Subgroups — C₂×C₁₃×#3360 #15747636

Order 3328.

1906 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#556	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#554	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3360	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#488	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₃×#487	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃×#479	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₃×#476	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#463	C₂	1	2	yes	maximal
9	C₂×C₁₃×#461	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₈×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄×C₁₃×SD₁₆	C₂	1	2	yes	maximal, complemented
12	C₂×C₄×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic
13	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
14	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
15	C₁₃×#556	—	2	4	no	—
16	C₁₃×#556	C₂²	1	8	yes	complemented
17	C₁₃×#554	—	2	4	no	—
18	C₁₃×#554	C₂²	1	8	yes	complemented
19	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#126	—	2	2	no	—
22	C₂×C₁₃×#125	C₂²	1	2	yes	—
23	C₂×C₁₃×#124	C₂²	1	2	yes	—
24	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
25	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
26	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
27	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
28	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#117	—	2	1	no	—
33	C₂²×C₁₃×C₄⋊C₄	—	2	1	no	—
34	C₁₃×#488	C₂²	1	16	yes	complemented
35	C₁₃×#487	C₂²	1	8	yes	complemented
36	C₁₃×#479	C₂²	1	16	yes	complemented
37	C₁₃×#476	C₂²	1	8	yes	complemented
38	C₁₃×#463	C₂²	1	16	yes	—
39	C₁₃×#461	C₂²	1	8	yes	complemented
40	C₈×Q₈×C₁₃	C₂²	1	8	yes	complemented
41	C₄×C₁₃×SD₁₆	C₂²	1	16	yes	complemented
42	C₄×C₁₃×D₈	C₂²	1	8	yes	—
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	2	yes	—
49	C₂×C₁₃×#103	C₂²	1	2	yes	—
50	C₂×C₁₃×#102	C₂²	1	2	yes	—
51	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
52	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
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	2	yes	—
58	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
59	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
60	C₂³×C₄×C₁₃	—	2	1	no	—
61	C₂³×C₄×C₁₃	—	2	1	no	—
62	C₂³×C₄×C₁₃	—	2	2	no	—
63	C₂×C₁₃×SD₁₆	—	2	8	no	—
64	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
65	C₂×C₁₃×D₈	—	2	4	no	—
66	C₂×C₁₃×D₈	C₂³	1	4	yes	—
67	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
68	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
69	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
70	C₁₃×C₄⋊Q₈	—	2	2	no	—
71	C₁₃×C₄⋊Q₈	—	2	2	no	—
72	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
73	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
74	C₁₃×#126	—	2	16	no	—
75	C₁₃×#125	—	2	4	no	—
76	C₁₃×#125	C₂³	1	8	yes	—
77	C₁₃×#124	—	2	4	no	—
78	C₁₃×#124	C₂³	1	8	yes	—
79	C₁₃×C₂²⋊Q₈	—	2	8	no	—
80	C₁₃×C₂²⋊Q₈	—	2	8	no	—
81	C₁₃×C₂²⋊Q₈	—	2	16	no	—
82	C₄×Q₈×C₁₃	—	2	4	no	—
83	C₄×Q₈×C₁₃	D₄	1	4	yes	—
84	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
85	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
86	C₄×D₄×C₁₃	—	2	2	no	—
87	C₄×D₄×C₁₃	—	2	4	no	—
88	C₄×D₄×C₁₃	—	2	2	no	—
89	C₄×D₄×C₁₃	C₂³	1	4	yes	—
90	C₄×D₄×C₁₃	C₂³	1	4	yes	—
91	C₄×D₄×C₁₃	C₂³	1	8	yes	—
92	C₁₃×#117	—	2	8	no	—
93	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
94	C₂×C₁₃×C₄⋊C₄	—	2	1	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	8	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×C₁₃×C₂²⋊C₄	—	2	1	no	—
109	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
110	C₂×C₄²×C₁₃	—	2	2	no	—
111	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
112	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
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	8	yes	—
118	C₁₃×#103	C₂³	1	8	yes	—
119	C₁₃×#103	C₂³	1	8	yes	—
120	C₁₃×#102	C₂³	1	4	yes	—
121	C₁₃×#102	C₂³	1	4	yes	—
122	C₁₃×#102	C₂³	1	8	yes	—
123	C₄×C₈×C₁₃	C₂³	1	4	yes	—
124	C₄×C₈×C₁₃	C₂³	1	8	yes	—
125	C₂×#3360	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
126	C₂⁴×C₁₃	—	2	1	no	—
127	C₂⁴×C₁₃	—	2	1	no	—
128	C₂×Q₈×C₁₃	—	2	4	no	—
129	C₂×Q₈×C₁₃	—	2	2	no	—
130	C₂×Q₈×C₁₃	—	2	4	no	—
131	C₂×Q₈×C₁₃	—	2	4	no	—
132	C₂×Q₈×C₁₃	—	2	4	no	—
133	C₂×Q₈×C₁₃	—	8	2	no	—
134	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
135	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
136	C₂×D₄×C₁₃	—	2	1	no	—
137	C₂×D₄×C₁₃	—	2	1	no	—
138	C₂×D₄×C₁₃	—	2	2	no	—
139	C₂×D₄×C₁₃	—	2	2	no	—
140	C₂×D₄×C₁₃	—	2	2	no	—
141	C₂×D₄×C₁₃	#41	1	4	yes	—
142	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
143	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
144	C₂²×C₄×C₁₃	—	2	1	no	—
145	C₂²×C₄×C₁₃	—	2	2	no	—
146	C₂²×C₄×C₁₃	—	2	1	no	—
147	C₂²×C₄×C₁₃	—	2	2	no	—
148	C₂²×C₄×C₁₃	—	2	4	no	—
149	C₂²×C₄×C₁₃	—	2	4	no	—
150	C₂²×C₄×C₁₃	—	2	8	no	—
151	C₂²×C₄×C₁₃	—	4	4	no	—
152	C₂²×C₄×C₁₃	—	4	4	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×SD₁₆	—	2	16	no	—
160	C₁₃×D₈	—	2	8	no	—
161	C₂×C₈×C₁₃	—	2	2	no	—
162	C₂×C₈×C₁₃	—	2	4	no	—
163	C₂×C₈×C₁₃	—	2	2	no	—
164	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
165	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
166	C₂×C₈×C₁₃	C₂⁴	1	2	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	8	no	—
172	C₁₃×C₄⋊C₄	—	2	4	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	4	no	—
183	C₁₃×C₂²⋊C₄	—	2	8	no	—
184	C₁₃×C₂²⋊C₄	—	2	4	no	—
185	C₁₃×C₂²⋊C₄	—	2	8	no	—
186	C₄²×C₁₃	—	2	8	no	—
187	C₄²×C₁₃	C₂×D₄	1	2	yes	—
188	C₄²×C₁₃	C₂×D₄	1	4	yes	—
189	C₄²×C₁₃	C₂⁴	1	2	yes	—
190	C₄²×C₁₃	C₂⁴	1	4	yes	—
191	C₂×#556	C₂×C₁₃	1	1	yes	characteristic, complemented
192	C₂×#554	C₂×C₁₃	1	1	yes	characteristic, complemented
193	#3360	C₂×C₁₃	1	16	yes	direct product factor
194	C₂×#488	C₂×C₁₃	1	2	yes	complemented
195	C₂×#487	C₂×C₁₃	1	1	yes	characteristic, complemented
196	C₂×#479	C₂×C₁₃	1	2	yes	complemented
197	C₂×#476	C₂×C₁₃	1	1	yes	characteristic, complemented
198	C₂×#463	C₂×C₁₃	1	2	yes	—
199	C₂×#461	C₂×C₁₃	1	1	yes	characteristic, complemented
200	C₂×C₈×Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
201	C₂×C₄×SD₁₆	C₂×C₁₃	1	2	yes	complemented
202	C₂×C₄×D₈	C₂×C₁₃	1	1	yes	characteristic
203	C₂³×C₁₃	—	2	4	no	—
204	C₂³×C₁₃	—	2	2	no	—
205	C₂³×C₁₃	—	2	2	no	—
206	C₂³×C₁₃	—	4	2	no	—
207	C₂³×C₁₃	—	4	2	no	—
208	C₂³×C₁₃	—	4	2	no	—
209	C₂³×C₁₃	—	4	2	no	—
210	C₂³×C₁₃	—	4	2	no	—
211	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
212	Q₈×C₁₃	—	2	8	no	—
213	Q₈×C₁₃	—	2	4	no	—
214	Q₈×C₁₃	—	2	4	no	—
215	Q₈×C₁₃	—	4	4	no	—
216	Q₈×C₁₃	—	8	4	no	—
217	D₄×C₁₃	—	2	4	no	—
218	D₄×C₁₃	—	2	2	no	—
219	D₄×C₁₃	—	2	2	no	—
220	D₄×C₁₃	—	2	2	no	—
221	D₄×C₁₃	—	4	2	no	—
222	D₄×C₁₃	C₂×#41	1	4	yes	—
223	C₂×C₄×C₁₃	—	2	4	no	—
224	C₂×C₄×C₁₃	—	2	4	no	—
225	C₂×C₄×C₁₃	—	2	2	no	—
226	C₂×C₄×C₁₃	—	2	2	no	—
227	C₂×C₄×C₁₃	—	2	4	no	—
228	C₂×C₄×C₁₃	—	2	2	no	—
229	C₂×C₄×C₁₃	—	2	4	no	—
230	C₂×C₄×C₁₃	—	4	4	no	—
231	C₂×C₄×C₁₃	—	4	2	no	—
232	C₂×C₄×C₁₃	—	4	2	no	—
233	C₂×C₄×C₁₃	—	4	4	no	—
234	C₂×C₄×C₁₃	—	4	8	no	—
235	C₂×C₄×C₁₃	—	4	8	no	—
236	C₂×C₄×C₁₃	—	8	8	no	—
237	C₂×C₄×C₁₃	#135	1	4	yes	—
238	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
239	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
240	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
241	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
242	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
243	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
244	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
245	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
246	C₈×C₁₃	—	2	2	no	—
247	C₈×C₁₃	—	2	4	no	—
248	C₈×C₁₃	—	2	2	no	—
249	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
250	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
251	#556	—	2	4	no	—
252	#556	C₂²×C₁₃	1	8	yes	complemented
253	#554	—	2	4	no	—
254	#554	C₂²×C₁₃	1	8	yes	complemented
255	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
256	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
257	C₂×#126	—	2	2	no	—
258	C₂×#125	C₂²×C₁₃	1	2	yes	—
259	C₂×#124	C₂²×C₁₃	1	2	yes	—
260	C₂×C₂²⋊Q₈	—	2	1	no	—
261	C₂×C₂²⋊Q₈	—	2	1	no	—
262	C₂×C₂²⋊Q₈	—	2	2	no	—
263	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
264	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
265	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
266	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
267	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
268	C₂×#117	—	2	1	no	—
269	C₂²×C₄⋊C₄	—	2	1	no	—
270	#488	C₂²×C₁₃	1	16	yes	complemented
271	#487	C₂²×C₁₃	1	8	yes	complemented
272	#479	C₂²×C₁₃	1	16	yes	complemented
273	#476	C₂²×C₁₃	1	8	yes	complemented
274	#463	C₂²×C₁₃	1	16	yes	—
275	#461	C₂²×C₁₃	1	8	yes	complemented
276	C₈×Q₈	C₂²×C₁₃	1	8	yes	complemented
277	C₄×SD₁₆	C₂²×C₁₃	1	16	yes	complemented
278	C₄×D₈	C₂²×C₁₃	1	8	yes	—
279	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
280	C₂×#106	C₂²×C₁₃	1	2	yes	—
281	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
282	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
283	C₂×#103	C₂²×C₁₃	1	2	yes	—
284	C₂×#103	C₂²×C₁₃	1	2	yes	—
285	C₂×#103	C₂²×C₁₃	1	2	yes	—
286	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
287	C₂×#102	C₂²×C₁₃	1	2	yes	—
288	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
289	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
290	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
291	C₂²×C₁₃	—	2	4	no	—
292	C₂²×C₁₃	—	4	8	no	—
293	C₂²×C₁₃	—	4	2	no	—
294	C₂²×C₁₃	—	4	2	no	—
295	C₂²×C₁₃	—	4	2	no	—
296	C₂²×C₁₃	—	4	2	no	—
297	C₂²×C₁₃	—	4	2	no	—
298	C₂²×C₁₃	—	8	4	no	—
299	C₂²×C₁₃	#548	1	2	yes	—
300	C₂²×C₁₃	C₂×#135	1	2	yes	—
301	C₂²×C₁₃	#577	1	2	yes	—
302	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
303	C₄×C₁₃	—	2	4	no	—
304	C₄×C₁₃	—	2	4	no	—
305	C₄×C₁₃	—	2	2	no	—
306	C₄×C₁₃	—	4	4	no	—
307	C₄×C₁₃	—	4	2	no	—
308	C₄×C₁₃	—	4	2	no	—
309	C₄×C₁₃	—	4	4	no	—
310	C₄×C₁₃	#548	1	2	yes	—
311	C₄×C₁₃	C₂×#135	1	4	yes	—
312	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
313	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
314	C₂²×Q₈	—	2	1	no	—
315	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
316	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
317	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
318	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
319	C₂³×C₄	—	2	1	no	—
320	C₂³×C₄	—	2	1	no	—
321	C₂³×C₄	—	2	2	no	—
322	C₂×SD₁₆	—	2	8	no	—
323	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
324	C₂×D₈	—	2	4	no	—
325	C₂×D₈	C₂³×C₁₃	1	4	yes	—
326	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
327	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
328	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
329	C₄⋊Q₈	—	2	2	no	—
330	C₄⋊Q₈	—	2	2	no	—
331	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
332	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
333	#126	—	2	16	no	—
334	#125	—	2	4	no	—
335	#125	C₂³×C₁₃	1	8	yes	—
336	#124	—	2	4	no	—
337	#124	C₂³×C₁₃	1	8	yes	—
338	C₂²⋊Q₈	—	2	8	no	—
339	C₂²⋊Q₈	—	2	8	no	—
340	C₂²⋊Q₈	—	2	16	no	—
341	C₄×Q₈	—	2	4	no	—
342	C₄×Q₈	D₄×C₁₃	1	4	yes	—
343	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
344	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
345	C₄×D₄	—	2	2	no	—
346	C₄×D₄	—	2	4	no	—
347	C₄×D₄	—	2	2	no	—
348	C₄×D₄	C₂³×C₁₃	1	4	yes	—
349	C₄×D₄	C₂³×C₁₃	1	8	yes	—
350	C₄×D₄	C₂³×C₁₃	1	4	yes	—
351	#117	—	2	8	no	—
352	C₂×C₄⋊C₄	—	2	2	no	—
353	C₂×C₄⋊C₄	—	2	1	no	—
354	C₂×C₄⋊C₄	—	2	1	no	—
355	C₂×C₄⋊C₄	—	2	2	no	—
356	C₂×C₄⋊C₄	—	2	2	no	—
357	C₂×C₄⋊C₄	—	2	1	no	—
358	C₂×C₄⋊C₄	—	2	8	no	—
359	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
360	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
361	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
362	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
363	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
364	C₂×C₂²⋊C₄	—	2	2	no	—
365	C₂×C₂²⋊C₄	—	2	1	no	—
366	C₂×C₂²⋊C₄	—	2	2	no	—
367	C₂×C₂²⋊C₄	—	2	1	no	—
368	C₂×C₂²⋊C₄	—	2	2	no	—
369	C₂×C₄²	—	2	2	no	—
370	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
371	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
372	#107	C₂³×C₁₃	1	4	yes	—
373	#106	C₂³×C₁₃	1	8	yes	—
374	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
375	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
376	#103	C₂³×C₁₃	1	8	yes	—
377	#103	C₂³×C₁₃	1	8	yes	—
378	#103	C₂³×C₁₃	1	8	yes	—
379	#102	C₂³×C₁₃	1	4	yes	—
380	#102	C₂³×C₁₃	1	4	yes	—
381	#102	C₂³×C₁₃	1	8	yes	—
382	C₄×C₈	C₂³×C₁₃	1	4	yes	—
383	C₄×C₈	C₂³×C₁₃	1	8	yes	—
384	C₂×C₁₃	—	4	4	no	—
385	C₂×C₁₃	—	8	2	no	—
386	C₂×C₁₃	#3360	1	4	yes	direct product factor
387	C₂×C₁₃	C₂×#548	1	1	yes	characteristic
388	C₂×C₁₃	C₂²×#135	1	1	yes	characteristic
389	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
390	C₂⁴	—	2	1	no	—
391	C₂⁴	—	2	1	no	—
392	C₂×Q₈	—	2	4	no	—
393	C₂×Q₈	—	2	2	no	—
394	C₂×Q₈	—	2	4	no	—
395	C₂×Q₈	—	2	4	no	—
396	C₂×Q₈	—	2	4	no	—
397	C₂×Q₈	—	8	2	no	—
398	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
399	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
400	C₂×D₄	—	2	1	no	—
401	C₂×D₄	—	2	1	no	—
402	C₂×D₄	—	2	2	no	—
403	C₂×D₄	—	2	2	no	—
404	C₂×D₄	—	2	2	no	—
405	C₂×D₄	C₁₃×#41	1	4	yes	—
406	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
407	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
408	C₂²×C₄	—	2	1	no	—
409	C₂²×C₄	—	2	2	no	—
410	C₂²×C₄	—	2	1	no	—
411	C₂²×C₄	—	2	2	no	—
412	C₂²×C₄	—	2	4	no	—
413	C₂²×C₄	—	2	4	no	—
414	C₂²×C₄	—	2	8	no	—
415	C₂²×C₄	—	4	4	no	—
416	C₂²×C₄	—	4	4	no	—
417	C₂²×C₄	—	8	4	no	—
418	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
419	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
420	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
421	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
422	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
423	SD₁₆	—	2	16	no	—
424	D₈	—	2	8	no	—
425	C₂×C₈	—	2	2	no	—
426	C₂×C₈	—	2	4	no	—
427	C₂×C₈	—	2	2	no	—
428	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
429	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
430	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
431	C₄⋊C₄	—	2	8	no	—
432	C₄⋊C₄	—	2	4	no	—
433	C₄⋊C₄	—	2	4	no	—
434	C₄⋊C₄	—	2	8	no	—
435	C₄⋊C₄	—	2	8	no	—
436	C₄⋊C₄	—	2	4	no	—
437	C₄⋊C₄	—	2	1	no	—
438	C₄⋊C₄	—	2	1	no	—
439	C₄⋊C₄	—	2	2	no	—
440	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
441	C₄⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
442	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
443	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
444	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
445	C₂²⋊C₄	—	2	8	no	—
446	C₂²⋊C₄	—	2	4	no	—
447	C₂²⋊C₄	—	2	8	no	—
448	C₂²⋊C₄	—	2	4	no	—
449	C₂²⋊C₄	—	2	8	no	—
450	C₄²	—	2	8	no	—
451	C₄²	C₂×D₄×C₁₃	1	2	yes	—
452	C₄²	C₂×D₄×C₁₃	1	4	yes	—
453	C₄²	C₂⁴×C₁₃	1	2	yes	—
454	C₄²	C₂⁴×C₁₃	1	4	yes	—
455	C₁₃	C₂×#3360	1	1	yes	characteristic, direct product factor, Sylow
456	C₂³	—	2	4	no	—
457	C₂³	—	2	2	no	—
458	C₂³	—	2	2	no	—
459	C₂³	—	4	2	no	—
460	C₂³	—	4	2	no	—
461	C₂³	—	4	2	no	—
462	C₂³	—	4	2	no	—
463	C₂³	—	4	2	no	—
464	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
465	Q₈	—	2	8	no	—
466	Q₈	—	2	4	no	—
467	Q₈	—	2	4	no	—
468	Q₈	—	4	4	no	—
469	Q₈	—	8	4	no	—
470	D₄	—	2	4	no	—
471	D₄	—	2	2	no	—
472	D₄	—	2	2	no	—
473	D₄	—	2	2	no	—
474	D₄	—	4	2	no	—
475	D₄	C₂×C₁₃×#41	1	4	yes	—
476	C₂×C₄	—	2	4	no	—
477	C₂×C₄	—	2	4	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	4	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	4	no	—
483	C₂×C₄	—	4	4	no	—
484	C₂×C₄	—	4	2	no	—
485	C₂×C₄	—	4	2	no	—
486	C₂×C₄	—	4	4	no	—
487	C₂×C₄	—	4	8	no	—
488	C₂×C₄	—	4	8	no	—
489	C₂×C₄	—	8	8	no	—
490	C₂×C₄	C₁₃×#135	1	4	yes	—
491	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
492	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
493	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
494	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
495	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
496	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
497	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
498	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
499	C₈	—	2	2	no	—
500	C₈	—	2	4	no	—
501	C₈	—	2	2	no	—
502	C₂²	—	2	4	no	—
503	C₂²	—	4	2	no	—
504	C₂²	—	4	2	no	—
505	C₂²	—	4	8	no	—
506	C₂²	—	4	2	no	—
507	C₂²	—	4	2	no	—
508	C₂²	—	4	2	no	—
509	C₂²	—	8	4	no	—
510	C₂²	C₁₃×#548	1	2	yes	—
511	C₂²	C₂×C₁₃×#135	1	2	yes	—
512	C₂²	C₁₃×#577	1	2	yes	—
513	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
514	C₄	—	2	4	no	—
515	C₄	—	2	4	no	—
516	C₄	—	2	2	no	—
517	C₄	—	4	2	no	—
518	C₄	—	4	2	no	—
519	C₄	—	4	4	no	—
520	C₄	—	4	4	no	—
521	C₄	C₁₃×#548	1	2	yes	—
522	C₄	C₂×C₁₃×#135	1	4	yes	—
523	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
524	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
525	C₂	—	4	4	no	—
526	C₂	—	8	2	no	—
527	C₂	C₁₃×#3360	1	4	yes	direct product factor
528	C₂	C₂×C₁₃×#548	1	1	yes	characteristic
529	C₂	C₂²×C₁₃×#135	1	1	yes	characteristic
530	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×C₁₃×D₈	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
1. C₂×C₁₃×#556	C₂	semidirect
2. C₂×C₁₃×#554	C₂	semidirect
3. C₁₃×#3360	C₂	direct (N × H)
4. C₂×C₁₃×#488	C₂	semidirect
5. C₂×C₁₃×#487	C₂	semidirect
6. C₂×C₁₃×#479	C₂	semidirect
7. C₂×C₁₃×#476	C₂	semidirect
9. C₂×C₁₃×#461	C₂	semidirect
10. C₂×C₈×Q₈×C₁₃	C₂	semidirect
11. C₂×C₄×C₁₃×SD₁₆	C₂	semidirect
16. C₁₃×#556	C₂²	semidirect
18. C₁₃×#554	C₂²	semidirect
34. C₁₃×#488	C₂²	semidirect
35. C₁₃×#487	C₂²	semidirect
36. C₁₃×#479	C₂²	semidirect
37. C₁₃×#476	C₂²	semidirect
39. C₁₃×#461	C₂²	semidirect
40. C₈×Q₈×C₁₃	C₂²	semidirect
41. C₄×C₁₃×SD₁₆	C₂²	semidirect
125. C₂×#3360	C₁₃	direct (N × H)
191. C₂×#556	C₂×C₁₃	semidirect
192. C₂×#554	C₂×C₁₃	semidirect
193. #3360	C₂×C₁₃	direct (N × H)
194. C₂×#488	C₂×C₁₃	semidirect
195. C₂×#487	C₂×C₁₃	semidirect
196. C₂×#479	C₂×C₁₃	semidirect
197. C₂×#476	C₂×C₁₃	semidirect
199. C₂×#461	C₂×C₁₃	semidirect
200. C₂×C₈×Q₈	C₂×C₁₃	semidirect
201. C₂×C₄×SD₁₆	C₂×C₁₃	semidirect
252. #556	C₂²×C₁₃	semidirect
254. #554	C₂²×C₁₃	semidirect
270. #488	C₂²×C₁₃	semidirect
271. #487	C₂²×C₁₃	semidirect
272. #479	C₂²×C₁₃	semidirect
273. #476	C₂²×C₁₃	semidirect
275. #461	C₂²×C₁₃	semidirect
276. C₈×Q₈	C₂²×C₁₃	semidirect
277. C₄×SD₁₆	C₂²×C₁₃	semidirect
386. C₂×C₁₃	#3360	direct (N × H)
455. C₁₃	C₂×#3360	direct (N × H)
527. C₂	C₁₃×#3360	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×#556	2
C₂×C₁₃×#554	2
C₁₃×#3360	2
C₂×C₁₃×#488	2
C₂×C₁₃×#487	2
C₂×C₁₃×#479	2
C₂×C₁₃×#476	2
C₂×C₁₃×#463	2
C₂×C₁₃×#461	2
C₂×C₈×Q₈×C₁₃	2
C₂×C₄×C₁₃×SD₁₆	2
C₂×C₄×C₁₃×D₈	2
C₂×#3360	13

Subgroups — C2×C13×#3360 #15747636

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3360 #15747636