Subgroups — C₁₃×#19906 #15706245

Order 3328.

608 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3360	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3358	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3333	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3328	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1711	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1699	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1697	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1684	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1682	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1644	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1642	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1637	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1628	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1589	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈×C₁₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#556	C₂²	1	1	yes	characteristic
17	C₁₃×#554	C₂²	1	1	yes	characteristic
18	C₁₃×#550	C₂²	1	1	yes	characteristic
19	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
20	C₁₃×#488	—	2	1	no	—
21	C₁₃×#487	C₂²	1	1	yes	characteristic
22	C₁₃×#487	C₂²	1	1	yes	characteristic
23	C₁₃×#487	C₂²	1	1	yes	characteristic
24	C₁₃×#486	—	2	1	no	—
25	C₁₃×#486	C₂²	1	1	yes	characteristic
26	C₁₃×#486	C₂²	1	1	yes	characteristic
27	C₁₃×#486	C₂²	1	1	yes	characteristic
28	C₁₃×#485	—	2	1	no	—
29	C₁₃×#480	—	2	1	no	—
30	C₁₃×#479	—	2	1	no	—
31	C₁₃×#477	C₂²	1	1	yes	characteristic
32	C₁₃×#476	C₂²	1	1	yes	characteristic
33	C₁₃×#475	C₂²	1	1	yes	characteristic
34	C₁₃×#474	—	2	1	no	—
35	C₁₃×#474	C₂²	1	1	yes	characteristic
36	C₁₃×#470	—	2	1	no	—
37	C₁₃×#468	—	2	1	no	—
38	C₁₃×#463	—	2	1	no	—
39	C₁₃×#462	C₂²	1	1	yes	characteristic
40	C₁₃×#461	C₂²	1	1	yes	characteristic
41	C₁₃×#460	C₂²	1	1	yes	characteristic
42	C₁₃×#459	—	2	1	no	—
43	C₁₃×#459	C₂²	1	1	yes	characteristic
44	C₁₃×#452	—	2	1	no	—
45	C₁₃×#451	—	2	1	no	—
46	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
47	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
48	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
49	C₄×C₁₃×SD₁₆	—	2	1	no	—
50	C₄×C₁₃×D₈	—	2	1	no	—
51	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
52	C₁₃×#436	C₂²	1	1	yes	characteristic
53	C₁₃×#436	C₂²	1	1	yes	characteristic
54	C₁₃×#419	—	2	1	no	—
55	C₁₃×#417	—	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×#332	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×D₄⋊C₈	C₂²	1	1	yes	characteristic
65	C₁₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
66	C₈²×C₁₃	C₂²	1	1	yes	characteristic
67	C₂×C₁₃×#41	—	2	1	no	—
68	C₂²×Q₈×C₁₃	—	2	1	no	—
69	C₂×C₁₃×Q₁₆	—	2	1	no	—
70	C₂×C₁₃×Q₁₆	D₄	1	1	yes	characteristic
71	C₂×C₁₃×SD₁₆	—	2	1	no	—
72	C₂×C₁₃×SD₁₆	—	2	1	no	—
73	C₂×C₁₃×D₈	—	2	1	no	—
74	C₂×C₁₃×D₈	D₄	1	1	yes	characteristic
75	C₂×C₁₃×M₁₆	—	2	1	no	—
76	C₂×C₁₃×M₁₆	—	2	1	no	—
77	C₁₃×C₄⋊Q₈	—	2	1	no	—
78	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
79	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
80	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
81	C₁₃×#127	—	2	1	no	—
82	C₁₃×#127	C₂³	1	1	yes	characteristic
83	C₁₃×#126	—	4	1	no	—
84	C₁₃×#125	—	2	1	no	—
85	C₁₃×#124	—	2	1	no	—
86	C₁₃×C₂²⋊Q₈	—	2	1	no	—
87	C₁₃×C₂²⋊Q₈	—	2	1	no	—
88	C₁₃×C₂²⋊Q₈	—	2	1	no	—
89	C₁₃×C₂²⋊Q₈	—	4	1	no	—
90	C₁₃×C₂²⋊Q₈	—	4	1	no	—
91	C₁₃×#121	—	2	1	no	—
92	C₁₃×#121	—	4	1	no	—
93	C₄×Q₈×C₁₃	—	2	1	no	—
94	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
95	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
96	C₄×D₄×C₁₃	—	2	1	no	—
97	C₄×D₄×C₁₃	—	2	1	no	—
98	C₄×D₄×C₁₃	—	2	1	no	—
99	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
100	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
101	C₁₃×#117	—	2	1	no	—
102	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
103	C₁₃×#107	—	2	1	no	—
104	C₁₃×#107	—	2	1	no	—
105	C₁₃×#107	D₄	1	1	yes	characteristic
106	C₁₃×#107	D₄	1	1	yes	characteristic
107	C₁₃×#106	—	2	1	no	—
108	C₁₃×#106	—	2	1	no	—
109	C₁₃×C₄⋊C₈	—	2	1	no	—
110	C₁₃×C₄⋊C₈	—	2	1	no	—
111	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
112	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
113	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
114	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
115	C₁₃×#103	—	2	1	no	—
116	C₁₃×#103	—	2	1	no	—
117	C₁₃×#103	—	2	1	no	—
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	—	4	1	no	—
124	C₁₃×#103	D₄	1	1	yes	characteristic
125	C₁₃×#103	D₄	1	1	yes	characteristic
126	C₁₃×#102	—	2	1	no	—
127	C₁₃×#102	—	2	1	no	—
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	—	4	1	no	—
135	C₁₃×#102	D₄	1	1	yes	characteristic
136	C₁₃×#102	D₄	1	1	yes	characteristic
137	C₁₃×C₂²⋊C₈	—	2	1	no	—
138	C₁₃×C₂²⋊C₈	—	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	#19906	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	2	no	—
152	C₂×Q₈×C₁₃	—	8	1	no	—
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	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₁₃	—	2	1	no	—
163	C₂²×C₄×C₁₃	—	2	1	no	—
164	C₂²×C₄×C₁₃	—	4	1	no	—
165	C₂²×C₄×C₁₃	—	4	1	no	—
166	C₂²×C₄×C₁₃	—	4	1	no	—
167	C₁₃×Q₁₆	—	2	2	no	—
168	C₁₃×Q₁₆	—	8	1	no	—
169	C₁₃×SD₁₆	—	4	2	no	—
170	C₁₃×SD₁₆	—	8	1	no	—
171	C₁₃×D₈	—	4	1	no	—
172	C₁₃×D₈	—	4	2	no	—
173	C₁₃×M₁₆	—	8	1	no	—
174	C₁₃×M₁₆	—	8	1	no	—
175	C₂×C₈×C₁₃	—	2	1	no	—
176	C₂×C₈×C₁₃	—	2	1	no	—
177	C₂×C₈×C₁₃	—	2	1	no	—
178	C₂×C₈×C₁₃	—	2	1	no	—
179	C₂×C₈×C₁₃	—	2	1	no	—
180	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
181	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
182	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
183	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
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	—	2	1	no	—
189	C₁₃×C₄⋊C₄	—	2	1	no	—
190	C₁₃×C₄⋊C₄	—	2	1	no	—
191	C₁₃×C₄⋊C₄	—	2	1	no	—
192	C₁₃×C₄⋊C₄	—	4	1	no	—
193	C₁₃×C₄⋊C₄	—	4	1	no	—
194	C₁₃×C₄⋊C₄	—	4	1	no	—
195	C₁₃×C₄⋊C₄	—	4	1	no	—
196	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
197	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
198	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
199	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
200	C₁₃×C₂²⋊C₄	—	2	1	no	—
201	C₁₃×C₂²⋊C₄	—	2	1	no	—
202	C₁₃×C₂²⋊C₄	—	4	1	no	—
203	C₁₃×C₂²⋊C₄	—	4	1	no	—
204	C₁₃×C₂²⋊C₄	—	4	1	no	—
205	C₁₃×C₂²⋊C₄	—	4	1	no	—
206	C₁₃×C₂²⋊C₄	—	4	1	no	—
207	C₄²×C₁₃	—	2	1	no	—
208	C₄²×C₁₃	—	2	1	no	—
209	C₄²×C₁₃	—	4	1	no	—
210	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
211	#3360	C₂×C₁₃	1	1	yes	characteristic, complemented
212	#3358	C₂×C₁₃	1	1	yes	characteristic
213	#3333	C₂×C₁₃	1	1	yes	characteristic, complemented
214	#3328	C₂×C₁₃	1	1	yes	characteristic, complemented
215	#1711	C₂×C₁₃	1	1	yes	characteristic, complemented
216	#1699	C₂×C₁₃	1	1	yes	characteristic, complemented
217	#1697	C₂×C₁₃	1	1	yes	characteristic, complemented
218	#1684	C₂×C₁₃	1	1	yes	characteristic, complemented
219	#1682	C₂×C₁₃	1	1	yes	characteristic, complemented
220	#1644	C₂×C₁₃	1	1	yes	characteristic, complemented
221	#1642	C₂×C₁₃	1	1	yes	characteristic, complemented
222	#1637	C₂×C₁₃	1	1	yes	characteristic, complemented
223	#1628	C₂×C₁₃	1	1	yes	characteristic, complemented
224	#1589	C₂×C₁₃	1	1	yes	characteristic, complemented
225	C₈×Q₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
226	C₂³×C₁₃	—	2	1	no	—
227	C₂³×C₁₃	—	2	1	no	—
228	C₂³×C₁₃	—	4	1	no	—
229	Q₈×C₁₃	—	2	1	no	—
230	Q₈×C₁₃	—	2	1	no	—
231	Q₈×C₁₃	—	2	1	no	—
232	Q₈×C₁₃	—	4	1	no	—
233	Q₈×C₁₃	—	4	1	no	—
234	Q₈×C₁₃	—	4	1	no	—
235	Q₈×C₁₃	—	4	1	no	—
236	Q₈×C₁₃	—	8	2	no	—
237	Q₈×C₁₃	—	8	1	no	—
238	Q₈×C₁₃	#135	1	2	yes	—
239	D₄×C₁₃	—	2	1	no	—
240	D₄×C₁₃	—	2	1	no	—
241	D₄×C₁₃	—	2	1	no	—
242	D₄×C₁₃	—	2	1	no	—
243	D₄×C₁₃	—	4	1	no	—
244	D₄×C₁₃	—	4	1	no	—
245	D₄×C₁₃	—	4	1	no	—
246	D₄×C₁₃	—	4	1	no	—
247	D₄×C₁₃	—	8	2	no	—
248	D₄×C₁₃	—	8	1	no	—
249	D₄×C₁₃	—	16	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	—	2	1	no	—
254	C₂×C₄×C₁₃	—	2	1	no	—
255	C₂×C₄×C₁₃	—	2	1	no	—
256	C₂×C₄×C₁₃	—	4	1	no	—
257	C₂×C₄×C₁₃	—	4	1	no	—
258	C₂×C₄×C₁₃	—	4	1	no	—
259	C₂×C₄×C₁₃	—	4	1	no	—
260	C₂×C₄×C₁₃	—	4	1	no	—
261	C₂×C₄×C₁₃	—	4	1	no	—
262	C₂×C₄×C₁₃	—	4	1	no	—
263	C₂×C₄×C₁₃	—	8	2	no	—
264	C₂×C₄×C₁₃	—	8	2	no	—
265	C₂×C₄×C₁₃	—	16	1	no	—
266	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
267	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
268	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
269	C₈×C₁₃	—	2	1	no	—
270	C₈×C₁₃	—	2	1	no	—
271	C₈×C₁₃	—	2	1	no	—
272	C₈×C₁₃	—	2	1	no	—
273	C₈×C₁₃	—	4	1	no	—
274	C₈×C₁₃	—	4	1	no	—
275	C₈×C₁₃	—	4	1	no	—
276	C₈×C₁₃	—	4	1	no	—
277	C₈×C₁₃	—	4	1	no	—
278	#556	C₂²×C₁₃	1	1	yes	characteristic
279	#554	C₂²×C₁₃	1	1	yes	characteristic
280	#550	C₂²×C₁₃	1	1	yes	characteristic
281	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
282	#488	—	2	1	no	—
283	#487	C₂²×C₁₃	1	1	yes	characteristic
284	#487	C₂²×C₁₃	1	1	yes	characteristic
285	#487	C₂²×C₁₃	1	1	yes	characteristic
286	#486	—	2	1	no	—
287	#486	C₂²×C₁₃	1	1	yes	characteristic
288	#486	C₂²×C₁₃	1	1	yes	characteristic
289	#486	C₂²×C₁₃	1	1	yes	characteristic
290	#485	—	2	1	no	—
291	#480	—	2	1	no	—
292	#479	—	2	1	no	—
293	#477	C₂²×C₁₃	1	1	yes	characteristic
294	#476	C₂²×C₁₃	1	1	yes	characteristic
295	#475	C₂²×C₁₃	1	1	yes	characteristic
296	#474	—	2	1	no	—
297	#474	C₂²×C₁₃	1	1	yes	characteristic
298	#470	—	2	1	no	—
299	#468	—	2	1	no	—
300	#463	—	2	1	no	—
301	#462	C₂²×C₁₃	1	1	yes	characteristic
302	#461	C₂²×C₁₃	1	1	yes	characteristic
303	#460	C₂²×C₁₃	1	1	yes	characteristic
304	#459	—	2	1	no	—
305	#459	C₂²×C₁₃	1	1	yes	characteristic
306	#452	—	2	1	no	—
307	#451	—	2	1	no	—
308	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
309	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
310	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
311	C₄×SD₁₆	—	2	1	no	—
312	C₄×D₈	—	2	1	no	—
313	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
314	#436	C₂²×C₁₃	1	1	yes	characteristic
315	#436	C₂²×C₁₃	1	1	yes	characteristic
316	#419	—	2	1	no	—
317	#417	—	2	1	no	—
318	#335	C₂²×C₁₃	1	1	yes	characteristic
319	#335	C₂²×C₁₃	1	1	yes	characteristic
320	#333	C₂²×C₁₃	1	1	yes	characteristic
321	#332	C₂²×C₁₃	1	1	yes	characteristic
322	#332	C₂²×C₁₃	1	1	yes	characteristic
323	#331	C₂²×C₁₃	1	1	yes	characteristic
324	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
325	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
326	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
327	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
328	C₈²	C₂²×C₁₃	1	1	yes	characteristic
329	C₂²×C₁₃	—	4	1	no	—
330	C₂²×C₁₃	—	4	1	no	—
331	C₂²×C₁₃	—	4	1	no	—
332	C₂²×C₁₃	—	4	1	no	—
333	C₂²×C₁₃	—	4	1	no	—
334	C₂²×C₁₃	—	4	1	no	—
335	C₂²×C₁₃	—	8	1	no	—
336	C₂²×C₁₃	—	8	1	no	—
337	C₂²×C₁₃	—	8	1	no	—
338	C₂²×C₁₃	D₄²	1	1	yes	characteristic
339	C₄×C₁₃	—	2	2	no	—
340	C₄×C₁₃	—	2	1	no	—
341	C₄×C₁₃	—	4	1	no	—
342	C₄×C₁₃	—	4	1	no	—
343	C₄×C₁₃	—	4	1	no	—
344	C₄×C₁₃	—	4	1	no	—
345	C₄×C₁₃	—	4	1	no	—
346	C₄×C₁₃	—	8	1	no	—
347	C₄×C₁₃	—	8	1	no	—
348	C₄×C₁₃	—	8	1	no	—
349	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
350	C₄×C₁₃	#575	1	1	yes	characteristic
351	C₄×C₁₃	#576	1	1	yes	characteristic
352	C₄×C₁₃	#578	1	1	yes	characteristic
353	C₂×#41	—	2	1	no	—
354	C₂²×Q₈	—	2	1	no	—
355	C₂×Q₁₆	—	2	1	no	—
356	C₂×Q₁₆	D₄×C₁₃	1	1	yes	characteristic
357	C₂×SD₁₆	—	2	1	no	—
358	C₂×SD₁₆	—	2	1	no	—
359	C₂×D₈	—	2	1	no	—
360	C₂×D₈	D₄×C₁₃	1	1	yes	characteristic
361	C₂×M₁₆	—	2	1	no	—
362	C₂×M₁₆	—	2	1	no	—
363	C₄⋊Q₈	—	2	1	no	—
364	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
365	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
366	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
367	#127	—	2	1	no	—
368	#127	C₂³×C₁₃	1	1	yes	characteristic
369	#126	—	4	1	no	—
370	#125	—	2	1	no	—
371	#124	—	2	1	no	—
372	C₂²⋊Q₈	—	2	1	no	—
373	C₂²⋊Q₈	—	2	1	no	—
374	C₂²⋊Q₈	—	2	1	no	—
375	C₂²⋊Q₈	—	4	1	no	—
376	C₂²⋊Q₈	—	4	1	no	—
377	#121	—	2	1	no	—
378	#121	—	4	1	no	—
379	C₄×Q₈	—	2	1	no	—
380	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
381	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
382	C₄×D₄	—	2	1	no	—
383	C₄×D₄	—	2	1	no	—
384	C₄×D₄	—	2	1	no	—
385	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
386	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
387	#117	—	2	1	no	—
388	C₂×C₄⋊C₄	—	2	1	no	—
389	#107	—	2	1	no	—
390	#107	—	2	1	no	—
391	#107	D₄×C₁₃	1	1	yes	characteristic
392	#107	D₄×C₁₃	1	1	yes	characteristic
393	#106	—	2	1	no	—
394	#106	—	2	1	no	—
395	C₄⋊C₈	—	2	1	no	—
396	C₄⋊C₈	—	2	1	no	—
397	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
398	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
399	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
400	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
401	#103	—	2	1	no	—
402	#103	—	2	1	no	—
403	#103	—	2	1	no	—
404	#103	—	2	1	no	—
405	#103	—	2	1	no	—
406	#103	—	2	1	no	—
407	#103	—	2	1	no	—
408	#103	—	2	1	no	—
409	#103	—	4	1	no	—
410	#103	D₄×C₁₃	1	1	yes	characteristic
411	#103	D₄×C₁₃	1	1	yes	characteristic
412	#102	—	2	1	no	—
413	#102	—	2	1	no	—
414	#102	—	2	1	no	—
415	#102	—	2	1	no	—
416	#102	—	2	1	no	—
417	#102	—	2	1	no	—
418	#102	—	2	1	no	—
419	#102	—	2	1	no	—
420	#102	—	4	1	no	—
421	#102	D₄×C₁₃	1	1	yes	characteristic
422	#102	D₄×C₁₃	1	1	yes	characteristic
423	C₂²⋊C₈	—	2	1	no	—
424	C₂²⋊C₈	—	2	1	no	—
425	C₄×C₈	—	2	1	no	—
426	C₄×C₈	—	2	1	no	—
427	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
428	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
429	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
430	C₂×C₁₃	—	8	1	no	—
431	C₂×C₁₃	—	8	1	no	—
432	C₂×C₁₃	—	16	1	no	—
433	C₂×C₁₃	#3277	1	1	yes	characteristic
434	C₂×C₁₃	#3280	1	1	yes	characteristic
435	C₂×C₁₃	#3290	1	1	yes	characteristic
436	#41	—	4	2	no	—
437	#41	—	8	1	no	—
438	C₂×Q₈	—	2	1	no	—
439	C₂×Q₈	—	2	1	no	—
440	C₂×Q₈	—	2	1	no	—
441	C₂×Q₈	—	4	1	no	—
442	C₂×Q₈	—	4	2	no	—
443	C₂×Q₈	—	8	1	no	—
444	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
445	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
446	C₂×D₄	—	2	1	no	—
447	C₂×D₄	—	2	1	no	—
448	C₂×D₄	—	2	1	no	—
449	C₂×D₄	—	4	1	no	—
450	C₂×D₄	—	4	1	no	—
451	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
452	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
453	C₂²×C₄	—	2	1	no	—
454	C₂²×C₄	—	2	1	no	—
455	C₂²×C₄	—	4	1	no	—
456	C₂²×C₄	—	4	1	no	—
457	C₂²×C₄	—	4	1	no	—
458	Q₁₆	—	2	2	no	—
459	Q₁₆	—	8	1	no	—
460	SD₁₆	—	4	2	no	—
461	SD₁₆	—	8	1	no	—
462	D₈	—	4	1	no	—
463	D₈	—	4	2	no	—
464	M₁₆	—	8	1	no	—
465	M₁₆	—	8	1	no	—
466	C₂×C₈	—	2	1	no	—
467	C₂×C₈	—	2	1	no	—
468	C₂×C₈	—	2	1	no	—
469	C₂×C₈	—	2	1	no	—
470	C₂×C₈	—	2	1	no	—
471	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
472	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
473	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
474	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
475	C₄⋊C₄	—	2	1	no	—
476	C₄⋊C₄	—	2	1	no	—
477	C₄⋊C₄	—	2	1	no	—
478	C₄⋊C₄	—	2	1	no	—
479	C₄⋊C₄	—	2	1	no	—
480	C₄⋊C₄	—	2	1	no	—
481	C₄⋊C₄	—	2	1	no	—
482	C₄⋊C₄	—	2	1	no	—
483	C₄⋊C₄	—	4	1	no	—
484	C₄⋊C₄	—	4	1	no	—
485	C₄⋊C₄	—	4	1	no	—
486	C₄⋊C₄	—	4	1	no	—
487	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
488	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
489	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
490	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
491	C₂²⋊C₄	—	2	1	no	—
492	C₂²⋊C₄	—	2	1	no	—
493	C₂²⋊C₄	—	4	1	no	—
494	C₂²⋊C₄	—	4	1	no	—
495	C₂²⋊C₄	—	4	1	no	—
496	C₂²⋊C₄	—	4	1	no	—
497	C₂²⋊C₄	—	4	1	no	—
498	C₄²	—	2	1	no	—
499	C₄²	—	2	1	no	—
500	C₄²	—	4	1	no	—
501	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
502	C₁₃	#19906	1	1	yes	characteristic, direct product factor, Sylow
503	C₂³	—	2	1	no	—
504	C₂³	—	2	1	no	—
505	C₂³	—	4	1	no	—
506	Q₈	—	2	1	no	—
507	Q₈	—	2	1	no	—
508	Q₈	—	2	1	no	—
509	Q₈	—	4	1	no	—
510	Q₈	—	4	1	no	—
511	Q₈	—	4	1	no	—
512	Q₈	—	4	1	no	—
513	Q₈	—	8	2	no	—
514	Q₈	—	8	1	no	—
515	Q₈	C₁₃×#135	1	2	yes	—
516	D₄	—	2	1	no	—
517	D₄	—	2	1	no	—
518	D₄	—	2	1	no	—
519	D₄	—	2	1	no	—
520	D₄	—	4	1	no	—
521	D₄	—	4	1	no	—
522	D₄	—	4	1	no	—
523	D₄	—	4	1	no	—
524	D₄	—	8	2	no	—
525	D₄	—	8	1	no	—
526	D₄	—	16	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	4	1	no	—
534	C₂×C₄	—	4	1	no	—
535	C₂×C₄	—	4	1	no	—
536	C₂×C₄	—	4	1	no	—
537	C₂×C₄	—	4	1	no	—
538	C₂×C₄	—	4	1	no	—
539	C₂×C₄	—	4	1	no	—
540	C₂×C₄	—	8	2	no	—
541	C₂×C₄	—	8	2	no	—
542	C₂×C₄	—	16	1	no	—
543	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
544	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
545	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
546	C₈	—	2	1	no	—
547	C₈	—	2	1	no	—
548	C₈	—	2	1	no	—
549	C₈	—	2	1	no	—
550	C₈	—	4	1	no	—
551	C₈	—	4	1	no	—
552	C₈	—	4	1	no	—
553	C₈	—	4	1	no	—
554	C₈	—	4	1	no	—
555	C₂²	—	4	1	no	—
556	C₂²	—	4	1	no	—
557	C₂²	—	4	1	no	—
558	C₂²	—	4	1	no	—
559	C₂²	—	4	1	no	—
560	C₂²	—	4	1	no	—
561	C₂²	—	8	1	no	—
562	C₂²	—	8	1	no	—
563	C₂²	—	8	1	no	—
564	C₂²	D₄²×C₁₃	1	1	yes	characteristic
565	C₄	—	2	2	no	—
566	C₄	—	2	1	no	—
567	C₄	—	4	1	no	—
568	C₄	—	4	1	no	—
569	C₄	—	4	1	no	—
570	C₄	—	4	1	no	—
571	C₄	—	4	1	no	—
572	C₄	—	8	1	no	—
573	C₄	—	8	1	no	—
574	C₄	—	8	1	no	—
575	C₄	C₂×C₁₃×#135	1	1	yes	characteristic
576	C₄	C₁₃×#575	1	1	yes	characteristic
577	C₄	C₁₃×#576	1	1	yes	characteristic
578	C₄	C₁₃×#578	1	1	yes	characteristic
579	C₂	—	8	1	no	—
580	C₂	—	8	1	no	—
581	C₂	—	16	1	no	—
582	C₂	C₁₃×#3277	1	1	yes	characteristic
583	C₂	C₁₃×#3280	1	1	yes	characteristic
584	C₂	C₁₃×#3290	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃
prime radical	C₁₃×#3358	C₂
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. C₁₃×#3360	C₂	semidirect
3. C₁₃×#3333	C₂	semidirect
4. C₁₃×#3328	C₂	semidirect
5. C₁₃×#1711	C₂	semidirect
6. C₁₃×#1699	C₂	semidirect
7. C₁₃×#1697	C₂	semidirect
8. C₁₃×#1684	C₂	semidirect
9. C₁₃×#1682	C₂	semidirect
10. C₁₃×#1644	C₂	semidirect
11. C₁₃×#1642	C₂	semidirect
12. C₁₃×#1637	C₂	semidirect
13. C₁₃×#1628	C₂	semidirect
14. C₁₃×#1589	C₂	semidirect
15. C₈×C₁₃×Q₁₆	C₂	semidirect
144. #19906	C₁₃	direct (N × H)
211. #3360	C₂×C₁₃	semidirect
213. #3333	C₂×C₁₃	semidirect
214. #3328	C₂×C₁₃	semidirect
215. #1711	C₂×C₁₃	semidirect
216. #1699	C₂×C₁₃	semidirect
217. #1697	C₂×C₁₃	semidirect
218. #1684	C₂×C₁₃	semidirect
219. #1682	C₂×C₁₃	semidirect
220. #1644	C₂×C₁₃	semidirect
221. #1642	C₂×C₁₃	semidirect
222. #1637	C₂×C₁₃	semidirect
223. #1628	C₂×C₁₃	semidirect
224. #1589	C₂×C₁₃	semidirect
225. C₈×Q₁₆	C₂×C₁₃	semidirect
502. C₁₃	#19906	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×#3360	2
C₁₃×#3358	2
C₁₃×#3333	2
C₁₃×#3328	2
C₁₃×#1711	2
C₁₃×#1699	2
C₁₃×#1697	2
C₁₃×#1684	2
C₁₃×#1682	2
C₁₃×#1644	2
C₁₃×#1642	2
C₁₃×#1637	2
C₁₃×#1628	2
C₁₃×#1589	2
C₈×C₁₃×Q₁₆	2
#19906	13

Subgroups — C13×#19906 #15706245

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#19906 #15706245