Subgroups — C₂×C₁₃×#1551 #15704048

Order 3328.

1310 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#532	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#432	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₁₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1551	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₁₃×#333	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#331	C₂	1	2	yes	maximal, complemented
7	C₂²×C₁₃×#41	C₄	1	2	yes	—
8	C₂³×C₈×C₁₃	—	2	1	no	—
9	C₁₃×#532	—	2	2	no	—
10	C₁₃×#532	—	2	2	no	—
11	C₁₃×#532	C₄	1	4	yes	—
12	C₁₃×#532	C₂²	1	4	yes	—
13	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#124	C₄	1	2	yes	—
16	C₂×C₁₃×#121	—	2	1	no	—
17	C₂×C₁₃×#121	—	2	1	no	—
18	C₂×C₄×D₄×C₁₃	—	2	1	no	—
19	C₂×C₄×D₄×C₁₃	—	2	1	no	—
20	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
21	C₁₃×#432	—	2	2	no	—
22	C₁₃×#432	C₂²	1	4	yes	complemented
23	C₂×C₁₃×C₄⋊C₈	—	2	2	no	—
24	C₂×C₁₃×C₄⋊C₈	—	2	1	no	—
25	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
26	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
27	C₂×C₁₃×C₄⋊C₈	C₂²	1	4	yes	complemented
28	C₂×C₁₃×C₂²⋊C₈	—	2	1	no	—
29	C₂×C₁₃×#97	—	2	1	no	—
30	C₁₃×#333	C₂²	1	8	yes	complemented
31	C₁₃×#331	C₂²	1	8	yes	complemented
32	C₂×C₁₃×#41	—	2	4	no	—
33	C₂×C₁₃×#41	—	4	8	no	—
34	C₂×C₁₃×#41	C₂×C₄	1	8	yes	—
35	C₂²×Q₈×C₁₃	C₂×C₄	1	2	yes	—
36	C₂²×D₄×C₁₃	—	2	2	no	—
37	C₂²×D₄×C₁₃	—	2	1	no	—
38	C₂²×D₄×C₁₃	—	2	1	no	—
39	C₂²×D₄×C₁₃	C₂×C₄	1	2	yes	—
40	C₂³×C₄×C₁₃	—	2	2	no	—
41	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
42	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
43	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
44	C₂²×C₈×C₁₃	—	2	2	no	—
45	C₂²×C₈×C₁₃	—	2	2	no	—
46	C₂²×C₈×C₁₃	—	2	4	no	—
47	C₂²×C₈×C₁₃	—	4	4	no	—
48	C₁₃×C₄⋊Q₈	—	2	1	no	—
49	C₁₃×C₄⋊Q₈	—	2	1	no	—
50	C₁₃×C₄⋊Q₈	C₂×C₄	1	2	yes	—
51	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
52	C₁₃×#127	—	2	1	no	—
53	C₁₃×#127	—	2	1	no	—
54	C₁₃×#127	C₂×C₄	1	2	yes	—
55	C₁₃×#127	C₂³	1	2	yes	—
56	C₁₃×#124	—	2	4	no	—
57	C₁₃×#124	C₂×C₄	1	8	yes	—
58	C₁₃×#121	—	2	4	no	—
59	C₁₃×#121	—	2	4	no	—
60	C₁₃×#121	—	2	4	no	—
61	C₁₃×#121	—	2	4	no	—
62	C₄×D₄×C₁₃	—	2	4	no	—
63	C₄×D₄×C₁₃	—	2	4	no	—
64	C₄×D₄×C₁₃	—	2	4	no	—
65	C₄×D₄×C₁₃	—	2	4	no	—
66	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
67	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
68	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
69	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
70	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
71	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
72	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
73	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
74	C₂×C₄²×C₁₃	D₄	1	2	yes	—
75	C₂×C₄²×C₁₃	D₄	1	2	yes	—
76	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
78	C₁₃×C₄⋊C₈	—	2	2	no	—
79	C₁₃×C₄⋊C₈	—	2	4	no	—
80	C₁₃×C₄⋊C₈	—	2	2	no	—
81	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
82	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
83	C₁₃×C₂²⋊C₈	—	2	4	no	—
84	C₁₃×#97	—	2	4	no	—
85	C₂×#1551	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
86	C₂⁴×C₁₃	—	2	2	no	—
87	C₂⁴×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
88	C₁₃×#41	—	4	16	no	—
89	C₁₃×#41	—	4	16	no	—
90	C₂×Q₈×C₁₃	—	2	2	no	—
91	C₂×Q₈×C₁₃	—	4	4	no	—
92	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
93	C₂×D₄×C₁₃	—	2	8	no	—
94	C₂×D₄×C₁₃	—	2	2	no	—
95	C₂×D₄×C₁₃	—	2	2	no	—
96	C₂×D₄×C₁₃	—	2	2	no	—
97	C₂×D₄×C₁₃	—	2	2	no	—
98	C₂×D₄×C₁₃	—	2	2	no	—
99	C₂×D₄×C₁₃	—	4	4	no	—
100	C₂×D₄×C₁₃	—	4	8	no	—
101	C₂×D₄×C₁₃	—	4	4	no	—
102	C₂×D₄×C₁₃	—	4	2	no	—
103	C₂×D₄×C₁₃	—	4	2	no	—
104	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
105	C₂²×C₄×C₁₃	—	2	4	no	—
106	C₂²×C₄×C₁₃	—	2	4	no	—
107	C₂²×C₄×C₁₃	—	2	2	no	—
108	C₂²×C₄×C₁₃	—	2	2	no	—
109	C₂²×C₄×C₁₃	—	2	2	no	—
110	C₂²×C₄×C₁₃	—	2	8	no	—
111	C₂²×C₄×C₁₃	—	4	8	no	—
112	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
113	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
114	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
115	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
119	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
121	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
122	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
124	C₂×C₈×C₁₃	—	2	4	no	—
125	C₂×C₈×C₁₃	—	2	4	no	—
126	C₂×C₈×C₁₃	—	4	8	no	—
127	C₂×C₈×C₁₃	—	4	4	no	—
128	C₂×C₈×C₁₃	—	4	4	no	—
129	C₁₃×C₄⋊C₄	—	2	2	no	—
130	C₁₃×C₄⋊C₄	—	2	2	no	—
131	C₁₃×C₄⋊C₄	—	2	2	no	—
132	C₁₃×C₄⋊C₄	—	2	2	no	—
133	C₁₃×C₂²⋊C₄	—	2	8	no	—
134	C₁₃×C₂²⋊C₄	—	2	8	no	—
135	C₄²×C₁₃	C₂²⋊C₄	1	2	yes	—
136	C₄²×C₁₃	C₂²⋊C₄	1	2	yes	—
137	C₄²×C₁₃	C₂²⋊C₄	1	2	yes	—
138	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
139	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
140	C₄²×C₁₃	C₂×D₄	1	2	yes	—
141	C₄²×C₁₃	C₂×D₄	1	2	yes	—
142	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
143	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
144	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
145	C₂×#532	C₂×C₁₃	1	1	yes	characteristic
146	C₂×#432	C₂×C₁₃	1	1	yes	characteristic, complemented
147	C₂²×C₄⋊C₈	C₂×C₁₃	1	1	yes	characteristic, complemented
148	#1551	C₂×C₁₃	1	8	yes	direct product factor
149	C₂×#333	C₂×C₁₃	1	2	yes	complemented
150	C₂×#331	C₂×C₁₃	1	2	yes	complemented
151	C₂³×C₁₃	—	2	2	no	—
152	C₂³×C₁₃	—	2	2	no	—
153	C₂³×C₁₃	—	2	4	no	—
154	C₂³×C₁₃	—	4	4	no	—
155	C₂³×C₁₃	—	4	4	no	—
156	C₂³×C₁₃	—	4	4	no	—
157	C₂³×C₁₃	#100	1	4	yes	—
158	C₂³×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
159	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
160	Q₈×C₁₃	—	4	4	no	—
161	Q₈×C₁₃	—	4	4	no	—
162	D₄×C₁₃	—	4	4	no	—
163	D₄×C₁₃	—	4	4	no	—
164	D₄×C₁₃	—	4	16	no	—
165	D₄×C₁₃	—	4	4	no	—
166	D₄×C₁₃	—	4	2	no	—
167	D₄×C₁₃	—	4	2	no	—
168	D₄×C₁₃	—	4	4	no	—
169	D₄×C₁₃	—	4	4	no	—
170	C₂×C₄×C₁₃	—	2	2	no	—
171	C₂×C₄×C₁₃	—	2	4	no	—
172	C₂×C₄×C₁₃	—	2	2	no	—
173	C₂×C₄×C₁₃	—	2	4	no	—
174	C₂×C₄×C₁₃	—	2	2	no	—
175	C₂×C₄×C₁₃	—	2	2	no	—
176	C₂×C₄×C₁₃	—	2	4	no	—
177	C₂×C₄×C₁₃	—	2	2	no	—
178	C₂×C₄×C₁₃	—	2	2	no	—
179	C₂×C₄×C₁₃	—	2	4	no	—
180	C₂×C₄×C₁₃	—	2	4	no	—
181	C₂×C₄×C₁₃	—	2	4	no	—
182	C₂×C₄×C₁₃	—	4	16	no	—
183	C₂×C₄×C₁₃	—	4	4	no	—
184	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
185	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
186	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
187	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
188	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
189	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
190	C₂×C₄×C₁₃	#135	1	4	yes	—
191	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
192	C₂×C₄×C₁₃	#137	1	2	yes	—
193	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
194	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
196	C₈×C₁₃	—	4	4	no	—
197	C₈×C₁₃	—	4	4	no	—
198	C₂²×#41	C₄×C₁₃	1	2	yes	—
199	C₂³×C₈	—	2	1	no	—
200	#532	—	2	2	no	—
201	#532	—	2	2	no	—
202	#532	C₄×C₁₃	1	4	yes	—
203	#532	C₂²×C₁₃	1	4	yes	—
204	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
205	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
206	C₂×#124	C₄×C₁₃	1	2	yes	—
207	C₂×#121	—	2	1	no	—
208	C₂×#121	—	2	1	no	—
209	C₂×C₄×D₄	—	2	1	no	—
210	C₂×C₄×D₄	—	2	1	no	—
211	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
212	#432	—	2	2	no	—
213	#432	C₂²×C₁₃	1	4	yes	complemented
214	C₂×C₄⋊C₈	—	2	2	no	—
215	C₂×C₄⋊C₈	—	2	1	no	—
216	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
217	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
218	C₂×C₄⋊C₈	C₂²×C₁₃	1	4	yes	complemented
219	C₂×C₂²⋊C₈	—	2	1	no	—
220	C₂×#97	—	2	1	no	—
221	#333	C₂²×C₁₃	1	8	yes	complemented
222	#331	C₂²×C₁₃	1	8	yes	complemented
223	C₂²×C₁₃	—	2	8	no	—
224	C₂²×C₁₃	—	2	2	no	—
225	C₂²×C₁₃	—	2	2	no	—
226	C₂²×C₁₃	—	4	4	no	—
227	C₂²×C₁₃	—	4	4	no	—
228	C₂²×C₁₃	—	4	4	no	—
229	C₂²×C₁₃	—	8	8	no	—
230	C₂²×C₁₃	C₂×#100	1	4	yes	—
231	C₂²×C₁₃	C₂×#100	1	2	yes	—
232	C₂²×C₁₃	#416	1	2	yes	—
233	C₂²×C₁₃	#417	1	2	yes	—
234	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
235	C₄×C₁₃	—	2	2	no	—
236	C₄×C₁₃	—	2	1	no	—
237	C₄×C₁₃	—	2	1	no	—
238	C₄×C₁₃	—	2	2	no	—
239	C₄×C₁₃	—	2	2	no	—
240	C₄×C₁₃	—	4	4	no	—
241	C₄×C₁₃	#416	1	2	yes	—
242	C₄×C₁₃	#417	1	2	yes	—
243	C₄×C₁₃	C₂×#135	1	2	yes	—
244	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
245	C₄×C₁₃	C₂×#137	1	1	yes	characteristic
246	C₂×#41	—	2	4	no	—
247	C₂×#41	—	4	8	no	—
248	C₂×#41	C₂×C₄×C₁₃	1	8	yes	—
249	C₂²×Q₈	C₂×C₄×C₁₃	1	2	yes	—
250	C₂²×D₄	—	2	2	no	—
251	C₂²×D₄	—	2	1	no	—
252	C₂²×D₄	—	2	1	no	—
253	C₂²×D₄	C₂×C₄×C₁₃	1	2	yes	—
254	C₂³×C₄	—	2	2	no	—
255	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
256	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
257	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
258	C₂²×C₈	—	2	2	no	—
259	C₂²×C₈	—	2	4	no	—
260	C₂²×C₈	—	2	2	no	—
261	C₂²×C₈	—	4	4	no	—
262	C₄⋊Q₈	—	2	1	no	—
263	C₄⋊Q₈	—	2	1	no	—
264	C₄⋊Q₈	C₂×C₄×C₁₃	1	2	yes	—
265	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
266	#127	—	2	1	no	—
267	#127	—	2	1	no	—
268	#127	C₂×C₄×C₁₃	1	2	yes	—
269	#127	C₂³×C₁₃	1	2	yes	—
270	#124	—	2	4	no	—
271	#124	C₂×C₄×C₁₃	1	8	yes	—
272	#121	—	2	4	no	—
273	#121	—	2	4	no	—
274	#121	—	2	4	no	—
275	#121	—	2	4	no	—
276	C₄×D₄	—	2	4	no	—
277	C₄×D₄	—	2	4	no	—
278	C₄×D₄	—	2	4	no	—
279	C₄×D₄	—	2	4	no	—
280	C₂×C₄⋊C₄	—	2	1	no	—
281	C₂×C₄⋊C₄	—	2	1	no	—
282	C₂×C₂²⋊C₄	—	2	2	no	—
283	C₂×C₂²⋊C₄	—	2	2	no	—
284	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
285	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
286	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
287	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
288	C₂×C₄²	D₄×C₁₃	1	2	yes	—
289	C₂×C₄²	D₄×C₁₃	1	2	yes	—
290	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
291	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
292	C₄⋊C₈	—	2	2	no	—
293	C₄⋊C₈	—	2	4	no	—
294	C₄⋊C₈	—	2	2	no	—
295	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
296	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
297	C₂²⋊C₈	—	2	4	no	—
298	#97	—	2	4	no	—
299	C₂×C₁₃	—	2	4	no	—
300	C₂×C₁₃	—	8	4	no	—
301	C₂×C₁₃	#1551	1	4	yes	direct product factor
302	C₂×C₁₃	C₂²×#100	1	1	yes	characteristic
303	C₂×C₁₃	C₂×#416	1	1	yes	characteristic
304	C₂×C₁₃	C₂×#417	1	1	yes	characteristic
305	C₂⁴	—	2	2	no	—
306	C₂⁴	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
307	#41	—	4	16	no	—
308	#41	—	4	16	no	—
309	C₂×Q₈	—	2	2	no	—
310	C₂×Q₈	—	4	4	no	—
311	C₂×Q₈	C₂²×C₄×C₁₃	1	4	yes	—
312	C₂×D₄	—	2	8	no	—
313	C₂×D₄	—	2	2	no	—
314	C₂×D₄	—	2	2	no	—
315	C₂×D₄	—	2	2	no	—
316	C₂×D₄	—	2	2	no	—
317	C₂×D₄	—	2	2	no	—
318	C₂×D₄	—	4	4	no	—
319	C₂×D₄	—	4	8	no	—
320	C₂×D₄	—	4	4	no	—
321	C₂×D₄	—	4	2	no	—
322	C₂×D₄	—	4	2	no	—
323	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
324	C₂²×C₄	—	2	4	no	—
325	C₂²×C₄	—	2	4	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	2	8	no	—
330	C₂²×C₄	—	4	8	no	—
331	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
332	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
333	C₂²×C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
334	C₂²×C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
335	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
336	C₂²×C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
337	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
338	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
339	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
340	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
341	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
342	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
343	C₂×C₈	—	2	4	no	—
344	C₂×C₈	—	2	4	no	—
345	C₂×C₈	—	4	8	no	—
346	C₂×C₈	—	4	4	no	—
347	C₂×C₈	—	4	4	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	2	2	no	—
351	C₄⋊C₄	—	2	2	no	—
352	C₂²⋊C₄	—	2	8	no	—
353	C₂²⋊C₄	—	2	8	no	—
354	C₄²	C₁₃×C₂²⋊C₄	1	2	yes	—
355	C₄²	C₁₃×C₂²⋊C₄	1	2	yes	—
356	C₄²	C₁₃×C₂²⋊C₄	1	2	yes	—
357	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
358	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
359	C₄²	C₂×D₄×C₁₃	1	2	yes	—
360	C₄²	C₂×D₄×C₁₃	1	2	yes	—
361	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
362	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
363	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
364	C₁₃	C₂×#1551	1	1	yes	characteristic, direct product factor, Sylow
365	C₂³	—	2	2	no	—
366	C₂³	—	2	2	no	—
367	C₂³	—	2	4	no	—
368	C₂³	—	4	4	no	—
369	C₂³	—	4	4	no	—
370	C₂³	—	4	4	no	—
371	C₂³	C₁₃×#100	1	4	yes	—
372	C₂³	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
373	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
374	Q₈	—	4	4	no	—
375	Q₈	—	4	4	no	—
376	D₄	—	4	4	no	—
377	D₄	—	4	4	no	—
378	D₄	—	4	16	no	—
379	D₄	—	4	4	no	—
380	D₄	—	4	4	no	—
381	D₄	—	4	4	no	—
382	D₄	—	4	2	no	—
383	D₄	—	4	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	4	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	4	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	4	no	—
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	2	4	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	—	4	16	no	—
397	C₂×C₄	—	4	4	no	—
398	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
399	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
400	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
401	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
402	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
403	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
404	C₂×C₄	C₁₃×#135	1	4	yes	—
405	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
406	C₂×C₄	C₁₃×#137	1	2	yes	—
407	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
408	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
409	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
410	C₈	—	4	4	no	—
411	C₈	—	4	4	no	—
412	C₂²	—	2	8	no	—
413	C₂²	—	2	2	no	—
414	C₂²	—	2	2	no	—
415	C₂²	—	4	4	no	—
416	C₂²	—	4	4	no	—
417	C₂²	—	4	4	no	—
418	C₂²	—	8	8	no	—
419	C₂²	C₂×C₁₃×#100	1	4	yes	—
420	C₂²	C₂×C₁₃×#100	1	2	yes	—
421	C₂²	C₁₃×#416	1	2	yes	—
422	C₂²	C₁₃×#417	1	2	yes	—
423	C₂²	C₂²×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
424	C₄	—	2	2	no	—
425	C₄	—	2	1	no	—
426	C₄	—	2	1	no	—
427	C₄	—	2	2	no	—
428	C₄	—	2	2	no	—
429	C₄	—	4	4	no	—
430	C₄	C₁₃×#416	1	2	yes	—
431	C₄	C₁₃×#417	1	2	yes	—
432	C₄	C₂×C₁₃×#135	1	2	yes	—
433	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
434	C₄	C₂×C₁₃×#137	1	1	yes	characteristic
435	C₂	—	2	4	no	—
436	C₂	—	8	4	no	—
437	C₂	C₁₃×#1551	1	4	yes	direct product factor
438	C₂	C₂²×C₁₃×#100	1	1	yes	characteristic
439	C₂	C₂×C₁₃×#416	1	1	yes	characteristic
440	C₂	C₂×C₁₃×#417	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₄²	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#532	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#432	C₂	semidirect
3. C₂²×C₁₃×C₄⋊C₈	C₂	semidirect
4. C₁₃×#1551	C₂	direct (N × H)
5. C₂×C₁₃×#333	C₂	semidirect
6. C₂×C₁₃×#331	C₂	semidirect
22. C₁₃×#432	C₂²	semidirect
27. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
30. C₁₃×#333	C₂²	semidirect
31. C₁₃×#331	C₂²	semidirect
85. C₂×#1551	C₁₃	direct (N × H)
146. C₂×#432	C₂×C₁₃	semidirect
147. C₂²×C₄⋊C₈	C₂×C₁₃	semidirect
148. #1551	C₂×C₁₃	direct (N × H)
149. C₂×#333	C₂×C₁₃	semidirect
150. C₂×#331	C₂×C₁₃	semidirect
213. #432	C₂²×C₁₃	semidirect
218. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
221. #333	C₂²×C₁₃	semidirect
222. #331	C₂²×C₁₃	semidirect
301. C₂×C₁₃	#1551	direct (N × H)
364. C₁₃	C₂×#1551	direct (N × H)
437. C₂	C₁₃×#1551	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×#532	2
C₂×C₁₃×#432	2
C₂²×C₁₃×C₄⋊C₈	2
C₁₃×#1551	2
C₂×C₁₃×#333	2
C₂×C₁₃×#331	2
C₂×#1551	13

Subgroups — C2×C13×#1551 #15704048

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#1551 #15704048