Subgroups — C₂×C₁₃×#1505 #15703878

Order 3328.

1410 conjugacy classes of subgroups.

The subgroup lattice has 436 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	C₂×C₁₃×#376	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1505	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₁₃×#327	C₂	1	4	yes	maximal, complemented
6	C₂²×C₁₃×#41	—	2	1	no	—
7	C₁₃×#532	—	2	2	no	—
8	C₁₃×#532	—	2	2	no	—
9	C₁₃×#532	C₄	1	4	yes	complemented
10	C₁₃×#532	C₂²	1	4	yes	—
11	C₂×C₁₃×C₄⋊Q₈	C₄	1	1	yes	characteristic, complemented
12	C₂×C₁₃×#127	C₄	1	1	yes	characteristic, complemented
13	C₂×C₁₃×#124	—	2	1	no	—
14	C₂×C₁₃×#121	—	2	1	no	—
15	C₂×C₁₃×#121	C₂²	1	2	yes	—
16	C₂×C₄×D₄×C₁₃	—	2	1	no	—
17	C₂×C₄×D₄×C₁₃	C₄	1	2	yes	complemented
18	C₂²×C₄²×C₁₃	—	2	1	no	—
19	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
20	C₁₃×#432	—	2	2	no	—
21	C₁₃×#432	C₂²	1	4	yes	complemented
22	C₂×C₁₃×C₄⋊C₈	—	2	1	no	—
23	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
24	C₂×C₁₃×#97	—	2	1	no	—
25	C₁₃×#376	—	2	2	no	—
26	C₁₃×#376	C₂²	1	4	yes	complemented
27	C₂×C₁₃×#95	—	2	1	no	—
28	C₂×C₁₃×#95	C₂²	1	2	yes	—
29	C₁₃×#327	C₂²	1	16	yes	complemented
30	C₂×C₁₃×#41	—	2	4	no	—
31	C₂×C₁₃×#41	—	2	4	no	—
32	C₂×C₁₃×#41	—	4	8	no	—
33	C₂²×Q₈×C₁₃	—	2	1	no	—
34	C₂²×D₄×C₁₃	—	2	2	no	—
35	C₂²×D₄×C₁₃	—	2	1	no	—
36	C₂²×D₄×C₁₃	—	2	1	no	—
37	C₂²×D₄×C₁₃	C₂×C₄	1	2	yes	—
38	C₂³×C₄×C₁₃	—	2	2	no	—
39	C₂³×C₄×C₁₃	—	2	2	no	—
40	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
41	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
42	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
43	C₂²×C₈×C₁₃	—	2	2	no	—
44	C₁₃×C₄⋊Q₈	—	2	2	no	—
45	C₁₃×C₄⋊Q₈	C₂×C₄	1	4	yes	complemented
46	C₁₃×#127	—	2	2	no	—
47	C₁₃×#127	C₂×C₄	1	4	yes	complemented
48	C₁₃×#124	—	2	4	no	—
49	C₁₃×#124	—	2	4	no	—
50	C₁₃×#121	—	2	4	no	—
51	C₁₃×#121	—	2	4	no	—
52	C₁₃×#121	—	2	2	no	—
53	C₁₃×#121	—	2	2	no	—
54	C₁₃×#121	C₂×C₄	1	4	yes	—
55	C₁₃×#121	C₂³	1	4	yes	—
56	C₄×D₄×C₁₃	—	2	4	no	—
57	C₄×D₄×C₁₃	—	2	4	no	—
58	C₄×D₄×C₁₃	—	2	4	no	—
59	C₄×D₄×C₁₃	C₂×C₄	1	8	yes	complemented
60	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
61	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
62	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
63	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
64	C₂×C₄²×C₁₃	—	2	8	no	—
65	C₂×C₄²×C₁₃	—	2	4	no	—
66	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
69	C₂×C₄²×C₁₃	D₄	1	2	yes	—
70	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
71	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
72	C₂×C₄²×C₁₃	D₄	1	2	yes	—
73	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
74	C₁₃×C₄⋊C₈	—	2	4	no	—
75	C₁₃×C₂²⋊C₈	—	2	2	no	—
76	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
77	C₁₃×#97	—	2	4	no	—
78	C₁₃×#95	—	2	4	no	—
79	C₁₃×#95	—	2	2	no	—
80	C₁₃×#95	C₂³	1	4	yes	—
81	C₂×#1505	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
82	C₂⁴×C₁₃	—	2	2	no	—
83	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
84	C₁₃×#41	—	4	16	no	—
85	C₁₃×#41	—	4	16	no	—
86	C₂×Q₈×C₁₃	—	2	4	no	—
87	C₂×Q₈×C₁₃	—	4	4	no	—
88	C₂×D₄×C₁₃	—	2	4	no	—
89	C₂×D₄×C₁₃	—	2	4	no	—
90	C₂×D₄×C₁₃	—	2	2	no	—
91	C₂×D₄×C₁₃	—	2	4	no	—
92	C₂×D₄×C₁₃	—	2	4	no	—
93	C₂×D₄×C₁₃	—	4	4	no	—
94	C₂×D₄×C₁₃	—	4	4	no	—
95	C₂×D₄×C₁₃	—	4	8	no	—
96	C₂×D₄×C₁₃	—	4	4	no	—
97	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
98	C₂²×C₄×C₁₃	—	2	4	no	—
99	C₂²×C₄×C₁₃	—	2	4	no	—
100	C₂²×C₄×C₁₃	—	2	8	no	—
101	C₂²×C₄×C₁₃	—	2	2	no	—
102	C₂²×C₄×C₁₃	—	2	4	no	—
103	C₂²×C₄×C₁₃	—	2	8	no	—
104	C₂²×C₄×C₁₃	—	4	2	no	—
105	C₂²×C₄×C₁₃	—	4	8	no	—
106	C₂²×C₄×C₁₃	—	4	4	no	—
107	C₂²×C₄×C₁₃	—	4	4	no	—
108	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
109	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
110	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
118	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
122	C₂×C₈×C₁₃	—	2	4	no	—
123	C₂×C₈×C₁₃	—	4	4	no	—
124	C₁₃×C₄⋊C₄	—	2	4	no	—
125	C₁₃×C₄⋊C₄	—	2	2	no	—
126	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
127	C₁₃×C₂²⋊C₄	—	2	4	no	—
128	C₁₃×C₂²⋊C₄	—	2	8	no	—
129	C₁₃×C₂²⋊C₄	—	2	4	no	—
130	C₄²×C₁₃	—	2	16	no	—
131	C₄²×C₁₃	C₂²⋊C₄	1	2	yes	—
132	C₄²×C₁₃	C₂²⋊C₄	1	2	yes	—
133	C₄²×C₁₃	C₂²⋊C₄	1	2	yes	—
134	C₄²×C₁₃	C₂²⋊C₄	1	2	yes	—
135	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
136	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
137	C₄²×C₁₃	C₂×D₄	1	2	yes	—
138	C₄²×C₁₃	C₂×D₄	1	2	yes	—
139	C₂×#532	C₂×C₁₃	1	1	yes	characteristic
140	C₂×#432	C₂×C₁₃	1	1	yes	characteristic, complemented
141	C₂×#376	C₂×C₁₃	1	1	yes	characteristic, complemented
142	#1505	C₂×C₁₃	1	8	yes	direct product factor
143	C₂×#327	C₂×C₁₃	1	4	yes	complemented
144	C₂³×C₁₃	—	2	2	no	—
145	C₂³×C₁₃	—	2	2	no	—
146	C₂³×C₁₃	—	2	4	no	—
147	C₂³×C₁₃	—	4	4	no	—
148	C₂³×C₁₃	—	4	4	no	—
149	C₂³×C₁₃	—	4	4	no	—
150	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
151	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
152	C₂³×C₁₃	AGL(1,ℤ/8)	1	4	yes	—
153	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
154	Q₈×C₁₃	—	4	8	no	—
155	D₄×C₁₃	—	4	4	no	—
156	D₄×C₁₃	—	4	8	no	—
157	D₄×C₁₃	—	4	4	no	—
158	D₄×C₁₃	—	4	8	no	—
159	D₄×C₁₃	—	4	8	no	—
160	D₄×C₁₃	—	4	8	no	—
161	C₂×C₄×C₁₃	—	2	4	no	—
162	C₂×C₄×C₁₃	—	2	2	no	—
163	C₂×C₄×C₁₃	—	2	2	no	—
164	C₂×C₄×C₁₃	—	2	2	no	—
165	C₂×C₄×C₁₃	—	2	2	no	—
166	C₂×C₄×C₁₃	—	2	4	no	—
167	C₂×C₄×C₁₃	—	2	2	no	—
168	C₂×C₄×C₁₃	—	2	4	no	—
169	C₂×C₄×C₁₃	—	2	4	no	—
170	C₂×C₄×C₁₃	—	2	8	no	—
171	C₂×C₄×C₁₃	—	2	4	no	—
172	C₂×C₄×C₁₃	—	4	1	no	—
173	C₂×C₄×C₁₃	—	4	1	no	—
174	C₂×C₄×C₁₃	—	4	1	no	—
175	C₂×C₄×C₁₃	—	4	1	no	—
176	C₂×C₄×C₁₃	—	4	16	no	—
177	C₂×C₄×C₁₃	—	4	4	no	—
178	C₂×C₄×C₁₃	—	4	16	no	—
179	C₂×C₄×C₁₃	—	4	4	no	—
180	C₂×C₄×C₁₃	—	4	4	no	—
181	C₂×C₄×C₁₃	#104	1	4	yes	—
182	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
183	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
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	2	yes	—
188	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
189	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
190	C₈×C₁₃	—	4	4	no	—
191	C₂²×#41	—	2	1	no	—
192	#532	—	2	2	no	—
193	#532	—	2	2	no	—
194	#532	C₄×C₁₃	1	4	yes	complemented
195	#532	C₂²×C₁₃	1	4	yes	—
196	C₂×C₄⋊Q₈	C₄×C₁₃	1	1	yes	characteristic, complemented
197	C₂×#127	C₄×C₁₃	1	1	yes	characteristic, complemented
198	C₂×#124	—	2	1	no	—
199	C₂×#121	—	2	1	no	—
200	C₂×#121	C₂²×C₁₃	1	2	yes	—
201	C₂×C₄×D₄	—	2	1	no	—
202	C₂×C₄×D₄	C₄×C₁₃	1	2	yes	complemented
203	C₂²×C₄²	—	2	1	no	—
204	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
205	#432	—	2	2	no	—
206	#432	C₂²×C₁₃	1	4	yes	complemented
207	C₂×C₄⋊C₈	—	2	1	no	—
208	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
209	C₂×#97	—	2	1	no	—
210	#376	—	2	2	no	—
211	#376	C₂²×C₁₃	1	4	yes	complemented
212	C₂×#95	—	2	1	no	—
213	C₂×#95	C₂²×C₁₃	1	2	yes	—
214	#327	C₂²×C₁₃	1	16	yes	complemented
215	C₂²×C₁₃	—	2	1	no	—
216	C₂²×C₁₃	—	2	1	no	—
217	C₂²×C₁₃	—	2	1	no	—
218	C₂²×C₁₃	—	2	1	no	—
219	C₂²×C₁₃	—	2	8	no	—
220	C₂²×C₁₃	—	4	4	no	—
221	C₂²×C₁₃	—	4	4	no	—
222	C₂²×C₁₃	—	4	4	no	—
223	C₂²×C₁₃	—	8	8	no	—
224	C₂²×C₁₃	#410	1	2	yes	—
225	C₂²×C₁₃	#418	1	2	yes	—
226	C₂²×C₁₃	#418	1	2	yes	—
227	C₂²×C₁₃	C₂×#104	1	2	yes	—
228	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
229	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
230	C₄×C₁₃	—	2	1	no	—
231	C₄×C₁₃	—	2	1	no	—
232	C₄×C₁₃	—	2	1	no	—
233	C₄×C₁₃	—	2	1	no	—
234	C₄×C₁₃	—	2	2	no	—
235	C₄×C₁₃	—	2	2	no	—
236	C₄×C₁₃	—	2	2	no	—
237	C₄×C₁₃	—	4	8	no	—
238	C₄×C₁₃	—	4	4	no	—
239	C₄×C₁₃	C₂×#104	1	4	yes	—
240	C₂×#41	—	2	4	no	—
241	C₂×#41	—	2	4	no	—
242	C₂×#41	—	4	8	no	—
243	C₂²×Q₈	—	2	1	no	—
244	C₂²×D₄	—	2	2	no	—
245	C₂²×D₄	—	2	1	no	—
246	C₂²×D₄	—	2	1	no	—
247	C₂²×D₄	C₂×C₄×C₁₃	1	2	yes	—
248	C₂³×C₄	—	2	2	no	—
249	C₂³×C₄	—	2	2	no	—
250	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
251	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
252	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
253	C₂²×C₈	—	2	2	no	—
254	C₄⋊Q₈	—	2	2	no	—
255	C₄⋊Q₈	C₂×C₄×C₁₃	1	4	yes	complemented
256	#127	—	2	2	no	—
257	#127	C₂×C₄×C₁₃	1	4	yes	complemented
258	#124	—	2	4	no	—
259	#124	—	2	4	no	—
260	#121	—	2	4	no	—
261	#121	—	2	4	no	—
262	#121	—	2	2	no	—
263	#121	—	2	2	no	—
264	#121	C₂×C₄×C₁₃	1	4	yes	—
265	#121	C₂³×C₁₃	1	4	yes	—
266	C₄×D₄	—	2	4	no	—
267	C₄×D₄	—	2	4	no	—
268	C₄×D₄	—	2	4	no	—
269	C₄×D₄	C₂×C₄×C₁₃	1	8	yes	complemented
270	C₂×C₄⋊C₄	—	2	1	no	—
271	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
272	C₂×C₂²⋊C₄	—	2	2	no	—
273	C₂×C₂²⋊C₄	—	2	2	no	—
274	C₂×C₄²	—	2	8	no	—
275	C₂×C₄²	—	2	4	no	—
276	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
277	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
278	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
279	C₂×C₄²	D₄×C₁₃	1	2	yes	—
280	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
281	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
282	C₂×C₄²	D₄×C₁₃	1	2	yes	—
283	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
284	C₄⋊C₈	—	2	4	no	—
285	C₂²⋊C₈	—	2	2	no	—
286	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
287	#97	—	2	4	no	—
288	#95	—	2	4	no	—
289	#95	—	2	2	no	—
290	#95	C₂³×C₁₃	1	4	yes	—
291	C₂×C₁₃	—	2	2	no	—
292	C₂×C₁₃	—	2	2	no	—
293	C₂×C₁₃	—	8	4	no	—
294	C₂×C₁₃	#1505	1	4	yes	direct product factor
295	C₂×C₁₃	C₂×#410	1	1	yes	characteristic
296	C₂×C₁₃	C₂×#418	1	1	yes	characteristic
297	C₂×C₁₃	C₂²×#104	1	1	yes	characteristic
298	C₂⁴	—	2	2	no	—
299	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
300	#41	—	4	16	no	—
301	#41	—	4	16	no	—
302	C₂×Q₈	—	2	4	no	—
303	C₂×Q₈	—	4	4	no	—
304	C₂×D₄	—	2	4	no	—
305	C₂×D₄	—	2	4	no	—
306	C₂×D₄	—	2	2	no	—
307	C₂×D₄	—	2	4	no	—
308	C₂×D₄	—	2	4	no	—
309	C₂×D₄	—	4	4	no	—
310	C₂×D₄	—	4	4	no	—
311	C₂×D₄	—	4	8	no	—
312	C₂×D₄	—	4	4	no	—
313	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
314	C₂²×C₄	—	2	4	no	—
315	C₂²×C₄	—	2	4	no	—
316	C₂²×C₄	—	2	8	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	2	4	no	—
319	C₂²×C₄	—	2	8	no	—
320	C₂²×C₄	—	4	2	no	—
321	C₂²×C₄	—	4	8	no	—
322	C₂²×C₄	—	4	4	no	—
323	C₂²×C₄	—	4	4	no	—
324	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
325	C₂²×C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
326	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
327	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
328	C₂²×C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
329	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
330	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
331	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
332	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
333	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
334	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
335	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
336	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
337	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
338	C₂×C₈	—	2	4	no	—
339	C₂×C₈	—	4	4	no	—
340	C₄⋊C₄	—	2	4	no	—
341	C₄⋊C₄	—	2	2	no	—
342	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
343	C₂²⋊C₄	—	2	4	no	—
344	C₂²⋊C₄	—	2	8	no	—
345	C₂²⋊C₄	—	2	4	no	—
346	C₄²	—	2	16	no	—
347	C₄²	C₁₃×C₂²⋊C₄	1	2	yes	—
348	C₄²	C₁₃×C₂²⋊C₄	1	2	yes	—
349	C₄²	C₁₃×C₂²⋊C₄	1	2	yes	—
350	C₄²	C₁₃×C₂²⋊C₄	1	2	yes	—
351	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
352	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
353	C₄²	C₂×D₄×C₁₃	1	2	yes	—
354	C₄²	C₂×D₄×C₁₃	1	2	yes	—
355	C₁₃	C₂×#1505	1	1	yes	characteristic, direct product factor, Sylow
356	C₂³	—	2	2	no	—
357	C₂³	—	2	2	no	—
358	C₂³	—	2	4	no	—
359	C₂³	—	4	4	no	—
360	C₂³	—	4	4	no	—
361	C₂³	—	4	4	no	—
362	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
363	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
364	C₂³	C₁₃×AGL(1,ℤ/8)	1	4	yes	—
365	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
366	Q₈	—	4	8	no	—
367	D₄	—	4	4	no	—
368	D₄	—	4	4	no	—
369	D₄	—	4	8	no	—
370	D₄	—	4	8	no	—
371	D₄	—	4	8	no	—
372	D₄	—	4	8	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	4	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	4	no	—
380	C₂×C₄	—	2	4	no	—
381	C₂×C₄	—	2	4	no	—
382	C₂×C₄	—	2	8	no	—
383	C₂×C₄	—	2	4	no	—
384	C₂×C₄	—	4	1	no	—
385	C₂×C₄	—	4	1	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	4	16	no	—
389	C₂×C₄	—	4	16	no	—
390	C₂×C₄	—	4	4	no	—
391	C₂×C₄	—	4	4	no	—
392	C₂×C₄	—	4	4	no	—
393	C₂×C₄	C₁₃×#104	1	4	yes	—
394	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
395	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
396	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
397	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
398	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
399	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
400	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
401	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
402	C₈	—	4	4	no	—
403	C₂²	—	2	8	no	—
404	C₂²	—	2	1	no	—
405	C₂²	—	2	1	no	—
406	C₂²	—	2	1	no	—
407	C₂²	—	2	1	no	—
408	C₂²	—	4	4	no	—
409	C₂²	—	4	4	no	—
410	C₂²	—	4	4	no	—
411	C₂²	—	8	8	no	—
412	C₂²	C₁₃×#410	1	2	yes	—
413	C₂²	C₁₃×#418	1	2	yes	—
414	C₂²	C₁₃×#418	1	2	yes	—
415	C₂²	C₂×C₁₃×#104	1	2	yes	—
416	C₂²	C₂²×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
417	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
418	C₄	—	2	1	no	—
419	C₄	—	2	1	no	—
420	C₄	—	2	1	no	—
421	C₄	—	2	1	no	—
422	C₄	—	2	2	no	—
423	C₄	—	2	2	no	—
424	C₄	—	2	2	no	—
425	C₄	—	4	8	no	—
426	C₄	—	4	4	no	—
427	C₄	C₂×C₁₃×#104	1	4	yes	—
428	C₂	—	2	2	no	—
429	C₂	—	2	2	no	—
430	C₂	—	8	4	no	—
431	C₂	C₁₃×#1505	1	4	yes	direct product factor
432	C₂	C₂×C₁₃×#410	1	1	yes	characteristic
433	C₂	C₂×C₁₃×#418	1	1	yes	characteristic
434	C₂	C₂²×C₁₃×#104	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₂²×C₄	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. C₂×C₁₃×#376	C₂	semidirect
4. C₁₃×#1505	C₂	direct (N × H)
5. C₂×C₁₃×#327	C₂	semidirect
9. C₁₃×#532	C₄	semidirect
11. C₂×C₁₃×C₄⋊Q₈	C₄	semidirect
12. C₂×C₁₃×#127	C₄	semidirect
17. C₂×C₄×D₄×C₁₃	C₄	semidirect
21. C₁₃×#432	C₂²	semidirect
26. C₁₃×#376	C₂²	semidirect
29. C₁₃×#327	C₂²	semidirect
45. C₁₃×C₄⋊Q₈	C₂×C₄	semidirect
47. C₁₃×#127	C₂×C₄	semidirect
59. C₄×D₄×C₁₃	C₂×C₄	semidirect
81. C₂×#1505	C₁₃	direct (N × H)
140. C₂×#432	C₂×C₁₃	semidirect
141. C₂×#376	C₂×C₁₃	semidirect
142. #1505	C₂×C₁₃	direct (N × H)
143. C₂×#327	C₂×C₁₃	semidirect
194. #532	C₄×C₁₃	semidirect
196. C₂×C₄⋊Q₈	C₄×C₁₃	semidirect
197. C₂×#127	C₄×C₁₃	semidirect
202. C₂×C₄×D₄	C₄×C₁₃	semidirect
206. #432	C₂²×C₁₃	semidirect
211. #376	C₂²×C₁₃	semidirect
214. #327	C₂²×C₁₃	semidirect
255. C₄⋊Q₈	C₂×C₄×C₁₃	semidirect
257. #127	C₂×C₄×C₁₃	semidirect
269. C₄×D₄	C₂×C₄×C₁₃	semidirect
294. C₂×C₁₃	#1505	direct (N × H)
355. C₁₃	C₂×#1505	direct (N × H)
431. C₂	C₁₃×#1505	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
C₂×C₁₃×#376	2
C₁₃×#1505	2
C₂×C₁₃×#327	2
C₂×#1505	13

Subgroups — C2×C13×#1505 #15703878

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#1505 #15703878