Subgroups — C₁₃×#18678 #15705017

Order 3328.

1000 conjugacy classes of subgroups.

The subgroup lattice has 592 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	1	yes	maximal, characteristic, complemented
2	C₁₃×#3246	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3169	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3036	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1650	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1642	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1628	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1621	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1547	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1493	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×AGL(1,ℤ/8)	—	2	1	no	—
13	C₁₃×#559	—	2	2	no	—
14	C₁₃×#556	C₂²	1	2	yes	—
15	C₁₃×#555	—	2	1	no	—
16	C₁₃×#553	—	2	2	no	—
17	C₁₃×#550	C₂²	1	2	yes	—
18	C₁₃×#547	—	2	1	no	—
19	C₁₃×#538	—	2	2	no	—
20	C₁₃×#535	—	2	1	no	—
21	C₁₃×#533	C₂²	1	1	yes	characteristic
22	C₁₃×#532	C₂²	1	1	yes	characteristic
23	C₁₃×#532	C₂²	1	1	yes	characteristic
24	C₁₃×#525	—	2	2	no	—
25	C₁₃×#520	—	2	1	no	—
26	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
27	C₁₃×#500	C₂²	1	1	yes	characteristic, complemented
28	C₁₃×#493	C₂²	1	1	yes	characteristic, complemented
29	C₁₃×#486	C₂²	1	1	yes	characteristic, complemented
30	C₁₃×#486	C₂²	1	1	yes	characteristic, complemented
31	C₁₃×#476	—	2	1	no	—
32	C₁₃×#475	C₂²	1	2	yes	complemented
33	C₁₃×#466	—	2	2	no	—
34	C₁₃×#465	—	2	2	no	—
35	C₁₃×#463	—	2	2	no	—
36	C₁₃×#461	—	2	1	no	—
37	C₁₃×#461	C₂²	1	2	yes	—
38	C₁₃×#460	C₂²	1	2	yes	complemented
39	C₁₃×#459	C₂²	1	2	yes	—
40	C₄×C₁₃×D₈	—	2	2	no	—
41	C₁₃×#423	C₂²	1	1	yes	characteristic
42	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
43	C₁₃×#417	—	2	1	no	—
44	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
45	C₁₃×#332	C₂²	1	2	yes	complemented
46	C₁₃×#331	C₂²	1	2	yes	complemented
47	C₁₃×Q₈⋊C₈	C₂²	1	2	yes	complemented
48	C₁₃×Q₈⋊C₈	C₂²	1	2	yes	complemented
49	C₁₃×D₄⋊C₈	C₂²	1	2	yes	—
50	C₁₃×D₄⋊C₈	C₂²	1	2	yes	—
51	C₂×C₁₃×#41	—	2	2	no	—
52	C₂×C₁₃×#41	—	2	1	no	—
53	C₂×C₁₃×#41	—	2	1	no	—
54	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
55	C₂³×C₄×C₁₃	—	2	1	no	—
56	C₁₃×AGL(1,ℤ/8)	—	4	4	no	—
57	C₂×C₁₃×SD₁₆	—	2	2	no	—
58	C₂×C₁₃×SD₁₆	—	2	2	no	—
59	C₂×C₁₃×D₈	—	2	2	no	—
60	C₂×C₁₃×D₈	—	2	2	no	—
61	C₂×C₁₃×M₁₆	—	2	1	no	—
62	C₂²×C₈×C₁₃	—	2	1	no	—
63	C₂²×C₈×C₁₃	—	2	1	no	—
64	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
65	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
66	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
67	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
68	C₁₃×#127	—	2	2	no	—
69	C₁₃×#127	C₂³	1	1	yes	characteristic
70	C₁₃×#127	C₂³	1	1	yes	characteristic
71	C₁₃×#126	—	2	4	no	—
72	C₁₃×#125	—	2	1	no	—
73	C₁₃×#124	—	2	4	no	—
74	C₁₃×#124	—	2	2	no	—
75	C₁₃×#124	—	2	1	no	—
76	C₁₃×#124	—	2	1	no	—
77	C₁₃×#123	—	2	4	no	—
78	C₁₃×#123	—	2	4	no	—
79	C₁₃×C₂²⋊Q₈	—	2	2	no	—
80	C₁₃×C₂²⋊Q₈	—	2	1	no	—
81	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
82	C₁₃×#121	—	2	2	no	—
83	C₁₃×#121	—	2	2	no	—
84	C₁₃×#121	—	2	4	no	—
85	C₁₃×#121	—	2	1	no	—
86	C₁₃×#121	—	2	2	no	—
87	C₁₃×#121	—	2	1	no	—
88	C₁₃×#121	—	2	1	no	—
89	C₁₃×#121	D₄	1	2	yes	—
90	C₁₃×#120	—	2	4	no	—
91	C₄×Q₈×C₁₃	—	2	2	no	—
92	C₄×Q₈×C₁₃	—	2	1	no	—
93	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
94	C₄×D₄×C₁₃	—	2	4	no	—
95	C₄×D₄×C₁₃	—	2	4	no	—
96	C₄×D₄×C₁₃	—	2	2	no	—
97	C₄×D₄×C₁₃	—	2	1	no	—
98	C₄×D₄×C₁₃	—	2	1	no	—
99	C₄×D₄×C₁₃	—	2	1	no	—
100	C₄×D₄×C₁₃	—	2	1	no	—
101	C₄×D₄×C₁₃	—	2	1	no	—
102	C₄×D₄×C₁₃	D₄	1	2	yes	—
103	C₄×D₄×C₁₃	D₄	1	2	yes	—
104	C₄×D₄×C₁₃	C₂³	1	2	yes	—
105	C₁₃×#117	—	2	2	no	—
106	C₁₃×#117	—	2	1	no	—
107	C₁₃×#117	—	2	2	no	—
108	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
109	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
110	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
111	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
112	C₁₃×#107	—	2	2	no	—
113	C₁₃×#106	—	2	2	no	—
114	C₁₃×C₄⋊C₈	—	2	1	no	—
115	C₁₃×C₄⋊C₈	—	2	1	no	—
116	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
117	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
118	C₁₃×#103	—	2	2	no	—
119	C₁₃×#103	—	2	2	no	—
120	C₁₃×#102	—	2	2	no	—
121	C₁₃×#102	—	2	2	no	—
122	C₁₃×#102	—	2	2	no	—
123	C₁₃×#102	—	2	2	no	—
124	C₄×C₈×C₁₃	—	2	1	no	—
125	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
126	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
127	#18678	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
128	C₂⁴×C₁₃	—	2	1	no	—
129	C₁₃×#41	—	4	2	no	—
130	C₁₃×#41	—	4	2	no	—
131	C₁₃×#41	—	4	2	no	—
132	C₁₃×#41	—	4	2	no	—
133	C₁₃×#41	—	8	2	no	—
134	C₁₃×#41	—	8	2	no	—
135	C₂×Q₈×C₁₃	—	2	1	no	—
136	C₂×Q₈×C₁₃	—	2	1	no	—
137	C₂×Q₈×C₁₃	—	2	1	no	—
138	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
139	C₂×D₄×C₁₃	—	2	2	no	—
140	C₂×D₄×C₁₃	—	2	4	no	—
141	C₂×D₄×C₁₃	—	2	4	no	—
142	C₂×D₄×C₁₃	—	2	1	no	—
143	C₂×D₄×C₁₃	—	2	2	no	—
144	C₂×D₄×C₁₃	—	2	2	no	—
145	C₂×D₄×C₁₃	—	2	1	no	—
146	C₂×D₄×C₁₃	—	2	1	no	—
147	C₂×D₄×C₁₃	—	2	1	no	—
148	C₂×D₄×C₁₃	—	2	1	no	—
149	C₂×D₄×C₁₃	—	2	1	no	—
150	C₂×D₄×C₁₃	—	4	1	no	—
151	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
152	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
153	C₂²×C₄×C₁₃	—	2	4	no	—
154	C₂²×C₄×C₁₃	—	2	1	no	—
155	C₂²×C₄×C₁₃	—	2	2	no	—
156	C₂²×C₄×C₁₃	—	2	2	no	—
157	C₂²×C₄×C₁₃	—	2	2	no	—
158	C₂²×C₄×C₁₃	—	4	1	no	—
159	C₂²×C₄×C₁₃	—	8	1	no	—
160	C₂²×C₄×C₁₃	—	8	1	no	—
161	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
164	C₁₃×SD₁₆	—	4	4	no	—
165	C₁₃×SD₁₆	—	8	2	no	—
166	C₁₃×D₈	—	4	4	no	—
167	C₁₃×D₈	—	4	4	no	—
168	C₁₃×M₁₆	—	4	2	no	—
169	C₂×C₈×C₁₃	—	2	1	no	—
170	C₂×C₈×C₁₃	—	2	1	no	—
171	C₂×C₈×C₁₃	—	2	2	no	—
172	C₂×C₈×C₁₃	—	2	2	no	—
173	C₂×C₈×C₁₃	—	4	2	no	—
174	C₂×C₈×C₁₃	—	8	1	no	—
175	C₁₃×C₄⋊C₄	—	2	4	no	—
176	C₁₃×C₄⋊C₄	—	2	1	no	—
177	C₁₃×C₄⋊C₄	—	2	1	no	—
178	C₁₃×C₄⋊C₄	—	2	1	no	—
179	C₁₃×C₄⋊C₄	—	2	2	no	—
180	C₁₃×C₄⋊C₄	—	2	1	no	—
181	C₁₃×C₄⋊C₄	—	2	1	no	—
182	C₁₃×C₄⋊C₄	—	2	2	no	—
183	C₁₃×C₄⋊C₄	—	2	1	no	—
184	C₁₃×C₄⋊C₄	—	2	1	no	—
185	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
186	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
187	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
188	C₁₃×C₂²⋊C₄	—	2	4	no	—
189	C₁₃×C₂²⋊C₄	—	2	4	no	—
190	C₁₃×C₂²⋊C₄	—	2	4	no	—
191	C₁₃×C₂²⋊C₄	—	2	2	no	—
192	C₁₃×C₂²⋊C₄	—	2	2	no	—
193	C₁₃×C₂²⋊C₄	—	2	2	no	—
194	C₁₃×C₂²⋊C₄	—	2	2	no	—
195	C₁₃×C₂²⋊C₄	—	2	2	no	—
196	C₁₃×C₂²⋊C₄	—	4	1	no	—
197	C₁₃×C₂²⋊C₄	—	4	1	no	—
198	C₄²×C₁₃	—	2	4	no	—
199	C₄²×C₁₃	—	2	2	no	—
200	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
201	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
202	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
203	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
204	#3506	C₂×C₁₃	1	1	yes	characteristic, complemented
205	#3246	C₂×C₁₃	1	1	yes	characteristic, complemented
206	#3169	C₂×C₁₃	1	1	yes	characteristic, complemented
207	#3036	C₂×C₁₃	1	1	yes	characteristic, complemented
208	#1650	C₂×C₁₃	1	2	yes	complemented
209	#1642	C₂×C₁₃	1	2	yes	complemented
210	#1628	C₂×C₁₃	1	2	yes	complemented
211	#1621	C₂×C₁₃	1	2	yes	complemented
212	#1547	C₂×C₁₃	1	1	yes	characteristic, complemented
213	#1493	C₂×C₁₃	1	1	yes	characteristic, complemented
214	C₂×D₄⋊C₈	C₂×C₁₃	1	1	yes	characteristic, complemented
215	C₂³×C₁₃	—	2	2	no	—
216	C₂³×C₁₃	—	2	2	no	—
217	C₂³×C₁₃	—	4	2	no	—
218	C₂³×C₁₃	—	4	1	no	—
219	C₂³×C₁₃	—	8	1	no	—
220	C₂³×C₁₃	—	8	1	no	—
221	C₂³×C₁₃	#120	1	1	yes	characteristic
222	Q₈×C₁₃	—	2	2	no	—
223	Q₈×C₁₃	—	2	2	no	—
224	Q₈×C₁₃	—	4	1	no	—
225	Q₈×C₁₃	—	4	1	no	—
226	Q₈×C₁₃	—	4	1	no	—
227	Q₈×C₁₃	—	4	1	no	—
228	Q₈×C₁₃	—	8	1	no	—
229	D₄×C₁₃	—	2	2	no	—
230	D₄×C₁₃	—	2	2	no	—
231	D₄×C₁₃	—	4	2	no	—
232	D₄×C₁₃	—	4	2	no	—
233	D₄×C₁₃	—	4	4	no	—
234	D₄×C₁₃	—	4	1	no	—
235	D₄×C₁₃	—	4	1	no	—
236	D₄×C₁₃	—	4	1	no	—
237	D₄×C₁₃	—	4	1	no	—
238	D₄×C₁₃	—	4	1	no	—
239	D₄×C₁₃	—	4	1	no	—
240	D₄×C₁₃	—	4	1	no	—
241	D₄×C₁₃	—	4	1	no	—
242	D₄×C₁₃	—	4	2	no	—
243	D₄×C₁₃	—	8	4	no	—
244	D₄×C₁₃	—	8	4	no	—
245	D₄×C₁₃	—	8	2	no	—
246	C₂×C₄×C₁₃	—	2	1	no	—
247	C₂×C₄×C₁₃	—	2	1	no	—
248	C₂×C₄×C₁₃	—	2	2	no	—
249	C₂×C₄×C₁₃	—	2	2	no	—
250	C₂×C₄×C₁₃	—	2	2	no	—
251	C₂×C₄×C₁₃	—	2	2	no	—
252	C₂×C₄×C₁₃	—	4	1	no	—
253	C₂×C₄×C₁₃	—	4	2	no	—
254	C₂×C₄×C₁₃	—	4	2	no	—
255	C₂×C₄×C₁₃	—	4	4	no	—
256	C₂×C₄×C₁₃	—	4	1	no	—
257	C₂×C₄×C₁₃	—	8	2	no	—
258	C₂×C₄×C₁₃	—	8	1	no	—
259	C₂×C₄×C₁₃	—	8	4	no	—
260	C₂×C₄×C₁₃	—	8	2	no	—
261	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
262	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
263	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
264	C₂×C₄×C₁₃	#135	1	2	yes	—
265	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
266	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
267	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
268	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
269	C₈×C₁₃	—	2	2	no	—
270	C₈×C₁₃	—	4	1	no	—
271	C₈×C₁₃	—	4	2	no	—
272	C₈×C₁₃	—	4	2	no	—
273	C₂×AGL(1,ℤ/8)	—	2	1	no	—
274	#559	—	2	2	no	—
275	#556	C₂²×C₁₃	1	2	yes	—
276	#555	—	2	1	no	—
277	#553	—	2	2	no	—
278	#550	C₂²×C₁₃	1	2	yes	—
279	#547	—	2	1	no	—
280	#538	—	2	2	no	—
281	#535	—	2	1	no	—
282	#533	C₂²×C₁₃	1	1	yes	characteristic
283	#532	C₂²×C₁₃	1	1	yes	characteristic
284	#532	C₂²×C₁₃	1	1	yes	characteristic
285	#525	—	2	2	no	—
286	#520	—	2	1	no	—
287	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
288	#500	C₂²×C₁₃	1	1	yes	characteristic, complemented
289	#493	C₂²×C₁₃	1	1	yes	characteristic, complemented
290	#486	C₂²×C₁₃	1	1	yes	characteristic, complemented
291	#486	C₂²×C₁₃	1	1	yes	characteristic, complemented
292	#476	—	2	1	no	—
293	#475	C₂²×C₁₃	1	2	yes	complemented
294	#466	—	2	2	no	—
295	#465	—	2	2	no	—
296	#463	—	2	2	no	—
297	#461	—	2	1	no	—
298	#461	C₂²×C₁₃	1	2	yes	—
299	#460	C₂²×C₁₃	1	2	yes	complemented
300	#459	C₂²×C₁₃	1	2	yes	—
301	C₄×D₈	—	2	2	no	—
302	#423	C₂²×C₁₃	1	1	yes	characteristic
303	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
304	#417	—	2	1	no	—
305	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
306	#332	C₂²×C₁₃	1	2	yes	complemented
307	#331	C₂²×C₁₃	1	2	yes	complemented
308	Q₈⋊C₈	C₂²×C₁₃	1	2	yes	complemented
309	Q₈⋊C₈	C₂²×C₁₃	1	2	yes	complemented
310	D₄⋊C₈	C₂²×C₁₃	1	2	yes	—
311	D₄⋊C₈	C₂²×C₁₃	1	2	yes	—
312	C₂²×C₁₃	—	2	1	no	—
313	C₂²×C₁₃	—	2	1	no	—
314	C₂²×C₁₃	—	4	2	no	—
315	C₂²×C₁₃	—	4	2	no	—
316	C₂²×C₁₃	—	4	2	no	—
317	C₂²×C₁₃	—	4	2	no	—
318	C₂²×C₁₃	—	4	2	no	—
319	C₂²×C₁₃	—	4	2	no	—
320	C₂²×C₁₃	—	8	4	no	—
321	C₂²×C₁₃	—	8	1	no	—
322	C₂²×C₁₃	—	8	1	no	—
323	C₂²×C₁₃	—	8	1	no	—
324	C₂²×C₁₃	#449	1	2	yes	—
325	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
326	C₄×C₁₃	—	2	1	no	—
327	C₄×C₁₃	—	2	1	no	—
328	C₄×C₁₃	—	2	1	no	—
329	C₄×C₁₃	—	4	2	no	—
330	C₄×C₁₃	—	4	2	no	—
331	C₄×C₁₃	—	4	2	no	—
332	C₄×C₁₃	—	4	2	no	—
333	C₄×C₁₃	—	8	1	no	—
334	C₄×C₁₃	#449	1	2	yes	—
335	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
336	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
337	C₄×C₁₃	#576	1	1	yes	characteristic
338	C₄×C₁₃	#577	1	1	yes	characteristic
339	C₂×#41	—	2	2	no	—
340	C₂×#41	—	2	1	no	—
341	C₂×#41	—	2	1	no	—
342	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
343	C₂³×C₄	—	2	1	no	—
344	AGL(1,ℤ/8)	—	4	4	no	—
345	C₂×SD₁₆	—	2	2	no	—
346	C₂×SD₁₆	—	2	2	no	—
347	C₂×D₈	—	2	2	no	—
348	C₂×D₈	—	2	2	no	—
349	C₂×M₁₆	—	2	1	no	—
350	C₂²×C₈	—	2	1	no	—
351	C₂²×C₈	—	2	1	no	—
352	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
353	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
354	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
355	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
356	#127	—	2	2	no	—
357	#127	C₂³×C₁₃	1	1	yes	characteristic
358	#127	C₂³×C₁₃	1	1	yes	characteristic
359	#126	—	2	4	no	—
360	#125	—	2	1	no	—
361	#124	—	2	4	no	—
362	#124	—	2	2	no	—
363	#124	—	2	1	no	—
364	#124	—	2	1	no	—
365	#123	—	2	4	no	—
366	#123	—	2	4	no	—
367	C₂²⋊Q₈	—	2	2	no	—
368	C₂²⋊Q₈	—	2	1	no	—
369	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
370	#121	—	2	2	no	—
371	#121	—	2	2	no	—
372	#121	—	2	4	no	—
373	#121	—	2	1	no	—
374	#121	—	2	2	no	—
375	#121	—	2	1	no	—
376	#121	—	2	1	no	—
377	#121	D₄×C₁₃	1	2	yes	—
378	#120	—	2	4	no	—
379	C₄×Q₈	—	2	2	no	—
380	C₄×Q₈	—	2	1	no	—
381	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
382	C₄×D₄	—	2	4	no	—
383	C₄×D₄	—	2	4	no	—
384	C₄×D₄	—	2	2	no	—
385	C₄×D₄	—	2	1	no	—
386	C₄×D₄	—	2	1	no	—
387	C₄×D₄	—	2	1	no	—
388	C₄×D₄	—	2	1	no	—
389	C₄×D₄	—	2	1	no	—
390	C₄×D₄	D₄×C₁₃	1	2	yes	—
391	C₄×D₄	D₄×C₁₃	1	2	yes	—
392	C₄×D₄	C₂³×C₁₃	1	2	yes	—
393	#117	—	2	2	no	—
394	#117	—	2	1	no	—
395	#117	—	2	2	no	—
396	C₂×C₄⋊C₄	—	2	2	no	—
397	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
398	C₂×C₂²⋊C₄	—	2	1	no	—
399	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
400	#107	—	2	2	no	—
401	#106	—	2	2	no	—
402	C₄⋊C₈	—	2	1	no	—
403	C₄⋊C₈	—	2	1	no	—
404	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
405	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
406	#103	—	2	2	no	—
407	#103	—	2	2	no	—
408	#102	—	2	2	no	—
409	#102	—	2	2	no	—
410	#102	—	2	2	no	—
411	#102	—	2	2	no	—
412	C₄×C₈	—	2	1	no	—
413	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
414	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
415	C₂×C₁₃	—	2	2	no	—
416	C₂×C₁₃	—	8	2	no	—
417	C₂×C₁₃	—	8	2	no	—
418	C₂×C₁₃	—	16	1	no	—
419	C₂×C₁₃	C₂×#449	1	1	yes	characteristic
420	C₂×C₁₃	#3012	1	1	yes	characteristic
421	C₂×C₁₃	#3018	1	1	yes	characteristic
422	C₂⁴	—	2	1	no	—
423	#41	—	4	2	no	—
424	#41	—	4	2	no	—
425	#41	—	4	2	no	—
426	#41	—	4	2	no	—
427	#41	—	8	2	no	—
428	#41	—	8	2	no	—
429	C₂×Q₈	—	2	1	no	—
430	C₂×Q₈	—	2	1	no	—
431	C₂×Q₈	—	2	1	no	—
432	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
433	C₂×D₄	—	2	2	no	—
434	C₂×D₄	—	2	4	no	—
435	C₂×D₄	—	2	4	no	—
436	C₂×D₄	—	2	1	no	—
437	C₂×D₄	—	2	2	no	—
438	C₂×D₄	—	2	2	no	—
439	C₂×D₄	—	2	1	no	—
440	C₂×D₄	—	2	1	no	—
441	C₂×D₄	—	2	1	no	—
442	C₂×D₄	—	2	1	no	—
443	C₂×D₄	—	2	1	no	—
444	C₂×D₄	—	4	1	no	—
445	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
446	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
447	C₂²×C₄	—	2	4	no	—
448	C₂²×C₄	—	2	1	no	—
449	C₂²×C₄	—	2	2	no	—
450	C₂²×C₄	—	2	2	no	—
451	C₂²×C₄	—	2	2	no	—
452	C₂²×C₄	—	4	1	no	—
453	C₂²×C₄	—	8	1	no	—
454	C₂²×C₄	—	8	1	no	—
455	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
456	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
457	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
458	SD₁₆	—	4	4	no	—
459	SD₁₆	—	8	2	no	—
460	D₈	—	4	4	no	—
461	D₈	—	4	4	no	—
462	M₁₆	—	4	2	no	—
463	C₂×C₈	—	2	1	no	—
464	C₂×C₈	—	2	1	no	—
465	C₂×C₈	—	2	2	no	—
466	C₂×C₈	—	2	2	no	—
467	C₂×C₈	—	4	2	no	—
468	C₂×C₈	—	8	1	no	—
469	C₄⋊C₄	—	2	4	no	—
470	C₄⋊C₄	—	2	1	no	—
471	C₄⋊C₄	—	2	1	no	—
472	C₄⋊C₄	—	2	1	no	—
473	C₄⋊C₄	—	2	2	no	—
474	C₄⋊C₄	—	2	1	no	—
475	C₄⋊C₄	—	2	1	no	—
476	C₄⋊C₄	—	2	2	no	—
477	C₄⋊C₄	—	2	1	no	—
478	C₄⋊C₄	—	2	1	no	—
479	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
480	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
481	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
482	C₂²⋊C₄	—	2	4	no	—
483	C₂²⋊C₄	—	2	4	no	—
484	C₂²⋊C₄	—	2	4	no	—
485	C₂²⋊C₄	—	2	2	no	—
486	C₂²⋊C₄	—	2	2	no	—
487	C₂²⋊C₄	—	2	2	no	—
488	C₂²⋊C₄	—	2	2	no	—
489	C₂²⋊C₄	—	2	2	no	—
490	C₂²⋊C₄	—	4	1	no	—
491	C₂²⋊C₄	—	4	1	no	—
492	C₄²	—	2	4	no	—
493	C₄²	—	2	2	no	—
494	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
495	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
496	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
497	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
498	C₁₃	#18678	1	1	yes	characteristic, direct product factor, Sylow
499	C₂³	—	2	2	no	—
500	C₂³	—	2	2	no	—
501	C₂³	—	4	2	no	—
502	C₂³	—	4	1	no	—
503	C₂³	—	8	1	no	—
504	C₂³	—	8	1	no	—
505	C₂³	C₁₃×#120	1	1	yes	characteristic
506	Q₈	—	2	2	no	—
507	Q₈	—	2	2	no	—
508	Q₈	—	4	1	no	—
509	Q₈	—	4	1	no	—
510	Q₈	—	4	1	no	—
511	Q₈	—	4	1	no	—
512	Q₈	—	8	1	no	—
513	D₄	—	2	2	no	—
514	D₄	—	2	2	no	—
515	D₄	—	4	2	no	—
516	D₄	—	4	2	no	—
517	D₄	—	4	4	no	—
518	D₄	—	4	2	no	—
519	D₄	—	4	1	no	—
520	D₄	—	4	1	no	—
521	D₄	—	4	1	no	—
522	D₄	—	4	1	no	—
523	D₄	—	4	1	no	—
524	D₄	—	4	1	no	—
525	D₄	—	4	1	no	—
526	D₄	—	4	1	no	—
527	D₄	—	8	4	no	—
528	D₄	—	8	4	no	—
529	D₄	—	8	2	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	4	1	no	—
537	C₂×C₄	—	4	4	no	—
538	C₂×C₄	—	4	2	no	—
539	C₂×C₄	—	4	2	no	—
540	C₂×C₄	—	4	1	no	—
541	C₂×C₄	—	8	2	no	—
542	C₂×C₄	—	8	1	no	—
543	C₂×C₄	—	8	4	no	—
544	C₂×C₄	—	8	2	no	—
545	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
546	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
547	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
548	C₂×C₄	C₁₃×#135	1	2	yes	—
549	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
550	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
551	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
552	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
553	C₈	—	2	2	no	—
554	C₈	—	4	1	no	—
555	C₈	—	4	2	no	—
556	C₈	—	4	2	no	—
557	C₂²	—	2	1	no	—
558	C₂²	—	2	1	no	—
559	C₂²	—	4	2	no	—
560	C₂²	—	4	2	no	—
561	C₂²	—	4	2	no	—
562	C₂²	—	4	2	no	—
563	C₂²	—	4	2	no	—
564	C₂²	—	4	2	no	—
565	C₂²	—	8	4	no	—
566	C₂²	—	8	1	no	—
567	C₂²	—	8	1	no	—
568	C₂²	—	8	1	no	—
569	C₂²	C₁₃×#449	1	2	yes	—
570	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
571	C₄	—	2	1	no	—
572	C₄	—	2	1	no	—
573	C₄	—	2	1	no	—
574	C₄	—	4	2	no	—
575	C₄	—	4	2	no	—
576	C₄	—	4	2	no	—
577	C₄	—	4	2	no	—
578	C₄	—	8	1	no	—
579	C₄	C₁₃×#449	1	2	yes	—
580	C₄	C₂×C₁₃×#135	1	1	yes	characteristic
581	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
582	C₄	C₁₃×#576	1	1	yes	characteristic
583	C₄	C₁₃×#577	1	1	yes	characteristic
584	C₂	—	2	2	no	—
585	C₂	—	8	2	no	—
586	C₂	—	8	2	no	—
587	C₂	—	16	1	no	—
588	C₂	C₂×C₁₃×#449	1	1	yes	characteristic
589	C₂	C₁₃×#3012	1	1	yes	characteristic
590	C₂	C₁₃×#3018	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃
LCS	G ▷ C₄² ▷ C₂² ▷ 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×#3506	C₂	semidirect
2. C₁₃×#3246	C₂	semidirect
3. C₁₃×#3169	C₂	semidirect
4. C₁₃×#3036	C₂	semidirect
5. C₁₃×#1650	C₂	semidirect
6. C₁₃×#1642	C₂	semidirect
7. C₁₃×#1628	C₂	semidirect
8. C₁₃×#1621	C₂	semidirect
9. C₁₃×#1547	C₂	semidirect
10. C₁₃×#1493	C₂	semidirect
11. C₂×C₁₃×D₄⋊C₈	C₂	semidirect
27. C₁₃×#500	C₂²	semidirect
28. C₁₃×#493	C₂²	semidirect
29. C₁₃×#486	C₂²	semidirect
30. C₁₃×#486	C₂²	semidirect
32. C₁₃×#475	C₂²	semidirect
38. C₁₃×#460	C₂²	semidirect
45. C₁₃×#332	C₂²	semidirect
46. C₁₃×#331	C₂²	semidirect
47. C₁₃×Q₈⋊C₈	C₂²	semidirect
48. C₁₃×Q₈⋊C₈	C₂²	semidirect
127. #18678	C₁₃	direct (N × H)
204. #3506	C₂×C₁₃	semidirect
205. #3246	C₂×C₁₃	semidirect
206. #3169	C₂×C₁₃	semidirect
207. #3036	C₂×C₁₃	semidirect
208. #1650	C₂×C₁₃	semidirect
209. #1642	C₂×C₁₃	semidirect
210. #1628	C₂×C₁₃	semidirect
211. #1621	C₂×C₁₃	semidirect
212. #1547	C₂×C₁₃	semidirect
213. #1493	C₂×C₁₃	semidirect
214. C₂×D₄⋊C₈	C₂×C₁₃	semidirect
288. #500	C₂²×C₁₃	semidirect
289. #493	C₂²×C₁₃	semidirect
290. #486	C₂²×C₁₃	semidirect
291. #486	C₂²×C₁₃	semidirect
293. #475	C₂²×C₁₃	semidirect
299. #460	C₂²×C₁₃	semidirect
306. #332	C₂²×C₁₃	semidirect
307. #331	C₂²×C₁₃	semidirect
308. Q₈⋊C₈	C₂²×C₁₃	semidirect
309. Q₈⋊C₈	C₂²×C₁₃	semidirect
498. C₁₃	#18678	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×#3246	2
C₁₃×#3169	2
C₁₃×#3036	2
C₁₃×#1650	2
C₁₃×#1642	2
C₁₃×#1628	2
C₁₃×#1621	2
C₁₃×#1547	2
C₁₃×#1493	2
C₂×C₁₃×D₄⋊C₈	2
#18678	13

Subgroups — C13×#18678 #15705017

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#18678 #15705017