₁₃×#423	C₂²	semidirect
73. C₁₃×#417	C₂²	semidirect
166. #62003	C₁₃	direct (N × H)
246. #3517	C₂×C₁₃	semidirect
247. D₄×#41	C₂×C₁₃	semidirect
248. #3392	C₂×C₁₃	semidirect
249. #3391	C₂×C₁₃	semidirect
250. #3359	C₂×C₁₃	semidirect
251. #3358	C₂×C₁₃	semidirect
252. #3332	C₂×C₁₃	semidirect
253. #3330	C₂×C₁₃	semidirect
254. #3274	C₂×C₁₃	semidirect
255. #3272	C₂×C₁₃	semidirect
256. #3251	C₂×C₁₃	semidirect
257. #3207	C₂×C₁₃	semidirect
258. #3105	C₂×C₁₃	semidirect
259. #3036	C₂×C₁₃	semidirect
260. #2991	C₂×C₁₃	semidirect
271. Q₈×C₁₃	AGL(1,ℤ/8)	semidirect
315. #557	C₂²×C₁₃	semidirect
319. #550	C₂²×C₁₃	semidirect
320. #550	C₂²×C₁₃	semidirect
324. #547	C₂²×C₁₃	semidirect
329. #532	C₂²×C₁₃	semidirect
330. #529	C₂²×C₁₃	semidirect
335. #493	C₂²×C₁₃	semidirect
336. #492	C₂²×C₁₃	semidirect
337. #487	C₂²×C₁₃	semidirect
338. #486	C₂²×C₁₃	semidirect
339. #484	C₂²×C₁₃	semidirect
340. #481	C₂²×C₁₃	semidirect
342. #478	C₂²×C₁₃	semidirect
343. #475	C₂²×C₁₃	semidirect
344. #474	C₂²×C₁₃	semidirect
345. #469	C₂²×C₁₃	semidirect
346. #468	C₂²×C₁₃	semidirect
348. #463	C₂²×C₁₃	semidirect
349. #463	C₂²×C₁₃	semidirect
351. #461	C₂²×C₁₃	semidirect
352. #460	C₂²×C₁₃	semidirect
354. #459	C₂²×C₁₃	semidirect
355. #459	C₂²×C₁₃	semidirect
357. #449	C₂²×C₁₃	semidirect
358. #449	C₂²×C₁₃	semidirect
360. C₈×Q₈	C₂²×C₁₃	semidirect
361. C₈×Q₈	C₂²×C₁₃	semidirect
363. C₄×SD₁₆	C₂²×C₁₃	semidirect
365. C₄×D₈	C₂²×C₁₃	semidirect
366. #436	C₂²×C₁₃	semidirect
367. #436	C₂²×C₁₃	semidirect
368. #431	C₂²×C₁₃	semidirect
369. #423	C₂²×C₁₃	semidirect
370. #417	C₂²×C₁₃	semidirect
575. C₁₃	#62003	direct (N × H)
586. Q₈	C₁₃×AGL(1,ℤ/8)	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#3517	2
D₄×C₁₃×#41	2
C₁₃×#3392	2
C₁₃×#3391	2
C₁₃×#3359	2
C₁₃×#3358	2
C₁₃×#3332	2
C₁₃×#3330	2
C₁₃×#3274	2
C₁₃×#3272	2
C₁₃×#3251	2
C₁₃×#3207	2
C₁₃×#3105	2
C₁₃×#3036	2
C₁₃×#2991	2
#62003	13

Subgroups — C13×#62003 #15748342

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62003 #15748342