Subgroups — C₁₃×#62588 #15748927

Order 3328.

2046 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3518	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3498	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3362	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3358	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3325	C₂	1	6	yes	maximal, complemented
6	C₁₃×#3324	C₂	1	6	yes	maximal, complemented
7	C₁₃×#3235	C₂	1	3	yes	maximal, complemented
8	C₁₃×#3217	C₂	1	3	yes	maximal, complemented
9	C₁₃×#3171	C₂	1	3	yes	maximal, complemented
10	C₁₃×#3138	C₂	1	3	yes	maximal, complemented
11	C₁₃×#2971	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×H(5,𝔽₂)	—	2	1	no	—
13	Q₈²×C₁₃	C₂²	1	1	yes	characteristic, complemented
14	C₁₃×#556	—	2	3	no	—
15	C₁₃×#556	C₂²	1	3	yes	complemented
16	C₁₃×#555	C₂²	1	3	yes	complemented
17	C₁₃×#550	—	2	1	no	—
18	C₁₃×#550	C₂²	1	2	yes	—
19	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
20	C₁₃×#548	—	2	1	no	—
21	D₄²×C₁₃	—	2	3	no	—
22	D₄²×C₁₃	C₂²	1	6	yes	—
23	C₁₃×#542	—	2	3	no	—
24	C₁₃×#535	—	2	3	no	—
25	C₁₃×#533	C₂²	1	3	yes	complemented
26	C₁₃×#532	C₂²	1	3	yes	—
27	C₂×C₁₃×#127	C₂²	1	3	yes	—
28	C₁₃×#529	C₂²	1	3	yes	complemented
29	C₁₃×#519	—	2	1	no	—
30	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
31	C₁₃×#501	C₂²	1	3	yes	complemented
32	C₁₃×#496	C₂²	1	3	yes	complemented
33	C₁₃×#490	C₂²	1	3	yes	complemented
34	C₁₃×#490	C₂²	1	6	yes	complemented
35	C₁₃×#489	C₂²	1	1	yes	characteristic, complemented
36	C₁₃×#486	C₂²	1	6	yes	complemented
37	C₁₃×#486	C₂²	1	6	yes	complemented
38	C₁₃×#482	C₂²	1	12	yes	complemented
39	C₁₃×#476	C₂²	1	6	yes	complemented
40	C₁₃×#474	C₂²	1	6	yes	complemented
41	C₁₃×#469	C₂²	1	6	yes	complemented
42	C₁₃×#468	C₂²	1	6	yes	complemented
43	C₁₃×#460	C₂²	1	6	yes	complemented
44	C₁₃×#459	C₂²	1	6	yes	complemented
45	C₁₃×#450	C₂²	1	6	yes	complemented
46	C₁₃×#447	C₂²	1	6	yes	complemented
47	C₈×Q₈×C₁₃	C₂²	1	2	yes	complemented
48	C₄×C₁₃×SD₁₆	C₂²	1	6	yes	complemented
49	C₄×C₁₃×D₈	C₂²	1	6	yes	complemented
50	C₁₃×#436	C₂²	1	6	yes	complemented
51	C₁₃×#432	C₂²	1	3	yes	complemented
52	C₁₃×#418	C₂²	1	12	yes	complemented
53	C₄×C₁₃×M₁₆	C₂²	1	3	yes	complemented
54	C₁₃×H(5,𝔽₂)	—	4	8	no	—
55	C₂×C₁₃×#41	—	2	2	no	—
56	C₂×C₁₃×#41	—	2	3	no	—
57	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
58	C₂²×Q₈×C₁₃	—	2	1	no	—
59	C₂²×D₄×C₁₃	—	2	6	no	—
60	C₂²×D₄×C₁₃	—	2	3	no	—
61	C₂²×D₄×C₁₃	—	2	3	no	—
62	C₂²×D₄×C₁₃	C₂³	1	6	yes	—
63	C₂×C₁₃×SD₁₆	C₂³	1	6	yes	—
64	C₂×C₁₃×D₈	C₂³	1	6	yes	—
65	C₂×C₁₃×M₁₆	C₂³	1	6	yes	—
66	C₁₃×C₄⋊Q₈	—	2	3	no	—
67	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
68	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
69	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
70	C₁₃×#127	—	2	3	no	—
71	C₁₃×#127	—	2	3	no	—
72	C₁₃×#127	C₂³	1	6	yes	—
73	C₁₃×#127	C₂³	1	3	yes	—
74	C₁₃×#126	—	2	6	no	—
75	C₁₃×#126	—	2	3	no	—
76	C₁₃×#125	C₂³	1	3	yes	—
77	C₁₃×#124	—	2	3	no	—
78	C₁₃×#124	—	2	6	no	—
79	C₁₃×#124	—	2	3	no	—
80	C₁₃×#124	C₂³	1	1	yes	characteristic
81	C₁₃×#123	—	2	3	no	—
82	C₁₃×C₂²⋊Q₈	—	2	3	no	—
83	C₁₃×C₂²⋊Q₈	—	2	3	no	—
84	C₁₃×C₂²⋊Q₈	—	2	3	no	—
85	C₁₃×C₂²⋊Q₈	C₂³	1	3	yes	—
86	C₁₃×#121	—	2	3	no	—
87	C₁₃×#121	—	2	3	no	—
88	C₁₃×#121	—	2	6	no	—
89	C₁₃×#121	—	2	6	no	—
90	C₁₃×#121	C₂³	1	3	yes	—
91	C₁₃×#121	C₂³	1	6	yes	—
92	C₁₃×#120	—	2	12	no	—
93	C₄×Q₈×C₁₃	—	2	1	no	—
94	C₄×Q₈×C₁₃	—	2	3	no	—
95	C₄×Q₈×C₁₃	—	2	3	no	—
96	C₄×Q₈×C₁₃	—	2	3	no	—
97	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
98	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
99	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
100	C₄×D₄×C₁₃	—	2	3	no	—
101	C₄×D₄×C₁₃	—	2	3	no	—
102	C₄×D₄×C₁₃	D₄	1	3	yes	—
103	C₄×D₄×C₁₃	C₂³	1	3	yes	—
104	C₄×D₄×C₁₃	C₂³	1	6	yes	—
105	C₄×D₄×C₁₃	C₂³	1	3	yes	—
106	C₁₃×#117	—	2	3	no	—
107	C₁₃×#117	—	2	3	no	—
108	C₁₃×#117	D₄	1	3	yes	—
109	C₁₃×#117	C₂³	1	6	yes	—
110	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
111	C₁₃×#107	C₂³	1	6	yes	—
112	C₁₃×#106	C₂³	1	6	yes	—
113	C₁₃×C₄⋊C₈	C₂³	1	6	yes	—
114	C₁₃×#103	C₂³	1	2	yes	—
115	C₁₃×#102	C₂³	1	6	yes	—
116	C₁₃×#102	C₂³	1	6	yes	—
117	C₁₃×#102	C₂³	1	12	yes	—
118	C₁₃×#102	C₂³	1	12	yes	—
119	C₁₃×#102	C₂³	1	2	yes	—
120	C₁₃×C₂²⋊C₈	C₂³	1	6	yes	—
121	C₁₃×#97	C₂³	1	1	yes	characteristic
122	C₁₃×#97	C₂³	1	3	yes	—
123	C₄×C₈×C₁₃	C₂³	1	6	yes	—
124	#62588	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
125	C₂⁴×C₁₃	—	2	6	no	—
126	C₁₃×#41	—	2	4	no	—
127	C₁₃×#41	—	4	12	no	—
128	C₁₃×#41	—	4	8	no	—
129	C₂×Q₈×C₁₃	—	2	3	no	—
130	C₂×Q₈×C₁₃	—	2	1	no	—
131	C₂×Q₈×C₁₃	—	2	3	no	—
132	C₂×Q₈×C₁₃	—	4	4	no	—
133	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
134	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
135	C₂×D₄×C₁₃	—	2	6	no	—
136	C₂×D₄×C₁₃	—	2	3	no	—
137	C₂×D₄×C₁₃	—	2	3	no	—
138	C₂×D₄×C₁₃	—	2	6	no	—
139	C₂×D₄×C₁₃	—	2	3	no	—
140	C₂×D₄×C₁₃	—	2	6	no	—
141	C₂×D₄×C₁₃	—	2	6	no	—
142	C₂×D₄×C₁₃	—	4	12	no	—
143	C₂×D₄×C₁₃	—	4	12	no	—
144	C₂×D₄×C₁₃	—	4	24	no	—
145	C₂×D₄×C₁₃	—	8	6	no	—
146	C₂×D₄×C₁₃	C₂×D₄	1	3	yes	—
147	C₂×D₄×C₁₃	C₂⁴	1	6	yes	—
148	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
149	C₂²×C₄×C₁₃	—	2	3	no	—
150	C₂²×C₄×C₁₃	—	2	6	no	—
151	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
152	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
153	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
154	C₁₃×SD₁₆	—	4	6	no	—
155	C₁₃×D₈	—	4	6	no	—
156	C₁₃×M₁₆	—	4	6	no	—
157	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
158	C₂×C₈×C₁₃	C₂⁴	1	6	yes	—
159	C₁₃×C₄⋊C₄	—	2	3	no	—
160	C₁₃×C₄⋊C₄	—	2	3	no	—
161	C₁₃×C₄⋊C₄	—	2	3	no	—
162	C₁₃×C₄⋊C₄	—	2	1	no	—
163	C₁₃×C₄⋊C₄	—	2	3	no	—
164	C₁₃×C₄⋊C₄	—	2	3	no	—
165	C₁₃×C₄⋊C₄	—	2	3	no	—
166	C₁₃×C₄⋊C₄	C₂×D₄	1	3	yes	—
167	C₁₃×C₄⋊C₄	C₂×D₄	1	3	yes	—
168	C₁₃×C₄⋊C₄	C₂⁴	1	3	yes	—
169	C₁₃×C₄⋊C₄	C₂⁴	1	3	yes	—
170	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
171	C₁₃×C₂²⋊C₄	—	2	6	no	—
172	C₁₃×C₂²⋊C₄	—	2	3	no	—
173	C₁₃×C₂²⋊C₄	—	2	3	no	—
174	C₁₃×C₂²⋊C₄	—	2	1	no	—
175	C₁₃×C₂²⋊C₄	—	2	1	no	—
176	C₁₃×C₂²⋊C₄	—	2	6	no	—
177	C₁₃×C₂²⋊C₄	—	2	6	no	—
178	C₁₃×C₂²⋊C₄	—	2	3	no	—
179	C₁₃×C₂²⋊C₄	C₂×D₄	1	6	yes	—
180	C₄²×C₁₃	—	2	6	no	—
181	C₄²×C₁₃	—	2	3	no	—
182	C₄²×C₁₃	C₂×D₄	1	3	yes	—
183	C₄²×C₁₃	C₂×D₄	1	3	yes	—
184	C₄²×C₁₃	C₂⁴	1	3	yes	—
185	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
186	#3518	C₂×C₁₃	1	1	yes	characteristic, complemented
187	#3498	C₂×C₁₃	1	1	yes	characteristic, complemented
188	#3362	C₂×C₁₃	1	2	yes	complemented
189	#3358	C₂×C₁₃	1	2	yes	complemented
190	#3325	C₂×C₁₃	1	6	yes	complemented
191	#3324	C₂×C₁₃	1	6	yes	complemented
192	#3235	C₂×C₁₃	1	3	yes	complemented
193	#3217	C₂×C₁₃	1	3	yes	complemented
194	#3171	C₂×C₁₃	1	3	yes	complemented
195	#3138	C₂×C₁₃	1	3	yes	complemented
196	#2971	C₂×C₁₃	1	1	yes	characteristic, complemented
197	C₂³×C₁₃	—	2	1	no	—
198	C₂³×C₁₃	—	2	6	no	—
199	C₂³×C₁₃	—	4	12	no	—
200	C₂³×C₁₃	—	8	6	no	—
201	C₂³×C₁₃	—	8	6	no	—
202	C₂³×C₁₃	C₂²×D₄	1	3	yes	—
203	Q₈×C₁₃	—	2	2	no	—
204	Q₈×C₁₃	—	4	2	no	—
205	Q₈×C₁₃	—	4	6	no	—
206	Q₈×C₁₃	—	8	3	no	—
207	Q₈×C₁₃	AGL(1,ℤ/8)	1	4	yes	—
208	D₄×C₁₃	—	2	6	no	—
209	D₄×C₁₃	—	2	2	no	—
210	D₄×C₁₃	—	2	6	no	—
211	D₄×C₁₃	—	2	6	no	—
212	D₄×C₁₃	—	4	6	no	—
213	D₄×C₁₃	—	4	6	no	—
214	D₄×C₁₃	—	4	12	no	—
215	D₄×C₁₃	—	4	12	no	—
216	D₄×C₁₃	—	8	6	no	—
217	D₄×C₁₃	—	8	6	no	—
218	D₄×C₁₃	—	8	3	no	—
219	C₂×C₄×C₁₃	—	2	6	no	—
220	C₂×C₄×C₁₃	—	2	6	no	—
221	C₂×C₄×C₁₃	—	2	1	no	—
222	C₂×C₄×C₁₃	—	2	3	no	—
223	C₂×C₄×C₁₃	—	2	3	no	—
224	C₂×C₄×C₁₃	—	2	2	no	—
225	C₂×C₄×C₁₃	—	4	3	no	—
226	C₂×C₄×C₁₃	—	4	12	no	—
227	C₂×C₄×C₁₃	—	4	6	no	—
228	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
229	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
230	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
231	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
232	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
233	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
234	C₈×C₁₃	—	2	2	no	—
235	C₈×C₁₃	—	2	6	no	—
236	C₂×H(5,𝔽₂)	—	2	1	no	—
237	Q₈²	C₂²×C₁₃	1	1	yes	characteristic, complemented
238	#556	—	2	3	no	—
239	#556	C₂²×C₁₃	1	3	yes	complemented
240	#555	C₂²×C₁₃	1	3	yes	complemented
241	#550	—	2	1	no	—
242	#550	C₂²×C₁₃	1	2	yes	—
243	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
244	#548	—	2	1	no	—
245	D₄²	—	2	3	no	—
246	D₄²	C₂²×C₁₃	1	6	yes	—
247	#542	—	2	3	no	—
248	#535	—	2	3	no	—
249	#533	C₂²×C₁₃	1	3	yes	complemented
250	#532	C₂²×C₁₃	1	3	yes	—
251	C₂×#127	C₂²×C₁₃	1	3	yes	—
252	#529	C₂²×C₁₃	1	3	yes	complemented
253	#519	—	2	1	no	—
254	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
255	#501	C₂²×C₁₃	1	3	yes	complemented
256	#496	C₂²×C₁₃	1	3	yes	complemented
257	#490	C₂²×C₁₃	1	3	yes	complemented
258	#490	C₂²×C₁₃	1	6	yes	complemented
259	#489	C₂²×C₁₃	1	1	yes	characteristic, complemented
260	#486	C₂²×C₁₃	1	6	yes	complemented
261	#486	C₂²×C₁₃	1	6	yes	complemented
262	#482	C₂²×C₁₃	1	12	yes	complemented
263	#476	C₂²×C₁₃	1	6	yes	complemented
264	#474	C₂²×C₁₃	1	6	yes	complemented
265	#469	C₂²×C₁₃	1	6	yes	complemented
266	#468	C₂²×C₁₃	1	6	yes	complemented
267	#460	C₂²×C₁₃	1	6	yes	complemented
268	#459	C₂²×C₁₃	1	6	yes	complemented
269	#450	C₂²×C₁₃	1	6	yes	complemented
270	#447	C₂²×C₁₃	1	6	yes	complemented
271	C₈×Q₈	C₂²×C₁₃	1	2	yes	complemented
272	C₄×SD₁₆	C₂²×C₁₃	1	6	yes	complemented
273	C₄×D₈	C₂²×C₁₃	1	6	yes	complemented
274	#436	C₂²×C₁₃	1	6	yes	complemented
275	#432	C₂²×C₁₃	1	3	yes	complemented
276	#418	C₂²×C₁₃	1	12	yes	complemented
277	C₄×M₁₆	C₂²×C₁₃	1	3	yes	complemented
278	C₂²×C₁₃	—	2	3	no	—
279	C₂²×C₁₃	—	2	3	no	—
280	C₂²×C₁₃	—	2	3	no	—
281	C₂²×C₁₃	—	4	6	no	—
282	C₂²×C₁₃	—	4	1	no	—
283	C₂²×C₁₃	—	4	6	no	—
284	C₂²×C₁₃	—	4	1	no	—
285	C₂²×C₁₃	—	4	1	no	—
286	C₂²×C₁₃	—	4	6	no	—
287	C₂²×C₁₃	—	16	12	no	—
288	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
289	C₄×C₁₃	—	2	1	no	—
290	C₄×C₁₃	—	2	3	no	—
291	C₄×C₁₃	—	2	3	no	—
292	C₄×C₁₃	—	2	1	no	—
293	C₄×C₁₃	—	4	3	no	—
294	C₄×C₁₃	—	4	1	no	—
295	C₄×C₁₃	—	4	2	no	—
296	C₄×C₁₃	—	4	3	no	—
297	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	6	yes	—
298	C₄×C₁₃	#585	1	2	yes	—
299	H(5,𝔽₂)	—	4	8	no	—
300	C₂×#41	—	2	2	no	—
301	C₂×#41	—	2	3	no	—
302	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
303	C₂²×Q₈	—	2	1	no	—
304	C₂²×D₄	—	2	6	no	—
305	C₂²×D₄	—	2	3	no	—
306	C₂²×D₄	—	2	3	no	—
307	C₂²×D₄	C₂³×C₁₃	1	6	yes	—
308	C₂×SD₁₆	C₂³×C₁₃	1	6	yes	—
309	C₂×D₈	C₂³×C₁₃	1	6	yes	—
310	C₂×M₁₆	C₂³×C₁₃	1	6	yes	—
311	C₄⋊Q₈	—	2	3	no	—
312	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
313	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
314	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
315	#127	—	2	3	no	—
316	#127	—	2	3	no	—
317	#127	C₂³×C₁₃	1	3	yes	—
318	#127	C₂³×C₁₃	1	6	yes	—
319	#126	—	2	6	no	—
320	#126	—	2	3	no	—
321	#125	C₂³×C₁₃	1	3	yes	—
322	#124	—	2	3	no	—
323	#124	—	2	6	no	—
324	#124	—	2	3	no	—
325	#124	C₂³×C₁₃	1	1	yes	characteristic
326	#123	—	2	3	no	—
327	C₂²⋊Q₈	—	2	3	no	—
328	C₂²⋊Q₈	—	2	3	no	—
329	C₂²⋊Q₈	—	2	3	no	—
330	C₂²⋊Q₈	C₂³×C₁₃	1	3	yes	—
331	#121	—	2	3	no	—
332	#121	—	2	3	no	—
333	#121	—	2	6	no	—
334	#121	—	2	6	no	—
335	#121	C₂³×C₁₃	1	3	yes	—
336	#121	C₂³×C₁₃	1	6	yes	—
337	#120	—	2	12	no	—
338	C₄×Q₈	—	2	1	no	—
339	C₄×Q₈	—	2	3	no	—
340	C₄×Q₈	—	2	3	no	—
341	C₄×Q₈	—	2	3	no	—
342	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
343	C₄×Q₈	C₂³×C₁₃	1	3	yes	—
344	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
345	C₄×D₄	—	2	3	no	—
346	C₄×D₄	—	2	3	no	—
347	C₄×D₄	D₄×C₁₃	1	3	yes	—
348	C₄×D₄	C₂³×C₁₃	1	3	yes	—
349	C₄×D₄	C₂³×C₁₃	1	6	yes	—
350	C₄×D₄	C₂³×C₁₃	1	3	yes	—
351	#117	—	2	3	no	—
352	#117	—	2	3	no	—
353	#117	D₄×C₁₃	1	3	yes	—
354	#117	C₂³×C₁₃	1	6	yes	—
355	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
356	#107	C₂³×C₁₃	1	6	yes	—
357	#106	C₂³×C₁₃	1	6	yes	—
358	C₄⋊C₈	C₂³×C₁₃	1	6	yes	—
359	#103	C₂³×C₁₃	1	2	yes	—
360	#102	C₂³×C₁₃	1	6	yes	—
361	#102	C₂³×C₁₃	1	6	yes	—
362	#102	C₂³×C₁₃	1	12	yes	—
363	#102	C₂³×C₁₃	1	12	yes	—
364	#102	C₂³×C₁₃	1	2	yes	—
365	C₂²⋊C₈	C₂³×C₁₃	1	6	yes	—
366	#97	C₂³×C₁₃	1	1	yes	characteristic
367	#97	C₂³×C₁₃	1	3	yes	—
368	C₄×C₈	C₂³×C₁₃	1	6	yes	—
369	C₂×C₁₃	—	4	3	no	—
370	C₂×C₁₃	—	8	1	no	—
371	C₂×C₁₃	—	8	6	no	—
372	C₂×C₁₃	#3500	1	1	yes	characteristic
373	C₂×C₁₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
374	C₂×C₁₃	#3585	1	1	yes	characteristic
375	C₂⁴	—	2	6	no	—
376	#41	—	2	4	no	—
377	#41	—	4	12	no	—
378	#41	—	4	8	no	—
379	C₂×Q₈	—	2	3	no	—
380	C₂×Q₈	—	2	1	no	—
381	C₂×Q₈	—	2	3	no	—
382	C₂×Q₈	—	4	4	no	—
383	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
384	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
385	C₂×D₄	—	2	6	no	—
386	C₂×D₄	—	2	3	no	—
387	C₂×D₄	—	2	3	no	—
388	C₂×D₄	—	2	6	no	—
389	C₂×D₄	—	2	3	no	—
390	C₂×D₄	—	2	6	no	—
391	C₂×D₄	—	2	6	no	—
392	C₂×D₄	—	4	12	no	—
393	C₂×D₄	—	4	12	no	—
394	C₂×D₄	—	4	24	no	—
395	C₂×D₄	—	8	6	no	—
396	C₂×D₄	C₂×D₄×C₁₃	1	3	yes	—
397	C₂×D₄	C₂⁴×C₁₃	1	6	yes	—
398	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
399	C₂²×C₄	—	2	3	no	—
400	C₂²×C₄	—	2	6	no	—
401	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
402	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
403	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
404	SD₁₆	—	4	6	no	—
405	D₈	—	4	6	no	—
406	M₁₆	—	4	6	no	—
407	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
408	C₂×C₈	C₂⁴×C₁₃	1	6	yes	—
409	C₄⋊C₄	—	2	3	no	—
410	C₄⋊C₄	—	2	3	no	—
411	C₄⋊C₄	—	2	3	no	—
412	C₄⋊C₄	—	2	1	no	—
413	C₄⋊C₄	—	2	3	no	—
414	C₄⋊C₄	—	2	3	no	—
415	C₄⋊C₄	—	2	3	no	—
416	C₄⋊C₄	C₂×D₄×C₁₃	1	3	yes	—
417	C₄⋊C₄	C₂×D₄×C₁₃	1	3	yes	—
418	C₄⋊C₄	C₂⁴×C₁₃	1	3	yes	—
419	C₄⋊C₄	C₂⁴×C₁₃	1	3	yes	—
420	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
421	C₂²⋊C₄	—	2	6	no	—
422	C₂²⋊C₄	—	2	3	no	—
423	C₂²⋊C₄	—	2	3	no	—
424	C₂²⋊C₄	—	2	1	no	—
425	C₂²⋊C₄	—	2	1	no	—
426	C₂²⋊C₄	—	2	6	no	—
427	C₂²⋊C₄	—	2	6	no	—
428	C₂²⋊C₄	—	2	3	no	—
429	C₂²⋊C₄	C₂×D₄×C₁₃	1	6	yes	—
430	C₄²	—	2	6	no	—
431	C₄²	—	2	3	no	—
432	C₄²	C₂×D₄×C₁₃	1	3	yes	—
433	C₄²	C₂×D₄×C₁₃	1	3	yes	—
434	C₄²	C₂⁴×C₁₃	1	3	yes	—
435	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
436	C₁₃	#62588	1	1	yes	characteristic, direct product factor, Sylow
437	C₂³	—	2	1	no	—
438	C₂³	—	2	6	no	—
439	C₂³	—	4	12	no	—
440	C₂³	—	8	6	no	—
441	C₂³	—	8	6	no	—
442	C₂³	C₂²×D₄×C₁₃	1	3	yes	—
443	Q₈	—	2	2	no	—
444	Q₈	—	4	2	no	—
445	Q₈	—	4	6	no	—
446	Q₈	—	8	3	no	—
447	Q₈	C₁₃×AGL(1,ℤ/8)	1	4	yes	—
448	D₄	—	2	6	no	—
449	D₄	—	2	2	no	—
450	D₄	—	2	6	no	—
451	D₄	—	2	6	no	—
452	D₄	—	4	6	no	—
453	D₄	—	4	6	no	—
454	D₄	—	4	12	no	—
455	D₄	—	4	12	no	—
456	D₄	—	8	6	no	—
457	D₄	—	8	6	no	—
458	D₄	—	8	3	no	—
459	C₂×C₄	—	2	6	no	—
460	C₂×C₄	—	2	6	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	3	no	—
463	C₂×C₄	—	2	3	no	—
464	C₂×C₄	—	2	2	no	—
465	C₂×C₄	—	4	3	no	—
466	C₂×C₄	—	4	12	no	—
467	C₂×C₄	—	4	6	no	—
468	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
469	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
470	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
471	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
472	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
473	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
474	C₈	—	2	2	no	—
475	C₈	—	2	6	no	—
476	C₂²	—	2	3	no	—
477	C₂²	—	2	3	no	—
478	C₂²	—	2	3	no	—
479	C₂²	—	4	1	no	—
480	C₂²	—	4	6	no	—
481	C₂²	—	4	6	no	—
482	C₂²	—	4	1	no	—
483	C₂²	—	4	6	no	—
484	C₂²	—	4	1	no	—
485	C₂²	—	16	12	no	—
486	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
487	C₄	—	2	1	no	—
488	C₄	—	2	1	no	—
489	C₄	—	2	3	no	—
490	C₄	—	2	3	no	—
491	C₄	—	4	2	no	—
492	C₄	—	4	3	no	—
493	C₄	—	4	3	no	—
494	C₄	—	4	1	no	—
495	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	6	yes	—
496	C₄	C₁₃×#585	1	2	yes	—
497	C₂	—	4	3	no	—
498	C₂	—	8	6	no	—
499	C₂	—	8	1	no	—
500	C₂	C₁₃×#3500	1	1	yes	characteristic
501	C₂	C₂²×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
502	C₂	C₁₃×#3585	1	1	yes	characteristic

	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 ◁ C₄×C₁₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3518	C₂	semidirect
2. C₁₃×#3498	C₂	semidirect
3. C₁₃×#3362	C₂	semidirect
4. C₁₃×#3358	C₂	semidirect
5. C₁₃×#3325	C₂	semidirect
6. C₁₃×#3324	C₂	semidirect
7. C₁₃×#3235	C₂	semidirect
8. C₁₃×#3217	C₂	semidirect
9. C₁₃×#3171	C₂	semidirect
10. C₁₃×#3138	C₂	semidirect
11. C₁₃×#2971	C₂	semidirect
13. Q₈²×C₁₃	C₂²	semidirect
15. C₁₃×#556	C₂²	semidirect
16. C₁₃×#555	C₂²	semidirect
19. D₄×Q₈×C₁₃	C₂²	semidirect
25. C₁₃×#533	C₂²	semidirect
28. C₁₃×#529	C₂²	semidirect
31. C₁₃×#501	C₂²	semidirect
32. C₁₃×#496	C₂²	semidirect
33. C₁₃×#490	C₂²	semidirect
34. C₁₃×#490	C₂²	semidirect
35. C₁₃×#489	C₂²	semidirect
36. C₁₃×#486	C₂²	semidirect
37. C₁₃×#486	C₂²	semidirect
38. C₁₃×#482	C₂²	semidirect
39. C₁₃×#476	C₂²	semidirect
40. C₁₃×#474	C₂²	semidirect
41. C₁₃×#469	C₂²	semidirect
42. C₁₃×#468	C₂²	semidirect
43. C₁₃×#460	C₂²	semidirect
44. C₁₃×#459	C₂²	semidirect
45. C₁₃×#450	C₂²	semidirect
46. C₁₃×#447	C₂²	semidirect
47. C₈×Q₈×C₁₃	C₂²	semidirect
48. C₄×C₁₃×SD₁₆	C₂²	semidirect
49. C₄×C₁₃×D₈	C₂²	semidirect
50. C₁₃×#436	C₂²	semidirect
51. C₁₃×#432	C₂²	semidirect
52. C₁₃×#418	C₂²	semidirect
53. C₄×C₁₃×M₁₆	C₂²	semidirect
124. #62588	C₁₃	direct (N × H)
186. #3518	C₂×C₁₃	semidirect
187. #3498	C₂×C₁₃	semidirect
188. #3362	C₂×C₁₃	semidirect
189. #3358	C₂×C₁₃	semidirect
190. #3325	C₂×C₁₃	semidirect
191. #3324	C₂×C₁₃	semidirect
192. #3235	C₂×C₁₃	semidirect
193. #3217	C₂×C₁₃	semidirect
194. #3171	C₂×C₁₃	semidirect
195. #3138	C₂×C₁₃	semidirect
196. #2971	C₂×C₁₃	semidirect
237. Q₈²	C₂²×C₁₃	semidirect
239. #556	C₂²×C₁₃	semidirect
240. #555	C₂²×C₁₃	semidirect
243. D₄×Q₈	C₂²×C₁₃	semidirect
249. #533	C₂²×C₁₃	semidirect
252. #529	C₂²×C₁₃	semidirect
255. #501	C₂²×C₁₃	semidirect
256. #496	C₂²×C₁₃	semidirect
257. #490	C₂²×C₁₃	semidirect
258. #490	C₂²×C₁₃	semidirect
259. #489	C₂²×C₁₃	semidirect
260. #486	C₂²×C₁₃	semidirect
261. #486	C₂²×C₁₃	semidirect
262. #482	C₂²×C₁₃	semidirect
263. #476	C₂²×C₁₃	semidirect
264. #474	C₂²×C₁₃	semidirect
265. #469	C₂²×C₁₃	semidirect
266. #468	C₂²×C₁₃	semidirect
267. #460	C₂²×C₁₃	semidirect
268. #459	C₂²×C₁₃	semidirect
269. #450	C₂²×C₁₃	semidirect
270. #447	C₂²×C₁₃	semidirect
271. C₈×Q₈	C₂²×C₁₃	semidirect
272. C₄×SD₁₆	C₂²×C₁₃	semidirect
273. C₄×D₈	C₂²×C₁₃	semidirect
274. #436	C₂²×C₁₃	semidirect
275. #432	C₂²×C₁₃	semidirect
276. #418	C₂²×C₁₃	semidirect
277. C₄×M₁₆	C₂²×C₁₃	semidirect
436. C₁₃	#62588	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×#3518	2
C₁₃×#3498	2
C₁₃×#3362	2
C₁₃×#3358	2
C₁₃×#3325	2
C₁₃×#3324	2
C₁₃×#3235	2
C₁₃×#3217	2
C₁₃×#3171	2
C₁₃×#3138	2
C₁₃×#2971	2
#62588	13

Subgroups — C13×#62588 #15748927

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62588 #15748927