Subgroups — C₂×C₁₃×#3369 #15747649

Order 3328.

1842 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈²×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#556	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3369	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#489	C₂	1	2	yes	maximal
5	C₂×C₁₃×#487	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃×#475	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₃×#476	C₂	1	1	yes	maximal, characteristic
8	C₂×C₁₃×#464	C₂	1	2	yes	maximal
9	C₂×C₁₃×#462	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×#446	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×#441	C₂	1	2	yes	maximal, complemented
12	C₂×C₄×C₁₃×SD₁₆	C₂	1	1	yes	maximal, characteristic
13	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	—
14	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
15	Q₈²×C₁₃	—	2	4	no	—
16	Q₈²×C₁₃	C₂²	1	8	yes	complemented
17	C₁₃×#556	—	2	4	no	—
18	C₁₃×#556	C₂²	1	8	yes	—
19	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
20	C₂×C₁₃×C₄⋊Q₈	—	2	2	no	—
21	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
24	C₂×C₁₃×#126	—	2	2	no	—
25	C₂×C₁₃×#124	C₂²	1	2	yes	—
26	C₂×C₁₃×C₂²⋊Q₈	—	2	1	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	2	yes	—
31	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×#117	—	2	1	no	—
34	C₁₃×#489	C₂²	1	16	yes	—
35	C₁₃×#487	C₂²	1	8	yes	complemented
36	C₁₃×#476	C₂²	1	8	yes	—
37	C₁₃×#475	C₂²	1	16	yes	complemented
38	C₁₃×#464	C₂²	1	16	yes	—
39	C₁₃×#462	C₂²	1	8	yes	complemented
40	C₁₃×#446	C₂²	1	8	yes	complemented
41	C₁₃×#441	C₂²	1	16	yes	complemented
42	C₄×C₁₃×SD₁₆	C₂²	1	8	yes	—
43	C₂×C₁₃×#106	C₂²	1	2	yes	—
44	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
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	2	yes	—
49	C₂×C₁₃×#103	C₂²	1	2	yes	—
50	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
51	C₂×C₁₃×#102	C₂²	1	2	yes	—
52	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
53	C₂×C₁₃×#97	C₂²	1	2	yes	—
54	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
55	C₂²×Q₈×C₁₃	—	2	2	no	—
56	C₂²×Q₈×C₁₃	—	2	1	no	—
57	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
58	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
59	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
60	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₁₃	—	2	1	no	—
62	C₂×C₁₃×Q₁₆	—	2	8	no	—
63	C₂×C₁₃×Q₁₆	C₂³	1	8	yes	—
64	C₂×C₁₃×SD₁₆	—	2	4	no	—
65	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
66	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
67	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
68	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
69	C₁₃×C₄⋊Q₈	—	2	8	no	—
70	C₁₃×C₄⋊Q₈	—	2	16	no	—
71	C₁₃×C₄⋊Q₈	—	2	2	no	—
72	C₁₃×C₄⋊Q₈	—	2	2	no	—
73	C₁₃×C₄⋊Q₈	—	2	4	no	—
74	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
75	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	—
76	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
77	C₁₃×#126	—	2	16	no	—
78	C₁₃×#124	—	2	4	no	—
79	C₁₃×#124	C₂³	1	8	yes	—
80	C₁₃×C₂²⋊Q₈	—	2	8	no	—
81	C₄×Q₈×C₁₃	—	2	8	no	—
82	C₄×Q₈×C₁₃	—	2	4	no	—
83	C₄×Q₈×C₁₃	—	2	2	no	—
84	C₄×Q₈×C₁₃	—	2	4	no	—
85	C₄×Q₈×C₁₃	D₄	1	4	yes	—
86	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
87	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
88	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
89	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
90	C₄×D₄×C₁₃	—	2	2	no	—
91	C₄×D₄×C₁₃	C₂³	1	4	yes	—
92	C₁₃×#117	—	2	8	no	—
93	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
94	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
95	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
96	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
97	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
98	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
99	C₂×C₁₃×C₄⋊C₄	—	2	1	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	1	no	—
107	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
108	C₂×C₄²×C₁₃	—	2	2	no	—
109	C₂×C₄²×C₁₃	—	2	2	no	—
110	C₂×C₄²×C₁₃	—	2	1	no	—
111	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
112	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
113	C₁₃×#106	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	8	yes	—
119	C₁₃×#103	C₂³	1	8	yes	—
120	C₁₃×#103	C₂³	1	8	yes	—
121	C₁₃×#102	C₂³	1	4	yes	—
122	C₁₃×#102	C₂³	1	8	yes	—
123	C₁₃×#97	C₂³	1	8	yes	—
124	C₄×C₈×C₁₃	C₂³	1	4	yes	—
125	C₂×#3369	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
126	C₂⁴×C₁₃	—	2	1	no	—
127	C₂×Q₈×C₁₃	—	2	4	no	—
128	C₂×Q₈×C₁₃	—	2	1	no	—
129	C₂×Q₈×C₁₃	—	2	2	no	—
130	C₂×Q₈×C₁₃	—	2	8	no	—
131	C₂×Q₈×C₁₃	—	2	4	no	—
132	C₂×Q₈×C₁₃	—	2	2	no	—
133	C₂×Q₈×C₁₃	—	2	4	no	—
134	C₂×Q₈×C₁₃	—	2	4	no	—
135	C₂×Q₈×C₁₃	—	8	4	no	—
136	C₂×Q₈×C₁₃	—	8	2	no	—
137	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
138	C₂×Q₈×C₁₃	#41	1	4	yes	—
139	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
140	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
141	C₂×D₄×C₁₃	—	2	1	no	—
142	C₂×D₄×C₁₃	—	2	2	no	—
143	C₂×D₄×C₁₃	—	2	2	no	—
144	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
145	C₂²×C₄×C₁₃	—	2	1	no	—
146	C₂²×C₄×C₁₃	—	2	1	no	—
147	C₂²×C₄×C₁₃	—	2	2	no	—
148	C₂²×C₄×C₁₃	—	2	2	no	—
149	C₂²×C₄×C₁₃	—	2	1	no	—
150	C₂²×C₄×C₁₃	—	2	4	no	—
151	C₂²×C₄×C₁₃	—	4	4	no	—
152	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
153	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
154	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
157	C₁₃×Q₁₆	—	2	16	no	—
158	C₁₃×SD₁₆	—	2	8	no	—
159	C₂×C₈×C₁₃	—	2	2	no	—
160	C₂×C₈×C₁₃	—	2	4	no	—
161	C₂×C₈×C₁₃	—	2	2	no	—
162	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
163	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
164	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
165	C₁₃×C₄⋊C₄	—	2	4	no	—
166	C₁₃×C₄⋊C₄	—	2	8	no	—
167	C₁₃×C₄⋊C₄	—	2	4	no	—
168	C₁₃×C₄⋊C₄	—	2	8	no	—
169	C₁₃×C₄⋊C₄	—	2	8	no	—
170	C₁₃×C₄⋊C₄	—	2	4	no	—
171	C₁₃×C₄⋊C₄	—	2	4	no	—
172	C₁₃×C₄⋊C₄	—	2	1	no	—
173	C₁₃×C₄⋊C₄	—	2	2	no	—
174	C₁₃×C₄⋊C₄	—	2	1	no	—
175	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
176	C₁₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
177	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
178	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
179	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
180	C₁₃×C₂²⋊C₄	—	2	8	no	—
181	C₁₃×C₂²⋊C₄	—	2	4	no	—
182	C₁₃×C₂²⋊C₄	—	2	8	no	—
183	C₄²×C₁₃	—	2	8	no	—
184	C₄²×C₁₃	—	2	8	no	—
185	C₄²×C₁₃	—	2	4	no	—
186	C₄²×C₁₃	C₂×D₄	1	2	yes	—
187	C₄²×C₁₃	C₂×D₄	1	4	yes	—
188	C₄²×C₁₃	C₂⁴	1	2	yes	—
189	C₄²×C₁₃	C₂⁴	1	4	yes	—
190	C₂×Q₈²	C₂×C₁₃	1	1	yes	characteristic, complemented
191	C₂×#556	C₂×C₁₃	1	1	yes	characteristic
192	#3369	C₂×C₁₃	1	16	yes	direct product factor
193	C₂×#489	C₂×C₁₃	1	2	yes	—
194	C₂×#487	C₂×C₁₃	1	1	yes	characteristic, complemented
195	C₂×#475	C₂×C₁₃	1	2	yes	complemented
196	C₂×#476	C₂×C₁₃	1	1	yes	characteristic
197	C₂×#464	C₂×C₁₃	1	2	yes	—
198	C₂×#462	C₂×C₁₃	1	1	yes	characteristic, complemented
199	C₂×#446	C₂×C₁₃	1	1	yes	characteristic, complemented
200	C₂×#441	C₂×C₁₃	1	2	yes	complemented
201	C₂×C₄×SD₁₆	C₂×C₁₃	1	1	yes	characteristic
202	C₂³×C₁₃	—	2	2	no	—
203	C₂³×C₁₃	—	4	2	no	—
204	C₂³×C₁₃	—	4	2	no	—
205	C₂³×C₁₃	—	4	2	no	—
206	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
207	Q₈×C₁₃	—	2	4	no	—
208	Q₈×C₁₃	—	2	8	no	—
209	Q₈×C₁₃	—	2	2	no	—
210	Q₈×C₁₃	—	2	4	no	—
211	Q₈×C₁₃	—	2	4	no	—
212	Q₈×C₁₃	—	4	4	no	—
213	Q₈×C₁₃	—	8	8	no	—
214	Q₈×C₁₃	—	8	4	no	—
215	Q₈×C₁₃	C₂×#41	1	4	yes	—
216	D₄×C₁₃	—	2	2	no	—
217	D₄×C₁₃	—	2	2	no	—
218	D₄×C₁₃	—	4	2	no	—
219	C₂×C₄×C₁₃	—	2	4	no	—
220	C₂×C₄×C₁₃	—	2	4	no	—
221	C₂×C₄×C₁₃	—	2	4	no	—
222	C₂×C₄×C₁₃	—	2	2	no	—
223	C₂×C₄×C₁₃	—	2	2	no	—
224	C₂×C₄×C₁₃	—	2	2	no	—
225	C₂×C₄×C₁₃	—	2	4	no	—
226	C₂×C₄×C₁₃	—	2	4	no	—
227	C₂×C₄×C₁₃	—	2	2	no	—
228	C₂×C₄×C₁₃	—	4	4	no	—
229	C₂×C₄×C₁₃	—	4	2	no	—
230	C₂×C₄×C₁₃	—	4	4	no	—
231	C₂×C₄×C₁₃	—	4	2	no	—
232	C₂×C₄×C₁₃	—	4	8	no	—
233	C₂×C₄×C₁₃	#137	1	4	yes	—
234	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
235	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
236	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
237	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
238	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
239	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
240	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
241	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
242	C₈×C₁₃	—	2	2	no	—
243	C₈×C₁₃	—	2	4	no	—
244	C₈×C₁₃	—	2	2	no	—
245	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	—
246	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
247	Q₈²	—	2	4	no	—
248	Q₈²	C₂²×C₁₃	1	8	yes	complemented
249	#556	—	2	4	no	—
250	#556	C₂²×C₁₃	1	8	yes	—
251	C₂×C₄⋊Q₈	—	2	1	no	—
252	C₂×C₄⋊Q₈	—	2	2	no	—
253	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
254	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
255	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
256	C₂×#126	—	2	2	no	—
257	C₂×#124	C₂²×C₁₃	1	2	yes	—
258	C₂×C₂²⋊Q₈	—	2	1	no	—
259	C₂×C₄×Q₈	—	2	1	no	—
260	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
261	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
262	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
263	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
264	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
265	C₂×#117	—	2	1	no	—
266	#489	C₂²×C₁₃	1	16	yes	—
267	#487	C₂²×C₁₃	1	8	yes	complemented
268	#476	C₂²×C₁₃	1	8	yes	—
269	#475	C₂²×C₁₃	1	16	yes	complemented
270	#464	C₂²×C₁₃	1	16	yes	—
271	#462	C₂²×C₁₃	1	8	yes	complemented
272	#446	C₂²×C₁₃	1	8	yes	complemented
273	#441	C₂²×C₁₃	1	16	yes	complemented
274	C₄×SD₁₆	C₂²×C₁₃	1	8	yes	—
275	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
276	C₂×#106	C₂²×C₁₃	1	2	yes	—
277	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
278	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
279	C₂×#103	C₂²×C₁₃	1	2	yes	—
280	C₂×#103	C₂²×C₁₃	1	2	yes	—
281	C₂×#103	C₂²×C₁₃	1	2	yes	—
282	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
283	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
284	C₂×#102	C₂²×C₁₃	1	2	yes	—
285	C₂×#97	C₂²×C₁₃	1	2	yes	—
286	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
287	C₂²×C₁₃	—	4	2	no	—
288	C₂²×C₁₃	—	4	2	no	—
289	C₂²×C₁₃	—	4	2	no	—
290	C₂²×C₁₃	—	8	4	no	—
291	C₂²×C₁₃	#548	1	2	yes	—
292	C₂²×C₁₃	C₂×#137	1	2	yes	—
293	C₂²×C₁₃	#577	1	2	yes	—
294	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
295	C₄×C₁₃	—	2	4	no	—
296	C₄×C₁₃	—	2	4	no	—
297	C₄×C₁₃	—	2	4	no	—
298	C₄×C₁₃	—	2	2	no	—
299	C₄×C₁₃	—	4	4	no	—
300	C₄×C₁₃	—	4	2	no	—
301	C₄×C₁₃	—	4	4	no	—
302	C₄×C₁₃	—	4	2	no	—
303	C₄×C₁₃	#548	1	2	yes	—
304	C₄×C₁₃	C₂×#137	1	4	yes	—
305	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
306	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
307	C₂²×Q₈	—	2	2	no	—
308	C₂²×Q₈	—	2	1	no	—
309	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
310	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
311	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
312	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
313	C₂³×C₄	—	2	1	no	—
314	C₂×Q₁₆	—	2	8	no	—
315	C₂×Q₁₆	C₂³×C₁₃	1	8	yes	—
316	C₂×SD₁₆	—	2	4	no	—
317	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
318	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
319	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
320	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
321	C₄⋊Q₈	—	2	8	no	—
322	C₄⋊Q₈	—	2	16	no	—
323	C₄⋊Q₈	—	2	2	no	—
324	C₄⋊Q₈	—	2	2	no	—
325	C₄⋊Q₈	—	2	4	no	—
326	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
327	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	—
328	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
329	#126	—	2	16	no	—
330	#124	—	2	4	no	—
331	#124	C₂³×C₁₃	1	8	yes	—
332	C₂²⋊Q₈	—	2	8	no	—
333	C₄×Q₈	—	2	8	no	—
334	C₄×Q₈	—	2	4	no	—
335	C₄×Q₈	—	2	2	no	—
336	C₄×Q₈	—	2	4	no	—
337	C₄×Q₈	D₄×C₁₃	1	4	yes	—
338	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
339	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
340	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
341	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
342	C₄×D₄	—	2	2	no	—
343	C₄×D₄	C₂³×C₁₃	1	4	yes	—
344	#117	—	2	8	no	—
345	C₂×C₄⋊C₄	—	2	1	no	—
346	C₂×C₄⋊C₄	—	2	2	no	—
347	C₂×C₄⋊C₄	—	2	1	no	—
348	C₂×C₄⋊C₄	—	2	2	no	—
349	C₂×C₄⋊C₄	—	2	2	no	—
350	C₂×C₄⋊C₄	—	2	1	no	—
351	C₂×C₄⋊C₄	—	2	1	no	—
352	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
353	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
354	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
355	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
356	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
357	C₂×C₂²⋊C₄	—	2	2	no	—
358	C₂×C₂²⋊C₄	—	2	1	no	—
359	C₂×C₂²⋊C₄	—	2	2	no	—
360	C₂×C₄²	—	2	2	no	—
361	C₂×C₄²	—	2	2	no	—
362	C₂×C₄²	—	2	1	no	—
363	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
364	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
365	#106	C₂³×C₁₃	1	4	yes	—
366	#106	C₂³×C₁₃	1	8	yes	—
367	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
368	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
369	#103	C₂³×C₁₃	1	4	yes	—
370	#103	C₂³×C₁₃	1	8	yes	—
371	#103	C₂³×C₁₃	1	8	yes	—
372	#103	C₂³×C₁₃	1	8	yes	—
373	#102	C₂³×C₁₃	1	4	yes	—
374	#102	C₂³×C₁₃	1	8	yes	—
375	#97	C₂³×C₁₃	1	8	yes	—
376	C₄×C₈	C₂³×C₁₃	1	4	yes	—
377	C₂×C₁₃	—	8	2	no	—
378	C₂×C₁₃	#3369	1	4	yes	direct product factor
379	C₂×C₁₃	C₂×#548	1	1	yes	characteristic
380	C₂×C₁₃	C₂²×#137	1	1	yes	characteristic
381	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
382	C₂⁴	—	2	1	no	—
383	C₂×Q₈	—	2	4	no	—
384	C₂×Q₈	—	2	1	no	—
385	C₂×Q₈	—	2	2	no	—
386	C₂×Q₈	—	2	8	no	—
387	C₂×Q₈	—	2	4	no	—
388	C₂×Q₈	—	2	2	no	—
389	C₂×Q₈	—	2	4	no	—
390	C₂×Q₈	—	2	4	no	—
391	C₂×Q₈	—	8	4	no	—
392	C₂×Q₈	—	8	2	no	—
393	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
394	C₂×Q₈	C₁₃×#41	1	4	yes	—
395	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
396	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
397	C₂×D₄	—	2	1	no	—
398	C₂×D₄	—	2	2	no	—
399	C₂×D₄	—	2	2	no	—
400	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
401	C₂²×C₄	—	2	1	no	—
402	C₂²×C₄	—	2	1	no	—
403	C₂²×C₄	—	2	2	no	—
404	C₂²×C₄	—	2	2	no	—
405	C₂²×C₄	—	2	1	no	—
406	C₂²×C₄	—	2	4	no	—
407	C₂²×C₄	—	4	4	no	—
408	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
409	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
410	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
411	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
412	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
413	Q₁₆	—	2	16	no	—
414	SD₁₆	—	2	8	no	—
415	C₂×C₈	—	2	2	no	—
416	C₂×C₈	—	2	4	no	—
417	C₂×C₈	—	2	2	no	—
418	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
419	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
420	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
421	C₄⋊C₄	—	2	4	no	—
422	C₄⋊C₄	—	2	8	no	—
423	C₄⋊C₄	—	2	4	no	—
424	C₄⋊C₄	—	2	8	no	—
425	C₄⋊C₄	—	2	8	no	—
426	C₄⋊C₄	—	2	4	no	—
427	C₄⋊C₄	—	2	4	no	—
428	C₄⋊C₄	—	2	1	no	—
429	C₄⋊C₄	—	2	1	no	—
430	C₄⋊C₄	—	2	2	no	—
431	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
432	C₄⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
433	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
434	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
435	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
436	C₂²⋊C₄	—	2	8	no	—
437	C₂²⋊C₄	—	2	4	no	—
438	C₂²⋊C₄	—	2	8	no	—
439	C₄²	—	2	8	no	—
440	C₄²	—	2	8	no	—
441	C₄²	—	2	4	no	—
442	C₄²	C₂×D₄×C₁₃	1	2	yes	—
443	C₄²	C₂×D₄×C₁₃	1	4	yes	—
444	C₄²	C₂⁴×C₁₃	1	2	yes	—
445	C₄²	C₂⁴×C₁₃	1	4	yes	—
446	C₁₃	C₂×#3369	1	1	yes	characteristic, direct product factor, Sylow
447	C₂³	—	2	2	no	—
448	C₂³	—	4	2	no	—
449	C₂³	—	4	2	no	—
450	C₂³	—	4	2	no	—
451	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
452	Q₈	—	2	4	no	—
453	Q₈	—	2	8	no	—
454	Q₈	—	2	2	no	—
455	Q₈	—	2	4	no	—
456	Q₈	—	2	4	no	—
457	Q₈	—	4	4	no	—
458	Q₈	—	8	8	no	—
459	Q₈	—	8	4	no	—
460	Q₈	C₂×C₁₃×#41	1	4	yes	—
461	D₄	—	2	2	no	—
462	D₄	—	2	2	no	—
463	D₄	—	4	2	no	—
464	C₂×C₄	—	2	4	no	—
465	C₂×C₄	—	2	4	no	—
466	C₂×C₄	—	2	4	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	4	no	—
471	C₂×C₄	—	2	4	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	4	4	no	—
474	C₂×C₄	—	4	2	no	—
475	C₂×C₄	—	4	4	no	—
476	C₂×C₄	—	4	2	no	—
477	C₂×C₄	—	4	8	no	—
478	C₂×C₄	C₁₃×#137	1	4	yes	—
479	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
480	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
481	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
482	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
483	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
484	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
485	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
486	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
487	C₈	—	2	2	no	—
488	C₈	—	2	4	no	—
489	C₈	—	2	2	no	—
490	C₂²	—	4	2	no	—
491	C₂²	—	4	2	no	—
492	C₂²	—	4	2	no	—
493	C₂²	—	8	4	no	—
494	C₂²	C₁₃×#548	1	2	yes	—
495	C₂²	C₂×C₁₃×#137	1	2	yes	—
496	C₂²	C₁₃×#577	1	2	yes	—
497	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
498	C₄	—	2	4	no	—
499	C₄	—	2	4	no	—
500	C₄	—	2	2	no	—
501	C₄	—	2	4	no	—
502	C₄	—	4	2	no	—
503	C₄	—	4	4	no	—
504	C₄	—	4	2	no	—
505	C₄	—	4	4	no	—
506	C₄	C₁₃×#548	1	2	yes	—
507	C₄	C₂×C₁₃×#137	1	4	yes	—
508	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
509	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
510	C₂	—	8	2	no	—
511	C₂	C₁₃×#3369	1	4	yes	direct product factor
512	C₂	C₂×C₁₃×#548	1	1	yes	characteristic
513	C₂	C₂²×C₁₃×#137	1	1	yes	characteristic
514	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	C₂²×D₄×C₁₃	C₂³
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
1. C₂×Q₈²×C₁₃	C₂	semidirect
3. C₁₃×#3369	C₂	direct (N × H)
5. C₂×C₁₃×#487	C₂	semidirect
6. C₂×C₁₃×#475	C₂	semidirect
9. C₂×C₁₃×#462	C₂	semidirect
10. C₂×C₁₃×#446	C₂	semidirect
11. C₂×C₁₃×#441	C₂	semidirect
16. Q₈²×C₁₃	C₂²	semidirect
35. C₁₃×#487	C₂²	semidirect
37. C₁₃×#475	C₂²	semidirect
39. C₁₃×#462	C₂²	semidirect
40. C₁₃×#446	C₂²	semidirect
41. C₁₃×#441	C₂²	semidirect
125. C₂×#3369	C₁₃	direct (N × H)
190. C₂×Q₈²	C₂×C₁₃	semidirect
192. #3369	C₂×C₁₃	direct (N × H)
194. C₂×#487	C₂×C₁₃	semidirect
195. C₂×#475	C₂×C₁₃	semidirect
198. C₂×#462	C₂×C₁₃	semidirect
199. C₂×#446	C₂×C₁₃	semidirect
200. C₂×#441	C₂×C₁₃	semidirect
248. Q₈²	C₂²×C₁₃	semidirect
267. #487	C₂²×C₁₃	semidirect
269. #475	C₂²×C₁₃	semidirect
271. #462	C₂²×C₁₃	semidirect
272. #446	C₂²×C₁₃	semidirect
273. #441	C₂²×C₁₃	semidirect
378. C₂×C₁₃	#3369	direct (N × H)
446. C₁₃	C₂×#3369	direct (N × H)
511. C₂	C₁₃×#3369	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×Q₈²×C₁₃	2
C₂×C₁₃×#556	2
C₁₃×#3369	2
C₂×C₁₃×#489	2
C₂×C₁₃×#487	2
C₂×C₁₃×#475	2
C₂×C₁₃×#476	2
C₂×C₁₃×#464	2
C₂×C₁₃×#462	2
C₂×C₁₃×#446	2
C₂×C₁₃×#441	2
C₂×C₄×C₁₃×SD₁₆	2
C₂×#3369	13

Subgroups — C2×C13×#3369 #15747649

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3369 #15747649