Subgroups — C₁₃×#33526 #15719865

Order 3328.

1150 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#576	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#509	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#508	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3061	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2189	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2187	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2186	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2184	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2139	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×#357	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2113	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×H(5,𝔽₂)	—	2	1	no	—
13	C₁₃×#576	—	2	4	no	—
14	C₁₃×#576	—	2	4	no	—
15	C₂×C₁₃×AGL(1,ℤ/8)	—	2	1	no	—
16	C₂×C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
17	C₂×C₁₃×#135	C₂²	1	2	yes	—
18	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic, complemented
20	C₂²×C₁₃×D₈	C₂²	1	2	yes	—
21	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
23	C₁₃×#537	—	2	1	no	—
24	C₁₃×#509	—	2	4	no	—
25	C₁₃×#508	—	2	4	no	—
26	C₂×C₁₃×Q₃₂	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₁₃×SD₃₂	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₁₃×SD₃₂	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₁₃×SD₃₂	C₂²	1	2	yes	complemented
30	C₂×C₁₃×D₁₆	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₁₃×D₁₆	C₂²	1	2	yes	complemented
32	C₂×C₁₃×M₃₂	C₂²	1	1	yes	characteristic, complemented
33	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic, complemented
34	C₁₃×#468	—	2	2	no	—
35	C₁₃×#467	C₂²	1	2	yes	complemented
36	C₁₃×#466	C₂²	1	2	yes	complemented
37	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic, complemented
38	C₁₃×#417	—	2	1	no	—
39	C₁₃×#358	C₂²	1	2	yes	complemented
40	C₁₃×#357	C₂²	1	2	yes	complemented
41	C₁₃×#357	C₂²	1	2	yes	complemented
42	C₁₃×#357	C₂²	1	2	yes	complemented
43	C₁₃×C₂²⋊C₁₆	C₂²	1	2	yes	complemented
44	C₁₃×C₂²⋊C₁₆	C₂²	1	2	yes	complemented
45	C₁₃×H(5,𝔽₂)	—	2	8	no	—
46	C₁₃×H(5,𝔽₂)	—	4	4	no	—
47	C₂×C₁₃×#41	—	2	2	no	—
48	C₂×C₁₃×#41	—	2	1	no	—
49	C₂×C₁₃×#41	—	2	1	no	—
50	C₂×C₁₃×#41	—	4	1	no	—
51	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
52	C₂²×D₄×C₁₃	—	2	2	no	—
53	C₂²×D₄×C₁₃	—	2	1	no	—
54	C₂²×D₄×C₁₃	—	4	2	no	—
55	C₂²×D₄×C₁₃	—	4	1	no	—
56	C₁₃×AGL(1,ℤ/8)	—	2	8	no	—
57	C₁₃×AGL(1,ℤ/8)	—	2	16	no	—
58	C₁₃×#135	—	2	4	no	—
59	C₁₃×#135	—	2	4	no	—
60	C₁₃×#135	—	2	2	no	—
61	C₁₃×#135	—	2	2	no	—
62	C₁₃×#135	—	2	2	no	—
63	C₁₃×#135	D₄	1	4	yes	complemented
64	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
65	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
66	C₂×C₁₃×SD₁₆	—	2	2	no	—
67	C₂×C₁₃×SD₁₆	—	2	1	no	—
68	C₂×C₁₃×SD₁₆	—	2	1	no	—
69	C₂×C₁₃×D₈	—	2	4	no	—
70	C₂×C₁₃×D₈	—	2	4	no	—
71	C₂×C₁₃×D₈	—	2	2	no	—
72	C₂×C₁₃×D₈	—	2	1	no	—
73	C₂×C₁₃×D₈	—	2	2	no	—
74	C₂×C₁₃×D₈	D₄	1	4	yes	complemented
75	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
76	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
77	C₂×C₁₃×D₈	C₂³	1	2	yes	—
78	C₁₃×#131	—	2	2	no	—
79	C₁₃×#131	—	2	2	no	—
80	C₂×C₁₃×M₁₆	D₄	1	1	yes	characteristic
81	C₂×C₁₃×M₁₆	D₄	1	2	yes	—
82	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
83	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
84	C₁₃×C₂²⋊Q₈	—	2	2	no	—
85	C₁₃×C₂²⋊Q₈	—	4	1	no	—
86	C₁₃×#121	—	2	2	no	—
87	C₁₃×#121	—	4	1	no	—
88	C₁₃×#121	—	4	2	no	—
89	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
90	C₁₃×Q₃₂	—	2	2	no	—
91	C₁₃×SD₃₂	—	2	2	no	—
92	C₁₃×SD₃₂	—	2	2	no	—
93	C₁₃×SD₃₂	—	2	4	no	—
94	C₁₃×D₁₆	—	2	2	no	—
95	C₁₃×D₁₆	—	2	4	no	—
96	C₁₃×M₃₂	—	2	2	no	—
97	C₂×C₁₃×C₁₆	—	2	2	no	—
98	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
99	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
100	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
101	C₁₃×#107	—	2	1	no	—
102	C₁₃×#107	C₂³	1	2	yes	—
103	C₁₃×#103	—	2	2	no	—
104	C₁₃×#102	—	2	2	no	—
105	#33526	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
106	C₂⁴×C₁₃	—	4	2	no	—
107	C₂⁴×C₁₃	—	4	1	no	—
108	C₁₃×#41	—	2	2	no	—
109	C₁₃×#41	—	2	2	no	—
110	C₁₃×#41	—	2	8	no	—
111	C₁₃×#41	—	2	4	no	—
112	C₁₃×#41	—	4	4	no	—
113	C₁₃×#41	—	4	8	no	—
114	C₁₃×#41	—	4	2	no	—
115	C₁₃×#41	—	4	2	no	—
116	C₁₃×#41	—	4	2	no	—
117	C₂×Q₈×C₁₃	—	2	1	no	—
118	C₂×Q₈×C₁₃	—	2	1	no	—
119	C₂×Q₈×C₁₃	D₈	1	1	yes	characteristic
120	C₂×D₄×C₁₃	—	2	8	no	—
121	C₂×D₄×C₁₃	—	2	4	no	—
122	C₂×D₄×C₁₃	—	2	1	no	—
123	C₂×D₄×C₁₃	—	2	2	no	—
124	C₂×D₄×C₁₃	—	2	1	no	—
125	C₂×D₄×C₁₃	—	4	4	no	—
126	C₂×D₄×C₁₃	—	4	16	no	—
127	C₂×D₄×C₁₃	—	4	8	no	—
128	C₂×D₄×C₁₃	—	4	2	no	—
129	C₂×D₄×C₁₃	—	4	1	no	—
130	C₂×D₄×C₁₃	—	4	1	no	—
131	C₂×D₄×C₁₃	—	4	2	no	—
132	C₂×D₄×C₁₃	—	4	2	no	—
133	C₂×D₄×C₁₃	—	4	1	no	—
134	C₂×D₄×C₁₃	—	4	2	no	—
135	C₂×D₄×C₁₃	D₈	1	2	yes	—
136	C₂×D₄×C₁₃	D₈	1	1	yes	characteristic
137	C₂²×C₄×C₁₃	—	4	2	no	—
138	C₂²×C₄×C₁₃	—	4	1	no	—
139	C₂²×C₄×C₁₃	—	4	1	no	—
140	C₂²×C₄×C₁₃	—	4	1	no	—
141	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
142	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
143	C₁₃×Q₁₆	—	2	1	no	—
144	C₁₃×Q₁₆	—	2	1	no	—
145	C₁₃×Q₁₆	—	2	1	no	—
146	C₁₃×Q₁₆	C₂×D₄	1	2	yes	—
147	C₁₃×SD₁₆	—	2	8	no	—
148	C₁₃×SD₁₆	—	2	4	no	—
149	C₁₃×SD₁₆	—	4	2	no	—
150	C₁₃×D₈	—	2	8	no	—
151	C₁₃×D₈	—	2	4	no	—
152	C₁₃×D₈	—	2	2	no	—
153	C₁₃×D₈	—	2	1	no	—
154	C₁₃×D₈	—	2	1	no	—
155	C₁₃×D₈	—	2	1	no	—
156	C₁₃×D₈	C₂×D₄	1	2	yes	—
157	C₁₃×D₈	C₂×D₄	1	4	yes	—
158	C₁₃×M₁₆	—	2	2	no	—
159	C₁₃×M₁₆	—	2	4	no	—
160	C₂×C₈×C₁₃	—	2	2	no	—
161	C₂×C₈×C₁₃	—	2	2	no	—
162	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
163	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
164	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
165	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
166	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
167	C₁₃×C₄⋊C₄	—	2	2	no	—
168	C₁₃×C₄⋊C₄	—	4	1	no	—
169	C₁₃×C₄⋊C₄	—	4	2	no	—
170	C₁₃×C₂²⋊C₄	—	4	2	no	—
171	C₁₃×C₂²⋊C₄	—	4	2	no	—
172	C₁₃×C₁₆	—	2	1	no	—
173	C₁₃×C₁₆	—	2	1	no	—
174	C₁₃×C₁₆	—	2	2	no	—
175	C₂×#576	C₂×C₁₃	1	1	yes	characteristic, complemented
176	C₂×#509	C₂×C₁₃	1	1	yes	characteristic, complemented
177	C₂×#508	C₂×C₁₃	1	1	yes	characteristic, complemented
178	#3061	C₂×C₁₃	1	1	yes	characteristic, complemented
179	#2189	C₂×C₁₃	1	2	yes	complemented
180	#2187	C₂×C₁₃	1	2	yes	complemented
181	#2186	C₂×C₁₃	1	2	yes	complemented
182	#2184	C₂×C₁₃	1	2	yes	complemented
183	#2139	C₂×C₁₃	1	1	yes	characteristic, complemented
184	C₂×#357	C₂×C₁₃	1	1	yes	characteristic, complemented
185	#2113	C₂×C₁₃	1	1	yes	characteristic, complemented
186	C₂³×C₁₃	—	4	8	no	—
187	C₂³×C₁₃	—	4	2	no	—
188	C₂³×C₁₃	—	4	1	no	—
189	C₂³×C₁₃	—	4	4	no	—
190	C₂³×C₁₃	—	4	1	no	—
191	C₂³×C₁₃	—	16	1	no	—
192	C₂³×C₁₃	—	16	1	no	—
193	C₂³×C₁₃	—	16	2	no	—
194	C₂³×C₁₃	—	16	2	no	—
195	C₂³×C₁₃	C₂×D₈	1	2	yes	—
196	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
197	Q₈×C₁₃	—	2	2	no	—
198	Q₈×C₁₃	—	2	2	no	—
199	Q₈×C₁₃	—	4	1	no	—
200	Q₈×C₁₃	—	4	1	no	—
201	Q₈×C₁₃	—	4	1	no	—
202	D₄×C₁₃	—	2	4	no	—
203	D₄×C₁₃	—	2	2	no	—
204	D₄×C₁₃	—	2	4	no	—
205	D₄×C₁₃	—	2	2	no	—
206	D₄×C₁₃	—	4	8	no	—
207	D₄×C₁₃	—	4	8	no	—
208	D₄×C₁₃	—	4	4	no	—
209	D₄×C₁₃	—	4	1	no	—
210	D₄×C₁₃	—	4	1	no	—
211	D₄×C₁₃	—	4	2	no	—
212	D₄×C₁₃	—	4	1	no	—
213	D₄×C₁₃	—	4	4	no	—
214	D₄×C₁₃	—	8	2	no	—
215	D₄×C₁₃	—	16	2	no	—
216	C₂×C₄×C₁₃	—	2	2	no	—
217	C₂×C₄×C₁₃	—	2	2	no	—
218	C₂×C₄×C₁₃	—	4	8	no	—
219	C₂×C₄×C₁₃	—	4	1	no	—
220	C₂×C₄×C₁₃	—	4	4	no	—
221	C₂×C₄×C₁₃	—	4	2	no	—
222	C₂×C₄×C₁₃	—	4	1	no	—
223	C₂×C₄×C₁₃	—	8	2	no	—
224	C₂×C₄×C₁₃	—	16	1	no	—
225	C₂×C₄×C₁₃	#120	1	2	yes	—
226	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
227	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
228	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
229	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
230	C₈×C₁₃	—	2	2	no	—
231	C₈×C₁₃	#120	1	2	yes	—
232	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
233	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
234	C₂×H(5,𝔽₂)	—	2	1	no	—
235	#576	—	2	4	no	—
236	#576	—	2	4	no	—
237	C₂×AGL(1,ℤ/8)	—	2	1	no	—
238	C₂×AGL(1,ℤ/8)	—	2	2	no	—
239	C₂×#135	C₂²×C₁₃	1	2	yes	—
240	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
241	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic, complemented
242	C₂²×D₈	C₂²×C₁₃	1	2	yes	—
243	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
244	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
245	#537	—	2	1	no	—
246	#509	—	2	4	no	—
247	#508	—	2	4	no	—
248	C₂×Q₃₂	C₂²×C₁₃	1	1	yes	characteristic, complemented
249	C₂×SD₃₂	C₂²×C₁₃	1	1	yes	characteristic, complemented
250	C₂×SD₃₂	C₂²×C₁₃	1	1	yes	characteristic, complemented
251	C₂×SD₃₂	C₂²×C₁₃	1	2	yes	complemented
252	C₂×D₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
253	C₂×D₁₆	C₂²×C₁₃	1	2	yes	complemented
254	C₂×M₃₂	C₂²×C₁₃	1	1	yes	characteristic, complemented
255	C₂²×C₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
256	#468	—	2	2	no	—
257	#467	C₂²×C₁₃	1	2	yes	complemented
258	#466	C₂²×C₁₃	1	2	yes	complemented
259	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic, complemented
260	#417	—	2	1	no	—
261	#358	C₂²×C₁₃	1	2	yes	complemented
262	#357	C₂²×C₁₃	1	2	yes	complemented
263	#357	C₂²×C₁₃	1	2	yes	complemented
264	#357	C₂²×C₁₃	1	2	yes	complemented
265	C₂²⋊C₁₆	C₂²×C₁₃	1	2	yes	complemented
266	C₂²⋊C₁₆	C₂²×C₁₃	1	2	yes	complemented
267	C₂²×C₁₃	—	2	1	no	—
268	C₂²×C₁₃	—	2	1	no	—
269	C₂²×C₁₃	—	2	2	no	—
270	C₂²×C₁₃	—	2	2	no	—
271	C₂²×C₁₃	—	2	2	no	—
272	C₂²×C₁₃	—	4	4	no	—
273	C₂²×C₁₃	—	4	2	no	—
274	C₂²×C₁₃	—	8	2	no	—
275	C₂²×C₁₃	—	8	1	no	—
276	C₂²×C₁₃	—	8	2	no	—
277	C₂²×C₁₃	—	8	1	no	—
278	C₂²×C₁₃	—	8	1	no	—
279	C₂²×C₁₃	—	8	1	no	—
280	C₂²×C₁₃	—	8	1	no	—
281	C₂²×C₁₃	—	16	4	no	—
282	C₂²×C₁₃	—	16	8	no	—
283	C₂²×C₁₃	#447	1	2	yes	—
284	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
285	C₄×C₁₃	—	2	2	no	—
286	C₄×C₁₃	—	4	2	no	—
287	C₄×C₁₃	—	8	2	no	—
288	C₄×C₁₃	—	8	1	no	—
289	C₄×C₁₃	#447	1	2	yes	—
290	C₄×C₁₃	C₂×#120	1	1	yes	characteristic
291	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
292	H(5,𝔽₂)	—	2	8	no	—
293	H(5,𝔽₂)	—	4	4	no	—
294	C₂×#41	—	2	2	no	—
295	C₂×#41	—	2	1	no	—
296	C₂×#41	—	2	1	no	—
297	C₂×#41	—	4	1	no	—
298	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
299	C₂²×D₄	—	2	2	no	—
300	C₂²×D₄	—	2	1	no	—
301	C₂²×D₄	—	4	2	no	—
302	C₂²×D₄	—	4	1	no	—
303	AGL(1,ℤ/8)	—	2	8	no	—
304	AGL(1,ℤ/8)	—	2	16	no	—
305	#135	—	2	4	no	—
306	#135	—	2	4	no	—
307	#135	—	2	2	no	—
308	#135	—	2	2	no	—
309	#135	—	2	2	no	—
310	#135	D₄×C₁₃	1	4	yes	complemented
311	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
312	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
313	C₂×SD₁₆	—	2	2	no	—
314	C₂×SD₁₆	—	2	1	no	—
315	C₂×SD₁₆	—	2	1	no	—
316	C₂×D₈	—	2	4	no	—
317	C₂×D₈	—	2	4	no	—
318	C₂×D₈	—	2	2	no	—
319	C₂×D₈	—	2	1	no	—
320	C₂×D₈	—	2	2	no	—
321	C₂×D₈	D₄×C₁₃	1	4	yes	complemented
322	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
323	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
324	C₂×D₈	C₂³×C₁₃	1	2	yes	—
325	#131	—	2	2	no	—
326	#131	—	2	2	no	—
327	C₂×M₁₆	D₄×C₁₃	1	1	yes	characteristic
328	C₂×M₁₆	D₄×C₁₃	1	2	yes	—
329	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
330	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
331	C₂²⋊Q₈	—	2	2	no	—
332	C₂²⋊Q₈	—	4	1	no	—
333	#121	—	2	2	no	—
334	#121	—	4	1	no	—
335	#121	—	4	2	no	—
336	C₂×C₄⋊C₄	—	2	1	no	—
337	Q₃₂	—	2	2	no	—
338	SD₃₂	—	2	2	no	—
339	SD₃₂	—	2	2	no	—
340	SD₃₂	—	2	4	no	—
341	D₁₆	—	2	2	no	—
342	D₁₆	—	2	4	no	—
343	M₃₂	—	2	2	no	—
344	C₂×C₁₆	—	2	2	no	—
345	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
346	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
347	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
348	#107	—	2	1	no	—
349	#107	C₂³×C₁₃	1	2	yes	—
350	#103	—	2	2	no	—
351	#102	—	2	2	no	—
352	C₂×C₁₃	—	2	2	no	—
353	C₂×C₁₃	—	4	2	no	—
354	C₂×C₁₃	—	8	4	no	—
355	C₂×C₁₃	—	8	2	no	—
356	C₂×C₁₃	—	16	1	no	—
357	C₂×C₁₃	C₂×#447	1	1	yes	characteristic
358	C₂×C₁₃	#3415	1	1	yes	characteristic
359	C₂×C₁₃	#3416	1	1	yes	characteristic
360	C₂⁴	—	4	2	no	—
361	C₂⁴	—	4	1	no	—
362	#41	—	2	2	no	—
363	#41	—	2	2	no	—
364	#41	—	2	8	no	—
365	#41	—	2	4	no	—
366	#41	—	4	4	no	—
367	#41	—	4	8	no	—
368	#41	—	4	2	no	—
369	#41	—	4	2	no	—
370	#41	—	4	2	no	—
371	C₂×Q₈	—	2	1	no	—
372	C₂×Q₈	—	2	1	no	—
373	C₂×Q₈	C₁₃×D₈	1	1	yes	characteristic
374	C₂×D₄	—	2	8	no	—
375	C₂×D₄	—	2	4	no	—
376	C₂×D₄	—	2	1	no	—
377	C₂×D₄	—	2	2	no	—
378	C₂×D₄	—	2	1	no	—
379	C₂×D₄	—	4	4	no	—
380	C₂×D₄	—	4	16	no	—
381	C₂×D₄	—	4	8	no	—
382	C₂×D₄	—	4	2	no	—
383	C₂×D₄	—	4	1	no	—
384	C₂×D₄	—	4	1	no	—
385	C₂×D₄	—	4	2	no	—
386	C₂×D₄	—	4	2	no	—
387	C₂×D₄	—	4	1	no	—
388	C₂×D₄	—	4	2	no	—
389	C₂×D₄	C₁₃×D₈	1	2	yes	—
390	C₂×D₄	C₁₃×D₈	1	1	yes	characteristic
391	C₂²×C₄	—	4	2	no	—
392	C₂²×C₄	—	4	1	no	—
393	C₂²×C₄	—	4	1	no	—
394	C₂²×C₄	—	4	1	no	—
395	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
396	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
397	Q₁₆	—	2	1	no	—
398	Q₁₆	—	2	1	no	—
399	Q₁₆	—	2	1	no	—
400	Q₁₆	C₂×D₄×C₁₃	1	2	yes	—
401	SD₁₆	—	2	8	no	—
402	SD₁₆	—	2	4	no	—
403	SD₁₆	—	4	2	no	—
404	D₈	—	2	8	no	—
405	D₈	—	2	4	no	—
406	D₈	—	2	2	no	—
407	D₈	—	2	1	no	—
408	D₈	—	2	1	no	—
409	D₈	—	2	1	no	—
410	D₈	C₂×D₄×C₁₃	1	2	yes	—
411	D₈	C₂×D₄×C₁₃	1	4	yes	—
412	M₁₆	—	2	2	no	—
413	M₁₆	—	2	4	no	—
414	C₂×C₈	—	2	2	no	—
415	C₂×C₈	—	2	2	no	—
416	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
417	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
418	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
419	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
420	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
421	C₄⋊C₄	—	2	2	no	—
422	C₄⋊C₄	—	4	1	no	—
423	C₄⋊C₄	—	4	2	no	—
424	C₂²⋊C₄	—	4	2	no	—
425	C₂²⋊C₄	—	4	2	no	—
426	C₁₆	—	2	1	no	—
427	C₁₆	—	2	1	no	—
428	C₁₆	—	2	2	no	—
429	C₁₃	#33526	1	1	yes	characteristic, direct product factor, Sylow
430	C₂³	—	4	8	no	—
431	C₂³	—	4	2	no	—
432	C₂³	—	4	1	no	—
433	C₂³	—	4	4	no	—
434	C₂³	—	4	1	no	—
435	C₂³	—	16	1	no	—
436	C₂³	—	16	1	no	—
437	C₂³	—	16	2	no	—
438	C₂³	—	16	2	no	—
439	C₂³	C₂×C₁₃×D₈	1	2	yes	—
440	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
441	Q₈	—	2	2	no	—
442	Q₈	—	2	2	no	—
443	Q₈	—	4	1	no	—
444	Q₈	—	4	1	no	—
445	Q₈	—	4	1	no	—
446	D₄	—	2	4	no	—
447	D₄	—	2	2	no	—
448	D₄	—	2	2	no	—
449	D₄	—	2	4	no	—
450	D₄	—	4	8	no	—
451	D₄	—	4	8	no	—
452	D₄	—	4	4	no	—
453	D₄	—	4	4	no	—
454	D₄	—	4	1	no	—
455	D₄	—	4	1	no	—
456	D₄	—	4	2	no	—
457	D₄	—	4	1	no	—
458	D₄	—	8	2	no	—
459	D₄	—	16	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	4	8	no	—
463	C₂×C₄	—	4	1	no	—
464	C₂×C₄	—	4	4	no	—
465	C₂×C₄	—	4	2	no	—
466	C₂×C₄	—	4	1	no	—
467	C₂×C₄	—	8	2	no	—
468	C₂×C₄	—	16	1	no	—
469	C₂×C₄	C₁₃×#120	1	2	yes	—
470	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
471	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
472	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
473	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
474	C₈	—	2	2	no	—
475	C₈	C₁₃×#120	1	2	yes	—
476	C₈	C₂²×D₄×C₁₃	1	1	yes	characteristic
477	C₈	C₂²×D₄×C₁₃	1	1	yes	characteristic
478	C₂²	—	2	1	no	—
479	C₂²	—	2	1	no	—
480	C₂²	—	2	2	no	—
481	C₂²	—	2	2	no	—
482	C₂²	—	2	2	no	—
483	C₂²	—	4	4	no	—
484	C₂²	—	4	2	no	—
485	C₂²	—	8	2	no	—
486	C₂²	—	8	1	no	—
487	C₂²	—	8	2	no	—
488	C₂²	—	8	1	no	—
489	C₂²	—	8	1	no	—
490	C₂²	—	8	1	no	—
491	C₂²	—	8	1	no	—
492	C₂²	—	16	4	no	—
493	C₂²	—	16	8	no	—
494	C₂²	C₁₃×#447	1	2	yes	—
495	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
496	C₄	—	2	2	no	—
497	C₄	—	4	2	no	—
498	C₄	—	8	2	no	—
499	C₄	—	8	1	no	—
500	C₄	C₁₃×#447	1	2	yes	—
501	C₄	C₂×C₁₃×#120	1	1	yes	characteristic
502	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
503	C₂	—	2	2	no	—
504	C₂	—	4	2	no	—
505	C₂	—	8	4	no	—
506	C₂	—	8	2	no	—
507	C₂	—	16	1	no	—
508	C₂	C₂×C₁₃×#447	1	1	yes	characteristic
509	C₂	C₁₃×#3415	1	1	yes	characteristic
510	C₂	C₁₃×#3416	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₁₃×#41 ◁ C₂×C₁₃×#131 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#576	C₂	semidirect
2. C₂×C₁₃×#509	C₂	semidirect
3. C₂×C₁₃×#508	C₂	semidirect
4. C₁₃×#3061	C₂	semidirect
5. C₁₃×#2189	C₂	semidirect
6. C₁₃×#2187	C₂	semidirect
7. C₁₃×#2186	C₂	semidirect
8. C₁₃×#2184	C₂	semidirect
9. C₁₃×#2139	C₂	semidirect
10. C₂×C₁₃×#357	C₂	semidirect
11. C₁₃×#2113	C₂	semidirect
19. C₂×C₁₃×#135	C₂²	semidirect
26. C₂×C₁₃×Q₃₂	C₂²	semidirect
27. C₂×C₁₃×SD₃₂	C₂²	semidirect
28. C₂×C₁₃×SD₃₂	C₂²	semidirect
29. C₂×C₁₃×SD₃₂	C₂²	semidirect
30. C₂×C₁₃×D₁₆	C₂²	semidirect
31. C₂×C₁₃×D₁₆	C₂²	semidirect
32. C₂×C₁₃×M₃₂	C₂²	semidirect
33. C₂²×C₁₃×C₁₆	C₂²	semidirect
35. C₁₃×#467	C₂²	semidirect
36. C₁₃×#466	C₂²	semidirect
37. C₂×C₁₃×#107	C₂²	semidirect
39. C₁₃×#358	C₂²	semidirect
40. C₁₃×#357	C₂²	semidirect
41. C₁₃×#357	C₂²	semidirect
42. C₁₃×#357	C₂²	semidirect
43. C₁₃×C₂²⋊C₁₆	C₂²	semidirect
44. C₁₃×C₂²⋊C₁₆	C₂²	semidirect
63. C₁₃×#135	D₄	semidirect
74. C₂×C₁₃×D₈	D₄	semidirect
105. #33526	C₁₃	direct (N × H)
175. C₂×#576	C₂×C₁₃	semidirect
176. C₂×#509	C₂×C₁₃	semidirect
177. C₂×#508	C₂×C₁₃	semidirect
178. #3061	C₂×C₁₃	semidirect
179. #2189	C₂×C₁₃	semidirect
180. #2187	C₂×C₁₃	semidirect
181. #2186	C₂×C₁₃	semidirect
182. #2184	C₂×C₁₃	semidirect
183. #2139	C₂×C₁₃	semidirect
184. C₂×#357	C₂×C₁₃	semidirect
185. #2113	C₂×C₁₃	semidirect
241. C₂×#135	C₂²×C₁₃	semidirect
248. C₂×Q₃₂	C₂²×C₁₃	semidirect
249. C₂×SD₃₂	C₂²×C₁₃	semidirect
250. C₂×SD₃₂	C₂²×C₁₃	semidirect
251. C₂×SD₃₂	C₂²×C₁₃	semidirect
252. C₂×D₁₆	C₂²×C₁₃	semidirect
253. C₂×D₁₆	C₂²×C₁₃	semidirect
254. C₂×M₃₂	C₂²×C₁₃	semidirect
255. C₂²×C₁₆	C₂²×C₁₃	semidirect
257. #467	C₂²×C₁₃	semidirect
258. #466	C₂²×C₁₃	semidirect
259. C₂×#107	C₂²×C₁₃	semidirect
261. #358	C₂²×C₁₃	semidirect
262. #357	C₂²×C₁₃	semidirect
263. #357	C₂²×C₁₃	semidirect
264. #357	C₂²×C₁₃	semidirect
265. C₂²⋊C₁₆	C₂²×C₁₃	semidirect
266. C₂²⋊C₁₆	C₂²×C₁₃	semidirect
310. #135	D₄×C₁₃	semidirect
321. C₂×D₈	D₄×C₁₃	semidirect
429. C₁₃	#33526	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₁₃×#576	2
C₂×C₁₃×#509	2
C₂×C₁₃×#508	2
C₁₃×#3061	2
C₁₃×#2189	2
C₁₃×#2187	2
C₁₃×#2186	2
C₁₃×#2184	2
C₁₃×#2139	2
C₂×C₁₃×#357	2
C₁₃×#2113	2
#33526	13

Subgroups — C13×#33526 #15719865

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#33526 #15719865