Subgroups — C₂×C₁₃×#2436 #15721040

Order 3328.

5630 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₃×#124	C₂	1	2	yes	maximal, complemented
3	C₂²×C₁₃×#121	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2436	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₁₃×#393	C₂	1	4	yes	maximal, complemented
6	C₂×C₁₃×#391	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₃×#386	C₂	1	4	yes	maximal, complemented
8	C₂×C₄×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×Q₈×C₁₃	—	2	16	no	—
10	C₂³×Q₈×C₁₃	—	2	8	no	—
11	C₂³×Q₈×C₁₃	C₂²	1	2	yes	—
12	C₂³×Q₈×C₁₃	C₂²	1	2	yes	—
13	C₂³×Q₈×C₁₃	C₂²	1	8	yes	complemented
14	C₂³×D₄×C₁₃	C₂²	1	2	yes	—
15	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
16	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	—
17	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#124	—	2	16	no	—
19	C₂×C₁₃×#124	C₂²	1	16	yes	complemented
20	C₂×C₁₃×#121	—	2	8	no	—
21	C₂×C₁₃×#121	C₂²	1	8	yes	—
22	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
23	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
24	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	—
25	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
26	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
27	C₁₃×#393	C₂²	1	32	yes	complemented
28	C₁₃×#391	C₂²	1	16	yes	complemented
29	C₁₃×#386	C₂²	1	32	yes	complemented
30	C₄×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	complemented
31	C₂×C₁₃×#95	C₂²	1	2	yes	—
32	C₂×C₁₃×#95	C₂²	1	8	yes	—
33	C₂⁵×C₁₃	C₂³	1	2	yes	—
34	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
35	C₂²×Q₈×C₁₃	—	2	128	no	—
36	C₂²×Q₈×C₁₃	—	2	64	no	—
37	C₂²×Q₈×C₁₃	—	2	16	no	—
38	C₂²×Q₈×C₁₃	—	2	8	no	—
39	C₂²×Q₈×C₁₃	—	2	8	no	—
40	C₂²×Q₈×C₁₃	—	2	8	no	—
41	C₂²×Q₈×C₁₃	—	2	32	no	—
42	C₂²×Q₈×C₁₃	D₄	1	16	yes	complemented
43	C₂²×Q₈×C₁₃	C₂³	1	8	yes	—
44	C₂²×Q₈×C₁₃	C₂³	1	8	yes	—
45	C₂²×D₄×C₁₃	—	2	8	no	—
46	C₂²×D₄×C₁₃	—	2	16	no	—
47	C₂²×D₄×C₁₃	—	2	4	no	—
48	C₂²×D₄×C₁₃	—	2	8	no	—
49	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
50	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
51	C₂³×C₄×C₁₃	—	2	8	no	—
52	C₂³×C₄×C₁₃	—	2	16	no	—
53	C₂³×C₄×C₁₃	—	2	8	no	—
54	C₂³×C₄×C₁₃	D₄	1	8	yes	—
55	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
56	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
57	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
58	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
59	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
60	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
62	C₁₃×#124	—	2	64	no	—
63	C₁₃×#121	—	2	32	no	—
64	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
65	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
66	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
67	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
68	C₂×C₁₃×C₂²⋊C₄	—	2	32	no	—
69	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
70	C₂×C₁₃×C₂²⋊C₄	C₂³	1	32	yes	—
71	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
72	C₂×C₄²×C₁₃	—	2	8	no	—
73	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
74	C₁₃×#95	C₂³	1	8	yes	—
75	C₁₃×#95	C₂³	1	32	yes	—
76	C₂×#2436	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
77	C₂⁴×C₁₃	—	2	4	no	—
78	C₂⁴×C₁₃	—	2	4	no	—
79	C₂⁴×C₁₃	—	2	8	no	—
80	C₂⁴×C₁₃	—	2	4	no	—
81	C₂⁴×C₁₃	—	2	8	no	—
82	C₂⁴×C₁₃	—	2	8	no	—
83	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
84	C₂⁴×C₁₃	#41	1	8	yes	—
85	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
86	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
87	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
88	C₂×Q₈×C₁₃	—	2	256	no	—
89	C₂×Q₈×C₁₃	—	2	64	no	—
90	C₂×Q₈×C₁₃	—	2	64	no	—
91	C₂×Q₈×C₁₃	—	2	32	no	—
92	C₂×Q₈×C₁₃	—	2	16	no	—
93	C₂×Q₈×C₁₃	—	2	16	no	—
94	C₂×Q₈×C₁₃	—	2	16	no	—
95	C₂×Q₈×C₁₃	C₂×D₄	1	32	yes	complemented
96	C₂×D₄×C₁₃	—	2	16	no	—
97	C₂×D₄×C₁₃	—	2	32	no	—
98	C₂×D₄×C₁₃	—	2	8	no	—
99	C₂×D₄×C₁₃	—	2	16	no	—
100	C₂×D₄×C₁₃	—	4	32	no	—
101	C₂×D₄×C₁₃	—	4	16	no	—
102	C₂²×C₄×C₁₃	—	2	64	no	—
103	C₂²×C₄×C₁₃	—	2	16	no	—
104	C₂²×C₄×C₁₃	—	2	8	no	—
105	C₂²×C₄×C₁₃	—	2	8	no	—
106	C₂²×C₄×C₁₃	—	2	4	no	—
107	C₂²×C₄×C₁₃	—	2	32	no	—
108	C₂²×C₄×C₁₃	—	2	32	no	—
109	C₂²×C₄×C₁₃	—	2	16	no	—
110	C₂²×C₄×C₁₃	—	2	8	no	—
111	C₂²×C₄×C₁₃	—	2	4	no	—
112	C₂²×C₄×C₁₃	—	2	8	no	—
113	C₂²×C₄×C₁₃	—	2	8	no	—
114	C₂²×C₄×C₁₃	—	2	8	no	—
115	C₂²×C₄×C₁₃	C₂×D₄	1	16	yes	—
116	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
117	C₂²×C₄×C₁₃	C₂×D₄	1	16	yes	—
118	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
119	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
120	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
121	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
122	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
123	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
124	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
125	C₁₃×C₄⋊C₄	—	2	8	no	—
126	C₁₃×C₂²⋊C₄	—	2	16	no	—
127	C₁₃×C₂²⋊C₄	—	2	16	no	—
128	C₁₃×C₂²⋊C₄	—	2	64	no	—
129	C₄²×C₁₃	—	2	16	no	—
130	C₂⁴×Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
131	C₂²×#124	C₂×C₁₃	1	2	yes	complemented
132	C₂²×#121	C₂×C₁₃	1	1	yes	characteristic
133	#2436	C₂×C₁₃	1	16	yes	direct product factor
134	C₂×#393	C₂×C₁₃	1	4	yes	complemented
135	C₂×#391	C₂×C₁₃	1	2	yes	complemented
136	C₂×#386	C₂×C₁₃	1	4	yes	complemented
137	C₂×C₄×C₂²⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
138	C₂³×C₁₃	—	2	8	no	—
139	C₂³×C₁₃	—	2	8	no	—
140	C₂³×C₁₃	—	2	32	no	—
141	C₂³×C₁₃	—	2	4	no	—
142	C₂³×C₁₃	—	2	4	no	—
143	C₂³×C₁₃	—	2	8	no	—
144	C₂³×C₁₃	—	2	4	no	—
145	C₂³×C₁₃	—	2	8	no	—
146	C₂³×C₁₃	—	2	8	no	—
147	C₂³×C₁₃	—	4	8	no	—
148	C₂³×C₁₃	—	4	8	no	—
149	C₂³×C₁₃	—	4	8	no	—
150	C₂³×C₁₃	—	4	32	no	—
151	C₂³×C₁₃	#124	1	16	yes	complemented
152	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
153	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
154	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
155	C₂³×C₁₃	C₂×#41	1	8	yes	—
156	C₂³×C₁₃	C₂×#41	1	4	yes	—
157	C₂³×C₁₃	2₋¹⁺⁴	1	4	yes	—
158	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
159	Q₈×C₁₃	—	2	64	no	—
160	Q₈×C₁₃	—	2	64	no	—
161	D₄×C₁₃	—	4	32	no	—
162	D₄×C₁₃	—	4	16	no	—
163	C₂×C₄×C₁₃	—	2	64	no	—
164	C₂×C₄×C₁₃	—	2	32	no	—
165	C₂×C₄×C₁₃	—	2	8	no	—
166	C₂×C₄×C₁₃	—	2	8	no	—
167	C₂×C₄×C₁₃	—	2	8	no	—
168	C₂×C₄×C₁₃	—	2	4	no	—
169	C₂×C₄×C₁₃	—	2	32	no	—
170	C₂×C₄×C₁₃	—	2	8	no	—
171	C₂×C₄×C₁₃	—	2	4	no	—
172	C₂×C₄×C₁₃	—	2	8	no	—
173	C₂×C₄×C₁₃	—	2	8	no	—
174	C₂×C₄×C₁₃	—	2	8	no	—
175	C₂×C₄×C₁₃	—	4	8	no	—
176	C₂×C₄×C₁₃	—	4	16	no	—
177	C₂×C₄×C₁₃	#120	1	16	yes	—
178	C₂×C₄×C₁₃	C₂²×D₄	1	16	yes	—
179	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
180	C₂×C₄×C₁₃	C₂²×D₄	1	8	yes	—
181	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
182	C₂³×Q₈	—	2	16	no	—
183	C₂³×Q₈	—	2	8	no	—
184	C₂³×Q₈	C₂²×C₁₃	1	2	yes	—
185	C₂³×Q₈	C₂²×C₁₃	1	2	yes	—
186	C₂³×Q₈	C₂²×C₁₃	1	8	yes	complemented
187	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
188	C₂³×D₄	C₂²×C₁₃	1	2	yes	—
189	C₂⁴×C₄	C₂²×C₁₃	1	2	yes	—
190	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
191	C₂×#124	—	2	16	no	—
192	C₂×#124	C₂²×C₁₃	1	16	yes	complemented
193	C₂×#121	—	2	8	no	—
194	C₂×#121	C₂²×C₁₃	1	8	yes	—
195	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
196	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
197	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	—
198	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
199	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
200	#393	C₂²×C₁₃	1	32	yes	complemented
201	#391	C₂²×C₁₃	1	16	yes	complemented
202	#386	C₂²×C₁₃	1	32	yes	complemented
203	C₄×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	complemented
204	C₂×#95	C₂²×C₁₃	1	2	yes	—
205	C₂×#95	C₂²×C₁₃	1	8	yes	—
206	C₂²×C₁₃	—	2	4	no	—
207	C₂²×C₁₃	—	2	4	no	—
208	C₂²×C₁₃	—	2	32	no	—
209	C₂²×C₁₃	—	2	16	no	—
210	C₂²×C₁₃	—	4	4	no	—
211	C₂²×C₁₃	—	4	4	no	—
212	C₂²×C₁₃	—	4	4	no	—
213	C₂²×C₁₃	—	4	16	no	—
214	C₂²×C₁₃	—	8	16	no	—
215	C₂²×C₁₃	C₂×#120	1	4	yes	—
216	C₂²×C₁₃	C₂×#124	1	4	yes	—
217	C₂²×C₁₃	C₂×#124	1	8	yes	complemented
218	C₂²×C₁₃	#536	1	4	yes	—
219	C₂²×C₁₃	#548	1	16	yes	—
220	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
221	C₂²×C₁₃	C₂³×D₄	1	2	yes	—
222	C₂²×C₁₃	C₂²×#41	1	2	yes	—
223	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
224	C₄×C₁₃	—	2	16	no	—
225	C₄×C₁₃	—	2	4	no	—
226	C₄×C₁₃	—	4	4	no	—
227	C₄×C₁₃	—	4	8	no	—
228	C₄×C₁₃	C₂×#120	1	8	yes	—
229	C₂⁵	C₂³×C₁₃	1	2	yes	—
230	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
231	C₂²×Q₈	—	2	128	no	—
232	C₂²×Q₈	—	2	64	no	—
233	C₂²×Q₈	—	2	16	no	—
234	C₂²×Q₈	—	2	8	no	—
235	C₂²×Q₈	—	2	8	no	—
236	C₂²×Q₈	—	2	8	no	—
237	C₂²×Q₈	—	2	32	no	—
238	C₂²×Q₈	D₄×C₁₃	1	16	yes	complemented
239	C₂²×Q₈	C₂³×C₁₃	1	8	yes	—
240	C₂²×Q₈	C₂³×C₁₃	1	8	yes	—
241	C₂²×D₄	—	2	8	no	—
242	C₂²×D₄	—	2	16	no	—
243	C₂²×D₄	—	2	4	no	—
244	C₂²×D₄	—	2	8	no	—
245	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
246	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
247	C₂³×C₄	—	2	8	no	—
248	C₂³×C₄	—	2	16	no	—
249	C₂³×C₄	—	2	8	no	—
250	C₂³×C₄	D₄×C₁₃	1	8	yes	—
251	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
252	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
253	C₂³×C₄	C₂³×C₁₃	1	8	yes	—
254	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
255	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
256	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
257	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
258	#124	—	2	64	no	—
259	#121	—	2	32	no	—
260	C₂×C₄⋊C₄	—	2	4	no	—
261	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
262	C₂×C₂²⋊C₄	—	2	8	no	—
263	C₂×C₂²⋊C₄	—	2	8	no	—
264	C₂×C₂²⋊C₄	—	2	32	no	—
265	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
266	C₂×C₂²⋊C₄	C₂³×C₁₃	1	32	yes	—
267	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
268	C₂×C₄²	—	2	8	no	—
269	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
270	#95	C₂³×C₁₃	1	8	yes	—
271	#95	C₂³×C₁₃	1	32	yes	—
272	C₂×C₁₃	—	2	8	no	—
273	C₂×C₁₃	—	8	4	no	—
274	C₂×C₁₃	#2436	1	8	yes	direct product factor
275	C₂×C₁₃	C₂²×#120	1	1	yes	characteristic
276	C₂×C₁₃	C₂²×#124	1	1	yes	characteristic
277	C₂×C₁₃	C₂×#536	1	1	yes	characteristic
278	C₂×C₁₃	C₂×#548	1	4	yes	—
279	C₂⁴	—	2	4	no	—
280	C₂⁴	—	2	4	no	—
281	C₂⁴	—	2	8	no	—
282	C₂⁴	—	2	4	no	—
283	C₂⁴	—	2	8	no	—
284	C₂⁴	—	2	8	no	—
285	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
286	C₂⁴	C₁₃×#41	1	8	yes	—
287	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
288	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
289	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
290	C₂×Q₈	—	2	256	no	—
291	C₂×Q₈	—	2	64	no	—
292	C₂×Q₈	—	2	64	no	—
293	C₂×Q₈	—	2	32	no	—
294	C₂×Q₈	—	2	16	no	—
295	C₂×Q₈	—	2	16	no	—
296	C₂×Q₈	—	2	16	no	—
297	C₂×Q₈	C₂×D₄×C₁₃	1	32	yes	complemented
298	C₂×D₄	—	2	16	no	—
299	C₂×D₄	—	2	32	no	—
300	C₂×D₄	—	2	8	no	—
301	C₂×D₄	—	2	16	no	—
302	C₂×D₄	—	4	32	no	—
303	C₂×D₄	—	4	16	no	—
304	C₂²×C₄	—	2	64	no	—
305	C₂²×C₄	—	2	16	no	—
306	C₂²×C₄	—	2	8	no	—
307	C₂²×C₄	—	2	8	no	—
308	C₂²×C₄	—	2	4	no	—
309	C₂²×C₄	—	2	32	no	—
310	C₂²×C₄	—	2	32	no	—
311	C₂²×C₄	—	2	16	no	—
312	C₂²×C₄	—	2	8	no	—
313	C₂²×C₄	—	2	4	no	—
314	C₂²×C₄	—	2	8	no	—
315	C₂²×C₄	—	2	8	no	—
316	C₂²×C₄	—	2	8	no	—
317	C₂²×C₄	C₂×D₄×C₁₃	1	16	yes	—
318	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
319	C₂²×C₄	C₂×D₄×C₁₃	1	16	yes	—
320	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	—
321	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
322	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
323	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
324	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
325	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
326	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
327	C₄⋊C₄	—	2	8	no	—
328	C₂²⋊C₄	—	2	16	no	—
329	C₂²⋊C₄	—	2	16	no	—
330	C₂²⋊C₄	—	2	64	no	—
331	C₄²	—	2	16	no	—
332	C₁₃	C₂×#2436	1	1	yes	characteristic, direct product factor, Sylow
333	C₂³	—	2	8	no	—
334	C₂³	—	2	8	no	—
335	C₂³	—	2	32	no	—
336	C₂³	—	2	4	no	—
337	C₂³	—	2	4	no	—
338	C₂³	—	2	8	no	—
339	C₂³	—	2	4	no	—
340	C₂³	—	2	8	no	—
341	C₂³	—	2	8	no	—
342	C₂³	—	4	8	no	—
343	C₂³	—	4	8	no	—
344	C₂³	—	4	8	no	—
345	C₂³	—	4	32	no	—
346	C₂³	C₁₃×#124	1	16	yes	complemented
347	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
348	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
349	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
350	C₂³	C₂×C₁₃×#41	1	8	yes	—
351	C₂³	C₂×C₁₃×#41	1	4	yes	—
352	C₂³	C₁₃×2₋¹⁺⁴	1	4	yes	—
353	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
354	Q₈	—	2	64	no	—
355	Q₈	—	2	64	no	—
356	D₄	—	4	32	no	—
357	D₄	—	4	16	no	—
358	C₂×C₄	—	2	64	no	—
359	C₂×C₄	—	2	32	no	—
360	C₂×C₄	—	2	8	no	—
361	C₂×C₄	—	2	8	no	—
362	C₂×C₄	—	2	8	no	—
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	—	2	32	no	—
365	C₂×C₄	—	2	8	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	2	8	no	—
368	C₂×C₄	—	2	8	no	—
369	C₂×C₄	—	2	8	no	—
370	C₂×C₄	—	4	8	no	—
371	C₂×C₄	—	4	16	no	—
372	C₂×C₄	C₁₃×#120	1	16	yes	—
373	C₂×C₄	C₂²×D₄×C₁₃	1	16	yes	—
374	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
375	C₂×C₄	C₂²×D₄×C₁₃	1	8	yes	—
376	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
377	C₂²	—	2	4	no	—
378	C₂²	—	2	4	no	—
379	C₂²	—	2	32	no	—
380	C₂²	—	2	16	no	—
381	C₂²	—	4	4	no	—
382	C₂²	—	4	4	no	—
383	C₂²	—	4	4	no	—
384	C₂²	—	4	16	no	—
385	C₂²	—	8	16	no	—
386	C₂²	C₂×C₁₃×#120	1	4	yes	—
387	C₂²	C₂×C₁₃×#124	1	4	yes	—
388	C₂²	C₂×C₁₃×#124	1	8	yes	complemented
389	C₂²	C₁₃×#536	1	4	yes	—
390	C₂²	C₁₃×#548	1	16	yes	—
391	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
392	C₂²	C₂³×D₄×C₁₃	1	2	yes	—
393	C₂²	C₂²×C₁₃×#41	1	2	yes	—
394	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
395	C₄	—	2	16	no	—
396	C₄	—	2	4	no	—
397	C₄	—	4	4	no	—
398	C₄	—	4	8	no	—
399	C₄	C₂×C₁₃×#120	1	8	yes	—
400	C₂	—	2	8	no	—
401	C₂	—	8	4	no	—
402	C₂	C₁₃×#2436	1	8	yes	direct product factor
403	C₂	C₂²×C₁₃×#120	1	1	yes	characteristic
404	C₂	C₂²×C₁₃×#124	1	1	yes	characteristic
405	C₂	C₂×C₁₃×#536	1	1	yes	characteristic
406	C₂	C₂×C₁₃×#548	1	4	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. C₂⁴×Q₈×C₁₃	C₂	semidirect
2. C₂²×C₁₃×#124	C₂	semidirect
4. C₁₃×#2436	C₂	direct (N × H)
5. C₂×C₁₃×#393	C₂	semidirect
6. C₂×C₁₃×#391	C₂	semidirect
7. C₂×C₁₃×#386	C₂	semidirect
8. C₂×C₄×C₁₃×C₂²⋊C₄	C₂	semidirect
13. C₂³×Q₈×C₁₃	C₂²	semidirect
19. C₂×C₁₃×#124	C₂²	semidirect
27. C₁₃×#393	C₂²	semidirect
28. C₁₃×#391	C₂²	semidirect
29. C₁₃×#386	C₂²	semidirect
30. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
42. C₂²×Q₈×C₁₃	D₄	semidirect
76. C₂×#2436	C₁₃	direct (N × H)
95. C₂×Q₈×C₁₃	C₂×D₄	semidirect
130. C₂⁴×Q₈	C₂×C₁₃	semidirect
131. C₂²×#124	C₂×C₁₃	semidirect
133. #2436	C₂×C₁₃	direct (N × H)
134. C₂×#393	C₂×C₁₃	semidirect
135. C₂×#391	C₂×C₁₃	semidirect
136. C₂×#386	C₂×C₁₃	semidirect
137. C₂×C₄×C₂²⋊C₄	C₂×C₁₃	semidirect
151. C₂³×C₁₃	#124	semidirect
186. C₂³×Q₈	C₂²×C₁₃	semidirect
192. C₂×#124	C₂²×C₁₃	semidirect
200. #393	C₂²×C₁₃	semidirect
201. #391	C₂²×C₁₃	semidirect
202. #386	C₂²×C₁₃	semidirect
203. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
217. C₂²×C₁₃	C₂×#124	semidirect
238. C₂²×Q₈	D₄×C₁₃	semidirect
274. C₂×C₁₃	#2436	direct (N × H)
297. C₂×Q₈	C₂×D₄×C₁₃	semidirect
332. C₁₃	C₂×#2436	direct (N × H)
346. C₂³	C₁₃×#124	semidirect
388. C₂²	C₂×C₁₃×#124	semidirect
402. C₂	C₁₃×#2436	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×Q₈×C₁₃	2
C₂²×C₁₃×#124	2
C₂²×C₁₃×#121	2
C₁₃×#2436	2
C₂×C₁₃×#393	2
C₂×C₁₃×#391	2
C₂×C₁₃×#386	2
C₂×C₄×C₁₃×C₂²⋊C₄	2
C₂×#2436	13

Subgroups — C2×C13×#2436 #15721040

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2436 #15721040