Subgroups — C₂×C₁₃×#2431 #15721050

Order 3328.

6278 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	C₂³×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₃×#127	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₁₃×#124	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₁₃×#121	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2431	C₂	1	16	yes	maximal, direct product factor
6	C₂×C₁₃×#392	C₂	1	4	yes	maximal, complemented
7	C₂×C₁₃×#391	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#390	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#386	C₂	1	4	yes	maximal, complemented
10	C₂×C₄×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×C₁₃×#41	—	2	8	no	—
12	C₂²×C₁₃×#41	—	2	8	no	—
13	C₂²×C₁₃×#41	—	2	8	no	—
14	C₂²×C₁₃×#41	C₂²	1	8	yes	complemented
15	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
16	C₂³×D₄×C₁₃	C₂²	1	2	yes	—
17	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
18	C₂³×D₄×C₁₃	C₂²	1	4	yes	—
19	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
20	C₂³×D₄×C₁₃	C₂²	1	2	yes	—
21	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	—
22	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#127	—	2	8	no	—
24	C₂×C₁₃×#127	C₂²	1	8	yes	complemented
25	C₂×C₁₃×#124	—	2	8	no	—
26	C₂×C₁₃×#124	C₂²	1	8	yes	complemented
27	C₂×C₁₃×#121	—	2	8	no	—
28	C₂×C₁₃×#121	C₂²	1	8	yes	complemented
29	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
30	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
31	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
32	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
33	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
34	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
35	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
36	C₁₃×#392	C₂²	1	32	yes	complemented
37	C₁₃×#391	C₂²	1	8	yes	complemented
38	C₁₃×#390	C₂²	1	8	yes	complemented
39	C₁₃×#386	C₂²	1	32	yes	complemented
40	C₄×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	complemented
41	C₂×C₁₃×#95	C₂²	1	2	yes	—
42	C₂×C₁₃×#95	C₂²	1	4	yes	—
43	C₂⁵×C₁₃	C₂³	1	2	yes	—
44	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
45	C₂⁵×C₁₃	C₂³	1	2	yes	—
46	C₂×C₁₃×#41	—	2	128	no	—
47	C₂×C₁₃×#41	—	2	32	no	—
48	C₂×C₁₃×#41	—	2	32	no	—
49	C₂×C₁₃×#41	—	2	32	no	—
50	C₂²×Q₈×C₁₃	—	2	4	no	—
51	C₂²×Q₈×C₁₃	—	2	4	no	—
52	C₂²×Q₈×C₁₃	D₄	1	8	yes	complemented
53	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
54	C₂²×D₄×C₁₃	—	2	8	no	—
55	C₂²×D₄×C₁₃	—	2	8	no	—
56	C₂²×D₄×C₁₃	—	2	8	no	—
57	C₂²×D₄×C₁₃	—	2	16	no	—
58	C₂²×D₄×C₁₃	—	2	8	no	—
59	C₂²×D₄×C₁₃	—	2	4	no	—
60	C₂²×D₄×C₁₃	—	2	4	no	—
61	C₂²×D₄×C₁₃	—	2	4	no	—
62	C₂²×D₄×C₁₃	—	2	4	no	—
63	C₂²×D₄×C₁₃	—	2	4	no	—
64	C₂²×D₄×C₁₃	—	2	16	no	—
65	C₂²×D₄×C₁₃	—	4	8	no	—
66	C₂²×D₄×C₁₃	—	4	8	no	—
67	C₂²×D₄×C₁₃	D₄	1	8	yes	complemented
68	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
69	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
70	C₂²×D₄×C₁₃	C₂³	1	16	yes	—
71	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
72	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
73	C₂³×C₄×C₁₃	—	2	8	no	—
74	C₂³×C₄×C₁₃	—	2	8	no	—
75	C₂³×C₄×C₁₃	—	2	8	no	—
76	C₂³×C₄×C₁₃	—	2	4	no	—
77	C₂³×C₄×C₁₃	—	2	4	no	—
78	C₂³×C₄×C₁₃	D₄	1	8	yes	complemented
79	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
80	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
81	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
82	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
83	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
84	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
85	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
86	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
87	C₁₃×#127	—	2	32	no	—
88	C₁₃×#124	—	2	32	no	—
89	C₁₃×#121	—	2	32	no	—
90	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
91	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
92	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
93	C₂×C₁₃×C₂²⋊C₄	—	2	16	no	—
94	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
95	C₂×C₁₃×C₂²⋊C₄	—	4	8	no	—
96	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
97	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
98	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
99	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
100	C₂×C₄²×C₁₃	—	2	4	no	—
101	C₂×C₄²×C₁₃	—	2	4	no	—
102	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
103	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
104	C₁₃×#95	C₂³	1	8	yes	—
105	C₁₃×#95	C₂³	1	16	yes	—
106	C₂×#2431	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
107	C₂⁴×C₁₃	—	2	4	no	—
108	C₂⁴×C₁₃	—	2	2	no	—
109	C₂⁴×C₁₃	—	2	4	no	—
110	C₂⁴×C₁₃	—	2	2	no	—
111	C₂⁴×C₁₃	—	2	4	no	—
112	C₂⁴×C₁₃	—	2	8	no	—
113	C₂⁴×C₁₃	—	2	8	no	—
114	C₂⁴×C₁₃	—	2	4	no	—
115	C₂⁴×C₁₃	—	2	4	no	—
116	C₂⁴×C₁₃	—	2	4	no	—
117	C₂⁴×C₁₃	—	2	4	no	—
118	C₂⁴×C₁₃	—	2	8	no	—
119	C₂⁴×C₁₃	—	2	8	no	—
120	C₂⁴×C₁₃	C₂×D₄	1	8	yes	—
121	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
122	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
123	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
124	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
125	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
126	C₁₃×#41	—	2	256	no	—
127	C₂×Q₈×C₁₃	—	2	32	no	—
128	C₂×Q₈×C₁₃	—	2	8	no	—
129	C₂×Q₈×C₁₃	—	2	8	no	—
130	C₂×Q₈×C₁₃	C₂×D₄	1	16	yes	complemented
131	C₂×D₄×C₁₃	—	2	64	no	—
132	C₂×D₄×C₁₃	—	2	16	no	—
133	C₂×D₄×C₁₃	—	2	16	no	—
134	C₂×D₄×C₁₃	—	2	16	no	—
135	C₂×D₄×C₁₃	—	2	32	no	—
136	C₂×D₄×C₁₃	—	2	32	no	—
137	C₂×D₄×C₁₃	—	2	16	no	—
138	C₂×D₄×C₁₃	—	2	8	no	—
139	C₂×D₄×C₁₃	—	2	8	no	—
140	C₂×D₄×C₁₃	—	2	8	no	—
141	C₂×D₄×C₁₃	—	2	8	no	—
142	C₂×D₄×C₁₃	—	2	8	no	—
143	C₂×D₄×C₁₃	—	2	32	no	—
144	C₂×D₄×C₁₃	—	4	16	no	—
145	C₂×D₄×C₁₃	—	4	16	no	—
146	C₂×D₄×C₁₃	—	4	64	no	—
147	C₂×D₄×C₁₃	—	4	32	no	—
148	C₂×D₄×C₁₃	—	4	16	no	—
149	C₂×D₄×C₁₃	C₂×D₄	1	16	yes	complemented
150	C₂²×C₄×C₁₃	—	2	64	no	—
151	C₂²×C₄×C₁₃	—	2	4	no	—
152	C₂²×C₄×C₁₃	—	2	2	no	—
153	C₂²×C₄×C₁₃	—	2	2	no	—
154	C₂²×C₄×C₁₃	—	2	4	no	—
155	C₂²×C₄×C₁₃	—	2	4	no	—
156	C₂²×C₄×C₁₃	—	2	16	no	—
157	C₂²×C₄×C₁₃	—	2	4	no	—
158	C₂²×C₄×C₁₃	—	2	32	no	—
159	C₂²×C₄×C₁₃	—	2	16	no	—
160	C₂²×C₄×C₁₃	—	2	16	no	—
161	C₂²×C₄×C₁₃	—	2	8	no	—
162	C₂²×C₄×C₁₃	—	2	8	no	—
163	C₂²×C₄×C₁₃	—	2	4	no	—
164	C₂²×C₄×C₁₃	—	2	4	no	—
165	C₂²×C₄×C₁₃	—	2	4	no	—
166	C₂²×C₄×C₁₃	—	2	4	no	—
167	C₂²×C₄×C₁₃	—	2	8	no	—
168	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
169	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
170	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
171	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
172	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
173	C₂²×C₄×C₁₃	C₂×D₄	1	16	yes	complemented
174	C₂²×C₄×C₁₃	#41	1	8	yes	complemented
175	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
176	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
177	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
178	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
179	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
180	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
181	C₁₃×C₄⋊C₄	—	2	8	no	—
182	C₁₃×C₂²⋊C₄	—	2	16	no	—
183	C₁₃×C₂²⋊C₄	—	2	32	no	—
184	C₁₃×C₂²⋊C₄	—	2	16	no	—
185	C₁₃×C₂²⋊C₄	—	4	16	no	—
186	C₄²×C₁₃	—	2	8	no	—
187	C₄²×C₁₃	—	2	8	no	—
188	C₂³×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
189	C₂²×#127	C₂×C₁₃	1	1	yes	characteristic, complemented
190	C₂²×#124	C₂×C₁₃	1	1	yes	characteristic, complemented
191	C₂²×#121	C₂×C₁₃	1	1	yes	characteristic, complemented
192	#2431	C₂×C₁₃	1	16	yes	direct product factor
193	C₂×#392	C₂×C₁₃	1	4	yes	complemented
194	C₂×#391	C₂×C₁₃	1	1	yes	characteristic, complemented
195	C₂×#390	C₂×C₁₃	1	1	yes	characteristic, complemented
196	C₂×#386	C₂×C₁₃	1	4	yes	complemented
197	C₂×C₄×C₂²⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
198	C₂³×C₁₃	—	2	16	no	—
199	C₂³×C₁₃	—	2	8	no	—
200	C₂³×C₁₃	—	2	8	no	—
201	C₂³×C₁₃	—	2	8	no	—
202	C₂³×C₁₃	—	2	32	no	—
203	C₂³×C₁₃	—	2	4	no	—
204	C₂³×C₁₃	—	2	2	no	—
205	C₂³×C₁₃	—	2	4	no	—
206	C₂³×C₁₃	—	2	2	no	—
207	C₂³×C₁₃	—	2	4	no	—
208	C₂³×C₁₃	—	2	8	no	—
209	C₂³×C₁₃	—	2	8	no	—
210	C₂³×C₁₃	—	2	4	no	—
211	C₂³×C₁₃	—	2	4	no	—
212	C₂³×C₁₃	—	2	4	no	—
213	C₂³×C₁₃	—	2	4	no	—
214	C₂³×C₁₃	—	2	8	no	—
215	C₂³×C₁₃	—	2	8	no	—
216	C₂³×C₁₃	—	4	8	no	—
217	C₂³×C₁₃	—	4	8	no	—
218	C₂³×C₁₃	—	4	8	no	—
219	C₂³×C₁₃	—	4	8	no	—
220	C₂³×C₁₃	—	4	16	no	—
221	C₂³×C₁₃	—	4	8	no	—
222	C₂³×C₁₃	—	4	8	no	—
223	C₂³×C₁₃	—	4	8	no	—
224	C₂³×C₁₃	—	4	16	no	—
225	C₂³×C₁₃	—	4	16	no	—
226	C₂³×C₁₃	C₂²×D₄	1	8	yes	—
227	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
228	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
229	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
230	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
231	C₂³×C₁₃	C₂×#41	1	4	yes	—
232	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
233	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
234	Q₈×C₁₃	—	2	32	no	—
235	D₄×C₁₃	—	2	64	no	—
236	D₄×C₁₃	—	2	32	no	—
237	D₄×C₁₃	—	4	64	no	—
238	D₄×C₁₃	—	4	32	no	—
239	D₄×C₁₃	—	4	16	no	—
240	C₂×C₄×C₁₃	—	2	64	no	—
241	C₂×C₄×C₁₃	—	2	8	no	—
242	C₂×C₄×C₁₃	—	2	16	no	—
243	C₂×C₄×C₁₃	—	2	16	no	—
244	C₂×C₄×C₁₃	—	2	4	no	—
245	C₂×C₄×C₁₃	—	2	2	no	—
246	C₂×C₄×C₁₃	—	2	2	no	—
247	C₂×C₄×C₁₃	—	2	4	no	—
248	C₂×C₄×C₁₃	—	2	4	no	—
249	C₂×C₄×C₁₃	—	2	4	no	—
250	C₂×C₄×C₁₃	—	2	32	no	—
251	C₂×C₄×C₁₃	—	2	4	no	—
252	C₂×C₄×C₁₃	—	2	4	no	—
253	C₂×C₄×C₁₃	—	2	4	no	—
254	C₂×C₄×C₁₃	—	2	4	no	—
255	C₂×C₄×C₁₃	—	2	8	no	—
256	C₂×C₄×C₁₃	—	4	8	no	—
257	C₂×C₄×C₁₃	—	4	8	no	—
258	C₂×C₄×C₁₃	#120	1	16	yes	—
259	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
260	C₂×C₄×C₁₃	C₂²×D₄	1	8	yes	—
261	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
262	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
263	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
264	C₂×C₄×C₁₃	C₂×#41	1	8	yes	complemented
265	C₂²×#41	—	2	8	no	—
266	C₂²×#41	—	2	8	no	—
267	C₂²×#41	—	2	8	no	—
268	C₂²×#41	C₂²×C₁₃	1	8	yes	complemented
269	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
270	C₂³×D₄	C₂²×C₁₃	1	2	yes	—
271	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
272	C₂³×D₄	C₂²×C₁₃	1	4	yes	—
273	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
274	C₂³×D₄	C₂²×C₁₃	1	2	yes	—
275	C₂⁴×C₄	C₂²×C₁₃	1	2	yes	—
276	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
277	C₂×#127	—	2	8	no	—
278	C₂×#127	C₂²×C₁₃	1	8	yes	complemented
279	C₂×#124	—	2	8	no	—
280	C₂×#124	C₂²×C₁₃	1	8	yes	complemented
281	C₂×#121	—	2	8	no	—
282	C₂×#121	C₂²×C₁₃	1	8	yes	complemented
283	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
284	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
285	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
286	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
287	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
288	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
289	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
290	#392	C₂²×C₁₃	1	32	yes	complemented
291	#391	C₂²×C₁₃	1	8	yes	complemented
292	#390	C₂²×C₁₃	1	8	yes	complemented
293	#386	C₂²×C₁₃	1	32	yes	complemented
294	C₄×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	complemented
295	C₂×#95	C₂²×C₁₃	1	4	yes	—
296	C₂×#95	C₂²×C₁₃	1	2	yes	—
297	C₂²×C₁₃	—	2	8	no	—
298	C₂²×C₁₃	—	2	4	no	—
299	C₂²×C₁₃	—	2	4	no	—
300	C₂²×C₁₃	—	2	4	no	—
301	C₂²×C₁₃	—	2	16	no	—
302	C₂²×C₁₃	—	4	4	no	—
303	C₂²×C₁₃	—	4	4	no	—
304	C₂²×C₁₃	—	4	16	no	—
305	C₂²×C₁₃	—	4	32	no	—
306	C₂²×C₁₃	—	4	4	no	—
307	C₂²×C₁₃	—	4	4	no	—
308	C₂²×C₁₃	—	4	8	no	—
309	C₂²×C₁₃	—	4	4	no	—
310	C₂²×C₁₃	—	4	4	no	—
311	C₂²×C₁₃	—	4	4	no	—
312	C₂²×C₁₃	—	4	8	no	—
313	C₂²×C₁₃	—	4	8	no	—
314	C₂²×C₁₃	—	8	16	no	—
315	C₂²×C₁₃	C₂×#120	1	4	yes	—
316	C₂²×C₁₃	#532	1	4	yes	—
317	C₂²×C₁₃	#535	1	4	yes	—
318	C₂²×C₁₃	#546	1	8	yes	—
319	C₂²×C₁₃	#550	1	8	yes	—
320	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
321	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
322	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
323	C₂²×C₁₃	C₂²×#41	1	2	yes	—
324	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
325	C₄×C₁₃	—	2	4	no	—
326	C₄×C₁₃	—	2	8	no	—
327	C₄×C₁₃	—	2	8	no	—
328	C₄×C₁₃	—	4	4	no	—
329	C₄×C₁₃	—	4	4	no	—
330	C₄×C₁₃	C₂×#120	1	8	yes	—
331	C₂⁵	C₂³×C₁₃	1	2	yes	—
332	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
333	C₂⁵	C₂³×C₁₃	1	2	yes	—
334	C₂×#41	—	2	128	no	—
335	C₂×#41	—	2	32	no	—
336	C₂×#41	—	2	32	no	—
337	C₂×#41	—	2	32	no	—
338	C₂²×Q₈	—	2	4	no	—
339	C₂²×Q₈	—	2	4	no	—
340	C₂²×Q₈	D₄×C₁₃	1	8	yes	complemented
341	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
342	C₂²×D₄	—	2	8	no	—
343	C₂²×D₄	—	2	8	no	—
344	C₂²×D₄	—	2	8	no	—
345	C₂²×D₄	—	2	16	no	—
346	C₂²×D₄	—	2	8	no	—
347	C₂²×D₄	—	2	4	no	—
348	C₂²×D₄	—	2	4	no	—
349	C₂²×D₄	—	2	4	no	—
350	C₂²×D₄	—	2	4	no	—
351	C₂²×D₄	—	2	4	no	—
352	C₂²×D₄	—	2	16	no	—
353	C₂²×D₄	—	4	8	no	—
354	C₂²×D₄	—	4	8	no	—
355	C₂²×D₄	D₄×C₁₃	1	8	yes	complemented
356	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
357	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
358	C₂²×D₄	C₂³×C₁₃	1	16	yes	—
359	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
360	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
361	C₂³×C₄	—	2	8	no	—
362	C₂³×C₄	—	2	8	no	—
363	C₂³×C₄	—	2	8	no	—
364	C₂³×C₄	—	2	4	no	—
365	C₂³×C₄	—	2	4	no	—
366	C₂³×C₄	D₄×C₁₃	1	8	yes	complemented
367	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
368	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
369	C₂³×C₄	C₂³×C₁₃	1	8	yes	—
370	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
371	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
372	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
373	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
374	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
375	#127	—	2	32	no	—
376	#124	—	2	32	no	—
377	#121	—	2	32	no	—
378	C₂×C₄⋊C₄	—	2	4	no	—
379	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
380	C₂×C₂²⋊C₄	—	2	8	no	—
381	C₂×C₂²⋊C₄	—	2	16	no	—
382	C₂×C₂²⋊C₄	—	2	8	no	—
383	C₂×C₂²⋊C₄	—	4	8	no	—
384	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
385	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
386	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
387	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
388	C₂×C₄²	—	2	4	no	—
389	C₂×C₄²	—	2	4	no	—
390	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
391	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
392	#95	C₂³×C₁₃	1	8	yes	—
393	#95	C₂³×C₁₃	1	16	yes	—
394	C₂×C₁₃	—	4	4	no	—
395	C₂×C₁₃	—	4	8	no	—
396	C₂×C₁₃	—	8	4	no	—
397	C₂×C₁₃	#2431	1	8	yes	direct product factor
398	C₂×C₁₃	C₂²×#120	1	1	yes	characteristic
399	C₂×C₁₃	C₂×#532	1	1	yes	characteristic
400	C₂×C₁₃	C₂×#535	1	1	yes	characteristic
401	C₂×C₁₃	C₂×#546	1	2	yes	—
402	C₂×C₁₃	C₂×#550	1	2	yes	—
403	C₂⁴	—	2	4	no	—
404	C₂⁴	—	2	2	no	—
405	C₂⁴	—	2	4	no	—
406	C₂⁴	—	2	2	no	—
407	C₂⁴	—	2	4	no	—
408	C₂⁴	—	2	8	no	—
409	C₂⁴	—	2	8	no	—
410	C₂⁴	—	2	4	no	—
411	C₂⁴	—	2	4	no	—
412	C₂⁴	—	2	4	no	—
413	C₂⁴	—	2	4	no	—
414	C₂⁴	—	2	8	no	—
415	C₂⁴	—	2	8	no	—
416	C₂⁴	C₂×D₄×C₁₃	1	8	yes	—
417	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
418	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
419	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
420	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
421	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
422	#41	—	2	256	no	—
423	C₂×Q₈	—	2	32	no	—
424	C₂×Q₈	—	2	8	no	—
425	C₂×Q₈	—	2	8	no	—
426	C₂×Q₈	C₂×D₄×C₁₃	1	16	yes	complemented
427	C₂×D₄	—	2	64	no	—
428	C₂×D₄	—	2	16	no	—
429	C₂×D₄	—	2	16	no	—
430	C₂×D₄	—	2	16	no	—
431	C₂×D₄	—	2	32	no	—
432	C₂×D₄	—	2	32	no	—
433	C₂×D₄	—	2	16	no	—
434	C₂×D₄	—	2	8	no	—
435	C₂×D₄	—	2	8	no	—
436	C₂×D₄	—	2	8	no	—
437	C₂×D₄	—	2	8	no	—
438	C₂×D₄	—	2	8	no	—
439	C₂×D₄	—	2	32	no	—
440	C₂×D₄	—	4	16	no	—
441	C₂×D₄	—	4	16	no	—
442	C₂×D₄	—	4	64	no	—
443	C₂×D₄	—	4	32	no	—
444	C₂×D₄	—	4	16	no	—
445	C₂×D₄	C₂×D₄×C₁₃	1	16	yes	complemented
446	C₂²×C₄	—	2	64	no	—
447	C₂²×C₄	—	2	4	no	—
448	C₂²×C₄	—	2	2	no	—
449	C₂²×C₄	—	2	2	no	—
450	C₂²×C₄	—	2	4	no	—
451	C₂²×C₄	—	2	4	no	—
452	C₂²×C₄	—	2	16	no	—
453	C₂²×C₄	—	2	4	no	—
454	C₂²×C₄	—	2	32	no	—
455	C₂²×C₄	—	2	16	no	—
456	C₂²×C₄	—	2	16	no	—
457	C₂²×C₄	—	2	8	no	—
458	C₂²×C₄	—	2	8	no	—
459	C₂²×C₄	—	2	4	no	—
460	C₂²×C₄	—	2	4	no	—
461	C₂²×C₄	—	2	4	no	—
462	C₂²×C₄	—	2	4	no	—
463	C₂²×C₄	—	2	8	no	—
464	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
465	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	—
466	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
467	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
468	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
469	C₂²×C₄	C₂×D₄×C₁₃	1	16	yes	complemented
470	C₂²×C₄	C₁₃×#41	1	8	yes	complemented
471	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
472	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
473	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
474	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
475	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
476	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
477	C₄⋊C₄	—	2	8	no	—
478	C₂²⋊C₄	—	2	16	no	—
479	C₂²⋊C₄	—	2	32	no	—
480	C₂²⋊C₄	—	2	16	no	—
481	C₂²⋊C₄	—	4	16	no	—
482	C₄²	—	2	8	no	—
483	C₄²	—	2	8	no	—
484	C₁₃	C₂×#2431	1	1	yes	characteristic, direct product factor, Sylow
485	C₂³	—	2	16	no	—
486	C₂³	—	2	8	no	—
487	C₂³	—	2	8	no	—
488	C₂³	—	2	8	no	—
489	C₂³	—	2	32	no	—
490	C₂³	—	2	4	no	—
491	C₂³	—	2	2	no	—
492	C₂³	—	2	4	no	—
493	C₂³	—	2	2	no	—
494	C₂³	—	2	4	no	—
495	C₂³	—	2	8	no	—
496	C₂³	—	2	8	no	—
497	C₂³	—	2	4	no	—
498	C₂³	—	2	4	no	—
499	C₂³	—	2	4	no	—
500	C₂³	—	2	4	no	—
501	C₂³	—	2	8	no	—
502	C₂³	—	2	8	no	—
503	C₂³	—	4	8	no	—
504	C₂³	—	4	8	no	—
505	C₂³	—	4	8	no	—
506	C₂³	—	4	8	no	—
507	C₂³	—	4	16	no	—
508	C₂³	—	4	8	no	—
509	C₂³	—	4	8	no	—
510	C₂³	—	4	8	no	—
511	C₂³	—	4	16	no	—
512	C₂³	—	4	16	no	—
513	C₂³	C₂²×D₄×C₁₃	1	8	yes	—
514	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
515	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
516	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
517	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
518	C₂³	C₂×C₁₃×#41	1	4	yes	—
519	C₂³	C₁₃×H(5,𝔽₂)	1	4	yes	—
520	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
521	Q₈	—	2	32	no	—
522	D₄	—	2	64	no	—
523	D₄	—	2	32	no	—
524	D₄	—	4	64	no	—
525	D₄	—	4	32	no	—
526	D₄	—	4	16	no	—
527	C₂×C₄	—	2	64	no	—
528	C₂×C₄	—	2	8	no	—
529	C₂×C₄	—	2	16	no	—
530	C₂×C₄	—	2	16	no	—
531	C₂×C₄	—	2	4	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	2	4	no	—
535	C₂×C₄	—	2	4	no	—
536	C₂×C₄	—	2	4	no	—
537	C₂×C₄	—	2	32	no	—
538	C₂×C₄	—	2	4	no	—
539	C₂×C₄	—	2	4	no	—
540	C₂×C₄	—	2	4	no	—
541	C₂×C₄	—	2	4	no	—
542	C₂×C₄	—	2	8	no	—
543	C₂×C₄	—	4	8	no	—
544	C₂×C₄	—	4	8	no	—
545	C₂×C₄	C₁₃×#120	1	16	yes	—
546	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
547	C₂×C₄	C₂²×D₄×C₁₃	1	8	yes	—
548	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
549	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
550	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
551	C₂×C₄	C₂×C₁₃×#41	1	8	yes	complemented
552	C₂²	—	2	8	no	—
553	C₂²	—	2	4	no	—
554	C₂²	—	2	4	no	—
555	C₂²	—	2	4	no	—
556	C₂²	—	2	16	no	—
557	C₂²	—	4	4	no	—
558	C₂²	—	4	4	no	—
559	C₂²	—	4	16	no	—
560	C₂²	—	4	32	no	—
561	C₂²	—	4	4	no	—
562	C₂²	—	4	4	no	—
563	C₂²	—	4	8	no	—
564	C₂²	—	4	4	no	—
565	C₂²	—	4	4	no	—
566	C₂²	—	4	4	no	—
567	C₂²	—	4	8	no	—
568	C₂²	—	4	8	no	—
569	C₂²	—	8	16	no	—
570	C₂²	C₂×C₁₃×#120	1	4	yes	—
571	C₂²	C₁₃×#532	1	4	yes	—
572	C₂²	C₁₃×#535	1	4	yes	—
573	C₂²	C₁₃×#546	1	8	yes	—
574	C₂²	C₁₃×#550	1	8	yes	—
575	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
576	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
577	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
578	C₂²	C₂²×C₁₃×#41	1	2	yes	—
579	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
580	C₄	—	2	4	no	—
581	C₄	—	2	8	no	—
582	C₄	—	2	8	no	—
583	C₄	—	4	4	no	—
584	C₄	—	4	4	no	—
585	C₄	C₂×C₁₃×#120	1	8	yes	—
586	C₂	—	4	4	no	—
587	C₂	—	4	8	no	—
588	C₂	—	8	4	no	—
589	C₂	C₁₃×#2431	1	8	yes	direct product factor
590	C₂	C₂²×C₁₃×#120	1	1	yes	characteristic
591	C₂	C₂×C₁₃×#532	1	1	yes	characteristic
592	C₂	C₂×C₁₃×#535	1	1	yes	characteristic
593	C₂	C₂×C₁₃×#546	1	2	yes	—
594	C₂	C₂×C₁₃×#550	1	2	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×#127	C₂	semidirect
3. C₂²×C₁₃×#124	C₂	semidirect
4. C₂²×C₁₃×#121	C₂	semidirect
5. C₁₃×#2431	C₂	direct (N × H)
6. C₂×C₁₃×#392	C₂	semidirect
7. C₂×C₁₃×#391	C₂	semidirect
8. C₂×C₁₃×#390	C₂	semidirect
9. C₂×C₁₃×#386	C₂	semidirect
10. C₂×C₄×C₁₃×C₂²⋊C₄	C₂	semidirect
14. C₂²×C₁₃×#41	C₂²	semidirect
24. C₂×C₁₃×#127	C₂²	semidirect
26. C₂×C₁₃×#124	C₂²	semidirect
28. C₂×C₁₃×#121	C₂²	semidirect
36. C₁₃×#392	C₂²	semidirect
37. C₁₃×#391	C₂²	semidirect
38. C₁₃×#390	C₂²	semidirect
39. C₁₃×#386	C₂²	semidirect
40. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
52. C₂²×Q₈×C₁₃	D₄	semidirect
67. C₂²×D₄×C₁₃	D₄	semidirect
78. C₂³×C₄×C₁₃	D₄	semidirect
106. C₂×#2431	C₁₃	direct (N × H)
130. C₂×Q₈×C₁₃	C₂×D₄	semidirect
149. C₂×D₄×C₁₃	C₂×D₄	semidirect
173. C₂²×C₄×C₁₃	C₂×D₄	semidirect
174. C₂²×C₄×C₁₃	#41	semidirect
188. C₂³×#41	C₂×C₁₃	semidirect
189. C₂²×#127	C₂×C₁₃	semidirect
190. C₂²×#124	C₂×C₁₃	semidirect
191. C₂²×#121	C₂×C₁₃	semidirect
192. #2431	C₂×C₁₃	direct (N × H)
193. C₂×#392	C₂×C₁₃	semidirect
194. C₂×#391	C₂×C₁₃	semidirect
195. C₂×#390	C₂×C₁₃	semidirect
196. C₂×#386	C₂×C₁₃	semidirect
197. C₂×C₄×C₂²⋊C₄	C₂×C₁₃	semidirect
264. C₂×C₄×C₁₃	C₂×#41	semidirect
268. C₂²×#41	C₂²×C₁₃	semidirect
278. C₂×#127	C₂²×C₁₃	semidirect
280. C₂×#124	C₂²×C₁₃	semidirect
282. C₂×#121	C₂²×C₁₃	semidirect
290. #392	C₂²×C₁₃	semidirect
291. #391	C₂²×C₁₃	semidirect
292. #390	C₂²×C₁₃	semidirect
293. #386	C₂²×C₁₃	semidirect
294. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
340. C₂²×Q₈	D₄×C₁₃	semidirect
355. C₂²×D₄	D₄×C₁₃	semidirect
366. C₂³×C₄	D₄×C₁₃	semidirect
397. C₂×C₁₃	#2431	direct (N × H)
426. C₂×Q₈	C₂×D₄×C₁₃	semidirect
445. C₂×D₄	C₂×D₄×C₁₃	semidirect
469. C₂²×C₄	C₂×D₄×C₁₃	semidirect
470. C₂²×C₄	C₁₃×#41	semidirect
484. C₁₃	C₂×#2431	direct (N × H)
551. C₂×C₄	C₂×C₁₃×#41	semidirect
589. C₂	C₁₃×#2431	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×#127	2
C₂²×C₁₃×#124	2
C₂²×C₁₃×#121	2
C₁₃×#2431	2
C₂×C₁₃×#392	2
C₂×C₁₃×#391	2
C₂×C₁₃×#390	2
C₂×C₁₃×#386	2
C₂×C₄×C₁₃×C₂²⋊C₄	2
C₂×#2431	13

Subgroups — C2×C13×#2431 #15721050

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2431 #15721050