Subgroups — C₂×C₁₃×#1514 #15703895

Order 3328.

1302 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	C₂×C₁₃×#532	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#432	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#383	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1514	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	C₂²	1	1	yes	characteristic
19	C₁₃×#432	—	2	2	no	—
20	C₁₃×#432	C₂²	1	4	yes	complemented
21	C₂×C₁₃×C₄⋊C₈	—	2	1	no	—
22	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
23	C₂×C₁₃×#97	—	2	1	no	—
24	C₁₃×#383	—	2	2	no	—
25	C₁₃×#383	C₂²	1	4	yes	complemented
26	C₂×C₁₃×#95	—	2	1	no	—
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	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
67	C₂×C₄²×C₁₃	D₄	1	2	yes	—
68	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
69	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
70	C₂×C₄²×C₁₃	D₄	1	2	yes	—
71	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
72	C₁₃×C₄⋊C₈	—	2	4	no	—
73	C₁₃×C₂²⋊C₈	—	2	2	no	—
74	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
75	C₁₃×#97	—	2	4	no	—
76	C₁₃×#95	—	2	2	no	—
77	C₁₃×#95	—	2	4	no	—
78	C₁₃×#95	—	2	4	no	—
79	C₁₃×#95	C₂³	1	4	yes	—
80	C₂×#1514	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
81	C₂⁴×C₁₃	—	2	2	no	—
82	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
83	C₁₃×#41	—	4	16	no	—
84	C₁₃×#41	—	4	16	no	—
85	C₂×Q₈×C₁₃	—	2	4	no	—
86	C₂×Q₈×C₁₃	—	4	4	no	—
87	C₂×D₄×C₁₃	—	2	4	no	—
88	C₂×D₄×C₁₃	—	2	4	no	—
89	C₂×D₄×C₁₃	—	2	2	no	—
90	C₂×D₄×C₁₃	—	2	4	no	—
91	C₂×D₄×C₁₃	—	2	4	no	—
92	C₂×D₄×C₁₃	—	4	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	C₂²×C₄	1	4	yes	—
97	C₂²×C₄×C₁₃	—	2	4	no	—
98	C₂²×C₄×C₁₃	—	2	2	no	—
99	C₂²×C₄×C₁₃	—	2	8	no	—
100	C₂²×C₄×C₁₃	—	2	4	no	—
101	C₂²×C₄×C₁₃	—	4	2	no	—
102	C₂²×C₄×C₁₃	—	4	2	no	—
103	C₂²×C₄×C₁₃	—	4	8	no	—
104	C₂²×C₄×C₁₃	—	4	4	no	—
105	C₂²×C₄×C₁₃	—	4	4	no	—
106	C₂²×C₄×C₁₃	—	4	4	no	—
107	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
108	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
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	2	yes	—
113	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
121	C₂×C₈×C₁₃	—	2	4	no	—
122	C₂×C₈×C₁₃	—	4	4	no	—
123	C₁₃×C₄⋊C₄	—	2	4	no	—
124	C₁₃×C₄⋊C₄	—	2	2	no	—
125	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
126	C₁₃×C₂²⋊C₄	—	2	4	no	—
127	C₁₃×C₂²⋊C₄	—	2	8	no	—
128	C₁₃×C₂²⋊C₄	—	2	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	2	yes	—
134	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
135	C₄²×C₁₃	C₂×D₄	1	2	yes	—
136	C₄²×C₁₃	C₂×D₄	1	2	yes	—
137	C₂×#532	C₂×C₁₃	1	1	yes	characteristic
138	C₂×#432	C₂×C₁₃	1	1	yes	characteristic, complemented
139	C₂×#383	C₂×C₁₃	1	1	yes	characteristic, complemented
140	#1514	C₂×C₁₃	1	8	yes	direct product factor
141	C₂×#327	C₂×C₁₃	1	4	yes	complemented
142	C₂³×C₁₃	—	2	2	no	—
143	C₂³×C₁₃	—	2	2	no	—
144	C₂³×C₁₃	—	2	4	no	—
145	C₂³×C₁₃	—	4	4	no	—
146	C₂³×C₁₃	—	4	4	no	—
147	C₂³×C₁₃	—	4	4	no	—
148	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
149	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
150	C₂³×C₁₃	AGL(1,ℤ/8)	1	4	yes	—
151	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
152	Q₈×C₁₃	—	4	8	no	—
153	D₄×C₁₃	—	4	4	no	—
154	D₄×C₁₃	—	4	8	no	—
155	D₄×C₁₃	—	4	8	no	—
156	D₄×C₁₃	—	4	4	no	—
157	D₄×C₁₃	—	4	8	no	—
158	D₄×C₁₃	—	4	8	no	—
159	C₂×C₄×C₁₃	—	2	4	no	—
160	C₂×C₄×C₁₃	—	2	2	no	—
161	C₂×C₄×C₁₃	—	2	2	no	—
162	C₂×C₄×C₁₃	—	2	2	no	—
163	C₂×C₄×C₁₃	—	2	2	no	—
164	C₂×C₄×C₁₃	—	2	4	no	—
165	C₂×C₄×C₁₃	—	2	2	no	—
166	C₂×C₄×C₁₃	—	2	2	no	—
167	C₂×C₄×C₁₃	—	2	4	no	—
168	C₂×C₄×C₁₃	—	4	2	no	—
169	C₂×C₄×C₁₃	—	4	1	no	—
170	C₂×C₄×C₁₃	—	4	1	no	—
171	C₂×C₄×C₁₃	—	4	1	no	—
172	C₂×C₄×C₁₃	—	4	2	no	—
173	C₂×C₄×C₁₃	—	4	1	no	—
174	C₂×C₄×C₁₃	—	4	16	no	—
175	C₂×C₄×C₁₃	—	4	4	no	—
176	C₂×C₄×C₁₃	—	4	4	no	—
177	C₂×C₄×C₁₃	—	4	4	no	—
178	C₂×C₄×C₁₃	—	4	4	no	—
179	C₂×C₄×C₁₃	—	8	8	no	—
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×C₂²⋊C₄	1	2	yes	—
183	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
184	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
185	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
186	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
187	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
188	C₈×C₁₃	—	4	4	no	—
189	C₂²×#41	—	2	1	no	—
190	#532	—	2	2	no	—
191	#532	—	2	2	no	—
192	#532	C₄×C₁₃	1	4	yes	complemented
193	#532	C₂²×C₁₃	1	4	yes	—
194	C₂×C₄⋊Q₈	C₄×C₁₃	1	1	yes	characteristic, complemented
195	C₂×#127	C₄×C₁₃	1	1	yes	characteristic, complemented
196	C₂×#124	—	2	1	no	—
197	C₂×#121	—	2	1	no	—
198	C₂×#121	C₂²×C₁₃	1	2	yes	—
199	C₂×C₄×D₄	—	2	1	no	—
200	C₂×C₄×D₄	C₄×C₁₃	1	2	yes	complemented
201	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
202	#432	—	2	2	no	—
203	#432	C₂²×C₁₃	1	4	yes	complemented
204	C₂×C₄⋊C₈	—	2	1	no	—
205	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
206	C₂×#97	—	2	1	no	—
207	#383	—	2	2	no	—
208	#383	C₂²×C₁₃	1	4	yes	complemented
209	C₂×#95	—	2	1	no	—
210	C₂×#95	—	2	1	no	—
211	C₂×#95	C₂²×C₁₃	1	2	yes	—
212	#327	C₂²×C₁₃	1	16	yes	complemented
213	C₂²×C₁₃	—	2	1	no	—
214	C₂²×C₁₃	—	2	1	no	—
215	C₂²×C₁₃	—	2	1	no	—
216	C₂²×C₁₃	—	2	1	no	—
217	C₂²×C₁₃	—	2	8	no	—
218	C₂²×C₁₃	—	4	4	no	—
219	C₂²×C₁₃	—	4	4	no	—
220	C₂²×C₁₃	—	4	4	no	—
221	C₂²×C₁₃	—	8	8	no	—
222	C₂²×C₁₃	#410	1	2	yes	—
223	C₂²×C₁₃	#418	1	2	yes	—
224	C₂²×C₁₃	#418	1	2	yes	—
225	C₂²×C₁₃	#421	1	2	yes	—
226	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
227	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
228	C₄×C₁₃	—	2	1	no	—
229	C₄×C₁₃	—	2	1	no	—
230	C₄×C₁₃	—	2	1	no	—
231	C₄×C₁₃	—	2	1	no	—
232	C₄×C₁₃	—	2	2	no	—
233	C₄×C₁₃	—	2	2	no	—
234	C₄×C₁₃	—	2	2	no	—
235	C₄×C₁₃	—	2	2	no	—
236	C₄×C₁₃	—	4	4	no	—
237	C₄×C₁₃	—	8	4	no	—
238	C₂×#41	—	2	4	no	—
239	C₂×#41	—	2	4	no	—
240	C₂×#41	—	4	8	no	—
241	C₂²×Q₈	—	2	1	no	—
242	C₂²×D₄	—	2	2	no	—
243	C₂²×D₄	—	2	1	no	—
244	C₂²×D₄	—	2	1	no	—
245	C₂²×D₄	C₂×C₄×C₁₃	1	2	yes	—
246	C₂³×C₄	—	2	2	no	—
247	C₂³×C₄	—	2	2	no	—
248	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
249	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
250	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
251	C₂²×C₈	—	2	2	no	—
252	C₄⋊Q₈	—	2	2	no	—
253	C₄⋊Q₈	C₂×C₄×C₁₃	1	4	yes	complemented
254	#127	—	2	2	no	—
255	#127	C₂×C₄×C₁₃	1	4	yes	complemented
256	#124	—	2	4	no	—
257	#124	—	2	4	no	—
258	#121	—	2	4	no	—
259	#121	—	2	4	no	—
260	#121	—	2	2	no	—
261	#121	—	2	2	no	—
262	#121	C₂×C₄×C₁₃	1	4	yes	—
263	#121	C₂³×C₁₃	1	4	yes	—
264	C₄×D₄	—	2	4	no	—
265	C₄×D₄	—	2	4	no	—
266	C₄×D₄	—	2	4	no	—
267	C₄×D₄	C₂×C₄×C₁₃	1	8	yes	complemented
268	C₂×C₄⋊C₄	—	2	1	no	—
269	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
270	C₂×C₂²⋊C₄	—	2	2	no	—
271	C₂×C₂²⋊C₄	—	2	2	no	—
272	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
273	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
274	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
275	C₂×C₄²	D₄×C₁₃	1	2	yes	—
276	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
277	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
278	C₂×C₄²	D₄×C₁₃	1	2	yes	—
279	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
280	C₄⋊C₈	—	2	4	no	—
281	C₂²⋊C₈	—	2	2	no	—
282	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
283	#97	—	2	4	no	—
284	#95	—	2	4	no	—
285	#95	—	2	4	no	—
286	#95	—	2	2	no	—
287	#95	C₂³×C₁₃	1	4	yes	—
288	C₂×C₁₃	—	2	2	no	—
289	C₂×C₁₃	—	2	2	no	—
290	C₂×C₁₃	—	8	4	no	—
291	C₂×C₁₃	#1514	1	4	yes	direct product factor
292	C₂×C₁₃	C₂×#410	1	1	yes	characteristic
293	C₂×C₁₃	C₂×#418	1	1	yes	characteristic
294	C₂×C₁₃	C₂×#421	1	1	yes	characteristic
295	C₂⁴	—	2	2	no	—
296	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
297	#41	—	4	16	no	—
298	#41	—	4	16	no	—
299	C₂×Q₈	—	2	4	no	—
300	C₂×Q₈	—	4	4	no	—
301	C₂×D₄	—	2	4	no	—
302	C₂×D₄	—	2	4	no	—
303	C₂×D₄	—	2	2	no	—
304	C₂×D₄	—	2	4	no	—
305	C₂×D₄	—	2	4	no	—
306	C₂×D₄	—	4	4	no	—
307	C₂×D₄	—	4	4	no	—
308	C₂×D₄	—	4	4	no	—
309	C₂×D₄	—	4	8	no	—
310	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
311	C₂²×C₄	—	2	4	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	2	8	no	—
314	C₂²×C₄	—	2	4	no	—
315	C₂²×C₄	—	4	2	no	—
316	C₂²×C₄	—	4	2	no	—
317	C₂²×C₄	—	4	8	no	—
318	C₂²×C₄	—	4	4	no	—
319	C₂²×C₄	—	4	4	no	—
320	C₂²×C₄	—	4	4	no	—
321	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
322	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
323	C₂²×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
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	C₂²×C₄×C₁₃	1	1	yes	characteristic
328	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
329	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
330	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
331	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
332	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
333	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
334	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
335	C₂×C₈	—	2	4	no	—
336	C₂×C₈	—	4	4	no	—
337	C₄⋊C₄	—	2	4	no	—
338	C₄⋊C₄	—	2	2	no	—
339	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
340	C₂²⋊C₄	—	2	4	no	—
341	C₂²⋊C₄	—	2	8	no	—
342	C₂²⋊C₄	—	2	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	C₁₃×C₂²⋊C₄	1	2	yes	—
347	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
348	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
349	C₄²	C₂×D₄×C₁₃	1	2	yes	—
350	C₄²	C₂×D₄×C₁₃	1	2	yes	—
351	C₁₃	C₂×#1514	1	1	yes	characteristic, direct product factor, Sylow
352	C₂³	—	2	2	no	—
353	C₂³	—	2	2	no	—
354	C₂³	—	2	4	no	—
355	C₂³	—	4	4	no	—
356	C₂³	—	4	4	no	—
357	C₂³	—	4	4	no	—
358	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
359	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
360	C₂³	C₁₃×AGL(1,ℤ/8)	1	4	yes	—
361	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
362	Q₈	—	4	8	no	—
363	D₄	—	4	4	no	—
364	D₄	—	4	4	no	—
365	D₄	—	4	8	no	—
366	D₄	—	4	8	no	—
367	D₄	—	4	8	no	—
368	D₄	—	4	8	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	4	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	4	no	—
377	C₂×C₄	—	2	4	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	1	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	1	no	—
384	C₂×C₄	—	4	16	no	—
385	C₂×C₄	—	4	4	no	—
386	C₂×C₄	—	4	4	no	—
387	C₂×C₄	—	4	4	no	—
388	C₂×C₄	—	4	4	no	—
389	C₂×C₄	—	8	8	no	—
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×C₂²⋊C₄	1	2	yes	—
393	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
394	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
395	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
396	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
397	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
398	C₈	—	4	4	no	—
399	C₂²	—	2	8	no	—
400	C₂²	—	2	1	no	—
401	C₂²	—	2	1	no	—
402	C₂²	—	2	1	no	—
403	C₂²	—	2	1	no	—
404	C₂²	—	4	4	no	—
405	C₂²	—	4	4	no	—
406	C₂²	—	4	4	no	—
407	C₂²	—	8	8	no	—
408	C₂²	C₁₃×#410	1	2	yes	—
409	C₂²	C₁₃×#418	1	2	yes	—
410	C₂²	C₁₃×#418	1	2	yes	—
411	C₂²	C₁₃×#421	1	2	yes	—
412	C₂²	C₂²×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
413	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
414	C₄	—	2	1	no	—
415	C₄	—	2	1	no	—
416	C₄	—	2	1	no	—
417	C₄	—	2	1	no	—
418	C₄	—	2	2	no	—
419	C₄	—	2	2	no	—
420	C₄	—	2	2	no	—
421	C₄	—	2	2	no	—
422	C₄	—	4	4	no	—
423	C₄	—	8	4	no	—
424	C₂	—	2	2	no	—
425	C₂	—	2	2	no	—
426	C₂	—	8	4	no	—
427	C₂	C₁₃×#1514	1	4	yes	direct product factor
428	C₂	C₂×C₁₃×#410	1	1	yes	characteristic
429	C₂	C₂×C₁₃×#418	1	1	yes	characteristic
430	C₂	C₂×C₁₃×#421	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×#383	C₂	semidirect
4. C₁₃×#1514	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
20. C₁₃×#432	C₂²	semidirect
25. C₁₃×#383	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
80. C₂×#1514	C₁₃	direct (N × H)
138. C₂×#432	C₂×C₁₃	semidirect
139. C₂×#383	C₂×C₁₃	semidirect
140. #1514	C₂×C₁₃	direct (N × H)
141. C₂×#327	C₂×C₁₃	semidirect
192. #532	C₄×C₁₃	semidirect
194. C₂×C₄⋊Q₈	C₄×C₁₃	semidirect
195. C₂×#127	C₄×C₁₃	semidirect
200. C₂×C₄×D₄	C₄×C₁₃	semidirect
203. #432	C₂²×C₁₃	semidirect
208. #383	C₂²×C₁₃	semidirect
212. #327	C₂²×C₁₃	semidirect
253. C₄⋊Q₈	C₂×C₄×C₁₃	semidirect
255. #127	C₂×C₄×C₁₃	semidirect
267. C₄×D₄	C₂×C₄×C₁₃	semidirect
291. C₂×C₁₃	#1514	direct (N × H)
351. C₁₃	C₂×#1514	direct (N × H)
427. C₂	C₁₃×#1514	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×#383	2
C₁₃×#1514	2
C₂×C₁₃×#327	2
C₂×#1514	13

Subgroups — C2×C13×#1514 #15703895

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#1514 #15703895