Subgroups — C₂×C₁₃×#2406 #15721072

Order 3328.

5718 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₁₃×#41	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₃×#123	C₂	1	2	yes	maximal, complemented
3	C₂³×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2406	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₁₃×#395	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#394	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₃×#386	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×#385	C₂	1	4	yes	maximal, complemented
9	C₂×C₁₃×#381	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₁₃×#41	—	2	16	no	—
11	C₂²×C₁₃×#41	—	2	8	no	—
12	C₂²×C₁₃×#41	C₂²	1	8	yes	—
13	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
14	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
15	C₂³×D₄×C₁₃	C₂²	1	2	yes	—
16	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	—
17	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
18	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
19	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#123	—	2	16	no	—
21	C₂×C₁₃×#123	C₂²	1	16	yes	complemented
22	C₂²×C₁₃×C₄⋊C₄	—	2	8	no	—
23	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
24	C₂²×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
25	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
26	C₂²×C₁₃×C₄⋊C₄	C₂²	1	8	yes	complemented
27	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
28	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
29	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
30	C₁₃×#395	C₂²	1	16	yes	complemented
31	C₁₃×#394	C₂²	1	16	yes	complemented
32	C₁₃×#386	C₂²	1	16	yes	complemented
33	C₁₃×#385	C₂²	1	32	yes	complemented
34	C₁₃×#381	C₂²	1	8	yes	complemented
35	C₂×C₁₃×#95	C₂²	1	2	yes	—
36	C₂×C₁₃×#95	C₂²	1	2	yes	—
37	C₂×C₁₃×#95	C₂²	1	4	yes	—
38	C₂⁵×C₁₃	C₂³	1	2	yes	—
39	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
40	C₂×C₁₃×#41	—	2	128	no	—
41	C₂×C₁₃×#41	—	2	64	no	—
42	C₂×C₁₃×#41	—	2	32	no	—
43	C₂²×Q₈×C₁₃	—	2	8	no	—
44	C₂²×Q₈×C₁₃	—	2	4	no	—
45	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
46	C₂²×D₄×C₁₃	—	2	8	no	—
47	C₂²×D₄×C₁₃	—	2	8	no	—
48	C₂²×D₄×C₁₃	—	2	8	no	—
49	C₂²×D₄×C₁₃	—	2	4	no	—
50	C₂²×D₄×C₁₃	D₄	1	16	yes	—
51	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
52	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
53	C₂³×C₄×C₁₃	—	2	4	no	—
54	C₂³×C₄×C₁₃	—	2	8	no	—
55	C₂³×C₄×C₁₃	—	2	8	no	—
56	C₂³×C₄×C₁₃	—	2	8	no	—
57	C₂³×C₄×C₁₃	—	2	8	no	—
58	C₂³×C₄×C₁₃	—	2	8	no	—
59	C₂³×C₄×C₁₃	—	2	4	no	—
60	C₂³×C₄×C₁₃	—	2	8	no	—
61	C₂³×C₄×C₁₃	D₄	1	8	yes	—
62	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
63	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
64	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
65	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
66	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
67	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
68	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
69	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
70	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
72	C₁₃×#123	—	2	64	no	—
73	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
74	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
75	C₂×C₁₃×C₄⋊C₄	—	2	32	no	—
76	C₂×C₁₃×C₄⋊C₄	—	2	16	no	—
77	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
78	C₂×C₁₃×C₄⋊C₄	C₂³	1	16	yes	—
79	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
80	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
81	C₂×C₁₃×C₂²⋊C₄	—	2	16	no	—
82	C₂×C₁₃×C₂²⋊C₄	—	2	16	no	—
83	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
84	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
85	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
86	C₁₃×#95	C₂³	1	8	yes	—
87	C₁₃×#95	C₂³	1	8	yes	—
88	C₁₃×#95	C₂³	1	16	yes	—
89	C₂×#2406	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
90	C₂⁴×C₁₃	—	2	4	no	—
91	C₂⁴×C₁₃	—	2	4	no	—
92	C₂⁴×C₁₃	—	2	4	no	—
93	C₂⁴×C₁₃	—	2	4	no	—
94	C₂⁴×C₁₃	—	2	8	no	—
95	C₂⁴×C₁₃	—	2	8	no	—
96	C₂⁴×C₁₃	C₂×D₄	1	8	yes	—
97	C₂⁴×C₁₃	C₂×D₄	1	8	yes	—
98	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
99	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
100	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
101	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
102	C₁₃×#41	—	2	256	no	—
103	C₂×Q₈×C₁₃	—	2	32	no	—
104	C₂×Q₈×C₁₃	—	2	16	no	—
105	C₂×Q₈×C₁₃	—	2	8	no	—
106	C₂×D₄×C₁₃	—	2	32	no	—
107	C₂×D₄×C₁₃	—	2	64	no	—
108	C₂×D₄×C₁₃	—	2	16	no	—
109	C₂×D₄×C₁₃	—	2	16	no	—
110	C₂×D₄×C₁₃	—	2	16	no	—
111	C₂×D₄×C₁₃	—	2	8	no	—
112	C₂×D₄×C₁₃	C₂×D₄	1	32	yes	—
113	C₂²×C₄×C₁₃	—	2	32	no	—
114	C₂²×C₄×C₁₃	—	2	64	no	—
115	C₂²×C₄×C₁₃	—	2	32	no	—
116	C₂²×C₄×C₁₃	—	2	8	no	—
117	C₂²×C₄×C₁₃	—	2	4	no	—
118	C₂²×C₄×C₁₃	—	2	4	no	—
119	C₂²×C₄×C₁₃	—	2	4	no	—
120	C₂²×C₄×C₁₃	—	2	4	no	—
121	C₂²×C₄×C₁₃	—	2	4	no	—
122	C₂²×C₄×C₁₃	—	2	16	no	—
123	C₂²×C₄×C₁₃	—	2	16	no	—
124	C₂²×C₄×C₁₃	—	2	4	no	—
125	C₂²×C₄×C₁₃	—	2	16	no	—
126	C₂²×C₄×C₁₃	—	2	16	no	—
127	C₂²×C₄×C₁₃	—	2	16	no	—
128	C₂²×C₄×C₁₃	—	2	8	no	—
129	C₂²×C₄×C₁₃	—	2	8	no	—
130	C₂²×C₄×C₁₃	—	2	8	no	—
131	C₂²×C₄×C₁₃	—	2	4	no	—
132	C₂²×C₄×C₁₃	—	2	16	no	—
133	C₂²×C₄×C₁₃	—	2	8	no	—
134	C₂²×C₄×C₁₃	—	2	8	no	—
135	C₂²×C₄×C₁₃	—	4	16	no	—
136	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
137	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
138	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
139	C₂²×C₄×C₁₃	C₂×D₄	1	16	yes	—
140	C₂²×C₄×C₁₃	#41	1	8	yes	complemented
141	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
142	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
143	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
144	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
145	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
146	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
147	C₁₃×C₄⋊C₄	—	2	16	no	—
148	C₁₃×C₄⋊C₄	—	2	16	no	—
149	C₁₃×C₄⋊C₄	—	2	32	no	—
150	C₁₃×C₂²⋊C₄	—	2	16	no	—
151	C₁₃×C₂²⋊C₄	—	2	32	no	—
152	C₁₃×C₂²⋊C₄	—	2	32	no	—
153	C₂³×#41	C₂×C₁₃	1	1	yes	characteristic
154	C₂²×#123	C₂×C₁₃	1	2	yes	complemented
155	C₂³×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
156	#2406	C₂×C₁₃	1	16	yes	direct product factor
157	C₂×#395	C₂×C₁₃	1	2	yes	complemented
158	C₂×#394	C₂×C₁₃	1	2	yes	complemented
159	C₂×#386	C₂×C₁₃	1	2	yes	complemented
160	C₂×#385	C₂×C₁₃	1	4	yes	complemented
161	C₂×#381	C₂×C₁₃	1	1	yes	characteristic, complemented
162	C₂³×C₁₃	—	2	8	no	—
163	C₂³×C₁₃	—	2	8	no	—
164	C₂³×C₁₃	—	2	32	no	—
165	C₂³×C₁₃	—	2	4	no	—
166	C₂³×C₁₃	—	2	4	no	—
167	C₂³×C₁₃	—	2	16	no	—
168	C₂³×C₁₃	—	2	32	no	—
169	C₂³×C₁₃	—	2	4	no	—
170	C₂³×C₁₃	—	2	4	no	—
171	C₂³×C₁₃	—	2	8	no	—
172	C₂³×C₁₃	—	2	8	no	—
173	C₂³×C₁₃	—	4	8	no	—
174	C₂³×C₁₃	—	4	8	no	—
175	C₂³×C₁₃	—	4	16	no	—
176	C₂³×C₁₃	#120	1	16	yes	—
177	C₂³×C₁₃	C₂²×D₄	1	8	yes	—
178	C₂³×C₁₃	C₂²×D₄	1	8	yes	—
179	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
180	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
181	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
182	C₂³×C₁₃	C₂×#41	1	4	yes	—
183	C₂³×C₁₃	2₋¹⁺⁴	1	4	yes	—
184	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
185	Q₈×C₁₃	—	2	32	no	—
186	D₄×C₁₃	—	2	32	no	—
187	D₄×C₁₃	—	2	64	no	—
188	C₂×C₄×C₁₃	—	2	32	no	—
189	C₂×C₄×C₁₃	—	2	64	no	—
190	C₂×C₄×C₁₃	—	2	8	no	—
191	C₂×C₄×C₁₃	—	2	16	no	—
192	C₂×C₄×C₁₃	—	2	8	no	—
193	C₂×C₄×C₁₃	—	2	32	no	—
194	C₂×C₄×C₁₃	—	2	16	no	—
195	C₂×C₄×C₁₃	—	2	4	no	—
196	C₂×C₄×C₁₃	—	2	4	no	—
197	C₂×C₄×C₁₃	—	2	4	no	—
198	C₂×C₄×C₁₃	—	2	4	no	—
199	C₂×C₄×C₁₃	—	2	4	no	—
200	C₂×C₄×C₁₃	—	2	4	no	—
201	C₂×C₄×C₁₃	—	2	8	no	—
202	C₂×C₄×C₁₃	—	2	8	no	—
203	C₂×C₄×C₁₃	—	2	4	no	—
204	C₂×C₄×C₁₃	—	2	8	no	—
205	C₂×C₄×C₁₃	—	2	8	no	—
206	C₂×C₄×C₁₃	—	4	16	no	—
207	C₂×C₄×C₁₃	—	4	8	no	—
208	C₂×C₄×C₁₃	—	4	16	no	—
209	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
210	C₂×C₄×C₁₃	C₂²×D₄	1	8	yes	—
211	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
212	C₂×C₄×C₁₃	C₂×#41	1	8	yes	complemented
213	C₂²×#41	—	2	16	no	—
214	C₂²×#41	—	2	8	no	—
215	C₂²×#41	C₂²×C₁₃	1	8	yes	—
216	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
217	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
218	C₂³×D₄	C₂²×C₁₃	1	2	yes	—
219	C₂⁴×C₄	C₂²×C₁₃	1	2	yes	—
220	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
221	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
222	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
223	C₂×#123	—	2	16	no	—
224	C₂×#123	C₂²×C₁₃	1	16	yes	complemented
225	C₂²×C₄⋊C₄	—	2	8	no	—
226	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
227	C₂²×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
228	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
229	C₂²×C₄⋊C₄	C₂²×C₁₃	1	8	yes	complemented
230	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
231	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
232	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
233	#395	C₂²×C₁₃	1	16	yes	complemented
234	#394	C₂²×C₁₃	1	16	yes	complemented
235	#386	C₂²×C₁₃	1	16	yes	complemented
236	#385	C₂²×C₁₃	1	32	yes	complemented
237	#381	C₂²×C₁₃	1	8	yes	complemented
238	C₂×#95	C₂²×C₁₃	1	2	yes	—
239	C₂×#95	C₂²×C₁₃	1	4	yes	—
240	C₂×#95	C₂²×C₁₃	1	2	yes	—
241	C₂²×C₁₃	—	2	32	no	—
242	C₂²×C₁₃	—	2	4	no	—
243	C₂²×C₁₃	—	2	4	no	—
244	C₂²×C₁₃	—	2	16	no	—
245	C₂²×C₁₃	—	2	8	no	—
246	C₂²×C₁₃	—	2	16	no	—
247	C₂²×C₁₃	—	4	32	no	—
248	C₂²×C₁₃	—	4	4	no	—
249	C₂²×C₁₃	—	4	4	no	—
250	C₂²×C₁₃	—	4	8	no	—
251	C₂²×C₁₃	C₂×#120	1	8	yes	—
252	C₂²×C₁₃	C₂×#120	1	4	yes	—
253	C₂²×C₁₃	#525	1	4	yes	—
254	C₂²×C₁₃	#536	1	4	yes	—
255	C₂²×C₁₃	#547	1	16	yes	—
256	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
257	C₂²×C₁₃	C₂³×D₄	1	2	yes	—
258	C₂²×C₁₃	C₂²×#41	1	2	yes	—
259	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
260	C₄×C₁₃	—	2	4	no	—
261	C₄×C₁₃	—	2	8	no	—
262	C₄×C₁₃	—	2	4	no	—
263	C₄×C₁₃	—	2	8	no	—
264	C₄×C₁₃	—	4	4	no	—
265	C₄×C₁₃	—	4	8	no	—
266	C₂⁵	C₂³×C₁₃	1	2	yes	—
267	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
268	C₂×#41	—	2	128	no	—
269	C₂×#41	—	2	64	no	—
270	C₂×#41	—	2	32	no	—
271	C₂²×Q₈	—	2	8	no	—
272	C₂²×Q₈	—	2	4	no	—
273	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
274	C₂²×D₄	—	2	8	no	—
275	C₂²×D₄	—	2	8	no	—
276	C₂²×D₄	—	2	8	no	—
277	C₂²×D₄	—	2	4	no	—
278	C₂²×D₄	D₄×C₁₃	1	16	yes	—
279	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
280	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
281	C₂³×C₄	—	2	4	no	—
282	C₂³×C₄	—	2	8	no	—
283	C₂³×C₄	—	2	8	no	—
284	C₂³×C₄	—	2	8	no	—
285	C₂³×C₄	—	2	8	no	—
286	C₂³×C₄	—	2	8	no	—
287	C₂³×C₄	—	2	4	no	—
288	C₂³×C₄	—	2	8	no	—
289	C₂³×C₄	D₄×C₁₃	1	8	yes	—
290	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
291	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
292	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
293	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
294	C₂³×C₄	C₂³×C₁₃	1	8	yes	—
295	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
296	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
297	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
298	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
299	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
300	#123	—	2	64	no	—
301	C₂×C₄⋊C₄	—	2	8	no	—
302	C₂×C₄⋊C₄	—	2	8	no	—
303	C₂×C₄⋊C₄	—	2	32	no	—
304	C₂×C₄⋊C₄	—	2	16	no	—
305	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
306	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
307	C₂×C₄⋊C₄	C₂³×C₁₃	1	16	yes	—
308	C₂×C₂²⋊C₄	—	2	8	no	—
309	C₂×C₂²⋊C₄	—	2	16	no	—
310	C₂×C₂²⋊C₄	—	2	16	no	—
311	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
312	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
313	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
314	#95	C₂³×C₁₃	1	8	yes	—
315	#95	C₂³×C₁₃	1	8	yes	—
316	#95	C₂³×C₁₃	1	16	yes	—
317	C₂×C₁₃	—	2	8	no	—
318	C₂×C₁₃	—	4	8	no	—
319	C₂×C₁₃	#2406	1	8	yes	direct product factor
320	C₂×C₁₃	C₂²×#120	1	1	yes	characteristic
321	C₂×C₁₃	C₂×#525	1	1	yes	characteristic
322	C₂×C₁₃	C₂×#536	1	1	yes	characteristic
323	C₂×C₁₃	C₂×#547	1	4	yes	—
324	C₂⁴	—	2	4	no	—
325	C₂⁴	—	2	4	no	—
326	C₂⁴	—	2	4	no	—
327	C₂⁴	—	2	4	no	—
328	C₂⁴	—	2	8	no	—
329	C₂⁴	—	2	8	no	—
330	C₂⁴	C₂×D₄×C₁₃	1	8	yes	—
331	C₂⁴	C₂×D₄×C₁₃	1	8	yes	—
332	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
333	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
334	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
335	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
336	#41	—	2	256	no	—
337	C₂×Q₈	—	2	32	no	—
338	C₂×Q₈	—	2	16	no	—
339	C₂×Q₈	—	2	8	no	—
340	C₂×D₄	—	2	32	no	—
341	C₂×D₄	—	2	64	no	—
342	C₂×D₄	—	2	16	no	—
343	C₂×D₄	—	2	16	no	—
344	C₂×D₄	—	2	16	no	—
345	C₂×D₄	—	2	8	no	—
346	C₂×D₄	C₂×D₄×C₁₃	1	32	yes	—
347	C₂²×C₄	—	2	64	no	—
348	C₂²×C₄	—	2	32	no	—
349	C₂²×C₄	—	2	32	no	—
350	C₂²×C₄	—	2	8	no	—
351	C₂²×C₄	—	2	4	no	—
352	C₂²×C₄	—	2	4	no	—
353	C₂²×C₄	—	2	4	no	—
354	C₂²×C₄	—	2	4	no	—
355	C₂²×C₄	—	2	4	no	—
356	C₂²×C₄	—	2	16	no	—
357	C₂²×C₄	—	2	16	no	—
358	C₂²×C₄	—	2	4	no	—
359	C₂²×C₄	—	2	16	no	—
360	C₂²×C₄	—	2	16	no	—
361	C₂²×C₄	—	2	16	no	—
362	C₂²×C₄	—	2	8	no	—
363	C₂²×C₄	—	2	8	no	—
364	C₂²×C₄	—	2	8	no	—
365	C₂²×C₄	—	2	4	no	—
366	C₂²×C₄	—	2	16	no	—
367	C₂²×C₄	—	2	8	no	—
368	C₂²×C₄	—	2	8	no	—
369	C₂²×C₄	—	4	16	no	—
370	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
371	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	—
372	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
373	C₂²×C₄	C₂×D₄×C₁₃	1	16	yes	—
374	C₂²×C₄	C₁₃×#41	1	8	yes	complemented
375	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
376	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
377	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
378	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
379	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
380	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
381	C₄⋊C₄	—	2	16	no	—
382	C₄⋊C₄	—	2	16	no	—
383	C₄⋊C₄	—	2	32	no	—
384	C₂²⋊C₄	—	2	16	no	—
385	C₂²⋊C₄	—	2	32	no	—
386	C₂²⋊C₄	—	2	32	no	—
387	C₁₃	C₂×#2406	1	1	yes	characteristic, direct product factor, Sylow
388	C₂³	—	2	8	no	—
389	C₂³	—	2	8	no	—
390	C₂³	—	2	32	no	—
391	C₂³	—	2	4	no	—
392	C₂³	—	2	4	no	—
393	C₂³	—	2	16	no	—
394	C₂³	—	2	32	no	—
395	C₂³	—	2	4	no	—
396	C₂³	—	2	4	no	—
397	C₂³	—	2	8	no	—
398	C₂³	—	2	8	no	—
399	C₂³	—	4	8	no	—
400	C₂³	—	4	8	no	—
401	C₂³	—	4	16	no	—
402	C₂³	C₁₃×#120	1	16	yes	—
403	C₂³	C₂²×D₄×C₁₃	1	8	yes	—
404	C₂³	C₂²×D₄×C₁₃	1	8	yes	—
405	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
406	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
407	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
408	C₂³	C₂×C₁₃×#41	1	4	yes	—
409	C₂³	C₁₃×2₋¹⁺⁴	1	4	yes	—
410	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
411	Q₈	—	2	32	no	—
412	D₄	—	2	32	no	—
413	D₄	—	2	64	no	—
414	C₂×C₄	—	2	32	no	—
415	C₂×C₄	—	2	64	no	—
416	C₂×C₄	—	2	8	no	—
417	C₂×C₄	—	2	16	no	—
418	C₂×C₄	—	2	8	no	—
419	C₂×C₄	—	2	32	no	—
420	C₂×C₄	—	2	16	no	—
421	C₂×C₄	—	2	4	no	—
422	C₂×C₄	—	2	4	no	—
423	C₂×C₄	—	2	4	no	—
424	C₂×C₄	—	2	4	no	—
425	C₂×C₄	—	2	4	no	—
426	C₂×C₄	—	2	4	no	—
427	C₂×C₄	—	2	8	no	—
428	C₂×C₄	—	2	8	no	—
429	C₂×C₄	—	2	4	no	—
430	C₂×C₄	—	2	8	no	—
431	C₂×C₄	—	2	8	no	—
432	C₂×C₄	—	4	16	no	—
433	C₂×C₄	—	4	8	no	—
434	C₂×C₄	—	4	16	no	—
435	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
436	C₂×C₄	C₂²×D₄×C₁₃	1	8	yes	—
437	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
438	C₂×C₄	C₂×C₁₃×#41	1	8	yes	complemented
439	C₂²	—	2	32	no	—
440	C₂²	—	2	4	no	—
441	C₂²	—	2	4	no	—
442	C₂²	—	2	16	no	—
443	C₂²	—	2	8	no	—
444	C₂²	—	2	16	no	—
445	C₂²	—	4	32	no	—
446	C₂²	—	4	4	no	—
447	C₂²	—	4	4	no	—
448	C₂²	—	4	8	no	—
449	C₂²	C₂×C₁₃×#120	1	8	yes	—
450	C₂²	C₂×C₁₃×#120	1	4	yes	—
451	C₂²	C₁₃×#525	1	4	yes	—
452	C₂²	C₁₃×#536	1	4	yes	—
453	C₂²	C₁₃×#547	1	16	yes	—
454	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
455	C₂²	C₂³×D₄×C₁₃	1	2	yes	—
456	C₂²	C₂²×C₁₃×#41	1	2	yes	—
457	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
458	C₄	—	2	4	no	—
459	C₄	—	2	8	no	—
460	C₄	—	2	4	no	—
461	C₄	—	2	8	no	—
462	C₄	—	4	4	no	—
463	C₄	—	4	8	no	—
464	C₂	—	2	8	no	—
465	C₂	—	4	8	no	—
466	C₂	C₁₃×#2406	1	8	yes	direct product factor
467	C₂	C₂²×C₁₃×#120	1	1	yes	characteristic
468	C₂	C₂×C₁₃×#525	1	1	yes	characteristic
469	C₂	C₂×C₁₃×#536	1	1	yes	characteristic
470	C₂	C₂×C₁₃×#547	1	4	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂³×C₁₃×#41	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
2. C₂²×C₁₃×#123	C₂	semidirect
3. C₂³×C₁₃×C₄⋊C₄	C₂	semidirect
4. C₁₃×#2406	C₂	direct (N × H)
5. C₂×C₁₃×#395	C₂	semidirect
6. C₂×C₁₃×#394	C₂	semidirect
7. C₂×C₁₃×#386	C₂	semidirect
8. C₂×C₁₃×#385	C₂	semidirect
9. C₂×C₁₃×#381	C₂	semidirect
21. C₂×C₁₃×#123	C₂²	semidirect
26. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
30. C₁₃×#395	C₂²	semidirect
31. C₁₃×#394	C₂²	semidirect
32. C₁₃×#386	C₂²	semidirect
33. C₁₃×#385	C₂²	semidirect
34. C₁₃×#381	C₂²	semidirect
89. C₂×#2406	C₁₃	direct (N × H)
140. C₂²×C₄×C₁₃	#41	semidirect
154. C₂²×#123	C₂×C₁₃	semidirect
155. C₂³×C₄⋊C₄	C₂×C₁₃	semidirect
156. #2406	C₂×C₁₃	direct (N × H)
157. C₂×#395	C₂×C₁₃	semidirect
158. C₂×#394	C₂×C₁₃	semidirect
159. C₂×#386	C₂×C₁₃	semidirect
160. C₂×#385	C₂×C₁₃	semidirect
161. C₂×#381	C₂×C₁₃	semidirect
212. C₂×C₄×C₁₃	C₂×#41	semidirect
224. C₂×#123	C₂²×C₁₃	semidirect
229. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
233. #395	C₂²×C₁₃	semidirect
234. #394	C₂²×C₁₃	semidirect
235. #386	C₂²×C₁₃	semidirect
236. #385	C₂²×C₁₃	semidirect
237. #381	C₂²×C₁₃	semidirect
319. C₂×C₁₃	#2406	direct (N × H)
374. C₂²×C₄	C₁₃×#41	semidirect
387. C₁₃	C₂×#2406	direct (N × H)
438. C₂×C₄	C₂×C₁₃×#41	semidirect
466. C₂	C₁₃×#2406	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₁₃×#41	2
C₂²×C₁₃×#123	2
C₂³×C₁₃×C₄⋊C₄	2
C₁₃×#2406	2
C₂×C₁₃×#395	2
C₂×C₁₃×#394	2
C₂×C₁₃×#386	2
C₂×C₁₃×#385	2
C₂×C₁₃×#381	2
C₂×#2406	13

Subgroups — C2×C13×#2406 #15721072

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2406 #15721072