Subgroups — C₁₃×#19844 #15706183

Order 3328.

590 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×C₁₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3369	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3362	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#3304	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#1719	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1698	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1684	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1682	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1675	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1645	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1638	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1631	C₂	1	1	yes	maximal, characteristic
13	C₁₃×#1623	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1584	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×SD₁₆⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
16	Q₈²×C₁₃	C₂²	1	1	yes	characteristic
17	Q₈²×C₁₃	C₂²	1	1	yes	characteristic
18	C₁₃×#556	C₂²	1	1	yes	characteristic
19	C₁₃×#550	C₂²	1	1	yes	characteristic
20	C₁₃×#500	—	2	1	no	—
21	C₁₃×#500	C₂²	1	1	yes	characteristic
22	C₁₃×#492	C₂²	1	1	yes	characteristic
23	C₁₃×#489	—	2	1	no	—
24	C₁₃×#487	C₂²	1	1	yes	characteristic
25	C₁₃×#487	C₂²	1	1	yes	characteristic
26	C₁₃×#486	—	2	1	no	—
27	C₁₃×#486	C₂²	1	1	yes	characteristic
28	C₁₃×#486	C₂²	1	1	yes	characteristic
29	C₁₃×#482	—	2	1	no	—
30	C₁₃×#477	—	2	1	no	—
31	C₁₃×#477	—	2	1	no	—
32	C₁₃×#477	C₂²	1	1	yes	characteristic
33	C₁₃×#477	C₂²	1	1	yes	characteristic
34	C₁₃×#476	—	2	1	no	—
35	C₁₃×#476	C₂²	1	1	yes	characteristic
36	C₁₃×#476	C₂²	1	1	yes	characteristic
37	C₁₃×#475	—	2	1	no	—
38	C₁₃×#475	C₂²	1	1	yes	characteristic
39	C₁₃×#465	—	2	1	no	—
40	C₁₃×#464	—	2	1	no	—
41	C₁₃×#462	C₂²	1	1	yes	characteristic
42	C₁₃×#460	—	2	1	no	—
43	C₁₃×#460	C₂²	1	1	yes	characteristic
44	C₁₃×#460	C₂²	1	1	yes	characteristic
45	C₁₃×#452	—	2	1	no	—
46	C₁₃×#446	C₂²	1	1	yes	characteristic
47	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
48	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
49	C₁₃×#441	—	2	1	no	—
50	C₄×C₁₃×Q₁₆	—	2	1	no	—
51	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
52	C₄×C₁₃×SD₁₆	—	2	1	no	—
53	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
54	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
55	C₁₃×#416	—	2	1	no	—
56	C₁₃×#335	C₂²	1	1	yes	characteristic
57	C₁₃×#335	C₂²	1	1	yes	characteristic
58	C₁₃×#333	C₂²	1	1	yes	characteristic
59	C₁₃×#333	C₂²	1	1	yes	characteristic
60	C₁₃×#332	C₂²	1	1	yes	characteristic
61	C₁₃×#331	C₂²	1	1	yes	characteristic
62	C₁₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
63	C₁₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
64	C₁₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
65	C₁₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
66	C₁₃×#322	C₂²	1	1	yes	characteristic
67	C₂×C₁₃×#41	—	2	1	no	—
68	C₂×C₁₃×Q₁₆	—	2	1	no	—
69	C₂×C₁₃×Q₁₆	D₄	1	1	yes	characteristic
70	C₂×C₁₃×SD₁₆	—	2	1	no	—
71	C₂×C₁₃×SD₁₆	—	2	1	no	—
72	C₂×C₁₃×SD₁₆	—	4	1	no	—
73	C₂×C₁₃×SD₁₆	D₄	1	1	yes	characteristic
74	C₂²×C₈×C₁₃	—	2	1	no	—
75	C₁₃×C₄⋊Q₈	—	2	1	no	—
76	C₁₃×C₄⋊Q₈	—	2	1	no	—
77	C₁₃×C₄⋊Q₈	—	2	1	no	—
78	C₁₃×C₄⋊Q₈	—	2	1	no	—
79	C₁₃×C₄⋊Q₈	—	4	1	no	—
80	C₁₃×C₄⋊Q₈	—	4	1	no	—
81	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
82	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
83	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
84	C₁₃×#127	—	2	1	no	—
85	C₁₃×#127	C₂³	1	1	yes	characteristic
86	C₁₃×#126	—	4	1	no	—
87	C₁₃×#124	—	2	1	no	—
88	C₁₃×C₂²⋊Q₈	—	2	1	no	—
89	C₁₃×#121	—	2	1	no	—
90	C₁₃×#121	—	4	1	no	—
91	C₄×Q₈×C₁₃	—	2	1	no	—
92	C₄×Q₈×C₁₃	—	2	1	no	—
93	C₄×Q₈×C₁₃	—	2	1	no	—
94	C₄×Q₈×C₁₃	—	2	1	no	—
95	C₄×Q₈×C₁₃	—	2	1	no	—
96	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
97	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
98	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
99	C₄×D₄×C₁₃	—	2	1	no	—
100	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
101	C₁₃×#117	—	2	1	no	—
102	C₁₃×#107	—	2	1	no	—
103	C₁₃×#107	—	2	1	no	—
104	C₁₃×#107	—	2	1	no	—
105	C₁₃×#107	—	2	1	no	—
106	C₁₃×#107	D₄	1	1	yes	characteristic
107	C₁₃×#106	—	2	1	no	—
108	C₁₃×#106	—	2	1	no	—
109	C₁₃×#106	—	2	1	no	—
110	C₁₃×#106	D₄	1	1	yes	characteristic
111	C₁₃×C₄⋊C₈	—	2	1	no	—
112	C₁₃×C₄⋊C₈	—	2	1	no	—
113	C₁₃×C₄⋊C₈	—	2	1	no	—
114	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
115	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
116	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
117	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
118	C₁₃×#103	—	2	1	no	—
119	C₁₃×#103	—	2	1	no	—
120	C₁₃×#103	—	2	1	no	—
121	C₁₃×#103	—	2	1	no	—
122	C₁₃×#103	—	2	1	no	—
123	C₁₃×#103	—	2	1	no	—
124	C₁₃×#103	—	4	1	no	—
125	C₁₃×#103	D₄	1	1	yes	characteristic
126	C₁₃×#103	D₄	1	1	yes	characteristic
127	C₁₃×#103	D₄	1	1	yes	characteristic
128	C₁₃×#102	—	2	1	no	—
129	C₁₃×#102	—	2	1	no	—
130	C₁₃×#102	—	2	1	no	—
131	C₁₃×#102	—	2	1	no	—
132	C₁₃×#102	—	2	1	no	—
133	C₁₃×#102	—	2	1	no	—
134	C₁₃×#102	—	2	1	no	—
135	C₁₃×#102	—	2	1	no	—
136	C₁₃×#102	D₄	1	1	yes	characteristic
137	C₁₃×C₂²⋊C₈	—	2	1	no	—
138	C₁₃×#97	—	2	1	no	—
139	C₄×C₈×C₁₃	—	2	1	no	—
140	C₄×C₈×C₁₃	—	2	1	no	—
141	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
142	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
144	#19844	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
145	C₁₃×#41	—	4	2	no	—
146	C₁₃×#41	—	8	1	no	—
147	C₂×Q₈×C₁₃	—	2	1	no	—
148	C₂×Q₈×C₁₃	—	2	1	no	—
149	C₂×Q₈×C₁₃	—	2	1	no	—
150	C₂×Q₈×C₁₃	—	4	1	no	—
151	C₂×Q₈×C₁₃	—	4	1	no	—
152	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
153	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
154	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
155	C₂×D₄×C₁₃	—	2	1	no	—
156	C₂×D₄×C₁₃	—	2	1	no	—
157	C₂×D₄×C₁₃	—	2	1	no	—
158	C₂×D₄×C₁₃	—	4	1	no	—
159	C₂×D₄×C₁₃	—	4	1	no	—
160	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₁₃	—	2	1	no	—
162	C₂²×C₄×C₁₃	—	4	1	no	—
163	C₁₃×Q₁₆	—	2	2	no	—
164	C₁₃×Q₁₆	—	4	2	no	—
165	C₁₃×SD₁₆	—	2	2	no	—
166	C₁₃×SD₁₆	—	4	2	no	—
167	C₁₃×SD₁₆	—	8	1	no	—
168	C₁₃×SD₁₆	—	8	2	no	—
169	C₂×C₈×C₁₃	—	2	1	no	—
170	C₂×C₈×C₁₃	—	2	1	no	—
171	C₂×C₈×C₁₃	—	2	1	no	—
172	C₂×C₈×C₁₃	—	2	1	no	—
173	C₂×C₈×C₁₃	—	2	1	no	—
174	C₂×C₈×C₁₃	—	8	1	no	—
175	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
176	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
177	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
178	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
179	C₁₃×C₄⋊C₄	—	2	1	no	—
180	C₁₃×C₄⋊C₄	—	2	1	no	—
181	C₁₃×C₄⋊C₄	—	2	1	no	—
182	C₁₃×C₄⋊C₄	—	2	1	no	—
183	C₁₃×C₄⋊C₄	—	2	1	no	—
184	C₁₃×C₄⋊C₄	—	2	1	no	—
185	C₁₃×C₄⋊C₄	—	2	1	no	—
186	C₁₃×C₄⋊C₄	—	2	1	no	—
187	C₁₃×C₄⋊C₄	—	2	1	no	—
188	C₁₃×C₄⋊C₄	—	4	1	no	—
189	C₁₃×C₄⋊C₄	—	4	1	no	—
190	C₁₃×C₄⋊C₄	—	4	1	no	—
191	C₁₃×C₄⋊C₄	—	4	1	no	—
192	C₁₃×C₄⋊C₄	—	4	1	no	—
193	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
194	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
195	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
196	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
197	C₁₃×C₂²⋊C₄	—	2	1	no	—
198	C₁₃×C₂²⋊C₄	—	4	1	no	—
199	C₁₃×C₂²⋊C₄	—	4	1	no	—
200	C₁₃×C₂²⋊C₄	—	4	1	no	—
201	C₄²×C₁₃	—	2	1	no	—
202	C₄²×C₁₃	—	2	1	no	—
203	C₄²×C₁₃	—	2	1	no	—
204	C₄²×C₁₃	—	4	1	no	—
205	C₄²×C₁₃	—	4	1	no	—
206	C₄²×C₁₃	—	4	1	no	—
207	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
208	Q₈×Q₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
209	#3369	C₂×C₁₃	1	1	yes	characteristic, complemented
210	#3362	C₂×C₁₃	1	1	yes	characteristic
211	#3304	C₂×C₁₃	1	1	yes	characteristic
212	#1719	C₂×C₁₃	1	1	yes	characteristic, complemented
213	#1698	C₂×C₁₃	1	1	yes	characteristic, complemented
214	#1684	C₂×C₁₃	1	1	yes	characteristic, complemented
215	#1682	C₂×C₁₃	1	1	yes	characteristic, complemented
216	#1675	C₂×C₁₃	1	1	yes	characteristic, complemented
217	#1645	C₂×C₁₃	1	1	yes	characteristic, complemented
218	#1638	C₂×C₁₃	1	1	yes	characteristic, complemented
219	#1631	C₂×C₁₃	1	1	yes	characteristic
220	#1623	C₂×C₁₃	1	1	yes	characteristic, complemented
221	#1584	C₂×C₁₃	1	1	yes	characteristic, complemented
222	SD₁₆⋊C₈	C₂×C₁₃	1	1	yes	characteristic, complemented
223	C₂³×C₁₃	—	2	1	no	—
224	C₂³×C₁₃	—	4	1	no	—
225	Q₈×C₁₃	—	2	1	no	—
226	Q₈×C₁₃	—	2	1	no	—
227	Q₈×C₁₃	—	2	1	no	—
228	Q₈×C₁₃	—	2	1	no	—
229	Q₈×C₁₃	—	4	1	no	—
230	Q₈×C₁₃	—	4	1	no	—
231	Q₈×C₁₃	—	8	1	no	—
232	Q₈×C₁₃	—	8	1	no	—
233	Q₈×C₁₃	—	16	1	no	—
234	Q₈×C₁₃	—	16	1	no	—
235	Q₈×C₁₃	#135	1	2	yes	—
236	Q₈×C₁₃	#137	1	2	yes	—
237	D₄×C₁₃	—	2	1	no	—
238	D₄×C₁₃	—	2	1	no	—
239	D₄×C₁₃	—	4	1	no	—
240	D₄×C₁₃	—	4	1	no	—
241	D₄×C₁₃	—	4	1	no	—
242	D₄×C₁₃	—	4	1	no	—
243	D₄×C₁₃	—	8	2	no	—
244	D₄×C₁₃	—	8	1	no	—
245	D₄×C₁₃	—	16	1	no	—
246	C₂×C₄×C₁₃	—	2	1	no	—
247	C₂×C₄×C₁₃	—	2	1	no	—
248	C₂×C₄×C₁₃	—	2	1	no	—
249	C₂×C₄×C₁₃	—	2	1	no	—
250	C₂×C₄×C₁₃	—	2	1	no	—
251	C₂×C₄×C₁₃	—	2	1	no	—
252	C₂×C₄×C₁₃	—	2	1	no	—
253	C₂×C₄×C₁₃	—	4	1	no	—
254	C₂×C₄×C₁₃	—	4	1	no	—
255	C₂×C₄×C₁₃	—	4	1	no	—
256	C₂×C₄×C₁₃	—	4	1	no	—
257	C₂×C₄×C₁₃	—	4	1	no	—
258	C₂×C₄×C₁₃	—	8	2	no	—
259	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
260	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
261	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
262	C₈×C₁₃	—	2	1	no	—
263	C₈×C₁₃	—	2	1	no	—
264	C₈×C₁₃	—	2	1	no	—
265	C₈×C₁₃	—	2	1	no	—
266	C₈×C₁₃	—	4	1	no	—
267	C₈×C₁₃	—	4	1	no	—
268	C₈×C₁₃	—	4	1	no	—
269	C₈×C₁₃	—	4	1	no	—
270	C₈×C₁₃	—	4	1	no	—
271	Q₈²	C₂²×C₁₃	1	1	yes	characteristic
272	Q₈²	C₂²×C₁₃	1	1	yes	characteristic
273	#556	C₂²×C₁₃	1	1	yes	characteristic
274	#550	C₂²×C₁₃	1	1	yes	characteristic
275	#500	—	2	1	no	—
276	#500	C₂²×C₁₃	1	1	yes	characteristic
277	#492	C₂²×C₁₃	1	1	yes	characteristic
278	#489	—	2	1	no	—
279	#487	C₂²×C₁₃	1	1	yes	characteristic
280	#487	C₂²×C₁₃	1	1	yes	characteristic
281	#486	—	2	1	no	—
282	#486	C₂²×C₁₃	1	1	yes	characteristic
283	#486	C₂²×C₁₃	1	1	yes	characteristic
284	#482	—	2	1	no	—
285	#477	—	2	1	no	—
286	#477	—	2	1	no	—
287	#477	C₂²×C₁₃	1	1	yes	characteristic
288	#477	C₂²×C₁₃	1	1	yes	characteristic
289	#476	—	2	1	no	—
290	#476	C₂²×C₁₃	1	1	yes	characteristic
291	#476	C₂²×C₁₃	1	1	yes	characteristic
292	#475	—	2	1	no	—
293	#475	C₂²×C₁₃	1	1	yes	characteristic
294	#465	—	2	1	no	—
295	#464	—	2	1	no	—
296	#462	C₂²×C₁₃	1	1	yes	characteristic
297	#460	—	2	1	no	—
298	#460	C₂²×C₁₃	1	1	yes	characteristic
299	#460	C₂²×C₁₃	1	1	yes	characteristic
300	#452	—	2	1	no	—
301	#446	C₂²×C₁₃	1	1	yes	characteristic
302	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
303	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
304	#441	—	2	1	no	—
305	C₄×Q₁₆	—	2	1	no	—
306	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
307	C₄×SD₁₆	—	2	1	no	—
308	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
309	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
310	#416	—	2	1	no	—
311	#335	C₂²×C₁₃	1	1	yes	characteristic
312	#335	C₂²×C₁₃	1	1	yes	characteristic
313	#333	C₂²×C₁₃	1	1	yes	characteristic
314	#333	C₂²×C₁₃	1	1	yes	characteristic
315	#332	C₂²×C₁₃	1	1	yes	characteristic
316	#331	C₂²×C₁₃	1	1	yes	characteristic
317	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
318	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
319	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
320	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
321	#322	C₂²×C₁₃	1	1	yes	characteristic
322	C₂²×C₁₃	—	4	1	no	—
323	C₂²×C₁₃	—	4	1	no	—
324	C₂²×C₁₃	—	4	1	no	—
325	C₂²×C₁₃	—	8	1	no	—
326	C₂²×C₁₃	—	8	1	no	—
327	C₂²×C₁₃	—	8	1	no	—
328	C₂²×C₁₃	D₄²	1	1	yes	characteristic
329	C₄×C₁₃	—	2	2	no	—
330	C₄×C₁₃	—	2	2	no	—
331	C₄×C₁₃	—	2	1	no	—
332	C₄×C₁₃	—	4	1	no	—
333	C₄×C₁₃	—	4	1	no	—
334	C₄×C₁₃	—	4	1	no	—
335	C₄×C₁₃	—	4	1	no	—
336	C₄×C₁₃	—	4	1	no	—
337	C₄×C₁₃	—	8	1	no	—
338	C₄×C₁₃	—	8	1	no	—
339	C₄×C₁₃	—	8	1	no	—
340	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
341	C₄×C₁₃	C₂×#137	1	1	yes	characteristic
342	C₄×C₁₃	#577	1	1	yes	characteristic
343	C₄×C₁₃	#578	1	1	yes	characteristic
344	C₂×#41	—	2	1	no	—
345	C₂×Q₁₆	—	2	1	no	—
346	C₂×Q₁₆	D₄×C₁₃	1	1	yes	characteristic
347	C₂×SD₁₆	—	2	1	no	—
348	C₂×SD₁₆	—	2	1	no	—
349	C₂×SD₁₆	—	4	1	no	—
350	C₂×SD₁₆	D₄×C₁₃	1	1	yes	characteristic
351	C₂²×C₈	—	2	1	no	—
352	C₄⋊Q₈	—	2	1	no	—
353	C₄⋊Q₈	—	2	1	no	—
354	C₄⋊Q₈	—	2	1	no	—
355	C₄⋊Q₈	—	2	1	no	—
356	C₄⋊Q₈	—	4	1	no	—
357	C₄⋊Q₈	—	4	1	no	—
358	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
359	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
360	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
361	#127	—	2	1	no	—
362	#127	C₂³×C₁₃	1	1	yes	characteristic
363	#126	—	4	1	no	—
364	#124	—	2	1	no	—
365	C₂²⋊Q₈	—	2	1	no	—
366	#121	—	2	1	no	—
367	#121	—	4	1	no	—
368	C₄×Q₈	—	2	1	no	—
369	C₄×Q₈	—	2	1	no	—
370	C₄×Q₈	—	2	1	no	—
371	C₄×Q₈	—	2	1	no	—
372	C₄×Q₈	—	2	1	no	—
373	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
374	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
375	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
376	C₄×D₄	—	2	1	no	—
377	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
378	#117	—	2	1	no	—
379	#107	—	2	1	no	—
380	#107	—	2	1	no	—
381	#107	—	2	1	no	—
382	#107	—	2	1	no	—
383	#107	D₄×C₁₃	1	1	yes	characteristic
384	#106	—	2	1	no	—
385	#106	—	2	1	no	—
386	#106	—	2	1	no	—
387	#106	D₄×C₁₃	1	1	yes	characteristic
388	C₄⋊C₈	—	2	1	no	—
389	C₄⋊C₈	—	2	1	no	—
390	C₄⋊C₈	—	2	1	no	—
391	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
392	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
393	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
394	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
395	#103	—	2	1	no	—
396	#103	—	2	1	no	—
397	#103	—	2	1	no	—
398	#103	—	2	1	no	—
399	#103	—	2	1	no	—
400	#103	—	2	1	no	—
401	#103	—	4	1	no	—
402	#103	D₄×C₁₃	1	1	yes	characteristic
403	#103	D₄×C₁₃	1	1	yes	characteristic
404	#103	D₄×C₁₃	1	1	yes	characteristic
405	#102	—	2	1	no	—
406	#102	—	2	1	no	—
407	#102	—	2	1	no	—
408	#102	—	2	1	no	—
409	#102	—	2	1	no	—
410	#102	—	2	1	no	—
411	#102	—	2	1	no	—
412	#102	—	2	1	no	—
413	#102	D₄×C₁₃	1	1	yes	characteristic
414	C₂²⋊C₈	—	2	1	no	—
415	#97	—	2	1	no	—
416	C₄×C₈	—	2	1	no	—
417	C₄×C₈	—	2	1	no	—
418	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
419	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
420	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
421	C₂×C₁₃	—	8	1	no	—
422	C₂×C₁₃	—	16	1	no	—
423	C₂×C₁₃	#3266	1	1	yes	characteristic
424	C₂×C₁₃	#3285	1	1	yes	characteristic
425	C₂×C₁₃	#3288	1	1	yes	characteristic
426	#41	—	4	2	no	—
427	#41	—	8	1	no	—
428	C₂×Q₈	—	2	1	no	—
429	C₂×Q₈	—	2	1	no	—
430	C₂×Q₈	—	2	1	no	—
431	C₂×Q₈	—	4	1	no	—
432	C₂×Q₈	—	4	1	no	—
433	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
434	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
435	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
436	C₂×D₄	—	2	1	no	—
437	C₂×D₄	—	2	1	no	—
438	C₂×D₄	—	2	1	no	—
439	C₂×D₄	—	4	1	no	—
440	C₂×D₄	—	4	1	no	—
441	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
442	C₂²×C₄	—	2	1	no	—
443	C₂²×C₄	—	4	1	no	—
444	Q₁₆	—	2	2	no	—
445	Q₁₆	—	4	2	no	—
446	SD₁₆	—	2	2	no	—
447	SD₁₆	—	4	2	no	—
448	SD₁₆	—	8	1	no	—
449	SD₁₆	—	8	2	no	—
450	C₂×C₈	—	2	1	no	—
451	C₂×C₈	—	2	1	no	—
452	C₂×C₈	—	2	1	no	—
453	C₂×C₈	—	2	1	no	—
454	C₂×C₈	—	2	1	no	—
455	C₂×C₈	—	8	1	no	—
456	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
457	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
458	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
459	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
460	C₄⋊C₄	—	2	1	no	—
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	—	2	1	no	—
463	C₄⋊C₄	—	2	1	no	—
464	C₄⋊C₄	—	2	1	no	—
465	C₄⋊C₄	—	2	1	no	—
466	C₄⋊C₄	—	2	1	no	—
467	C₄⋊C₄	—	2	1	no	—
468	C₄⋊C₄	—	2	1	no	—
469	C₄⋊C₄	—	4	1	no	—
470	C₄⋊C₄	—	4	1	no	—
471	C₄⋊C₄	—	4	1	no	—
472	C₄⋊C₄	—	4	1	no	—
473	C₄⋊C₄	—	4	1	no	—
474	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
475	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
476	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
477	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
478	C₂²⋊C₄	—	2	1	no	—
479	C₂²⋊C₄	—	4	1	no	—
480	C₂²⋊C₄	—	4	1	no	—
481	C₂²⋊C₄	—	4	1	no	—
482	C₄²	—	2	1	no	—
483	C₄²	—	2	1	no	—
484	C₄²	—	2	1	no	—
485	C₄²	—	4	1	no	—
486	C₄²	—	4	1	no	—
487	C₄²	—	4	1	no	—
488	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
489	C₁₃	#19844	1	1	yes	characteristic, direct product factor, Sylow
490	C₂³	—	2	1	no	—
491	C₂³	—	4	1	no	—
492	Q₈	—	2	1	no	—
493	Q₈	—	2	1	no	—
494	Q₈	—	2	1	no	—
495	Q₈	—	2	1	no	—
496	Q₈	—	4	1	no	—
497	Q₈	—	4	1	no	—
498	Q₈	—	8	1	no	—
499	Q₈	—	8	1	no	—
500	Q₈	—	16	1	no	—
501	Q₈	—	16	1	no	—
502	Q₈	C₁₃×#135	1	2	yes	—
503	Q₈	C₁₃×#137	1	2	yes	—
504	D₄	—	2	1	no	—
505	D₄	—	2	1	no	—
506	D₄	—	4	1	no	—
507	D₄	—	4	1	no	—
508	D₄	—	4	1	no	—
509	D₄	—	4	1	no	—
510	D₄	—	8	2	no	—
511	D₄	—	8	1	no	—
512	D₄	—	16	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	4	1	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	8	2	no	—
526	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
527	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
528	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
529	C₈	—	2	1	no	—
530	C₈	—	2	1	no	—
531	C₈	—	2	1	no	—
532	C₈	—	2	1	no	—
533	C₈	—	4	1	no	—
534	C₈	—	4	1	no	—
535	C₈	—	4	1	no	—
536	C₈	—	4	1	no	—
537	C₈	—	4	1	no	—
538	C₂²	—	4	1	no	—
539	C₂²	—	4	1	no	—
540	C₂²	—	4	1	no	—
541	C₂²	—	8	1	no	—
542	C₂²	—	8	1	no	—
543	C₂²	—	8	1	no	—
544	C₂²	D₄²×C₁₃	1	1	yes	characteristic
545	C₄	—	2	2	no	—
546	C₄	—	2	2	no	—
547	C₄	—	2	1	no	—
548	C₄	—	4	1	no	—
549	C₄	—	4	1	no	—
550	C₄	—	4	1	no	—
551	C₄	—	4	1	no	—
552	C₄	—	4	1	no	—
553	C₄	—	8	1	no	—
554	C₄	—	8	1	no	—
555	C₄	—	8	1	no	—
556	C₄	C₂×C₁₃×#135	1	1	yes	characteristic
557	C₄	C₂×C₁₃×#137	1	1	yes	characteristic
558	C₄	C₁₃×#577	1	1	yes	characteristic
559	C₄	C₁₃×#578	1	1	yes	characteristic
560	C₂	—	8	1	no	—
561	C₂	—	16	1	no	—
562	C₂	C₁₃×#3266	1	1	yes	characteristic
563	C₂	C₁₃×#3285	1	1	yes	characteristic
564	C₂	C₁₃×#3288	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃
prime radical	C₁₃×#550	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₄²×C₁₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. Q₈×C₁₃×Q₁₆	C₂	semidirect
2. C₁₃×#3369	C₂	semidirect
5. C₁₃×#1719	C₂	semidirect
6. C₁₃×#1698	C₂	semidirect
7. C₁₃×#1684	C₂	semidirect
8. C₁₃×#1682	C₂	semidirect
9. C₁₃×#1675	C₂	semidirect
10. C₁₃×#1645	C₂	semidirect
11. C₁₃×#1638	C₂	semidirect
13. C₁₃×#1623	C₂	semidirect
14. C₁₃×#1584	C₂	semidirect
15. C₁₃×SD₁₆⋊C₈	C₂	semidirect
144. #19844	C₁₃	direct (N × H)
208. Q₈×Q₁₆	C₂×C₁₃	semidirect
209. #3369	C₂×C₁₃	semidirect
212. #1719	C₂×C₁₃	semidirect
213. #1698	C₂×C₁₃	semidirect
214. #1684	C₂×C₁₃	semidirect
215. #1682	C₂×C₁₃	semidirect
216. #1675	C₂×C₁₃	semidirect
217. #1645	C₂×C₁₃	semidirect
218. #1638	C₂×C₁₃	semidirect
220. #1623	C₂×C₁₃	semidirect
221. #1584	C₂×C₁₃	semidirect
222. SD₁₆⋊C₈	C₂×C₁₃	semidirect
489. C₁₃	#19844	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
Q₈×C₁₃×Q₁₆	2
C₁₃×#3369	2
C₁₃×#3362	2
C₁₃×#3304	2
C₁₃×#1719	2
C₁₃×#1698	2
C₁₃×#1684	2
C₁₃×#1682	2
C₁₃×#1675	2
C₁₃×#1645	2
C₁₃×#1638	2
C₁₃×#1631	2
C₁₃×#1623	2
C₁₃×#1584	2
C₁₃×SD₁₆⋊C₈	2
#19844	13

Subgroups — C13×#19844 #15706183

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#19844 #15706183