Subgroups — C₁₃×#18681 #15705020

Order 3328.

946 conjugacy classes of subgroups.

The subgroup lattice has 562 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
2	C₁₃×#3246	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3170	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3077	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1647	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1646	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1635	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1634	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, complemented
11	C₂×C₁₃×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#559	—	2	2	no	—
13	C₁₃×#556	—	2	1	no	—
14	C₁₃×#555	C₂²	1	2	yes	—
15	C₁₃×#553	—	2	2	no	—
16	C₁₃×#550	—	2	1	no	—
17	C₁₃×#547	C₂²	1	2	yes	—
18	C₁₃×#538	—	2	2	no	—
19	C₁₃×#535	—	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×#525	—	2	2	no	—
24	C₁₃×#520	—	2	1	no	—
25	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
26	C₁₃×#500	C₂²	1	1	yes	characteristic, complemented
27	C₁₃×#494	C₂²	1	1	yes	characteristic, complemented
28	C₁₃×#487	C₂²	1	1	yes	characteristic, complemented
29	C₁₃×#487	C₂²	1	1	yes	characteristic, complemented
30	C₁₃×#478	—	2	2	no	—
31	C₁₃×#476	C₂²	1	2	yes	—
32	C₁₃×#476	C₂²	1	2	yes	complemented
33	C₁₃×#475	—	2	1	no	—
34	C₁₃×#474	C₂²	1	2	yes	—
35	C₁₃×#467	—	2	2	no	—
36	C₁₃×#465	—	2	2	no	—
37	C₁₃×#461	C₂²	1	2	yes	complemented
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×#418	—	2	1	no	—
44	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
45	C₁₃×#333	C₂²	1	2	yes	complemented
46	C₁₃×#332	C₂²	1	2	yes	complemented
47	C₁₃×D₄⋊C₈	C₂²	1	2	yes	—
48	C₁₃×D₄⋊C₈	C₂²	1	2	yes	—
49	C₁₃×D₄⋊C₈	C₂²	1	2	yes	complemented
50	C₁₃×D₄⋊C₈	C₂²	1	2	yes	complemented
51	C₂×C₁₃×#41	—	2	2	no	—
52	C₂×C₁₃×#41	—	2	1	no	—
53	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
54	C₂³×C₄×C₁₃	—	2	1	no	—
55	C₂×C₁₃×Q₁₆	—	2	2	no	—
56	C₂×C₁₃×SD₁₆	—	2	2	no	—
57	C₂×C₁₃×M₁₆	—	2	1	no	—
58	C₂²×C₈×C₁₃	—	2	1	no	—
59	C₂²×C₈×C₁₃	—	2	1	no	—
60	C₁₃×C₄⋊Q₈	D₄	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×C₄⋊Q₈	C₂³	1	1	yes	characteristic
65	C₁₃×#127	—	2	2	no	—
66	C₁₃×#127	D₄	1	1	yes	characteristic
67	C₁₃×#126	—	2	4	no	—
68	C₁₃×#125	—	2	1	no	—
69	C₁₃×#125	—	2	1	no	—
70	C₁₃×#124	—	2	2	no	—
71	C₁₃×#124	—	2	4	no	—
72	C₁₃×#124	—	2	1	no	—
73	C₁₃×#123	—	2	4	no	—
74	C₁₃×#123	—	2	4	no	—
75	C₁₃×C₂²⋊Q₈	—	2	1	no	—
76	C₁₃×C₂²⋊Q₈	—	2	2	no	—
77	C₁₃×C₂²⋊Q₈	—	2	1	no	—
78	C₁₃×C₂²⋊Q₈	—	2	1	no	—
79	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
80	C₁₃×#121	—	2	4	no	—
81	C₁₃×#121	—	2	2	no	—
82	C₁₃×#121	—	2	2	no	—
83	C₁₃×#121	—	2	2	no	—
84	C₁₃×#121	—	2	1	no	—
85	C₁₃×#121	D₄	1	2	yes	—
86	C₁₃×#120	—	2	4	no	—
87	C₄×Q₈×C₁₃	—	2	2	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	D₄	1	2	yes	—
92	C₄×D₄×C₁₃	—	2	4	no	—
93	C₄×D₄×C₁₃	—	2	2	no	—
94	C₄×D₄×C₁₃	—	2	4	no	—
95	C₄×D₄×C₁₃	—	2	1	no	—
96	C₄×D₄×C₁₃	—	2	1	no	—
97	C₄×D₄×C₁₃	—	2	1	no	—
98	C₄×D₄×C₁₃	D₄	1	2	yes	—
99	C₄×D₄×C₁₃	C₂³	1	2	yes	—
100	C₄×D₄×C₁₃	C₂³	1	2	yes	—
101	C₁₃×#117	—	2	1	no	—
102	C₁₃×#117	—	2	2	no	—
103	C₁₃×#117	—	2	2	no	—
104	C₁₃×#117	—	2	1	no	—
105	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
106	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
107	C₂×C₁₃×C₂²⋊C₄	—	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×#102	—	2	2	no	—
121	C₁₃×#102	—	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	#18681	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
127	C₂⁴×C₁₃	—	2	1	no	—
128	C₁₃×#41	—	4	2	no	—
129	C₁₃×#41	—	4	2	no	—
130	C₁₃×#41	—	8	2	no	—
131	C₁₃×#41	—	8	2	no	—
132	C₂×Q₈×C₁₃	—	2	1	no	—
133	C₂×Q₈×C₁₃	—	2	1	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×D₄×C₁₃	—	2	2	no	—
138	C₂×D₄×C₁₃	—	2	4	no	—
139	C₂×D₄×C₁₃	—	2	4	no	—
140	C₂×D₄×C₁₃	—	2	1	no	—
141	C₂×D₄×C₁₃	—	2	1	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	C₂×D₄	1	2	yes	—
146	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
147	C₂²×C₄×C₁₃	—	2	4	no	—
148	C₂²×C₄×C₁₃	—	2	1	no	—
149	C₂²×C₄×C₁₃	—	2	2	no	—
150	C₂²×C₄×C₁₃	—	2	2	no	—
151	C₂²×C₄×C₁₃	—	2	2	no	—
152	C₂²×C₄×C₁₃	—	8	1	no	—
153	C₂²×C₄×C₁₃	—	8	1	no	—
154	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
157	C₁₃×Q₁₆	—	4	4	no	—
158	C₁₃×SD₁₆	—	8	2	no	—
159	C₁₃×M₁₆	—	4	2	no	—
160	C₂×C₈×C₁₃	—	2	1	no	—
161	C₂×C₈×C₁₃	—	2	1	no	—
162	C₂×C₈×C₁₃	—	2	2	no	—
163	C₂×C₈×C₁₃	—	2	2	no	—
164	C₂×C₈×C₁₃	—	4	2	no	—
165	C₂×C₈×C₁₃	—	8	1	no	—
166	C₁₃×C₄⋊C₄	—	2	4	no	—
167	C₁₃×C₄⋊C₄	—	2	1	no	—
168	C₁₃×C₄⋊C₄	—	2	2	no	—
169	C₁₃×C₄⋊C₄	—	2	1	no	—
170	C₁₃×C₄⋊C₄	—	2	2	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	—	2	1	no	—
175	C₁₃×C₄⋊C₄	—	2	1	no	—
176	C₁₃×C₄⋊C₄	—	2	1	no	—
177	C₁₃×C₄⋊C₄	—	2	1	no	—
178	C₁₃×C₄⋊C₄	—	4	1	no	—
179	C₁₃×C₄⋊C₄	—	4	1	no	—
180	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
181	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
182	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
183	C₁₃×C₂²⋊C₄	—	2	4	no	—
184	C₁₃×C₂²⋊C₄	—	2	4	no	—
185	C₁₃×C₂²⋊C₄	—	2	4	no	—
186	C₁₃×C₂²⋊C₄	—	2	2	no	—
187	C₁₃×C₂²⋊C₄	—	2	2	no	—
188	C₁₃×C₂²⋊C₄	—	2	2	no	—
189	C₁₃×C₂²⋊C₄	—	2	2	no	—
190	C₁₃×C₂²⋊C₄	—	2	2	no	—
191	C₁₃×C₂²⋊C₄	—	4	1	no	—
192	C₄²×C₁₃	—	2	4	no	—
193	C₄²×C₁₃	—	2	2	no	—
194	C₄²×C₁₃	—	4	1	no	—
195	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
196	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
197	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
198	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
199	#3506	C₂×C₁₃	1	1	yes	characteristic
200	#3246	C₂×C₁₃	1	1	yes	characteristic, complemented
201	#3170	C₂×C₁₃	1	1	yes	characteristic, complemented
202	#3077	C₂×C₁₃	1	1	yes	characteristic, complemented
203	#1647	C₂×C₁₃	1	2	yes	complemented
204	#1646	C₂×C₁₃	1	2	yes	complemented
205	#1635	C₂×C₁₃	1	2	yes	complemented
206	#1634	C₂×C₁₃	1	2	yes	complemented
207	#1550	C₂×C₁₃	1	1	yes	characteristic, complemented
208	#1492	C₂×C₁₃	1	1	yes	characteristic, complemented
209	C₂×D₄⋊C₈	C₂×C₁₃	1	1	yes	characteristic, complemented
210	C₂³×C₁₃	—	2	2	no	—
211	C₂³×C₁₃	—	2	2	no	—
212	C₂³×C₁₃	—	4	2	no	—
213	C₂³×C₁₃	—	8	1	no	—
214	C₂³×C₁₃	—	8	1	no	—
215	C₂³×C₁₃	#120	1	1	yes	characteristic
216	Q₈×C₁₃	—	4	2	no	—
217	Q₈×C₁₃	—	4	2	no	—
218	Q₈×C₁₃	—	4	1	no	—
219	Q₈×C₁₃	—	4	1	no	—
220	Q₈×C₁₃	—	4	2	no	—
221	Q₈×C₁₃	—	4	1	no	—
222	Q₈×C₁₃	—	4	1	no	—
223	D₄×C₁₃	—	2	2	no	—
224	D₄×C₁₃	—	2	2	no	—
225	D₄×C₁₃	—	2	2	no	—
226	D₄×C₁₃	—	2	2	no	—
227	D₄×C₁₃	—	4	4	no	—
228	D₄×C₁₃	—	4	2	no	—
229	D₄×C₁₃	—	4	2	no	—
230	D₄×C₁₃	—	8	1	no	—
231	D₄×C₁₃	—	8	4	no	—
232	D₄×C₁₃	—	8	4	no	—
233	C₂×C₄×C₁₃	—	2	1	no	—
234	C₂×C₄×C₁₃	—	2	1	no	—
235	C₂×C₄×C₁₃	—	2	2	no	—
236	C₂×C₄×C₁₃	—	2	2	no	—
237	C₂×C₄×C₁₃	—	2	2	no	—
238	C₂×C₄×C₁₃	—	2	2	no	—
239	C₂×C₄×C₁₃	—	4	1	no	—
240	C₂×C₄×C₁₃	—	4	2	no	—
241	C₂×C₄×C₁₃	—	4	2	no	—
242	C₂×C₄×C₁₃	—	4	2	no	—
243	C₂×C₄×C₁₃	—	4	2	no	—
244	C₂×C₄×C₁₃	—	4	1	no	—
245	C₂×C₄×C₁₃	—	4	1	no	—
246	C₂×C₄×C₁₃	—	8	2	no	—
247	C₂×C₄×C₁₃	—	8	1	no	—
248	C₂×C₄×C₁₃	—	8	4	no	—
249	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
250	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
251	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
252	C₂×C₄×C₁₃	#135	1	2	yes	—
253	C₂×C₄×C₁₃	#137	1	2	yes	—
254	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
255	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
256	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
257	C₈×C₁₃	—	2	2	no	—
258	C₈×C₁₃	—	4	1	no	—
259	C₈×C₁₃	—	4	2	no	—
260	C₈×C₁₃	—	4	2	no	—
261	#559	—	2	2	no	—
262	#556	—	2	1	no	—
263	#555	C₂²×C₁₃	1	2	yes	—
264	#553	—	2	2	no	—
265	#550	—	2	1	no	—
266	#547	C₂²×C₁₃	1	2	yes	—
267	#538	—	2	2	no	—
268	#535	—	2	1	no	—
269	#533	C₂²×C₁₃	1	1	yes	characteristic
270	#533	C₂²×C₁₃	1	1	yes	characteristic
271	#532	C₂²×C₁₃	1	1	yes	characteristic
272	#525	—	2	2	no	—
273	#520	—	2	1	no	—
274	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
275	#500	C₂²×C₁₃	1	1	yes	characteristic, complemented
276	#494	C₂²×C₁₃	1	1	yes	characteristic, complemented
277	#487	C₂²×C₁₃	1	1	yes	characteristic, complemented
278	#487	C₂²×C₁₃	1	1	yes	characteristic, complemented
279	#478	—	2	2	no	—
280	#476	C₂²×C₁₃	1	2	yes	—
281	#476	C₂²×C₁₃	1	2	yes	complemented
282	#475	—	2	1	no	—
283	#474	C₂²×C₁₃	1	2	yes	—
284	#467	—	2	2	no	—
285	#465	—	2	2	no	—
286	#461	C₂²×C₁₃	1	2	yes	complemented
287	#460	—	2	1	no	—
288	C₄×Q₁₆	—	2	2	no	—
289	#428	—	2	1	no	—
290	#423	C₂²×C₁₃	1	1	yes	characteristic
291	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
292	#418	—	2	1	no	—
293	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
294	#333	C₂²×C₁₃	1	2	yes	complemented
295	#332	C₂²×C₁₃	1	2	yes	complemented
296	D₄⋊C₈	C₂²×C₁₃	1	2	yes	—
297	D₄⋊C₈	C₂²×C₁₃	1	2	yes	—
298	D₄⋊C₈	C₂²×C₁₃	1	2	yes	complemented
299	D₄⋊C₈	C₂²×C₁₃	1	2	yes	complemented
300	C₂²×C₁₃	—	2	1	no	—
301	C₂²×C₁₃	—	2	1	no	—
302	C₂²×C₁₃	—	4	2	no	—
303	C₂²×C₁₃	—	4	2	no	—
304	C₂²×C₁₃	—	4	2	no	—
305	C₂²×C₁₃	—	4	2	no	—
306	C₂²×C₁₃	—	4	2	no	—
307	C₂²×C₁₃	—	4	2	no	—
308	C₂²×C₁₃	—	8	4	no	—
309	C₂²×C₁₃	#452	1	2	yes	—
310	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
311	C₄×C₁₃	—	2	1	no	—
312	C₄×C₁₃	—	2	1	no	—
313	C₄×C₁₃	—	2	1	no	—
314	C₄×C₁₃	—	4	2	no	—
315	C₄×C₁₃	—	4	2	no	—
316	C₄×C₁₃	—	4	2	no	—
317	C₄×C₁₃	—	4	2	no	—
318	C₄×C₁₃	—	8	1	no	—
319	C₄×C₁₃	—	8	1	no	—
320	C₄×C₁₃	#452	1	2	yes	—
321	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
322	C₄×C₁₃	C₂×#137	1	1	yes	characteristic
323	C₄×C₁₃	#576	1	1	yes	characteristic
324	C₄×C₁₃	#577	1	1	yes	characteristic
325	C₂×#41	—	2	2	no	—
326	C₂×#41	—	2	1	no	—
327	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
328	C₂³×C₄	—	2	1	no	—
329	C₂×Q₁₆	—	2	2	no	—
330	C₂×SD₁₆	—	2	2	no	—
331	C₂×M₁₆	—	2	1	no	—
332	C₂²×C₈	—	2	1	no	—
333	C₂²×C₈	—	2	1	no	—
334	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
335	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
336	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
337	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
338	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
339	#127	—	2	2	no	—
340	#127	D₄×C₁₃	1	1	yes	characteristic
341	#126	—	2	4	no	—
342	#125	—	2	1	no	—
343	#125	—	2	1	no	—
344	#124	—	2	2	no	—
345	#124	—	2	4	no	—
346	#124	—	2	1	no	—
347	#123	—	2	4	no	—
348	#123	—	2	4	no	—
349	C₂²⋊Q₈	—	2	1	no	—
350	C₂²⋊Q₈	—	2	2	no	—
351	C₂²⋊Q₈	—	2	1	no	—
352	C₂²⋊Q₈	—	2	1	no	—
353	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
354	#121	—	2	4	no	—
355	#121	—	2	2	no	—
356	#121	—	2	2	no	—
357	#121	—	2	2	no	—
358	#121	—	2	1	no	—
359	#121	D₄×C₁₃	1	2	yes	—
360	#120	—	2	4	no	—
361	C₄×Q₈	—	2	2	no	—
362	C₄×Q₈	—	2	1	no	—
363	C₄×Q₈	—	2	1	no	—
364	C₄×Q₈	—	2	1	no	—
365	C₄×Q₈	D₄×C₁₃	1	2	yes	—
366	C₄×D₄	—	2	4	no	—
367	C₄×D₄	—	2	2	no	—
368	C₄×D₄	—	2	4	no	—
369	C₄×D₄	—	2	1	no	—
370	C₄×D₄	—	2	1	no	—
371	C₄×D₄	—	2	1	no	—
372	C₄×D₄	D₄×C₁₃	1	2	yes	—
373	C₄×D₄	C₂³×C₁₃	1	2	yes	—
374	C₄×D₄	C₂³×C₁₃	1	2	yes	—
375	#117	—	2	1	no	—
376	#117	—	2	2	no	—
377	#117	—	2	2	no	—
378	#117	—	2	1	no	—
379	C₂×C₄⋊C₄	—	2	2	no	—
380	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
381	C₂×C₂²⋊C₄	—	2	1	no	—
382	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
383	#107	—	2	2	no	—
384	#107	—	2	2	no	—
385	#106	—	2	2	no	—
386	#106	—	2	2	no	—
387	C₄⋊C₈	—	2	1	no	—
388	C₄⋊C₈	—	2	1	no	—
389	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
390	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
391	#103	—	2	2	no	—
392	#103	—	2	2	no	—
393	#103	—	2	2	no	—
394	#102	—	2	2	no	—
395	#102	—	2	2	no	—
396	#102	—	2	2	no	—
397	C₄×C₈	—	2	1	no	—
398	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
399	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
400	C₂×C₁₃	—	2	2	no	—
401	C₂×C₁₃	—	8	2	no	—
402	C₂×C₁₃	—	8	2	no	—
403	C₂×C₁₃	C₂×#452	1	1	yes	characteristic
404	C₂×C₁₃	#3012	1	1	yes	characteristic
405	C₂×C₁₃	#3018	1	1	yes	characteristic
406	C₂⁴	—	2	1	no	—
407	#41	—	4	2	no	—
408	#41	—	4	2	no	—
409	#41	—	8	2	no	—
410	#41	—	8	2	no	—
411	C₂×Q₈	—	2	1	no	—
412	C₂×Q₈	—	2	1	no	—
413	C₂×Q₈	—	2	1	no	—
414	C₂×Q₈	—	2	1	no	—
415	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
416	C₂×D₄	—	2	2	no	—
417	C₂×D₄	—	2	4	no	—
418	C₂×D₄	—	2	4	no	—
419	C₂×D₄	—	2	1	no	—
420	C₂×D₄	—	2	1	no	—
421	C₂×D₄	—	2	1	no	—
422	C₂×D₄	—	2	2	no	—
423	C₂×D₄	—	2	2	no	—
424	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
425	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
426	C₂²×C₄	—	2	4	no	—
427	C₂²×C₄	—	2	1	no	—
428	C₂²×C₄	—	2	2	no	—
429	C₂²×C₄	—	2	2	no	—
430	C₂²×C₄	—	2	2	no	—
431	C₂²×C₄	—	8	1	no	—
432	C₂²×C₄	—	8	1	no	—
433	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
434	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
435	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
436	Q₁₆	—	4	4	no	—
437	SD₁₆	—	8	2	no	—
438	M₁₆	—	4	2	no	—
439	C₂×C₈	—	2	1	no	—
440	C₂×C₈	—	2	1	no	—
441	C₂×C₈	—	2	2	no	—
442	C₂×C₈	—	2	2	no	—
443	C₂×C₈	—	4	2	no	—
444	C₂×C₈	—	8	1	no	—
445	C₄⋊C₄	—	2	4	no	—
446	C₄⋊C₄	—	2	1	no	—
447	C₄⋊C₄	—	2	2	no	—
448	C₄⋊C₄	—	2	1	no	—
449	C₄⋊C₄	—	2	2	no	—
450	C₄⋊C₄	—	2	1	no	—
451	C₄⋊C₄	—	2	1	no	—
452	C₄⋊C₄	—	2	1	no	—
453	C₄⋊C₄	—	2	1	no	—
454	C₄⋊C₄	—	2	1	no	—
455	C₄⋊C₄	—	2	1	no	—
456	C₄⋊C₄	—	2	1	no	—
457	C₄⋊C₄	—	4	1	no	—
458	C₄⋊C₄	—	4	1	no	—
459	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
460	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
461	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
462	C₂²⋊C₄	—	2	4	no	—
463	C₂²⋊C₄	—	2	4	no	—
464	C₂²⋊C₄	—	2	4	no	—
465	C₂²⋊C₄	—	2	2	no	—
466	C₂²⋊C₄	—	2	2	no	—
467	C₂²⋊C₄	—	2	2	no	—
468	C₂²⋊C₄	—	2	2	no	—
469	C₂²⋊C₄	—	2	2	no	—
470	C₂²⋊C₄	—	4	1	no	—
471	C₄²	—	2	4	no	—
472	C₄²	—	2	2	no	—
473	C₄²	—	4	1	no	—
474	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
475	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
476	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
477	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
478	C₁₃	#18681	1	1	yes	characteristic, direct product factor, Sylow
479	C₂³	—	2	2	no	—
480	C₂³	—	2	2	no	—
481	C₂³	—	4	2	no	—
482	C₂³	—	8	1	no	—
483	C₂³	—	8	1	no	—
484	C₂³	C₁₃×#120	1	1	yes	characteristic
485	Q₈	—	4	2	no	—
486	Q₈	—	4	2	no	—
487	Q₈	—	4	2	no	—
488	Q₈	—	4	1	no	—
489	Q₈	—	4	1	no	—
490	Q₈	—	4	1	no	—
491	Q₈	—	4	1	no	—
492	D₄	—	2	2	no	—
493	D₄	—	2	2	no	—
494	D₄	—	2	2	no	—
495	D₄	—	2	2	no	—
496	D₄	—	4	4	no	—
497	D₄	—	4	2	no	—
498	D₄	—	4	2	no	—
499	D₄	—	8	1	no	—
500	D₄	—	8	4	no	—
501	D₄	—	8	4	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	2	2	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	4	1	no	—
509	C₂×C₄	—	4	2	no	—
510	C₂×C₄	—	4	2	no	—
511	C₂×C₄	—	4	2	no	—
512	C₂×C₄	—	4	2	no	—
513	C₂×C₄	—	4	1	no	—
514	C₂×C₄	—	4	1	no	—
515	C₂×C₄	—	8	2	no	—
516	C₂×C₄	—	8	1	no	—
517	C₂×C₄	—	8	4	no	—
518	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
519	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
520	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
521	C₂×C₄	C₁₃×#135	1	2	yes	—
522	C₂×C₄	C₁₃×#137	1	2	yes	—
523	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
524	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
525	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
526	C₈	—	2	2	no	—
527	C₈	—	4	1	no	—
528	C₈	—	4	2	no	—
529	C₈	—	4	2	no	—
530	C₂²	—	2	1	no	—
531	C₂²	—	2	1	no	—
532	C₂²	—	4	2	no	—
533	C₂²	—	4	2	no	—
534	C₂²	—	4	2	no	—
535	C₂²	—	4	2	no	—
536	C₂²	—	4	2	no	—
537	C₂²	—	4	2	no	—
538	C₂²	—	8	4	no	—
539	C₂²	C₁₃×#452	1	2	yes	—
540	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
541	C₄	—	2	1	no	—
542	C₄	—	2	1	no	—
543	C₄	—	2	1	no	—
544	C₄	—	4	2	no	—
545	C₄	—	4	2	no	—
546	C₄	—	4	2	no	—
547	C₄	—	4	2	no	—
548	C₄	—	8	1	no	—
549	C₄	—	8	1	no	—
550	C₄	C₁₃×#452	1	2	yes	—
551	C₄	C₂×C₁₃×#135	1	1	yes	characteristic
552	C₄	C₂×C₁₃×#137	1	1	yes	characteristic
553	C₄	C₁₃×#576	1	1	yes	characteristic
554	C₄	C₁₃×#577	1	1	yes	characteristic
555	C₂	—	2	2	no	—
556	C₂	—	8	2	no	—
557	C₂	—	8	2	no	—
558	C₂	C₂×C₁₃×#452	1	1	yes	characteristic
559	C₂	C₁₃×#3012	1	1	yes	characteristic
560	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×#3506	C₂
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
2. C₁₃×#3246	C₂	semidirect
3. C₁₃×#3170	C₂	semidirect
4. C₁₃×#3077	C₂	semidirect
5. C₁₃×#1647	C₂	semidirect
6. C₁₃×#1646	C₂	semidirect
7. C₁₃×#1635	C₂	semidirect
8. C₁₃×#1634	C₂	semidirect
9. C₁₃×#1550	C₂	semidirect
10. C₁₃×#1492	C₂	semidirect
11. C₂×C₁₃×D₄⋊C₈	C₂	semidirect
26. C₁₃×#500	C₂²	semidirect
27. C₁₃×#494	C₂²	semidirect
28. C₁₃×#487	C₂²	semidirect
29. C₁₃×#487	C₂²	semidirect
32. C₁₃×#476	C₂²	semidirect
37. C₁₃×#461	C₂²	semidirect
45. C₁₃×#333	C₂²	semidirect
46. C₁₃×#332	C₂²	semidirect
49. C₁₃×D₄⋊C₈	C₂²	semidirect
50. C₁₃×D₄⋊C₈	C₂²	semidirect
126. #18681	C₁₃	direct (N × H)
200. #3246	C₂×C₁₃	semidirect
201. #3170	C₂×C₁₃	semidirect
202. #3077	C₂×C₁₃	semidirect
203. #1647	C₂×C₁₃	semidirect
204. #1646	C₂×C₁₃	semidirect
205. #1635	C₂×C₁₃	semidirect
206. #1634	C₂×C₁₃	semidirect
207. #1550	C₂×C₁₃	semidirect
208. #1492	C₂×C₁₃	semidirect
209. C₂×D₄⋊C₈	C₂×C₁₃	semidirect
275. #500	C₂²×C₁₃	semidirect
276. #494	C₂²×C₁₃	semidirect
277. #487	C₂²×C₁₃	semidirect
278. #487	C₂²×C₁₃	semidirect
281. #476	C₂²×C₁₃	semidirect
286. #461	C₂²×C₁₃	semidirect
294. #333	C₂²×C₁₃	semidirect
295. #332	C₂²×C₁₃	semidirect
298. D₄⋊C₈	C₂²×C₁₃	semidirect
299. D₄⋊C₈	C₂²×C₁₃	semidirect
478. C₁₃	#18681	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×#3170	2
C₁₃×#3077	2
C₁₃×#1647	2
C₁₃×#1646	2
C₁₃×#1635	2
C₁₃×#1634	2
C₁₃×#1550	2
C₁₃×#1492	2
C₂×C₁₃×D₄⋊C₈	2
#18681	13

Subgroups — C13×#18681 #15705020

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#18681 #15705020