Subgroups — C₂×C₁₃×#2404 #15721067

Order 3328.

7222 conjugacy classes of subgroups.

The subgroup lattice has 536 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, complemented
2	C₂²×C₁₃×#120	C₂	1	2	yes	maximal, complemented
3	C₂³×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2404	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₁₃×#393	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#392	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₃×#386	C₂	1	4	yes	maximal, complemented
8	C₂×C₁₃×#386	C₂	1	2	yes	maximal, complemented
9	C₂×C₁₃×#381	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂⁶×C₁₃	C₂²	1	1	yes	characteristic
11	C₂²×C₁₃×#41	—	2	16	no	—
12	C₂²×C₁₃×#41	—	2	8	no	—
13	C₂²×C₁₃×#41	C₂²	1	8	yes	complemented
14	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
15	C₂³×D₄×C₁₃	C₂²	1	4	yes	—
16	C₂³×D₄×C₁₃	C₂²	1	2	yes	—
17	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
18	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
19	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
20	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	complemented
21	C₂×C₁₃×#120	—	2	16	no	—
22	C₂×C₁₃×#120	C₂²	1	16	yes	complemented
23	C₂²×C₁₃×C₂²⋊C₄	—	2	8	no	—
24	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
25	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
26	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
27	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
28	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	complemented
29	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
30	C₁₃×#393	C₂²	1	16	yes	complemented
31	C₁₃×#392	C₂²	1	16	yes	complemented
32	C₁₃×#386	C₂²	1	32	yes	complemented
33	C₁₃×#386	C₂²	1	16	yes	complemented
34	C₁₃×#381	C₂²	1	8	yes	complemented
35	C₂×C₁₃×#95	C₂²	1	2	yes	complemented
36	C₂×C₁₃×#95	C₂²	1	2	yes	complemented
37	C₂×C₁₃×#95	C₂²	1	4	yes	complemented
38	C₂⁵×C₁₃	—	2	4	no	—
39	C₂⁵×C₁₃	—	2	8	no	—
40	C₂⁵×C₁₃	—	2	8	no	—
41	C₂⁵×C₁₃	—	4	4	no	—
42	C₂⁵×C₁₃	C₂³	1	2	yes	—
43	C₂⁵×C₁₃	C₂³	1	2	yes	—
44	C₂⁵×C₁₃	C₂³	1	4	yes	—
45	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
46	C₂×C₁₃×#41	—	2	128	no	—
47	C₂×C₁₃×#41	—	2	64	no	—
48	C₂×C₁₃×#41	—	2	32	no	—
49	C₂²×Q₈×C₁₃	—	2	8	no	—
50	C₂²×Q₈×C₁₃	—	2	4	no	—
51	C₂²×Q₈×C₁₃	C₂³	1	4	yes	complemented
52	C₂²×D₄×C₁₃	—	2	8	no	—
53	C₂²×D₄×C₁₃	—	2	8	no	—
54	C₂²×D₄×C₁₃	—	2	8	no	—
55	C₂²×D₄×C₁₃	—	2	16	no	—
56	C₂²×D₄×C₁₃	—	2	16	no	—
57	C₂²×D₄×C₁₃	—	2	4	no	—
58	C₂²×D₄×C₁₃	—	4	8	no	—
59	C₂²×D₄×C₁₃	D₄	1	16	yes	complemented
60	C₂²×D₄×C₁₃	C₂³	1	16	yes	—
61	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
62	C₂²×D₄×C₁₃	C₂³	1	4	yes	complemented
63	C₂³×C₄×C₁₃	—	2	8	no	—
64	C₂³×C₄×C₁₃	—	2	8	no	—
65	C₂³×C₄×C₁₃	—	2	8	no	—
66	C₂³×C₄×C₁₃	—	2	8	no	—
67	C₂³×C₄×C₁₃	—	2	4	no	—
68	C₂³×C₄×C₁₃	—	4	4	no	—
69	C₂³×C₄×C₁₃	D₄	1	8	yes	complemented
70	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
71	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
72	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
73	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
75	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
76	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
77	C₂³×C₄×C₁₃	C₂³	1	8	yes	complemented
78	C₁₃×#120	—	2	64	no	—
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	—	2	32	no	—
84	C₂×C₁₃×C₂²⋊C₄	—	4	8	no	—
85	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
86	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
87	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
88	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
89	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	complemented
90	C₁₃×#95	C₂³	1	8	yes	complemented
91	C₁₃×#95	C₂³	1	8	yes	complemented
92	C₁₃×#95	C₂³	1	16	yes	complemented
93	C₂×#2404	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
94	C₂⁴×C₁₃	—	2	4	no	—
95	C₂⁴×C₁₃	—	2	4	no	—
96	C₂⁴×C₁₃	—	2	32	no	—
97	C₂⁴×C₁₃	—	2	8	no	—
98	C₂⁴×C₁₃	—	2	4	no	—
99	C₂⁴×C₁₃	—	2	8	no	—
100	C₂⁴×C₁₃	—	2	4	no	—
101	C₂⁴×C₁₃	—	2	4	no	—
102	C₂⁴×C₁₃	—	2	8	no	—
103	C₂⁴×C₁₃	—	2	4	no	—
104	C₂⁴×C₁₃	—	2	16	no	—
105	C₂⁴×C₁₃	—	2	8	no	—
106	C₂⁴×C₁₃	—	2	8	no	—
107	C₂⁴×C₁₃	—	2	16	no	—
108	C₂⁴×C₁₃	—	4	8	no	—
109	C₂⁴×C₁₃	—	4	64	no	—
110	C₂⁴×C₁₃	—	4	16	no	—
111	C₂⁴×C₁₃	—	4	16	no	—
112	C₂⁴×C₁₃	C₂×D₄	1	8	yes	—
113	C₂⁴×C₁₃	C₂×D₄	1	8	yes	—
114	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
115	C₂⁴×C₁₃	#41	1	8	yes	complemented
116	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
117	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
118	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
119	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
120	C₁₃×#41	—	2	256	no	—
121	C₂×Q₈×C₁₃	—	2	32	no	—
122	C₂×Q₈×C₁₃	—	2	16	no	—
123	C₂×Q₈×C₁₃	—	2	8	no	—
124	C₂×D₄×C₁₃	—	2	32	no	—
125	C₂×D₄×C₁₃	—	2	64	no	—
126	C₂×D₄×C₁₃	—	2	16	no	—
127	C₂×D₄×C₁₃	—	2	16	no	—
128	C₂×D₄×C₁₃	—	2	16	no	—
129	C₂×D₄×C₁₃	—	2	32	no	—
130	C₂×D₄×C₁₃	—	2	32	no	—
131	C₂×D₄×C₁₃	—	2	8	no	—
132	C₂×D₄×C₁₃	—	4	16	no	—
133	C₂×D₄×C₁₃	—	4	64	no	—
134	C₂×D₄×C₁₃	C₂×D₄	1	32	yes	complemented
135	C₂²×C₄×C₁₃	—	2	64	no	—
136	C₂²×C₄×C₁₃	—	2	32	no	—
137	C₂²×C₄×C₁₃	—	2	4	no	—
138	C₂²×C₄×C₁₃	—	2	4	no	—
139	C₂²×C₄×C₁₃	—	2	4	no	—
140	C₂²×C₄×C₁₃	—	2	4	no	—
141	C₂²×C₄×C₁₃	—	2	16	no	—
142	C₂²×C₄×C₁₃	—	2	16	no	—
143	C₂²×C₄×C₁₃	—	2	16	no	—
144	C₂²×C₄×C₁₃	—	2	16	no	—
145	C₂²×C₄×C₁₃	—	2	8	no	—
146	C₂²×C₄×C₁₃	—	2	4	no	—
147	C₂²×C₄×C₁₃	—	2	8	no	—
148	C₂²×C₄×C₁₃	—	2	8	no	—
149	C₂²×C₄×C₁₃	—	2	8	no	—
150	C₂²×C₄×C₁₃	—	2	8	no	—
151	C₂²×C₄×C₁₃	—	4	8	no	—
152	C₂²×C₄×C₁₃	—	4	16	no	—
153	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
154	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
155	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
156	C₂²×C₄×C₁₃	C₂×D₄	1	16	yes	complemented
157	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
158	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
159	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
160	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
161	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
162	C₁₃×C₂²⋊C₄	—	2	16	no	—
163	C₁₃×C₂²⋊C₄	—	2	16	no	—
164	C₁₃×C₂²⋊C₄	—	2	16	no	—
165	C₁₃×C₂²⋊C₄	—	2	32	no	—
166	C₁₃×C₂²⋊C₄	—	4	16	no	—
167	C₂³×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
168	C₂²×#120	C₂×C₁₃	1	2	yes	complemented
169	C₂³×C₂²⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
170	#2404	C₂×C₁₃	1	16	yes	direct product factor
171	C₂×#393	C₂×C₁₃	1	2	yes	complemented
172	C₂×#392	C₂×C₁₃	1	2	yes	complemented
173	C₂×#386	C₂×C₁₃	1	4	yes	complemented
174	C₂×#386	C₂×C₁₃	1	2	yes	complemented
175	C₂×#381	C₂×C₁₃	1	1	yes	characteristic, complemented
176	C₂³×C₁₃	—	2	8	no	—
177	C₂³×C₁₃	—	2	8	no	—
178	C₂³×C₁₃	—	2	32	no	—
179	C₂³×C₁₃	—	2	4	no	—
180	C₂³×C₁₃	—	2	4	no	—
181	C₂³×C₁₃	—	2	32	no	—
182	C₂³×C₁₃	—	2	16	no	—
183	C₂³×C₁₃	—	2	16	no	—
184	C₂³×C₁₃	—	2	32	no	—
185	C₂³×C₁₃	—	2	32	no	—
186	C₂³×C₁₃	—	2	4	no	—
187	C₂³×C₁₃	—	2	8	no	—
188	C₂³×C₁₃	—	2	4	no	—
189	C₂³×C₁₃	—	2	4	no	—
190	C₂³×C₁₃	—	2	8	no	—
191	C₂³×C₁₃	—	2	4	no	—
192	C₂³×C₁₃	—	2	8	no	—
193	C₂³×C₁₃	—	2	8	no	—
194	C₂³×C₁₃	—	4	64	no	—
195	C₂³×C₁₃	—	4	128	no	—
196	C₂³×C₁₃	—	4	16	no	—
197	C₂³×C₁₃	—	4	16	no	—
198	C₂³×C₁₃	—	4	8	no	—
199	C₂³×C₁₃	—	4	8	no	—
200	C₂³×C₁₃	—	4	8	no	—
201	C₂³×C₁₃	—	4	8	no	—
202	C₂³×C₁₃	—	4	16	no	—
203	C₂³×C₁₃	—	4	16	no	—
204	C₂³×C₁₃	#120	1	16	yes	—
205	C₂³×C₁₃	C₂²×D₄	1	8	yes	—
206	C₂³×C₁₃	C₂²×D₄	1	8	yes	—
207	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
208	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
209	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
210	C₂³×C₁₃	C₂×#41	1	4	yes	—
211	C₂³×C₁₃	C₂×#41	1	8	yes	complemented
212	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
213	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
214	Q₈×C₁₃	—	2	32	no	—
215	D₄×C₁₃	—	2	32	no	—
216	D₄×C₁₃	—	2	64	no	—
217	D₄×C₁₃	—	4	64	no	—
218	C₂×C₄×C₁₃	—	2	64	no	—
219	C₂×C₄×C₁₃	—	2	8	no	—
220	C₂×C₄×C₁₃	—	2	16	no	—
221	C₂×C₄×C₁₃	—	2	8	no	—
222	C₂×C₄×C₁₃	—	2	32	no	—
223	C₂×C₄×C₁₃	—	2	4	no	—
224	C₂×C₄×C₁₃	—	2	4	no	—
225	C₂×C₄×C₁₃	—	2	4	no	—
226	C₂×C₄×C₁₃	—	2	4	no	—
227	C₂×C₄×C₁₃	—	2	4	no	—
228	C₂×C₄×C₁₃	—	2	8	no	—
229	C₂×C₄×C₁₃	—	2	8	no	—
230	C₂×C₄×C₁₃	—	2	8	no	—
231	C₂×C₄×C₁₃	—	2	8	no	—
232	C₂×C₄×C₁₃	—	4	16	no	—
233	C₂×C₄×C₁₃	—	4	8	no	—
234	C₂×C₄×C₁₃	—	4	16	no	—
235	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
236	C₂×C₄×C₁₃	C₂²×D₄	1	8	yes	—
237	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
238	C₂⁶	C₂²×C₁₃	1	1	yes	characteristic
239	C₂²×#41	—	2	16	no	—
240	C₂²×#41	—	2	8	no	—
241	C₂²×#41	C₂²×C₁₃	1	8	yes	complemented
242	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
243	C₂³×D₄	C₂²×C₁₃	1	4	yes	—
244	C₂³×D₄	C₂²×C₁₃	1	2	yes	—
245	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
246	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
247	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
248	C₂⁴×C₄	C₂²×C₁₃	1	2	yes	complemented
249	C₂×#120	—	2	16	no	—
250	C₂×#120	C₂²×C₁₃	1	16	yes	complemented
251	C₂²×C₂²⋊C₄	—	2	8	no	—
252	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
253	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
254	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
255	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
256	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	complemented
257	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	complemented
258	#393	C₂²×C₁₃	1	16	yes	complemented
259	#392	C₂²×C₁₃	1	16	yes	complemented
260	#386	C₂²×C₁₃	1	32	yes	complemented
261	#386	C₂²×C₁₃	1	16	yes	complemented
262	#381	C₂²×C₁₃	1	8	yes	complemented
263	C₂×#95	C₂²×C₁₃	1	2	yes	complemented
264	C₂×#95	C₂²×C₁₃	1	4	yes	complemented
265	C₂×#95	C₂²×C₁₃	1	2	yes	complemented
266	C₂²×C₁₃	—	2	32	no	—
267	C₂²×C₁₃	—	2	4	no	—
268	C₂²×C₁₃	—	2	4	no	—
269	C₂²×C₁₃	—	2	16	no	—
270	C₂²×C₁₃	—	2	8	no	—
271	C₂²×C₁₃	—	2	8	no	—
272	C₂²×C₁₃	—	2	16	no	—
273	C₂²×C₁₃	—	2	16	no	—
274	C₂²×C₁₃	—	4	64	no	—
275	C₂²×C₁₃	—	4	32	no	—
276	C₂²×C₁₃	—	4	32	no	—
277	C₂²×C₁₃	—	4	4	no	—
278	C₂²×C₁₃	—	4	4	no	—
279	C₂²×C₁₃	—	4	4	no	—
280	C₂²×C₁₃	—	4	4	no	—
281	C₂²×C₁₃	—	4	8	no	—
282	C₂²×C₁₃	—	4	8	no	—
283	C₂²×C₁₃	C₂×#120	1	8	yes	—
284	C₂²×C₁₃	C₂×#120	1	4	yes	—
285	C₂²×C₁₃	#525	1	4	yes	—
286	C₂²×C₁₃	#535	1	4	yes	—
287	C₂²×C₁₃	#546	1	16	yes	—
288	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
289	C₂²×C₁₃	C₂³×D₄	1	2	yes	—
290	C₂²×C₁₃	C₂²×#41	1	2	yes	—
291	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
292	C₄×C₁₃	—	2	4	no	—
293	C₄×C₁₃	—	2	8	no	—
294	C₄×C₁₃	—	2	4	no	—
295	C₄×C₁₃	—	4	4	no	—
296	C₄×C₁₃	—	4	8	no	—
297	C₂⁵	—	2	4	no	—
298	C₂⁵	—	2	8	no	—
299	C₂⁵	—	2	8	no	—
300	C₂⁵	—	4	4	no	—
301	C₂⁵	C₂³×C₁₃	1	2	yes	—
302	C₂⁵	C₂³×C₁₃	1	2	yes	—
303	C₂⁵	C₂³×C₁₃	1	4	yes	—
304	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
305	C₂×#41	—	2	128	no	—
306	C₂×#41	—	2	64	no	—
307	C₂×#41	—	2	32	no	—
308	C₂²×Q₈	—	2	8	no	—
309	C₂²×Q₈	—	2	4	no	—
310	C₂²×Q₈	C₂³×C₁₃	1	4	yes	complemented
311	C₂²×D₄	—	2	8	no	—
312	C₂²×D₄	—	2	8	no	—
313	C₂²×D₄	—	2	8	no	—
314	C₂²×D₄	—	2	16	no	—
315	C₂²×D₄	—	2	16	no	—
316	C₂²×D₄	—	2	4	no	—
317	C₂²×D₄	—	4	8	no	—
318	C₂²×D₄	D₄×C₁₃	1	16	yes	complemented
319	C₂²×D₄	C₂³×C₁₃	1	16	yes	—
320	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
321	C₂²×D₄	C₂³×C₁₃	1	4	yes	complemented
322	C₂³×C₄	—	2	8	no	—
323	C₂³×C₄	—	2	8	no	—
324	C₂³×C₄	—	2	8	no	—
325	C₂³×C₄	—	2	8	no	—
326	C₂³×C₄	—	2	4	no	—
327	C₂³×C₄	—	4	4	no	—
328	C₂³×C₄	D₄×C₁₃	1	8	yes	complemented
329	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
330	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
331	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
332	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
333	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
334	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
335	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
336	C₂³×C₄	C₂³×C₁₃	1	8	yes	complemented
337	#120	—	2	64	no	—
338	C₂×C₂²⋊C₄	—	2	8	no	—
339	C₂×C₂²⋊C₄	—	2	8	no	—
340	C₂×C₂²⋊C₄	—	2	8	no	—
341	C₂×C₂²⋊C₄	—	2	16	no	—
342	C₂×C₂²⋊C₄	—	2	32	no	—
343	C₂×C₂²⋊C₄	—	4	8	no	—
344	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
345	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
346	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
347	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
348	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	complemented
349	#95	C₂³×C₁₃	1	8	yes	complemented
350	#95	C₂³×C₁₃	1	8	yes	complemented
351	#95	C₂³×C₁₃	1	16	yes	complemented
352	C₂×C₁₃	—	2	8	no	—
353	C₂×C₁₃	—	4	8	no	—
354	C₂×C₁₃	—	4	8	no	—
355	C₂×C₁₃	#2404	1	8	yes	direct product factor
356	C₂×C₁₃	C₂²×#120	1	1	yes	characteristic
357	C₂×C₁₃	C₂×#525	1	1	yes	characteristic
358	C₂×C₁₃	C₂×#535	1	1	yes	characteristic
359	C₂×C₁₃	C₂×#546	1	4	yes	—
360	C₂⁴	—	2	4	no	—
361	C₂⁴	—	2	4	no	—
362	C₂⁴	—	2	32	no	—
363	C₂⁴	—	2	8	no	—
364	C₂⁴	—	2	4	no	—
365	C₂⁴	—	2	8	no	—
366	C₂⁴	—	2	4	no	—
367	C₂⁴	—	2	4	no	—
368	C₂⁴	—	2	8	no	—
369	C₂⁴	—	2	4	no	—
370	C₂⁴	—	2	16	no	—
371	C₂⁴	—	2	8	no	—
372	C₂⁴	—	2	8	no	—
373	C₂⁴	—	2	16	no	—
374	C₂⁴	—	4	8	no	—
375	C₂⁴	—	4	64	no	—
376	C₂⁴	—	4	16	no	—
377	C₂⁴	—	4	16	no	—
378	C₂⁴	C₂×D₄×C₁₃	1	8	yes	—
379	C₂⁴	C₂×D₄×C₁₃	1	8	yes	—
380	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
381	C₂⁴	C₁₃×#41	1	8	yes	complemented
382	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
383	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
384	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
385	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
386	#41	—	2	256	no	—
387	C₂×Q₈	—	2	32	no	—
388	C₂×Q₈	—	2	16	no	—
389	C₂×Q₈	—	2	8	no	—
390	C₂×D₄	—	2	32	no	—
391	C₂×D₄	—	2	64	no	—
392	C₂×D₄	—	2	16	no	—
393	C₂×D₄	—	2	16	no	—
394	C₂×D₄	—	2	16	no	—
395	C₂×D₄	—	2	32	no	—
396	C₂×D₄	—	2	32	no	—
397	C₂×D₄	—	2	8	no	—
398	C₂×D₄	—	4	16	no	—
399	C₂×D₄	—	4	64	no	—
400	C₂×D₄	C₂×D₄×C₁₃	1	32	yes	complemented
401	C₂²×C₄	—	2	64	no	—
402	C₂²×C₄	—	2	32	no	—
403	C₂²×C₄	—	2	4	no	—
404	C₂²×C₄	—	2	4	no	—
405	C₂²×C₄	—	2	4	no	—
406	C₂²×C₄	—	2	4	no	—
407	C₂²×C₄	—	2	16	no	—
408	C₂²×C₄	—	2	16	no	—
409	C₂²×C₄	—	2	16	no	—
410	C₂²×C₄	—	2	16	no	—
411	C₂²×C₄	—	2	8	no	—
412	C₂²×C₄	—	2	4	no	—
413	C₂²×C₄	—	2	8	no	—
414	C₂²×C₄	—	2	8	no	—
415	C₂²×C₄	—	2	8	no	—
416	C₂²×C₄	—	2	8	no	—
417	C₂²×C₄	—	4	8	no	—
418	C₂²×C₄	—	4	16	no	—
419	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
420	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	—
421	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
422	C₂²×C₄	C₂×D₄×C₁₃	1	16	yes	complemented
423	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
424	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
425	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
426	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
427	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
428	C₂²⋊C₄	—	2	16	no	—
429	C₂²⋊C₄	—	2	16	no	—
430	C₂²⋊C₄	—	2	16	no	—
431	C₂²⋊C₄	—	2	32	no	—
432	C₂²⋊C₄	—	4	16	no	—
433	C₁₃	C₂×#2404	1	1	yes	characteristic, direct product factor, Sylow
434	C₂³	—	2	8	no	—
435	C₂³	—	2	8	no	—
436	C₂³	—	2	32	no	—
437	C₂³	—	2	4	no	—
438	C₂³	—	2	4	no	—
439	C₂³	—	2	32	no	—
440	C₂³	—	2	16	no	—
441	C₂³	—	2	16	no	—
442	C₂³	—	2	32	no	—
443	C₂³	—	2	32	no	—
444	C₂³	—	2	4	no	—
445	C₂³	—	2	8	no	—
446	C₂³	—	2	4	no	—
447	C₂³	—	2	4	no	—
448	C₂³	—	2	8	no	—
449	C₂³	—	2	4	no	—
450	C₂³	—	2	8	no	—
451	C₂³	—	2	8	no	—
452	C₂³	—	4	64	no	—
453	C₂³	—	4	128	no	—
454	C₂³	—	4	16	no	—
455	C₂³	—	4	16	no	—
456	C₂³	—	4	8	no	—
457	C₂³	—	4	8	no	—
458	C₂³	—	4	8	no	—
459	C₂³	—	4	8	no	—
460	C₂³	—	4	16	no	—
461	C₂³	—	4	16	no	—
462	C₂³	C₁₃×#120	1	16	yes	—
463	C₂³	C₂²×D₄×C₁₃	1	8	yes	—
464	C₂³	C₂²×D₄×C₁₃	1	8	yes	—
465	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
466	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
467	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
468	C₂³	C₂×C₁₃×#41	1	4	yes	—
469	C₂³	C₂×C₁₃×#41	1	8	yes	complemented
470	C₂³	C₁₃×H(5,𝔽₂)	1	4	yes	—
471	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
472	Q₈	—	2	32	no	—
473	D₄	—	2	32	no	—
474	D₄	—	2	64	no	—
475	D₄	—	4	64	no	—
476	C₂×C₄	—	2	64	no	—
477	C₂×C₄	—	2	8	no	—
478	C₂×C₄	—	2	16	no	—
479	C₂×C₄	—	2	8	no	—
480	C₂×C₄	—	2	32	no	—
481	C₂×C₄	—	2	4	no	—
482	C₂×C₄	—	2	4	no	—
483	C₂×C₄	—	2	4	no	—
484	C₂×C₄	—	2	4	no	—
485	C₂×C₄	—	2	4	no	—
486	C₂×C₄	—	2	8	no	—
487	C₂×C₄	—	2	8	no	—
488	C₂×C₄	—	2	8	no	—
489	C₂×C₄	—	2	8	no	—
490	C₂×C₄	—	4	16	no	—
491	C₂×C₄	—	4	8	no	—
492	C₂×C₄	—	4	16	no	—
493	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
494	C₂×C₄	C₂²×D₄×C₁₃	1	8	yes	—
495	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
496	C₂²	—	2	32	no	—
497	C₂²	—	2	4	no	—
498	C₂²	—	2	4	no	—
499	C₂²	—	2	16	no	—
500	C₂²	—	2	8	no	—
501	C₂²	—	2	8	no	—
502	C₂²	—	2	16	no	—
503	C₂²	—	2	16	no	—
504	C₂²	—	4	64	no	—
505	C₂²	—	4	32	no	—
506	C₂²	—	4	32	no	—
507	C₂²	—	4	4	no	—
508	C₂²	—	4	4	no	—
509	C₂²	—	4	4	no	—
510	C₂²	—	4	4	no	—
511	C₂²	—	4	8	no	—
512	C₂²	—	4	8	no	—
513	C₂²	C₂×C₁₃×#120	1	8	yes	—
514	C₂²	C₂×C₁₃×#120	1	4	yes	—
515	C₂²	C₁₃×#525	1	4	yes	—
516	C₂²	C₁₃×#535	1	4	yes	—
517	C₂²	C₁₃×#546	1	16	yes	—
518	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
519	C₂²	C₂³×D₄×C₁₃	1	2	yes	—
520	C₂²	C₂²×C₁₃×#41	1	2	yes	—
521	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
522	C₄	—	2	4	no	—
523	C₄	—	2	8	no	—
524	C₄	—	2	4	no	—
525	C₄	—	4	4	no	—
526	C₄	—	4	8	no	—
527	C₂	—	2	8	no	—
528	C₂	—	4	8	no	—
529	C₂	—	4	8	no	—
530	C₂	C₁₃×#2404	1	8	yes	direct product factor
531	C₂	C₂²×C₁₃×#120	1	1	yes	characteristic
532	C₂	C₂×C₁₃×#525	1	1	yes	characteristic
533	C₂	C₂×C₁₃×#535	1	1	yes	characteristic
534	C₂	C₂×C₁₃×#546	1	4	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
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. C₂³×C₁₃×#41	C₂	semidirect
2. C₂²×C₁₃×#120	C₂	semidirect
3. C₂³×C₁₃×C₂²⋊C₄	C₂	semidirect
4. C₁₃×#2404	C₂	direct (N × H)
5. C₂×C₁₃×#393	C₂	semidirect
6. C₂×C₁₃×#392	C₂	semidirect
7. C₂×C₁₃×#386	C₂	semidirect
8. C₂×C₁₃×#386	C₂	semidirect
9. C₂×C₁₃×#381	C₂	semidirect
13. C₂²×C₁₃×#41	C₂²	semidirect
14. C₂³×Q₈×C₁₃	C₂²	semidirect
17. C₂³×D₄×C₁₃	C₂²	semidirect
20. C₂⁴×C₄×C₁₃	C₂²	semidirect
22. C₂×C₁₃×#120	C₂²	semidirect
28. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
29. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
30. C₁₃×#393	C₂²	semidirect
31. C₁₃×#392	C₂²	semidirect
32. C₁₃×#386	C₂²	semidirect
33. C₁₃×#386	C₂²	semidirect
34. C₁₃×#381	C₂²	semidirect
35. C₂×C₁₃×#95	C₂²	semidirect
36. C₂×C₁₃×#95	C₂²	semidirect
37. C₂×C₁₃×#95	C₂²	semidirect
51. C₂²×Q₈×C₁₃	C₂³	semidirect
59. C₂²×D₄×C₁₃	D₄	semidirect
62. C₂²×D₄×C₁₃	C₂³	semidirect
69. C₂³×C₄×C₁₃	D₄	semidirect
77. C₂³×C₄×C₁₃	C₂³	semidirect
89. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
90. C₁₃×#95	C₂³	semidirect
91. C₁₃×#95	C₂³	semidirect
92. C₁₃×#95	C₂³	semidirect
93. C₂×#2404	C₁₃	direct (N × H)
115. C₂⁴×C₁₃	#41	semidirect
134. C₂×D₄×C₁₃	C₂×D₄	semidirect
156. C₂²×C₄×C₁₃	C₂×D₄	semidirect
167. C₂³×#41	C₂×C₁₃	semidirect
168. C₂²×#120	C₂×C₁₃	semidirect
169. C₂³×C₂²⋊C₄	C₂×C₁₃	semidirect
170. #2404	C₂×C₁₃	direct (N × H)
171. C₂×#393	C₂×C₁₃	semidirect
172. C₂×#392	C₂×C₁₃	semidirect
173. C₂×#386	C₂×C₁₃	semidirect
174. C₂×#386	C₂×C₁₃	semidirect
175. C₂×#381	C₂×C₁₃	semidirect
211. C₂³×C₁₃	C₂×#41	semidirect
241. C₂²×#41	C₂²×C₁₃	semidirect
242. C₂³×Q₈	C₂²×C₁₃	semidirect
245. C₂³×D₄	C₂²×C₁₃	semidirect
248. C₂⁴×C₄	C₂²×C₁₃	semidirect
250. C₂×#120	C₂²×C₁₃	semidirect
256. C₂²×C₂²⋊C₄	C₂²×C₁₃	semidirect
257. C₂²×C₂²⋊C₄	C₂²×C₁₃	semidirect
258. #393	C₂²×C₁₃	semidirect
259. #392	C₂²×C₁₃	semidirect
260. #386	C₂²×C₁₃	semidirect
261. #386	C₂²×C₁₃	semidirect
262. #381	C₂²×C₁₃	semidirect
263. C₂×#95	C₂²×C₁₃	semidirect
264. C₂×#95	C₂²×C₁₃	semidirect
265. C₂×#95	C₂²×C₁₃	semidirect
310. C₂²×Q₈	C₂³×C₁₃	semidirect
318. C₂²×D₄	D₄×C₁₃	semidirect
321. C₂²×D₄	C₂³×C₁₃	semidirect
328. C₂³×C₄	D₄×C₁₃	semidirect
336. C₂³×C₄	C₂³×C₁₃	semidirect
348. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
349. #95	C₂³×C₁₃	semidirect
350. #95	C₂³×C₁₃	semidirect
351. #95	C₂³×C₁₃	semidirect
355. C₂×C₁₃	#2404	direct (N × H)
381. C₂⁴	C₁₃×#41	semidirect
400. C₂×D₄	C₂×D₄×C₁₃	semidirect
422. C₂²×C₄	C₂×D₄×C₁₃	semidirect
433. C₁₃	C₂×#2404	direct (N × H)
469. C₂³	C₂×C₁₃×#41	semidirect
530. C₂	C₁₃×#2404	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×#120	2
C₂³×C₁₃×C₂²⋊C₄	2
C₁₃×#2404	2
C₂×C₁₃×#393	2
C₂×C₁₃×#392	2
C₂×C₁₃×#386	2
C₂×C₁₃×#381	2
C₂×#2404	13

Subgroups — C2×C13×#2404 #15721067

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2404 #15721067