Subgroups — C₁₃×#18722 #15705061

Order 3328.

1004 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3549	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#3226	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3206	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3141	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1646	C₂	1	4	yes	maximal, complemented
6	C₁₃×#1639	C₂	1	4	yes	maximal, complemented
7	C₁₃×#1543	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1484	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1484	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×H(3,𝔽₄)	—	2	2	no	—
11	C₁₃×#555	—	2	1	no	—
12	C₁₃×#555	—	2	1	no	—
13	C₁₃×#555	C₂²	1	2	yes	—
14	D₄²×C₁₃	—	2	1	no	—
15	D₄²×C₁₃	—	2	1	no	—
16	D₄²×C₁₃	C₂²	1	2	yes	—
17	C₁₃×#535	—	2	2	no	—
18	C₁₃×#535	—	2	2	no	—
19	C₁₃×#535	—	2	2	no	—
20	C₁₃×#532	C₂²	1	1	yes	characteristic
21	C₁₃×#532	C₂²	1	1	yes	characteristic
22	C₁₃×#532	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
24	C₁₃×#500	—	2	1	no	—
25	C₁₃×#492	—	2	1	no	—
26	C₁₃×#489	—	2	2	no	—
27	C₁₃×#487	—	2	1	no	—
28	C₁₃×#487	C₂²	1	2	yes	complemented
29	C₁₃×#486	—	2	1	no	—
30	C₁₃×#486	C₂²	1	2	yes	—
31	C₁₃×#480	—	2	2	no	—
32	C₁₃×#474	C₂²	1	4	yes	complemented
33	C₁₃×#461	C₂²	1	4	yes	complemented
34	C₁₃×#448	—	2	2	no	—
35	C₁₃×#431	C₂²	1	1	yes	characteristic, complemented
36	C₁₃×#431	C₂²	1	1	yes	characteristic, complemented
37	C₁₃×#417	—	2	2	no	—
38	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic, complemented
39	C₁₃×#333	C₂²	1	2	yes	complemented
40	C₁₃×#331	C₂²	1	2	yes	—
41	C₁₃×D₄⋊C₈	C₂²	1	4	yes	complemented
42	C₁₃×D₄⋊C₈	C₂²	1	4	yes	complemented
43	C₂×C₁₃×#41	—	2	1	no	—
44	C₂×C₁₃×#41	—	2	1	no	—
45	C₂×C₁₃×#41	D₄	1	2	yes	—
46	C₂²×Q₈×C₁₃	—	2	1	no	—
47	C₂²×D₄×C₁₃	—	2	2	no	—
48	C₂²×D₄×C₁₃	—	2	2	no	—
49	C₂²×D₄×C₁₃	—	2	2	no	—
50	C₂×C₁₃×SD₁₆	—	2	4	no	—
51	C₂×C₁₃×M₁₆	—	2	1	no	—
52	C₁₃×C₄⋊Q₈	—	2	1	no	—
53	C₁₃×C₄⋊Q₈	—	2	1	no	—
54	C₁₃×C₄⋊Q₈	—	2	1	no	—
55	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
56	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
57	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
58	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
59	C₁₃×#127	—	2	4	no	—
60	C₁₃×#127	D₄	1	1	yes	characteristic
61	C₁₃×#127	D₄	1	1	yes	characteristic
62	C₁₃×#127	C₂³	1	1	yes	characteristic
63	C₁₃×#124	—	2	4	no	—
64	C₁₃×#124	—	2	4	no	—
65	C₁₃×#124	—	2	4	no	—
66	C₁₃×#124	—	2	1	no	—
67	C₁₃×#124	—	2	1	no	—
68	C₁₃×#124	D₄	1	2	yes	—
69	C₁₃×#121	—	2	2	no	—
70	C₁₃×#121	—	2	2	no	—
71	C₁₃×#121	—	2	2	no	—
72	C₁₃×#121	—	2	2	no	—
73	C₁₃×#121	—	2	1	no	—
74	C₁₃×#121	—	2	1	no	—
75	C₁₃×#121	—	2	1	no	—
76	C₁₃×#121	—	2	1	no	—
77	C₁₃×#121	—	2	2	no	—
78	C₁₃×#121	—	2	2	no	—
79	C₁₃×#121	D₄	1	2	yes	—
80	C₁₃×#121	D₄	1	2	yes	—
81	C₁₃×#120	—	2	4	no	—
82	C₁₃×#120	—	2	4	no	—
83	C₁₃×#120	—	2	4	no	—
84	C₁₃×#120	—	2	4	no	—
85	C₄×D₄×C₁₃	—	2	1	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	C₂³	1	2	yes	—
90	C₄×D₄×C₁₃	C₂³	1	2	yes	—
91	C₁₃×#117	—	2	2	no	—
92	C₁₃×#117	—	2	2	no	—
93	C₁₃×#117	—	2	2	no	—
94	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
95	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
96	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
97	C₁₃×#107	—	2	4	no	—
98	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
99	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
100	C₁₃×#103	—	2	4	no	—
101	C₁₃×#103	—	2	4	no	—
102	C₁₃×#102	—	2	4	no	—
103	C₁₃×#102	—	2	4	no	—
104	C₁₃×C₂²⋊C₈	—	2	1	no	—
105	C₁₃×C₂²⋊C₈	—	2	1	no	—
106	C₁₃×#97	—	2	1	no	—
107	C₄×C₈×C₁₃	—	2	1	no	—
108	C₄×C₈×C₁₃	—	2	1	no	—
109	C₄×C₈×C₁₃	C₂³	1	2	yes	—
110	#18722	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
111	C₂⁴×C₁₃	—	2	4	no	—
112	C₁₃×#41	—	4	4	no	—
113	C₁₃×#41	—	8	2	no	—
114	C₁₃×#41	—	8	2	no	—
115	C₂×Q₈×C₁₃	—	2	1	no	—
116	C₂×Q₈×C₁₃	—	2	1	no	—
117	C₂×Q₈×C₁₃	—	2	2	no	—
118	C₂×Q₈×C₁₃	—	4	1	no	—
119	C₂×Q₈×C₁₃	—	8	2	no	—
120	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
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	2	no	—
126	C₂×D₄×C₁₃	—	2	2	no	—
127	C₂×D₄×C₁₃	—	2	1	no	—
128	C₂×D₄×C₁₃	—	2	1	no	—
129	C₂×D₄×C₁₃	—	2	1	no	—
130	C₂×D₄×C₁₃	—	2	1	no	—
131	C₂×D₄×C₁₃	—	2	1	no	—
132	C₂×D₄×C₁₃	—	2	1	no	—
133	C₂×D₄×C₁₃	—	8	4	no	—
134	C₂×D₄×C₁₃	—	8	4	no	—
135	C₂×D₄×C₁₃	—	8	4	no	—
136	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
137	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
138	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
139	C₂²×C₄×C₁₃	—	2	2	no	—
140	C₂²×C₄×C₁₃	—	2	2	no	—
141	C₂²×C₄×C₁₃	—	2	2	no	—
142	C₂²×C₄×C₁₃	—	4	1	no	—
143	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
146	C₁₃×SD₁₆	—	8	4	no	—
147	C₁₃×M₁₆	—	4	2	no	—
148	C₂×C₈×C₁₃	—	2	2	no	—
149	C₂×C₈×C₁₃	—	2	2	no	—
150	C₂×C₈×C₁₃	—	2	2	no	—
151	C₁₃×C₄⋊C₄	—	2	1	no	—
152	C₁₃×C₄⋊C₄	—	2	1	no	—
153	C₁₃×C₄⋊C₄	—	2	1	no	—
154	C₁₃×C₄⋊C₄	—	2	1	no	—
155	C₁₃×C₄⋊C₄	—	2	2	no	—
156	C₁₃×C₄⋊C₄	—	2	2	no	—
157	C₁₃×C₄⋊C₄	—	4	1	no	—
158	C₁₃×C₄⋊C₄	—	4	1	no	—
159	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
160	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
161	C₁₃×C₂²⋊C₄	—	2	4	no	—
162	C₁₃×C₂²⋊C₄	—	2	4	no	—
163	C₁₃×C₂²⋊C₄	—	2	4	no	—
164	C₁₃×C₂²⋊C₄	—	2	2	no	—
165	C₁₃×C₂²⋊C₄	—	2	2	no	—
166	C₁₃×C₂²⋊C₄	—	2	2	no	—
167	C₁₃×C₂²⋊C₄	—	2	2	no	—
168	C₁₃×C₂²⋊C₄	—	2	2	no	—
169	C₁₃×C₂²⋊C₄	—	2	2	no	—
170	C₄²×C₁₃	—	2	4	no	—
171	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
172	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
173	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
174	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
175	#3549	C₂×C₁₃	1	1	yes	characteristic
176	#3226	C₂×C₁₃	1	1	yes	characteristic, complemented
177	#3206	C₂×C₁₃	1	1	yes	characteristic, complemented
178	#3141	C₂×C₁₃	1	1	yes	characteristic, complemented
179	#1646	C₂×C₁₃	1	4	yes	complemented
180	#1639	C₂×C₁₃	1	4	yes	complemented
181	#1543	C₂×C₁₃	1	1	yes	characteristic, complemented
182	#1484	C₂×C₁₃	1	1	yes	characteristic, complemented
183	#1484	C₂×C₁₃	1	1	yes	characteristic, complemented
184	C₂³×C₁₃	—	2	2	no	—
185	C₂³×C₁₃	—	2	2	no	—
186	C₂³×C₁₃	—	2	2	no	—
187	C₂³×C₁₃	—	8	4	no	—
188	C₂³×C₁₃	—	8	4	no	—
189	C₂³×C₁₃	—	8	4	no	—
190	C₂³×C₁₃	#120	1	1	yes	characteristic
191	Q₈×C₁₃	—	4	2	no	—
192	Q₈×C₁₃	—	4	4	no	—
193	Q₈×C₁₃	—	8	1	no	—
194	Q₈×C₁₃	—	8	1	no	—
195	Q₈×C₁₃	—	8	2	no	—
196	D₄×C₁₃	—	2	4	no	—
197	D₄×C₁₃	—	2	4	no	—
198	D₄×C₁₃	—	4	2	no	—
199	D₄×C₁₃	—	4	2	no	—
200	D₄×C₁₃	—	4	2	no	—
201	D₄×C₁₃	—	4	2	no	—
202	D₄×C₁₃	—	4	2	no	—
203	D₄×C₁₃	—	8	1	no	—
204	D₄×C₁₃	—	8	1	no	—
205	D₄×C₁₃	—	8	2	no	—
206	D₄×C₁₃	—	8	2	no	—
207	D₄×C₁₃	—	8	2	no	—
208	D₄×C₁₃	—	8	4	no	—
209	D₄×C₁₃	—	8	4	no	—
210	D₄×C₁₃	—	8	4	no	—
211	C₂×C₄×C₁₃	—	2	2	no	—
212	C₂×C₄×C₁₃	—	2	2	no	—
213	C₂×C₄×C₁₃	—	2	2	no	—
214	C₂×C₄×C₁₃	—	2	2	no	—
215	C₂×C₄×C₁₃	—	2	2	no	—
216	C₂×C₄×C₁₃	—	2	2	no	—
217	C₂×C₄×C₁₃	—	4	4	no	—
218	C₂×C₄×C₁₃	—	4	4	no	—
219	C₂×C₄×C₁₃	—	4	4	no	—
220	C₂×C₄×C₁₃	—	4	2	no	—
221	C₂×C₄×C₁₃	—	8	2	no	—
222	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
223	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
224	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
225	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
226	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
227	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
228	C₈×C₁₃	—	4	2	no	—
229	C₈×C₁₃	—	4	2	no	—
230	C₈×C₁₃	—	4	2	no	—
231	H(3,𝔽₄)	—	2	2	no	—
232	#555	—	2	1	no	—
233	#555	—	2	1	no	—
234	#555	C₂²×C₁₃	1	2	yes	—
235	D₄²	—	2	1	no	—
236	D₄²	—	2	1	no	—
237	D₄²	C₂²×C₁₃	1	2	yes	—
238	#535	—	2	2	no	—
239	#535	—	2	2	no	—
240	#535	—	2	2	no	—
241	#532	C₂²×C₁₃	1	1	yes	characteristic
242	#532	C₂²×C₁₃	1	1	yes	characteristic
243	#532	C₂²×C₁₃	1	1	yes	characteristic
244	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
245	#500	—	2	1	no	—
246	#492	—	2	1	no	—
247	#489	—	2	2	no	—
248	#487	—	2	1	no	—
249	#487	C₂²×C₁₃	1	2	yes	complemented
250	#486	—	2	1	no	—
251	#486	C₂²×C₁₃	1	2	yes	—
252	#480	—	2	2	no	—
253	#474	C₂²×C₁₃	1	4	yes	complemented
254	#461	C₂²×C₁₃	1	4	yes	complemented
255	#448	—	2	2	no	—
256	#431	C₂²×C₁₃	1	1	yes	characteristic, complemented
257	#431	C₂²×C₁₃	1	1	yes	characteristic, complemented
258	#417	—	2	2	no	—
259	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
260	#333	C₂²×C₁₃	1	2	yes	complemented
261	#331	C₂²×C₁₃	1	2	yes	—
262	D₄⋊C₈	C₂²×C₁₃	1	4	yes	complemented
263	D₄⋊C₈	C₂²×C₁₃	1	4	yes	complemented
264	C₂²×C₁₃	—	2	1	no	—
265	C₂²×C₁₃	—	2	1	no	—
266	C₂²×C₁₃	—	2	1	no	—
267	C₂²×C₁₃	—	4	2	no	—
268	C₂²×C₁₃	—	4	2	no	—
269	C₂²×C₁₃	—	4	2	no	—
270	C₂²×C₁₃	—	4	2	no	—
271	C₂²×C₁₃	—	4	2	no	—
272	C₂²×C₁₃	—	4	2	no	—
273	C₂²×C₁₃	—	4	2	no	—
274	C₂²×C₁₃	—	4	2	no	—
275	C₂²×C₁₃	—	4	2	no	—
276	C₂²×C₁₃	—	16	8	no	—
277	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
278	C₄×C₁₃	—	2	1	no	—
279	C₄×C₁₃	—	2	1	no	—
280	C₄×C₁₃	—	2	1	no	—
281	C₄×C₁₃	—	4	2	no	—
282	C₄×C₁₃	—	4	2	no	—
283	C₄×C₁₃	—	4	2	no	—
284	C₄×C₁₃	—	8	2	no	—
285	C₄×C₁₃	#455	1	2	yes	—
286	C₄×C₁₃	#576	1	2	yes	—
287	C₄×C₁₃	#577	1	2	yes	—
288	C₂×#41	—	2	1	no	—
289	C₂×#41	—	2	1	no	—
290	C₂×#41	D₄×C₁₃	1	2	yes	—
291	C₂²×Q₈	—	2	1	no	—
292	C₂²×D₄	—	2	2	no	—
293	C₂²×D₄	—	2	2	no	—
294	C₂²×D₄	—	2	2	no	—
295	C₂×SD₁₆	—	2	4	no	—
296	C₂×M₁₆	—	2	1	no	—
297	C₄⋊Q₈	—	2	1	no	—
298	C₄⋊Q₈	—	2	1	no	—
299	C₄⋊Q₈	—	2	1	no	—
300	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
301	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
302	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
303	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
304	#127	—	2	4	no	—
305	#127	D₄×C₁₃	1	1	yes	characteristic
306	#127	D₄×C₁₃	1	1	yes	characteristic
307	#127	C₂³×C₁₃	1	1	yes	characteristic
308	#124	—	2	4	no	—
309	#124	—	2	4	no	—
310	#124	—	2	4	no	—
311	#124	—	2	1	no	—
312	#124	—	2	1	no	—
313	#124	D₄×C₁₃	1	2	yes	—
314	#121	—	2	2	no	—
315	#121	—	2	2	no	—
316	#121	—	2	2	no	—
317	#121	—	2	2	no	—
318	#121	—	2	1	no	—
319	#121	—	2	1	no	—
320	#121	—	2	1	no	—
321	#121	—	2	1	no	—
322	#121	—	2	2	no	—
323	#121	—	2	2	no	—
324	#121	D₄×C₁₃	1	2	yes	—
325	#121	D₄×C₁₃	1	2	yes	—
326	#120	—	2	4	no	—
327	#120	—	2	4	no	—
328	#120	—	2	4	no	—
329	#120	—	2	4	no	—
330	C₄×D₄	—	2	1	no	—
331	C₄×D₄	—	2	1	no	—
332	C₄×D₄	—	2	1	no	—
333	C₄×D₄	—	2	1	no	—
334	C₄×D₄	C₂³×C₁₃	1	2	yes	—
335	C₄×D₄	C₂³×C₁₃	1	2	yes	—
336	#117	—	2	2	no	—
337	#117	—	2	2	no	—
338	#117	—	2	2	no	—
339	C₂×C₄⋊C₄	—	2	1	no	—
340	C₂×C₄⋊C₄	—	2	1	no	—
341	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
342	#107	—	2	4	no	—
343	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
344	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
345	#103	—	2	4	no	—
346	#103	—	2	4	no	—
347	#102	—	2	4	no	—
348	#102	—	2	4	no	—
349	C₂²⋊C₈	—	2	1	no	—
350	C₂²⋊C₈	—	2	1	no	—
351	#97	—	2	1	no	—
352	C₄×C₈	—	2	1	no	—
353	C₄×C₈	—	2	1	no	—
354	C₄×C₈	C₂³×C₁₃	1	2	yes	—
355	C₂×C₁₃	—	4	1	no	—
356	C₂×C₁₃	—	8	2	no	—
357	C₂×C₁₃	—	8	2	no	—
358	C₂×C₁₃	—	8	2	no	—
359	C₂×C₁₃	#3008	1	1	yes	characteristic
360	C₂×C₁₃	#3009	1	1	yes	characteristic
361	C₂×C₁₃	C₂×#455	1	1	yes	characteristic
362	C₂⁴	—	2	4	no	—
363	#41	—	4	4	no	—
364	#41	—	8	2	no	—
365	#41	—	8	2	no	—
366	C₂×Q₈	—	2	1	no	—
367	C₂×Q₈	—	2	1	no	—
368	C₂×Q₈	—	2	2	no	—
369	C₂×Q₈	—	4	1	no	—
370	C₂×Q₈	—	8	2	no	—
371	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
372	C₂×D₄	—	2	4	no	—
373	C₂×D₄	—	2	4	no	—
374	C₂×D₄	—	2	4	no	—
375	C₂×D₄	—	2	2	no	—
376	C₂×D₄	—	2	2	no	—
377	C₂×D₄	—	2	2	no	—
378	C₂×D₄	—	2	1	no	—
379	C₂×D₄	—	2	1	no	—
380	C₂×D₄	—	2	1	no	—
381	C₂×D₄	—	2	1	no	—
382	C₂×D₄	—	2	1	no	—
383	C₂×D₄	—	2	1	no	—
384	C₂×D₄	—	8	4	no	—
385	C₂×D₄	—	8	4	no	—
386	C₂×D₄	—	8	4	no	—
387	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
388	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
389	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
390	C₂²×C₄	—	2	2	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	—	4	1	no	—
394	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
395	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
396	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
397	SD₁₆	—	8	4	no	—
398	M₁₆	—	4	2	no	—
399	C₂×C₈	—	2	2	no	—
400	C₂×C₈	—	2	2	no	—
401	C₂×C₈	—	2	2	no	—
402	C₄⋊C₄	—	2	1	no	—
403	C₄⋊C₄	—	2	1	no	—
404	C₄⋊C₄	—	2	1	no	—
405	C₄⋊C₄	—	2	1	no	—
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	—	2	2	no	—
408	C₄⋊C₄	—	4	1	no	—
409	C₄⋊C₄	—	4	1	no	—
410	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
411	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
412	C₂²⋊C₄	—	2	4	no	—
413	C₂²⋊C₄	—	2	4	no	—
414	C₂²⋊C₄	—	2	4	no	—
415	C₂²⋊C₄	—	2	2	no	—
416	C₂²⋊C₄	—	2	2	no	—
417	C₂²⋊C₄	—	2	2	no	—
418	C₂²⋊C₄	—	2	2	no	—
419	C₂²⋊C₄	—	2	2	no	—
420	C₂²⋊C₄	—	2	2	no	—
421	C₄²	—	2	4	no	—
422	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
423	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
424	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
425	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
426	C₁₃	#18722	1	1	yes	characteristic, direct product factor, Sylow
427	C₂³	—	2	2	no	—
428	C₂³	—	2	2	no	—
429	C₂³	—	2	2	no	—
430	C₂³	—	8	4	no	—
431	C₂³	—	8	4	no	—
432	C₂³	—	8	4	no	—
433	C₂³	C₁₃×#120	1	1	yes	characteristic
434	Q₈	—	4	2	no	—
435	Q₈	—	4	4	no	—
436	Q₈	—	8	1	no	—
437	Q₈	—	8	1	no	—
438	Q₈	—	8	2	no	—
439	D₄	—	2	4	no	—
440	D₄	—	2	4	no	—
441	D₄	—	4	2	no	—
442	D₄	—	4	2	no	—
443	D₄	—	4	2	no	—
444	D₄	—	4	2	no	—
445	D₄	—	4	2	no	—
446	D₄	—	8	1	no	—
447	D₄	—	8	1	no	—
448	D₄	—	8	2	no	—
449	D₄	—	8	2	no	—
450	D₄	—	8	2	no	—
451	D₄	—	8	4	no	—
452	D₄	—	8	4	no	—
453	D₄	—	8	4	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	4	4	no	—
461	C₂×C₄	—	4	4	no	—
462	C₂×C₄	—	4	4	no	—
463	C₂×C₄	—	4	2	no	—
464	C₂×C₄	—	8	2	no	—
465	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
466	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
467	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
468	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
469	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
470	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
471	C₈	—	4	2	no	—
472	C₈	—	4	2	no	—
473	C₈	—	4	2	no	—
474	C₂²	—	2	1	no	—
475	C₂²	—	2	1	no	—
476	C₂²	—	2	1	no	—
477	C₂²	—	4	2	no	—
478	C₂²	—	4	2	no	—
479	C₂²	—	4	2	no	—
480	C₂²	—	4	2	no	—
481	C₂²	—	4	2	no	—
482	C₂²	—	4	2	no	—
483	C₂²	—	4	2	no	—
484	C₂²	—	4	2	no	—
485	C₂²	—	4	2	no	—
486	C₂²	—	16	8	no	—
487	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
488	C₄	—	2	1	no	—
489	C₄	—	2	1	no	—
490	C₄	—	2	1	no	—
491	C₄	—	4	2	no	—
492	C₄	—	4	2	no	—
493	C₄	—	4	2	no	—
494	C₄	—	8	2	no	—
495	C₄	C₁₃×#455	1	2	yes	—
496	C₄	C₁₃×#576	1	2	yes	—
497	C₄	C₁₃×#577	1	2	yes	—
498	C₂	—	4	1	no	—
499	C₂	—	8	2	no	—
500	C₂	—	8	2	no	—
501	C₂	—	8	2	no	—
502	C₂	C₁₃×#3008	1	1	yes	characteristic
503	C₂	C₁₃×#3009	1	1	yes	characteristic
504	C₂	C₂×C₁₃×#455	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃
prime radical	C₁₃×#3549	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×#3226	C₂	semidirect
3. C₁₃×#3206	C₂	semidirect
4. C₁₃×#3141	C₂	semidirect
5. C₁₃×#1646	C₂	semidirect
6. C₁₃×#1639	C₂	semidirect
7. C₁₃×#1543	C₂	semidirect
8. C₁₃×#1484	C₂	semidirect
9. C₁₃×#1484	C₂	semidirect
23. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
28. C₁₃×#487	C₂²	semidirect
32. C₁₃×#474	C₂²	semidirect
33. C₁₃×#461	C₂²	semidirect
35. C₁₃×#431	C₂²	semidirect
36. C₁₃×#431	C₂²	semidirect
38. C₄×C₁₃×M₁₆	C₂²	semidirect
39. C₁₃×#333	C₂²	semidirect
41. C₁₃×D₄⋊C₈	C₂²	semidirect
42. C₁₃×D₄⋊C₈	C₂²	semidirect
110. #18722	C₁₃	direct (N × H)
176. #3226	C₂×C₁₃	semidirect
177. #3206	C₂×C₁₃	semidirect
178. #3141	C₂×C₁₃	semidirect
179. #1646	C₂×C₁₃	semidirect
180. #1639	C₂×C₁₃	semidirect
181. #1543	C₂×C₁₃	semidirect
182. #1484	C₂×C₁₃	semidirect
183. #1484	C₂×C₁₃	semidirect
244. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
249. #487	C₂²×C₁₃	semidirect
253. #474	C₂²×C₁₃	semidirect
254. #461	C₂²×C₁₃	semidirect
256. #431	C₂²×C₁₃	semidirect
257. #431	C₂²×C₁₃	semidirect
259. C₄×M₁₆	C₂²×C₁₃	semidirect
260. #333	C₂²×C₁₃	semidirect
262. D₄⋊C₈	C₂²×C₁₃	semidirect
263. D₄⋊C₈	C₂²×C₁₃	semidirect
426. C₁₃	#18722	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×#3549	2
C₁₃×#3226	2
C₁₃×#3206	2
C₁₃×#3141	2
C₁₃×#1646	2
C₁₃×#1639	2
C₁₃×#1543	2
C₁₃×#1484	2
#18722	13

Subgroups — C13×#18722 #15705061

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#18722 #15705061