Subgroups — C₂×C₁₃×#3231 #15747183

Order 3328.

1778 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#533	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#533	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3231	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#500	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#498	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃×#487	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#487	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#485	C₂	1	4	yes	maximal
9	C₂×C₁₃×#479	C₂	1	4	yes	maximal, complemented
10	C₂×C₁₃×#431	C₂	1	1	yes	maximal, characteristic
11	C₁₃×#533	—	2	4	no	—
12	C₁₃×#533	—	2	4	no	—
13	C₁₃×#533	C₂²	1	8	yes	—
14	C₁₃×#533	C₂²	1	8	yes	—
15	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#125	—	2	1	no	—
20	C₂×C₁₃×#125	C₂²	1	2	yes	—
21	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
22	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
23	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
24	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
25	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
26	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
27	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
28	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
29	C₂×C₁₃×#117	—	2	1	no	—
30	C₂×C₁₃×#117	C₂²	1	2	yes	—
31	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
32	C₁₃×#500	C₂²	1	8	yes	complemented
33	C₁₃×#498	C₂²	1	8	yes	complemented
34	C₁₃×#487	C₂²	1	8	yes	complemented
35	C₁₃×#487	C₂²	1	8	yes	complemented
36	C₁₃×#485	C₂²	1	32	yes	—
37	C₁₃×#479	C₂²	1	32	yes	complemented
38	C₁₃×#431	C₂²	1	8	yes	—
39	C₂×C₁₃×#107	C₂²	1	4	yes	—
40	C₂×C₁₃×#106	C₂²	1	4	yes	—
41	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
42	C₂×C₁₃×#103	C₂²	1	4	yes	—
43	C₂×C₁₃×#103	C₂²	1	4	yes	—
44	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
45	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
46	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
47	C₂²×Q₈×C₁₃	—	2	1	no	—
48	C₂²×Q₈×C₁₃	—	2	1	no	—
49	C₂²×Q₈×C₁₃	—	2	1	no	—
50	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
51	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
52	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
53	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
55	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
56	C₁₃×C₄⋊Q₈	—	2	2	no	—
57	C₁₃×C₄⋊Q₈	—	2	2	no	—
58	C₁₃×C₄⋊Q₈	—	2	2	no	—
59	C₁₃×C₄⋊Q₈	—	2	2	no	—
60	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
61	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
62	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
63	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
64	C₁₃×#125	—	2	8	no	—
65	C₁₃×#125	—	2	4	no	—
66	C₁₃×#125	C₂³	1	8	yes	—
67	C₁₃×C₂²⋊Q₈	—	2	8	no	—
68	C₁₃×C₂²⋊Q₈	—	2	8	no	—
69	C₁₃×C₂²⋊Q₈	—	2	8	no	—
70	C₁₃×C₂²⋊Q₈	—	2	4	no	—
71	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
72	C₄×Q₈×C₁₃	—	2	8	no	—
73	C₄×Q₈×C₁₃	—	2	8	no	—
74	C₄×Q₈×C₁₃	—	2	8	no	—
75	C₄×Q₈×C₁₃	—	2	4	no	—
76	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
77	C₁₃×#117	—	2	8	no	—
78	C₁₃×#117	—	2	4	no	—
79	C₁₃×#117	C₂³	1	8	yes	—
80	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
81	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
82	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
83	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
84	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
85	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
86	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
87	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
88	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
89	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
90	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
91	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
92	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
93	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
94	C₂×C₄²×C₁₃	—	2	2	no	—
95	C₂×C₄²×C₁₃	—	2	2	no	—
96	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
97	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
98	C₂×C₄²×C₁₃	D₄	1	4	yes	—
99	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
100	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
101	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
102	C₁₃×#107	C₂³	1	16	yes	—
103	C₁₃×#106	C₂³	1	16	yes	—
104	C₁₃×C₄⋊C₈	C₂³	1	8	yes	—
105	C₁₃×#103	C₂³	1	16	yes	—
106	C₁₃×#103	C₂³	1	16	yes	—
107	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	—
108	C₄×C₈×C₁₃	C₂³	1	4	yes	—
109	C₄×C₈×C₁₃	C₂³	1	4	yes	—
110	C₂×#3231	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
111	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
112	C₂×Q₈×C₁₃	—	2	2	no	—
113	C₂×Q₈×C₁₃	—	2	4	no	—
114	C₂×Q₈×C₁₃	—	2	4	no	—
115	C₂×Q₈×C₁₃	—	2	4	no	—
116	C₂×Q₈×C₁₃	—	2	8	no	—
117	C₂×Q₈×C₁₃	—	4	4	no	—
118	C₂×Q₈×C₁₃	—	4	4	no	—
119	C₂×Q₈×C₁₃	—	4	4	no	—
120	C₂×Q₈×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	2	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	C₂×D₄	1	2	yes	—
129	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
130	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
131	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
137	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
138	C₂×C₈×C₁₃	—	2	4	no	—
139	C₂×C₈×C₁₃	—	2	4	no	—
140	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
141	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
142	C₁₃×C₄⋊C₄	—	2	4	no	—
143	C₁₃×C₄⋊C₄	—	2	4	no	—
144	C₁₃×C₄⋊C₄	—	2	8	no	—
145	C₁₃×C₄⋊C₄	—	2	8	no	—
146	C₁₃×C₄⋊C₄	—	2	4	no	—
147	C₁₃×C₄⋊C₄	—	2	4	no	—
148	C₁₃×C₄⋊C₄	—	2	4	no	—
149	C₁₃×C₄⋊C₄	—	2	8	no	—
150	C₁₃×C₄⋊C₄	—	2	8	no	—
151	C₁₃×C₄⋊C₄	—	2	2	no	—
152	C₁₃×C₄⋊C₄	—	2	2	no	—
153	C₁₃×C₄⋊C₄	—	2	2	no	—
154	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
155	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
156	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
157	C₁₃×C₂²⋊C₄	—	2	8	no	—
158	C₁₃×C₂²⋊C₄	—	2	8	no	—
159	C₄²×C₁₃	—	2	8	no	—
160	C₄²×C₁₃	—	2	8	no	—
161	C₄²×C₁₃	C₂×D₄	1	4	yes	—
162	C₄²×C₁₃	C₂×D₄	1	4	yes	—
163	C₄²×C₁₃	C₂×D₄	1	2	yes	—
164	C₄²×C₁₃	C₂×D₄	1	2	yes	—
165	C₄²×C₁₃	C₂⁴	1	2	yes	—
166	C₄²×C₁₃	C₂⁴	1	2	yes	—
167	C₂×#533	C₂×C₁₃	1	1	yes	characteristic
168	C₂×#533	C₂×C₁₃	1	1	yes	characteristic
169	#3231	C₂×C₁₃	1	16	yes	direct product factor
170	C₂×#500	C₂×C₁₃	1	1	yes	characteristic, complemented
171	C₂×#498	C₂×C₁₃	1	1	yes	characteristic, complemented
172	C₂×#487	C₂×C₁₃	1	1	yes	characteristic, complemented
173	C₂×#487	C₂×C₁₃	1	1	yes	characteristic, complemented
174	C₂×#485	C₂×C₁₃	1	4	yes	—
175	C₂×#479	C₂×C₁₃	1	4	yes	complemented
176	C₂×#431	C₂×C₁₃	1	1	yes	characteristic
177	C₂³×C₁₃	—	2	2	no	—
178	C₂³×C₁₃	—	2	2	no	—
179	C₂³×C₁₃	—	2	2	no	—
180	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
181	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
182	Q₈×C₁₃	—	2	8	no	—
183	Q₈×C₁₃	—	4	4	no	—
184	Q₈×C₁₃	—	4	8	no	—
185	Q₈×C₁₃	—	4	8	no	—
186	Q₈×C₁₃	—	4	8	no	—
187	C₂×C₄×C₁₃	—	2	2	no	—
188	C₂×C₄×C₁₃	—	2	2	no	—
189	C₂×C₄×C₁₃	—	2	2	no	—
190	C₂×C₄×C₁₃	—	2	4	no	—
191	C₂×C₄×C₁₃	—	2	8	no	—
192	C₂×C₄×C₁₃	—	2	8	no	—
193	C₂×C₄×C₁₃	—	2	4	no	—
194	C₂×C₄×C₁₃	—	2	4	no	—
195	C₂×C₄×C₁₃	—	2	4	no	—
196	C₂×C₄×C₁₃	—	2	4	no	—
197	C₂×C₄×C₁₃	—	2	4	no	—
198	C₂×C₄×C₁₃	—	4	4	no	—
199	C₂×C₄×C₁₃	—	4	4	no	—
200	C₂×C₄×C₁₃	—	4	4	no	—
201	C₂×C₄×C₁₃	—	4	4	no	—
202	C₂×C₄×C₁₃	#135	1	4	yes	—
203	C₂×C₄×C₁₃	#137	1	4	yes	—
204	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
205	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
206	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
207	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
208	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
209	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
210	C₂×C₄×C₁₃	2₋¹⁺⁴	1	4	yes	—
211	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
212	C₈×C₁₃	—	2	4	no	—
213	C₈×C₁₃	—	2	4	no	—
214	#533	—	2	4	no	—
215	#533	—	2	4	no	—
216	#533	C₂²×C₁₃	1	8	yes	—
217	#533	C₂²×C₁₃	1	8	yes	—
218	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
219	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
220	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
221	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
222	C₂×#125	—	2	1	no	—
223	C₂×#125	C₂²×C₁₃	1	2	yes	—
224	C₂×C₂²⋊Q₈	—	2	1	no	—
225	C₂×C₂²⋊Q₈	—	2	1	no	—
226	C₂×C₂²⋊Q₈	—	2	1	no	—
227	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
228	C₂×C₄×Q₈	—	2	1	no	—
229	C₂×C₄×Q₈	—	2	1	no	—
230	C₂×C₄×Q₈	—	2	1	no	—
231	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
232	C₂×#117	—	2	1	no	—
233	C₂×#117	C₂²×C₁₃	1	2	yes	—
234	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
235	#500	C₂²×C₁₃	1	8	yes	complemented
236	#498	C₂²×C₁₃	1	8	yes	complemented
237	#487	C₂²×C₁₃	1	8	yes	complemented
238	#487	C₂²×C₁₃	1	8	yes	complemented
239	#485	C₂²×C₁₃	1	32	yes	—
240	#479	C₂²×C₁₃	1	32	yes	complemented
241	#431	C₂²×C₁₃	1	8	yes	—
242	C₂×#107	C₂²×C₁₃	1	4	yes	—
243	C₂×#106	C₂²×C₁₃	1	4	yes	—
244	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
245	C₂×#103	C₂²×C₁₃	1	4	yes	—
246	C₂×#103	C₂²×C₁₃	1	4	yes	—
247	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
248	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
249	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
250	C₂²×C₁₃	—	2	2	no	—
251	C₂²×C₁₃	—	2	2	no	—
252	C₂²×C₁₃	—	2	2	no	—
253	C₂²×C₁₃	—	4	4	no	—
254	C₂²×C₁₃	#536	1	2	yes	—
255	C₂²×C₁₃	C₂×#135	1	2	yes	—
256	C₂²×C₁₃	C₂×#137	1	2	yes	—
257	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
258	C₄×C₁₃	—	2	2	no	—
259	C₄×C₁₃	—	2	2	no	—
260	C₄×C₁₃	—	2	2	no	—
261	C₄×C₁₃	—	4	4	no	—
262	C₄×C₁₃	—	4	4	no	—
263	C₄×C₁₃	—	4	4	no	—
264	C₄×C₁₃	—	4	4	no	—
265	C₄×C₁₃	#536	1	2	yes	—
266	C₄×C₁₃	C₂×#135	1	4	yes	—
267	C₄×C₁₃	C₂×#137	1	4	yes	—
268	C₄×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
269	C₂²×Q₈	—	2	1	no	—
270	C₂²×Q₈	—	2	1	no	—
271	C₂²×Q₈	—	2	1	no	—
272	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
273	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
274	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
275	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
276	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
277	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
278	C₄⋊Q₈	—	2	2	no	—
279	C₄⋊Q₈	—	2	2	no	—
280	C₄⋊Q₈	—	2	2	no	—
281	C₄⋊Q₈	—	2	2	no	—
282	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
283	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
284	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
285	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
286	#125	—	2	8	no	—
287	#125	—	2	4	no	—
288	#125	C₂³×C₁₃	1	8	yes	—
289	C₂²⋊Q₈	—	2	8	no	—
290	C₂²⋊Q₈	—	2	8	no	—
291	C₂²⋊Q₈	—	2	8	no	—
292	C₂²⋊Q₈	—	2	4	no	—
293	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
294	C₄×Q₈	—	2	8	no	—
295	C₄×Q₈	—	2	8	no	—
296	C₄×Q₈	—	2	8	no	—
297	C₄×Q₈	—	2	4	no	—
298	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
299	#117	—	2	8	no	—
300	#117	—	2	4	no	—
301	#117	C₂³×C₁₃	1	8	yes	—
302	C₂×C₄⋊C₄	—	2	1	no	—
303	C₂×C₄⋊C₄	—	2	1	no	—
304	C₂×C₄⋊C₄	—	2	2	no	—
305	C₂×C₄⋊C₄	—	2	2	no	—
306	C₂×C₄⋊C₄	—	2	1	no	—
307	C₂×C₄⋊C₄	—	2	1	no	—
308	C₂×C₄⋊C₄	—	2	1	no	—
309	C₂×C₄⋊C₄	—	2	2	no	—
310	C₂×C₄⋊C₄	—	2	2	no	—
311	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
312	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
313	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
314	C₂×C₂²⋊C₄	—	2	2	no	—
315	C₂×C₂²⋊C₄	—	2	2	no	—
316	C₂×C₄²	—	2	2	no	—
317	C₂×C₄²	—	2	2	no	—
318	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
319	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
320	C₂×C₄²	D₄×C₁₃	1	4	yes	—
321	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
322	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
323	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
324	#107	C₂³×C₁₃	1	16	yes	—
325	#106	C₂³×C₁₃	1	16	yes	—
326	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
327	#103	C₂³×C₁₃	1	16	yes	—
328	#103	C₂³×C₁₃	1	16	yes	—
329	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	—
330	C₄×C₈	C₂³×C₁₃	1	4	yes	—
331	C₄×C₈	C₂³×C₁₃	1	4	yes	—
332	C₂×C₁₃	—	4	2	no	—
333	C₂×C₁₃	#3231	1	4	yes	direct product factor
334	C₂×C₁₃	C₂×#536	1	1	yes	characteristic
335	C₂×C₁₃	C₂²×#135	1	1	yes	characteristic
336	C₂×C₁₃	C₂²×#137	1	1	yes	characteristic
337	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
338	C₂×Q₈	—	2	2	no	—
339	C₂×Q₈	—	2	4	no	—
340	C₂×Q₈	—	2	4	no	—
341	C₂×Q₈	—	2	4	no	—
342	C₂×Q₈	—	2	8	no	—
343	C₂×Q₈	—	4	4	no	—
344	C₂×Q₈	—	4	4	no	—
345	C₂×Q₈	—	4	4	no	—
346	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
347	C₂²×C₄	—	2	4	no	—
348	C₂²×C₄	—	2	4	no	—
349	C₂²×C₄	—	2	4	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
355	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
356	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
357	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
358	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
359	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
360	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
361	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
362	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
363	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
364	C₂×C₈	—	2	4	no	—
365	C₂×C₈	—	2	4	no	—
366	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
367	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
368	C₄⋊C₄	—	2	4	no	—
369	C₄⋊C₄	—	2	4	no	—
370	C₄⋊C₄	—	2	8	no	—
371	C₄⋊C₄	—	2	8	no	—
372	C₄⋊C₄	—	2	4	no	—
373	C₄⋊C₄	—	2	4	no	—
374	C₄⋊C₄	—	2	4	no	—
375	C₄⋊C₄	—	2	8	no	—
376	C₄⋊C₄	—	2	8	no	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
381	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
382	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
383	C₂²⋊C₄	—	2	8	no	—
384	C₂²⋊C₄	—	2	8	no	—
385	C₄²	—	2	8	no	—
386	C₄²	—	2	8	no	—
387	C₄²	C₂×D₄×C₁₃	1	4	yes	—
388	C₄²	C₂×D₄×C₁₃	1	4	yes	—
389	C₄²	C₂×D₄×C₁₃	1	2	yes	—
390	C₄²	C₂×D₄×C₁₃	1	2	yes	—
391	C₄²	C₂⁴×C₁₃	1	2	yes	—
392	C₄²	C₂⁴×C₁₃	1	2	yes	—
393	C₁₃	C₂×#3231	1	1	yes	characteristic, direct product factor, Sylow
394	C₂³	—	2	2	no	—
395	C₂³	—	2	2	no	—
396	C₂³	—	2	2	no	—
397	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
398	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
399	Q₈	—	2	8	no	—
400	Q₈	—	4	4	no	—
401	Q₈	—	4	8	no	—
402	Q₈	—	4	8	no	—
403	Q₈	—	4	8	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	2	8	no	—
409	C₂×C₄	—	2	8	no	—
410	C₂×C₄	—	2	4	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	4	no	—
413	C₂×C₄	—	2	4	no	—
414	C₂×C₄	—	2	4	no	—
415	C₂×C₄	—	4	4	no	—
416	C₂×C₄	—	4	4	no	—
417	C₂×C₄	—	4	4	no	—
418	C₂×C₄	—	4	4	no	—
419	C₂×C₄	C₁₃×#135	1	4	yes	—
420	C₂×C₄	C₁₃×#137	1	4	yes	—
421	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
422	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
423	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
424	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
425	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
426	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
427	C₂×C₄	C₁₃×2₋¹⁺⁴	1	4	yes	—
428	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
429	C₈	—	2	4	no	—
430	C₈	—	2	4	no	—
431	C₂²	—	2	2	no	—
432	C₂²	—	2	2	no	—
433	C₂²	—	2	2	no	—
434	C₂²	—	4	4	no	—
435	C₂²	C₁₃×#536	1	2	yes	—
436	C₂²	C₂×C₁₃×#135	1	2	yes	—
437	C₂²	C₂×C₁₃×#137	1	2	yes	—
438	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
439	C₄	—	2	2	no	—
440	C₄	—	2	2	no	—
441	C₄	—	2	2	no	—
442	C₄	—	4	4	no	—
443	C₄	—	4	4	no	—
444	C₄	—	4	4	no	—
445	C₄	—	4	4	no	—
446	C₄	C₁₃×#536	1	2	yes	—
447	C₄	C₂×C₁₃×#135	1	4	yes	—
448	C₄	C₂×C₁₃×#137	1	4	yes	—
449	C₄	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
450	C₂	—	4	2	no	—
451	C₂	C₁₃×#3231	1	4	yes	direct product factor
452	C₂	C₂×C₁₃×#536	1	1	yes	characteristic
453	C₂	C₂²×C₁₃×#135	1	1	yes	characteristic
454	C₂	C₂²×C₁₃×#137	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₂⁴×C₁₃	C₂×D₄
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
3. C₁₃×#3231	C₂	direct (N × H)
4. C₂×C₁₃×#500	C₂	semidirect
5. C₂×C₁₃×#498	C₂	semidirect
6. C₂×C₁₃×#487	C₂	semidirect
7. C₂×C₁₃×#487	C₂	semidirect
9. C₂×C₁₃×#479	C₂	semidirect
32. C₁₃×#500	C₂²	semidirect
33. C₁₃×#498	C₂²	semidirect
34. C₁₃×#487	C₂²	semidirect
35. C₁₃×#487	C₂²	semidirect
37. C₁₃×#479	C₂²	semidirect
110. C₂×#3231	C₁₃	direct (N × H)
169. #3231	C₂×C₁₃	direct (N × H)
170. C₂×#500	C₂×C₁₃	semidirect
171. C₂×#498	C₂×C₁₃	semidirect
172. C₂×#487	C₂×C₁₃	semidirect
173. C₂×#487	C₂×C₁₃	semidirect
175. C₂×#479	C₂×C₁₃	semidirect
235. #500	C₂²×C₁₃	semidirect
236. #498	C₂²×C₁₃	semidirect
237. #487	C₂²×C₁₃	semidirect
238. #487	C₂²×C₁₃	semidirect
240. #479	C₂²×C₁₃	semidirect
333. C₂×C₁₃	#3231	direct (N × H)
393. C₁₃	C₂×#3231	direct (N × H)
451. C₂	C₁₃×#3231	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×#533	2
C₁₃×#3231	2
C₂×C₁₃×#500	2
C₂×C₁₃×#498	2
C₂×C₁₃×#487	2
C₂×C₁₃×#485	2
C₂×C₁₃×#479	2
C₂×C₁₃×#431	2
C₂×#3231	13

Subgroups — C2×C13×#3231 #15747183

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3231 #15747183