Subgroups — C₂×C₁₃×#1545 #15704040

Order 3328.

1934 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×#127	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#431	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#423	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1545	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₁₃×#331	C₂	1	4	yes	maximal, complemented
6	C₂³×D₄×C₁₃	—	2	1	no	—
7	C₂³×D₄×C₁₃	—	2	1	no	—
8	C₂³×D₄×C₁₃	C₄	1	2	yes	—
9	C₂²×C₁₃×M₁₆	—	2	1	no	—
10	C₂×C₁₃×#127	—	2	1	no	—
11	C₂×C₁₃×#127	—	2	1	no	—
12	C₂×C₁₃×#127	—	2	2	no	—
13	C₂×C₁₃×#127	—	2	2	no	—
14	C₂×C₁₃×#127	C₄	1	4	yes	—
15	C₂×C₁₃×#127	C₄	1	2	yes	—
16	C₂×C₁₃×#127	C₂²	1	2	yes	—
17	C₂×C₁₃×#127	C₂²	1	4	yes	—
18	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
19	C₁₃×#431	—	2	2	no	—
20	C₁₃×#431	C₂²	1	4	yes	complemented
21	C₁₃×#423	—	2	2	no	—
22	C₁₃×#423	C₂²	1	4	yes	complemented
23	C₂×C₁₃×C₄⋊C₈	—	2	1	no	—
24	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	complemented
25	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	complemented
26	C₂×C₁₃×C₂²⋊C₈	—	2	1	no	—
27	C₂×C₄×C₈×C₁₃	—	2	1	no	—
28	C₁₃×#331	C₂²	1	16	yes	complemented
29	C₂⁵×C₁₃	—	2	2	no	—
30	C₂²×D₄×C₁₃	—	2	4	no	—
31	C₂²×D₄×C₁₃	—	2	2	no	—
32	C₂²×D₄×C₁₃	—	2	4	no	—
33	C₂²×D₄×C₁₃	—	2	2	no	—
34	C₂²×D₄×C₁₃	—	2	4	no	—
35	C₂²×D₄×C₁₃	—	2	2	no	—
36	C₂²×D₄×C₁₃	—	2	4	no	—
37	C₂²×D₄×C₁₃	—	2	4	no	—
38	C₂²×D₄×C₁₃	—	2	2	no	—
39	C₂²×D₄×C₁₃	—	2	2	no	—
40	C₂²×D₄×C₁₃	—	4	8	no	—
41	C₂²×D₄×C₁₃	—	4	8	no	—
42	C₂²×D₄×C₁₃	—	4	4	no	—
43	C₂²×D₄×C₁₃	—	4	4	no	—
44	C₂²×D₄×C₁₃	C₂×C₄	1	8	yes	—
45	C₂²×D₄×C₁₃	C₂×C₄	1	4	yes	—
46	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
47	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
48	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
49	C₂×C₁₃×M₁₆	—	2	4	no	—
50	C₂×C₁₃×M₁₆	—	4	4	no	—
51	C₂²×C₈×C₁₃	—	2	2	no	—
52	C₂²×C₈×C₁₃	—	2	2	no	—
53	C₁₃×#127	—	2	4	no	—
54	C₁₃×#127	—	2	4	no	—
55	C₁₃×#127	—	2	4	no	—
56	C₁₃×#127	—	2	4	no	—
57	C₁₃×#127	—	2	2	no	—
58	C₁₃×#127	—	2	2	no	—
59	C₁₃×#127	—	2	4	no	—
60	C₁₃×#127	C₂×C₄	1	4	yes	—
61	C₁₃×#127	C₂×C₄	1	8	yes	—
62	C₁₃×#127	C₂³	1	4	yes	—
63	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
64	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
66	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
67	C₂×C₄²×C₁₃	D₄	1	2	yes	—
68	C₂×C₄²×C₁₃	D₄	1	2	yes	—
69	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
71	C₁₃×C₄⋊C₈	—	2	4	no	—
72	C₁₃×C₄⋊C₈	—	2	2	no	—
73	C₁₃×C₄⋊C₈	—	2	2	no	—
74	C₁₃×C₄⋊C₈	C₂³	1	4	yes	complemented
75	C₁₃×C₄⋊C₈	C₂³	1	4	yes	complemented
76	C₁₃×C₂²⋊C₈	—	2	4	no	—
77	C₄×C₈×C₁₃	—	2	4	no	—
78	C₂×#1545	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
79	C₂⁴×C₁₃	—	2	8	no	—
80	C₂⁴×C₁₃	—	2	4	no	—
81	C₂⁴×C₁₃	—	4	8	no	—
82	C₂⁴×C₁₃	—	4	8	no	—
83	C₂⁴×C₁₃	—	4	8	no	—
84	C₂⁴×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
85	C₂×D₄×C₁₃	—	2	4	no	—
86	C₂×D₄×C₁₃	—	2	8	no	—
87	C₂×D₄×C₁₃	—	2	8	no	—
88	C₂×D₄×C₁₃	—	2	8	no	—
89	C₂×D₄×C₁₃	—	2	4	no	—
90	C₂×D₄×C₁₃	—	2	4	no	—
91	C₂×D₄×C₁₃	—	2	4	no	—
92	C₂×D₄×C₁₃	—	2	4	no	—
93	C₂×D₄×C₁₃	—	4	8	no	—
94	C₂×D₄×C₁₃	—	4	8	no	—
95	C₂×D₄×C₁₃	—	4	16	no	—
96	C₂×D₄×C₁₃	—	4	16	no	—
97	C₂×D₄×C₁₃	—	4	16	no	—
98	C₂×D₄×C₁₃	—	4	16	no	—
99	C₂×D₄×C₁₃	—	4	8	no	—
100	C₂×D₄×C₁₃	—	4	16	no	—
101	C₂×D₄×C₁₃	—	4	8	no	—
102	C₂×D₄×C₁₃	—	4	4	no	—
103	C₂×D₄×C₁₃	—	4	8	no	—
104	C₂×D₄×C₁₃	—	4	8	no	—
105	C₂×D₄×C₁₃	—	4	4	no	—
106	C₂×D₄×C₁₃	—	4	8	no	—
107	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
108	C₂²×C₄×C₁₃	—	2	4	no	—
109	C₂²×C₄×C₁₃	—	2	4	no	—
110	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
111	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
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	2	yes	—
115	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₃	D₈	1	4	yes	—
117	C₂²×C₄×C₁₃	SD₁₆	1	4	yes	—
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	C₁₃×M₁₆	—	4	8	no	—
125	C₂×C₈×C₁₃	—	2	4	no	—
126	C₂×C₈×C₁₃	—	2	4	no	—
127	C₂×C₈×C₁₃	—	4	4	no	—
128	C₂×C₈×C₁₃	—	4	4	no	—
129	C₄²×C₁₃	C₂²⋊C₄	1	2	yes	—
130	C₄²×C₁₃	C₂²⋊C₄	1	2	yes	—
131	C₄²×C₁₃	C₂²⋊C₄	1	2	yes	—
132	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
133	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
134	C₄²×C₁₃	C₂×D₄	1	2	yes	—
135	C₄²×C₁₃	C₂×D₄	1	2	yes	—
136	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
137	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
138	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
139	C₂²×#127	C₂×C₁₃	1	1	yes	characteristic
140	C₂×#431	C₂×C₁₃	1	1	yes	characteristic, complemented
141	C₂×#423	C₂×C₁₃	1	1	yes	characteristic, complemented
142	#1545	C₂×C₁₃	1	8	yes	direct product factor
143	C₂×#331	C₂×C₁₃	1	4	yes	complemented
144	C₂³×C₁₃	—	2	2	no	—
145	C₂³×C₁₃	—	2	2	no	—
146	C₂³×C₁₃	—	2	8	no	—
147	C₂³×C₁₃	—	4	16	no	—
148	C₂³×C₁₃	—	4	16	no	—
149	C₂³×C₁₃	—	4	8	no	—
150	C₂³×C₁₃	—	4	16	no	—
151	C₂³×C₁₃	—	4	8	no	—
152	C₂³×C₁₃	—	4	8	no	—
153	C₂³×C₁₃	—	8	32	no	—
154	C₂³×C₁₃	#102	1	4	yes	—
155	C₂³×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
156	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
157	D₄×C₁₃	—	4	8	no	—
158	D₄×C₁₃	—	4	16	no	—
159	D₄×C₁₃	—	4	8	no	—
160	D₄×C₁₃	—	4	4	no	—
161	D₄×C₁₃	—	4	4	no	—
162	D₄×C₁₃	—	4	8	no	—
163	D₄×C₁₃	—	4	16	no	—
164	D₄×C₁₃	—	4	8	no	—
165	D₄×C₁₃	—	4	16	no	—
166	D₄×C₁₃	—	4	8	no	—
167	C₂×C₄×C₁₃	—	2	2	no	—
168	C₂×C₄×C₁₃	—	2	2	no	—
169	C₂×C₄×C₁₃	—	2	4	no	—
170	C₂×C₄×C₁₃	—	2	4	no	—
171	C₂×C₄×C₁₃	—	2	4	no	—
172	C₂×C₄×C₁₃	—	2	4	no	—
173	C₂×C₄×C₁₃	#100	1	4	yes	—
174	C₂×C₄×C₁₃	#102	1	8	yes	—
175	C₂×C₄×C₁₃	#102	1	4	yes	—
176	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
177	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
178	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
179	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
180	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
181	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
182	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
183	C₂×C₄×C₁₃	C₂×D₈	1	4	yes	—
184	C₂×C₄×C₁₃	C₂×SD₁₆	1	4	yes	—
185	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
186	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	4	yes	—
187	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
188	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
189	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
190	C₈×C₁₃	—	4	4	no	—
191	C₈×C₁₃	—	4	4	no	—
192	C₂³×D₄	—	2	1	no	—
193	C₂³×D₄	—	2	1	no	—
194	C₂³×D₄	C₄×C₁₃	1	2	yes	—
195	C₂²×M₁₆	—	2	1	no	—
196	C₂×#127	—	2	1	no	—
197	C₂×#127	—	2	1	no	—
198	C₂×#127	—	2	2	no	—
199	C₂×#127	—	2	2	no	—
200	C₂×#127	C₄×C₁₃	1	4	yes	—
201	C₂×#127	C₄×C₁₃	1	2	yes	—
202	C₂×#127	C₂²×C₁₃	1	2	yes	—
203	C₂×#127	C₂²×C₁₃	1	4	yes	—
204	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
205	#431	—	2	2	no	—
206	#431	C₂²×C₁₃	1	4	yes	complemented
207	#423	—	2	2	no	—
208	#423	C₂²×C₁₃	1	4	yes	complemented
209	C₂×C₄⋊C₈	—	2	1	no	—
210	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	complemented
211	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	complemented
212	C₂×C₂²⋊C₈	—	2	1	no	—
213	C₂×C₄×C₈	—	2	1	no	—
214	#331	C₂²×C₁₃	1	16	yes	complemented
215	C₂²×C₁₃	—	2	8	no	—
216	C₂²×C₁₃	—	2	2	no	—
217	C₂²×C₁₃	—	2	2	no	—
218	C₂²×C₁₃	—	4	8	no	—
219	C₂²×C₁₃	—	4	8	no	—
220	C₂²×C₁₃	—	4	8	no	—
221	C₂²×C₁₃	—	8	32	no	—
222	C₂²×C₁₃	—	8	16	no	—
223	C₂²×C₁₃	C₂×#100	1	2	yes	—
224	C₂²×C₁₃	C₂×#102	1	4	yes	—
225	C₂²×C₁₃	C₂×#102	1	2	yes	—
226	C₂²×C₁₃	#418	1	2	yes	—
227	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
228	C₄×C₁₃	—	2	1	no	—
229	C₄×C₁₃	—	2	1	no	—
230	C₄×C₁₃	—	2	2	no	—
231	C₄×C₁₃	C₂×#100	1	4	yes	—
232	C₄×C₁₃	C₂×#102	1	2	yes	—
233	C₄×C₁₃	C₂×#102	1	4	yes	—
234	C₄×C₁₃	#418	1	2	yes	—
235	C₄×C₁₃	C₂²×D₈	1	1	yes	characteristic
236	C₄×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
237	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
238	C₂⁵	—	2	2	no	—
239	C₂²×D₄	—	2	4	no	—
240	C₂²×D₄	—	2	2	no	—
241	C₂²×D₄	—	2	2	no	—
242	C₂²×D₄	—	2	4	no	—
243	C₂²×D₄	—	2	4	no	—
244	C₂²×D₄	—	2	2	no	—
245	C₂²×D₄	—	2	4	no	—
246	C₂²×D₄	—	2	2	no	—
247	C₂²×D₄	—	2	4	no	—
248	C₂²×D₄	—	2	2	no	—
249	C₂²×D₄	—	4	8	no	—
250	C₂²×D₄	—	4	8	no	—
251	C₂²×D₄	—	4	4	no	—
252	C₂²×D₄	—	4	4	no	—
253	C₂²×D₄	C₂×C₄×C₁₃	1	4	yes	—
254	C₂²×D₄	C₂×C₄×C₁₃	1	8	yes	—
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	C₂×M₁₆	—	2	4	no	—
259	C₂×M₁₆	—	4	4	no	—
260	C₂²×C₈	—	2	2	no	—
261	C₂²×C₈	—	2	2	no	—
262	#127	—	2	4	no	—
263	#127	—	2	4	no	—
264	#127	—	2	4	no	—
265	#127	—	2	4	no	—
266	#127	—	2	2	no	—
267	#127	—	2	2	no	—
268	#127	—	2	4	no	—
269	#127	C₂×C₄×C₁₃	1	4	yes	—
270	#127	C₂×C₄×C₁₃	1	8	yes	—
271	#127	C₂³×C₁₃	1	4	yes	—
272	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
273	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
274	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
275	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
276	C₂×C₄²	D₄×C₁₃	1	2	yes	—
277	C₂×C₄²	D₄×C₁₃	1	2	yes	—
278	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
279	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
280	C₄⋊C₈	—	2	4	no	—
281	C₄⋊C₈	—	2	2	no	—
282	C₄⋊C₈	—	2	2	no	—
283	C₄⋊C₈	C₂³×C₁₃	1	4	yes	complemented
284	C₄⋊C₈	C₂³×C₁₃	1	4	yes	complemented
285	C₂²⋊C₈	—	2	4	no	—
286	C₄×C₈	—	2	4	no	—
287	C₂×C₁₃	—	2	4	no	—
288	C₂×C₁₃	—	8	8	no	—
289	C₂×C₁₃	#1545	1	4	yes	direct product factor
290	C₂×C₁₃	C₂²×#100	1	1	yes	characteristic
291	C₂×C₁₃	C₂²×#102	1	1	yes	characteristic
292	C₂×C₁₃	C₂×#418	1	1	yes	characteristic
293	C₂⁴	—	2	8	no	—
294	C₂⁴	—	2	4	no	—
295	C₂⁴	—	4	8	no	—
296	C₂⁴	—	4	8	no	—
297	C₂⁴	—	4	8	no	—
298	C₂⁴	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
299	C₂×D₄	—	2	4	no	—
300	C₂×D₄	—	2	8	no	—
301	C₂×D₄	—	2	8	no	—
302	C₂×D₄	—	2	8	no	—
303	C₂×D₄	—	2	4	no	—
304	C₂×D₄	—	2	4	no	—
305	C₂×D₄	—	2	4	no	—
306	C₂×D₄	—	2	4	no	—
307	C₂×D₄	—	4	8	no	—
308	C₂×D₄	—	4	8	no	—
309	C₂×D₄	—	4	16	no	—
310	C₂×D₄	—	4	16	no	—
311	C₂×D₄	—	4	16	no	—
312	C₂×D₄	—	4	16	no	—
313	C₂×D₄	—	4	8	no	—
314	C₂×D₄	—	4	16	no	—
315	C₂×D₄	—	4	8	no	—
316	C₂×D₄	—	4	4	no	—
317	C₂×D₄	—	4	8	no	—
318	C₂×D₄	—	4	8	no	—
319	C₂×D₄	—	4	4	no	—
320	C₂×D₄	—	4	8	no	—
321	C₂×D₄	C₂²×C₄×C₁₃	1	8	yes	—
322	C₂²×C₄	—	2	4	no	—
323	C₂²×C₄	—	2	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	2	yes	—
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	C₁₃×D₈	1	4	yes	—
331	C₂²×C₄	C₁₃×SD₁₆	1	4	yes	—
332	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
333	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
334	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
335	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
336	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
337	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
338	M₁₆	—	4	8	no	—
339	C₂×C₈	—	2	4	no	—
340	C₂×C₈	—	2	4	no	—
341	C₂×C₈	—	4	4	no	—
342	C₂×C₈	—	4	4	no	—
343	C₄²	C₁₃×C₂²⋊C₄	1	2	yes	—
344	C₄²	C₁₃×C₂²⋊C₄	1	2	yes	—
345	C₄²	C₁₃×C₂²⋊C₄	1	2	yes	—
346	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
347	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
348	C₄²	C₂×D₄×C₁₃	1	2	yes	—
349	C₄²	C₂×D₄×C₁₃	1	2	yes	—
350	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
351	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
352	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
353	C₁₃	C₂×#1545	1	1	yes	characteristic, direct product factor, Sylow
354	C₂³	—	2	2	no	—
355	C₂³	—	2	2	no	—
356	C₂³	—	2	8	no	—
357	C₂³	—	4	16	no	—
358	C₂³	—	4	16	no	—
359	C₂³	—	4	8	no	—
360	C₂³	—	4	16	no	—
361	C₂³	—	4	8	no	—
362	C₂³	—	4	8	no	—
363	C₂³	—	8	32	no	—
364	C₂³	C₁₃×#102	1	4	yes	—
365	C₂³	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
366	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
367	D₄	—	4	8	no	—
368	D₄	—	4	8	no	—
369	D₄	—	4	16	no	—
370	D₄	—	4	16	no	—
371	D₄	—	4	8	no	—
372	D₄	—	4	16	no	—
373	D₄	—	4	8	no	—
374	D₄	—	4	4	no	—
375	D₄	—	4	4	no	—
376	D₄	—	4	8	no	—
377	C₂×C₄	—	2	2	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	4	no	—
383	C₂×C₄	C₁₃×#100	1	4	yes	—
384	C₂×C₄	C₁₃×#102	1	8	yes	—
385	C₂×C₄	C₁₃×#102	1	4	yes	—
386	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
387	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
388	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
389	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
390	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
391	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
392	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
393	C₂×C₄	C₂×C₁₃×D₈	1	4	yes	—
394	C₂×C₄	C₂×C₁₃×SD₁₆	1	4	yes	—
395	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
396	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	4	yes	—
397	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
398	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
399	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
400	C₈	—	4	4	no	—
401	C₈	—	4	4	no	—
402	C₂²	—	2	8	no	—
403	C₂²	—	2	2	no	—
404	C₂²	—	2	2	no	—
405	C₂²	—	4	8	no	—
406	C₂²	—	4	8	no	—
407	C₂²	—	4	8	no	—
408	C₂²	—	8	32	no	—
409	C₂²	—	8	16	no	—
410	C₂²	C₂×C₁₃×#100	1	2	yes	—
411	C₂²	C₂×C₁₃×#102	1	4	yes	—
412	C₂²	C₂×C₁₃×#102	1	2	yes	—
413	C₂²	C₁₃×#418	1	2	yes	—
414	C₂²	C₂²×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
415	C₄	—	2	1	no	—
416	C₄	—	2	1	no	—
417	C₄	—	2	2	no	—
418	C₄	C₂×C₁₃×#100	1	4	yes	—
419	C₄	C₂×C₁₃×#102	1	2	yes	—
420	C₄	C₂×C₁₃×#102	1	4	yes	—
421	C₄	C₁₃×#418	1	2	yes	—
422	C₄	C₂²×C₁₃×D₈	1	1	yes	characteristic
423	C₄	C₂²×C₁₃×SD₁₆	1	1	yes	characteristic
424	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
425	C₂	—	2	4	no	—
426	C₂	—	8	8	no	—
427	C₂	C₁₃×#1545	1	4	yes	direct product factor
428	C₂	C₂²×C₁₃×#100	1	1	yes	characteristic
429	C₂	C₂²×C₁₃×#102	1	1	yes	characteristic
430	C₂	C₂×C₁₃×#418	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	C₂²×C₁₃×#127	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×#431	C₂	semidirect
3. C₂×C₁₃×#423	C₂	semidirect
4. C₁₃×#1545	C₂	direct (N × H)
5. C₂×C₁₃×#331	C₂	semidirect
20. C₁₃×#431	C₂²	semidirect
22. C₁₃×#423	C₂²	semidirect
24. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
25. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
28. C₁₃×#331	C₂²	semidirect
74. C₁₃×C₄⋊C₈	C₂³	semidirect
75. C₁₃×C₄⋊C₈	C₂³	semidirect
78. C₂×#1545	C₁₃	direct (N × H)
140. C₂×#431	C₂×C₁₃	semidirect
141. C₂×#423	C₂×C₁₃	semidirect
142. #1545	C₂×C₁₃	direct (N × H)
143. C₂×#331	C₂×C₁₃	semidirect
206. #431	C₂²×C₁₃	semidirect
208. #423	C₂²×C₁₃	semidirect
210. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
211. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
214. #331	C₂²×C₁₃	semidirect
283. C₄⋊C₈	C₂³×C₁₃	semidirect
284. C₄⋊C₈	C₂³×C₁₃	semidirect
289. C₂×C₁₃	#1545	direct (N × H)
353. C₁₃	C₂×#1545	direct (N × H)
427. C₂	C₁₃×#1545	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₃×#127	2
C₂×C₁₃×#431	2
C₂×C₁₃×#423	2
C₁₃×#1545	2
C₂×C₁₃×#331	2
C₂×#1545	13

Subgroups — C2×C13×#1545 #15704040

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#1545 #15704040