Subgroups — C₂×C₁₃×#3026 #15746734

Order 3328.

5318 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×H(5,𝔽₂)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#534	C₂	1	3	yes	maximal, complemented
3	C₁₃×#3026	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#458	C₂	1	4	yes	maximal, complemented
5	C₂×C₁₃×B(4,𝔽₂)	C₂	1	4	yes	maximal, complemented
6	C₂²×C₁₃×#99	C₂	1	3	yes	maximal, complemented
7	C₂×C₁₃×H(5,𝔽₂)	—	2	6	no	—
8	C₂×C₁₃×H(5,𝔽₂)	—	2	12	no	—
9	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	4	yes	—
10	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	8	yes	complemented
11	C₂²×C₁₃×#41	—	2	3	no	—
12	C₂³×D₄×C₁₃	—	2	3	no	—
13	C₂³×D₄×C₁₃	C₂²	1	3	yes	—
14	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
15	C₁₃×#534	—	2	12	no	—
16	C₁₃×#534	C₂²	1	24	yes	complemented
17	C₂×C₁₃×#123	—	2	3	no	—
18	C₂×C₁₃×#123	C₂²	1	6	yes	complemented
19	C₂×C₁₃×#121	—	2	6	no	—
20	C₂×C₁₃×#120	—	2	3	no	—
21	C₂×C₁₃×#120	C₂²	1	6	yes	complemented
22	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	3	yes	complemented
23	C₁₃×#458	C₂²	1	32	yes	complemented
24	C₁₃×B(4,𝔽₂)	C₂²	1	32	yes	complemented
25	C₂×C₁₃×#99	C₂²	1	12	yes	complemented
26	C₂×C₁₃×#99	C₂²	1	24	yes	complemented
27	C₂⁵×C₁₃	—	2	1	no	—
28	C₂⁵×C₁₃	D₄	1	3	yes	complemented
29	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
30	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic, complemented
31	C₁₃×H(5,𝔽₂)	—	2	48	no	—
32	C₁₃×H(5,𝔽₂)	—	2	24	no	—
33	C₁₃×H(5,𝔽₂)	—	2	48	no	—
34	C₁₃×H(5,𝔽₂)	C₂³	1	16	yes	—
35	C₂×C₁₃×#41	—	2	24	no	—
36	C₂×C₁₃×#41	—	2	12	no	—
37	C₂×C₁₃×#41	—	2	12	no	—
38	C₂×C₁₃×#41	—	2	24	no	—
39	C₂²×Q₈×C₁₃	—	2	1	no	—
40	C₂²×D₄×C₁₃	—	2	3	no	—
41	C₂²×D₄×C₁₃	—	2	24	no	—
42	C₂²×D₄×C₁₃	—	2	12	no	—
43	C₂²×D₄×C₁₃	—	2	6	no	—
44	C₂²×D₄×C₁₃	—	2	12	no	—
45	C₂²×D₄×C₁₃	—	2	6	no	—
46	C₂²×D₄×C₁₃	—	2	12	no	—
47	C₂²×D₄×C₁₃	—	2	24	no	—
48	C₂²×D₄×C₁₃	—	2	3	no	—
49	C₂²×D₄×C₁₃	—	2	3	no	—
50	C₂²×D₄×C₁₃	—	2	6	no	—
51	C₂²×D₄×C₁₃	—	2	6	no	—
52	C₂²×D₄×C₁₃	D₄	1	6	yes	complemented
53	C₂²×D₄×C₁₃	D₄	1	12	yes	complemented
54	C₂²×D₄×C₁₃	C₂³	1	6	yes	—
55	C₂²×D₄×C₁₃	C₂³	1	12	yes	—
56	C₂²×D₄×C₁₃	C₂³	1	4	yes	complemented
57	C₂³×C₄×C₁₃	—	2	3	no	—
58	C₂³×C₄×C₁₃	—	2	3	no	—
59	C₂³×C₄×C₁₃	D₄	1	3	yes	complemented
60	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic, complemented
61	C₁₃×#123	—	2	12	no	—
62	C₁₃×#123	—	2	24	no	—
63	C₁₃×#123	C₂³	1	24	yes	complemented
64	C₁₃×#121	—	2	48	no	—
65	C₁₃×#120	—	2	24	no	—
66	C₁₃×#120	—	2	12	no	—
67	C₁₃×#120	C₂³	1	24	yes	complemented
68	C₂×C₁₃×C₄⋊C₄	—	2	6	no	—
69	C₂×C₁₃×C₂²⋊C₄	—	2	3	no	—
70	C₂×C₁₃×C₂²⋊C₄	—	2	6	no	—
71	C₂×C₁₃×C₂²⋊C₄	—	2	6	no	—
72	C₂×C₁₃×C₂²⋊C₄	—	2	6	no	—
73	C₂×C₁₃×C₂²⋊C₄	C₂³	1	6	yes	complemented
74	C₂×C₁₃×C₂²⋊C₄	C₂³	1	12	yes	complemented
75	C₁₃×#99	C₂³	1	48	yes	complemented
76	C₂×#3026	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
77	C₂⁴×C₁₃	—	2	8	no	—
78	C₂⁴×C₁₃	—	2	4	no	—
79	C₂⁴×C₁₃	—	2	3	no	—
80	C₂⁴×C₁₃	—	2	6	no	—
81	C₂⁴×C₁₃	—	2	3	no	—
82	C₂⁴×C₁₃	—	2	3	no	—
83	C₂⁴×C₁₃	—	2	3	no	—
84	C₂⁴×C₁₃	—	8	2	no	—
85	C₂⁴×C₁₃	—	8	2	no	—
86	C₂⁴×C₁₃	—	8	6	no	—
87	C₂⁴×C₁₃	—	8	4	no	—
88	C₂⁴×C₁₃	C₂×D₄	1	6	yes	—
89	C₂⁴×C₁₃	C₂×D₄	1	3	yes	—
90	C₂⁴×C₁₃	C₂×D₄	1	3	yes	—
91	C₂⁴×C₁₃	C₂×D₄	1	6	yes	—
92	C₂⁴×C₁₃	C₂×D₄	1	12	yes	complemented
93	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
94	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
95	C₂⁴×C₁₃	C₂⁴	1	2	yes	complemented
96	C₁₃×#41	—	2	48	no	—
97	C₁₃×#41	—	2	96	no	—
98	C₁₃×#41	—	2	48	no	—
99	C₂×Q₈×C₁₃	—	2	8	no	—
100	C₂×Q₈×C₁₃	—	2	4	no	—
101	C₂×D₄×C₁₃	—	2	24	no	—
102	C₂×D₄×C₁₃	—	2	12	no	—
103	C₂×D₄×C₁₃	—	2	48	no	—
104	C₂×D₄×C₁₃	—	2	96	no	—
105	C₂×D₄×C₁₃	—	2	24	no	—
106	C₂×D₄×C₁₃	—	2	12	no	—
107	C₂×D₄×C₁₃	—	2	12	no	—
108	C₂×D₄×C₁₃	—	2	24	no	—
109	C₂×D₄×C₁₃	—	2	24	no	—
110	C₂×D₄×C₁₃	—	2	12	no	—
111	C₂×D₄×C₁₃	—	2	48	no	—
112	C₂×D₄×C₁₃	—	2	12	no	—
113	C₂×D₄×C₁₃	—	2	24	no	—
114	C₂×D₄×C₁₃	—	2	12	no	—
115	C₂×D₄×C₁₃	—	2	12	no	—
116	C₂×D₄×C₁₃	—	2	24	no	—
117	C₂×D₄×C₁₃	—	4	6	no	—
118	C₂×D₄×C₁₃	—	4	6	no	—
119	C₂×D₄×C₁₃	—	4	1	no	—
120	C₂×D₄×C₁₃	—	4	3	no	—
121	C₂×D₄×C₁₃	—	8	12	no	—
122	C₂×D₄×C₁₃	C₂×D₄	1	12	yes	—
123	C₂×D₄×C₁₃	C₂×D₄	1	24	yes	complemented
124	C₂×D₄×C₁₃	C₂⁴	1	12	yes	—
125	C₂²×C₄×C₁₃	—	2	24	no	—
126	C₂²×C₄×C₁₃	—	2	12	no	—
127	C₂²×C₄×C₁₃	—	2	3	no	—
128	C₂²×C₄×C₁₃	—	2	6	no	—
129	C₂²×C₄×C₁₃	—	2	3	no	—
130	C₂²×C₄×C₁₃	—	2	6	no	—
131	C₂²×C₄×C₁₃	—	2	3	no	—
132	C₂²×C₄×C₁₃	—	2	3	no	—
133	C₂²×C₄×C₁₃	—	2	12	no	—
134	C₂²×C₄×C₁₃	—	8	6	no	—
135	C₂²×C₄×C₁₃	C₂×D₄	1	6	yes	—
136	C₂²×C₄×C₁₃	C₂×D₄	1	12	yes	complemented
137	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	complemented
138	C₁₃×C₄⋊C₄	—	2	24	no	—
139	C₁₃×C₂²⋊C₄	—	2	6	no	—
140	C₁₃×C₂²⋊C₄	—	2	12	no	—
141	C₁₃×C₂²⋊C₄	—	2	24	no	—
142	C₁₃×C₂²⋊C₄	—	2	24	no	—
143	C₁₃×C₂²⋊C₄	C₂⁴	1	12	yes	complemented
144	C₂²×H(5,𝔽₂)	C₂×C₁₃	1	1	yes	characteristic, complemented
145	C₂×#534	C₂×C₁₃	1	3	yes	complemented
146	#3026	C₂×C₁₃	1	16	yes	direct product factor
147	C₂×#458	C₂×C₁₃	1	4	yes	complemented
148	C₂×B(4,𝔽₂)	C₂×C₁₃	1	4	yes	complemented
149	C₂²×#99	C₂×C₁₃	1	3	yes	complemented
150	C₂³×C₁₃	—	2	16	no	—
151	C₂³×C₁₃	—	2	12	no	—
152	C₂³×C₁₃	—	2	6	no	—
153	C₂³×C₁₃	—	2	6	no	—
154	C₂³×C₁₃	—	2	12	no	—
155	C₂³×C₁₃	—	2	6	no	—
156	C₂³×C₁₃	—	4	6	no	—
157	C₂³×C₁₃	—	4	6	no	—
158	C₂³×C₁₃	—	4	2	no	—
159	C₂³×C₁₃	—	4	12	no	—
160	C₂³×C₁₃	—	4	12	no	—
161	C₂³×C₁₃	—	4	12	no	—
162	C₂³×C₁₃	—	4	3	no	—
163	C₂³×C₁₃	—	4	1	no	—
164	C₂³×C₁₃	—	8	6	no	—
165	C₂³×C₁₃	—	8	6	no	—
166	C₂³×C₁₃	—	8	2	no	—
167	C₂³×C₁₃	—	8	2	no	—
168	C₂³×C₁₃	—	8	12	no	—
169	C₂³×C₁₃	—	8	12	no	—
170	C₂³×C₁₃	—	8	6	no	—
171	C₂³×C₁₃	—	8	16	no	—
172	C₂³×C₁₃	—	8	8	no	—
173	C₂³×C₁₃	#120	1	1	yes	characteristic
174	C₂³×C₁₃	#120	1	3	yes	—
175	C₂³×C₁₃	#120	1	6	yes	—
176	C₂³×C₁₃	#120	1	6	yes	—
177	C₂³×C₁₃	C₂²×D₄	1	3	yes	—
178	C₂³×C₁₃	C₂²×D₄	1	12	yes	—
179	C₂³×C₁₃	C₂²×D₄	1	3	yes	—
180	C₂³×C₁₃	C₂²×D₄	1	6	yes	—
181	C₂³×C₁₃	C₂²×D₄	1	6	yes	—
182	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
183	Q₈×C₁₃	—	2	16	no	—
184	D₄×C₁₃	—	2	48	no	—
185	D₄×C₁₃	—	2	24	no	—
186	D₄×C₁₃	—	2	48	no	—
187	D₄×C₁₃	—	2	24	no	—
188	D₄×C₁₃	—	4	4	no	—
189	D₄×C₁₃	—	4	12	no	—
190	D₄×C₁₃	—	8	24	no	—
191	C₂×C₄×C₁₃	—	2	48	no	—
192	C₂×C₄×C₁₃	—	2	12	no	—
193	C₂×C₄×C₁₃	—	2	6	no	—
194	C₂×C₄×C₁₃	—	2	12	no	—
195	C₂×C₄×C₁₃	—	2	6	no	—
196	C₂×C₄×C₁₃	—	2	12	no	—
197	C₂×C₄×C₁₃	—	2	6	no	—
198	C₂×C₄×C₁₃	—	4	12	no	—
199	C₂×C₄×C₁₃	—	4	3	no	—
200	C₂×C₄×C₁₃	—	4	1	no	—
201	C₂×C₄×C₁₃	—	8	12	no	—
202	C₂×C₄×C₁₃	C₂²×D₄	1	12	yes	—
203	C₂×H(5,𝔽₂)	—	2	6	no	—
204	C₂×H(5,𝔽₂)	—	2	12	no	—
205	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	4	yes	—
206	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	8	yes	complemented
207	C₂²×#41	—	2	3	no	—
208	C₂³×D₄	—	2	3	no	—
209	C₂³×D₄	C₂²×C₁₃	1	3	yes	—
210	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
211	#534	—	2	12	no	—
212	#534	C₂²×C₁₃	1	24	yes	complemented
213	C₂×#123	—	2	3	no	—
214	C₂×#123	C₂²×C₁₃	1	6	yes	complemented
215	C₂×#121	—	2	6	no	—
216	C₂×#120	—	2	3	no	—
217	C₂×#120	C₂²×C₁₃	1	6	yes	complemented
218	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	3	yes	complemented
219	#458	C₂²×C₁₃	1	32	yes	complemented
220	B(4,𝔽₂)	C₂²×C₁₃	1	32	yes	complemented
221	C₂×#99	C₂²×C₁₃	1	12	yes	complemented
222	C₂×#99	C₂²×C₁₃	1	24	yes	complemented
223	C₂²×C₁₃	—	2	6	no	—
224	C₂²×C₁₃	—	2	2	no	—
225	C₂²×C₁₃	—	2	6	no	—
226	C₂²×C₁₃	—	2	12	no	—
227	C₂²×C₁₃	—	4	6	no	—
228	C₂²×C₁₃	—	4	6	no	—
229	C₂²×C₁₃	—	4	6	no	—
230	C₂²×C₁₃	—	4	3	no	—
231	C₂²×C₁₃	—	4	1	no	—
232	C₂²×C₁₃	—	4	6	no	—
233	C₂²×C₁₃	—	4	12	no	—
234	C₂²×C₁₃	—	4	24	no	—
235	C₂²×C₁₃	—	4	12	no	—
236	C₂²×C₁₃	—	4	12	no	—
237	C₂²×C₁₃	—	4	2	no	—
238	C₂²×C₁₃	—	8	6	no	—
239	C₂²×C₁₃	—	8	12	no	—
240	C₂²×C₁₃	—	8	6	no	—
241	C₂²×C₁₃	—	8	16	no	—
242	C₂²×C₁₃	—	8	2	no	—
243	C₂²×C₁₃	C₂×#120	1	2	yes	—
244	C₂²×C₁₃	C₂×#120	1	3	yes	—
245	C₂²×C₁₃	C₂×#120	1	6	yes	—
246	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
247	C₂²×C₁₃	C₂³×D₄	1	3	yes	—
248	C₄×C₁₃	—	2	12	no	—
249	C₄×C₁₃	—	4	12	no	—
250	C₄×C₁₃	—	4	2	no	—
251	C₂⁵	—	2	1	no	—
252	C₂⁵	D₄×C₁₃	1	3	yes	complemented
253	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
254	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic, complemented
255	H(5,𝔽₂)	—	2	48	no	—
256	H(5,𝔽₂)	—	2	24	no	—
257	H(5,𝔽₂)	—	2	48	no	—
258	H(5,𝔽₂)	C₂³×C₁₃	1	16	yes	—
259	C₂×#41	—	2	12	no	—
260	C₂×#41	—	2	24	no	—
261	C₂×#41	—	2	12	no	—
262	C₂×#41	—	2	24	no	—
263	C₂²×Q₈	—	2	1	no	—
264	C₂²×D₄	—	2	3	no	—
265	C₂²×D₄	—	2	12	no	—
266	C₂²×D₄	—	2	24	no	—
267	C₂²×D₄	—	2	6	no	—
268	C₂²×D₄	—	2	12	no	—
269	C₂²×D₄	—	2	6	no	—
270	C₂²×D₄	—	2	12	no	—
271	C₂²×D₄	—	2	24	no	—
272	C₂²×D₄	—	2	3	no	—
273	C₂²×D₄	—	2	3	no	—
274	C₂²×D₄	—	2	6	no	—
275	C₂²×D₄	—	2	6	no	—
276	C₂²×D₄	D₄×C₁₃	1	6	yes	complemented
277	C₂²×D₄	D₄×C₁₃	1	12	yes	complemented
278	C₂²×D₄	C₂³×C₁₃	1	6	yes	—
279	C₂²×D₄	C₂³×C₁₃	1	12	yes	—
280	C₂²×D₄	C₂³×C₁₃	1	4	yes	complemented
281	C₂³×C₄	—	2	3	no	—
282	C₂³×C₄	—	2	3	no	—
283	C₂³×C₄	D₄×C₁₃	1	3	yes	complemented
284	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic, complemented
285	#123	—	2	12	no	—
286	#123	—	2	24	no	—
287	#123	C₂³×C₁₃	1	24	yes	complemented
288	#121	—	2	48	no	—
289	#120	—	2	24	no	—
290	#120	—	2	12	no	—
291	#120	C₂³×C₁₃	1	24	yes	complemented
292	C₂×C₄⋊C₄	—	2	6	no	—
293	C₂×C₂²⋊C₄	—	2	3	no	—
294	C₂×C₂²⋊C₄	—	2	6	no	—
295	C₂×C₂²⋊C₄	—	2	6	no	—
296	C₂×C₂²⋊C₄	—	2	6	no	—
297	C₂×C₂²⋊C₄	C₂³×C₁₃	1	6	yes	complemented
298	C₂×C₂²⋊C₄	C₂³×C₁₃	1	12	yes	complemented
299	#99	C₂³×C₁₃	1	48	yes	complemented
300	C₂×C₁₃	—	2	3	no	—
301	C₂×C₁₃	—	2	2	no	—
302	C₂×C₁₃	—	2	3	no	—
303	C₂×C₁₃	—	2	6	no	—
304	C₂×C₁₃	—	4	12	no	—
305	C₂×C₁₃	—	8	2	no	—
306	C₂×C₁₃	#3026	1	2	yes	direct product factor
307	C₂×C₁₃	C₂²×#120	1	1	yes	characteristic
308	C₂⁴	—	2	4	no	—
309	C₂⁴	—	2	8	no	—
310	C₂⁴	—	2	3	no	—
311	C₂⁴	—	2	3	no	—
312	C₂⁴	—	2	6	no	—
313	C₂⁴	—	2	3	no	—
314	C₂⁴	—	2	3	no	—
315	C₂⁴	—	8	2	no	—
316	C₂⁴	—	8	2	no	—
317	C₂⁴	—	8	6	no	—
318	C₂⁴	—	8	4	no	—
319	C₂⁴	C₂×D₄×C₁₃	1	6	yes	—
320	C₂⁴	C₂×D₄×C₁₃	1	3	yes	—
321	C₂⁴	C₂×D₄×C₁₃	1	3	yes	—
322	C₂⁴	C₂×D₄×C₁₃	1	6	yes	—
323	C₂⁴	C₂×D₄×C₁₃	1	12	yes	complemented
324	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
325	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
326	C₂⁴	C₂⁴×C₁₃	1	2	yes	complemented
327	#41	—	2	48	no	—
328	#41	—	2	96	no	—
329	#41	—	2	48	no	—
330	C₂×Q₈	—	2	4	no	—
331	C₂×Q₈	—	2	8	no	—
332	C₂×D₄	—	2	12	no	—
333	C₂×D₄	—	2	24	no	—
334	C₂×D₄	—	2	48	no	—
335	C₂×D₄	—	2	96	no	—
336	C₂×D₄	—	2	12	no	—
337	C₂×D₄	—	2	24	no	—
338	C₂×D₄	—	2	12	no	—
339	C₂×D₄	—	2	24	no	—
340	C₂×D₄	—	2	12	no	—
341	C₂×D₄	—	2	24	no	—
342	C₂×D₄	—	2	48	no	—
343	C₂×D₄	—	2	12	no	—
344	C₂×D₄	—	2	24	no	—
345	C₂×D₄	—	2	12	no	—
346	C₂×D₄	—	2	12	no	—
347	C₂×D₄	—	2	24	no	—
348	C₂×D₄	—	4	1	no	—
349	C₂×D₄	—	4	3	no	—
350	C₂×D₄	—	4	6	no	—
351	C₂×D₄	—	4	6	no	—
352	C₂×D₄	—	8	12	no	—
353	C₂×D₄	C₂×D₄×C₁₃	1	12	yes	—
354	C₂×D₄	C₂×D₄×C₁₃	1	24	yes	complemented
355	C₂×D₄	C₂⁴×C₁₃	1	12	yes	—
356	C₂²×C₄	—	2	12	no	—
357	C₂²×C₄	—	2	24	no	—
358	C₂²×C₄	—	2	3	no	—
359	C₂²×C₄	—	2	3	no	—
360	C₂²×C₄	—	2	6	no	—
361	C₂²×C₄	—	2	6	no	—
362	C₂²×C₄	—	2	3	no	—
363	C₂²×C₄	—	2	3	no	—
364	C₂²×C₄	—	2	12	no	—
365	C₂²×C₄	—	8	6	no	—
366	C₂²×C₄	C₂×D₄×C₁₃	1	6	yes	—
367	C₂²×C₄	C₂×D₄×C₁₃	1	12	yes	complemented
368	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	complemented
369	C₄⋊C₄	—	2	24	no	—
370	C₂²⋊C₄	—	2	6	no	—
371	C₂²⋊C₄	—	2	12	no	—
372	C₂²⋊C₄	—	2	24	no	—
373	C₂²⋊C₄	—	2	24	no	—
374	C₂²⋊C₄	C₂⁴×C₁₃	1	12	yes	complemented
375	C₁₃	C₂×#3026	1	1	yes	characteristic, direct product factor, Sylow
376	C₂³	—	2	16	no	—
377	C₂³	—	2	6	no	—
378	C₂³	—	2	12	no	—
379	C₂³	—	2	6	no	—
380	C₂³	—	2	12	no	—
381	C₂³	—	2	6	no	—
382	C₂³	—	4	6	no	—
383	C₂³	—	4	6	no	—
384	C₂³	—	4	2	no	—
385	C₂³	—	4	12	no	—
386	C₂³	—	4	12	no	—
387	C₂³	—	4	12	no	—
388	C₂³	—	4	3	no	—
389	C₂³	—	4	1	no	—
390	C₂³	—	8	6	no	—
391	C₂³	—	8	6	no	—
392	C₂³	—	8	2	no	—
393	C₂³	—	8	2	no	—
394	C₂³	—	8	12	no	—
395	C₂³	—	8	12	no	—
396	C₂³	—	8	6	no	—
397	C₂³	—	8	16	no	—
398	C₂³	—	8	8	no	—
399	C₂³	C₁₃×#120	1	1	yes	characteristic
400	C₂³	C₁₃×#120	1	3	yes	—
401	C₂³	C₁₃×#120	1	6	yes	—
402	C₂³	C₁₃×#120	1	6	yes	—
403	C₂³	C₂²×D₄×C₁₃	1	3	yes	—
404	C₂³	C₂²×D₄×C₁₃	1	12	yes	—
405	C₂³	C₂²×D₄×C₁₃	1	3	yes	—
406	C₂³	C₂²×D₄×C₁₃	1	6	yes	—
407	C₂³	C₂²×D₄×C₁₃	1	6	yes	—
408	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
409	Q₈	—	2	16	no	—
410	D₄	—	2	48	no	—
411	D₄	—	2	24	no	—
412	D₄	—	2	48	no	—
413	D₄	—	2	24	no	—
414	D₄	—	4	4	no	—
415	D₄	—	4	12	no	—
416	D₄	—	8	24	no	—
417	C₂×C₄	—	2	48	no	—
418	C₂×C₄	—	2	6	no	—
419	C₂×C₄	—	2	12	no	—
420	C₂×C₄	—	2	6	no	—
421	C₂×C₄	—	2	12	no	—
422	C₂×C₄	—	2	12	no	—
423	C₂×C₄	—	2	6	no	—
424	C₂×C₄	—	4	12	no	—
425	C₂×C₄	—	4	3	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	—	8	12	no	—
428	C₂×C₄	C₂²×D₄×C₁₃	1	12	yes	—
429	C₂²	—	2	6	no	—
430	C₂²	—	2	2	no	—
431	C₂²	—	2	6	no	—
432	C₂²	—	2	12	no	—
433	C₂²	—	4	6	no	—
434	C₂²	—	4	6	no	—
435	C₂²	—	4	6	no	—
436	C₂²	—	4	3	no	—
437	C₂²	—	4	1	no	—
438	C₂²	—	4	6	no	—
439	C₂²	—	4	12	no	—
440	C₂²	—	4	24	no	—
441	C₂²	—	4	12	no	—
442	C₂²	—	4	12	no	—
443	C₂²	—	4	2	no	—
444	C₂²	—	8	6	no	—
445	C₂²	—	8	12	no	—
446	C₂²	—	8	6	no	—
447	C₂²	—	8	16	no	—
448	C₂²	—	8	2	no	—
449	C₂²	C₂×C₁₃×#120	1	2	yes	—
450	C₂²	C₂×C₁₃×#120	1	3	yes	—
451	C₂²	C₂×C₁₃×#120	1	6	yes	—
452	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
453	C₂²	C₂³×D₄×C₁₃	1	3	yes	—
454	C₄	—	2	12	no	—
455	C₄	—	4	12	no	—
456	C₄	—	4	2	no	—
457	C₂	—	2	3	no	—
458	C₂	—	2	2	no	—
459	C₂	—	2	3	no	—
460	C₂	—	2	6	no	—
461	C₂	—	4	12	no	—
462	C₂	—	8	2	no	—
463	C₂	C₁₃×#3026	1	2	yes	direct product factor
464	C₂	C₂²×C₁₃×#120	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#120
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂⁵×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₃×H(5,𝔽₂)	C₂	semidirect
2. C₂×C₁₃×#534	C₂	semidirect
3. C₁₃×#3026	C₂	direct (N × H)
4. C₂×C₁₃×#458	C₂	semidirect
5. C₂×C₁₃×B(4,𝔽₂)	C₂	semidirect
6. C₂²×C₁₃×#99	C₂	semidirect
10. C₂×C₁₃×H(5,𝔽₂)	C₂²	semidirect
14. C₂³×D₄×C₁₃	C₂²	semidirect
16. C₁₃×#534	C₂²	semidirect
18. C₂×C₁₃×#123	C₂²	semidirect
21. C₂×C₁₃×#120	C₂²	semidirect
22. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
23. C₁₃×#458	C₂²	semidirect
24. C₁₃×B(4,𝔽₂)	C₂²	semidirect
25. C₂×C₁₃×#99	C₂²	semidirect
26. C₂×C₁₃×#99	C₂²	semidirect
28. C₂⁵×C₁₃	D₄	semidirect
30. C₂⁵×C₁₃	C₂³	semidirect
52. C₂²×D₄×C₁₃	D₄	semidirect
53. C₂²×D₄×C₁₃	D₄	semidirect
56. C₂²×D₄×C₁₃	C₂³	semidirect
59. C₂³×C₄×C₁₃	D₄	semidirect
60. C₂³×C₄×C₁₃	C₂³	semidirect
63. C₁₃×#123	C₂³	semidirect
67. C₁₃×#120	C₂³	semidirect
73. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
74. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
75. C₁₃×#99	C₂³	semidirect
76. C₂×#3026	C₁₃	direct (N × H)
92. C₂⁴×C₁₃	C₂×D₄	semidirect
95. C₂⁴×C₁₃	C₂⁴	semidirect
123. C₂×D₄×C₁₃	C₂×D₄	semidirect
136. C₂²×C₄×C₁₃	C₂×D₄	semidirect
137. C₂²×C₄×C₁₃	C₂⁴	semidirect
143. C₁₃×C₂²⋊C₄	C₂⁴	semidirect
144. C₂²×H(5,𝔽₂)	C₂×C₁₃	semidirect
145. C₂×#534	C₂×C₁₃	semidirect
146. #3026	C₂×C₁₃	direct (N × H)
147. C₂×#458	C₂×C₁₃	semidirect
148. C₂×B(4,𝔽₂)	C₂×C₁₃	semidirect
149. C₂²×#99	C₂×C₁₃	semidirect
206. C₂×H(5,𝔽₂)	C₂²×C₁₃	semidirect
210. C₂³×D₄	C₂²×C₁₃	semidirect
212. #534	C₂²×C₁₃	semidirect
214. C₂×#123	C₂²×C₁₃	semidirect
217. C₂×#120	C₂²×C₁₃	semidirect
218. C₂²×C₂²⋊C₄	C₂²×C₁₃	semidirect
219. #458	C₂²×C₁₃	semidirect
220. B(4,𝔽₂)	C₂²×C₁₃	semidirect
221. C₂×#99	C₂²×C₁₃	semidirect
222. C₂×#99	C₂²×C₁₃	semidirect
252. C₂⁵	D₄×C₁₃	semidirect
254. C₂⁵	C₂³×C₁₃	semidirect
276. C₂²×D₄	D₄×C₁₃	semidirect
277. C₂²×D₄	D₄×C₁₃	semidirect
280. C₂²×D₄	C₂³×C₁₃	semidirect
283. C₂³×C₄	D₄×C₁₃	semidirect
284. C₂³×C₄	C₂³×C₁₃	semidirect
287. #123	C₂³×C₁₃	semidirect
291. #120	C₂³×C₁₃	semidirect
297. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
298. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
299. #99	C₂³×C₁₃	semidirect
306. C₂×C₁₃	#3026	direct (N × H)
323. C₂⁴	C₂×D₄×C₁₃	semidirect
326. C₂⁴	C₂⁴×C₁₃	semidirect
354. C₂×D₄	C₂×D₄×C₁₃	semidirect
367. C₂²×C₄	C₂×D₄×C₁₃	semidirect
368. C₂²×C₄	C₂⁴×C₁₃	semidirect
374. C₂²⋊C₄	C₂⁴×C₁₃	semidirect
375. C₁₃	C₂×#3026	direct (N × H)
463. C₂	C₁₃×#3026	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×H(5,𝔽₂)	2
C₂×C₁₃×#534	2
C₁₃×#3026	2
C₂×C₁₃×#458	2
C₂×C₁₃×B(4,𝔽₂)	2
C₂²×C₁₃×#99	2
C₂×#3026	13

Subgroups — C2×C13×#3026 #15746734

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3026 #15746734