Subgroups — C₂×C₁₃×#3234 #15747186

Order 3328.

2050 conjugacy classes of subgroups.

The subgroup lattice has 472 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	C₂²×C₁₃×#125	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3234	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#501	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₃×#490	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#481	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₃×#480	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×#478	C₂	1	4	yes	maximal, complemented
9	C₂×C₁₃×#432	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₁₃×#41	—	2	1	no	—
11	C₁₃×#532	—	2	4	no	—
12	C₁₃×#532	C₂²	1	8	yes	—
13	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#125	—	2	1	no	—
16	C₂×C₁₃×#125	—	2	1	no	—
17	C₂×C₁₃×#125	—	2	4	no	—
18	C₂×C₁₃×#125	C₂²	1	2	yes	—
19	C₂×C₁₃×#125	C₂²	1	2	yes	—
20	C₂×C₁₃×#125	C₂²	1	8	yes	complemented
21	C₂×C₁₃×#124	—	2	1	no	—
22	C₂×C₁₃×#121	—	2	1	no	—
23	C₂×C₁₃×#121	C₂²	1	2	yes	—
24	C₂×C₄×D₄×C₁₃	—	2	1	no	—
25	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
26	C₂²×C₁₃×C₄⋊C₄	—	2	1	no	—
27	C₂²×C₁₃×C₄⋊C₄	—	2	1	no	—
28	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
30	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
31	C₁₃×#501	C₂²	1	16	yes	complemented
32	C₁₃×#490	C₂²	1	16	yes	complemented
33	C₁₃×#481	C₂²	1	16	yes	complemented
34	C₁₃×#480	C₂²	1	16	yes	complemented
35	C₁₃×#478	C₂²	1	32	yes	complemented
36	C₁₃×#432	C₂²	1	8	yes	complemented
37	C₂×C₁₃×#107	C₂²	1	4	yes	—
38	C₂×C₁₃×#106	C₂²	1	4	yes	—
39	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
40	C₂×C₁₃×#102	C₂²	1	4	yes	—
41	C₂×C₁₃×#102	C₂²	1	4	yes	—
42	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
43	C₂×C₁₃×#97	C₂²	1	2	yes	—
44	C₂×C₁₃×#41	—	2	8	no	—
45	C₂×C₁₃×#41	—	4	8	no	—
46	C₂²×Q₈×C₁₃	—	2	1	no	—
47	C₂²×D₄×C₁₃	—	2	2	no	—
48	C₂²×D₄×C₁₃	—	2	1	no	—
49	C₂²×D₄×C₁₃	—	2	1	no	—
50	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
51	C₂³×C₄×C₁₃	—	2	1	no	—
52	C₂³×C₄×C₁₃	—	2	1	no	—
53	C₂³×C₄×C₁₃	—	2	2	no	—
54	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
55	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
56	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
58	C₁₃×C₄⋊Q₈	—	2	2	no	—
59	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
60	C₁₃×#127	—	2	2	no	—
61	C₁₃×#127	C₂³	1	4	yes	—
62	C₁₃×#125	—	2	4	no	—
63	C₁₃×#125	—	2	4	no	—
64	C₁₃×#125	—	2	8	no	—
65	C₁₃×#125	—	2	8	no	—
66	C₁₃×#125	C₂³	1	8	yes	—
67	C₁₃×#125	C₂³	1	8	yes	—
68	C₁₃×#124	—	2	8	no	—
69	C₁₃×#121	—	2	8	no	—
70	C₁₃×#121	—	2	4	no	—
71	C₁₃×#121	C₂³	1	8	yes	—
72	C₄×D₄×C₁₃	—	2	8	no	—
73	C₄×D₄×C₁₃	—	2	4	no	—
74	C₄×D₄×C₁₃	C₂³	1	8	yes	—
75	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
76	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
77	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
78	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
79	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
80	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
81	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
82	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
83	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
84	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
85	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
86	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
87	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
88	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
89	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
90	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
91	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
92	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
93	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
94	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
95	C₂×C₄²×C₁₃	D₄	1	4	yes	—
96	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
97	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
98	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
99	C₁₃×#107	C₂³	1	16	yes	—
100	C₁₃×#106	C₂³	1	16	yes	—
101	C₁₃×C₄⋊C₈	C₂³	1	8	yes	—
102	C₁₃×#102	C₂³	1	16	yes	—
103	C₁₃×#102	C₂³	1	16	yes	—
104	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	—
105	C₁₃×#97	C₂³	1	8	yes	—
106	C₂×#3234	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
107	C₂⁴×C₁₃	—	2	2	no	—
108	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
109	C₁₃×#41	—	4	32	no	—
110	C₂×Q₈×C₁₃	—	2	4	no	—
111	C₂×Q₈×C₁₃	—	4	4	no	—
112	C₂×D₄×C₁₃	—	2	8	no	—
113	C₂×D₄×C₁₃	—	2	2	no	—
114	C₂×D₄×C₁₃	—	2	4	no	—
115	C₂×D₄×C₁₃	—	2	4	no	—
116	C₂×D₄×C₁₃	—	2	8	no	—
117	C₂×D₄×C₁₃	—	4	4	no	—
118	C₂×D₄×C₁₃	—	4	4	no	—
119	C₂×D₄×C₁₃	—	4	8	no	—
120	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
121	C₂²×C₄×C₁₃	—	2	4	no	—
122	C₂²×C₄×C₁₃	—	2	4	no	—
123	C₂²×C₄×C₁₃	—	2	4	no	—
124	C₂²×C₄×C₁₃	—	2	4	no	—
125	C₂²×C₄×C₁₃	—	2	2	no	—
126	C₂²×C₄×C₁₃	—	2	2	no	—
127	C₂²×C₄×C₁₃	—	2	2	no	—
128	C₂²×C₄×C₁₃	—	2	8	no	—
129	C₂²×C₄×C₁₃	—	4	2	no	—
130	C₂²×C₄×C₁₃	—	4	8	no	—
131	C₂²×C₄×C₁₃	—	4	4	no	—
132	C₂²×C₄×C₁₃	—	4	4	no	—
133	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
134	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
135	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
141	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
142	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
143	C₂×C₈×C₁₃	—	2	8	no	—
144	C₂×C₈×C₁₃	C₂⁴	1	8	yes	—
145	C₁₃×C₄⋊C₄	—	2	8	no	—
146	C₁₃×C₄⋊C₄	—	2	8	no	—
147	C₁₃×C₄⋊C₄	—	2	8	no	—
148	C₁₃×C₄⋊C₄	—	2	8	no	—
149	C₁₃×C₄⋊C₄	—	2	4	no	—
150	C₁₃×C₄⋊C₄	—	2	4	no	—
151	C₁₃×C₄⋊C₄	—	2	2	no	—
152	C₁₃×C₄⋊C₄	—	2	2	no	—
153	C₁₃×C₄⋊C₄	—	2	4	no	—
154	C₁₃×C₄⋊C₄	—	2	2	no	—
155	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
156	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
157	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
158	C₁₃×C₂²⋊C₄	—	2	8	no	—
159	C₁₃×C₂²⋊C₄	—	2	8	no	—
160	C₄²×C₁₃	C₂×D₄	1	4	yes	—
161	C₄²×C₁₃	C₂×D₄	1	2	yes	—
162	C₄²×C₁₃	C₂×D₄	1	4	yes	—
163	C₄²×C₁₃	C₂×D₄	1	2	yes	—
164	C₄²×C₁₃	C₂⁴	1	2	yes	—
165	C₄²×C₁₃	C₂⁴	1	2	yes	—
166	C₂×#532	C₂×C₁₃	1	1	yes	characteristic
167	C₂²×#125	C₂×C₁₃	1	1	yes	characteristic, complemented
168	#3234	C₂×C₁₃	1	16	yes	direct product factor
169	C₂×#501	C₂×C₁₃	1	2	yes	complemented
170	C₂×#490	C₂×C₁₃	1	2	yes	complemented
171	C₂×#481	C₂×C₁₃	1	2	yes	complemented
172	C₂×#480	C₂×C₁₃	1	2	yes	complemented
173	C₂×#478	C₂×C₁₃	1	4	yes	complemented
174	C₂×#432	C₂×C₁₃	1	1	yes	characteristic, complemented
175	C₂³×C₁₃	—	2	2	no	—
176	C₂³×C₁₃	—	2	2	no	—
177	C₂³×C₁₃	—	2	4	no	—
178	C₂³×C₁₃	—	4	4	no	—
179	C₂³×C₁₃	—	4	4	no	—
180	C₂³×C₁₃	—	4	4	no	—
181	C₂³×C₁₃	AGL(1,ℤ/8)	1	4	yes	—
182	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
183	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
184	Q₈×C₁₃	—	4	8	no	—
185	D₄×C₁₃	—	2	8	no	—
186	D₄×C₁₃	—	4	8	no	—
187	D₄×C₁₃	—	4	8	no	—
188	D₄×C₁₃	—	4	16	no	—
189	D₄×C₁₃	—	4	4	no	—
190	C₂×C₄×C₁₃	—	2	2	no	—
191	C₂×C₄×C₁₃	—	2	2	no	—
192	C₂×C₄×C₁₃	—	2	2	no	—
193	C₂×C₄×C₁₃	—	2	8	no	—
194	C₂×C₄×C₁₃	—	2	2	no	—
195	C₂×C₄×C₁₃	—	2	2	no	—
196	C₂×C₄×C₁₃	—	2	4	no	—
197	C₂×C₄×C₁₃	—	2	4	no	—
198	C₂×C₄×C₁₃	—	2	4	no	—
199	C₂×C₄×C₁₃	—	2	4	no	—
200	C₂×C₄×C₁₃	—	2	4	no	—
201	C₂×C₄×C₁₃	—	4	4	no	—
202	C₂×C₄×C₁₃	—	4	16	no	—
203	C₂×C₄×C₁₃	—	4	8	no	—
204	C₂×C₄×C₁₃	—	4	8	no	—
205	C₂×C₄×C₁₃	—	4	4	no	—
206	C₂×C₄×C₁₃	—	4	4	no	—
207	C₂×C₄×C₁₃	—	4	4	no	—
208	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
209	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
210	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
211	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
212	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
213	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
214	C₂×C₄×C₁₃	2₋¹⁺⁴	1	4	yes	—
215	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
216	C₈×C₁₃	—	2	8	no	—
217	C₂²×#41	—	2	1	no	—
218	#532	—	2	4	no	—
219	#532	C₂²×C₁₃	1	8	yes	—
220	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
221	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
222	C₂×#125	—	2	1	no	—
223	C₂×#125	—	2	1	no	—
224	C₂×#125	—	2	4	no	—
225	C₂×#125	C₂²×C₁₃	1	2	yes	—
226	C₂×#125	C₂²×C₁₃	1	2	yes	—
227	C₂×#125	C₂²×C₁₃	1	8	yes	complemented
228	C₂×#124	—	2	1	no	—
229	C₂×#121	—	2	1	no	—
230	C₂×#121	C₂²×C₁₃	1	2	yes	—
231	C₂×C₄×D₄	—	2	1	no	—
232	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
233	C₂²×C₄⋊C₄	—	2	1	no	—
234	C₂²×C₄⋊C₄	—	2	1	no	—
235	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
236	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
237	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
238	#501	C₂²×C₁₃	1	16	yes	complemented
239	#490	C₂²×C₁₃	1	16	yes	complemented
240	#481	C₂²×C₁₃	1	16	yes	complemented
241	#480	C₂²×C₁₃	1	16	yes	complemented
242	#478	C₂²×C₁₃	1	32	yes	complemented
243	#432	C₂²×C₁₃	1	8	yes	complemented
244	C₂×#107	C₂²×C₁₃	1	4	yes	—
245	C₂×#106	C₂²×C₁₃	1	4	yes	—
246	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
247	C₂×#102	C₂²×C₁₃	1	4	yes	—
248	C₂×#102	C₂²×C₁₃	1	4	yes	—
249	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
250	C₂×#97	C₂²×C₁₃	1	2	yes	—
251	C₂²×C₁₃	—	2	2	no	—
252	C₂²×C₁₃	—	2	8	no	—
253	C₂²×C₁₃	—	2	2	no	—
254	C₂²×C₁₃	—	4	4	no	—
255	C₂²×C₁₃	—	4	4	no	—
256	C₂²×C₁₃	—	4	4	no	—
257	C₂²×C₁₃	—	8	8	no	—
258	C₂²×C₁₃	#536	1	2	yes	—
259	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	4	yes	—
260	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
261	C₂²×C₁₃	#575	1	2	yes	—
262	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
263	C₄×C₁₃	—	2	2	no	—
264	C₄×C₁₃	—	2	2	no	—
265	C₄×C₁₃	—	2	2	no	—
266	C₄×C₁₃	—	2	2	no	—
267	C₄×C₁₃	—	2	2	no	—
268	C₄×C₁₃	—	4	4	no	—
269	C₄×C₁₃	—	4	4	no	—
270	C₄×C₁₃	—	4	4	no	—
271	C₄×C₁₃	#536	1	2	yes	—
272	C₄×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
273	C₂×#41	—	2	8	no	—
274	C₂×#41	—	4	8	no	—
275	C₂²×Q₈	—	2	1	no	—
276	C₂²×D₄	—	2	2	no	—
277	C₂²×D₄	—	2	1	no	—
278	C₂²×D₄	—	2	1	no	—
279	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
280	C₂³×C₄	—	2	1	no	—
281	C₂³×C₄	—	2	1	no	—
282	C₂³×C₄	—	2	2	no	—
283	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
284	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
285	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
286	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
287	C₄⋊Q₈	—	2	2	no	—
288	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
289	#127	—	2	2	no	—
290	#127	C₂³×C₁₃	1	4	yes	—
291	#125	—	2	4	no	—
292	#125	—	2	4	no	—
293	#125	—	2	8	no	—
294	#125	—	2	8	no	—
295	#125	C₂³×C₁₃	1	8	yes	—
296	#125	C₂³×C₁₃	1	8	yes	—
297	#124	—	2	8	no	—
298	#121	—	2	8	no	—
299	#121	—	2	4	no	—
300	#121	C₂³×C₁₃	1	8	yes	—
301	C₄×D₄	—	2	8	no	—
302	C₄×D₄	—	2	4	no	—
303	C₄×D₄	C₂³×C₁₃	1	8	yes	—
304	C₂×C₄⋊C₄	—	2	2	no	—
305	C₂×C₄⋊C₄	—	2	2	no	—
306	C₂×C₄⋊C₄	—	2	2	no	—
307	C₂×C₄⋊C₄	—	2	2	no	—
308	C₂×C₄⋊C₄	—	2	8	no	—
309	C₂×C₄⋊C₄	—	2	8	no	—
310	C₂×C₄⋊C₄	—	2	1	no	—
311	C₂×C₄⋊C₄	—	2	1	no	—
312	C₂×C₄⋊C₄	—	2	2	no	—
313	C₂×C₄⋊C₄	—	2	2	no	—
314	C₂×C₄⋊C₄	—	2	1	no	—
315	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
316	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
317	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
318	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
319	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
320	C₂×C₂²⋊C₄	—	2	2	no	—
321	C₂×C₂²⋊C₄	—	2	2	no	—
322	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
323	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
324	C₂×C₄²	D₄×C₁₃	1	4	yes	—
325	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
326	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
327	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
328	#107	C₂³×C₁₃	1	16	yes	—
329	#106	C₂³×C₁₃	1	16	yes	—
330	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
331	#102	C₂³×C₁₃	1	16	yes	—
332	#102	C₂³×C₁₃	1	16	yes	—
333	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	—
334	#97	C₂³×C₁₃	1	8	yes	—
335	C₂×C₁₃	—	2	4	no	—
336	C₂×C₁₃	—	8	4	no	—
337	C₂×C₁₃	#3234	1	4	yes	direct product factor
338	C₂×C₁₃	C₂×#536	1	1	yes	characteristic
339	C₂×C₁₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
340	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
341	C₂⁴	—	2	2	no	—
342	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
343	#41	—	4	32	no	—
344	C₂×Q₈	—	2	4	no	—
345	C₂×Q₈	—	4	4	no	—
346	C₂×D₄	—	2	8	no	—
347	C₂×D₄	—	2	2	no	—
348	C₂×D₄	—	2	4	no	—
349	C₂×D₄	—	2	4	no	—
350	C₂×D₄	—	2	8	no	—
351	C₂×D₄	—	4	4	no	—
352	C₂×D₄	—	4	4	no	—
353	C₂×D₄	—	4	8	no	—
354	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
355	C₂²×C₄	—	2	4	no	—
356	C₂²×C₄	—	2	4	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	2	4	no	—
359	C₂²×C₄	—	2	4	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	2	8	no	—
363	C₂²×C₄	—	4	2	no	—
364	C₂²×C₄	—	4	8	no	—
365	C₂²×C₄	—	4	4	no	—
366	C₂²×C₄	—	4	4	no	—
367	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
368	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
369	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
370	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
371	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
372	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
373	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
374	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
375	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
376	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
377	C₂×C₈	—	2	8	no	—
378	C₂×C₈	C₂⁴×C₁₃	1	8	yes	—
379	C₄⋊C₄	—	2	8	no	—
380	C₄⋊C₄	—	2	8	no	—
381	C₄⋊C₄	—	2	8	no	—
382	C₄⋊C₄	—	2	8	no	—
383	C₄⋊C₄	—	2	4	no	—
384	C₄⋊C₄	—	2	4	no	—
385	C₄⋊C₄	—	2	2	no	—
386	C₄⋊C₄	—	2	2	no	—
387	C₄⋊C₄	—	2	4	no	—
388	C₄⋊C₄	—	2	2	no	—
389	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
390	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
391	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
392	C₂²⋊C₄	—	2	8	no	—
393	C₂²⋊C₄	—	2	8	no	—
394	C₄²	C₂×D₄×C₁₃	1	4	yes	—
395	C₄²	C₂×D₄×C₁₃	1	2	yes	—
396	C₄²	C₂×D₄×C₁₃	1	4	yes	—
397	C₄²	C₂×D₄×C₁₃	1	2	yes	—
398	C₄²	C₂⁴×C₁₃	1	2	yes	—
399	C₄²	C₂⁴×C₁₃	1	2	yes	—
400	C₁₃	C₂×#3234	1	1	yes	characteristic, direct product factor, Sylow
401	C₂³	—	2	2	no	—
402	C₂³	—	2	2	no	—
403	C₂³	—	2	4	no	—
404	C₂³	—	4	4	no	—
405	C₂³	—	4	4	no	—
406	C₂³	—	4	4	no	—
407	C₂³	C₁₃×AGL(1,ℤ/8)	1	4	yes	—
408	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
409	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
410	Q₈	—	4	8	no	—
411	D₄	—	2	8	no	—
412	D₄	—	4	8	no	—
413	D₄	—	4	8	no	—
414	D₄	—	4	16	no	—
415	D₄	—	4	4	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	8	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	4	no	—
423	C₂×C₄	—	2	4	no	—
424	C₂×C₄	—	2	4	no	—
425	C₂×C₄	—	2	4	no	—
426	C₂×C₄	—	2	4	no	—
427	C₂×C₄	—	4	4	no	—
428	C₂×C₄	—	4	16	no	—
429	C₂×C₄	—	4	8	no	—
430	C₂×C₄	—	4	4	no	—
431	C₂×C₄	—	4	8	no	—
432	C₂×C₄	—	4	4	no	—
433	C₂×C₄	—	4	4	no	—
434	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
435	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
436	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
437	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
438	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
439	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
440	C₂×C₄	C₁₃×2₋¹⁺⁴	1	4	yes	—
441	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
442	C₈	—	2	8	no	—
443	C₂²	—	2	2	no	—
444	C₂²	—	2	2	no	—
445	C₂²	—	2	8	no	—
446	C₂²	—	4	4	no	—
447	C₂²	—	4	4	no	—
448	C₂²	—	4	4	no	—
449	C₂²	—	8	8	no	—
450	C₂²	C₁₃×#536	1	2	yes	—
451	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	4	yes	—
452	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
453	C₂²	C₁₃×#575	1	2	yes	—
454	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
455	C₄	—	2	2	no	—
456	C₄	—	2	2	no	—
457	C₄	—	2	2	no	—
458	C₄	—	2	2	no	—
459	C₄	—	2	2	no	—
460	C₄	—	4	4	no	—
461	C₄	—	4	4	no	—
462	C₄	—	4	4	no	—
463	C₄	C₁₃×#536	1	2	yes	—
464	C₄	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
465	C₂	—	2	4	no	—
466	C₂	—	8	4	no	—
467	C₂	C₁₃×#3234	1	4	yes	direct product factor
468	C₂	C₂×C₁₃×#536	1	1	yes	characteristic
469	C₂	C₂²×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
470	C₂	C₂×C₁₃×#575	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₂×C₁₃×#532	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ 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. C₂²×C₁₃×#125	C₂	semidirect
3. C₁₃×#3234	C₂	direct (N × H)
4. C₂×C₁₃×#501	C₂	semidirect
5. C₂×C₁₃×#490	C₂	semidirect
6. C₂×C₁₃×#481	C₂	semidirect
7. C₂×C₁₃×#480	C₂	semidirect
8. C₂×C₁₃×#478	C₂	semidirect
9. C₂×C₁₃×#432	C₂	semidirect
20. C₂×C₁₃×#125	C₂²	semidirect
31. C₁₃×#501	C₂²	semidirect
32. C₁₃×#490	C₂²	semidirect
33. C₁₃×#481	C₂²	semidirect
34. C₁₃×#480	C₂²	semidirect
35. C₁₃×#478	C₂²	semidirect
36. C₁₃×#432	C₂²	semidirect
106. C₂×#3234	C₁₃	direct (N × H)
167. C₂²×#125	C₂×C₁₃	semidirect
168. #3234	C₂×C₁₃	direct (N × H)
169. C₂×#501	C₂×C₁₃	semidirect
170. C₂×#490	C₂×C₁₃	semidirect
171. C₂×#481	C₂×C₁₃	semidirect
172. C₂×#480	C₂×C₁₃	semidirect
173. C₂×#478	C₂×C₁₃	semidirect
174. C₂×#432	C₂×C₁₃	semidirect
227. C₂×#125	C₂²×C₁₃	semidirect
238. #501	C₂²×C₁₃	semidirect
239. #490	C₂²×C₁₃	semidirect
240. #481	C₂²×C₁₃	semidirect
241. #480	C₂²×C₁₃	semidirect
242. #478	C₂²×C₁₃	semidirect
243. #432	C₂²×C₁₃	semidirect
337. C₂×C₁₃	#3234	direct (N × H)
400. C₁₃	C₂×#3234	direct (N × H)
467. C₂	C₁₃×#3234	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
C₂²×C₁₃×#125	2
C₁₃×#3234	2
C₂×C₁₃×#501	2
C₂×C₁₃×#490	2
C₂×C₁₃×#481	2
C₂×C₁₃×#480	2
C₂×C₁₃×#478	2
C₂×C₁₃×#432	2
C₂×#3234	13

Subgroups — C2×C13×#3234 #15747186

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3234 #15747186