Subgroups — C₁₃×#23991 #15710330

Order 3328.

1164 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3510	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3027	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3022	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2901	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2031	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2004	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1914	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1911	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1909	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1905	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1827	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#585	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×#137	C₂²	1	2	yes	—
14	C₁₃×#568	C₂²	1	1	yes	characteristic
15	C₁₃×#559	—	2	2	no	—
16	C₁₃×#556	—	2	2	no	—
17	C₁₃×#551	—	2	4	no	—
18	C₁₃×#542	—	2	2	no	—
19	C₁₃×#536	C₂²	1	1	yes	characteristic
20	C₁₃×#535	C₂²	1	2	yes	—
21	C₁₃×#535	C₂²	1	1	yes	characteristic
22	C₁₃×#533	C₂²	1	1	yes	characteristic, complemented
23	C₁₃×#529	—	2	2	no	—
24	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic, complemented
25	C₁₃×#519	C₂²	1	1	yes	characteristic, complemented
26	C₁₃×#518	C₂²	1	1	yes	characteristic, complemented
27	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
28	C₁₃×B(4,𝔽₂)	—	2	4	no	—
29	C₁₃×#456	—	2	2	no	—
30	C₁₃×#455	—	2	2	no	—
31	C₁₃×#421	—	2	2	no	—
32	C₁₃×#421	C₂²	1	2	yes	—
33	C₁₃×#421	C₂²	1	2	yes	—
34	C₂×C₁₃×#104	—	2	2	no	—
35	C₂×C₁₃×#104	C₂²	1	2	yes	—
36	C₁₃×#419	C₂²	1	2	yes	complemented
37	C₁₃×#413	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×#100	C₂²	1	2	yes	complemented
39	C₁₃×#410	C₂²	1	2	yes	—
40	C₁₃×#410	C₂²	1	1	yes	characteristic
41	C₁₃×#344	C₂²	1	2	yes	complemented
42	C₁₃×#339	C₂²	1	2	yes	complemented
43	C₁₃×H(3,ℤ/4)	C₂²	1	2	yes	complemented
44	C₁₃×H(3,ℤ/4)	C₂²	1	2	yes	complemented
45	C₁₃×2₋¹⁺⁴	—	2	2	no	—
46	C₁₃×2₋¹⁺⁴	—	2	1	no	—
47	C₁₃×H(5,𝔽₂)	—	2	2	no	—
48	C₁₃×H(5,𝔽₂)	—	2	2	no	—
49	C₁₃×H(5,𝔽₂)	—	2	1	no	—
50	C₂×C₁₃×#41	—	2	2	no	—
51	C₂×C₁₃×#41	—	4	2	no	—
52	C₂×C₁₃×#41	C₂³	1	2	yes	—
53	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
54	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
55	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
56	C₁₃×#137	—	2	4	no	—
57	C₁₃×#137	—	4	2	no	—
58	C₂×C₁₃×Q₁₆	—	2	2	no	—
59	C₂×C₁₃×SD₁₆	—	2	2	no	—
60	C₁₃×#131	—	4	2	no	—
61	C₂×C₁₃×M₁₆	—	2	2	no	—
62	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
63	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
64	C₁₃×C₄⋊Q₈	—	2	1	no	—
65	C₁₃×C₄⋊Q₈	D₄	1	2	yes	complemented
66	C₁₃×#127	—	2	1	no	—
67	C₁₃×#127	—	2	2	no	—
68	C₁₃×#126	—	2	4	no	—
69	C₁₃×#126	—	2	4	no	—
70	C₁₃×#125	—	2	1	no	—
71	C₁₃×#124	—	2	4	no	—
72	C₁₃×#124	—	2	2	no	—
73	C₁₃×#124	—	2	1	no	—
74	C₁₃×#124	—	2	2	no	—
75	C₁₃×#124	—	2	1	no	—
76	C₁₃×#124	—	2	1	no	—
77	C₁₃×#124	D₄	1	2	yes	complemented
78	C₁₃×#123	—	2	4	no	—
79	C₁₃×#123	—	2	4	no	—
80	C₁₃×#123	—	2	2	no	—
81	C₁₃×C₂²⋊Q₈	—	2	4	no	—
82	C₁₃×C₂²⋊Q₈	—	2	2	no	—
83	C₁₃×C₂²⋊Q₈	—	2	2	no	—
84	C₁₃×#121	—	2	2	no	—
85	C₁₃×#121	—	4	2	no	—
86	C₁₃×#120	—	2	4	no	—
87	C₁₃×#120	D₄	1	4	yes	—
88	C₄×Q₈×C₁₃	—	2	1	no	—
89	C₄×Q₈×C₁₃	—	2	2	no	—
90	C₄×Q₈×C₁₃	—	2	2	no	—
91	C₄×Q₈×C₁₃	—	2	2	no	—
92	C₄×D₄×C₁₃	—	2	4	no	—
93	C₄×D₄×C₁₃	—	2	2	no	—
94	C₄×D₄×C₁₃	—	2	1	no	—
95	C₄×D₄×C₁₃	—	2	2	no	—
96	C₄×D₄×C₁₃	—	2	2	no	—
97	C₁₃×#117	—	2	4	no	—
98	C₁₃×#117	—	2	2	no	—
99	C₁₃×#117	D₄	1	2	yes	complemented
100	C₁₃×#117	C₂³	1	2	yes	—
101	C₁₃×#117	C₂³	1	1	yes	characteristic
102	C₁₃×#117	C₂³	1	1	yes	characteristic
103	C₁₃×#117	C₂³	1	1	yes	characteristic
104	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
105	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
106	C₂×C₄²×C₁₃	D₄	1	2	yes	complemented
107	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
108	C₁₃×#104	—	2	2	no	—
109	C₁₃×#104	—	2	4	no	—
110	C₁₃×#104	—	2	2	no	—
111	C₁₃×#104	—	2	4	no	—
112	C₁₃×#103	—	4	2	no	—
113	C₁₃×#101	—	2	1	no	—
114	C₁₃×#100	—	2	1	no	—
115	C₁₃×#100	—	4	2	no	—
116	C₁₃×#99	—	2	2	no	—
117	C₁₃×#99	—	2	4	no	—
118	#23991	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
119	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
120	C₁₃×#41	—	2	2	no	—
121	C₁₃×#41	—	2	2	no	—
122	C₁₃×#41	—	2	4	no	—
123	C₁₃×#41	—	2	2	no	—
124	C₁₃×#41	—	2	2	no	—
125	C₁₃×#41	—	2	2	no	—
126	C₁₃×#41	—	2	2	no	—
127	C₁₃×#41	—	4	4	no	—
128	C₁₃×#41	—	4	2	no	—
129	C₁₃×#41	—	4	2	no	—
130	C₁₃×#41	—	4	2	no	—
131	C₁₃×#41	—	4	2	no	—
132	C₂×Q₈×C₁₃	—	2	2	no	—
133	C₂×Q₈×C₁₃	—	2	1	no	—
134	C₂×Q₈×C₁₃	—	2	2	no	—
135	C₂×Q₈×C₁₃	—	2	2	no	—
136	C₂×Q₈×C₁₃	—	2	2	no	—
137	C₂×Q₈×C₁₃	—	4	2	no	—
138	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
139	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
140	C₂×Q₈×C₁₃	#41	1	2	yes	—
141	C₂×D₄×C₁₃	—	2	2	no	—
142	C₂×D₄×C₁₃	—	2	2	no	—
143	C₂×D₄×C₁₃	—	2	4	no	—
144	C₂×D₄×C₁₃	—	2	1	no	—
145	C₂×D₄×C₁₃	—	2	1	no	—
146	C₂×D₄×C₁₃	—	2	2	no	—
147	C₂×D₄×C₁₃	—	2	2	no	—
148	C₂×D₄×C₁₃	—	4	2	no	—
149	C₂×D₄×C₁₃	—	4	4	no	—
150	C₂×D₄×C₁₃	—	4	2	no	—
151	C₂×D₄×C₁₃	—	4	4	no	—
152	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
153	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
154	C₂×D₄×C₁₃	#41	1	2	yes	—
155	C₂²×C₄×C₁₃	—	2	1	no	—
156	C₂²×C₄×C₁₃	—	2	4	no	—
157	C₂²×C₄×C₁₃	—	2	2	no	—
158	C₂²×C₄×C₁₃	—	2	1	no	—
159	C₂²×C₄×C₁₃	—	2	2	no	—
160	C₂²×C₄×C₁₃	—	4	2	no	—
161	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
162	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
163	C₁₃×Q₁₆	—	4	4	no	—
164	C₁₃×SD₁₆	—	4	4	no	—
165	C₁₃×M₁₆	—	2	2	no	—
166	C₁₃×M₁₆	—	2	2	no	—
167	C₁₃×M₁₆	—	2	2	no	—
168	C₁₃×M₁₆	—	2	2	no	—
169	C₁₃×M₁₆	—	4	2	no	—
170	C₂×C₈×C₁₃	—	2	2	no	—
171	C₂×C₈×C₁₃	—	2	2	no	—
172	C₂×C₈×C₁₃	—	4	2	no	—
173	C₁₃×C₄⋊C₄	—	2	2	no	—
174	C₁₃×C₄⋊C₄	—	2	4	no	—
175	C₁₃×C₄⋊C₄	—	2	2	no	—
176	C₁₃×C₄⋊C₄	—	2	2	no	—
177	C₁₃×C₄⋊C₄	—	2	4	no	—
178	C₁₃×C₄⋊C₄	—	2	2	no	—
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	2	no	—
183	C₁₃×C₂²⋊C₄	—	2	4	no	—
184	C₁₃×C₂²⋊C₄	—	2	4	no	—
185	C₁₃×C₂²⋊C₄	—	2	4	no	—
186	C₁₃×C₂²⋊C₄	—	2	2	no	—
187	C₁₃×C₂²⋊C₄	—	2	4	no	—
188	C₁₃×C₂²⋊C₄	—	2	1	no	—
189	C₁₃×C₂²⋊C₄	—	2	1	no	—
190	C₁₃×C₂²⋊C₄	—	2	4	no	—
191	C₁₃×C₂²⋊C₄	—	2	2	no	—
192	C₁₃×C₂²⋊C₄	—	4	4	no	—
193	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
194	C₄²×C₁₃	—	2	4	no	—
195	C₄²×C₁₃	—	2	2	no	—
196	C₄²×C₁₃	—	2	1	no	—
197	C₄²×C₁₃	—	2	1	no	—
198	C₄²×C₁₃	—	2	2	no	—
199	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
200	C₄²×C₁₃	C₂×D₄	1	2	yes	—
201	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
202	C₄²×C₁₃	C₂×D₄	1	2	yes	—
203	#3510	C₂×C₁₃	1	1	yes	characteristic, complemented
204	#3027	C₂×C₁₃	1	1	yes	characteristic
205	#3022	C₂×C₁₃	1	1	yes	characteristic, complemented
206	#2901	C₂×C₁₃	1	1	yes	characteristic, complemented
207	#2031	C₂×C₁₃	1	2	yes	complemented
208	#2004	C₂×C₁₃	1	2	yes	complemented
209	#1914	C₂×C₁₃	1	1	yes	characteristic, complemented
210	#1911	C₂×C₁₃	1	2	yes	complemented
211	#1909	C₂×C₁₃	1	1	yes	characteristic, complemented
212	#1905	C₂×C₁₃	1	2	yes	complemented
213	#1827	C₂×C₁₃	1	1	yes	characteristic, complemented
214	C₂³×C₁₃	—	2	2	no	—
215	C₂³×C₁₃	—	2	4	no	—
216	C₂³×C₁₃	—	2	2	no	—
217	C₂³×C₁₃	—	4	2	no	—
218	C₂³×C₁₃	—	8	2	no	—
219	C₂³×C₁₃	#120	1	2	yes	—
220	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
221	Q₈×C₁₃	—	2	2	no	—
222	Q₈×C₁₃	—	2	2	no	—
223	Q₈×C₁₃	—	2	4	no	—
224	Q₈×C₁₃	—	2	2	no	—
225	Q₈×C₁₃	—	4	2	no	—
226	Q₈×C₁₃	—	4	1	no	—
227	Q₈×C₁₃	—	4	1	no	—
228	Q₈×C₁₃	—	8	2	no	—
229	D₄×C₁₃	—	2	4	no	—
230	D₄×C₁₃	—	2	2	no	—
231	D₄×C₁₃	—	2	2	no	—
232	D₄×C₁₃	—	2	2	no	—
233	D₄×C₁₃	—	4	2	no	—
234	D₄×C₁₃	—	4	4	no	—
235	D₄×C₁₃	—	4	2	no	—
236	D₄×C₁₃	—	4	2	no	—
237	D₄×C₁₃	—	4	1	no	—
238	D₄×C₁₃	—	4	1	no	—
239	D₄×C₁₃	—	4	2	no	—
240	D₄×C₁₃	—	8	4	no	—
241	D₄×C₁₃	—	16	4	no	—
242	C₂×C₄×C₁₃	—	2	2	no	—
243	C₂×C₄×C₁₃	—	2	2	no	—
244	C₂×C₄×C₁₃	—	2	2	no	—
245	C₂×C₄×C₁₃	—	2	1	no	—
246	C₂×C₄×C₁₃	—	2	2	no	—
247	C₂×C₄×C₁₃	—	2	2	no	—
248	C₂×C₄×C₁₃	—	2	1	no	—
249	C₂×C₄×C₁₃	—	2	2	no	—
250	C₂×C₄×C₁₃	—	2	2	no	—
251	C₂×C₄×C₁₃	—	4	4	no	—
252	C₂×C₄×C₁₃	—	4	2	no	—
253	C₂×C₄×C₁₃	—	4	2	no	—
254	C₂×C₄×C₁₃	—	4	2	no	—
255	C₂×C₄×C₁₃	—	4	2	no	—
256	C₂×C₄×C₁₃	—	4	2	no	—
257	C₂×C₄×C₁₃	—	8	2	no	—
258	C₂×C₄×C₁₃	—	8	4	no	—
259	C₂×C₄×C₁₃	—	8	1	no	—
260	C₂×C₄×C₁₃	#120	1	2	yes	—
261	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
262	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
263	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
264	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
265	C₈×C₁₃	—	4	2	no	—
266	C₈×C₁₃	—	4	2	no	—
267	#585	C₂²×C₁₃	1	1	yes	characteristic
268	C₂×#137	C₂²×C₁₃	1	2	yes	—
269	#568	C₂²×C₁₃	1	1	yes	characteristic
270	#559	—	2	2	no	—
271	#556	—	2	2	no	—
272	#551	—	2	4	no	—
273	#542	—	2	2	no	—
274	#536	C₂²×C₁₃	1	1	yes	characteristic
275	#535	C₂²×C₁₃	1	2	yes	—
276	#535	C₂²×C₁₃	1	1	yes	characteristic
277	#533	C₂²×C₁₃	1	1	yes	characteristic, complemented
278	#529	—	2	2	no	—
279	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic, complemented
280	#519	C₂²×C₁₃	1	1	yes	characteristic, complemented
281	#518	C₂²×C₁₃	1	1	yes	characteristic, complemented
282	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
283	B(4,𝔽₂)	—	2	4	no	—
284	#456	—	2	2	no	—
285	#455	—	2	2	no	—
286	#421	—	2	2	no	—
287	#421	C₂²×C₁₃	1	2	yes	—
288	#421	C₂²×C₁₃	1	2	yes	—
289	C₂×#104	—	2	2	no	—
290	C₂×#104	C₂²×C₁₃	1	2	yes	—
291	#419	C₂²×C₁₃	1	2	yes	complemented
292	#413	C₂²×C₁₃	1	1	yes	characteristic
293	C₂×#100	C₂²×C₁₃	1	2	yes	complemented
294	#410	C₂²×C₁₃	1	1	yes	characteristic
295	#410	C₂²×C₁₃	1	2	yes	—
296	#344	C₂²×C₁₃	1	2	yes	complemented
297	#339	C₂²×C₁₃	1	2	yes	complemented
298	H(3,ℤ/4)	C₂²×C₁₃	1	2	yes	complemented
299	H(3,ℤ/4)	C₂²×C₁₃	1	2	yes	complemented
300	C₂²×C₁₃	—	2	2	no	—
301	C₂²×C₁₃	—	4	1	no	—
302	C₂²×C₁₃	—	4	2	no	—
303	C₂²×C₁₃	—	4	4	no	—
304	C₂²×C₁₃	—	4	2	no	—
305	C₂²×C₁₃	—	4	2	no	—
306	C₂²×C₁₃	—	8	2	no	—
307	C₂²×C₁₃	—	8	4	no	—
308	C₂²×C₁₃	—	16	2	no	—
309	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
310	C₂²×C₁₃	#546	1	2	yes	—
311	C₄×C₁₃	—	2	2	no	—
312	C₄×C₁₃	—	4	2	no	—
313	C₄×C₁₃	—	4	1	no	—
314	C₄×C₁₃	—	4	2	no	—
315	C₄×C₁₃	—	4	1	no	—
316	C₄×C₁₃	—	4	2	no	—
317	C₄×C₁₃	—	4	2	no	—
318	C₄×C₁₃	—	4	2	no	—
319	C₄×C₁₃	—	8	2	no	—
320	C₄×C₁₃	#525	1	1	yes	characteristic
321	C₄×C₁₃	#535	1	1	yes	characteristic
322	C₄×C₁₃	#546	1	2	yes	—
323	2₋¹⁺⁴	—	2	2	no	—
324	2₋¹⁺⁴	—	2	1	no	—
325	H(5,𝔽₂)	—	2	2	no	—
326	H(5,𝔽₂)	—	2	2	no	—
327	H(5,𝔽₂)	—	2	1	no	—
328	C₂×#41	—	2	2	no	—
329	C₂×#41	—	4	2	no	—
330	C₂×#41	C₂³×C₁₃	1	2	yes	—
331	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
332	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
333	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
334	#137	—	2	4	no	—
335	#137	—	4	2	no	—
336	C₂×Q₁₆	—	2	2	no	—
337	C₂×SD₁₆	—	2	2	no	—
338	#131	—	4	2	no	—
339	C₂×M₁₆	—	2	2	no	—
340	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
341	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
342	C₄⋊Q₈	—	2	1	no	—
343	C₄⋊Q₈	D₄×C₁₃	1	2	yes	complemented
344	#127	—	2	1	no	—
345	#127	—	2	2	no	—
346	#126	—	2	4	no	—
347	#126	—	2	4	no	—
348	#125	—	2	1	no	—
349	#124	—	2	4	no	—
350	#124	—	2	2	no	—
351	#124	—	2	1	no	—
352	#124	—	2	2	no	—
353	#124	—	2	1	no	—
354	#124	—	2	1	no	—
355	#124	D₄×C₁₃	1	2	yes	complemented
356	#123	—	2	4	no	—
357	#123	—	2	4	no	—
358	#123	—	2	2	no	—
359	C₂²⋊Q₈	—	2	4	no	—
360	C₂²⋊Q₈	—	2	2	no	—
361	C₂²⋊Q₈	—	2	2	no	—
362	#121	—	2	2	no	—
363	#121	—	4	2	no	—
364	#120	—	2	4	no	—
365	#120	D₄×C₁₃	1	4	yes	—
366	C₄×Q₈	—	2	1	no	—
367	C₄×Q₈	—	2	2	no	—
368	C₄×Q₈	—	2	2	no	—
369	C₄×Q₈	—	2	2	no	—
370	C₄×D₄	—	2	4	no	—
371	C₄×D₄	—	2	2	no	—
372	C₄×D₄	—	2	1	no	—
373	C₄×D₄	—	2	2	no	—
374	C₄×D₄	—	2	2	no	—
375	#117	—	2	4	no	—
376	#117	—	2	2	no	—
377	#117	D₄×C₁₃	1	2	yes	complemented
378	#117	C₂³×C₁₃	1	2	yes	—
379	#117	C₂³×C₁₃	1	1	yes	characteristic
380	#117	C₂³×C₁₃	1	1	yes	characteristic
381	#117	C₂³×C₁₃	1	1	yes	characteristic
382	C₂×C₂²⋊C₄	—	2	2	no	—
383	C₂×C₂²⋊C₄	—	2	2	no	—
384	C₂×C₄²	D₄×C₁₃	1	2	yes	complemented
385	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
386	#104	—	2	2	no	—
387	#104	—	2	4	no	—
388	#104	—	2	2	no	—
389	#104	—	2	4	no	—
390	#103	—	4	2	no	—
391	#101	—	2	1	no	—
392	#100	—	2	1	no	—
393	#100	—	4	2	no	—
394	#99	—	2	2	no	—
395	#99	—	2	4	no	—
396	C₂×C₁₃	—	2	1	no	—
397	C₂×C₁₃	—	2	2	no	—
398	C₂×C₁₃	—	4	2	no	—
399	C₂×C₁₃	—	8	2	no	—
400	C₂×C₁₃	—	8	2	no	—
401	C₂×C₁₃	#2404	1	1	yes	characteristic
402	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
403	#41	—	2	2	no	—
404	#41	—	2	2	no	—
405	#41	—	2	4	no	—
406	#41	—	2	2	no	—
407	#41	—	2	2	no	—
408	#41	—	2	2	no	—
409	#41	—	2	2	no	—
410	#41	—	4	4	no	—
411	#41	—	4	2	no	—
412	#41	—	4	2	no	—
413	#41	—	4	2	no	—
414	#41	—	4	2	no	—
415	C₂×Q₈	—	2	2	no	—
416	C₂×Q₈	—	2	1	no	—
417	C₂×Q₈	—	2	2	no	—
418	C₂×Q₈	—	2	2	no	—
419	C₂×Q₈	—	2	2	no	—
420	C₂×Q₈	—	4	2	no	—
421	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
422	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
423	C₂×Q₈	C₁₃×#41	1	2	yes	—
424	C₂×D₄	—	2	2	no	—
425	C₂×D₄	—	2	2	no	—
426	C₂×D₄	—	2	4	no	—
427	C₂×D₄	—	2	1	no	—
428	C₂×D₄	—	2	1	no	—
429	C₂×D₄	—	2	2	no	—
430	C₂×D₄	—	2	2	no	—
431	C₂×D₄	—	4	2	no	—
432	C₂×D₄	—	4	4	no	—
433	C₂×D₄	—	4	2	no	—
434	C₂×D₄	—	4	4	no	—
435	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
436	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
437	C₂×D₄	C₁₃×#41	1	2	yes	—
438	C₂²×C₄	—	2	1	no	—
439	C₂²×C₄	—	2	4	no	—
440	C₂²×C₄	—	2	2	no	—
441	C₂²×C₄	—	2	1	no	—
442	C₂²×C₄	—	2	2	no	—
443	C₂²×C₄	—	4	2	no	—
444	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
445	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
446	Q₁₆	—	4	4	no	—
447	SD₁₆	—	4	4	no	—
448	M₁₆	—	2	2	no	—
449	M₁₆	—	2	2	no	—
450	M₁₆	—	2	2	no	—
451	M₁₆	—	2	2	no	—
452	M₁₆	—	4	2	no	—
453	C₂×C₈	—	2	2	no	—
454	C₂×C₈	—	2	2	no	—
455	C₂×C₈	—	4	2	no	—
456	C₄⋊C₄	—	2	2	no	—
457	C₄⋊C₄	—	2	4	no	—
458	C₄⋊C₄	—	2	2	no	—
459	C₄⋊C₄	—	2	2	no	—
460	C₄⋊C₄	—	2	4	no	—
461	C₄⋊C₄	—	2	2	no	—
462	C₄⋊C₄	—	2	1	no	—
463	C₄⋊C₄	—	2	1	no	—
464	C₄⋊C₄	—	2	1	no	—
465	C₄⋊C₄	—	2	2	no	—
466	C₂²⋊C₄	—	2	4	no	—
467	C₂²⋊C₄	—	2	4	no	—
468	C₂²⋊C₄	—	2	4	no	—
469	C₂²⋊C₄	—	2	2	no	—
470	C₂²⋊C₄	—	2	4	no	—
471	C₂²⋊C₄	—	2	1	no	—
472	C₂²⋊C₄	—	2	1	no	—
473	C₂²⋊C₄	—	2	4	no	—
474	C₂²⋊C₄	—	2	2	no	—
475	C₂²⋊C₄	—	4	4	no	—
476	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
477	C₄²	—	2	4	no	—
478	C₄²	—	2	2	no	—
479	C₄²	—	2	1	no	—
480	C₄²	—	2	1	no	—
481	C₄²	—	2	2	no	—
482	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
483	C₄²	C₂×D₄×C₁₃	1	2	yes	—
484	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
485	C₄²	C₂×D₄×C₁₃	1	2	yes	—
486	C₁₃	#23991	1	1	yes	characteristic, direct product factor, Sylow
487	C₂³	—	2	2	no	—
488	C₂³	—	2	4	no	—
489	C₂³	—	2	2	no	—
490	C₂³	—	4	2	no	—
491	C₂³	—	8	2	no	—
492	C₂³	C₁₃×#120	1	2	yes	—
493	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
494	Q₈	—	2	2	no	—
495	Q₈	—	2	2	no	—
496	Q₈	—	2	4	no	—
497	Q₈	—	2	2	no	—
498	Q₈	—	4	2	no	—
499	Q₈	—	4	1	no	—
500	Q₈	—	4	1	no	—
501	Q₈	—	8	2	no	—
502	D₄	—	2	4	no	—
503	D₄	—	2	2	no	—
504	D₄	—	2	2	no	—
505	D₄	—	2	2	no	—
506	D₄	—	4	2	no	—
507	D₄	—	4	4	no	—
508	D₄	—	4	2	no	—
509	D₄	—	4	2	no	—
510	D₄	—	4	1	no	—
511	D₄	—	4	1	no	—
512	D₄	—	4	2	no	—
513	D₄	—	8	4	no	—
514	D₄	—	16	4	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	2	2	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	2	no	—
523	C₂×C₄	—	2	2	no	—
524	C₂×C₄	—	4	4	no	—
525	C₂×C₄	—	4	2	no	—
526	C₂×C₄	—	4	2	no	—
527	C₂×C₄	—	4	2	no	—
528	C₂×C₄	—	4	2	no	—
529	C₂×C₄	—	4	2	no	—
530	C₂×C₄	—	8	2	no	—
531	C₂×C₄	—	8	4	no	—
532	C₂×C₄	—	8	1	no	—
533	C₂×C₄	C₁₃×#120	1	2	yes	—
534	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
535	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
536	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
537	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
538	C₈	—	4	2	no	—
539	C₈	—	4	2	no	—
540	C₂²	—	2	2	no	—
541	C₂²	—	4	1	no	—
542	C₂²	—	4	2	no	—
543	C₂²	—	4	4	no	—
544	C₂²	—	4	2	no	—
545	C₂²	—	4	2	no	—
546	C₂²	—	8	2	no	—
547	C₂²	—	8	4	no	—
548	C₂²	—	16	2	no	—
549	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
550	C₂²	C₁₃×#546	1	2	yes	—
551	C₄	—	2	2	no	—
552	C₄	—	4	2	no	—
553	C₄	—	4	1	no	—
554	C₄	—	4	2	no	—
555	C₄	—	4	1	no	—
556	C₄	—	4	2	no	—
557	C₄	—	4	2	no	—
558	C₄	—	4	2	no	—
559	C₄	—	8	2	no	—
560	C₄	C₁₃×#525	1	1	yes	characteristic
561	C₄	C₁₃×#535	1	1	yes	characteristic
562	C₄	C₁₃×#546	1	2	yes	—
563	C₂	—	2	1	no	—
564	C₂	—	2	2	no	—
565	C₂	—	4	2	no	—
566	C₂	—	8	2	no	—
567	C₂	—	8	2	no	—
568	C₂	C₁₃×#2404	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₃	#2404
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₁₃×#3027	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3510	C₂	semidirect
3. C₁₃×#3022	C₂	semidirect
4. C₁₃×#2901	C₂	semidirect
5. C₁₃×#2031	C₂	semidirect
6. C₁₃×#2004	C₂	semidirect
7. C₁₃×#1914	C₂	semidirect
8. C₁₃×#1911	C₂	semidirect
9. C₁₃×#1909	C₂	semidirect
10. C₁₃×#1905	C₂	semidirect
11. C₁₃×#1827	C₂	semidirect
22. C₁₃×#533	C₂²	semidirect
24. C₂×C₁₃×#124	C₂²	semidirect
25. C₁₃×#519	C₂²	semidirect
26. C₁₃×#518	C₂²	semidirect
36. C₁₃×#419	C₂²	semidirect
38. C₂×C₁₃×#100	C₂²	semidirect
41. C₁₃×#344	C₂²	semidirect
42. C₁₃×#339	C₂²	semidirect
43. C₁₃×H(3,ℤ/4)	C₂²	semidirect
44. C₁₃×H(3,ℤ/4)	C₂²	semidirect
65. C₁₃×C₄⋊Q₈	D₄	semidirect
77. C₁₃×#124	D₄	semidirect
99. C₁₃×#117	D₄	semidirect
106. C₂×C₄²×C₁₃	D₄	semidirect
118. #23991	C₁₃	direct (N × H)
203. #3510	C₂×C₁₃	semidirect
205. #3022	C₂×C₁₃	semidirect
206. #2901	C₂×C₁₃	semidirect
207. #2031	C₂×C₁₃	semidirect
208. #2004	C₂×C₁₃	semidirect
209. #1914	C₂×C₁₃	semidirect
210. #1911	C₂×C₁₃	semidirect
211. #1909	C₂×C₁₃	semidirect
212. #1905	C₂×C₁₃	semidirect
213. #1827	C₂×C₁₃	semidirect
277. #533	C₂²×C₁₃	semidirect
279. C₂×#124	C₂²×C₁₃	semidirect
280. #519	C₂²×C₁₃	semidirect
281. #518	C₂²×C₁₃	semidirect
291. #419	C₂²×C₁₃	semidirect
293. C₂×#100	C₂²×C₁₃	semidirect
296. #344	C₂²×C₁₃	semidirect
297. #339	C₂²×C₁₃	semidirect
298. H(3,ℤ/4)	C₂²×C₁₃	semidirect
299. H(3,ℤ/4)	C₂²×C₁₃	semidirect
343. C₄⋊Q₈	D₄×C₁₃	semidirect
355. #124	D₄×C₁₃	semidirect
377. #117	D₄×C₁₃	semidirect
384. C₂×C₄²	D₄×C₁₃	semidirect
486. C₁₃	#23991	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×#3510	2
C₁₃×#3027	2
C₁₃×#3022	2
C₁₃×#2901	2
C₁₃×#2031	2
C₁₃×#2004	2
C₁₃×#1914	2
C₁₃×#1911	2
C₁₃×#1909	2
C₁₃×#1905	2
C₁₃×#1827	2
#23991	13

Subgroups — C13×#23991 #15710330

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#23991 #15710330