Subgroups — C₁₃×#18669 #15705008

Order 3328.

882 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3507	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#3246	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3170	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3078	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1650	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1643	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1638	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1632	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1550	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1492	C₂	1	1	yes	maximal, characteristic
11	C₂×C₁₃×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#559	—	2	1	no	—
13	C₁₃×#557	—	2	1	no	—
14	C₁₃×#556	—	2	2	no	—
15	C₁₃×#556	C₂²	1	2	yes	—
16	C₁₃×#554	C₂²	1	2	yes	—
17	C₁₃×#552	—	2	2	no	—
18	C₁₃×#539	—	2	2	no	—
19	C₁₃×#536	—	2	1	no	—
20	C₁₃×#533	C₂²	1	1	yes	characteristic
21	C₁₃×#533	C₂²	1	1	yes	characteristic
22	C₁₃×#532	C₂²	1	1	yes	characteristic
23	C₁₃×#529	—	2	2	no	—
24	C₁₃×#520	—	2	1	no	—
25	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
26	C₁₃×#500	C₂²	1	1	yes	characteristic
27	C₁₃×#494	C₂²	1	1	yes	characteristic
28	C₁₃×#487	C₂²	1	1	yes	characteristic
29	C₁₃×#487	C₂²	1	1	yes	characteristic
30	C₁₃×#479	—	2	2	no	—
31	C₁₃×#477	C₂²	1	2	yes	—
32	C₁₃×#476	C₂²	1	2	yes	—
33	C₁₃×#475	—	2	1	no	—
34	C₁₃×#475	C₂²	1	2	yes	—
35	C₁₃×#467	—	2	2	no	—
36	C₁₃×#465	—	2	2	no	—
37	C₁₃×#461	C₂²	1	2	yes	—
38	C₁₃×#460	—	2	1	no	—
39	C₄×C₁₃×Q₁₆	—	2	2	no	—
40	C₁₃×#428	—	2	1	no	—
41	C₁₃×#423	C₂²	1	1	yes	characteristic
42	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
43	C₁₃×#419	—	2	1	no	—
44	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
45	C₁₃×#333	C₂²	1	2	yes	—
46	C₁₃×#332	C₂²	1	2	yes	—
47	C₁₃×Q₈⋊C₈	C₂²	1	2	yes	—
48	C₁₃×Q₈⋊C₈	C₂²	1	2	yes	—
49	C₁₃×D₄⋊C₈	C₂²	1	2	yes	—
50	C₁₃×D₄⋊C₈	C₂²	1	2	yes	—
51	C₂×C₁₃×#41	—	2	1	no	—
52	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
53	C₂×C₁₃×Q₁₆	—	2	2	no	—
54	C₂×C₁₃×SD₁₆	—	2	2	no	—
55	C₂×C₁₃×M₁₆	—	2	1	no	—
56	C₂²×C₈×C₁₃	—	2	1	no	—
57	C₂²×C₈×C₁₃	—	2	1	no	—
58	C₁₃×C₄⋊Q₈	—	2	2	no	—
59	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
60	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
61	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
62	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
63	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
64	C₁₃×#127	D₄	1	1	yes	characteristic
65	C₁₃×#126	—	2	4	no	—
66	C₁₃×#126	—	2	4	no	—
67	C₁₃×#125	—	2	4	no	—
68	C₁₃×#125	—	2	2	no	—
69	C₁₃×#125	—	2	1	no	—
70	C₁₃×#125	—	2	1	no	—
71	C₁₃×#124	—	2	2	no	—
72	C₁₃×#124	—	2	2	no	—
73	C₁₃×#124	—	2	1	no	—
74	C₁₃×#123	—	2	4	no	—
75	C₁₃×#123	—	2	4	no	—
76	C₁₃×C₂²⋊Q₈	—	2	2	no	—
77	C₁₃×C₂²⋊Q₈	—	2	2	no	—
78	C₁₃×C₂²⋊Q₈	—	2	4	no	—
79	C₁₃×C₂²⋊Q₈	—	2	1	no	—
80	C₁₃×C₂²⋊Q₈	—	2	1	no	—
81	C₁₃×C₂²⋊Q₈	—	2	1	no	—
82	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
83	C₁₃×#121	—	2	1	no	—
84	C₁₃×#121	D₄	1	2	yes	—
85	C₄×Q₈×C₁₃	—	2	2	no	—
86	C₄×Q₈×C₁₃	—	2	2	no	—
87	C₄×Q₈×C₁₃	—	2	1	no	—
88	C₄×Q₈×C₁₃	—	2	1	no	—
89	C₄×Q₈×C₁₃	—	2	1	no	—
90	C₄×Q₈×C₁₃	—	2	1	no	—
91	C₄×Q₈×C₁₃	—	2	1	no	—
92	C₄×Q₈×C₁₃	D₄	1	2	yes	—
93	C₄×Q₈×C₁₃	D₄	1	2	yes	—
94	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
95	C₄×D₄×C₁₃	—	2	4	no	—
96	C₄×D₄×C₁₃	—	2	2	no	—
97	C₄×D₄×C₁₃	—	2	2	no	—
98	C₄×D₄×C₁₃	—	2	1	no	—
99	C₄×D₄×C₁₃	C₂³	1	2	yes	—
100	C₁₃×#117	—	2	4	no	—
101	C₁₃×#117	—	2	1	no	—
102	C₁₃×#117	—	2	2	no	—
103	C₁₃×#117	—	2	1	no	—
104	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
105	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
106	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
107	C₂×C₄²×C₁₃	—	2	1	no	—
108	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
109	C₁₃×#107	—	2	2	no	—
110	C₁₃×#107	—	2	2	no	—
111	C₁₃×#106	—	2	2	no	—
112	C₁₃×#106	—	2	2	no	—
113	C₁₃×C₄⋊C₈	—	2	1	no	—
114	C₁₃×C₄⋊C₈	—	2	1	no	—
115	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
116	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
117	C₁₃×#103	—	2	2	no	—
118	C₁₃×#103	—	2	2	no	—
119	C₁₃×#103	—	2	2	no	—
120	C₁₃×#103	—	2	2	no	—
121	C₁₃×#103	—	2	2	no	—
122	C₁₃×#102	—	2	2	no	—
123	C₄×C₈×C₁₃	—	2	1	no	—
124	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
125	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
126	#18669	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
127	C₁₃×#41	—	4	2	no	—
128	C₁₃×#41	—	4	2	no	—
129	C₂×Q₈×C₁₃	—	2	1	no	—
130	C₂×Q₈×C₁₃	—	2	1	no	—
131	C₂×Q₈×C₁₃	—	2	1	no	—
132	C₂×Q₈×C₁₃	—	2	2	no	—
133	C₂×Q₈×C₁₃	—	2	2	no	—
134	C₂×Q₈×C₁₃	—	2	1	no	—
135	C₂×Q₈×C₁₃	—	2	1	no	—
136	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
137	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
138	C₂×D₄×C₁₃	—	2	2	no	—
139	C₂×D₄×C₁₃	—	2	1	no	—
140	C₂×D₄×C₁₃	—	2	1	no	—
141	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
142	C₂²×C₄×C₁₃	—	2	1	no	—
143	C₂²×C₄×C₁₃	—	2	4	no	—
144	C₂²×C₄×C₁₃	—	2	1	no	—
145	C₂²×C₄×C₁₃	—	2	2	no	—
146	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
149	C₁₃×Q₁₆	—	4	4	no	—
150	C₁₃×SD₁₆	—	8	2	no	—
151	C₁₃×M₁₆	—	4	2	no	—
152	C₂×C₈×C₁₃	—	2	1	no	—
153	C₂×C₈×C₁₃	—	2	1	no	—
154	C₂×C₈×C₁₃	—	2	2	no	—
155	C₂×C₈×C₁₃	—	2	2	no	—
156	C₂×C₈×C₁₃	—	4	2	no	—
157	C₂×C₈×C₁₃	—	8	1	no	—
158	C₁₃×C₄⋊C₄	—	2	4	no	—
159	C₁₃×C₄⋊C₄	—	2	4	no	—
160	C₁₃×C₄⋊C₄	—	2	4	no	—
161	C₁₃×C₄⋊C₄	—	2	2	no	—
162	C₁₃×C₄⋊C₄	—	2	1	no	—
163	C₁₃×C₄⋊C₄	—	2	2	no	—
164	C₁₃×C₄⋊C₄	—	2	1	no	—
165	C₁₃×C₄⋊C₄	—	2	2	no	—
166	C₁₃×C₄⋊C₄	—	2	1	no	—
167	C₁₃×C₄⋊C₄	—	2	2	no	—
168	C₁₃×C₄⋊C₄	—	2	1	no	—
169	C₁₃×C₄⋊C₄	—	2	1	no	—
170	C₁₃×C₄⋊C₄	—	2	1	no	—
171	C₁₃×C₄⋊C₄	—	2	1	no	—
172	C₁₃×C₄⋊C₄	—	2	1	no	—
173	C₁₃×C₄⋊C₄	—	2	1	no	—
174	C₁₃×C₄⋊C₄	—	4	1	no	—
175	C₁₃×C₄⋊C₄	—	4	1	no	—
176	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
177	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
178	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
179	C₁₃×C₂²⋊C₄	—	2	4	no	—
180	C₁₃×C₂²⋊C₄	—	2	4	no	—
181	C₁₃×C₂²⋊C₄	—	2	4	no	—
182	C₁₃×C₂²⋊C₄	—	2	2	no	—
183	C₁₃×C₂²⋊C₄	—	2	2	no	—
184	C₁₃×C₂²⋊C₄	—	2	2	no	—
185	C₁₃×C₂²⋊C₄	—	4	1	no	—
186	C₄²×C₁₃	—	2	4	no	—
187	C₄²×C₁₃	—	2	2	no	—
188	C₄²×C₁₃	—	2	2	no	—
189	C₄²×C₁₃	—	2	2	no	—
190	C₄²×C₁₃	—	4	1	no	—
191	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
192	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
193	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
194	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
195	#3507	C₂×C₁₃	1	1	yes	characteristic
196	#3246	C₂×C₁₃	1	1	yes	characteristic
197	#3170	C₂×C₁₃	1	1	yes	characteristic, complemented
198	#3078	C₂×C₁₃	1	1	yes	characteristic, complemented
199	#1650	C₂×C₁₃	1	2	yes	complemented
200	#1643	C₂×C₁₃	1	2	yes	complemented
201	#1638	C₂×C₁₃	1	2	yes	complemented
202	#1632	C₂×C₁₃	1	2	yes	complemented
203	#1550	C₂×C₁₃	1	1	yes	characteristic, complemented
204	#1492	C₂×C₁₃	1	1	yes	characteristic
205	C₂×Q₈⋊C₈	C₂×C₁₃	1	1	yes	characteristic, complemented
206	C₂³×C₁₃	—	2	2	no	—
207	C₂³×C₁₃	#120	1	1	yes	characteristic
208	Q₈×C₁₃	—	2	2	no	—
209	Q₈×C₁₃	—	2	2	no	—
210	Q₈×C₁₃	—	4	2	no	—
211	Q₈×C₁₃	—	4	2	no	—
212	Q₈×C₁₃	—	4	1	no	—
213	Q₈×C₁₃	—	4	1	no	—
214	Q₈×C₁₃	—	4	2	no	—
215	Q₈×C₁₃	—	4	2	no	—
216	Q₈×C₁₃	—	4	1	no	—
217	Q₈×C₁₃	—	4	1	no	—
218	D₄×C₁₃	—	2	2	no	—
219	D₄×C₁₃	—	2	2	no	—
220	D₄×C₁₃	—	4	4	no	—
221	D₄×C₁₃	—	4	2	no	—
222	D₄×C₁₃	—	8	1	no	—
223	C₂×C₄×C₁₃	—	2	1	no	—
224	C₂×C₄×C₁₃	—	2	1	no	—
225	C₂×C₄×C₁₃	—	2	2	no	—
226	C₂×C₄×C₁₃	—	2	2	no	—
227	C₂×C₄×C₁₃	—	2	2	no	—
228	C₂×C₄×C₁₃	—	2	2	no	—
229	C₂×C₄×C₁₃	—	2	2	no	—
230	C₂×C₄×C₁₃	—	4	1	no	—
231	C₂×C₄×C₁₃	—	4	2	no	—
232	C₂×C₄×C₁₃	—	4	2	no	—
233	C₂×C₄×C₁₃	—	4	2	no	—
234	C₂×C₄×C₁₃	—	4	1	no	—
235	C₂×C₄×C₁₃	—	4	1	no	—
236	C₂×C₄×C₁₃	—	8	1	no	—
237	C₂×C₄×C₁₃	—	8	4	no	—
238	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
239	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
240	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
241	C₂×C₄×C₁₃	#135	1	2	yes	—
242	C₂×C₄×C₁₃	#137	1	2	yes	—
243	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
244	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
245	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
246	C₈×C₁₃	—	2	2	no	—
247	C₈×C₁₃	—	4	1	no	—
248	C₈×C₁₃	—	4	2	no	—
249	C₈×C₁₃	—	4	2	no	—
250	#559	—	2	1	no	—
251	#557	—	2	1	no	—
252	#556	—	2	2	no	—
253	#556	C₂²×C₁₃	1	2	yes	—
254	#554	C₂²×C₁₃	1	2	yes	—
255	#552	—	2	2	no	—
256	#539	—	2	2	no	—
257	#536	—	2	1	no	—
258	#533	C₂²×C₁₃	1	1	yes	characteristic
259	#533	C₂²×C₁₃	1	1	yes	characteristic
260	#532	C₂²×C₁₃	1	1	yes	characteristic
261	#529	—	2	2	no	—
262	#520	—	2	1	no	—
263	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
264	#500	C₂²×C₁₃	1	1	yes	characteristic
265	#494	C₂²×C₁₃	1	1	yes	characteristic
266	#487	C₂²×C₁₃	1	1	yes	characteristic
267	#487	C₂²×C₁₃	1	1	yes	characteristic
268	#479	—	2	2	no	—
269	#477	C₂²×C₁₃	1	2	yes	—
270	#476	C₂²×C₁₃	1	2	yes	—
271	#475	—	2	1	no	—
272	#475	C₂²×C₁₃	1	2	yes	—
273	#467	—	2	2	no	—
274	#465	—	2	2	no	—
275	#461	C₂²×C₁₃	1	2	yes	—
276	#460	—	2	1	no	—
277	C₄×Q₁₆	—	2	2	no	—
278	#428	—	2	1	no	—
279	#423	C₂²×C₁₃	1	1	yes	characteristic
280	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
281	#419	—	2	1	no	—
282	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
283	#333	C₂²×C₁₃	1	2	yes	—
284	#332	C₂²×C₁₃	1	2	yes	—
285	Q₈⋊C₈	C₂²×C₁₃	1	2	yes	—
286	Q₈⋊C₈	C₂²×C₁₃	1	2	yes	—
287	D₄⋊C₈	C₂²×C₁₃	1	2	yes	—
288	D₄⋊C₈	C₂²×C₁₃	1	2	yes	—
289	C₂²×C₁₃	—	2	1	no	—
290	C₂²×C₁₃	—	2	1	no	—
291	C₂²×C₁₃	—	4	2	no	—
292	C₂²×C₁₃	—	4	2	no	—
293	C₂²×C₁₃	—	4	2	no	—
294	C₂²×C₁₃	#452	1	2	yes	—
295	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
296	C₄×C₁₃	—	2	1	no	—
297	C₄×C₁₃	—	2	1	no	—
298	C₄×C₁₃	—	2	1	no	—
299	C₄×C₁₃	—	4	2	no	—
300	C₄×C₁₃	—	4	2	no	—
301	C₄×C₁₃	—	4	2	no	—
302	C₄×C₁₃	—	4	2	no	—
303	C₄×C₁₃	—	4	2	no	—
304	C₄×C₁₃	—	8	1	no	—
305	C₄×C₁₃	—	8	1	no	—
306	C₄×C₁₃	#452	1	2	yes	—
307	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
308	C₄×C₁₃	C₂×#137	1	1	yes	characteristic
309	C₄×C₁₃	#577	1	1	yes	characteristic
310	C₄×C₁₃	#578	1	1	yes	characteristic
311	C₂×#41	—	2	1	no	—
312	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
313	C₂×Q₁₆	—	2	2	no	—
314	C₂×SD₁₆	—	2	2	no	—
315	C₂×M₁₆	—	2	1	no	—
316	C₂²×C₈	—	2	1	no	—
317	C₂²×C₈	—	2	1	no	—
318	C₄⋊Q₈	—	2	2	no	—
319	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
320	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
321	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
322	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
323	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
324	#127	D₄×C₁₃	1	1	yes	characteristic
325	#126	—	2	4	no	—
326	#126	—	2	4	no	—
327	#125	—	2	4	no	—
328	#125	—	2	2	no	—
329	#125	—	2	1	no	—
330	#125	—	2	1	no	—
331	#124	—	2	2	no	—
332	#124	—	2	2	no	—
333	#124	—	2	1	no	—
334	#123	—	2	4	no	—
335	#123	—	2	4	no	—
336	C₂²⋊Q₈	—	2	2	no	—
337	C₂²⋊Q₈	—	2	2	no	—
338	C₂²⋊Q₈	—	2	4	no	—
339	C₂²⋊Q₈	—	2	1	no	—
340	C₂²⋊Q₈	—	2	1	no	—
341	C₂²⋊Q₈	—	2	1	no	—
342	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
343	#121	—	2	1	no	—
344	#121	D₄×C₁₃	1	2	yes	—
345	C₄×Q₈	—	2	2	no	—
346	C₄×Q₈	—	2	2	no	—
347	C₄×Q₈	—	2	1	no	—
348	C₄×Q₈	—	2	1	no	—
349	C₄×Q₈	—	2	1	no	—
350	C₄×Q₈	—	2	1	no	—
351	C₄×Q₈	—	2	1	no	—
352	C₄×Q₈	D₄×C₁₃	1	2	yes	—
353	C₄×Q₈	D₄×C₁₃	1	2	yes	—
354	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
355	C₄×D₄	—	2	4	no	—
356	C₄×D₄	—	2	2	no	—
357	C₄×D₄	—	2	2	no	—
358	C₄×D₄	—	2	1	no	—
359	C₄×D₄	C₂³×C₁₃	1	2	yes	—
360	#117	—	2	4	no	—
361	#117	—	2	1	no	—
362	#117	—	2	2	no	—
363	#117	—	2	1	no	—
364	C₂×C₄⋊C₄	—	2	1	no	—
365	C₂×C₄⋊C₄	—	2	2	no	—
366	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
367	C₂×C₄²	—	2	1	no	—
368	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
369	#107	—	2	2	no	—
370	#107	—	2	2	no	—
371	#106	—	2	2	no	—
372	#106	—	2	2	no	—
373	C₄⋊C₈	—	2	1	no	—
374	C₄⋊C₈	—	2	1	no	—
375	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
376	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
377	#103	—	2	2	no	—
378	#103	—	2	2	no	—
379	#103	—	2	2	no	—
380	#103	—	2	2	no	—
381	#103	—	2	2	no	—
382	#102	—	2	2	no	—
383	C₄×C₈	—	2	1	no	—
384	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
385	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
386	C₂×C₁₃	—	2	2	no	—
387	C₂×C₁₃	—	8	2	no	—
388	C₂×C₁₃	C₂×#452	1	1	yes	characteristic
389	C₂×C₁₃	#3013	1	1	yes	characteristic
390	C₂×C₁₃	#3018	1	1	yes	characteristic
391	#41	—	4	2	no	—
392	#41	—	4	2	no	—
393	C₂×Q₈	—	2	1	no	—
394	C₂×Q₈	—	2	1	no	—
395	C₂×Q₈	—	2	1	no	—
396	C₂×Q₈	—	2	2	no	—
397	C₂×Q₈	—	2	2	no	—
398	C₂×Q₈	—	2	1	no	—
399	C₂×Q₈	—	2	1	no	—
400	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
401	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
402	C₂×D₄	—	2	2	no	—
403	C₂×D₄	—	2	1	no	—
404	C₂×D₄	—	2	1	no	—
405	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
406	C₂²×C₄	—	2	1	no	—
407	C₂²×C₄	—	2	4	no	—
408	C₂²×C₄	—	2	1	no	—
409	C₂²×C₄	—	2	2	no	—
410	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
411	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
412	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
413	Q₁₆	—	4	4	no	—
414	SD₁₆	—	8	2	no	—
415	M₁₆	—	4	2	no	—
416	C₂×C₈	—	2	1	no	—
417	C₂×C₈	—	2	1	no	—
418	C₂×C₈	—	2	2	no	—
419	C₂×C₈	—	2	2	no	—
420	C₂×C₈	—	4	2	no	—
421	C₂×C₈	—	8	1	no	—
422	C₄⋊C₄	—	2	4	no	—
423	C₄⋊C₄	—	2	4	no	—
424	C₄⋊C₄	—	2	4	no	—
425	C₄⋊C₄	—	2	2	no	—
426	C₄⋊C₄	—	2	1	no	—
427	C₄⋊C₄	—	2	2	no	—
428	C₄⋊C₄	—	2	1	no	—
429	C₄⋊C₄	—	2	2	no	—
430	C₄⋊C₄	—	2	1	no	—
431	C₄⋊C₄	—	2	2	no	—
432	C₄⋊C₄	—	2	1	no	—
433	C₄⋊C₄	—	2	1	no	—
434	C₄⋊C₄	—	2	1	no	—
435	C₄⋊C₄	—	2	1	no	—
436	C₄⋊C₄	—	2	1	no	—
437	C₄⋊C₄	—	2	1	no	—
438	C₄⋊C₄	—	4	1	no	—
439	C₄⋊C₄	—	4	1	no	—
440	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
441	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
442	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
443	C₂²⋊C₄	—	2	4	no	—
444	C₂²⋊C₄	—	2	4	no	—
445	C₂²⋊C₄	—	2	4	no	—
446	C₂²⋊C₄	—	2	2	no	—
447	C₂²⋊C₄	—	2	2	no	—
448	C₂²⋊C₄	—	2	2	no	—
449	C₂²⋊C₄	—	4	1	no	—
450	C₄²	—	2	4	no	—
451	C₄²	—	2	2	no	—
452	C₄²	—	2	2	no	—
453	C₄²	—	2	2	no	—
454	C₄²	—	4	1	no	—
455	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
456	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
457	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
458	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
459	C₁₃	#18669	1	1	yes	characteristic, direct product factor, Sylow
460	C₂³	—	2	2	no	—
461	C₂³	C₁₃×#120	1	1	yes	characteristic
462	Q₈	—	2	2	no	—
463	Q₈	—	2	2	no	—
464	Q₈	—	4	2	no	—
465	Q₈	—	4	2	no	—
466	Q₈	—	4	2	no	—
467	Q₈	—	4	2	no	—
468	Q₈	—	4	1	no	—
469	Q₈	—	4	1	no	—
470	Q₈	—	4	1	no	—
471	Q₈	—	4	1	no	—
472	D₄	—	2	2	no	—
473	D₄	—	2	2	no	—
474	D₄	—	4	4	no	—
475	D₄	—	4	2	no	—
476	D₄	—	8	1	no	—
477	C₂×C₄	—	2	1	no	—
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	4	1	no	—
485	C₂×C₄	—	4	2	no	—
486	C₂×C₄	—	4	2	no	—
487	C₂×C₄	—	4	2	no	—
488	C₂×C₄	—	4	1	no	—
489	C₂×C₄	—	4	1	no	—
490	C₂×C₄	—	8	1	no	—
491	C₂×C₄	—	8	4	no	—
492	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
493	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
494	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
495	C₂×C₄	C₁₃×#135	1	2	yes	—
496	C₂×C₄	C₁₃×#137	1	2	yes	—
497	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
498	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
499	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
500	C₈	—	2	2	no	—
501	C₈	—	4	1	no	—
502	C₈	—	4	2	no	—
503	C₈	—	4	2	no	—
504	C₂²	—	2	1	no	—
505	C₂²	—	2	1	no	—
506	C₂²	—	4	2	no	—
507	C₂²	—	4	2	no	—
508	C₂²	—	4	2	no	—
509	C₂²	C₁₃×#452	1	2	yes	—
510	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
511	C₄	—	2	1	no	—
512	C₄	—	2	1	no	—
513	C₄	—	2	1	no	—
514	C₄	—	4	2	no	—
515	C₄	—	4	2	no	—
516	C₄	—	4	2	no	—
517	C₄	—	4	2	no	—
518	C₄	—	4	2	no	—
519	C₄	—	8	1	no	—
520	C₄	—	8	1	no	—
521	C₄	C₁₃×#452	1	2	yes	—
522	C₄	C₂×C₁₃×#135	1	1	yes	characteristic
523	C₄	C₂×C₁₃×#137	1	1	yes	characteristic
524	C₄	C₁₃×#577	1	1	yes	characteristic
525	C₄	C₁₃×#578	1	1	yes	characteristic
526	C₂	—	2	2	no	—
527	C₂	—	8	2	no	—
528	C₂	C₂×C₁₃×#452	1	1	yes	characteristic
529	C₂	C₁₃×#3013	1	1	yes	characteristic
530	C₂	C₁₃×#3018	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃
prime radical	C₁₃×#532	C₂²
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
3. C₁₃×#3170	C₂	semidirect
4. C₁₃×#3078	C₂	semidirect
5. C₁₃×#1650	C₂	semidirect
6. C₁₃×#1643	C₂	semidirect
7. C₁₃×#1638	C₂	semidirect
8. C₁₃×#1632	C₂	semidirect
9. C₁₃×#1550	C₂	semidirect
11. C₂×C₁₃×Q₈⋊C₈	C₂	semidirect
126. #18669	C₁₃	direct (N × H)
197. #3170	C₂×C₁₃	semidirect
198. #3078	C₂×C₁₃	semidirect
199. #1650	C₂×C₁₃	semidirect
200. #1643	C₂×C₁₃	semidirect
201. #1638	C₂×C₁₃	semidirect
202. #1632	C₂×C₁₃	semidirect
203. #1550	C₂×C₁₃	semidirect
205. C₂×Q₈⋊C₈	C₂×C₁₃	semidirect
459. C₁₃	#18669	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×#3507	2
C₁₃×#3246	2
C₁₃×#3170	2
C₁₃×#3078	2
C₁₃×#1650	2
C₁₃×#1643	2
C₁₃×#1638	2
C₁₃×#1632	2
C₁₃×#1550	2
C₁₃×#1492	2
C₂×C₁₃×Q₈⋊C₈	2
#18669	13

Subgroups — C13×#18669 #15705008

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#18669 #15705008