Subgroups — C₁₃×#32950 #15719289

Order 3328.

1282 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3573	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#471	C₂	1	2	yes	maximal, complemented
3	C₁₃×#3057	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3022	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#3021	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#1915	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1914	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1903	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1902	C₂	1	2	yes	maximal, complemented
10	C₁₃×#1814	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1813	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#585	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×#137	C₂²	1	2	yes	—
14	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
15	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic, complemented
16	C₁₃×#568	—	2	4	no	—
17	C₁₃×#568	—	2	2	no	—
18	C₁₃×#568	C₂²	1	2	yes	—
19	C₁₃×#568	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#131	—	2	4	no	—
21	C₂×C₁₃×#131	—	2	2	no	—
22	C₂×C₁₃×#131	C₂²	1	2	yes	—
23	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
24	C₁₃×#536	C₂²	1	1	yes	characteristic
25	C₁₃×#535	C₂²	1	1	yes	characteristic
26	C₁₃×#471	—	2	4	no	—
27	C₁₃×#471	—	2	4	no	—
28	C₁₃×#468	—	2	2	no	—
29	C₁₃×#465	—	2	2	no	—
30	C₁₃×#456	—	2	2	no	—
31	C₁₃×#455	—	2	2	no	—
32	C₁₃×#454	—	2	2	no	—
33	C₁₃×#453	—	2	2	no	—
34	C₂×C₁₃×#108	C₂²	1	2	yes	complemented
35	C₁₃×#427	C₂²	1	1	yes	characteristic, complemented
36	C₁₃×#421	C₂²	1	2	yes	—
37	C₁₃×#421	C₂²	1	2	yes	—
38	C₁₃×#419	C₂²	1	1	yes	characteristic, complemented
39	C₁₃×#418	C₂²	1	1	yes	characteristic, complemented
40	C₁₃×#413	C₂²	1	1	yes	characteristic
41	C₁₃×#413	C₂²	1	1	yes	characteristic
42	C₂×C₁₃×#101	C₂²	1	2	yes	complemented
43	C₂×C₁₃×#100	C₂²	1	2	yes	complemented
44	C₁₃×#344	C₂²	1	2	yes	complemented
45	C₁₃×#344	C₂²	1	2	yes	complemented
46	C₁₃×#338	C₂²	1	2	yes	complemented
47	C₁₃×2₋¹⁺⁴	—	2	2	no	—
48	C₁₃×2₋¹⁺⁴	D₄	1	2	yes	—
49	C₁₃×H(5,𝔽₂)	—	2	2	no	—
50	C₁₃×H(5,𝔽₂)	—	2	2	no	—
51	C₁₃×H(5,𝔽₂)	D₄	1	2	yes	—
52	C₂×C₁₃×#41	—	2	4	no	—
53	C₂×C₁₃×#41	—	2	2	no	—
54	C₂×C₁₃×#41	C₂³	1	2	yes	—
55	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
56	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
57	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
58	C₁₃×#137	—	2	4	no	—
59	C₁₃×#137	—	2	4	no	—
60	C₁₃×AGL(1,ℤ/8)	—	2	4	no	—
61	C₁₃×AGL(1,ℤ/8)	—	2	4	no	—
62	C₂×C₁₃×Q₁₆	—	2	2	no	—
63	C₂×C₁₃×SD₁₆	—	2	2	no	—
64	C₂×C₁₃×SD₁₆	—	2	2	no	—
65	C₂×C₁₃×SD₁₆	—	2	1	no	—
66	C₂×C₁₃×SD₁₆	—	2	1	no	—
67	C₂×C₁₃×SD₁₆	—	2	2	no	—
68	C₂×C₁₃×SD₁₆	—	2	2	no	—
69	C₂×C₁₃×D₈	—	2	2	no	—
70	C₁₃×#131	—	2	4	no	—
71	C₁₃×#131	—	2	8	no	—
72	C₁₃×#131	—	2	4	no	—
73	C₁₃×#131	—	2	4	no	—
74	C₁₃×#131	—	2	4	no	—
75	C₁₃×#131	—	2	2	no	—
76	C₁₃×#131	—	2	2	no	—
77	C₁₃×#131	—	2	4	no	—
78	C₁₃×#131	—	2	2	no	—
79	C₁₃×#131	—	2	2	no	—
80	C₁₃×#131	D₄	1	4	yes	complemented
81	C₁₃×#131	D₄	1	4	yes	complemented
82	C₂×C₁₃×M₁₆	—	2	8	no	—
83	C₂×C₁₃×M₁₆	—	2	4	no	—
84	C₂×C₁₃×M₁₆	—	2	2	no	—
85	C₂×C₁₃×M₁₆	—	2	4	no	—
86	C₂×C₁₃×M₁₆	—	2	2	no	—
87	C₂×C₁₃×M₁₆	D₄	1	2	yes	—
88	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
89	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
90	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
91	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
92	C₂²×C₈×C₁₃	—	2	4	no	—
93	C₂²×C₈×C₁₃	—	2	2	no	—
94	C₂²×C₈×C₁₃	D₄	1	2	yes	—
95	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
96	C₁₃×C₄⋊Q₈	—	2	1	no	—
97	C₁₃×#127	—	2	1	no	—
98	C₁₃×#124	—	2	1	no	—
99	C₁₃×#124	—	2	1	no	—
100	C₁₃×#123	—	2	2	no	—
101	C₁₃×C₂²⋊Q₈	—	2	2	no	—
102	C₁₃×#121	—	2	2	no	—
103	C₁₃×#120	—	2	2	no	—
104	C₁₃×#117	C₂³	1	1	yes	characteristic
105	C₁₃×#117	C₂³	1	1	yes	characteristic
106	C₁₃×#108	—	2	2	no	—
107	C₁₃×#108	—	2	2	no	—
108	C₁₃×#107	—	2	1	no	—
109	C₁₃×#106	—	2	1	no	—
110	C₁₃×#104	—	2	4	no	—
111	C₁₃×#104	—	2	4	no	—
112	C₁₃×#103	—	2	2	no	—
113	C₁₃×#102	—	2	2	no	—
114	C₁₃×#101	—	2	1	no	—
115	C₁₃×#101	—	2	1	no	—
116	C₁₃×#101	—	2	4	no	—
117	C₁₃×#100	—	2	1	no	—
118	C₁₃×#100	—	2	1	no	—
119	C₁₃×#100	—	2	4	no	—
120	#32950	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
121	C₂⁴×C₁₃	—	2	1	no	—
122	C₁₃×#41	—	2	4	no	—
123	C₁₃×#41	—	2	8	no	—
124	C₁₃×#41	—	2	4	no	—
125	C₁₃×#41	—	2	4	no	—
126	C₁₃×#41	—	2	4	no	—
127	C₁₃×#41	—	2	4	no	—
128	C₁₃×#41	—	2	2	no	—
129	C₁₃×#41	—	2	2	no	—
130	C₁₃×#41	—	2	2	no	—
131	C₁₃×#41	—	2	2	no	—
132	C₁₃×#41	C₂×D₄	1	4	yes	—
133	C₁₃×#41	C₂×D₄	1	4	yes	—
134	C₂×Q₈×C₁₃	—	2	2	no	—
135	C₂×Q₈×C₁₃	—	2	4	no	—
136	C₂×Q₈×C₁₃	—	2	2	no	—
137	C₂×Q₈×C₁₃	—	2	1	no	—
138	C₂×Q₈×C₁₃	—	2	1	no	—
139	C₂×Q₈×C₁₃	—	2	2	no	—
140	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
141	C₂×Q₈×C₁₃	#41	1	2	yes	—
142	C₂×D₄×C₁₃	—	2	8	no	—
143	C₂×D₄×C₁₃	—	2	2	no	—
144	C₂×D₄×C₁₃	—	2	4	no	—
145	C₂×D₄×C₁₃	—	2	2	no	—
146	C₂×D₄×C₁₃	—	2	4	no	—
147	C₂×D₄×C₁₃	—	2	2	no	—
148	C₂×D₄×C₁₃	—	2	1	no	—
149	C₂×D₄×C₁₃	—	2	1	no	—
150	C₂×D₄×C₁₃	—	2	2	no	—
151	C₂×D₄×C₁₃	—	4	2	no	—
152	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
153	C₂×D₄×C₁₃	#41	1	2	yes	—
154	C₂×D₄×C₁₃	#41	1	2	yes	—
155	C₂²×C₄×C₁₃	—	2	4	no	—
156	C₂²×C₄×C₁₃	—	2	2	no	—
157	C₂²×C₄×C₁₃	—	2	1	no	—
158	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
159	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
160	C₁₃×Q₁₆	—	4	4	no	—
161	C₁₃×SD₁₆	—	4	4	no	—
162	C₁₃×SD₁₆	—	4	4	no	—
163	C₁₃×SD₁₆	—	4	1	no	—
164	C₁₃×SD₁₆	—	4	1	no	—
165	C₁₃×SD₁₆	—	4	2	no	—
166	C₁₃×D₈	—	4	4	no	—
167	C₁₃×M₁₆	—	2	4	no	—
168	C₁₃×M₁₆	—	2	8	no	—
169	C₁₃×M₁₆	—	2	2	no	—
170	C₁₃×M₁₆	—	2	2	no	—
171	C₁₃×M₁₆	—	2	4	no	—
172	C₁₃×M₁₆	—	2	4	no	—
173	C₁₃×M₁₆	—	2	4	no	—
174	C₁₃×M₁₆	—	2	2	no	—
175	C₁₃×M₁₆	—	2	2	no	—
176	C₁₃×M₁₆	—	2	2	no	—
177	C₁₃×M₁₆	—	2	2	no	—
178	C₁₃×M₁₆	C₂×D₄	1	4	yes	—
179	C₂×C₈×C₁₃	—	2	4	no	—
180	C₂×C₈×C₁₃	—	2	8	no	—
181	C₂×C₈×C₁₃	—	2	2	no	—
182	C₂×C₈×C₁₃	—	2	4	no	—
183	C₂×C₈×C₁₃	—	2	2	no	—
184	C₂×C₈×C₁₃	—	2	4	no	—
185	C₂×C₈×C₁₃	—	2	2	no	—
186	C₂×C₈×C₁₃	—	2	2	no	—
187	C₂×C₈×C₁₃	—	2	2	no	—
188	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
189	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
190	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
191	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
192	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
193	C₁₃×C₄⋊C₄	—	2	1	no	—
194	C₁₃×C₄⋊C₄	—	2	1	no	—
195	C₁₃×C₄⋊C₄	—	4	2	no	—
196	C₁₃×C₂²⋊C₄	—	2	1	no	—
197	C₁₃×C₂²⋊C₄	—	2	1	no	—
198	C₁₃×C₂²⋊C₄	—	4	2	no	—
199	C₁₃×C₂²⋊C₄	—	4	2	no	—
200	C₄²×C₁₃	—	2	1	no	—
201	C₄²×C₁₃	—	2	1	no	—
202	#3573	C₂×C₁₃	1	1	yes	characteristic, complemented
203	C₂×#471	C₂×C₁₃	1	2	yes	complemented
204	#3057	C₂×C₁₃	1	1	yes	characteristic, complemented
205	#3022	C₂×C₁₃	1	1	yes	characteristic, complemented
206	#3021	C₂×C₁₃	1	1	yes	characteristic
207	#1915	C₂×C₁₃	1	1	yes	characteristic, complemented
208	#1914	C₂×C₁₃	1	1	yes	characteristic, complemented
209	#1903	C₂×C₁₃	1	2	yes	complemented
210	#1902	C₂×C₁₃	1	2	yes	complemented
211	#1814	C₂×C₁₃	1	2	yes	complemented
212	#1813	C₂×C₁₃	1	1	yes	characteristic, complemented
213	C₂³×C₁₃	—	2	4	no	—
214	C₂³×C₁₃	—	2	2	no	—
215	C₂³×C₁₃	—	4	1	no	—
216	C₂³×C₁₃	—	4	2	no	—
217	C₂³×C₁₃	—	16	1	no	—
218	C₂³×C₁₃	#121	1	2	yes	—
219	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
220	Q₈×C₁₃	—	2	4	no	—
221	Q₈×C₁₃	—	2	2	no	—
222	Q₈×C₁₃	—	2	2	no	—
223	Q₈×C₁₃	—	4	1	no	—
224	Q₈×C₁₃	—	4	2	no	—
225	Q₈×C₁₃	—	4	1	no	—
226	Q₈×C₁₃	#121	1	4	yes	—
227	D₄×C₁₃	—	2	8	no	—
228	D₄×C₁₃	—	2	4	no	—
229	D₄×C₁₃	—	2	4	no	—
230	D₄×C₁₃	—	2	4	no	—
231	D₄×C₁₃	—	2	4	no	—
232	D₄×C₁₃	—	2	2	no	—
233	D₄×C₁₃	—	2	2	no	—
234	D₄×C₁₃	—	4	1	no	—
235	D₄×C₁₃	—	4	2	no	—
236	D₄×C₁₃	—	4	1	no	—
237	D₄×C₁₃	—	16	2	no	—
238	D₄×C₁₃	#121	1	4	yes	—
239	C₂×C₄×C₁₃	—	2	4	no	—
240	C₂×C₄×C₁₃	—	2	8	no	—
241	C₂×C₄×C₁₃	—	2	2	no	—
242	C₂×C₄×C₁₃	—	2	4	no	—
243	C₂×C₄×C₁₃	—	2	2	no	—
244	C₂×C₄×C₁₃	—	2	4	no	—
245	C₂×C₄×C₁₃	—	2	2	no	—
246	C₂×C₄×C₁₃	—	4	1	no	—
247	C₂×C₄×C₁₃	—	4	1	no	—
248	C₂×C₄×C₁₃	—	4	1	no	—
249	C₂×C₄×C₁₃	—	4	2	no	—
250	C₂×C₄×C₁₃	#121	1	2	yes	—
251	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
252	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
253	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
254	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
255	C₈×C₁₃	—	2	4	no	—
256	C₈×C₁₃	—	2	2	no	—
257	C₈×C₁₃	—	4	2	no	—
258	C₈×C₁₃	—	4	2	no	—
259	C₈×C₁₃	#120	1	1	yes	characteristic
260	C₈×C₁₃	#120	1	2	yes	—
261	C₈×C₁₃	#120	1	1	yes	characteristic
262	#585	C₂²×C₁₃	1	1	yes	characteristic
263	C₂×#137	C₂²×C₁₃	1	2	yes	—
264	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	—
265	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
266	#568	—	2	4	no	—
267	#568	—	2	2	no	—
268	#568	C₂²×C₁₃	1	2	yes	—
269	#568	C₂²×C₁₃	1	1	yes	characteristic
270	C₂×#131	—	2	4	no	—
271	C₂×#131	—	2	2	no	—
272	C₂×#131	C₂²×C₁₃	1	2	yes	—
273	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
274	#536	C₂²×C₁₃	1	1	yes	characteristic
275	#535	C₂²×C₁₃	1	1	yes	characteristic
276	#471	—	2	4	no	—
277	#471	—	2	4	no	—
278	#468	—	2	2	no	—
279	#465	—	2	2	no	—
280	#456	—	2	2	no	—
281	#455	—	2	2	no	—
282	#454	—	2	2	no	—
283	#453	—	2	2	no	—
284	C₂×#108	C₂²×C₁₃	1	2	yes	complemented
285	#427	C₂²×C₁₃	1	1	yes	characteristic, complemented
286	#421	C₂²×C₁₃	1	2	yes	—
287	#421	C₂²×C₁₃	1	2	yes	—
288	#419	C₂²×C₁₃	1	1	yes	characteristic, complemented
289	#418	C₂²×C₁₃	1	1	yes	characteristic, complemented
290	#413	C₂²×C₁₃	1	1	yes	characteristic
291	#413	C₂²×C₁₃	1	1	yes	characteristic
292	C₂×#101	C₂²×C₁₃	1	2	yes	complemented
293	C₂×#100	C₂²×C₁₃	1	2	yes	complemented
294	#344	C₂²×C₁₃	1	2	yes	complemented
295	#344	C₂²×C₁₃	1	2	yes	complemented
296	#338	C₂²×C₁₃	1	2	yes	complemented
297	C₂²×C₁₃	—	2	2	no	—
298	C₂²×C₁₃	—	2	4	no	—
299	C₂²×C₁₃	—	4	1	no	—
300	C₂²×C₁₃	—	4	2	no	—
301	C₂²×C₁₃	—	8	2	no	—
302	C₂²×C₁₃	—	8	2	no	—
303	C₂²×C₁₃	—	8	4	no	—
304	C₂²×C₁₃	—	8	1	no	—
305	C₂²×C₁₃	—	16	2	no	—
306	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
307	C₂²×C₁₃	#525	1	2	yes	—
308	C₄×C₁₃	—	2	4	no	—
309	C₄×C₁₃	—	2	2	no	—
310	C₄×C₁₃	—	8	1	no	—
311	C₄×C₁₃	—	8	1	no	—
312	C₄×C₁₃	—	8	1	no	—
313	C₄×C₁₃	C₂×#120	1	1	yes	characteristic
314	C₄×C₁₃	C₂×#121	1	2	yes	—
315	C₄×C₁₃	#525	1	1	yes	characteristic
316	2₋¹⁺⁴	—	2	2	no	—
317	2₋¹⁺⁴	D₄×C₁₃	1	2	yes	—
318	H(5,𝔽₂)	—	2	2	no	—
319	H(5,𝔽₂)	—	2	2	no	—
320	H(5,𝔽₂)	D₄×C₁₃	1	2	yes	—
321	C₂×#41	—	2	4	no	—
322	C₂×#41	—	2	2	no	—
323	C₂×#41	C₂³×C₁₃	1	2	yes	—
324	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
325	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
326	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
327	#137	—	2	4	no	—
328	#137	—	2	4	no	—
329	AGL(1,ℤ/8)	—	2	4	no	—
330	AGL(1,ℤ/8)	—	2	4	no	—
331	C₂×Q₁₆	—	2	2	no	—
332	C₂×SD₁₆	—	2	2	no	—
333	C₂×SD₁₆	—	2	2	no	—
334	C₂×SD₁₆	—	2	1	no	—
335	C₂×SD₁₆	—	2	1	no	—
336	C₂×SD₁₆	—	2	2	no	—
337	C₂×SD₁₆	—	2	2	no	—
338	C₂×D₈	—	2	2	no	—
339	#131	—	2	4	no	—
340	#131	—	2	8	no	—
341	#131	—	2	4	no	—
342	#131	—	2	4	no	—
343	#131	—	2	4	no	—
344	#131	—	2	2	no	—
345	#131	—	2	2	no	—
346	#131	—	2	4	no	—
347	#131	—	2	2	no	—
348	#131	—	2	2	no	—
349	#131	D₄×C₁₃	1	4	yes	complemented
350	#131	D₄×C₁₃	1	4	yes	complemented
351	C₂×M₁₆	—	2	8	no	—
352	C₂×M₁₆	—	2	4	no	—
353	C₂×M₁₆	—	2	2	no	—
354	C₂×M₁₆	—	2	4	no	—
355	C₂×M₁₆	—	2	2	no	—
356	C₂×M₁₆	D₄×C₁₃	1	2	yes	—
357	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
358	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
359	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
360	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
361	C₂²×C₈	—	2	4	no	—
362	C₂²×C₈	—	2	2	no	—
363	C₂²×C₈	D₄×C₁₃	1	2	yes	—
364	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
365	C₄⋊Q₈	—	2	1	no	—
366	#127	—	2	1	no	—
367	#124	—	2	1	no	—
368	#124	—	2	1	no	—
369	#123	—	2	2	no	—
370	C₂²⋊Q₈	—	2	2	no	—
371	#121	—	2	2	no	—
372	#120	—	2	2	no	—
373	#117	C₂³×C₁₃	1	1	yes	characteristic
374	#117	C₂³×C₁₃	1	1	yes	characteristic
375	#108	—	2	2	no	—
376	#108	—	2	2	no	—
377	#107	—	2	1	no	—
378	#106	—	2	1	no	—
379	#104	—	2	4	no	—
380	#104	—	2	4	no	—
381	#103	—	2	2	no	—
382	#102	—	2	2	no	—
383	#101	—	2	1	no	—
384	#101	—	2	1	no	—
385	#101	—	2	4	no	—
386	#100	—	2	1	no	—
387	#100	—	2	1	no	—
388	#100	—	2	4	no	—
389	C₂×C₁₃	—	2	1	no	—
390	C₂×C₁₃	—	2	2	no	—
391	C₂×C₁₃	—	4	2	no	—
392	C₂×C₁₃	—	4	4	no	—
393	C₂×C₁₃	—	16	1	no	—
394	C₂×C₁₃	#2847	1	1	yes	characteristic
395	C₂⁴	—	2	1	no	—
396	#41	—	2	4	no	—
397	#41	—	2	8	no	—
398	#41	—	2	4	no	—
399	#41	—	2	4	no	—
400	#41	—	2	4	no	—
401	#41	—	2	4	no	—
402	#41	—	2	2	no	—
403	#41	—	2	2	no	—
404	#41	—	2	2	no	—
405	#41	—	2	2	no	—
406	#41	C₂×D₄×C₁₃	1	4	yes	—
407	#41	C₂×D₄×C₁₃	1	4	yes	—
408	C₂×Q₈	—	2	2	no	—
409	C₂×Q₈	—	2	4	no	—
410	C₂×Q₈	—	2	2	no	—
411	C₂×Q₈	—	2	1	no	—
412	C₂×Q₈	—	2	1	no	—
413	C₂×Q₈	—	2	2	no	—
414	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
415	C₂×Q₈	C₁₃×#41	1	2	yes	—
416	C₂×D₄	—	2	8	no	—
417	C₂×D₄	—	2	2	no	—
418	C₂×D₄	—	2	4	no	—
419	C₂×D₄	—	2	2	no	—
420	C₂×D₄	—	2	4	no	—
421	C₂×D₄	—	2	2	no	—
422	C₂×D₄	—	2	1	no	—
423	C₂×D₄	—	2	1	no	—
424	C₂×D₄	—	2	2	no	—
425	C₂×D₄	—	4	2	no	—
426	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
427	C₂×D₄	C₁₃×#41	1	2	yes	—
428	C₂×D₄	C₁₃×#41	1	2	yes	—
429	C₂²×C₄	—	2	4	no	—
430	C₂²×C₄	—	2	2	no	—
431	C₂²×C₄	—	2	1	no	—
432	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
433	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
434	Q₁₆	—	4	4	no	—
435	SD₁₆	—	4	4	no	—
436	SD₁₆	—	4	4	no	—
437	SD₁₆	—	4	1	no	—
438	SD₁₆	—	4	1	no	—
439	SD₁₆	—	4	2	no	—
440	D₈	—	4	4	no	—
441	M₁₆	—	2	4	no	—
442	M₁₆	—	2	8	no	—
443	M₁₆	—	2	2	no	—
444	M₁₆	—	2	2	no	—
445	M₁₆	—	2	4	no	—
446	M₁₆	—	2	4	no	—
447	M₁₆	—	2	4	no	—
448	M₁₆	—	2	2	no	—
449	M₁₆	—	2	2	no	—
450	M₁₆	—	2	2	no	—
451	M₁₆	—	2	2	no	—
452	M₁₆	C₂×D₄×C₁₃	1	4	yes	—
453	C₂×C₈	—	2	4	no	—
454	C₂×C₈	—	2	8	no	—
455	C₂×C₈	—	2	2	no	—
456	C₂×C₈	—	2	4	no	—
457	C₂×C₈	—	2	2	no	—
458	C₂×C₈	—	2	4	no	—
459	C₂×C₈	—	2	2	no	—
460	C₂×C₈	—	2	2	no	—
461	C₂×C₈	—	2	2	no	—
462	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
463	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
464	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
465	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
466	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
467	C₄⋊C₄	—	2	1	no	—
468	C₄⋊C₄	—	2	1	no	—
469	C₄⋊C₄	—	4	2	no	—
470	C₂²⋊C₄	—	2	1	no	—
471	C₂²⋊C₄	—	2	1	no	—
472	C₂²⋊C₄	—	4	2	no	—
473	C₂²⋊C₄	—	4	2	no	—
474	C₄²	—	2	1	no	—
475	C₄²	—	2	1	no	—
476	C₁₃	#32950	1	1	yes	characteristic, direct product factor, Sylow
477	C₂³	—	2	4	no	—
478	C₂³	—	2	2	no	—
479	C₂³	—	4	1	no	—
480	C₂³	—	4	2	no	—
481	C₂³	—	16	1	no	—
482	C₂³	C₁₃×#121	1	2	yes	—
483	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
484	Q₈	—	2	4	no	—
485	Q₈	—	2	2	no	—
486	Q₈	—	2	2	no	—
487	Q₈	—	4	1	no	—
488	Q₈	—	4	2	no	—
489	Q₈	—	4	1	no	—
490	Q₈	C₁₃×#121	1	4	yes	—
491	D₄	—	2	8	no	—
492	D₄	—	2	4	no	—
493	D₄	—	2	4	no	—
494	D₄	—	2	4	no	—
495	D₄	—	2	4	no	—
496	D₄	—	2	2	no	—
497	D₄	—	2	2	no	—
498	D₄	—	4	1	no	—
499	D₄	—	4	2	no	—
500	D₄	—	4	1	no	—
501	D₄	—	16	2	no	—
502	D₄	C₁₃×#121	1	4	yes	—
503	C₂×C₄	—	2	4	no	—
504	C₂×C₄	—	2	8	no	—
505	C₂×C₄	—	2	2	no	—
506	C₂×C₄	—	2	4	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	4	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	4	1	no	—
511	C₂×C₄	—	4	1	no	—
512	C₂×C₄	—	4	1	no	—
513	C₂×C₄	—	4	2	no	—
514	C₂×C₄	C₁₃×#121	1	2	yes	—
515	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
516	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
517	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
518	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
519	C₈	—	2	4	no	—
520	C₈	—	2	2	no	—
521	C₈	—	4	2	no	—
522	C₈	—	4	2	no	—
523	C₈	C₁₃×#120	1	1	yes	characteristic
524	C₈	C₁₃×#120	1	2	yes	—
525	C₈	C₁₃×#120	1	1	yes	characteristic
526	C₂²	—	2	2	no	—
527	C₂²	—	2	4	no	—
528	C₂²	—	4	1	no	—
529	C₂²	—	4	2	no	—
530	C₂²	—	8	2	no	—
531	C₂²	—	8	2	no	—
532	C₂²	—	8	4	no	—
533	C₂²	—	8	1	no	—
534	C₂²	—	16	2	no	—
535	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
536	C₂²	C₁₃×#525	1	2	yes	—
537	C₄	—	2	4	no	—
538	C₄	—	2	2	no	—
539	C₄	—	8	1	no	—
540	C₄	—	8	1	no	—
541	C₄	—	8	1	no	—
542	C₄	C₂×C₁₃×#120	1	1	yes	characteristic
543	C₄	C₂×C₁₃×#121	1	2	yes	—
544	C₄	C₁₃×#525	1	1	yes	characteristic
545	C₂	—	2	1	no	—
546	C₂	—	2	2	no	—
547	C₂	—	4	2	no	—
548	C₂	—	4	4	no	—
549	C₂	—	16	1	no	—
550	C₂	C₁₃×#2847	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₃	#2847
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₁₃×#3021	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×#3573	C₂	semidirect
2. C₂×C₁₃×#471	C₂	semidirect
3. C₁₃×#3057	C₂	semidirect
4. C₁₃×#3022	C₂	semidirect
6. C₁₃×#1915	C₂	semidirect
7. C₁₃×#1914	C₂	semidirect
8. C₁₃×#1903	C₂	semidirect
9. C₁₃×#1902	C₂	semidirect
10. C₁₃×#1814	C₂	semidirect
11. C₁₃×#1813	C₂	semidirect
15. C₂²×C₁₃×SD₁₆	C₂²	semidirect
34. C₂×C₁₃×#108	C₂²	semidirect
35. C₁₃×#427	C₂²	semidirect
38. C₁₃×#419	C₂²	semidirect
39. C₁₃×#418	C₂²	semidirect
42. C₂×C₁₃×#101	C₂²	semidirect
43. C₂×C₁₃×#100	C₂²	semidirect
44. C₁₃×#344	C₂²	semidirect
45. C₁₃×#344	C₂²	semidirect
46. C₁₃×#338	C₂²	semidirect
80. C₁₃×#131	D₄	semidirect
81. C₁₃×#131	D₄	semidirect
120. #32950	C₁₃	direct (N × H)
202. #3573	C₂×C₁₃	semidirect
203. C₂×#471	C₂×C₁₃	semidirect
204. #3057	C₂×C₁₃	semidirect
205. #3022	C₂×C₁₃	semidirect
207. #1915	C₂×C₁₃	semidirect
208. #1914	C₂×C₁₃	semidirect
209. #1903	C₂×C₁₃	semidirect
210. #1902	C₂×C₁₃	semidirect
211. #1814	C₂×C₁₃	semidirect
212. #1813	C₂×C₁₃	semidirect
265. C₂²×SD₁₆	C₂²×C₁₃	semidirect
284. C₂×#108	C₂²×C₁₃	semidirect
285. #427	C₂²×C₁₃	semidirect
288. #419	C₂²×C₁₃	semidirect
289. #418	C₂²×C₁₃	semidirect
292. C₂×#101	C₂²×C₁₃	semidirect
293. C₂×#100	C₂²×C₁₃	semidirect
294. #344	C₂²×C₁₃	semidirect
295. #344	C₂²×C₁₃	semidirect
296. #338	C₂²×C₁₃	semidirect
349. #131	D₄×C₁₃	semidirect
350. #131	D₄×C₁₃	semidirect
476. C₁₃	#32950	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×#3573	2
C₂×C₁₃×#471	2
C₁₃×#3057	2
C₁₃×#3022	2
C₁₃×#3021	2
C₁₃×#1915	2
C₁₃×#1914	2
C₁₃×#1903	2
C₁₃×#1902	2
C₁₃×#1814	2
C₁₃×#1813	2
#32950	13

Subgroups — C13×#32950 #15719289

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#32950 #15719289