Subgroups — C₁₃×#18702 #15705041

Order 3328.

868 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3550	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#3255	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3254	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#3160	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1652	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1651	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1650	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1649	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1561	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1493	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1492	C₂	1	1	yes	maximal, characteristic
12	C₁₃×#563	—	2	2	no	—
13	C₁₃×#559	—	2	1	no	—
14	Q₈²×C₁₃	—	2	1	no	—
15	C₁₃×#556	—	2	1	no	—
16	C₁₃×#556	C₂²	1	2	yes	—
17	D₄×Q₈×C₁₃	—	2	1	no	—
18	D₄×Q₈×C₁₃	C₂²	1	2	yes	—
19	C₁₃×#542	—	2	2	no	—
20	C₁₃×#542	—	2	2	no	—
21	C₁₃×#536	—	2	2	no	—
22	C₁₃×#533	C₂²	1	1	yes	characteristic
23	C₁₃×#533	C₂²	1	1	yes	characteristic
24	C₁₃×#533	C₂²	1	1	yes	characteristic
25	C₁₃×#532	C₂²	1	1	yes	characteristic
26	C₁₃×#500	C₂²	1	1	yes	characteristic
27	C₁₃×#500	C₂²	1	1	yes	characteristic
28	C₁₃×#499	—	2	2	no	—
29	C₁₃×#498	C₂²	1	1	yes	characteristic
30	C₁₃×#498	C₂²	1	1	yes	characteristic
31	C₁₃×#477	—	2	1	no	—
32	C₁₃×#475	—	2	1	no	—
33	C₁₃×#475	C₂²	1	2	yes	—
34	C₁₃×#474	C₂²	1	2	yes	—
35	C₁₃×#470	—	2	2	no	—
36	C₁₃×#468	—	2	2	no	—
37	C₁₃×#462	—	2	1	no	—
38	C₁₃×#462	C₂²	1	2	yes	—
39	C₁₃×#461	C₂²	1	2	yes	—
40	C₁₃×#460	—	2	1	no	—
41	C₁₃×#427	—	2	2	no	—
42	C₁₃×#423	C₂²	1	1	yes	characteristic
43	C₁₃×#423	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
45	C₁₃×#332	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	—	2	2	no	—
53	C₂×C₁₃×Q₁₆	—	2	2	no	—
54	C₂×C₁₃×SD₁₆	—	2	2	no	—
55	C₂×C₁₃×M₁₆	—	2	1	no	—
56	C₂×C₁₃×M₁₆	—	2	1	no	—
57	C₂²×C₈×C₁₃	—	2	1	no	—
58	C₁₃×C₄⋊Q₈	—	2	4	no	—
59	C₁₃×C₄⋊Q₈	—	2	2	no	—
60	C₁₃×C₄⋊Q₈	—	2	2	no	—
61	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
62	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
63	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
64	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
65	C₁₃×C₄⋊Q₈	C₂³	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	D₄	1	1	yes	characteristic
69	C₁₃×#126	—	2	4	no	—
70	C₁₃×#126	—	2	4	no	—
71	C₁₃×#125	—	2	1	no	—
72	C₁₃×#125	—	2	1	no	—
73	C₁₃×#125	D₄	1	2	yes	—
74	C₁₃×#124	—	2	4	no	—
75	C₁₃×#124	—	2	2	no	—
76	C₁₃×#124	—	2	2	no	—
77	C₁₃×#124	—	2	1	no	—
78	C₁₃×#123	—	2	4	no	—
79	C₁₃×#123	—	2	4	no	—
80	C₁₃×C₂²⋊Q₈	—	2	4	no	—
81	C₁₃×C₂²⋊Q₈	—	2	2	no	—
82	C₁₃×C₂²⋊Q₈	—	2	1	no	—
83	C₁₃×C₂²⋊Q₈	—	2	1	no	—
84	C₁₃×C₂²⋊Q₈	—	2	1	no	—
85	C₁₃×C₂²⋊Q₈	—	2	2	no	—
86	C₁₃×C₂²⋊Q₈	—	2	4	no	—
87	C₁₃×C₂²⋊Q₈	—	2	1	no	—
88	C₁₃×C₂²⋊Q₈	—	2	1	no	—
89	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
90	C₁₃×#121	—	2	1	no	—
91	C₁₃×#121	D₄	1	2	yes	—
92	C₄×Q₈×C₁₃	—	2	2	no	—
93	C₄×Q₈×C₁₃	—	2	2	no	—
94	C₄×Q₈×C₁₃	—	2	1	no	—
95	C₄×Q₈×C₁₃	—	2	1	no	—
96	C₄×Q₈×C₁₃	—	2	1	no	—
97	C₄×Q₈×C₁₃	—	2	1	no	—
98	C₄×Q₈×C₁₃	—	2	1	no	—
99	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
100	C₄×D₄×C₁₃	—	2	2	no	—
101	C₄×D₄×C₁₃	—	2	2	no	—
102	C₄×D₄×C₁₃	—	2	1	no	—
103	C₄×D₄×C₁₃	C₂³	1	2	yes	—
104	C₁₃×#117	—	2	1	no	—
105	C₁₃×#117	—	2	2	no	—
106	C₁₃×#117	—	2	1	no	—
107	C₁₃×#117	D₄	1	2	yes	—
108	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
109	C₁₃×#107	—	2	2	no	—
110	C₁₃×#107	—	2	2	no	—
111	C₁₃×#107	—	2	2	no	—
112	C₁₃×#106	—	2	2	no	—
113	C₁₃×#106	—	2	2	no	—
114	C₁₃×#106	—	2	2	no	—
115	C₁₃×C₄⋊C₈	—	2	1	no	—
116	C₁₃×C₄⋊C₈	—	2	1	no	—
117	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
118	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
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	#18702	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
127	C₁₃×#41	—	8	1	no	—
128	C₁₃×#41	—	8	1	no	—
129	C₂×Q₈×C₁₃	—	2	4	no	—
130	C₂×Q₈×C₁₃	—	2	1	no	—
131	C₂×Q₈×C₁₃	—	2	1	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	—	8	2	no	—
137	C₂×Q₈×C₁₃	—	8	2	no	—
138	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
139	C₂×D₄×C₁₃	—	2	2	no	—
140	C₂×D₄×C₁₃	—	2	1	no	—
141	C₂×D₄×C₁₃	—	2	1	no	—
142	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
143	C₂²×C₄×C₁₃	—	2	4	no	—
144	C₂²×C₄×C₁₃	—	2	2	no	—
145	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
148	C₁₃×Q₁₆	—	8	2	no	—
149	C₁₃×SD₁₆	—	8	2	no	—
150	C₁₃×M₁₆	—	8	1	no	—
151	C₁₃×M₁₆	—	8	1	no	—
152	C₂×C₈×C₁₃	—	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	C₁₃×C₄⋊C₄	—	2	4	no	—
158	C₁₃×C₄⋊C₄	—	2	4	no	—
159	C₁₃×C₄⋊C₄	—	2	1	no	—
160	C₁₃×C₄⋊C₄	—	2	1	no	—
161	C₁₃×C₄⋊C₄	—	2	1	no	—
162	C₁₃×C₄⋊C₄	—	2	1	no	—
163	C₁₃×C₄⋊C₄	—	2	2	no	—
164	C₁₃×C₄⋊C₄	—	2	2	no	—
165	C₁₃×C₄⋊C₄	—	2	2	no	—
166	C₁₃×C₄⋊C₄	—	2	1	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	1	no	—
171	C₁₃×C₄⋊C₄	—	2	1	no	—
172	C₁₃×C₄⋊C₄	—	2	1	no	—
173	C₁₃×C₄⋊C₄	—	4	1	no	—
174	C₁₃×C₄⋊C₄	—	4	1	no	—
175	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
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	—	2	2	no	—
186	C₁₃×C₂²⋊C₄	—	4	1	no	—
187	C₄²×C₁₃	—	2	4	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	#3550	C₂×C₁₃	1	1	yes	characteristic
196	#3255	C₂×C₁₃	1	1	yes	characteristic, complemented
197	#3254	C₂×C₁₃	1	1	yes	characteristic
198	#3160	C₂×C₁₃	1	1	yes	characteristic, complemented
199	#1652	C₂×C₁₃	1	2	yes	complemented
200	#1651	C₂×C₁₃	1	2	yes	complemented
201	#1650	C₂×C₁₃	1	2	yes	complemented
202	#1649	C₂×C₁₃	1	2	yes	complemented
203	#1561	C₂×C₁₃	1	1	yes	characteristic, complemented
204	#1493	C₂×C₁₃	1	1	yes	characteristic, complemented
205	#1492	C₂×C₁₃	1	1	yes	characteristic
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	1	no	—
211	Q₈×C₁₃	—	4	1	no	—
212	Q₈×C₁₃	—	4	1	no	—
213	Q₈×C₁₃	—	4	1	no	—
214	Q₈×C₁₃	—	4	2	no	—
215	Q₈×C₁₃	—	4	1	no	—
216	Q₈×C₁₃	—	4	1	no	—
217	Q₈×C₁₃	—	4	1	no	—
218	Q₈×C₁₃	—	4	1	no	—
219	Q₈×C₁₃	—	8	1	no	—
220	Q₈×C₁₃	—	8	4	no	—
221	D₄×C₁₃	—	2	2	no	—
222	D₄×C₁₃	—	2	2	no	—
223	D₄×C₁₃	—	4	2	no	—
224	D₄×C₁₃	—	8	1	no	—
225	D₄×C₁₃	—	8	2	no	—
226	C₂×C₄×C₁₃	—	2	1	no	—
227	C₂×C₄×C₁₃	—	2	1	no	—
228	C₂×C₄×C₁₃	—	2	1	no	—
229	C₂×C₄×C₁₃	—	2	1	no	—
230	C₂×C₄×C₁₃	—	2	2	no	—
231	C₂×C₄×C₁₃	—	2	2	no	—
232	C₂×C₄×C₁₃	—	2	2	no	—
233	C₂×C₄×C₁₃	—	2	2	no	—
234	C₂×C₄×C₁₃	—	2	2	no	—
235	C₂×C₄×C₁₃	—	2	2	no	—
236	C₂×C₄×C₁₃	—	4	2	no	—
237	C₂×C₄×C₁₃	—	4	2	no	—
238	C₂×C₄×C₁₃	—	4	1	no	—
239	C₂×C₄×C₁₃	—	4	1	no	—
240	C₂×C₄×C₁₃	—	8	4	no	—
241	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
242	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
243	C₂×C₄×C₁₃	#120	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	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
247	C₈×C₁₃	—	2	2	no	—
248	C₈×C₁₃	—	2	2	no	—
249	C₈×C₁₃	—	4	2	no	—
250	C₈×C₁₃	—	4	2	no	—
251	#563	—	2	2	no	—
252	#559	—	2	1	no	—
253	Q₈²	—	2	1	no	—
254	#556	—	2	1	no	—
255	#556	C₂²×C₁₃	1	2	yes	—
256	D₄×Q₈	—	2	1	no	—
257	D₄×Q₈	C₂²×C₁₃	1	2	yes	—
258	#542	—	2	2	no	—
259	#542	—	2	2	no	—
260	#536	—	2	2	no	—
261	#533	C₂²×C₁₃	1	1	yes	characteristic
262	#533	C₂²×C₁₃	1	1	yes	characteristic
263	#533	C₂²×C₁₃	1	1	yes	characteristic
264	#532	C₂²×C₁₃	1	1	yes	characteristic
265	#500	C₂²×C₁₃	1	1	yes	characteristic
266	#500	C₂²×C₁₃	1	1	yes	characteristic
267	#499	—	2	2	no	—
268	#498	C₂²×C₁₃	1	1	yes	characteristic
269	#498	C₂²×C₁₃	1	1	yes	characteristic
270	#477	—	2	1	no	—
271	#475	—	2	1	no	—
272	#475	C₂²×C₁₃	1	2	yes	—
273	#474	C₂²×C₁₃	1	2	yes	—
274	#470	—	2	2	no	—
275	#468	—	2	2	no	—
276	#462	—	2	1	no	—
277	#462	C₂²×C₁₃	1	2	yes	—
278	#461	C₂²×C₁₃	1	2	yes	—
279	#460	—	2	1	no	—
280	#427	—	2	2	no	—
281	#423	C₂²×C₁₃	1	1	yes	characteristic
282	#423	C₂²×C₁₃	1	1	yes	characteristic
283	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
284	#332	C₂²×C₁₃	1	2	yes	—
285	#332	C₂²×C₁₃	1	2	yes	—
286	Q₈⋊C₈	C₂²×C₁₃	1	2	yes	—
287	Q₈⋊C₈	C₂²×C₁₃	1	2	yes	—
288	D₄⋊C₈	C₂²×C₁₃	1	2	yes	—
289	D₄⋊C₈	C₂²×C₁₃	1	2	yes	—
290	C₂²×C₁₃	—	2	1	no	—
291	C₂²×C₁₃	—	2	1	no	—
292	C₂²×C₁₃	—	2	1	no	—
293	C₂²×C₁₃	—	4	2	no	—
294	C₂²×C₁₃	—	4	2	no	—
295	C₂²×C₁₃	—	4	2	no	—
296	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
297	C₄×C₁₃	—	2	1	no	—
298	C₄×C₁₃	—	2	1	no	—
299	C₄×C₁₃	—	2	1	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	—	4	2	no	—
305	C₄×C₁₃	—	8	1	no	—
306	C₄×C₁₃	—	8	1	no	—
307	C₄×C₁₃	#456	1	2	yes	—
308	C₄×C₁₃	#576	1	1	yes	characteristic
309	C₄×C₁₃	#577	1	1	yes	characteristic
310	C₄×C₁₃	#577	1	1	yes	characteristic
311	C₄×C₁₃	#578	1	1	yes	characteristic
312	C₂×#41	—	2	1	no	—
313	C₂²×Q₈	—	2	2	no	—
314	C₂×Q₁₆	—	2	2	no	—
315	C₂×SD₁₆	—	2	2	no	—
316	C₂×M₁₆	—	2	1	no	—
317	C₂×M₁₆	—	2	1	no	—
318	C₂²×C₈	—	2	1	no	—
319	C₄⋊Q₈	—	2	4	no	—
320	C₄⋊Q₈	—	2	2	no	—
321	C₄⋊Q₈	—	2	2	no	—
322	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
323	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
324	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
325	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
326	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
327	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
328	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
329	#127	D₄×C₁₃	1	1	yes	characteristic
330	#126	—	2	4	no	—
331	#126	—	2	4	no	—
332	#125	—	2	1	no	—
333	#125	—	2	1	no	—
334	#125	D₄×C₁₃	1	2	yes	—
335	#124	—	2	4	no	—
336	#124	—	2	2	no	—
337	#124	—	2	2	no	—
338	#124	—	2	1	no	—
339	#123	—	2	4	no	—
340	#123	—	2	4	no	—
341	C₂²⋊Q₈	—	2	4	no	—
342	C₂²⋊Q₈	—	2	2	no	—
343	C₂²⋊Q₈	—	2	1	no	—
344	C₂²⋊Q₈	—	2	1	no	—
345	C₂²⋊Q₈	—	2	1	no	—
346	C₂²⋊Q₈	—	2	2	no	—
347	C₂²⋊Q₈	—	2	4	no	—
348	C₂²⋊Q₈	—	2	1	no	—
349	C₂²⋊Q₈	—	2	1	no	—
350	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
351	#121	—	2	1	no	—
352	#121	D₄×C₁₃	1	2	yes	—
353	C₄×Q₈	—	2	2	no	—
354	C₄×Q₈	—	2	2	no	—
355	C₄×Q₈	—	2	1	no	—
356	C₄×Q₈	—	2	1	no	—
357	C₄×Q₈	—	2	1	no	—
358	C₄×Q₈	—	2	1	no	—
359	C₄×Q₈	—	2	1	no	—
360	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
361	C₄×D₄	—	2	2	no	—
362	C₄×D₄	—	2	2	no	—
363	C₄×D₄	—	2	1	no	—
364	C₄×D₄	C₂³×C₁₃	1	2	yes	—
365	#117	—	2	1	no	—
366	#117	—	2	2	no	—
367	#117	—	2	1	no	—
368	#117	D₄×C₁₃	1	2	yes	—
369	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
370	#107	—	2	2	no	—
371	#107	—	2	2	no	—
372	#107	—	2	2	no	—
373	#106	—	2	2	no	—
374	#106	—	2	2	no	—
375	#106	—	2	2	no	—
376	C₄⋊C₈	—	2	1	no	—
377	C₄⋊C₈	—	2	1	no	—
378	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
379	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
380	#103	—	2	2	no	—
381	#103	—	2	2	no	—
382	#103	—	2	2	no	—
383	#102	—	2	2	no	—
384	C₄×C₈	—	2	1	no	—
385	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
386	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
387	C₂×C₁₃	—	4	1	no	—
388	C₂×C₁₃	—	8	2	no	—
389	C₂×C₁₃	#3012	1	1	yes	characteristic
390	C₂×C₁₃	#3013	1	1	yes	characteristic
391	C₂×C₁₃	C₂×#456	1	1	yes	characteristic
392	#41	—	8	1	no	—
393	#41	—	8	1	no	—
394	C₂×Q₈	—	2	4	no	—
395	C₂×Q₈	—	2	1	no	—
396	C₂×Q₈	—	2	1	no	—
397	C₂×Q₈	—	2	1	no	—
398	C₂×Q₈	—	2	1	no	—
399	C₂×Q₈	—	2	1	no	—
400	C₂×Q₈	—	2	1	no	—
401	C₂×Q₈	—	8	2	no	—
402	C₂×Q₈	—	8	2	no	—
403	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
404	C₂×D₄	—	2	2	no	—
405	C₂×D₄	—	2	1	no	—
406	C₂×D₄	—	2	1	no	—
407	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
408	C₂²×C₄	—	2	4	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	—	8	2	no	—
414	SD₁₆	—	8	2	no	—
415	M₁₆	—	8	1	no	—
416	M₁₆	—	8	1	no	—
417	C₂×C₈	—	2	4	no	—
418	C₂×C₈	—	2	1	no	—
419	C₂×C₈	—	2	1	no	—
420	C₂×C₈	—	2	2	no	—
421	C₂×C₈	—	2	2	no	—
422	C₄⋊C₄	—	2	4	no	—
423	C₄⋊C₄	—	2	4	no	—
424	C₄⋊C₄	—	2	1	no	—
425	C₄⋊C₄	—	2	1	no	—
426	C₄⋊C₄	—	2	1	no	—
427	C₄⋊C₄	—	2	1	no	—
428	C₄⋊C₄	—	2	2	no	—
429	C₄⋊C₄	—	2	2	no	—
430	C₄⋊C₄	—	2	2	no	—
431	C₄⋊C₄	—	2	1	no	—
432	C₄⋊C₄	—	2	1	no	—
433	C₄⋊C₄	—	2	2	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	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
444	C₂²⋊C₄	—	2	4	no	—
445	C₂²⋊C₄	—	2	4	no	—
446	C₂²⋊C₄	—	2	4	no	—
447	C₂²⋊C₄	—	2	2	no	—
448	C₂²⋊C₄	—	2	2	no	—
449	C₂²⋊C₄	—	2	2	no	—
450	C₂²⋊C₄	—	2	2	no	—
451	C₂²⋊C₄	—	4	1	no	—
452	C₄²	—	2	4	no	—
453	C₄²	—	2	2	no	—
454	C₄²	—	2	2	no	—
455	C₄²	—	4	1	no	—
456	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
457	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
458	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
459	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
460	C₁₃	#18702	1	1	yes	characteristic, direct product factor, Sylow
461	C₂³	—	2	2	no	—
462	C₂³	C₁₃×#120	1	1	yes	characteristic
463	Q₈	—	2	2	no	—
464	Q₈	—	2	2	no	—
465	Q₈	—	4	2	no	—
466	Q₈	—	4	1	no	—
467	Q₈	—	4	1	no	—
468	Q₈	—	4	1	no	—
469	Q₈	—	4	1	no	—
470	Q₈	—	4	1	no	—
471	Q₈	—	4	1	no	—
472	Q₈	—	4	1	no	—
473	Q₈	—	4	1	no	—
474	Q₈	—	8	1	no	—
475	Q₈	—	8	4	no	—
476	D₄	—	2	2	no	—
477	D₄	—	2	2	no	—
478	D₄	—	4	2	no	—
479	D₄	—	8	1	no	—
480	D₄	—	8	2	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	2	1	no	—
484	C₂×C₄	—	2	1	no	—
485	C₂×C₄	—	2	1	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	4	2	no	—
492	C₂×C₄	—	4	2	no	—
493	C₂×C₄	—	4	1	no	—
494	C₂×C₄	—	4	1	no	—
495	C₂×C₄	—	8	4	no	—
496	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
497	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
498	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
499	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
500	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
501	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
502	C₈	—	2	2	no	—
503	C₈	—	2	2	no	—
504	C₈	—	4	2	no	—
505	C₈	—	4	2	no	—
506	C₂²	—	2	1	no	—
507	C₂²	—	2	1	no	—
508	C₂²	—	2	1	no	—
509	C₂²	—	4	2	no	—
510	C₂²	—	4	2	no	—
511	C₂²	—	4	2	no	—
512	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
513	C₄	—	2	1	no	—
514	C₄	—	2	1	no	—
515	C₄	—	2	1	no	—
516	C₄	—	4	2	no	—
517	C₄	—	4	2	no	—
518	C₄	—	4	2	no	—
519	C₄	—	4	2	no	—
520	C₄	—	4	2	no	—
521	C₄	—	8	1	no	—
522	C₄	—	8	1	no	—
523	C₄	C₁₃×#456	1	2	yes	—
524	C₄	C₁₃×#576	1	1	yes	characteristic
525	C₄	C₁₃×#577	1	1	yes	characteristic
526	C₄	C₁₃×#577	1	1	yes	characteristic
527	C₄	C₁₃×#578	1	1	yes	characteristic
528	C₂	—	4	1	no	—
529	C₂	—	8	2	no	—
530	C₂	C₁₃×#3012	1	1	yes	characteristic
531	C₂	C₁₃×#3013	1	1	yes	characteristic
532	C₂	C₂×C₁₃×#456	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
2. C₁₃×#3255	C₂	semidirect
4. C₁₃×#3160	C₂	semidirect
5. C₁₃×#1652	C₂	semidirect
6. C₁₃×#1651	C₂	semidirect
7. C₁₃×#1650	C₂	semidirect
8. C₁₃×#1649	C₂	semidirect
9. C₁₃×#1561	C₂	semidirect
10. C₁₃×#1493	C₂	semidirect
126. #18702	C₁₃	direct (N × H)
196. #3255	C₂×C₁₃	semidirect
198. #3160	C₂×C₁₃	semidirect
199. #1652	C₂×C₁₃	semidirect
200. #1651	C₂×C₁₃	semidirect
201. #1650	C₂×C₁₃	semidirect
202. #1649	C₂×C₁₃	semidirect
203. #1561	C₂×C₁₃	semidirect
204. #1493	C₂×C₁₃	semidirect
460. C₁₃	#18702	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×#3550	2
C₁₃×#3255	2
C₁₃×#3254	2
C₁₃×#3160	2
C₁₃×#1652	2
C₁₃×#1651	2
C₁₃×#1650	2
C₁₃×#1649	2
C₁₃×#1561	2
C₁₃×#1493	2
C₁₃×#1492	2
#18702	13

Subgroups — C13×#18702 #15705041

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#18702 #15705041