Subgroups — C₂×C₁₃×#3276 #15747374

Order 3328.

2742 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×#137	C₂	1	2	yes	maximal, complemented
2	C₂×D₄×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#547	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#3276	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₁₃×#494	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃×#470	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₃×#462	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#461	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#452	C₂	1	2	yes	maximal, complemented
10	C₂×C₁₃×#451	C₂	1	2	yes	maximal, complemented
11	C₂×C₄×C₁₃×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#436	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₁₃×#41	C₂²	1	2	yes	—
14	C₂³×Q₈×C₁₃	C₂²	1	2	yes	—
15	C₂×C₁₃×#137	—	2	16	no	—
16	C₂×C₁₃×#137	C₂²	1	16	yes	complemented
17	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	—
18	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	—
19	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	—
20	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
21	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
22	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	—
23	D₄×Q₈×C₁₃	—	2	4	no	—
24	D₄×Q₈×C₁₃	C₂²	1	8	yes	complemented
25	C₁₃×#547	—	2	4	no	—
26	C₁₃×#547	C₂²	1	8	yes	—
27	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
28	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#123	—	2	2	no	—
31	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
32	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
33	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
34	C₂×C₁₃×#121	—	2	1	no	—
35	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
36	C₂×C₄×D₄×C₁₃	—	2	1	no	—
37	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
39	C₂²×C₁₃×C₄⋊C₄	—	2	1	no	—
40	C₁₃×#494	C₂²	1	8	yes	complemented
41	C₁₃×#470	C₂²	1	16	yes	complemented
42	C₁₃×#462	C₂²	1	8	yes	complemented
43	C₁₃×#461	C₂²	1	8	yes	complemented
44	C₁₃×#452	C₂²	1	16	yes	complemented
45	C₁₃×#451	C₂²	1	16	yes	complemented
46	C₄×C₁₃×SD₁₆	C₂²	1	8	yes	complemented
47	C₁₃×#436	C₂²	1	8	yes	complemented
48	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
49	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
50	C₂×C₁₃×#103	C₂²	1	2	yes	—
51	C₂×C₁₃×#103	C₂²	1	2	yes	—
52	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
53	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
54	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
55	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
56	C₂×C₁₃×#41	—	2	4	no	—
57	C₂×C₁₃×#41	—	2	8	no	—
58	C₂×C₁₃×#41	—	4	4	no	—
59	C₂×C₁₃×#41	C₂³	1	8	yes	—
60	C₂²×Q₈×C₁₃	—	2	2	no	—
61	C₂²×Q₈×C₁₃	—	2	4	no	—
62	C₂²×Q₈×C₁₃	—	2	8	no	—
63	C₂²×Q₈×C₁₃	—	4	4	no	—
64	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
65	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
66	C₂²×Q₈×C₁₃	C₂³	1	8	yes	—
67	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
68	C₂²×D₄×C₁₃	—	2	2	no	—
69	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
70	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₁₃	—	2	2	no	—
72	C₂³×C₄×C₁₃	—	2	1	no	—
73	C₂³×C₄×C₁₃	—	2	2	no	—
74	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
75	C₁₃×#137	—	2	64	no	—
76	C₂×C₁₃×Q₁₆	—	2	8	no	—
77	C₂×C₁₃×Q₁₆	—	2	8	no	—
78	C₂×C₁₃×Q₁₆	—	4	4	no	—
79	C₂×C₁₃×Q₁₆	C₂³	1	8	yes	—
80	C₂×C₁₃×Q₁₆	C₂³	1	8	yes	—
81	C₂×C₁₃×Q₁₆	C₂³	1	8	yes	—
82	C₂×C₁₃×SD₁₆	—	2	8	no	—
83	C₂×C₁₃×SD₁₆	D₄	1	8	yes	complemented
84	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
85	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
86	C₂×C₁₃×M₁₆	—	2	8	no	—
87	C₂×C₁₃×M₁₆	C₂³	1	8	yes	—
88	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
89	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
90	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
91	C₁₃×C₄⋊Q₈	—	2	8	no	—
92	C₁₃×C₄⋊Q₈	—	2	2	no	—
93	C₁₃×C₄⋊Q₈	—	2	2	no	—
94	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
95	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
96	C₁₃×#123	—	2	16	no	—
97	C₁₃×C₂²⋊Q₈	—	2	4	no	—
98	C₁₃×C₂²⋊Q₈	—	2	4	no	—
99	C₁₃×C₂²⋊Q₈	—	2	16	no	—
100	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
101	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
102	C₁₃×#121	—	2	8	no	—
103	C₄×Q₈×C₁₃	—	2	2	no	—
104	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
105	C₄×D₄×C₁₃	—	2	8	no	—
106	C₄×D₄×C₁₃	—	2	2	no	—
107	C₄×D₄×C₁₃	D₄	1	4	yes	—
108	C₄×D₄×C₁₃	C₂³	1	4	yes	—
109	C₄×D₄×C₁₃	C₂³	1	4	yes	—
110	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
111	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
112	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
113	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
114	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
115	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
116	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
117	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
118	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
119	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
120	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
121	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
122	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
123	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
124	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
125	C₂×C₄²×C₁₃	—	2	1	no	—
126	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
127	C₁₃×#106	C₂³	1	4	yes	—
128	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
129	C₁₃×#103	C₂³	1	4	yes	—
130	C₁₃×#103	C₂³	1	8	yes	—
131	C₁₃×#103	C₂³	1	8	yes	—
132	C₁₃×#102	C₂³	1	4	yes	—
133	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	—
134	C₄×C₈×C₁₃	C₂³	1	4	yes	—
135	C₂×#3276	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
136	C₂⁴×C₁₃	—	2	1	no	—
137	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
138	C₁₃×#41	—	2	16	no	—
139	C₁₃×#41	—	4	8	no	—
140	C₁₃×#41	—	4	16	no	—
141	C₂×Q₈×C₁₃	—	2	1	no	—
142	C₂×Q₈×C₁₃	—	2	8	no	—
143	C₂×Q₈×C₁₃	—	2	2	no	—
144	C₂×Q₈×C₁₃	—	2	2	no	—
145	C₂×Q₈×C₁₃	—	2	2	no	—
146	C₂×Q₈×C₁₃	—	2	16	no	—
147	C₂×Q₈×C₁₃	—	2	4	no	—
148	C₂×Q₈×C₁₃	—	2	4	no	—
149	C₂×Q₈×C₁₃	—	2	4	no	—
150	C₂×Q₈×C₁₃	—	2	4	no	—
151	C₂×Q₈×C₁₃	—	4	8	no	—
152	C₂×Q₈×C₁₃	—	4	8	no	—
153	C₂×Q₈×C₁₃	—	4	16	no	—
154	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
155	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
156	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
157	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
158	C₂×D₄×C₁₃	—	2	8	no	—
159	C₂×D₄×C₁₃	—	2	4	no	—
160	C₂×D₄×C₁₃	—	2	1	no	—
161	C₂×D₄×C₁₃	—	2	2	no	—
162	C₂×D₄×C₁₃	—	4	8	no	—
163	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
164	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
165	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
166	C₂²×C₄×C₁₃	—	2	1	no	—
167	C₂²×C₄×C₁₃	—	2	4	no	—
168	C₂²×C₄×C₁₃	—	2	4	no	—
169	C₂²×C₄×C₁₃	—	2	8	no	—
170	C₂²×C₄×C₁₃	—	2	1	no	—
171	C₂²×C₄×C₁₃	—	2	1	no	—
172	C₂²×C₄×C₁₃	—	2	2	no	—
173	C₂²×C₄×C₁₃	—	2	2	no	—
174	C₂²×C₄×C₁₃	—	2	4	no	—
175	C₂²×C₄×C₁₃	—	2	8	no	—
176	C₂²×C₄×C₁₃	—	4	8	no	—
177	C₂²×C₄×C₁₃	—	4	8	no	—
178	C₂²×C₄×C₁₃	—	4	4	no	—
179	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
180	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
181	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
182	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
183	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
184	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
185	C₁₃×Q₁₆	—	2	16	no	—
186	C₁₃×Q₁₆	—	2	16	no	—
187	C₁₃×Q₁₆	—	4	8	no	—
188	C₁₃×SD₁₆	—	2	16	no	—
189	C₁₃×SD₁₆	C₂×D₄	1	16	yes	complemented
190	C₁₃×M₁₆	—	2	16	no	—
191	C₂×C₈×C₁₃	—	2	4	no	—
192	C₂×C₈×C₁₃	—	2	2	no	—
193	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
194	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
195	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
196	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
197	C₁₃×C₄⋊C₄	—	2	4	no	—
198	C₁₃×C₄⋊C₄	—	2	8	no	—
199	C₁₃×C₄⋊C₄	—	2	4	no	—
200	C₁₃×C₄⋊C₄	—	2	4	no	—
201	C₁₃×C₄⋊C₄	—	2	4	no	—
202	C₁₃×C₄⋊C₄	—	2	8	no	—
203	C₁₃×C₄⋊C₄	—	2	4	no	—
204	C₁₃×C₄⋊C₄	—	2	1	no	—
205	C₁₃×C₄⋊C₄	—	2	1	no	—
206	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
207	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
208	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
209	C₁₃×C₂²⋊C₄	—	2	8	no	—
210	C₁₃×C₂²⋊C₄	—	2	8	no	—
211	C₁₃×C₂²⋊C₄	—	2	4	no	—
212	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
213	C₄²×C₁₃	—	2	4	no	—
214	C₄²×C₁₃	C₂×D₄	1	2	yes	—
215	C₄²×C₁₃	C₂⁴	1	2	yes	—
216	C₂²×#137	C₂×C₁₃	1	2	yes	complemented
217	C₂×D₄×Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
218	C₂×#547	C₂×C₁₃	1	1	yes	characteristic
219	#3276	C₂×C₁₃	1	16	yes	direct product factor
220	C₂×#494	C₂×C₁₃	1	1	yes	characteristic, complemented
221	C₂×#470	C₂×C₁₃	1	2	yes	complemented
222	C₂×#462	C₂×C₁₃	1	1	yes	characteristic, complemented
223	C₂×#461	C₂×C₁₃	1	1	yes	characteristic, complemented
224	C₂×#452	C₂×C₁₃	1	2	yes	complemented
225	C₂×#451	C₂×C₁₃	1	2	yes	complemented
226	C₂×C₄×SD₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
227	C₂×#436	C₂×C₁₃	1	1	yes	characteristic, complemented
228	C₂³×C₁₃	—	2	4	no	—
229	C₂³×C₁₃	—	2	4	no	—
230	C₂³×C₁₃	—	2	4	no	—
231	C₂³×C₁₃	—	2	4	no	—
232	C₂³×C₁₃	—	2	2	no	—
233	C₂³×C₁₃	—	4	2	no	—
234	C₂³×C₁₃	—	4	2	no	—
235	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
236	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
237	Q₈×C₁₃	—	2	4	no	—
238	Q₈×C₁₃	—	2	2	no	—
239	Q₈×C₁₃	—	2	4	no	—
240	Q₈×C₁₃	—	2	4	no	—
241	Q₈×C₁₃	—	2	4	no	—
242	Q₈×C₁₃	—	2	4	no	—
243	Q₈×C₁₃	—	4	16	no	—
244	Q₈×C₁₃	—	4	4	no	—
245	Q₈×C₁₃	—	4	4	no	—
246	Q₈×C₁₃	C₂²×D₄	1	4	yes	—
247	D₄×C₁₃	—	2	4	no	—
248	D₄×C₁₃	—	2	8	no	—
249	D₄×C₁₃	—	2	2	no	—
250	D₄×C₁₃	—	4	16	no	—
251	D₄×C₁₃	C₂²×D₄	1	4	yes	—
252	C₂×C₄×C₁₃	—	2	4	no	—
253	C₂×C₄×C₁₃	—	2	4	no	—
254	C₂×C₄×C₁₃	—	2	2	no	—
255	C₂×C₄×C₁₃	—	2	2	no	—
256	C₂×C₄×C₁₃	—	2	8	no	—
257	C₂×C₄×C₁₃	—	2	4	no	—
258	C₂×C₄×C₁₃	—	2	4	no	—
259	C₂×C₄×C₁₃	—	2	2	no	—
260	C₂×C₄×C₁₃	—	2	2	no	—
261	C₂×C₄×C₁₃	—	2	4	no	—
262	C₂×C₄×C₁₃	—	2	4	no	—
263	C₂×C₄×C₁₃	—	4	16	no	—
264	C₂×C₄×C₁₃	—	4	16	no	—
265	C₂×C₄×C₁₃	—	4	4	no	—
266	C₂×C₄×C₁₃	—	4	4	no	—
267	C₂×C₄×C₁₃	—	4	2	no	—
268	C₂×C₄×C₁₃	—	4	2	no	—
269	C₂×C₄×C₁₃	—	4	8	no	—
270	C₂×C₄×C₁₃	#137	1	4	yes	complemented
271	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
272	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
273	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
274	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
275	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
276	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
277	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
278	C₈×C₁₃	—	2	4	no	—
279	C₈×C₁₃	—	2	2	no	—
280	C₈×C₁₃	C₂²×D₄	1	4	yes	—
281	C₂²×#41	C₂²×C₁₃	1	2	yes	—
282	C₂³×Q₈	C₂²×C₁₃	1	2	yes	—
283	C₂×#137	—	2	16	no	—
284	C₂×#137	C₂²×C₁₃	1	16	yes	complemented
285	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	—
286	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	—
287	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	—
288	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
289	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
290	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	—
291	D₄×Q₈	—	2	4	no	—
292	D₄×Q₈	C₂²×C₁₃	1	8	yes	complemented
293	#547	—	2	4	no	—
294	#547	C₂²×C₁₃	1	8	yes	—
295	C₂×C₄⋊Q₈	—	2	1	no	—
296	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
297	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
298	C₂×#123	—	2	2	no	—
299	C₂×C₂²⋊Q₈	—	2	2	no	—
300	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
301	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
302	C₂×#121	—	2	1	no	—
303	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
304	C₂×C₄×D₄	—	2	1	no	—
305	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
306	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
307	C₂²×C₄⋊C₄	—	2	1	no	—
308	#494	C₂²×C₁₃	1	8	yes	complemented
309	#470	C₂²×C₁₃	1	16	yes	complemented
310	#462	C₂²×C₁₃	1	8	yes	complemented
311	#461	C₂²×C₁₃	1	8	yes	complemented
312	#452	C₂²×C₁₃	1	16	yes	complemented
313	#451	C₂²×C₁₃	1	16	yes	complemented
314	C₄×SD₁₆	C₂²×C₁₃	1	8	yes	complemented
315	#436	C₂²×C₁₃	1	8	yes	complemented
316	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
317	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
318	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
319	C₂×#103	C₂²×C₁₃	1	2	yes	—
320	C₂×#103	C₂²×C₁₃	1	2	yes	—
321	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
322	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
323	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
324	C₂²×C₁₃	—	2	4	no	—
325	C₂²×C₁₃	—	2	4	no	—
326	C₂²×C₁₃	—	2	4	no	—
327	C₂²×C₁₃	—	2	4	no	—
328	C₂²×C₁₃	—	4	8	no	—
329	C₂²×C₁₃	—	4	8	no	—
330	C₂²×C₁₃	—	4	2	no	—
331	C₂²×C₁₃	—	4	2	no	—
332	C₂²×C₁₃	D₄²	1	2	yes	—
333	C₂²×C₁₃	C₂×#137	1	2	yes	—
334	C₂²×C₁₃	#578	1	2	yes	—
335	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
336	C₄×C₁₃	—	2	4	no	—
337	C₄×C₁₃	—	2	4	no	—
338	C₄×C₁₃	—	2	2	no	—
339	C₄×C₁₃	—	4	4	no	—
340	C₄×C₁₃	—	4	4	no	—
341	C₄×C₁₃	—	4	2	no	—
342	C₄×C₁₃	—	4	2	no	—
343	C₄×C₁₃	D₄²	1	2	yes	—
344	C₄×C₁₃	C₂×#137	1	4	yes	complemented
345	C₄×C₁₃	C₂³×D₄	1	1	yes	characteristic
346	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
347	C₂×#41	—	2	4	no	—
348	C₂×#41	—	2	8	no	—
349	C₂×#41	—	4	4	no	—
350	C₂×#41	C₂³×C₁₃	1	8	yes	—
351	C₂²×Q₈	—	2	2	no	—
352	C₂²×Q₈	—	2	4	no	—
353	C₂²×Q₈	—	2	8	no	—
354	C₂²×Q₈	—	4	4	no	—
355	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
356	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
357	C₂²×Q₈	C₂³×C₁₃	1	8	yes	—
358	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
359	C₂²×D₄	—	2	2	no	—
360	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
361	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
362	C₂³×C₄	—	2	2	no	—
363	C₂³×C₄	—	2	1	no	—
364	C₂³×C₄	—	2	2	no	—
365	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
366	#137	—	2	64	no	—
367	C₂×Q₁₆	—	2	8	no	—
368	C₂×Q₁₆	—	2	8	no	—
369	C₂×Q₁₆	—	4	4	no	—
370	C₂×Q₁₆	C₂³×C₁₃	1	8	yes	—
371	C₂×Q₁₆	C₂³×C₁₃	1	8	yes	—
372	C₂×Q₁₆	C₂³×C₁₃	1	8	yes	—
373	C₂×SD₁₆	—	2	8	no	—
374	C₂×SD₁₆	D₄×C₁₃	1	8	yes	complemented
375	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
376	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
377	C₂×M₁₆	—	2	8	no	—
378	C₂×M₁₆	C₂³×C₁₃	1	8	yes	—
379	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
380	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
381	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
382	C₄⋊Q₈	—	2	8	no	—
383	C₄⋊Q₈	—	2	2	no	—
384	C₄⋊Q₈	—	2	2	no	—
385	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
386	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
387	#123	—	2	16	no	—
388	C₂²⋊Q₈	—	2	4	no	—
389	C₂²⋊Q₈	—	2	4	no	—
390	C₂²⋊Q₈	—	2	16	no	—
391	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
392	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
393	#121	—	2	8	no	—
394	C₄×Q₈	—	2	2	no	—
395	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
396	C₄×D₄	—	2	8	no	—
397	C₄×D₄	—	2	2	no	—
398	C₄×D₄	D₄×C₁₃	1	4	yes	—
399	C₄×D₄	C₂³×C₁₃	1	4	yes	—
400	C₄×D₄	C₂³×C₁₃	1	4	yes	—
401	C₂×C₄⋊C₄	—	2	1	no	—
402	C₂×C₄⋊C₄	—	2	2	no	—
403	C₂×C₄⋊C₄	—	2	1	no	—
404	C₂×C₄⋊C₄	—	2	1	no	—
405	C₂×C₄⋊C₄	—	2	1	no	—
406	C₂×C₄⋊C₄	—	2	2	no	—
407	C₂×C₄⋊C₄	—	2	1	no	—
408	C₂×C₄⋊C₄	—	2	8	no	—
409	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
410	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
411	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
412	C₂×C₂²⋊C₄	—	2	2	no	—
413	C₂×C₂²⋊C₄	—	2	2	no	—
414	C₂×C₂²⋊C₄	—	2	1	no	—
415	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
416	C₂×C₄²	—	2	1	no	—
417	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
418	#106	C₂³×C₁₃	1	4	yes	—
419	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
420	#103	C₂³×C₁₃	1	4	yes	—
421	#103	C₂³×C₁₃	1	8	yes	—
422	#103	C₂³×C₁₃	1	8	yes	—
423	#102	C₂³×C₁₃	1	4	yes	—
424	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	—
425	C₄×C₈	C₂³×C₁₃	1	4	yes	—
426	C₂×C₁₃	—	4	4	no	—
427	C₂×C₁₃	—	4	4	no	—
428	C₂×C₁₃	#3276	1	4	yes	direct product factor
429	C₂×C₁₃	C₂×D₄²	1	1	yes	characteristic
430	C₂×C₁₃	C₂²×#137	1	1	yes	characteristic
431	C₂×C₁₃	C₂×#578	1	1	yes	characteristic
432	C₂⁴	—	2	1	no	—
433	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
434	#41	—	2	16	no	—
435	#41	—	4	8	no	—
436	#41	—	4	16	no	—
437	C₂×Q₈	—	2	1	no	—
438	C₂×Q₈	—	2	8	no	—
439	C₂×Q₈	—	2	2	no	—
440	C₂×Q₈	—	2	2	no	—
441	C₂×Q₈	—	2	2	no	—
442	C₂×Q₈	—	2	16	no	—
443	C₂×Q₈	—	2	4	no	—
444	C₂×Q₈	—	2	4	no	—
445	C₂×Q₈	—	2	4	no	—
446	C₂×Q₈	—	2	4	no	—
447	C₂×Q₈	—	4	8	no	—
448	C₂×Q₈	—	4	8	no	—
449	C₂×Q₈	—	4	16	no	—
450	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
451	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
452	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
453	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
454	C₂×D₄	—	2	8	no	—
455	C₂×D₄	—	2	4	no	—
456	C₂×D₄	—	2	1	no	—
457	C₂×D₄	—	2	2	no	—
458	C₂×D₄	—	4	8	no	—
459	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
460	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
461	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
462	C₂²×C₄	—	2	1	no	—
463	C₂²×C₄	—	2	4	no	—
464	C₂²×C₄	—	2	4	no	—
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	2	1	no	—
467	C₂²×C₄	—	2	2	no	—
468	C₂²×C₄	—	2	2	no	—
469	C₂²×C₄	—	2	8	no	—
470	C₂²×C₄	—	2	4	no	—
471	C₂²×C₄	—	2	8	no	—
472	C₂²×C₄	—	4	8	no	—
473	C₂²×C₄	—	4	8	no	—
474	C₂²×C₄	—	4	4	no	—
475	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
476	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
477	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
478	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
479	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
480	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
481	Q₁₆	—	2	16	no	—
482	Q₁₆	—	2	16	no	—
483	Q₁₆	—	4	8	no	—
484	SD₁₆	—	2	16	no	—
485	SD₁₆	C₂×D₄×C₁₃	1	16	yes	complemented
486	M₁₆	—	2	16	no	—
487	C₂×C₈	—	2	4	no	—
488	C₂×C₈	—	2	2	no	—
489	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
490	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
491	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
492	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
493	C₄⋊C₄	—	2	4	no	—
494	C₄⋊C₄	—	2	8	no	—
495	C₄⋊C₄	—	2	4	no	—
496	C₄⋊C₄	—	2	4	no	—
497	C₄⋊C₄	—	2	4	no	—
498	C₄⋊C₄	—	2	8	no	—
499	C₄⋊C₄	—	2	4	no	—
500	C₄⋊C₄	—	2	1	no	—
501	C₄⋊C₄	—	2	1	no	—
502	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
503	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
504	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
505	C₂²⋊C₄	—	2	8	no	—
506	C₂²⋊C₄	—	2	8	no	—
507	C₂²⋊C₄	—	2	4	no	—
508	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
509	C₄²	—	2	4	no	—
510	C₄²	C₂×D₄×C₁₃	1	2	yes	—
511	C₄²	C₂⁴×C₁₃	1	2	yes	—
512	C₁₃	C₂×#3276	1	1	yes	characteristic, direct product factor, Sylow
513	C₂³	—	2	4	no	—
514	C₂³	—	2	4	no	—
515	C₂³	—	2	4	no	—
516	C₂³	—	2	4	no	—
517	C₂³	—	2	2	no	—
518	C₂³	—	4	2	no	—
519	C₂³	—	4	2	no	—
520	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
521	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
522	Q₈	—	2	4	no	—
523	Q₈	—	2	2	no	—
524	Q₈	—	2	4	no	—
525	Q₈	—	2	4	no	—
526	Q₈	—	2	4	no	—
527	Q₈	—	2	4	no	—
528	Q₈	—	4	16	no	—
529	Q₈	—	4	4	no	—
530	Q₈	—	4	4	no	—
531	Q₈	C₂²×D₄×C₁₃	1	4	yes	—
532	D₄	—	2	4	no	—
533	D₄	—	2	8	no	—
534	D₄	—	2	2	no	—
535	D₄	—	4	16	no	—
536	D₄	C₂²×D₄×C₁₃	1	4	yes	—
537	C₂×C₄	—	2	4	no	—
538	C₂×C₄	—	2	4	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	2	8	no	—
542	C₂×C₄	—	2	4	no	—
543	C₂×C₄	—	2	4	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	—	2	2	no	—
546	C₂×C₄	—	2	4	no	—
547	C₂×C₄	—	2	4	no	—
548	C₂×C₄	—	4	16	no	—
549	C₂×C₄	—	4	16	no	—
550	C₂×C₄	—	4	4	no	—
551	C₂×C₄	—	4	4	no	—
552	C₂×C₄	—	4	2	no	—
553	C₂×C₄	—	4	2	no	—
554	C₂×C₄	—	4	8	no	—
555	C₂×C₄	C₁₃×#137	1	4	yes	complemented
556	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
557	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
558	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
559	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
560	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
561	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
562	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
563	C₈	—	2	4	no	—
564	C₈	—	2	2	no	—
565	C₈	C₂²×D₄×C₁₃	1	4	yes	—
566	C₂²	—	2	4	no	—
567	C₂²	—	2	4	no	—
568	C₂²	—	2	4	no	—
569	C₂²	—	2	4	no	—
570	C₂²	—	4	8	no	—
571	C₂²	—	4	8	no	—
572	C₂²	—	4	2	no	—
573	C₂²	—	4	2	no	—
574	C₂²	D₄²×C₁₃	1	2	yes	—
575	C₂²	C₂×C₁₃×#137	1	2	yes	—
576	C₂²	C₁₃×#578	1	2	yes	—
577	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
578	C₄	—	2	2	no	—
579	C₄	—	2	4	no	—
580	C₄	—	2	4	no	—
581	C₄	—	4	2	no	—
582	C₄	—	4	2	no	—
583	C₄	—	4	4	no	—
584	C₄	—	4	4	no	—
585	C₄	D₄²×C₁₃	1	2	yes	—
586	C₄	C₂×C₁₃×#137	1	4	yes	complemented
587	C₄	C₂³×D₄×C₁₃	1	1	yes	characteristic
588	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
589	C₂	—	4	4	no	—
590	C₂	—	4	4	no	—
591	C₂	C₁₃×#3276	1	4	yes	direct product factor
592	C₂	C₂×D₄²×C₁₃	1	1	yes	characteristic
593	C₂	C₂²×C₁₃×#137	1	1	yes	characteristic
594	C₂	C₂×C₁₃×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₂×C₁₃×#547	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄×D₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₃×#137	C₂	semidirect
2. C₂×D₄×Q₈×C₁₃	C₂	semidirect
4. C₁₃×#3276	C₂	direct (N × H)
5. C₂×C₁₃×#494	C₂	semidirect
6. C₂×C₁₃×#470	C₂	semidirect
7. C₂×C₁₃×#462	C₂	semidirect
8. C₂×C₁₃×#461	C₂	semidirect
9. C₂×C₁₃×#452	C₂	semidirect
10. C₂×C₁₃×#451	C₂	semidirect
11. C₂×C₄×C₁₃×SD₁₆	C₂	semidirect
12. C₂×C₁₃×#436	C₂	semidirect
16. C₂×C₁₃×#137	C₂²	semidirect
24. D₄×Q₈×C₁₃	C₂²	semidirect
40. C₁₃×#494	C₂²	semidirect
41. C₁₃×#470	C₂²	semidirect
42. C₁₃×#462	C₂²	semidirect
43. C₁₃×#461	C₂²	semidirect
44. C₁₃×#452	C₂²	semidirect
45. C₁₃×#451	C₂²	semidirect
46. C₄×C₁₃×SD₁₆	C₂²	semidirect
47. C₁₃×#436	C₂²	semidirect
83. C₂×C₁₃×SD₁₆	D₄	semidirect
135. C₂×#3276	C₁₃	direct (N × H)
189. C₁₃×SD₁₆	C₂×D₄	semidirect
216. C₂²×#137	C₂×C₁₃	semidirect
217. C₂×D₄×Q₈	C₂×C₁₃	semidirect
219. #3276	C₂×C₁₃	direct (N × H)
220. C₂×#494	C₂×C₁₃	semidirect
221. C₂×#470	C₂×C₁₃	semidirect
222. C₂×#462	C₂×C₁₃	semidirect
223. C₂×#461	C₂×C₁₃	semidirect
224. C₂×#452	C₂×C₁₃	semidirect
225. C₂×#451	C₂×C₁₃	semidirect
226. C₂×C₄×SD₁₆	C₂×C₁₃	semidirect
227. C₂×#436	C₂×C₁₃	semidirect
270. C₂×C₄×C₁₃	#137	semidirect
284. C₂×#137	C₂²×C₁₃	semidirect
292. D₄×Q₈	C₂²×C₁₃	semidirect
308. #494	C₂²×C₁₃	semidirect
309. #470	C₂²×C₁₃	semidirect
310. #462	C₂²×C₁₃	semidirect
311. #461	C₂²×C₁₃	semidirect
312. #452	C₂²×C₁₃	semidirect
313. #451	C₂²×C₁₃	semidirect
314. C₄×SD₁₆	C₂²×C₁₃	semidirect
315. #436	C₂²×C₁₃	semidirect
344. C₄×C₁₃	C₂×#137	semidirect
374. C₂×SD₁₆	D₄×C₁₃	semidirect
428. C₂×C₁₃	#3276	direct (N × H)
485. SD₁₆	C₂×D₄×C₁₃	semidirect
512. C₁₃	C₂×#3276	direct (N × H)
555. C₂×C₄	C₁₃×#137	semidirect
586. C₄	C₂×C₁₃×#137	semidirect
591. C₂	C₁₃×#3276	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₁₃×#137	2
C₂×D₄×Q₈×C₁₃	2
C₂×C₁₃×#547	2
C₁₃×#3276	2
C₂×C₁₃×#494	2
C₂×C₁₃×#470	2
C₂×C₁₃×#462	2
C₂×C₁₃×#461	2
C₂×C₁₃×#452	2
C₂×C₁₃×#451	2
C₂×C₄×C₁₃×SD₁₆	2
C₂×C₁₃×#436	2
C₂×#3276	13

Subgroups — C2×C13×#3276 #15747374

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3276 #15747374