Subgroups — C₁₃×#18657 #15704996

Order 3328.

940 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×#3511	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#3206	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#500	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3079	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1650	C₂	1	4	yes	maximal, complemented
6	C₁₃×#1647	C₂	1	4	yes	maximal, complemented
7	C₁₃×#1549	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1492	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1476	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#556	C₂²	1	2	yes	—
11	C₁₃×#555	—	2	1	no	—
12	C₁₃×#554	—	2	1	no	—
13	C₁₃×#553	—	2	2	no	—
14	C₁₃×#548	—	2	2	no	—
15	C₁₃×#547	C₂²	1	2	yes	—
16	C₁₃×#542	—	2	2	no	—
17	C₁₃×#537	—	2	1	no	—
18	C₁₃×#533	—	2	1	no	—
19	C₁₃×#532	—	2	1	no	—
20	C₁₃×#532	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
23	C₁₃×#520	—	2	1	no	—
24	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
25	C₁₃×#500	—	2	2	no	—
26	C₁₃×#500	C₂²	1	4	yes	—
27	C₁₃×#492	—	2	1	no	—
28	C₁₃×#487	—	2	1	no	—
29	C₁₃×#477	—	2	1	no	—
30	C₁₃×#476	—	2	1	no	—
31	C₁₃×#475	C₂²	1	2	yes	—
32	C₁₃×#474	C₂²	1	2	yes	—
33	C₁₃×#461	C₂²	1	4	yes	—
34	C₁₃×#448	—	2	2	no	—
35	C₁₃×#431	C₂²	1	1	yes	characteristic
36	C₁₃×#428	—	2	1	no	—
37	C₂×C₁₃×#107	—	2	2	no	—
38	C₁₃×#423	C₂²	1	1	yes	characteristic
39	C₁₃×#417	—	2	1	no	—
40	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
41	C₁₃×#332	C₂²	1	4	yes	—
42	C₁₃×Q₈⋊C₈	C₂²	1	2	yes	—
43	C₁₃×D₄⋊C₈	C₂²	1	2	yes	—
44	C₁₃×D₄⋊C₈	C₂²	1	4	yes	—
45	C₂×C₁₃×#41	—	2	2	no	—
46	C₂×C₁₃×#41	—	2	1	no	—
47	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
48	C₂²×Q₈×C₁₃	—	2	1	no	—
49	C₂²×Q₈×C₁₃	—	2	1	no	—
50	C₂×C₁₃×SD₁₆	—	2	4	no	—
51	C₂×C₁₃×M₁₆	—	2	1	no	—
52	C₂²×C₈×C₁₃	—	2	1	no	—
53	C₁₃×C₄⋊Q₈	—	2	1	no	—
54	C₁₃×C₄⋊Q₈	—	2	1	no	—
55	C₁₃×C₄⋊Q₈	—	2	1	no	—
56	C₁₃×C₄⋊Q₈	—	2	1	no	—
57	C₁₃×C₄⋊Q₈	—	2	1	no	—
58	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
59	C₁₃×C₄⋊Q₈	D₄	1	2	yes	—
60	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
61	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
62	C₁₃×#127	D₄	1	1	yes	characteristic
63	C₁₃×#126	—	2	4	no	—
64	C₁₃×#125	—	2	2	no	—
65	C₁₃×#124	—	2	4	no	—
66	C₁₃×#124	—	2	2	no	—
67	C₁₃×#124	—	2	1	no	—
68	C₁₃×#123	—	2	4	no	—
69	C₁₃×C₂²⋊Q₈	—	2	2	no	—
70	C₁₃×C₂²⋊Q₈	—	2	4	no	—
71	C₁₃×C₂²⋊Q₈	—	2	2	no	—
72	C₁₃×C₂²⋊Q₈	—	2	2	no	—
73	C₁₃×#121	—	2	2	no	—
74	C₁₃×#121	—	2	2	no	—
75	C₁₃×#121	—	2	4	no	—
76	C₁₃×#121	—	2	2	no	—
77	C₁₃×#121	—	2	1	no	—
78	C₁₃×#121	D₄	1	2	yes	—
79	C₄×Q₈×C₁₃	—	2	2	no	—
80	C₄×Q₈×C₁₃	—	2	2	no	—
81	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
82	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
83	C₄×D₄×C₁₃	—	2	2	no	—
84	C₄×D₄×C₁₃	—	2	4	no	—
85	C₄×D₄×C₁₃	—	2	2	no	—
86	C₄×D₄×C₁₃	—	2	1	no	—
87	C₄×D₄×C₁₃	—	2	1	no	—
88	C₄×D₄×C₁₃	—	2	1	no	—
89	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
90	C₄×D₄×C₁₃	C₂³	1	2	yes	—
91	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
92	C₁₃×#117	—	2	2	no	—
93	C₁₃×#117	—	2	2	no	—
94	C₁₃×#117	—	2	1	no	—
95	C₁₃×#117	D₄	1	1	yes	characteristic
96	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
97	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
98	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
99	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
100	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
101	C₂×C₄²×C₁₃	—	2	1	no	—
102	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
103	C₁₃×#107	—	2	8	no	—
104	C₁₃×#107	—	2	2	no	—
105	C₁₃×#106	—	2	2	no	—
106	C₁₃×C₄⋊C₈	—	2	1	no	—
107	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
108	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
109	C₁₃×#103	—	2	2	no	—
110	C₁₃×#103	—	2	4	no	—
111	C₁₃×#102	—	2	2	no	—
112	C₁₃×C₂²⋊C₈	—	2	1	no	—
113	C₄×C₈×C₁₃	—	2	1	no	—
114	C₄×C₈×C₁₃	—	2	1	no	—
115	C₄×C₈×C₁₃	C₂³	1	2	yes	—
116	#18657	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
117	C₁₃×#41	—	2	2	no	—
118	C₁₃×#41	—	2	2	no	—
119	C₁₃×#41	—	4	2	no	—
120	C₁₃×#41	—	4	2	no	—
121	C₁₃×#41	—	8	4	no	—
122	C₂×Q₈×C₁₃	—	2	1	no	—
123	C₂×Q₈×C₁₃	—	2	2	no	—
124	C₂×Q₈×C₁₃	—	2	2	no	—
125	C₂×Q₈×C₁₃	—	2	2	no	—
126	C₂×Q₈×C₁₃	—	4	1	no	—
127	C₂×Q₈×C₁₃	—	8	2	no	—
128	C₂×Q₈×C₁₃	—	8	2	no	—
129	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
130	C₂×D₄×C₁₃	—	2	1	no	—
131	C₂×D₄×C₁₃	—	2	2	no	—
132	C₂×D₄×C₁₃	—	2	4	no	—
133	C₂×D₄×C₁₃	—	2	1	no	—
134	C₂×D₄×C₁₃	—	2	1	no	—
135	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
136	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
137	C₂²×C₄×C₁₃	—	2	4	no	—
138	C₂²×C₄×C₁₃	—	2	2	no	—
139	C₂²×C₄×C₁₃	—	2	1	no	—
140	C₂²×C₄×C₁₃	—	2	1	no	—
141	C₂²×C₄×C₁₃	—	2	1	no	—
142	C₂²×C₄×C₁₃	—	2	2	no	—
143	C₂²×C₄×C₁₃	—	4	1	no	—
144	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
147	C₁₃×SD₁₆	—	8	4	no	—
148	C₁₃×M₁₆	—	4	2	no	—
149	C₂×C₈×C₁₃	—	2	4	no	—
150	C₂×C₈×C₁₃	—	2	2	no	—
151	C₂×C₈×C₁₃	—	2	2	no	—
152	C₂×C₈×C₁₃	—	2	2	no	—
153	C₁₃×C₄⋊C₄	—	2	4	no	—
154	C₁₃×C₄⋊C₄	—	2	4	no	—
155	C₁₃×C₄⋊C₄	—	2	2	no	—
156	C₁₃×C₄⋊C₄	—	2	2	no	—
157	C₁₃×C₄⋊C₄	—	2	1	no	—
158	C₁₃×C₄⋊C₄	—	2	1	no	—
159	C₁₃×C₄⋊C₄	—	2	2	no	—
160	C₁₃×C₄⋊C₄	—	2	1	no	—
161	C₁₃×C₄⋊C₄	—	2	2	no	—
162	C₁₃×C₄⋊C₄	—	2	2	no	—
163	C₁₃×C₄⋊C₄	—	4	1	no	—
164	C₁₃×C₄⋊C₄	—	4	1	no	—
165	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
166	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
167	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
168	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
169	C₁₃×C₂²⋊C₄	—	2	4	no	—
170	C₁₃×C₂²⋊C₄	—	2	4	no	—
171	C₁₃×C₂²⋊C₄	—	2	4	no	—
172	C₁₃×C₂²⋊C₄	—	2	1	no	—
173	C₁₃×C₂²⋊C₄	—	2	1	no	—
174	C₁₃×C₂²⋊C₄	—	2	2	no	—
175	C₁₃×C₂²⋊C₄	—	2	1	no	—
176	C₁₃×C₂²⋊C₄	—	2	2	no	—
177	C₄²×C₁₃	—	2	4	no	—
178	C₄²×C₁₃	—	2	1	no	—
179	C₄²×C₁₃	—	2	1	no	—
180	C₄²×C₁₃	—	2	1	no	—
181	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
182	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
183	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
184	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
185	#3511	C₂×C₁₃	1	1	yes	characteristic
186	#3206	C₂×C₁₃	1	1	yes	characteristic, complemented
187	C₂×#500	C₂×C₁₃	1	1	yes	characteristic, complemented
188	#3079	C₂×C₁₃	1	1	yes	characteristic, complemented
189	#1650	C₂×C₁₃	1	4	yes	complemented
190	#1647	C₂×C₁₃	1	4	yes	complemented
191	#1549	C₂×C₁₃	1	1	yes	characteristic, complemented
192	#1492	C₂×C₁₃	1	1	yes	characteristic, complemented
193	#1476	C₂×C₁₃	1	1	yes	characteristic, complemented
194	C₂³×C₁₃	—	2	1	no	—
195	C₂³×C₁₃	—	2	2	no	—
196	C₂³×C₁₃	#120	1	1	yes	characteristic
197	Q₈×C₁₃	—	2	1	no	—
198	Q₈×C₁₃	—	2	1	no	—
199	Q₈×C₁₃	—	4	4	no	—
200	Q₈×C₁₃	—	4	2	no	—
201	Q₈×C₁₃	—	4	4	no	—
202	Q₈×C₁₃	—	8	2	no	—
203	Q₈×C₁₃	—	8	2	no	—
204	D₄×C₁₃	—	2	1	no	—
205	D₄×C₁₃	—	2	1	no	—
206	D₄×C₁₃	—	2	4	no	—
207	D₄×C₁₃	—	4	2	no	—
208	D₄×C₁₃	—	4	4	no	—
209	D₄×C₁₃	—	4	2	no	—
210	D₄×C₁₃	—	4	2	no	—
211	D₄×C₁₃	—	8	4	no	—
212	C₂×C₄×C₁₃	—	2	2	no	—
213	C₂×C₄×C₁₃	—	2	2	no	—
214	C₂×C₄×C₁₃	—	2	1	no	—
215	C₂×C₄×C₁₃	—	2	1	no	—
216	C₂×C₄×C₁₃	—	2	2	no	—
217	C₂×C₄×C₁₃	—	2	1	no	—
218	C₂×C₄×C₁₃	—	2	4	no	—
219	C₂×C₄×C₁₃	—	4	2	no	—
220	C₂×C₄×C₁₃	—	4	2	no	—
221	C₂×C₄×C₁₃	—	4	2	no	—
222	C₂×C₄×C₁₃	—	4	2	no	—
223	C₂×C₄×C₁₃	—	4	2	no	—
224	C₂×C₄×C₁₃	—	4	2	no	—
225	C₂×C₄×C₁₃	—	8	2	no	—
226	C₂×C₄×C₁₃	—	8	4	no	—
227	C₂×C₄×C₁₃	—	8	2	no	—
228	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
229	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
230	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
231	C₂×C₄×C₁₃	#135	1	2	yes	—
232	C₂×C₄×C₁₃	#137	1	2	yes	—
233	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
234	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
235	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
236	C₈×C₁₃	—	2	4	no	—
237	C₈×C₁₃	—	4	2	no	—
238	C₈×C₁₃	—	4	2	no	—
239	#556	C₂²×C₁₃	1	2	yes	—
240	#555	—	2	1	no	—
241	#554	—	2	1	no	—
242	#553	—	2	2	no	—
243	#548	—	2	2	no	—
244	#547	C₂²×C₁₃	1	2	yes	—
245	#542	—	2	2	no	—
246	#537	—	2	1	no	—
247	#533	—	2	1	no	—
248	#532	—	2	1	no	—
249	#532	C₂²×C₁₃	1	1	yes	characteristic
250	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
251	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
252	#520	—	2	1	no	—
253	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
254	#500	—	2	2	no	—
255	#500	C₂²×C₁₃	1	4	yes	—
256	#492	—	2	1	no	—
257	#487	—	2	1	no	—
258	#477	—	2	1	no	—
259	#476	—	2	1	no	—
260	#475	C₂²×C₁₃	1	2	yes	—
261	#474	C₂²×C₁₃	1	2	yes	—
262	#461	C₂²×C₁₃	1	4	yes	—
263	#448	—	2	2	no	—
264	#431	C₂²×C₁₃	1	1	yes	characteristic
265	#428	—	2	1	no	—
266	C₂×#107	—	2	2	no	—
267	#423	C₂²×C₁₃	1	1	yes	characteristic
268	#417	—	2	1	no	—
269	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
270	#332	C₂²×C₁₃	1	4	yes	—
271	Q₈⋊C₈	C₂²×C₁₃	1	2	yes	—
272	D₄⋊C₈	C₂²×C₁₃	1	2	yes	—
273	D₄⋊C₈	C₂²×C₁₃	1	4	yes	—
274	C₂²×C₁₃	—	2	1	no	—
275	C₂²×C₁₃	—	2	1	no	—
276	C₂²×C₁₃	—	4	1	no	—
277	C₂²×C₁₃	—	4	2	no	—
278	C₂²×C₁₃	—	4	1	no	—
279	C₂²×C₁₃	—	4	2	no	—
280	C₂²×C₁₃	—	4	1	no	—
281	C₂²×C₁₃	—	4	2	no	—
282	C₂²×C₁₃	#452	1	2	yes	—
283	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
284	C₄×C₁₃	—	2	1	no	—
285	C₄×C₁₃	—	2	1	no	—
286	C₄×C₁₃	—	4	1	no	—
287	C₄×C₁₃	—	4	2	no	—
288	C₄×C₁₃	—	4	1	no	—
289	C₄×C₁₃	—	4	4	no	—
290	C₄×C₁₃	—	4	1	no	—
291	C₄×C₁₃	—	8	2	no	—
292	C₄×C₁₃	#452	1	2	yes	—
293	C₄×C₁₃	#456	1	2	yes	—
294	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
295	C₄×C₁₃	C₂×#137	1	1	yes	characteristic
296	C₄×C₁₃	#576	1	2	yes	—
297	C₂×#41	—	2	2	no	—
298	C₂×#41	—	2	1	no	—
299	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
300	C₂²×Q₈	—	2	1	no	—
301	C₂²×Q₈	—	2	1	no	—
302	C₂×SD₁₆	—	2	4	no	—
303	C₂×M₁₆	—	2	1	no	—
304	C₂²×C₈	—	2	1	no	—
305	C₄⋊Q₈	—	2	1	no	—
306	C₄⋊Q₈	—	2	1	no	—
307	C₄⋊Q₈	—	2	1	no	—
308	C₄⋊Q₈	—	2	1	no	—
309	C₄⋊Q₈	—	2	1	no	—
310	C₄⋊Q₈	D₄×C₁₃	1	2	yes	—
311	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
312	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
313	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
314	#127	D₄×C₁₃	1	1	yes	characteristic
315	#126	—	2	4	no	—
316	#125	—	2	2	no	—
317	#124	—	2	4	no	—
318	#124	—	2	2	no	—
319	#124	—	2	1	no	—
320	#123	—	2	4	no	—
321	C₂²⋊Q₈	—	2	2	no	—
322	C₂²⋊Q₈	—	2	4	no	—
323	C₂²⋊Q₈	—	2	2	no	—
324	C₂²⋊Q₈	—	2	2	no	—
325	#121	—	2	2	no	—
326	#121	—	2	2	no	—
327	#121	—	2	4	no	—
328	#121	—	2	2	no	—
329	#121	—	2	1	no	—
330	#121	D₄×C₁₃	1	2	yes	—
331	C₄×Q₈	—	2	2	no	—
332	C₄×Q₈	—	2	2	no	—
333	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
334	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
335	C₄×D₄	—	2	2	no	—
336	C₄×D₄	—	2	4	no	—
337	C₄×D₄	—	2	2	no	—
338	C₄×D₄	—	2	1	no	—
339	C₄×D₄	—	2	1	no	—
340	C₄×D₄	—	2	1	no	—
341	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
342	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
343	C₄×D₄	C₂³×C₁₃	1	2	yes	—
344	#117	—	2	2	no	—
345	#117	—	2	2	no	—
346	#117	—	2	1	no	—
347	#117	D₄×C₁₃	1	1	yes	characteristic
348	C₂×C₄⋊C₄	—	2	1	no	—
349	C₂×C₄⋊C₄	—	2	2	no	—
350	C₂×C₄⋊C₄	—	2	1	no	—
351	C₂×C₄⋊C₄	—	2	1	no	—
352	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
353	C₂×C₄²	—	2	1	no	—
354	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
355	#107	—	2	8	no	—
356	#107	—	2	2	no	—
357	#106	—	2	2	no	—
358	C₄⋊C₈	—	2	1	no	—
359	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
360	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
361	#103	—	2	2	no	—
362	#103	—	2	4	no	—
363	#102	—	2	2	no	—
364	C₂²⋊C₈	—	2	1	no	—
365	C₄×C₈	—	2	1	no	—
366	C₄×C₈	—	2	1	no	—
367	C₄×C₈	C₂³×C₁₃	1	2	yes	—
368	C₂×C₁₃	—	2	2	no	—
369	C₂×C₁₃	—	8	1	no	—
370	C₂×C₁₃	—	8	2	no	—
371	C₂×C₁₃	C₂×#452	1	1	yes	characteristic
372	C₂×C₁₃	#3008	1	1	yes	characteristic
373	C₂×C₁₃	C₂×#456	1	1	yes	characteristic
374	#41	—	2	2	no	—
375	#41	—	2	2	no	—
376	#41	—	4	2	no	—
377	#41	—	4	2	no	—
378	#41	—	8	4	no	—
379	C₂×Q₈	—	2	1	no	—
380	C₂×Q₈	—	2	2	no	—
381	C₂×Q₈	—	2	2	no	—
382	C₂×Q₈	—	2	2	no	—
383	C₂×Q₈	—	4	1	no	—
384	C₂×Q₈	—	8	2	no	—
385	C₂×Q₈	—	8	2	no	—
386	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
387	C₂×D₄	—	2	1	no	—
388	C₂×D₄	—	2	2	no	—
389	C₂×D₄	—	2	4	no	—
390	C₂×D₄	—	2	1	no	—
391	C₂×D₄	—	2	1	no	—
392	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
393	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
394	C₂²×C₄	—	2	4	no	—
395	C₂²×C₄	—	2	2	no	—
396	C₂²×C₄	—	2	1	no	—
397	C₂²×C₄	—	2	1	no	—
398	C₂²×C₄	—	2	1	no	—
399	C₂²×C₄	—	2	2	no	—
400	C₂²×C₄	—	4	1	no	—
401	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
402	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
403	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
404	SD₁₆	—	8	4	no	—
405	M₁₆	—	4	2	no	—
406	C₂×C₈	—	2	4	no	—
407	C₂×C₈	—	2	2	no	—
408	C₂×C₈	—	2	2	no	—
409	C₂×C₈	—	2	2	no	—
410	C₄⋊C₄	—	2	4	no	—
411	C₄⋊C₄	—	2	4	no	—
412	C₄⋊C₄	—	2	2	no	—
413	C₄⋊C₄	—	2	2	no	—
414	C₄⋊C₄	—	2	1	no	—
415	C₄⋊C₄	—	2	1	no	—
416	C₄⋊C₄	—	2	2	no	—
417	C₄⋊C₄	—	2	1	no	—
418	C₄⋊C₄	—	2	2	no	—
419	C₄⋊C₄	—	2	2	no	—
420	C₄⋊C₄	—	4	1	no	—
421	C₄⋊C₄	—	4	1	no	—
422	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
423	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
424	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
425	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
426	C₂²⋊C₄	—	2	4	no	—
427	C₂²⋊C₄	—	2	4	no	—
428	C₂²⋊C₄	—	2	4	no	—
429	C₂²⋊C₄	—	2	1	no	—
430	C₂²⋊C₄	—	2	1	no	—
431	C₂²⋊C₄	—	2	2	no	—
432	C₂²⋊C₄	—	2	1	no	—
433	C₂²⋊C₄	—	2	2	no	—
434	C₄²	—	2	4	no	—
435	C₄²	—	2	1	no	—
436	C₄²	—	2	1	no	—
437	C₄²	—	2	1	no	—
438	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
439	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
440	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
441	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
442	C₁₃	#18657	1	1	yes	characteristic, direct product factor, Sylow
443	C₂³	—	2	1	no	—
444	C₂³	—	2	2	no	—
445	C₂³	C₁₃×#120	1	1	yes	characteristic
446	Q₈	—	2	1	no	—
447	Q₈	—	2	1	no	—
448	Q₈	—	4	2	no	—
449	Q₈	—	4	4	no	—
450	Q₈	—	4	4	no	—
451	Q₈	—	8	2	no	—
452	Q₈	—	8	2	no	—
453	D₄	—	2	1	no	—
454	D₄	—	2	1	no	—
455	D₄	—	2	4	no	—
456	D₄	—	4	2	no	—
457	D₄	—	4	4	no	—
458	D₄	—	4	2	no	—
459	D₄	—	4	2	no	—
460	D₄	—	8	4	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	1	no	—
467	C₂×C₄	—	2	4	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	—	4	2	no	—
470	C₂×C₄	—	4	2	no	—
471	C₂×C₄	—	4	2	no	—
472	C₂×C₄	—	4	2	no	—
473	C₂×C₄	—	4	2	no	—
474	C₂×C₄	—	8	2	no	—
475	C₂×C₄	—	8	4	no	—
476	C₂×C₄	—	8	2	no	—
477	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
478	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
479	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
480	C₂×C₄	C₁₃×#135	1	2	yes	—
481	C₂×C₄	C₁₃×#137	1	2	yes	—
482	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
483	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
484	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
485	C₈	—	2	4	no	—
486	C₈	—	4	2	no	—
487	C₈	—	4	2	no	—
488	C₂²	—	2	1	no	—
489	C₂²	—	2	1	no	—
490	C₂²	—	4	1	no	—
491	C₂²	—	4	2	no	—
492	C₂²	—	4	1	no	—
493	C₂²	—	4	2	no	—
494	C₂²	—	4	1	no	—
495	C₂²	—	4	2	no	—
496	C₂²	C₁₃×#452	1	2	yes	—
497	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
498	C₄	—	2	1	no	—
499	C₄	—	2	1	no	—
500	C₄	—	4	1	no	—
501	C₄	—	4	4	no	—
502	C₄	—	4	1	no	—
503	C₄	—	4	1	no	—
504	C₄	—	4	2	no	—
505	C₄	—	8	2	no	—
506	C₄	C₁₃×#452	1	2	yes	—
507	C₄	C₁₃×#456	1	2	yes	—
508	C₄	C₂×C₁₃×#135	1	1	yes	characteristic
509	C₄	C₂×C₁₃×#137	1	1	yes	characteristic
510	C₄	C₁₃×#576	1	2	yes	—
511	C₂	—	2	2	no	—
512	C₂	—	8	1	no	—
513	C₂	—	8	2	no	—
514	C₂	C₂×C₁₃×#452	1	1	yes	characteristic
515	C₂	C₁₃×#3008	1	1	yes	characteristic
516	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×#3511	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×#3206	C₂	semidirect
3. C₂×C₁₃×#500	C₂	semidirect
4. C₁₃×#3079	C₂	semidirect
5. C₁₃×#1650	C₂	semidirect
6. C₁₃×#1647	C₂	semidirect
7. C₁₃×#1549	C₂	semidirect
8. C₁₃×#1492	C₂	semidirect
9. C₁₃×#1476	C₂	semidirect
116. #18657	C₁₃	direct (N × H)
186. #3206	C₂×C₁₃	semidirect
187. C₂×#500	C₂×C₁₃	semidirect
188. #3079	C₂×C₁₃	semidirect
189. #1650	C₂×C₁₃	semidirect
190. #1647	C₂×C₁₃	semidirect
191. #1549	C₂×C₁₃	semidirect
192. #1492	C₂×C₁₃	semidirect
193. #1476	C₂×C₁₃	semidirect
442. C₁₃	#18657	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×#3511	2
C₁₃×#3206	2
C₂×C₁₃×#500	2
C₁₃×#3079	2
C₁₃×#1650	2
C₁₃×#1647	2
C₁₃×#1549	2
C₁₃×#1492	2
C₁₃×#1476	2
#18657	13

Subgroups — C13×#18657 #15704996

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#18657 #15704996