Subgroups — C₁₃×#61664 #15748003

Order 3328.

2136 conjugacy classes of subgroups.

The subgroup lattice has 578 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, complemented
2	C₁₃×#3499	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3329	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3303	C₂	1	4	yes	maximal, complemented
5	D₄×C₁₃×SD₁₆	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3272	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3206	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3200	C₂	1	4	yes	maximal, complemented
9	C₁₃×#3106	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3010	C₂	1	4	yes	maximal, complemented
11	C₁₃×#2979	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	2	yes	complemented
13	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
14	C₂²×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
15	C₁₃×H(3,𝔽₄)	—	2	2	no	—
16	C₁₃×#555	—	2	1	no	—
17	C₁₃×#555	C₂²	1	4	yes	—
18	D₄×Q₈×C₁₃	C₂²	1	4	yes	complemented
19	C₁₃×#547	—	2	4	no	—
20	C₁₃×#547	C₂²	1	4	yes	complemented
21	D₄²×C₁₃	—	2	1	no	—
22	D₄²×C₁₃	C₂²	1	4	yes	—
23	C₁₃×#536	—	2	2	no	—
24	C₁₃×#536	C₂²	1	2	yes	complemented
25	C₁₃×#535	—	2	4	no	—
26	C₁₃×#535	C₂²	1	4	yes	—
27	C₁₃×#532	—	2	1	no	—
28	C₁₃×#532	C₂²	1	2	yes	—
29	C₁₃×#532	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
31	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
32	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic, complemented
33	C₁₃×#492	C₂²	1	4	yes	—
34	C₁₃×#487	C₂²	1	4	yes	complemented
35	C₁₃×#485	C₂²	1	8	yes	complemented
36	C₁₃×#482	C₂²	1	4	yes	complemented
37	C₁₃×#477	C₂²	1	2	yes	complemented
38	C₁₃×#476	C₂²	1	2	yes	complemented
39	C₁₃×#468	C₂²	1	8	yes	complemented
40	C₁₃×#465	C₂²	1	8	yes	complemented
41	C₁₃×#461	C₂²	1	4	yes	complemented
42	C₁₃×#461	C₂²	1	4	yes	complemented
43	C₁₃×#460	C₂²	1	2	yes	—
44	C₁₃×#459	C₂²	1	2	yes	—
45	C₁₃×#450	C₂²	1	8	yes	complemented
46	C₁₃×#449	C₂²	1	4	yes	complemented
47	C₁₃×#449	C₂²	1	8	yes	complemented
48	C₁₃×#448	C₂²	1	8	yes	complemented
49	C₁₃×#448	C₂²	1	8	yes	complemented
50	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
51	C₄×C₁₃×D₈	C₂²	1	4	yes	complemented
52	C₁₃×#436	C₂²	1	4	yes	complemented
53	C₈×D₄×C₁₃	C₂²	1	4	yes	complemented
54	C₁₃×#431	C₂²	1	2	yes	complemented
55	C₁₃×#419	C₂²	1	4	yes	complemented
56	C₁₃×#416	C₂²	1	4	yes	complemented
57	C₁₃×#408	C₂²	1	4	yes	complemented
58	C₁₃×2₋¹⁺⁴	—	4	4	no	—
59	C₁₃×2₋¹⁺⁴	—	4	4	no	—
60	C₂×C₁₃×#41	—	2	2	no	—
61	C₂×C₁₃×#41	—	2	4	no	—
62	C₂×C₁₃×#41	—	2	2	no	—
63	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
64	C₂×C₁₃×#41	C₂³	1	4	yes	—
65	C₂×C₁₃×#41	C₂³	1	2	yes	—
66	C₂²×Q₈×C₁₃	—	2	2	no	—
67	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
68	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
69	C₂²×D₄×C₁₃	—	2	4	no	—
70	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
71	C₁₃×AGL(1,ℤ/8)	—	4	8	no	—
72	C₂×C₁₃×SD₁₆	—	4	8	no	—
73	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
74	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
75	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
76	C₂×C₁₃×D₈	C₂³	1	4	yes	—
77	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
78	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
79	C₁₃×C₄⋊Q₈	—	2	2	no	—
80	C₁₃×C₄⋊Q₈	—	2	4	no	—
81	C₁₃×C₄⋊Q₈	—	2	1	no	—
82	C₁₃×C₄⋊Q₈	—	2	1	no	—
83	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
84	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
85	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
86	C₁₃×#127	—	2	4	no	—
87	C₁₃×#127	D₄	1	1	yes	characteristic
88	C₁₃×#127	C₂³	1	2	yes	—
89	C₁₃×#124	—	2	4	no	—
90	C₁₃×#124	—	2	2	no	—
91	C₁₃×#124	—	2	8	no	—
92	C₁₃×#124	—	2	2	no	—
93	C₁₃×#124	D₄	1	2	yes	—
94	C₁₃×#123	—	2	4	no	—
95	C₁₃×#123	—	2	8	no	—
96	C₁₃×C₂²⋊Q₈	—	2	8	no	—
97	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
98	C₁₃×#121	—	2	4	no	—
99	C₁₃×#121	—	2	4	no	—
100	C₁₃×#121	—	2	2	no	—
101	C₁₃×#121	—	2	4	no	—
102	C₁₃×#121	D₄	1	4	yes	—
103	C₁₃×#121	C₂³	1	4	yes	—
104	C₁₃×#121	C₂³	1	8	yes	—
105	C₁₃×#120	—	2	4	no	—
106	C₁₃×#120	—	2	4	no	—
107	C₁₃×#120	—	2	8	no	—
108	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
109	C₄×D₄×C₁₃	—	2	4	no	—
110	C₄×D₄×C₁₃	—	2	2	no	—
111	C₄×D₄×C₁₃	—	2	2	no	—
112	C₄×D₄×C₁₃	C₂³	1	2	yes	—
113	C₄×D₄×C₁₃	C₂³	1	4	yes	—
114	C₄×D₄×C₁₃	C₂³	1	4	yes	—
115	C₁₃×#117	—	2	4	no	—
116	C₁₃×#117	—	2	1	no	—
117	C₁₃×#117	C₂³	1	4	yes	—
118	C₁₃×#117	C₂³	1	1	yes	characteristic
119	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
120	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
121	C₂×C₄²×C₁₃	—	2	1	no	—
122	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
123	C₁₃×#107	C₂³	1	4	yes	—
124	C₁₃×#106	C₂³	1	4	yes	—
125	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
126	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
127	C₁₃×#103	C₂³	1	8	yes	—
128	C₁₃×#103	C₂³	1	4	yes	—
129	C₁₃×#103	C₂³	1	8	yes	—
130	C₁₃×#102	C₂³	1	4	yes	—
131	C₁₃×#102	C₂³	1	4	yes	—
132	C₁₃×#102	C₂³	1	4	yes	—
133	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
134	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	—
135	C₄×C₈×C₁₃	C₂³	1	4	yes	—
136	#61664	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
137	C₂⁴×C₁₃	—	2	4	no	—
138	C₁₃×#41	—	2	2	no	—
139	C₁₃×#41	—	2	2	no	—
140	C₁₃×#41	—	2	8	no	—
141	C₁₃×#41	—	4	2	no	—
142	C₁₃×#41	—	4	2	no	—
143	C₁₃×#41	—	4	4	no	—
144	C₁₃×#41	—	4	8	no	—
145	C₁₃×#41	—	4	16	no	—
146	C₁₃×#41	—	8	4	no	—
147	C₂×Q₈×C₁₃	—	2	4	no	—
148	C₂×Q₈×C₁₃	—	2	2	no	—
149	C₂×Q₈×C₁₃	—	2	2	no	—
150	C₂×Q₈×C₁₃	—	2	8	no	—
151	C₂×Q₈×C₁₃	—	4	4	no	—
152	C₂×Q₈×C₁₃	—	4	2	no	—
153	C₂×Q₈×C₁₃	—	4	2	no	—
154	C₂×Q₈×C₁₃	—	4	8	no	—
155	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
156	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
157	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
158	C₂×D₄×C₁₃	—	2	1	no	—
159	C₂×D₄×C₁₃	—	2	4	no	—
160	C₂×D₄×C₁₃	—	2	8	no	—
161	C₂×D₄×C₁₃	—	2	4	no	—
162	C₂×D₄×C₁₃	—	2	2	no	—
163	C₂×D₄×C₁₃	—	2	2	no	—
164	C₂×D₄×C₁₃	—	2	4	no	—
165	C₂×D₄×C₁₃	—	4	4	no	—
166	C₂×D₄×C₁₃	—	4	4	no	—
167	C₂×D₄×C₁₃	—	8	8	no	—
168	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
169	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
170	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
171	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
172	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
173	C₂²×C₄×C₁₃	—	2	1	no	—
174	C₂²×C₄×C₁₃	—	2	2	no	—
175	C₂²×C₄×C₁₃	—	2	4	no	—
176	C₂²×C₄×C₁₃	—	2	2	no	—
177	C₂²×C₄×C₁₃	—	2	4	no	—
178	C₂²×C₄×C₁₃	—	2	4	no	—
179	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
180	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
181	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
182	C₁₃×SD₁₆	—	2	8	no	—
183	C₁₃×SD₁₆	—	4	8	no	—
184	C₁₃×SD₁₆	—	4	8	no	—
185	C₁₃×D₈	—	2	8	no	—
186	C₁₃×M₁₆	—	4	4	no	—
187	C₂×C₈×C₁₃	—	4	4	no	—
188	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
189	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
190	C₁₃×C₄⋊C₄	—	2	4	no	—
191	C₁₃×C₄⋊C₄	—	2	4	no	—
192	C₁₃×C₄⋊C₄	—	2	8	no	—
193	C₁₃×C₄⋊C₄	—	2	2	no	—
194	C₁₃×C₄⋊C₄	—	2	2	no	—
195	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
196	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
197	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
198	C₁₃×C₂²⋊C₄	—	2	1	no	—
199	C₁₃×C₂²⋊C₄	—	2	4	no	—
200	C₁₃×C₂²⋊C₄	—	2	8	no	—
201	C₁₃×C₂²⋊C₄	—	2	2	no	—
202	C₁₃×C₂²⋊C₄	—	2	8	no	—
203	C₁₃×C₂²⋊C₄	—	2	4	no	—
204	C₁₃×C₂²⋊C₄	—	2	4	no	—
205	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
206	C₄²×C₁₃	—	2	1	no	—
207	C₄²×C₁₃	—	2	2	no	—
208	C₄²×C₁₃	—	2	4	no	—
209	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
210	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
211	C₄²×C₁₃	C₂⁴	1	2	yes	—
212	#3549	C₂×C₁₃	1	1	yes	characteristic, complemented
213	#3499	C₂×C₁₃	1	1	yes	characteristic, complemented
214	#3329	C₂×C₁₃	1	4	yes	complemented
215	#3303	C₂×C₁₃	1	4	yes	complemented
216	D₄×SD₁₆	C₂×C₁₃	1	4	yes	complemented
217	#3272	C₂×C₁₃	1	4	yes	complemented
218	#3206	C₂×C₁₃	1	2	yes	complemented
219	#3200	C₂×C₁₃	1	4	yes	complemented
220	#3106	C₂×C₁₃	1	2	yes	complemented
221	#3010	C₂×C₁₃	1	4	yes	complemented
222	#2979	C₂×C₁₃	1	1	yes	characteristic, complemented
223	C₂³×C₁₃	—	2	1	no	—
224	C₂³×C₁₃	—	2	4	no	—
225	C₂³×C₁₃	—	8	4	no	—
226	C₂³×C₁₃	—	8	8	no	—
227	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
228	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
229	Q₈×C₁₃	—	2	1	no	—
230	Q₈×C₁₃	—	2	4	no	—
231	Q₈×C₁₃	—	2	4	no	—
232	Q₈×C₁₃	—	4	2	no	—
233	Q₈×C₁₃	—	4	8	no	—
234	Q₈×C₁₃	—	4	4	no	—
235	Q₈×C₁₃	—	8	2	no	—
236	Q₈×C₁₃	H(5,𝔽₂)	1	2	yes	—
237	D₄×C₁₃	—	2	4	no	—
238	D₄×C₁₃	—	2	8	no	—
239	D₄×C₁₃	—	2	1	no	—
240	D₄×C₁₃	—	2	4	no	—
241	D₄×C₁₃	—	2	4	no	—
242	D₄×C₁₃	—	4	2	no	—
243	D₄×C₁₃	—	4	4	no	—
244	D₄×C₁₃	—	4	8	no	—
245	D₄×C₁₃	—	4	4	no	—
246	D₄×C₁₃	—	8	4	no	—
247	D₄×C₁₃	—	8	2	no	—
248	D₄×C₁₃	—	8	8	no	—
249	D₄×C₁₃	—	8	4	no	—
250	D₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
251	C₂×C₄×C₁₃	—	2	4	no	—
252	C₂×C₄×C₁₃	—	2	1	no	—
253	C₂×C₄×C₁₃	—	2	4	no	—
254	C₂×C₄×C₁₃	—	2	4	no	—
255	C₂×C₄×C₁₃	—	2	4	no	—
256	C₂×C₄×C₁₃	—	2	1	no	—
257	C₂×C₄×C₁₃	—	2	1	no	—
258	C₂×C₄×C₁₃	—	2	2	no	—
259	C₂×C₄×C₁₃	—	2	4	no	—
260	C₂×C₄×C₁₃	—	2	4	no	—
261	C₂×C₄×C₁₃	—	4	8	no	—
262	C₂×C₄×C₁₃	—	4	8	no	—
263	C₂×C₄×C₁₃	—	4	4	no	—
264	C₂×C₄×C₁₃	—	4	4	no	—
265	C₂×C₄×C₁₃	—	4	8	no	—
266	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
267	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
268	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
269	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
270	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
271	C₈×C₁₃	—	2	4	no	—
272	C₈×C₁₃	—	2	4	no	—
273	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	2	yes	complemented
274	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	4	yes	complemented
275	C₂²×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
276	H(3,𝔽₄)	—	2	2	no	—
277	#555	—	2	1	no	—
278	#555	C₂²×C₁₃	1	4	yes	—
279	D₄×Q₈	C₂²×C₁₃	1	4	yes	complemented
280	#547	—	2	4	no	—
281	#547	C₂²×C₁₃	1	4	yes	complemented
282	D₄²	—	2	1	no	—
283	D₄²	C₂²×C₁₃	1	4	yes	—
284	#536	—	2	2	no	—
285	#536	C₂²×C₁₃	1	2	yes	complemented
286	#535	—	2	4	no	—
287	#535	C₂²×C₁₃	1	4	yes	—
288	#532	—	2	1	no	—
289	#532	C₂²×C₁₃	1	2	yes	—
290	#532	C₂²×C₁₃	1	1	yes	characteristic
291	C₂×C₄⋊Q₈	—	2	1	no	—
292	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
293	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic, complemented
294	#492	C₂²×C₁₃	1	4	yes	—
295	#487	C₂²×C₁₃	1	4	yes	complemented
296	#485	C₂²×C₁₃	1	8	yes	complemented
297	#482	C₂²×C₁₃	1	4	yes	complemented
298	#477	C₂²×C₁₃	1	2	yes	complemented
299	#476	C₂²×C₁₃	1	2	yes	complemented
300	#468	C₂²×C₁₃	1	8	yes	complemented
301	#465	C₂²×C₁₃	1	8	yes	complemented
302	#461	C₂²×C₁₃	1	4	yes	complemented
303	#461	C₂²×C₁₃	1	4	yes	complemented
304	#460	C₂²×C₁₃	1	2	yes	—
305	#459	C₂²×C₁₃	1	2	yes	—
306	#450	C₂²×C₁₃	1	8	yes	complemented
307	#449	C₂²×C₁₃	1	4	yes	complemented
308	#449	C₂²×C₁₃	1	8	yes	complemented
309	#448	C₂²×C₁₃	1	8	yes	complemented
310	#448	C₂²×C₁₃	1	8	yes	complemented
311	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
312	C₄×D₈	C₂²×C₁₃	1	4	yes	complemented
313	#436	C₂²×C₁₃	1	4	yes	complemented
314	C₈×D₄	C₂²×C₁₃	1	4	yes	complemented
315	#431	C₂²×C₁₃	1	2	yes	complemented
316	#419	C₂²×C₁₃	1	4	yes	complemented
317	#416	C₂²×C₁₃	1	4	yes	complemented
318	#408	C₂²×C₁₃	1	4	yes	complemented
319	C₂²×C₁₃	—	2	1	no	—
320	C₂²×C₁₃	—	2	2	no	—
321	C₂²×C₁₃	—	2	4	no	—
322	C₂²×C₁₃	—	2	2	no	—
323	C₂²×C₁₃	—	2	8	no	—
324	C₂²×C₁₃	—	4	2	no	—
325	C₂²×C₁₃	—	4	4	no	—
326	C₂²×C₁₃	—	4	4	no	—
327	C₂²×C₁₃	—	4	4	no	—
328	C₂²×C₁₃	—	16	8	no	—
329	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
330	C₄×C₁₃	—	2	1	no	—
331	C₄×C₁₃	—	2	2	no	—
332	C₄×C₁₃	—	2	4	no	—
333	C₄×C₁₃	—	2	2	no	—
334	C₄×C₁₃	—	4	4	no	—
335	C₄×C₁₃	—	4	2	no	—
336	C₄×C₁₃	—	4	4	no	—
337	C₄×C₁₃	#577	1	4	yes	—
338	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
339	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
340	2₋¹⁺⁴	—	4	4	no	—
341	2₋¹⁺⁴	—	4	4	no	—
342	C₂×#41	—	2	2	no	—
343	C₂×#41	—	2	4	no	—
344	C₂×#41	—	2	2	no	—
345	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
346	C₂×#41	C₂³×C₁₃	1	4	yes	—
347	C₂×#41	C₂³×C₁₃	1	2	yes	—
348	C₂²×Q₈	—	2	2	no	—
349	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
350	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
351	C₂²×D₄	—	2	4	no	—
352	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
353	AGL(1,ℤ/8)	—	4	8	no	—
354	C₂×SD₁₆	—	4	8	no	—
355	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
356	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
357	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
358	C₂×D₈	C₂³×C₁₃	1	4	yes	—
359	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
360	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
361	C₄⋊Q₈	—	2	2	no	—
362	C₄⋊Q₈	—	2	4	no	—
363	C₄⋊Q₈	—	2	1	no	—
364	C₄⋊Q₈	—	2	1	no	—
365	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
366	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
367	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
368	#127	—	2	4	no	—
369	#127	D₄×C₁₃	1	1	yes	characteristic
370	#127	C₂³×C₁₃	1	2	yes	—
371	#124	—	2	4	no	—
372	#124	—	2	2	no	—
373	#124	—	2	8	no	—
374	#124	—	2	2	no	—
375	#124	D₄×C₁₃	1	2	yes	—
376	#123	—	2	4	no	—
377	#123	—	2	8	no	—
378	C₂²⋊Q₈	—	2	8	no	—
379	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
380	#121	—	2	4	no	—
381	#121	—	2	4	no	—
382	#121	—	2	2	no	—
383	#121	—	2	4	no	—
384	#121	D₄×C₁₃	1	4	yes	—
385	#121	C₂³×C₁₃	1	4	yes	—
386	#121	C₂³×C₁₃	1	8	yes	—
387	#120	—	2	4	no	—
388	#120	—	2	4	no	—
389	#120	—	2	8	no	—
390	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
391	C₄×D₄	—	2	4	no	—
392	C₄×D₄	—	2	2	no	—
393	C₄×D₄	—	2	2	no	—
394	C₄×D₄	C₂³×C₁₃	1	2	yes	—
395	C₄×D₄	C₂³×C₁₃	1	4	yes	—
396	C₄×D₄	C₂³×C₁₃	1	4	yes	—
397	#117	—	2	4	no	—
398	#117	—	2	1	no	—
399	#117	C₂³×C₁₃	1	1	yes	characteristic
400	#117	C₂³×C₁₃	1	4	yes	—
401	C₂×C₄⋊C₄	—	2	2	no	—
402	C₂×C₄⋊C₄	—	2	4	no	—
403	C₂×C₄²	—	2	1	no	—
404	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
405	#107	C₂³×C₁₃	1	4	yes	—
406	#106	C₂³×C₁₃	1	4	yes	—
407	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
408	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
409	#103	C₂³×C₁₃	1	8	yes	—
410	#103	C₂³×C₁₃	1	4	yes	—
411	#103	C₂³×C₁₃	1	8	yes	—
412	#102	C₂³×C₁₃	1	4	yes	—
413	#102	C₂³×C₁₃	1	4	yes	—
414	#102	C₂³×C₁₃	1	4	yes	—
415	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
416	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	—
417	C₄×C₈	C₂³×C₁₃	1	4	yes	—
418	C₂×C₁₃	—	4	1	no	—
419	C₂×C₁₃	—	4	4	no	—
420	C₂×C₁₃	—	4	2	no	—
421	C₂×C₁₃	—	8	4	no	—
422	C₂×C₁₃	#3484	1	1	yes	characteristic
423	C₂×C₁₃	C₂×#577	1	2	yes	—
424	C₂⁴	—	2	4	no	—
425	#41	—	2	2	no	—
426	#41	—	2	2	no	—
427	#41	—	2	8	no	—
428	#41	—	4	2	no	—
429	#41	—	4	2	no	—
430	#41	—	4	4	no	—
431	#41	—	4	8	no	—
432	#41	—	4	16	no	—
433	#41	—	8	4	no	—
434	C₂×Q₈	—	2	4	no	—
435	C₂×Q₈	—	2	2	no	—
436	C₂×Q₈	—	2	2	no	—
437	C₂×Q₈	—	2	8	no	—
438	C₂×Q₈	—	4	4	no	—
439	C₂×Q₈	—	4	2	no	—
440	C₂×Q₈	—	4	2	no	—
441	C₂×Q₈	—	4	8	no	—
442	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
443	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
444	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
445	C₂×D₄	—	2	1	no	—
446	C₂×D₄	—	2	4	no	—
447	C₂×D₄	—	2	8	no	—
448	C₂×D₄	—	2	4	no	—
449	C₂×D₄	—	2	2	no	—
450	C₂×D₄	—	2	2	no	—
451	C₂×D₄	—	2	4	no	—
452	C₂×D₄	—	4	4	no	—
453	C₂×D₄	—	4	4	no	—
454	C₂×D₄	—	8	8	no	—
455	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
456	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
457	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
458	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
459	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
460	C₂²×C₄	—	2	1	no	—
461	C₂²×C₄	—	2	2	no	—
462	C₂²×C₄	—	2	4	no	—
463	C₂²×C₄	—	2	2	no	—
464	C₂²×C₄	—	2	4	no	—
465	C₂²×C₄	—	2	4	no	—
466	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
467	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
468	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
469	SD₁₆	—	2	8	no	—
470	SD₁₆	—	4	8	no	—
471	SD₁₆	—	4	8	no	—
472	D₈	—	2	8	no	—
473	M₁₆	—	4	4	no	—
474	C₂×C₈	—	4	4	no	—
475	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
476	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
477	C₄⋊C₄	—	2	4	no	—
478	C₄⋊C₄	—	2	4	no	—
479	C₄⋊C₄	—	2	8	no	—
480	C₄⋊C₄	—	2	2	no	—
481	C₄⋊C₄	—	2	2	no	—
482	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
483	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
484	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
485	C₂²⋊C₄	—	2	1	no	—
486	C₂²⋊C₄	—	2	4	no	—
487	C₂²⋊C₄	—	2	8	no	—
488	C₂²⋊C₄	—	2	2	no	—
489	C₂²⋊C₄	—	2	8	no	—
490	C₂²⋊C₄	—	2	4	no	—
491	C₂²⋊C₄	—	2	4	no	—
492	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
493	C₄²	—	2	1	no	—
494	C₄²	—	2	2	no	—
495	C₄²	—	2	4	no	—
496	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
497	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
498	C₄²	C₂⁴×C₁₃	1	2	yes	—
499	C₁₃	#61664	1	1	yes	characteristic, direct product factor, Sylow
500	C₂³	—	2	1	no	—
501	C₂³	—	2	4	no	—
502	C₂³	—	8	4	no	—
503	C₂³	—	8	8	no	—
504	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
505	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
506	Q₈	—	2	1	no	—
507	Q₈	—	2	4	no	—
508	Q₈	—	2	4	no	—
509	Q₈	—	4	2	no	—
510	Q₈	—	4	8	no	—
511	Q₈	—	4	4	no	—
512	Q₈	—	8	2	no	—
513	Q₈	C₁₃×H(5,𝔽₂)	1	2	yes	—
514	D₄	—	2	4	no	—
515	D₄	—	2	8	no	—
516	D₄	—	2	1	no	—
517	D₄	—	2	4	no	—
518	D₄	—	2	4	no	—
519	D₄	—	4	2	no	—
520	D₄	—	4	4	no	—
521	D₄	—	4	8	no	—
522	D₄	—	4	4	no	—
523	D₄	—	8	4	no	—
524	D₄	—	8	2	no	—
525	D₄	—	8	8	no	—
526	D₄	—	8	4	no	—
527	D₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
528	C₂×C₄	—	2	4	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	2	4	no	—
531	C₂×C₄	—	2	4	no	—
532	C₂×C₄	—	2	4	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	4	no	—
537	C₂×C₄	—	2	4	no	—
538	C₂×C₄	—	4	8	no	—
539	C₂×C₄	—	4	8	no	—
540	C₂×C₄	—	4	4	no	—
541	C₂×C₄	—	4	8	no	—
542	C₂×C₄	—	4	4	no	—
543	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
544	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
545	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
546	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
547	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
548	C₈	—	2	4	no	—
549	C₈	—	2	4	no	—
550	C₂²	—	2	2	no	—
551	C₂²	—	2	8	no	—
552	C₂²	—	2	1	no	—
553	C₂²	—	2	2	no	—
554	C₂²	—	2	4	no	—
555	C₂²	—	4	2	no	—
556	C₂²	—	4	4	no	—
557	C₂²	—	4	4	no	—
558	C₂²	—	4	4	no	—
559	C₂²	—	16	8	no	—
560	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
561	C₄	—	2	2	no	—
562	C₄	—	2	1	no	—
563	C₄	—	2	2	no	—
564	C₄	—	2	4	no	—
565	C₄	—	4	2	no	—
566	C₄	—	4	4	no	—
567	C₄	—	4	4	no	—
568	C₄	C₁₃×#577	1	4	yes	—
569	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
570	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
571	C₂	—	4	4	no	—
572	C₂	—	4	1	no	—
573	C₂	—	4	2	no	—
574	C₂	—	8	4	no	—
575	C₂	C₁₃×#3484	1	1	yes	characteristic
576	C₂	C₂×C₁₃×#577	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₁₃×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3549	C₂	semidirect
2. C₁₃×#3499	C₂	semidirect
3. C₁₃×#3329	C₂	semidirect
4. C₁₃×#3303	C₂	semidirect
5. D₄×C₁₃×SD₁₆	C₂	semidirect
6. C₁₃×#3272	C₂	semidirect
7. C₁₃×#3206	C₂	semidirect
8. C₁₃×#3200	C₂	semidirect
9. C₁₃×#3106	C₂	semidirect
10. C₁₃×#3010	C₂	semidirect
11. C₁₃×#2979	C₂	semidirect
12. C₂×C₁₃×2₋¹⁺⁴	C₂²	semidirect
13. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
14. C₂²×C₁₃×SD₁₆	C₂²	semidirect
18. D₄×Q₈×C₁₃	C₂²	semidirect
20. C₁₃×#547	C₂²	semidirect
24. C₁₃×#536	C₂²	semidirect
31. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
32. C₄×C₁₃×#41	C₂²	semidirect
34. C₁₃×#487	C₂²	semidirect
35. C₁₃×#485	C₂²	semidirect
36. C₁₃×#482	C₂²	semidirect
37. C₁₃×#477	C₂²	semidirect
38. C₁₃×#476	C₂²	semidirect
39. C₁₃×#468	C₂²	semidirect
40. C₁₃×#465	C₂²	semidirect
41. C₁₃×#461	C₂²	semidirect
42. C₁₃×#461	C₂²	semidirect
45. C₁₃×#450	C₂²	semidirect
46. C₁₃×#449	C₂²	semidirect
47. C₁₃×#449	C₂²	semidirect
48. C₁₃×#448	C₂²	semidirect
49. C₁₃×#448	C₂²	semidirect
50. C₄×C₁₃×SD₁₆	C₂²	semidirect
51. C₄×C₁₃×D₈	C₂²	semidirect
52. C₁₃×#436	C₂²	semidirect
53. C₈×D₄×C₁₃	C₂²	semidirect
54. C₁₃×#431	C₂²	semidirect
55. C₁₃×#419	C₂²	semidirect
56. C₁₃×#416	C₂²	semidirect
57. C₁₃×#408	C₂²	semidirect
136. #61664	C₁₃	direct (N × H)
212. #3549	C₂×C₁₃	semidirect
213. #3499	C₂×C₁₃	semidirect
214. #3329	C₂×C₁₃	semidirect
215. #3303	C₂×C₁₃	semidirect
216. D₄×SD₁₆	C₂×C₁₃	semidirect
217. #3272	C₂×C₁₃	semidirect
218. #3206	C₂×C₁₃	semidirect
219. #3200	C₂×C₁₃	semidirect
220. #3106	C₂×C₁₃	semidirect
221. #3010	C₂×C₁₃	semidirect
222. #2979	C₂×C₁₃	semidirect
273. C₂×2₋¹⁺⁴	C₂²×C₁₃	semidirect
274. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
275. C₂²×SD₁₆	C₂²×C₁₃	semidirect
279. D₄×Q₈	C₂²×C₁₃	semidirect
281. #547	C₂²×C₁₃	semidirect
285. #536	C₂²×C₁₃	semidirect
292. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
293. C₄×#41	C₂²×C₁₃	semidirect
295. #487	C₂²×C₁₃	semidirect
296. #485	C₂²×C₁₃	semidirect
297. #482	C₂²×C₁₃	semidirect
298. #477	C₂²×C₁₃	semidirect
299. #476	C₂²×C₁₃	semidirect
300. #468	C₂²×C₁₃	semidirect
301. #465	C₂²×C₁₃	semidirect
302. #461	C₂²×C₁₃	semidirect
303. #461	C₂²×C₁₃	semidirect
306. #450	C₂²×C₁₃	semidirect
307. #449	C₂²×C₁₃	semidirect
308. #449	C₂²×C₁₃	semidirect
309. #448	C₂²×C₁₃	semidirect
310. #448	C₂²×C₁₃	semidirect
311. C₄×SD₁₆	C₂²×C₁₃	semidirect
312. C₄×D₈	C₂²×C₁₃	semidirect
313. #436	C₂²×C₁₃	semidirect
314. C₈×D₄	C₂²×C₁₃	semidirect
315. #431	C₂²×C₁₃	semidirect
316. #419	C₂²×C₁₃	semidirect
317. #416	C₂²×C₁₃	semidirect
318. #408	C₂²×C₁₃	semidirect
499. C₁₃	#61664	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×#3499	2
C₁₃×#3329	2
C₁₃×#3303	2
D₄×C₁₃×SD₁₆	2
C₁₃×#3272	2
C₁₃×#3206	2
C₁₃×#3200	2
C₁₃×#3106	2
C₁₃×#3010	2
C₁₃×#2979	2
#61664	13

Subgroups — C13×#61664 #15748003

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61664 #15748003