Subgroups — C₂×C₁₃×#3365 #15747641

Order 3328.

1894 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#559	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#557	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3365	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#488	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₃×#486	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₃×#475	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#478	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×#464	C₂	1	2	yes	maximal, complemented
9	C₂×C₁₃×#460	C₂	1	1	yes	maximal, characteristic
10	C₂×C₈×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄×C₁₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄×C₁₃×SD₁₆	C₂	1	2	yes	maximal, complemented
13	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
14	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
15	C₁₃×#559	—	2	4	no	—
16	C₁₃×#559	C₂²	1	8	yes	—
17	C₁₃×#557	—	2	4	no	—
18	C₁₃×#557	C₂²	1	8	yes	complemented
19	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
20	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#125	—	2	2	no	—
23	C₂×C₁₃×#125	C₂²	1	2	yes	—
24	C₂×C₁₃×#124	—	2	1	no	—
25	C₂×C₁₃×#124	C₂²	1	2	yes	—
26	C₂×C₁₃×#123	—	2	2	no	—
27	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
28	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
29	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
30	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
31	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₁₃	—	2	1	no	—
33	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
34	C₁₃×#488	C₂²	1	16	yes	complemented
35	C₁₃×#486	C₂²	1	8	yes	—
36	C₁₃×#478	C₂²	1	16	yes	complemented
37	C₁₃×#475	C₂²	1	8	yes	complemented
38	C₁₃×#464	C₂²	1	16	yes	complemented
39	C₁₃×#460	C₂²	1	8	yes	—
40	C₈×Q₈×C₁₃	C₂²	1	8	yes	complemented
41	C₄×C₁₃×Q₁₆	C₂²	1	8	yes	complemented
42	C₄×C₁₃×SD₁₆	C₂²	1	16	yes	complemented
43	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
44	C₂×C₁₃×#106	C₂²	1	2	yes	—
45	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
46	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
47	C₂×C₁₃×#103	C₂²	1	2	yes	—
48	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
49	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
50	C₂×C₁₃×#102	C₂²	1	2	yes	—
51	C₂×C₁₃×#102	C₂²	1	2	yes	—
52	C₂×C₁₃×#102	C₂²	1	2	yes	—
53	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
54	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
55	C₂²×Q₈×C₁₃	—	2	1	no	—
56	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
57	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
58	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
59	C₂²×D₄×C₁₃	—	2	1	no	—
60	C₂²×D₄×C₁₃	—	2	1	no	—
61	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
62	C₂³×C₄×C₁₃	—	2	2	no	—
63	C₂×C₁₃×Q₁₆	—	2	4	no	—
64	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
65	C₂×C₁₃×SD₁₆	—	2	8	no	—
66	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
67	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
68	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
69	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
70	C₁₃×C₄⋊Q₈	—	2	8	no	—
71	C₁₃×C₄⋊Q₈	—	2	2	no	—
72	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
73	C₁₃×#127	—	2	2	no	—
74	C₁₃×#127	C₂³	1	4	yes	—
75	C₁₃×#125	—	2	16	no	—
76	C₁₃×#125	—	2	4	no	—
77	C₁₃×#125	C₂³	1	8	yes	—
78	C₁₃×#124	—	2	8	no	—
79	C₁₃×#124	—	2	4	no	—
80	C₁₃×#124	C₂³	1	8	yes	—
81	C₁₃×#123	—	2	16	no	—
82	C₄×Q₈×C₁₃	—	2	8	no	—
83	C₄×Q₈×C₁₃	—	2	4	no	—
84	C₄×Q₈×C₁₃	—	2	2	no	—
85	C₄×Q₈×C₁₃	—	2	2	no	—
86	C₄×Q₈×C₁₃	D₄	1	4	yes	—
87	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
88	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
89	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
90	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
91	C₄×D₄×C₁₃	—	2	8	no	—
92	C₄×D₄×C₁₃	—	2	4	no	—
93	C₄×D₄×C₁₃	C₂³	1	8	yes	—
94	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
95	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
96	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
97	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
98	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
99	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
100	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
101	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
102	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
103	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
104	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
105	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
106	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
107	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
108	C₂×C₄²×C₁₃	—	2	1	no	—
109	C₂×C₄²×C₁₃	—	2	2	no	—
110	C₂×C₄²×C₁₃	—	2	1	no	—
111	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
112	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
113	C₁₃×#107	C₂³	1	4	yes	—
114	C₁₃×#106	C₂³	1	8	yes	—
115	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
116	C₁₃×C₄⋊C₈	C₂³	1	8	yes	—
117	C₁₃×#103	C₂³	1	4	yes	—
118	C₁₃×#103	C₂³	1	4	yes	—
119	C₁₃×#103	C₂³	1	8	yes	—
120	C₁₃×#102	C₂³	1	8	yes	—
121	C₁₃×#102	C₂³	1	8	yes	—
122	C₁₃×#102	C₂³	1	8	yes	—
123	C₄×C₈×C₁₃	C₂³	1	8	yes	—
124	C₄×C₈×C₁₃	C₂³	1	4	yes	—
125	C₂×#3365	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
126	C₂⁴×C₁₃	—	2	2	no	—
127	C₂×Q₈×C₁₃	—	2	4	no	—
128	C₂×Q₈×C₁₃	—	2	1	no	—
129	C₂×Q₈×C₁₃	—	2	1	no	—
130	C₂×Q₈×C₁₃	—	2	4	no	—
131	C₂×Q₈×C₁₃	—	2	2	no	—
132	C₂×Q₈×C₁₃	—	2	2	no	—
133	C₂×Q₈×C₁₃	—	2	2	no	—
134	C₂×Q₈×C₁₃	—	4	4	no	—
135	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
136	C₂×Q₈×C₁₃	#41	1	4	yes	—
137	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
138	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
139	C₂×D₄×C₁₃	—	2	2	no	—
140	C₂×D₄×C₁₃	—	2	4	no	—
141	C₂×D₄×C₁₃	—	2	4	no	—
142	C₂×D₄×C₁₃	—	2	4	no	—
143	C₂×D₄×C₁₃	—	2	4	no	—
144	C₂×D₄×C₁₃	—	4	4	no	—
145	C₂×D₄×C₁₃	—	8	2	no	—
146	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
147	C₂²×C₄×C₁₃	—	2	1	no	—
148	C₂²×C₄×C₁₃	—	2	1	no	—
149	C₂²×C₄×C₁₃	—	2	1	no	—
150	C₂²×C₄×C₁₃	—	2	1	no	—
151	C₂²×C₄×C₁₃	—	2	2	no	—
152	C₂²×C₄×C₁₃	—	2	8	no	—
153	C₂²×C₄×C₁₃	—	8	4	no	—
154	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
155	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
156	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
159	C₁₃×Q₁₆	—	2	8	no	—
160	C₁₃×SD₁₆	—	2	16	no	—
161	C₂×C₈×C₁₃	—	2	4	no	—
162	C₂×C₈×C₁₃	—	2	2	no	—
163	C₂×C₈×C₁₃	—	2	2	no	—
164	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
165	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
166	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
167	C₁₃×C₄⋊C₄	—	2	8	no	—
168	C₁₃×C₄⋊C₄	—	2	4	no	—
169	C₁₃×C₄⋊C₄	—	2	4	no	—
170	C₁₃×C₄⋊C₄	—	2	8	no	—
171	C₁₃×C₄⋊C₄	—	2	4	no	—
172	C₁₃×C₄⋊C₄	—	2	8	no	—
173	C₁₃×C₄⋊C₄	—	2	1	no	—
174	C₁₃×C₄⋊C₄	—	2	1	no	—
175	C₁₃×C₄⋊C₄	—	2	2	no	—
176	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
177	C₁₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
178	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
179	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
180	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
181	C₁₃×C₂²⋊C₄	—	2	8	no	—
182	C₁₃×C₂²⋊C₄	—	2	8	no	—
183	C₁₃×C₂²⋊C₄	—	2	8	no	—
184	C₄²×C₁₃	—	2	4	no	—
185	C₄²×C₁₃	—	2	8	no	—
186	C₄²×C₁₃	—	2	4	no	—
187	C₄²×C₁₃	C₂×D₄	1	4	yes	—
188	C₄²×C₁₃	C₂×D₄	1	2	yes	—
189	C₄²×C₁₃	C₂⁴	1	4	yes	—
190	C₄²×C₁₃	C₂⁴	1	2	yes	—
191	C₂×#559	C₂×C₁₃	1	1	yes	characteristic
192	C₂×#557	C₂×C₁₃	1	1	yes	characteristic, complemented
193	#3365	C₂×C₁₃	1	16	yes	direct product factor
194	C₂×#488	C₂×C₁₃	1	2	yes	complemented
195	C₂×#486	C₂×C₁₃	1	1	yes	characteristic
196	C₂×#475	C₂×C₁₃	1	1	yes	characteristic, complemented
197	C₂×#478	C₂×C₁₃	1	2	yes	complemented
198	C₂×#464	C₂×C₁₃	1	2	yes	complemented
199	C₂×#460	C₂×C₁₃	1	1	yes	characteristic
200	C₂×C₈×Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
201	C₂×C₄×Q₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
202	C₂×C₄×SD₁₆	C₂×C₁₃	1	2	yes	complemented
203	C₂³×C₁₃	—	2	4	no	—
204	C₂³×C₁₃	—	4	4	no	—
205	C₂³×C₁₃	—	4	4	no	—
206	C₂³×C₁₃	—	4	4	no	—
207	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
208	Q₈×C₁₃	—	2	4	no	—
209	Q₈×C₁₃	—	2	8	no	—
210	Q₈×C₁₃	—	2	2	no	—
211	Q₈×C₁₃	—	2	2	no	—
212	Q₈×C₁₃	—	2	2	no	—
213	Q₈×C₁₃	—	4	2	no	—
214	Q₈×C₁₃	—	4	8	no	—
215	Q₈×C₁₃	C₂×#41	1	4	yes	—
216	D₄×C₁₃	—	2	4	no	—
217	D₄×C₁₃	—	2	4	no	—
218	D₄×C₁₃	—	4	4	no	—
219	D₄×C₁₃	—	4	8	no	—
220	D₄×C₁₃	—	8	4	no	—
221	C₂×C₄×C₁₃	—	2	4	no	—
222	C₂×C₄×C₁₃	—	2	4	no	—
223	C₂×C₄×C₁₃	—	2	4	no	—
224	C₂×C₄×C₁₃	—	2	2	no	—
225	C₂×C₄×C₁₃	—	2	2	no	—
226	C₂×C₄×C₁₃	—	2	2	no	—
227	C₂×C₄×C₁₃	—	2	2	no	—
228	C₂×C₄×C₁₃	—	2	2	no	—
229	C₂×C₄×C₁₃	—	2	4	no	—
230	C₂×C₄×C₁₃	—	4	2	no	—
231	C₂×C₄×C₁₃	—	4	4	no	—
232	C₂×C₄×C₁₃	—	4	2	no	—
233	C₂×C₄×C₁₃	—	4	2	no	—
234	C₂×C₄×C₁₃	—	8	8	no	—
235	C₂×C₄×C₁₃	#135	1	4	yes	—
236	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
237	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
238	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
239	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
240	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
241	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
242	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
243	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
244	C₈×C₁₃	—	2	4	no	—
245	C₈×C₁₃	—	2	2	no	—
246	C₈×C₁₃	—	2	2	no	—
247	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
248	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
249	#559	—	2	4	no	—
250	#559	C₂²×C₁₃	1	8	yes	—
251	#557	—	2	4	no	—
252	#557	C₂²×C₁₃	1	8	yes	complemented
253	C₂×C₄⋊Q₈	—	2	1	no	—
254	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
255	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
256	C₂×#125	—	2	2	no	—
257	C₂×#125	C₂²×C₁₃	1	2	yes	—
258	C₂×#124	—	2	1	no	—
259	C₂×#124	C₂²×C₁₃	1	2	yes	—
260	C₂×#123	—	2	2	no	—
261	C₂×C₄×Q₈	—	2	1	no	—
262	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
263	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
264	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
265	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
266	C₂×C₄×D₄	—	2	1	no	—
267	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
268	#488	C₂²×C₁₃	1	16	yes	complemented
269	#486	C₂²×C₁₃	1	8	yes	—
270	#478	C₂²×C₁₃	1	16	yes	complemented
271	#475	C₂²×C₁₃	1	8	yes	complemented
272	#464	C₂²×C₁₃	1	16	yes	complemented
273	#460	C₂²×C₁₃	1	8	yes	—
274	C₈×Q₈	C₂²×C₁₃	1	8	yes	complemented
275	C₄×Q₁₆	C₂²×C₁₃	1	8	yes	complemented
276	C₄×SD₁₆	C₂²×C₁₃	1	16	yes	complemented
277	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
278	C₂×#106	C₂²×C₁₃	1	2	yes	—
279	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
280	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
281	C₂×#103	C₂²×C₁₃	1	2	yes	—
282	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
283	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
284	C₂×#102	C₂²×C₁₃	1	2	yes	—
285	C₂×#102	C₂²×C₁₃	1	2	yes	—
286	C₂×#102	C₂²×C₁₃	1	2	yes	—
287	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
288	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
289	C₂²×C₁₃	—	4	4	no	—
290	C₂²×C₁₃	—	4	4	no	—
291	C₂²×C₁₃	—	4	4	no	—
292	C₂²×C₁₃	—	8	8	no	—
293	C₂²×C₁₃	#548	1	2	yes	—
294	C₂²×C₁₃	C₂×#135	1	2	yes	—
295	C₂²×C₁₃	#577	1	2	yes	—
296	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
297	C₄×C₁₃	—	2	4	no	—
298	C₄×C₁₃	—	2	4	no	—
299	C₄×C₁₃	—	2	4	no	—
300	C₄×C₁₃	—	2	2	no	—
301	C₄×C₁₃	—	4	2	no	—
302	C₄×C₁₃	—	4	4	no	—
303	C₄×C₁₃	—	4	2	no	—
304	C₄×C₁₃	—	4	2	no	—
305	C₄×C₁₃	#548	1	2	yes	—
306	C₄×C₁₃	C₂×#135	1	4	yes	—
307	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
308	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
309	C₂²×Q₈	—	2	1	no	—
310	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
311	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
312	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
313	C₂²×D₄	—	2	1	no	—
314	C₂²×D₄	—	2	1	no	—
315	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
316	C₂³×C₄	—	2	2	no	—
317	C₂×Q₁₆	—	2	4	no	—
318	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
319	C₂×SD₁₆	—	2	8	no	—
320	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
321	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
322	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
323	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
324	C₄⋊Q₈	—	2	8	no	—
325	C₄⋊Q₈	—	2	2	no	—
326	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
327	#127	—	2	2	no	—
328	#127	C₂³×C₁₃	1	4	yes	—
329	#125	—	2	16	no	—
330	#125	—	2	4	no	—
331	#125	C₂³×C₁₃	1	8	yes	—
332	#124	—	2	8	no	—
333	#124	—	2	4	no	—
334	#124	C₂³×C₁₃	1	8	yes	—
335	#123	—	2	16	no	—
336	C₄×Q₈	—	2	8	no	—
337	C₄×Q₈	—	2	4	no	—
338	C₄×Q₈	—	2	2	no	—
339	C₄×Q₈	—	2	2	no	—
340	C₄×Q₈	D₄×C₁₃	1	4	yes	—
341	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
342	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
343	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
344	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
345	C₄×D₄	—	2	8	no	—
346	C₄×D₄	—	2	4	no	—
347	C₄×D₄	C₂³×C₁₃	1	8	yes	—
348	C₂×C₄⋊C₄	—	2	2	no	—
349	C₂×C₄⋊C₄	—	2	1	no	—
350	C₂×C₄⋊C₄	—	2	1	no	—
351	C₂×C₄⋊C₄	—	2	2	no	—
352	C₂×C₄⋊C₄	—	2	1	no	—
353	C₂×C₄⋊C₄	—	2	2	no	—
354	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
355	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
356	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
357	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
358	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
359	C₂×C₂²⋊C₄	—	2	2	no	—
360	C₂×C₂²⋊C₄	—	2	2	no	—
361	C₂×C₂²⋊C₄	—	2	2	no	—
362	C₂×C₄²	—	2	1	no	—
363	C₂×C₄²	—	2	2	no	—
364	C₂×C₄²	—	2	1	no	—
365	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
366	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
367	#107	C₂³×C₁₃	1	4	yes	—
368	#106	C₂³×C₁₃	1	8	yes	—
369	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
370	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
371	#103	C₂³×C₁₃	1	4	yes	—
372	#103	C₂³×C₁₃	1	4	yes	—
373	#103	C₂³×C₁₃	1	8	yes	—
374	#102	C₂³×C₁₃	1	8	yes	—
375	#102	C₂³×C₁₃	1	8	yes	—
376	#102	C₂³×C₁₃	1	8	yes	—
377	C₄×C₈	C₂³×C₁₃	1	8	yes	—
378	C₄×C₈	C₂³×C₁₃	1	4	yes	—
379	C₂×C₁₃	—	8	4	no	—
380	C₂×C₁₃	#3365	1	4	yes	direct product factor
381	C₂×C₁₃	C₂×#548	1	1	yes	characteristic
382	C₂×C₁₃	C₂²×#135	1	1	yes	characteristic
383	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
384	C₂⁴	—	2	2	no	—
385	C₂×Q₈	—	2	4	no	—
386	C₂×Q₈	—	2	1	no	—
387	C₂×Q₈	—	2	1	no	—
388	C₂×Q₈	—	2	4	no	—
389	C₂×Q₈	—	2	2	no	—
390	C₂×Q₈	—	2	2	no	—
391	C₂×Q₈	—	2	2	no	—
392	C₂×Q₈	—	4	4	no	—
393	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
394	C₂×Q₈	C₁₃×#41	1	4	yes	—
395	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
396	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
397	C₂×D₄	—	2	2	no	—
398	C₂×D₄	—	2	4	no	—
399	C₂×D₄	—	2	4	no	—
400	C₂×D₄	—	2	4	no	—
401	C₂×D₄	—	2	4	no	—
402	C₂×D₄	—	4	4	no	—
403	C₂×D₄	—	8	2	no	—
404	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
405	C₂²×C₄	—	2	1	no	—
406	C₂²×C₄	—	2	1	no	—
407	C₂²×C₄	—	2	1	no	—
408	C₂²×C₄	—	2	1	no	—
409	C₂²×C₄	—	2	2	no	—
410	C₂²×C₄	—	2	8	no	—
411	C₂²×C₄	—	8	4	no	—
412	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
413	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
414	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
415	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
416	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
417	Q₁₆	—	2	8	no	—
418	SD₁₆	—	2	16	no	—
419	C₂×C₈	—	2	4	no	—
420	C₂×C₈	—	2	2	no	—
421	C₂×C₈	—	2	2	no	—
422	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
423	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
424	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
425	C₄⋊C₄	—	2	8	no	—
426	C₄⋊C₄	—	2	4	no	—
427	C₄⋊C₄	—	2	4	no	—
428	C₄⋊C₄	—	2	8	no	—
429	C₄⋊C₄	—	2	4	no	—
430	C₄⋊C₄	—	2	8	no	—
431	C₄⋊C₄	—	2	1	no	—
432	C₄⋊C₄	—	2	1	no	—
433	C₄⋊C₄	—	2	2	no	—
434	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
435	C₄⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
436	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
437	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
438	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
439	C₂²⋊C₄	—	2	8	no	—
440	C₂²⋊C₄	—	2	8	no	—
441	C₂²⋊C₄	—	2	8	no	—
442	C₄²	—	2	4	no	—
443	C₄²	—	2	8	no	—
444	C₄²	—	2	4	no	—
445	C₄²	C₂×D₄×C₁₃	1	4	yes	—
446	C₄²	C₂×D₄×C₁₃	1	2	yes	—
447	C₄²	C₂⁴×C₁₃	1	4	yes	—
448	C₄²	C₂⁴×C₁₃	1	2	yes	—
449	C₁₃	C₂×#3365	1	1	yes	characteristic, direct product factor, Sylow
450	C₂³	—	2	4	no	—
451	C₂³	—	4	4	no	—
452	C₂³	—	4	4	no	—
453	C₂³	—	4	4	no	—
454	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
455	Q₈	—	2	4	no	—
456	Q₈	—	2	8	no	—
457	Q₈	—	2	2	no	—
458	Q₈	—	2	2	no	—
459	Q₈	—	2	2	no	—
460	Q₈	—	4	2	no	—
461	Q₈	—	4	8	no	—
462	Q₈	C₂×C₁₃×#41	1	4	yes	—
463	D₄	—	2	4	no	—
464	D₄	—	2	4	no	—
465	D₄	—	4	4	no	—
466	D₄	—	4	8	no	—
467	D₄	—	8	4	no	—
468	C₂×C₄	—	2	4	no	—
469	C₂×C₄	—	2	4	no	—
470	C₂×C₄	—	2	4	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	2	4	no	—
477	C₂×C₄	—	4	2	no	—
478	C₂×C₄	—	4	4	no	—
479	C₂×C₄	—	4	2	no	—
480	C₂×C₄	—	4	2	no	—
481	C₂×C₄	—	8	8	no	—
482	C₂×C₄	C₁₃×#135	1	4	yes	—
483	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
484	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
485	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
486	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
487	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
488	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
489	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
490	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
491	C₈	—	2	4	no	—
492	C₈	—	2	2	no	—
493	C₈	—	2	2	no	—
494	C₂²	—	4	4	no	—
495	C₂²	—	4	4	no	—
496	C₂²	—	4	4	no	—
497	C₂²	—	8	8	no	—
498	C₂²	C₁₃×#548	1	2	yes	—
499	C₂²	C₂×C₁₃×#135	1	2	yes	—
500	C₂²	C₁₃×#577	1	2	yes	—
501	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
502	C₄	—	2	4	no	—
503	C₄	—	2	4	no	—
504	C₄	—	2	2	no	—
505	C₄	—	2	4	no	—
506	C₄	—	4	4	no	—
507	C₄	—	4	2	no	—
508	C₄	—	4	2	no	—
509	C₄	—	4	2	no	—
510	C₄	C₁₃×#548	1	2	yes	—
511	C₄	C₂×C₁₃×#135	1	4	yes	—
512	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
513	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
514	C₂	—	8	4	no	—
515	C₂	C₁₃×#3365	1	4	yes	direct product factor
516	C₂	C₂×C₁₃×#548	1	1	yes	characteristic
517	C₂	C₂²×C₁₃×#135	1	1	yes	characteristic
518	C₂	C₂×C₁₃×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₂×C₁₃×#127	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄×Q₈×C₁₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₂×C₁₃×#557	C₂	semidirect
3. C₁₃×#3365	C₂	direct (N × H)
4. C₂×C₁₃×#488	C₂	semidirect
6. C₂×C₁₃×#475	C₂	semidirect
7. C₂×C₁₃×#478	C₂	semidirect
8. C₂×C₁₃×#464	C₂	semidirect
10. C₂×C₈×Q₈×C₁₃	C₂	semidirect
11. C₂×C₄×C₁₃×Q₁₆	C₂	semidirect
12. C₂×C₄×C₁₃×SD₁₆	C₂	semidirect
18. C₁₃×#557	C₂²	semidirect
34. C₁₃×#488	C₂²	semidirect
36. C₁₃×#478	C₂²	semidirect
37. C₁₃×#475	C₂²	semidirect
38. C₁₃×#464	C₂²	semidirect
40. C₈×Q₈×C₁₃	C₂²	semidirect
41. C₄×C₁₃×Q₁₆	C₂²	semidirect
42. C₄×C₁₃×SD₁₆	C₂²	semidirect
125. C₂×#3365	C₁₃	direct (N × H)
192. C₂×#557	C₂×C₁₃	semidirect
193. #3365	C₂×C₁₃	direct (N × H)
194. C₂×#488	C₂×C₁₃	semidirect
196. C₂×#475	C₂×C₁₃	semidirect
197. C₂×#478	C₂×C₁₃	semidirect
198. C₂×#464	C₂×C₁₃	semidirect
200. C₂×C₈×Q₈	C₂×C₁₃	semidirect
201. C₂×C₄×Q₁₆	C₂×C₁₃	semidirect
202. C₂×C₄×SD₁₆	C₂×C₁₃	semidirect
252. #557	C₂²×C₁₃	semidirect
268. #488	C₂²×C₁₃	semidirect
270. #478	C₂²×C₁₃	semidirect
271. #475	C₂²×C₁₃	semidirect
272. #464	C₂²×C₁₃	semidirect
274. C₈×Q₈	C₂²×C₁₃	semidirect
275. C₄×Q₁₆	C₂²×C₁₃	semidirect
276. C₄×SD₁₆	C₂²×C₁₃	semidirect
380. C₂×C₁₃	#3365	direct (N × H)
449. C₁₃	C₂×#3365	direct (N × H)
515. C₂	C₁₃×#3365	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×#559	2
C₂×C₁₃×#557	2
C₁₃×#3365	2
C₂×C₁₃×#488	2
C₂×C₁₃×#486	2
C₂×C₁₃×#475	2
C₂×C₁₃×#478	2
C₂×C₁₃×#464	2
C₂×C₁₃×#460	2
C₂×C₈×Q₈×C₁₃	2
C₂×C₄×C₁₃×Q₁₆	2
C₂×C₄×C₁₃×SD₁₆	2
C₂×#3365	13

Subgroups — C2×C13×#3365 #15747641

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3365 #15747641