Subgroups — C₁₃×#18712 #15705051

Order 3328.

1084 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3543	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3247	C₂	1	2	yes	maximal, complemented
3	C₁₃×#3151	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1631	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1630	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1629	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1621	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1620	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1619	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×#331	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1483	C₂	1	2	yes	maximal, complemented
12	C₂×C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
13	C₁₃×#560	—	2	2	no	—
14	C₁₃×#559	C₂²	1	1	yes	characteristic
15	C₁₃×#550	C₂²	1	2	yes	—
16	C₁₃×#546	—	2	2	no	—
17	D₄²×C₁₃	—	2	2	no	—
18	D₄²×C₁₃	C₂²	1	1	yes	characteristic
19	C₁₃×#540	—	2	2	no	—
20	C₁₃×#535	—	2	2	no	—
21	C₁₃×#534	—	2	2	no	—
22	C₁₃×#532	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
24	C₁₃×#529	C₂²	1	2	yes	—
25	C₁₃×#496	—	2	2	no	—
26	C₁₃×#493	C₂²	1	1	yes	characteristic
27	C₁₃×#493	C₂²	1	1	yes	characteristic, complemented
28	C₁₃×#492	C₂²	1	1	yes	characteristic
29	C₁₃×#492	C₂²	1	1	yes	characteristic, complemented
30	C₁₃×#478	—	2	2	no	—
31	C₁₃×#477	C₂²	1	2	yes	complemented
32	C₁₃×#476	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×#460	C₂²	1	2	yes	complemented
37	C₁₃×#459	C₂²	1	2	yes	complemented
38	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	complemented
39	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic, complemented
40	C₁₃×#331	C₂²	1	1	yes	characteristic
41	C₁₃×#331	C₂²	1	1	yes	characteristic
42	C₁₃×#331	C₂²	1	2	yes	complemented
43	C₁₃×Q₈⋊C₈	C₂²	1	2	yes	complemented
44	C₁₃×Q₈⋊C₈	C₂²	1	2	yes	complemented
45	C₁₃×D₄⋊C₈	C₂²	1	2	yes	complemented
46	C₁₃×D₄⋊C₈	C₂²	1	2	yes	complemented
47	C₂×C₁₃×#41	—	2	2	no	—
48	C₂×C₁₃×#41	—	2	1	no	—
49	C₂²×D₄×C₁₃	—	2	2	no	—
50	C₂²×D₄×C₁₃	—	2	2	no	—
51	C₂²×D₄×C₁₃	—	2	2	no	—
52	C₂²×D₄×C₁₃	D₄	1	2	yes	—
53	C₁₃×AGL(1,ℤ/8)	—	4	8	no	—
54	C₂×C₁₃×SD₁₆	—	2	2	no	—
55	C₂×C₁₃×SD₁₆	—	2	2	no	—
56	C₂×C₁₃×SD₁₆	—	2	2	no	—
57	C₂×C₁₃×D₈	—	2	2	no	—
58	C₂×C₁₃×D₈	—	2	2	no	—
59	C₂×C₁₃×D₈	—	2	2	no	—
60	C₂×C₁₃×M₁₆	—	2	1	no	—
61	C₂²×C₈×C₁₃	—	2	2	no	—
62	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
63	C₁₃×#127	—	2	2	no	—
64	C₁₃×#127	—	2	2	no	—
65	C₁₃×#127	D₄	1	2	yes	—
66	C₁₃×#127	C₂³	1	1	yes	characteristic
67	C₁₃×#127	C₂³	1	1	yes	characteristic
68	C₁₃×#127	C₂³	1	1	yes	characteristic
69	C₁₃×#126	—	2	2	no	—
70	C₁₃×#125	D₄	1	2	yes	—
71	C₁₃×#124	—	2	2	no	—
72	C₁₃×#124	—	2	1	no	—
73	C₁₃×#124	D₄	1	2	yes	—
74	C₁₃×#123	—	2	2	no	—
75	C₁₃×#123	—	2	4	no	—
76	C₁₃×#123	—	2	2	no	—
77	C₁₃×#123	—	2	2	no	—
78	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
79	C₁₃×#121	—	2	4	no	—
80	C₁₃×#121	—	2	4	no	—
81	C₁₃×#121	—	2	4	no	—
82	C₁₃×#121	—	2	4	no	—
83	C₁₃×#121	—	2	2	no	—
84	C₁₃×#121	—	2	2	no	—
85	C₁₃×#121	—	2	2	no	—
86	C₁₃×#121	D₄	1	2	yes	—
87	C₁₃×#120	—	2	2	no	—
88	C₁₃×#120	—	2	4	no	—
89	C₁₃×#120	—	2	4	no	—
90	C₁₃×#120	—	2	2	no	—
91	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
92	C₄×D₄×C₁₃	—	2	2	no	—
93	C₄×D₄×C₁₃	—	2	2	no	—
94	C₄×D₄×C₁₃	—	2	2	no	—
95	C₄×D₄×C₁₃	—	2	2	no	—
96	C₄×D₄×C₁₃	C₂³	1	2	yes	—
97	C₁₃×#117	—	2	2	no	—
98	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
99	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
100	C₁₃×#107	—	2	2	no	—
101	C₁₃×#106	—	2	2	no	—
102	C₁₃×C₄⋊C₈	—	2	2	no	—
103	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
104	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
105	C₁₃×#103	—	2	2	no	—
106	C₁₃×#102	—	2	2	no	—
107	C₁₃×#102	—	2	2	no	—
108	C₁₃×#102	—	2	2	no	—
109	C₁₃×#97	—	2	1	no	—
110	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
111	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
112	#18712	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
113	C₂⁴×C₁₃	—	2	2	no	—
114	C₂⁴×C₁₃	—	2	2	no	—
115	C₁₃×#41	—	4	4	no	—
116	C₁₃×#41	—	8	2	no	—
117	C₁₃×#41	—	8	2	no	—
118	C₂×Q₈×C₁₃	—	2	1	no	—
119	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
120	C₂×D₄×C₁₃	—	2	2	no	—
121	C₂×D₄×C₁₃	—	2	4	no	—
122	C₂×D₄×C₁₃	—	2	4	no	—
123	C₂×D₄×C₁₃	—	2	4	no	—
124	C₂×D₄×C₁₃	—	2	2	no	—
125	C₂×D₄×C₁₃	—	2	4	no	—
126	C₂×D₄×C₁₃	—	2	2	no	—
127	C₂×D₄×C₁₃	—	2	2	no	—
128	C₂×D₄×C₁₃	—	2	2	no	—
129	C₂×D₄×C₁₃	—	2	1	no	—
130	C₂×D₄×C₁₃	—	4	4	no	—
131	C₂×D₄×C₁₃	—	4	1	no	—
132	C₂×D₄×C₁₃	—	8	2	no	—
133	C₂×D₄×C₁₃	—	8	2	no	—
134	C₂×D₄×C₁₃	—	8	2	no	—
135	C₂×D₄×C₁₃	—	8	2	no	—
136	C₂×D₄×C₁₃	—	8	4	no	—
137	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
138	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
139	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
140	C₂²×C₄×C₁₃	—	2	4	no	—
141	C₂²×C₄×C₁₃	—	2	2	no	—
142	C₂²×C₄×C₁₃	—	2	2	no	—
143	C₂²×C₄×C₁₃	—	4	1	no	—
144	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
145	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
146	C₁₃×SD₁₆	—	4	4	no	—
147	C₁₃×SD₁₆	—	4	4	no	—
148	C₁₃×SD₁₆	—	8	2	no	—
149	C₁₃×D₈	—	4	4	no	—
150	C₁₃×D₈	—	4	4	no	—
151	C₁₃×D₈	—	8	2	no	—
152	C₁₃×M₁₆	—	2	4	no	—
153	C₂×C₈×C₁₃	—	2	1	no	—
154	C₂×C₈×C₁₃	—	2	1	no	—
155	C₂×C₈×C₁₃	—	2	2	no	—
156	C₂×C₈×C₁₃	—	2	2	no	—
157	C₂×C₈×C₁₃	—	8	2	no	—
158	C₁₃×C₄⋊C₄	—	2	2	no	—
159	C₁₃×C₄⋊C₄	—	2	2	no	—
160	C₁₃×C₄⋊C₄	—	2	2	no	—
161	C₁₃×C₄⋊C₄	—	2	2	no	—
162	C₁₃×C₄⋊C₄	—	2	2	no	—
163	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
164	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
165	C₁₃×C₂²⋊C₄	—	2	2	no	—
166	C₁₃×C₂²⋊C₄	—	2	2	no	—
167	C₁₃×C₂²⋊C₄	—	2	4	no	—
168	C₁₃×C₂²⋊C₄	—	2	4	no	—
169	C₁₃×C₂²⋊C₄	—	2	2	no	—
170	C₁₃×C₂²⋊C₄	—	2	2	no	—
171	C₁₃×C₂²⋊C₄	—	2	2	no	—
172	C₁₃×C₂²⋊C₄	—	2	2	no	—
173	C₁₃×C₂²⋊C₄	—	2	2	no	—
174	C₁₃×C₂²⋊C₄	—	4	2	no	—
175	C₄²×C₁₃	—	2	2	no	—
176	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
177	C₄²×C₁₃	C₂×D₄	1	2	yes	—
178	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
179	#3543	C₂×C₁₃	1	1	yes	characteristic, complemented
180	#3247	C₂×C₁₃	1	2	yes	complemented
181	#3151	C₂×C₁₃	1	1	yes	characteristic, complemented
182	#1631	C₂×C₁₃	1	2	yes	complemented
183	#1630	C₂×C₁₃	1	1	yes	characteristic, complemented
184	#1629	C₂×C₁₃	1	1	yes	characteristic, complemented
185	#1621	C₂×C₁₃	1	2	yes	complemented
186	#1620	C₂×C₁₃	1	1	yes	characteristic, complemented
187	#1619	C₂×C₁₃	1	1	yes	characteristic, complemented
188	C₂×#331	C₂×C₁₃	1	1	yes	characteristic, complemented
189	#1483	C₂×C₁₃	1	2	yes	complemented
190	C₂³×C₁₃	—	2	2	no	—
191	C₂³×C₁₃	—	2	2	no	—
192	C₂³×C₁₃	—	2	2	no	—
193	C₂³×C₁₃	—	4	4	no	—
194	C₂³×C₁₃	—	4	1	no	—
195	C₂³×C₁₃	—	8	4	no	—
196	C₂³×C₁₃	—	8	4	no	—
197	C₂³×C₁₃	—	8	2	no	—
198	C₂³×C₁₃	#120	1	1	yes	characteristic
199	Q₈×C₁₃	—	2	2	no	—
200	Q₈×C₁₃	—	2	2	no	—
201	Q₈×C₁₃	—	4	2	no	—
202	D₄×C₁₃	—	2	2	no	—
203	D₄×C₁₃	—	2	2	no	—
204	D₄×C₁₃	—	4	2	no	—
205	D₄×C₁₃	—	4	2	no	—
206	D₄×C₁₃	—	4	2	no	—
207	D₄×C₁₃	—	4	4	no	—
208	D₄×C₁₃	—	4	2	no	—
209	D₄×C₁₃	—	4	2	no	—
210	D₄×C₁₃	—	4	2	no	—
211	D₄×C₁₃	—	4	2	no	—
212	D₄×C₁₃	—	4	2	no	—
213	D₄×C₁₃	—	4	2	no	—
214	D₄×C₁₃	—	8	2	no	—
215	D₄×C₁₃	—	8	4	no	—
216	D₄×C₁₃	—	8	4	no	—
217	D₄×C₁₃	—	8	4	no	—
218	D₄×C₁₃	—	8	4	no	—
219	D₄×C₁₃	—	8	2	no	—
220	C₂×C₄×C₁₃	—	2	2	no	—
221	C₂×C₄×C₁₃	—	2	2	no	—
222	C₂×C₄×C₁₃	—	2	2	no	—
223	C₂×C₄×C₁₃	—	2	2	no	—
224	C₂×C₄×C₁₃	—	2	2	no	—
225	C₂×C₄×C₁₃	—	2	2	no	—
226	C₂×C₄×C₁₃	—	4	2	no	—
227	C₂×C₄×C₁₃	—	4	2	no	—
228	C₂×C₄×C₁₃	—	4	1	no	—
229	C₂×C₄×C₁₃	—	8	2	no	—
230	C₂×C₄×C₁₃	—	8	2	no	—
231	C₂×C₄×C₁₃	—	8	4	no	—
232	C₂×C₄×C₁₃	#120	1	2	yes	—
233	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
234	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
235	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
236	C₈×C₁₃	—	2	2	no	—
237	C₈×C₁₃	—	2	2	no	—
238	C₈×C₁₃	—	4	2	no	—
239	C₈×C₁₃	—	4	2	no	—
240	C₂×AGL(1,ℤ/8)	—	2	2	no	—
241	#560	—	2	2	no	—
242	#559	C₂²×C₁₃	1	1	yes	characteristic
243	#550	C₂²×C₁₃	1	2	yes	—
244	#546	—	2	2	no	—
245	D₄²	—	2	2	no	—
246	D₄²	C₂²×C₁₃	1	1	yes	characteristic
247	#540	—	2	2	no	—
248	#535	—	2	2	no	—
249	#534	—	2	2	no	—
250	#532	C₂²×C₁₃	1	1	yes	characteristic, complemented
251	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
252	#529	C₂²×C₁₃	1	2	yes	—
253	#496	—	2	2	no	—
254	#493	C₂²×C₁₃	1	1	yes	characteristic
255	#493	C₂²×C₁₃	1	1	yes	characteristic, complemented
256	#492	C₂²×C₁₃	1	1	yes	characteristic
257	#492	C₂²×C₁₃	1	1	yes	characteristic, complemented
258	#478	—	2	2	no	—
259	#477	C₂²×C₁₃	1	2	yes	complemented
260	#476	C₂²×C₁₃	1	2	yes	complemented
261	#466	—	2	2	no	—
262	#465	—	2	2	no	—
263	#463	—	2	2	no	—
264	#460	C₂²×C₁₃	1	2	yes	complemented
265	#459	C₂²×C₁₃	1	2	yes	complemented
266	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	complemented
267	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
268	#331	C₂²×C₁₃	1	1	yes	characteristic
269	#331	C₂²×C₁₃	1	1	yes	characteristic
270	#331	C₂²×C₁₃	1	2	yes	complemented
271	Q₈⋊C₈	C₂²×C₁₃	1	2	yes	complemented
272	Q₈⋊C₈	C₂²×C₁₃	1	2	yes	complemented
273	D₄⋊C₈	C₂²×C₁₃	1	2	yes	complemented
274	D₄⋊C₈	C₂²×C₁₃	1	2	yes	complemented
275	C₂²×C₁₃	—	2	2	no	—
276	C₂²×C₁₃	—	4	2	no	—
277	C₂²×C₁₃	—	4	4	no	—
278	C₂²×C₁₃	—	4	2	no	—
279	C₂²×C₁₃	—	4	4	no	—
280	C₂²×C₁₃	—	4	2	no	—
281	C₂²×C₁₃	—	4	2	no	—
282	C₂²×C₁₃	—	4	2	no	—
283	C₂²×C₁₃	—	8	2	no	—
284	C₂²×C₁₃	—	8	1	no	—
285	C₂²×C₁₃	—	16	4	no	—
286	C₂²×C₁₃	—	16	4	no	—
287	C₂²×C₁₃	#453	1	2	yes	—
288	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
289	C₄×C₁₃	—	2	2	no	—
290	C₄×C₁₃	—	2	1	no	—
291	C₄×C₁₃	—	2	1	no	—
292	C₄×C₁₃	—	4	2	no	—
293	C₄×C₁₃	—	4	2	no	—
294	C₄×C₁₃	—	4	2	no	—
295	C₄×C₁₃	—	8	1	no	—
296	C₄×C₁₃	#576	1	2	yes	—
297	C₄×C₁₃	#577	1	2	yes	—
298	C₂×#41	—	2	2	no	—
299	C₂×#41	—	2	1	no	—
300	C₂²×D₄	—	2	2	no	—
301	C₂²×D₄	—	2	2	no	—
302	C₂²×D₄	—	2	2	no	—
303	C₂²×D₄	D₄×C₁₃	1	2	yes	—
304	AGL(1,ℤ/8)	—	4	8	no	—
305	C₂×SD₁₆	—	2	2	no	—
306	C₂×SD₁₆	—	2	2	no	—
307	C₂×SD₁₆	—	2	2	no	—
308	C₂×D₈	—	2	2	no	—
309	C₂×D₈	—	2	2	no	—
310	C₂×D₈	—	2	2	no	—
311	C₂×M₁₆	—	2	1	no	—
312	C₂²×C₈	—	2	2	no	—
313	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
314	#127	—	2	2	no	—
315	#127	—	2	2	no	—
316	#127	D₄×C₁₃	1	2	yes	—
317	#127	C₂³×C₁₃	1	1	yes	characteristic
318	#127	C₂³×C₁₃	1	1	yes	characteristic
319	#127	C₂³×C₁₃	1	1	yes	characteristic
320	#126	—	2	2	no	—
321	#125	D₄×C₁₃	1	2	yes	—
322	#124	—	2	2	no	—
323	#124	—	2	1	no	—
324	#124	D₄×C₁₃	1	2	yes	—
325	#123	—	2	2	no	—
326	#123	—	2	4	no	—
327	#123	—	2	2	no	—
328	#123	—	2	2	no	—
329	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
330	#121	—	2	4	no	—
331	#121	—	2	4	no	—
332	#121	—	2	4	no	—
333	#121	—	2	4	no	—
334	#121	—	2	2	no	—
335	#121	—	2	2	no	—
336	#121	—	2	2	no	—
337	#121	D₄×C₁₃	1	2	yes	—
338	#120	—	2	2	no	—
339	#120	—	2	4	no	—
340	#120	—	2	4	no	—
341	#120	—	2	2	no	—
342	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
343	C₄×D₄	—	2	2	no	—
344	C₄×D₄	—	2	2	no	—
345	C₄×D₄	—	2	2	no	—
346	C₄×D₄	—	2	2	no	—
347	C₄×D₄	C₂³×C₁₃	1	2	yes	—
348	#117	—	2	2	no	—
349	C₂×C₂²⋊C₄	—	2	2	no	—
350	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
351	#107	—	2	2	no	—
352	#106	—	2	2	no	—
353	C₄⋊C₈	—	2	2	no	—
354	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
355	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
356	#103	—	2	2	no	—
357	#102	—	2	2	no	—
358	#102	—	2	2	no	—
359	#102	—	2	2	no	—
360	#97	—	2	1	no	—
361	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
362	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
363	C₂×C₁₃	—	2	2	no	—
364	C₂×C₁₃	—	8	2	no	—
365	C₂×C₁₃	—	8	2	no	—
366	C₂×C₁₃	—	8	2	no	—
367	C₂×C₁₃	—	16	1	no	—
368	C₂×C₁₃	#3012	1	2	yes	—
369	C₂×C₁₃	C₂×#453	1	1	yes	characteristic
370	C₂⁴	—	2	2	no	—
371	C₂⁴	—	2	2	no	—
372	#41	—	4	4	no	—
373	#41	—	8	2	no	—
374	#41	—	8	2	no	—
375	C₂×Q₈	—	2	1	no	—
376	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
377	C₂×D₄	—	2	2	no	—
378	C₂×D₄	—	2	4	no	—
379	C₂×D₄	—	2	4	no	—
380	C₂×D₄	—	2	4	no	—
381	C₂×D₄	—	2	2	no	—
382	C₂×D₄	—	2	4	no	—
383	C₂×D₄	—	2	2	no	—
384	C₂×D₄	—	2	2	no	—
385	C₂×D₄	—	2	2	no	—
386	C₂×D₄	—	2	1	no	—
387	C₂×D₄	—	4	4	no	—
388	C₂×D₄	—	4	1	no	—
389	C₂×D₄	—	8	2	no	—
390	C₂×D₄	—	8	2	no	—
391	C₂×D₄	—	8	2	no	—
392	C₂×D₄	—	8	2	no	—
393	C₂×D₄	—	8	4	no	—
394	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
395	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
396	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
397	C₂²×C₄	—	2	4	no	—
398	C₂²×C₄	—	2	2	no	—
399	C₂²×C₄	—	2	2	no	—
400	C₂²×C₄	—	4	1	no	—
401	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
402	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
403	SD₁₆	—	4	4	no	—
404	SD₁₆	—	4	4	no	—
405	SD₁₆	—	8	2	no	—
406	D₈	—	4	4	no	—
407	D₈	—	4	4	no	—
408	D₈	—	8	2	no	—
409	M₁₆	—	2	4	no	—
410	C₂×C₈	—	2	1	no	—
411	C₂×C₈	—	2	1	no	—
412	C₂×C₈	—	2	2	no	—
413	C₂×C₈	—	2	2	no	—
414	C₂×C₈	—	8	2	no	—
415	C₄⋊C₄	—	2	2	no	—
416	C₄⋊C₄	—	2	2	no	—
417	C₄⋊C₄	—	2	2	no	—
418	C₄⋊C₄	—	2	2	no	—
419	C₄⋊C₄	—	2	2	no	—
420	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
421	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
422	C₂²⋊C₄	—	2	2	no	—
423	C₂²⋊C₄	—	2	2	no	—
424	C₂²⋊C₄	—	2	4	no	—
425	C₂²⋊C₄	—	2	4	no	—
426	C₂²⋊C₄	—	2	2	no	—
427	C₂²⋊C₄	—	2	2	no	—
428	C₂²⋊C₄	—	2	2	no	—
429	C₂²⋊C₄	—	2	2	no	—
430	C₂²⋊C₄	—	2	2	no	—
431	C₂²⋊C₄	—	4	2	no	—
432	C₄²	—	2	2	no	—
433	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
434	C₄²	C₂×D₄×C₁₃	1	2	yes	—
435	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
436	C₁₃	#18712	1	1	yes	characteristic, direct product factor, Sylow
437	C₂³	—	2	2	no	—
438	C₂³	—	2	2	no	—
439	C₂³	—	2	2	no	—
440	C₂³	—	4	4	no	—
441	C₂³	—	4	1	no	—
442	C₂³	—	8	4	no	—
443	C₂³	—	8	4	no	—
444	C₂³	—	8	2	no	—
445	C₂³	C₁₃×#120	1	1	yes	characteristic
446	Q₈	—	2	2	no	—
447	Q₈	—	2	2	no	—
448	Q₈	—	4	2	no	—
449	D₄	—	2	2	no	—
450	D₄	—	2	2	no	—
451	D₄	—	4	2	no	—
452	D₄	—	4	2	no	—
453	D₄	—	4	2	no	—
454	D₄	—	4	4	no	—
455	D₄	—	4	2	no	—
456	D₄	—	4	2	no	—
457	D₄	—	4	2	no	—
458	D₄	—	4	2	no	—
459	D₄	—	4	2	no	—
460	D₄	—	4	2	no	—
461	D₄	—	8	2	no	—
462	D₄	—	8	4	no	—
463	D₄	—	8	4	no	—
464	D₄	—	8	4	no	—
465	D₄	—	8	4	no	—
466	D₄	—	8	2	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	4	2	no	—
474	C₂×C₄	—	4	2	no	—
475	C₂×C₄	—	4	1	no	—
476	C₂×C₄	—	8	2	no	—
477	C₂×C₄	—	8	2	no	—
478	C₂×C₄	—	8	4	no	—
479	C₂×C₄	C₁₃×#120	1	2	yes	—
480	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
481	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
482	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
483	C₈	—	2	2	no	—
484	C₈	—	2	2	no	—
485	C₈	—	4	2	no	—
486	C₈	—	4	2	no	—
487	C₂²	—	2	2	no	—
488	C₂²	—	4	2	no	—
489	C₂²	—	4	4	no	—
490	C₂²	—	4	2	no	—
491	C₂²	—	4	4	no	—
492	C₂²	—	4	2	no	—
493	C₂²	—	4	2	no	—
494	C₂²	—	4	2	no	—
495	C₂²	—	8	2	no	—
496	C₂²	—	8	1	no	—
497	C₂²	—	16	4	no	—
498	C₂²	—	16	4	no	—
499	C₂²	C₁₃×#453	1	2	yes	—
500	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
501	C₄	—	2	2	no	—
502	C₄	—	2	1	no	—
503	C₄	—	2	1	no	—
504	C₄	—	4	2	no	—
505	C₄	—	4	2	no	—
506	C₄	—	4	2	no	—
507	C₄	—	8	1	no	—
508	C₄	C₁₃×#576	1	2	yes	—
509	C₄	C₁₃×#577	1	2	yes	—
510	C₂	—	2	2	no	—
511	C₂	—	8	2	no	—
512	C₂	—	8	2	no	—
513	C₂	—	8	2	no	—
514	C₂	—	16	1	no	—
515	C₂	C₁₃×#3012	1	2	yes	—
516	C₂	C₂×C₁₃×#453	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×#3543	C₂	semidirect
2. C₁₃×#3247	C₂	semidirect
3. C₁₃×#3151	C₂	semidirect
4. C₁₃×#1631	C₂	semidirect
5. C₁₃×#1630	C₂	semidirect
6. C₁₃×#1629	C₂	semidirect
7. C₁₃×#1621	C₂	semidirect
8. C₁₃×#1620	C₂	semidirect
9. C₁₃×#1619	C₂	semidirect
10. C₂×C₁₃×#331	C₂	semidirect
11. C₁₃×#1483	C₂	semidirect
22. C₁₃×#532	C₂²	semidirect
27. C₁₃×#493	C₂²	semidirect
29. C₁₃×#492	C₂²	semidirect
31. C₁₃×#477	C₂²	semidirect
32. C₁₃×#476	C₂²	semidirect
36. C₁₃×#460	C₂²	semidirect
37. C₁₃×#459	C₂²	semidirect
38. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
39. C₄×C₁₃×M₁₆	C₂²	semidirect
42. C₁₃×#331	C₂²	semidirect
43. C₁₃×Q₈⋊C₈	C₂²	semidirect
44. C₁₃×Q₈⋊C₈	C₂²	semidirect
45. C₁₃×D₄⋊C₈	C₂²	semidirect
46. C₁₃×D₄⋊C₈	C₂²	semidirect
112. #18712	C₁₃	direct (N × H)
179. #3543	C₂×C₁₃	semidirect
180. #3247	C₂×C₁₃	semidirect
181. #3151	C₂×C₁₃	semidirect
182. #1631	C₂×C₁₃	semidirect
183. #1630	C₂×C₁₃	semidirect
184. #1629	C₂×C₁₃	semidirect
185. #1621	C₂×C₁₃	semidirect
186. #1620	C₂×C₁₃	semidirect
187. #1619	C₂×C₁₃	semidirect
188. C₂×#331	C₂×C₁₃	semidirect
189. #1483	C₂×C₁₃	semidirect
250. #532	C₂²×C₁₃	semidirect
255. #493	C₂²×C₁₃	semidirect
257. #492	C₂²×C₁₃	semidirect
259. #477	C₂²×C₁₃	semidirect
260. #476	C₂²×C₁₃	semidirect
264. #460	C₂²×C₁₃	semidirect
265. #459	C₂²×C₁₃	semidirect
266. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
267. C₄×M₁₆	C₂²×C₁₃	semidirect
270. #331	C₂²×C₁₃	semidirect
271. Q₈⋊C₈	C₂²×C₁₃	semidirect
272. Q₈⋊C₈	C₂²×C₁₃	semidirect
273. D₄⋊C₈	C₂²×C₁₃	semidirect
274. D₄⋊C₈	C₂²×C₁₃	semidirect
436. C₁₃	#18712	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×#3543	2
C₁₃×#3247	2
C₁₃×#3151	2
C₁₃×#1631	2
C₁₃×#1630	2
C₁₃×#1629	2
C₁₃×#1621	2
C₁₃×#1620	2
C₁₃×#1619	2
C₂×C₁₃×#331	2
C₁₃×#1483	2
#18712	13

Subgroups — C13×#18712 #15705051

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#18712 #15705051