Subgroups — C₂×C₁₃×#2620 #15720950

Order 3328.

3566 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×#124	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₁₃×#121	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₁₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2620	C₂	1	16	yes	maximal, direct product factor
6	C₂×C₁₃×#396	C₂	1	4	yes	maximal, complemented
7	C₂×C₁₃×#394	C₂	1	4	yes	maximal, complemented
8	C₂×C₁₃×#391	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#390	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×#384	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
12	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
13	C₂³×D₄×C₁₃	C₂²	1	2	yes	—
14	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#124	—	2	8	no	—
16	C₂×C₁₃×#124	C₂²	1	8	yes	complemented
17	C₂×C₁₃×C₂²⋊Q₈	—	2	8	no	—
18	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	8	yes	complemented
19	C₂×C₁₃×#121	—	2	8	no	—
20	C₂×C₁₃×#121	C₂²	1	8	yes	—
21	C₂×C₁₃×#117	—	2	8	no	—
22	C₂×C₁₃×#117	C₂²	1	8	yes	complemented
23	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
26	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
27	C₂²×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
28	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
29	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
30	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
31	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
32	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
33	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
34	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
35	C₁₃×#396	C₂²	1	32	yes	complemented
36	C₁₃×#394	C₂²	1	32	yes	complemented
37	C₁₃×#391	C₂²	1	8	yes	complemented
38	C₁₃×#390	C₂²	1	8	yes	complemented
39	C₁₃×#384	C₂²	1	8	yes	complemented
40	C₂×C₁₃×#95	C₂²	1	4	yes	—
41	C₂⁵×C₁₃	C₂³	1	2	yes	—
42	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
43	C₂²×Q₈×C₁₃	—	2	4	no	—
44	C₂²×Q₈×C₁₃	—	2	4	no	—
45	C₂²×Q₈×C₁₃	—	2	4	no	—
46	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
47	C₂²×D₄×C₁₃	—	2	8	no	—
48	C₂²×D₄×C₁₃	—	2	4	no	—
49	C₂²×D₄×C₁₃	—	2	4	no	—
50	C₂²×D₄×C₁₃	—	2	4	no	—
51	C₂²×D₄×C₁₃	—	4	8	no	—
52	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
53	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
54	C₂³×C₄×C₁₃	—	2	4	no	—
55	C₂³×C₄×C₁₃	—	2	4	no	—
56	C₂³×C₄×C₁₃	D₄	1	8	yes	—
57	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
58	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
59	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
60	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
61	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
62	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
63	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
65	C₁₃×#124	—	2	32	no	—
66	C₁₃×C₂²⋊Q₈	—	2	32	no	—
67	C₁₃×#121	—	2	32	no	—
68	C₁₃×#117	—	2	32	no	—
69	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
70	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
71	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
72	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
73	C₂×C₁₃×C₄⋊C₄	—	4	8	no	—
74	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
75	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
76	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
77	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
78	C₂×C₁₃×C₄⋊C₄	C₂³	1	16	yes	—
79	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
80	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
81	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
82	C₂×C₁₃×C₂²⋊C₄	—	2	16	no	—
83	C₂×C₁₃×C₂²⋊C₄	—	4	8	no	—
84	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
85	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
86	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
87	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
88	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
89	C₂×C₄²×C₁₃	—	2	4	no	—
90	C₂×C₄²×C₁₃	D₄	1	8	yes	complemented
91	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
92	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
93	C₁₃×#95	C₂³	1	16	yes	—
94	C₂×#2620	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
95	C₂⁴×C₁₃	—	2	2	no	—
96	C₂⁴×C₁₃	—	2	2	no	—
97	C₂⁴×C₁₃	—	2	4	no	—
98	C₂⁴×C₁₃	—	2	4	no	—
99	C₂⁴×C₁₃	—	2	4	no	—
100	C₂⁴×C₁₃	—	2	4	no	—
101	C₂⁴×C₁₃	—	2	4	no	—
102	C₂⁴×C₁₃	—	2	8	no	—
103	C₂⁴×C₁₃	—	2	8	no	—
104	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
105	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
106	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
107	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
108	C₂×Q₈×C₁₃	—	2	8	no	—
109	C₂×Q₈×C₁₃	—	2	8	no	—
110	C₂×Q₈×C₁₃	—	2	8	no	—
111	C₂×Q₈×C₁₃	—	4	16	no	—
112	C₂×D₄×C₁₃	—	2	16	no	—
113	C₂×D₄×C₁₃	—	2	8	no	—
114	C₂×D₄×C₁₃	—	2	8	no	—
115	C₂×D₄×C₁₃	—	2	8	no	—
116	C₂×D₄×C₁₃	—	4	16	no	—
117	C₂×D₄×C₁₃	—	4	32	no	—
118	C₂×D₄×C₁₃	—	4	16	no	—
119	C₂²×C₄×C₁₃	—	2	2	no	—
120	C₂²×C₄×C₁₃	—	2	2	no	—
121	C₂²×C₄×C₁₃	—	2	4	no	—
122	C₂²×C₄×C₁₃	—	2	4	no	—
123	C₂²×C₄×C₁₃	—	2	32	no	—
124	C₂²×C₄×C₁₃	—	2	8	no	—
125	C₂²×C₄×C₁₃	—	2	8	no	—
126	C₂²×C₄×C₁₃	—	2	4	no	—
127	C₂²×C₄×C₁₃	—	2	4	no	—
128	C₂²×C₄×C₁₃	—	2	4	no	—
129	C₂²×C₄×C₁₃	—	2	4	no	—
130	C₂²×C₄×C₁₃	—	2	4	no	—
131	C₂²×C₄×C₁₃	—	2	4	no	—
132	C₂²×C₄×C₁₃	—	2	4	no	—
133	C₂²×C₄×C₁₃	—	2	8	no	—
134	C₂²×C₄×C₁₃	—	2	8	no	—
135	C₂²×C₄×C₁₃	—	2	4	no	—
136	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
137	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
138	C₂²×C₄×C₁₃	C₂×D₄	1	16	yes	—
139	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
140	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
141	C₂²×C₄×C₁₃	#41	1	4	yes	—
142	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
143	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
144	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
145	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
146	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
147	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
148	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
149	C₁₃×C₄⋊C₄	—	2	16	no	—
150	C₁₃×C₄⋊C₄	—	2	8	no	—
151	C₁₃×C₄⋊C₄	—	2	8	no	—
152	C₁₃×C₄⋊C₄	—	2	16	no	—
153	C₁₃×C₄⋊C₄	—	4	16	no	—
154	C₁₃×C₂²⋊C₄	—	2	16	no	—
155	C₁₃×C₂²⋊C₄	—	2	16	no	—
156	C₁₃×C₂²⋊C₄	—	2	16	no	—
157	C₁₃×C₂²⋊C₄	—	2	32	no	—
158	C₁₃×C₂²⋊C₄	—	4	16	no	—
159	C₄²×C₁₃	—	2	8	no	—
160	C₄²×C₁₃	C₂×D₄	1	16	yes	complemented
161	C₂²×#124	C₂×C₁₃	1	1	yes	characteristic, complemented
162	C₂²×C₂²⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
163	C₂²×#121	C₂×C₁₃	1	1	yes	characteristic
164	C₂²×#117	C₂×C₁₃	1	1	yes	characteristic, complemented
165	#2620	C₂×C₁₃	1	16	yes	direct product factor
166	C₂×#396	C₂×C₁₃	1	4	yes	complemented
167	C₂×#394	C₂×C₁₃	1	4	yes	complemented
168	C₂×#391	C₂×C₁₃	1	1	yes	characteristic, complemented
169	C₂×#390	C₂×C₁₃	1	1	yes	characteristic, complemented
170	C₂×#384	C₂×C₁₃	1	1	yes	characteristic, complemented
171	C₂³×C₁₃	—	2	8	no	—
172	C₂³×C₁₃	—	2	8	no	—
173	C₂³×C₁₃	—	2	8	no	—
174	C₂³×C₁₃	—	2	2	no	—
175	C₂³×C₁₃	—	2	2	no	—
176	C₂³×C₁₃	—	2	4	no	—
177	C₂³×C₁₃	—	2	4	no	—
178	C₂³×C₁₃	—	2	4	no	—
179	C₂³×C₁₃	—	2	4	no	—
180	C₂³×C₁₃	—	2	4	no	—
181	C₂³×C₁₃	—	2	8	no	—
182	C₂³×C₁₃	—	2	8	no	—
183	C₂³×C₁₃	—	4	8	no	—
184	C₂³×C₁₃	—	4	8	no	—
185	C₂³×C₁₃	—	4	8	no	—
186	C₂³×C₁₃	—	4	8	no	—
187	C₂³×C₁₃	—	4	8	no	—
188	C₂³×C₁₃	—	4	16	no	—
189	C₂³×C₁₃	—	4	16	no	—
190	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
191	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
192	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
193	C₂³×C₁₃	C₂×#41	1	2	yes	—
194	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
195	C₂³×C₁₃	2₋¹⁺⁴	1	4	yes	—
196	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
197	Q₈×C₁₃	—	4	16	no	—
198	D₄×C₁₃	—	4	32	no	—
199	D₄×C₁₃	—	4	16	no	—
200	C₂×C₄×C₁₃	—	2	8	no	—
201	C₂×C₄×C₁₃	—	2	16	no	—
202	C₂×C₄×C₁₃	—	2	2	no	—
203	C₂×C₄×C₁₃	—	2	2	no	—
204	C₂×C₄×C₁₃	—	2	4	no	—
205	C₂×C₄×C₁₃	—	2	4	no	—
206	C₂×C₄×C₁₃	—	2	32	no	—
207	C₂×C₄×C₁₃	—	2	4	no	—
208	C₂×C₄×C₁₃	—	2	4	no	—
209	C₂×C₄×C₁₃	—	2	4	no	—
210	C₂×C₄×C₁₃	—	2	4	no	—
211	C₂×C₄×C₁₃	—	2	4	no	—
212	C₂×C₄×C₁₃	—	2	4	no	—
213	C₂×C₄×C₁₃	—	2	4	no	—
214	C₂×C₄×C₁₃	—	2	8	no	—
215	C₂×C₄×C₁₃	—	2	8	no	—
216	C₂×C₄×C₁₃	—	2	4	no	—
217	C₂×C₄×C₁₃	—	4	8	no	—
218	C₂×C₄×C₁₃	—	4	8	no	—
219	C₂×C₄×C₁₃	—	4	8	no	—
220	C₂×C₄×C₁₃	—	4	8	no	—
221	C₂×C₄×C₁₃	#121	1	16	yes	—
222	C₂×C₄×C₁₃	C₂²×D₄	1	8	yes	—
223	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
224	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
225	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
226	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
227	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
228	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
229	C₂³×D₄	C₂²×C₁₃	1	2	yes	—
230	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
231	C₂×#124	—	2	8	no	—
232	C₂×#124	C₂²×C₁₃	1	8	yes	complemented
233	C₂×C₂²⋊Q₈	—	2	8	no	—
234	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	8	yes	complemented
235	C₂×#121	—	2	8	no	—
236	C₂×#121	C₂²×C₁₃	1	8	yes	—
237	C₂×#117	—	2	8	no	—
238	C₂×#117	C₂²×C₁₃	1	8	yes	complemented
239	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
240	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
241	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
242	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
243	C₂²×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
244	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
245	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
246	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
247	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
248	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
249	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
250	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
251	#396	C₂²×C₁₃	1	32	yes	complemented
252	#394	C₂²×C₁₃	1	32	yes	complemented
253	#391	C₂²×C₁₃	1	8	yes	complemented
254	#390	C₂²×C₁₃	1	8	yes	complemented
255	#384	C₂²×C₁₃	1	8	yes	complemented
256	C₂×#95	C₂²×C₁₃	1	4	yes	—
257	C₂²×C₁₃	—	2	4	no	—
258	C₂²×C₁₃	—	2	4	no	—
259	C₂²×C₁₃	—	2	4	no	—
260	C₂²×C₁₃	—	4	16	no	—
261	C₂²×C₁₃	—	4	4	no	—
262	C₂²×C₁₃	—	4	4	no	—
263	C₂²×C₁₃	—	4	4	no	—
264	C₂²×C₁₃	—	4	4	no	—
265	C₂²×C₁₃	—	4	4	no	—
266	C₂²×C₁₃	—	4	8	no	—
267	C₂²×C₁₃	—	4	8	no	—
268	C₂²×C₁₃	—	8	16	no	—
269	C₂²×C₁₃	C₂×#121	1	4	yes	—
270	C₂²×C₁₃	#535	1	4	yes	—
271	C₂²×C₁₃	#536	1	4	yes	—
272	C₂²×C₁₃	#537	1	8	yes	—
273	C₂²×C₁₃	#542	1	8	yes	—
274	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
275	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
276	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
277	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
278	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
279	C₄×C₁₃	—	2	4	no	—
280	C₄×C₁₃	—	2	8	no	—
281	C₄×C₁₃	—	4	4	no	—
282	C₄×C₁₃	—	4	4	no	—
283	C₄×C₁₃	—	4	4	no	—
284	C₄×C₁₃	—	4	4	no	—
285	C₄×C₁₃	C₂×#121	1	8	yes	—
286	C₂⁵	C₂³×C₁₃	1	2	yes	—
287	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
288	C₂²×Q₈	—	2	4	no	—
289	C₂²×Q₈	—	2	4	no	—
290	C₂²×Q₈	—	2	4	no	—
291	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
292	C₂²×D₄	—	2	8	no	—
293	C₂²×D₄	—	2	4	no	—
294	C₂²×D₄	—	2	4	no	—
295	C₂²×D₄	—	2	4	no	—
296	C₂²×D₄	—	4	8	no	—
297	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
298	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
299	C₂³×C₄	—	2	4	no	—
300	C₂³×C₄	—	2	4	no	—
301	C₂³×C₄	D₄×C₁₃	1	8	yes	—
302	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
303	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
304	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
305	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
306	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
307	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
308	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
309	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
310	#124	—	2	32	no	—
311	C₂²⋊Q₈	—	2	32	no	—
312	#121	—	2	32	no	—
313	#117	—	2	32	no	—
314	C₂×C₄⋊C₄	—	2	8	no	—
315	C₂×C₄⋊C₄	—	2	4	no	—
316	C₂×C₄⋊C₄	—	2	4	no	—
317	C₂×C₄⋊C₄	—	2	8	no	—
318	C₂×C₄⋊C₄	—	4	8	no	—
319	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
320	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
321	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
322	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
323	C₂×C₄⋊C₄	C₂³×C₁₃	1	16	yes	—
324	C₂×C₂²⋊C₄	—	2	8	no	—
325	C₂×C₂²⋊C₄	—	2	8	no	—
326	C₂×C₂²⋊C₄	—	2	8	no	—
327	C₂×C₂²⋊C₄	—	2	16	no	—
328	C₂×C₂²⋊C₄	—	4	8	no	—
329	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
330	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
331	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
332	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
333	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
334	C₂×C₄²	—	2	4	no	—
335	C₂×C₄²	D₄×C₁₃	1	8	yes	complemented
336	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
337	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
338	#95	C₂³×C₁₃	1	16	yes	—
339	C₂×C₁₃	—	4	4	no	—
340	C₂×C₁₃	—	8	4	no	—
341	C₂×C₁₃	#2620	1	8	yes	direct product factor
342	C₂×C₁₃	C₂²×#121	1	1	yes	characteristic
343	C₂×C₁₃	C₂×#535	1	1	yes	characteristic
344	C₂×C₁₃	C₂×#536	1	1	yes	characteristic
345	C₂×C₁₃	C₂×#537	1	2	yes	—
346	C₂×C₁₃	C₂×#542	1	2	yes	—
347	C₂⁴	—	2	2	no	—
348	C₂⁴	—	2	2	no	—
349	C₂⁴	—	2	4	no	—
350	C₂⁴	—	2	4	no	—
351	C₂⁴	—	2	4	no	—
352	C₂⁴	—	2	4	no	—
353	C₂⁴	—	2	4	no	—
354	C₂⁴	—	2	8	no	—
355	C₂⁴	—	2	8	no	—
356	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
357	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
358	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
359	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
360	C₂×Q₈	—	2	8	no	—
361	C₂×Q₈	—	2	8	no	—
362	C₂×Q₈	—	2	8	no	—
363	C₂×Q₈	—	4	16	no	—
364	C₂×D₄	—	2	16	no	—
365	C₂×D₄	—	2	8	no	—
366	C₂×D₄	—	2	8	no	—
367	C₂×D₄	—	2	8	no	—
368	C₂×D₄	—	4	16	no	—
369	C₂×D₄	—	4	32	no	—
370	C₂×D₄	—	4	16	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	4	no	—
374	C₂²×C₄	—	2	4	no	—
375	C₂²×C₄	—	2	32	no	—
376	C₂²×C₄	—	2	8	no	—
377	C₂²×C₄	—	2	8	no	—
378	C₂²×C₄	—	2	4	no	—
379	C₂²×C₄	—	2	4	no	—
380	C₂²×C₄	—	2	4	no	—
381	C₂²×C₄	—	2	4	no	—
382	C₂²×C₄	—	2	4	no	—
383	C₂²×C₄	—	2	4	no	—
384	C₂²×C₄	—	2	4	no	—
385	C₂²×C₄	—	2	8	no	—
386	C₂²×C₄	—	2	8	no	—
387	C₂²×C₄	—	2	4	no	—
388	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	—
389	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
390	C₂²×C₄	C₂×D₄×C₁₃	1	16	yes	—
391	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
392	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
393	C₂²×C₄	C₁₃×#41	1	4	yes	—
394	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
395	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
396	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
397	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
398	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
399	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
400	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
401	C₄⋊C₄	—	2	16	no	—
402	C₄⋊C₄	—	2	8	no	—
403	C₄⋊C₄	—	2	8	no	—
404	C₄⋊C₄	—	2	16	no	—
405	C₄⋊C₄	—	4	16	no	—
406	C₂²⋊C₄	—	2	16	no	—
407	C₂²⋊C₄	—	2	16	no	—
408	C₂²⋊C₄	—	2	16	no	—
409	C₂²⋊C₄	—	2	32	no	—
410	C₂²⋊C₄	—	4	16	no	—
411	C₄²	—	2	8	no	—
412	C₄²	C₂×D₄×C₁₃	1	16	yes	complemented
413	C₁₃	C₂×#2620	1	1	yes	characteristic, direct product factor, Sylow
414	C₂³	—	2	8	no	—
415	C₂³	—	2	8	no	—
416	C₂³	—	2	8	no	—
417	C₂³	—	2	2	no	—
418	C₂³	—	2	2	no	—
419	C₂³	—	2	4	no	—
420	C₂³	—	2	4	no	—
421	C₂³	—	2	4	no	—
422	C₂³	—	2	4	no	—
423	C₂³	—	2	4	no	—
424	C₂³	—	2	8	no	—
425	C₂³	—	2	8	no	—
426	C₂³	—	4	8	no	—
427	C₂³	—	4	8	no	—
428	C₂³	—	4	8	no	—
429	C₂³	—	4	8	no	—
430	C₂³	—	4	8	no	—
431	C₂³	—	4	16	no	—
432	C₂³	—	4	16	no	—
433	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
434	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
435	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
436	C₂³	C₂×C₁₃×#41	1	2	yes	—
437	C₂³	C₁₃×H(5,𝔽₂)	1	4	yes	—
438	C₂³	C₁₃×2₋¹⁺⁴	1	4	yes	—
439	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
440	Q₈	—	4	16	no	—
441	D₄	—	4	32	no	—
442	D₄	—	4	16	no	—
443	C₂×C₄	—	2	8	no	—
444	C₂×C₄	—	2	16	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	4	no	—
448	C₂×C₄	—	2	4	no	—
449	C₂×C₄	—	2	32	no	—
450	C₂×C₄	—	2	4	no	—
451	C₂×C₄	—	2	4	no	—
452	C₂×C₄	—	2	4	no	—
453	C₂×C₄	—	2	4	no	—
454	C₂×C₄	—	2	4	no	—
455	C₂×C₄	—	2	4	no	—
456	C₂×C₄	—	2	4	no	—
457	C₂×C₄	—	2	8	no	—
458	C₂×C₄	—	2	8	no	—
459	C₂×C₄	—	2	4	no	—
460	C₂×C₄	—	4	8	no	—
461	C₂×C₄	—	4	8	no	—
462	C₂×C₄	—	4	8	no	—
463	C₂×C₄	—	4	8	no	—
464	C₂×C₄	C₁₃×#121	1	16	yes	—
465	C₂×C₄	C₂²×D₄×C₁₃	1	8	yes	—
466	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
467	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
468	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
469	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
470	C₂²	—	2	4	no	—
471	C₂²	—	2	4	no	—
472	C₂²	—	2	4	no	—
473	C₂²	—	4	16	no	—
474	C₂²	—	4	4	no	—
475	C₂²	—	4	4	no	—
476	C₂²	—	4	4	no	—
477	C₂²	—	4	4	no	—
478	C₂²	—	4	4	no	—
479	C₂²	—	4	8	no	—
480	C₂²	—	4	8	no	—
481	C₂²	—	8	16	no	—
482	C₂²	C₂×C₁₃×#121	1	4	yes	—
483	C₂²	C₁₃×#535	1	4	yes	—
484	C₂²	C₁₃×#536	1	4	yes	—
485	C₂²	C₁₃×#537	1	8	yes	—
486	C₂²	C₁₃×#542	1	8	yes	—
487	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
488	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
489	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
490	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
491	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
492	C₄	—	2	4	no	—
493	C₄	—	2	8	no	—
494	C₄	—	4	4	no	—
495	C₄	—	4	4	no	—
496	C₄	—	4	4	no	—
497	C₄	—	4	4	no	—
498	C₄	C₂×C₁₃×#121	1	8	yes	—
499	C₂	—	4	4	no	—
500	C₂	—	8	4	no	—
501	C₂	C₁₃×#2620	1	8	yes	direct product factor
502	C₂	C₂²×C₁₃×#121	1	1	yes	characteristic
503	C₂	C₂×C₁₃×#535	1	1	yes	characteristic
504	C₂	C₂×C₁₃×#536	1	1	yes	characteristic
505	C₂	C₂×C₁₃×#537	1	2	yes	—
506	C₂	C₂×C₁₃×#542	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂²×C₁₃×#121	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₃×#124	C₂	semidirect
2. C₂²×C₁₃×C₂²⋊Q₈	C₂	semidirect
4. C₂²×C₁₃×#117	C₂	semidirect
5. C₁₃×#2620	C₂	direct (N × H)
6. C₂×C₁₃×#396	C₂	semidirect
7. C₂×C₁₃×#394	C₂	semidirect
8. C₂×C₁₃×#391	C₂	semidirect
9. C₂×C₁₃×#390	C₂	semidirect
10. C₂×C₁₃×#384	C₂	semidirect
16. C₂×C₁₃×#124	C₂²	semidirect
18. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
22. C₂×C₁₃×#117	C₂²	semidirect
35. C₁₃×#396	C₂²	semidirect
36. C₁₃×#394	C₂²	semidirect
37. C₁₃×#391	C₂²	semidirect
38. C₁₃×#390	C₂²	semidirect
39. C₁₃×#384	C₂²	semidirect
90. C₂×C₄²×C₁₃	D₄	semidirect
94. C₂×#2620	C₁₃	direct (N × H)
160. C₄²×C₁₃	C₂×D₄	semidirect
161. C₂²×#124	C₂×C₁₃	semidirect
162. C₂²×C₂²⋊Q₈	C₂×C₁₃	semidirect
164. C₂²×#117	C₂×C₁₃	semidirect
165. #2620	C₂×C₁₃	direct (N × H)
166. C₂×#396	C₂×C₁₃	semidirect
167. C₂×#394	C₂×C₁₃	semidirect
168. C₂×#391	C₂×C₁₃	semidirect
169. C₂×#390	C₂×C₁₃	semidirect
170. C₂×#384	C₂×C₁₃	semidirect
232. C₂×#124	C₂²×C₁₃	semidirect
234. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
238. C₂×#117	C₂²×C₁₃	semidirect
251. #396	C₂²×C₁₃	semidirect
252. #394	C₂²×C₁₃	semidirect
253. #391	C₂²×C₁₃	semidirect
254. #390	C₂²×C₁₃	semidirect
255. #384	C₂²×C₁₃	semidirect
335. C₂×C₄²	D₄×C₁₃	semidirect
341. C₂×C₁₃	#2620	direct (N × H)
412. C₄²	C₂×D₄×C₁₃	semidirect
413. C₁₃	C₂×#2620	direct (N × H)
501. C₂	C₁₃×#2620	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×#124	2
C₂²×C₁₃×C₂²⋊Q₈	2
C₂²×C₁₃×#121	2
C₂²×C₁₃×#117	2
C₁₃×#2620	2
C₂×C₁₃×#396	2
C₂×C₁₃×#394	2
C₂×C₁₃×#391	2
C₂×C₁₃×#390	2
C₂×C₁₃×#384	2
C₂×#2620	13

Subgroups — C2×C13×#2620 #15720950

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2620 #15720950