Subgroups — C₂×C₁₃×#2023 #15709786

Order 3328.

1734 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₃×#102	C₂	1	2	yes	maximal
3	C₂×C₁₃×#390	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2023	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₁₃×#340	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#336	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂³×Q₈×C₁₃	—	2	1	no	—
8	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
9	C₂³×C₈×C₁₃	C₂²	1	2	yes	—
10	C₂×C₁₃×C₄⋊Q₈	—	2	8	no	—
11	C₂×C₁₃×C₄⋊Q₈	—	2	2	no	—
12	C₂×C₁₃×C₄⋊Q₈	C₂²	1	4	yes	complemented
13	C₂²×C₁₃×C₄⋊C₄	—	2	1	no	—
14	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
15	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
16	C₂²×C₁₃×C₂²⋊C₄	—	2	1	no	—
17	C₂²×C₁₃×C₂²⋊C₄	—	2	1	no	—
18	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#102	—	2	8	no	—
20	C₂×C₁₃×#102	C₂²	1	8	yes	—
21	C₁₃×#390	—	2	2	no	—
22	C₁₃×#390	C₂²	1	4	yes	—
23	C₁₃×#340	C₂²	1	8	yes	complemented
24	C₁₃×#336	C₂²	1	4	yes	complemented
25	C₂⁵×C₁₃	—	2	1	no	—
26	C₂²×Q₈×C₁₃	—	2	8	no	—
27	C₂²×Q₈×C₁₃	—	2	4	no	—
28	C₂²×Q₈×C₁₃	—	4	4	no	—
29	C₂²×Q₈×C₁₃	—	4	4	no	—
30	C₂²×D₄×C₁₃	—	2	4	no	—
31	C₂²×D₄×C₁₃	—	2	1	no	—
32	C₂²×D₄×C₁₃	—	2	4	no	—
33	C₂²×D₄×C₁₃	—	2	2	no	—
34	C₂²×D₄×C₁₃	Q₈	1	4	yes	complemented
35	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
36	C₂³×C₄×C₁₃	—	2	2	no	—
37	C₂³×C₄×C₁₃	—	2	1	no	—
38	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
39	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
40	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
41	C₂²×C₈×C₁₃	—	2	4	no	—
42	C₂²×C₈×C₁₃	—	2	4	no	—
43	C₂²×C₈×C₁₃	—	2	4	no	—
44	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
45	C₁₃×C₄⋊Q₈	—	2	16	no	—
46	C₁₃×C₄⋊Q₈	—	2	16	no	—
47	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
48	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
49	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
50	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
51	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
52	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
53	C₂×C₁₃×C₄⋊C₄	D₄	1	8	yes	—
54	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
55	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
56	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
57	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
58	C₂×C₁₃×C₂²⋊C₄	—	4	4	no	—
59	C₂×C₁₃×C₂²⋊C₄	—	4	4	no	—
60	C₂×C₄²×C₁₃	—	2	4	no	—
61	C₂×C₄²×C₁₃	D₄	1	2	yes	—
62	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
63	C₁₃×#102	—	2	16	no	—
64	C₂×#2023	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
65	C₂⁴×C₁₃	—	2	4	no	—
66	C₂⁴×C₁₃	—	2	2	no	—
67	C₂⁴×C₁₃	—	4	2	no	—
68	C₂⁴×C₁₃	—	4	2	no	—
69	C₂⁴×C₁₃	—	4	2	no	—
70	C₂⁴×C₁₃	—	4	2	no	—
71	C₂⁴×C₁₃	—	4	2	no	—
72	C₂⁴×C₁₃	—	4	2	no	—
73	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
74	C₂×Q₈×C₁₃	—	2	16	no	—
75	C₂×Q₈×C₁₃	—	4	8	no	—
76	C₂×Q₈×C₁₃	—	4	32	no	—
77	C₂×Q₈×C₁₃	—	4	8	no	—
78	C₂×D₄×C₁₃	—	2	16	no	—
79	C₂×D₄×C₁₃	—	2	4	no	—
80	C₂×D₄×C₁₃	—	2	4	no	—
81	C₂×D₄×C₁₃	—	2	4	no	—
82	C₂×D₄×C₁₃	—	2	2	no	—
83	C₂×D₄×C₁₃	—	4	2	no	—
84	C₂×D₄×C₁₃	—	4	8	no	—
85	C₂×D₄×C₁₃	—	4	2	no	—
86	C₂×D₄×C₁₃	C₂×Q₈	1	4	yes	complemented
87	C₂²×C₄×C₁₃	—	2	2	no	—
88	C₂²×C₄×C₁₃	—	2	2	no	—
89	C₂²×C₄×C₁₃	—	2	2	no	—
90	C₂²×C₄×C₁₃	—	2	2	no	—
91	C₂²×C₄×C₁₃	—	2	8	no	—
92	C₂²×C₄×C₁₃	—	2	4	no	—
93	C₂²×C₄×C₁₃	—	2	2	no	—
94	C₂²×C₄×C₁₃	—	4	4	no	—
95	C₂²×C₄×C₁₃	—	4	4	no	—
96	C₂²×C₄×C₁₃	—	4	2	no	—
97	C₂²×C₄×C₁₃	—	4	2	no	—
98	C₂²×C₄×C₁₃	—	4	2	no	—
99	C₂²×C₄×C₁₃	D₈	1	4	yes	—
100	C₂²×C₄×C₁₃	SD₁₆	1	4	yes	—
101	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
105	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
106	C₂²×C₄×C₁₃	#41	1	4	yes	—
107	C₂²×C₄×C₁₃	#41	1	2	yes	—
108	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
109	C₂×C₈×C₁₃	—	2	4	no	—
110	C₂×C₈×C₁₃	—	2	4	no	—
111	C₂×C₈×C₁₃	—	2	4	no	—
112	C₂×C₈×C₁₃	—	4	8	no	—
113	C₁₃×C₄⋊C₄	—	2	16	no	—
114	C₁₃×C₄⋊C₄	—	2	8	no	—
115	C₁₃×C₄⋊C₄	—	2	4	no	—
116	C₁₃×C₄⋊C₄	—	2	4	no	—
117	C₁₃×C₄⋊C₄	—	4	2	no	—
118	C₁₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
119	C₁₃×C₂²⋊C₄	—	4	8	no	—
120	C₁₃×C₂²⋊C₄	—	4	8	no	—
121	C₄²×C₁₃	—	2	4	no	—
122	C₄²×C₁₃	—	2	4	no	—
123	C₂²×C₄⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
124	C₂²×#102	C₂×C₁₃	1	2	yes	—
125	C₂×#390	C₂×C₁₃	1	1	yes	characteristic
126	#2023	C₂×C₁₃	1	8	yes	direct product factor
127	C₂×#340	C₂×C₁₃	1	2	yes	complemented
128	C₂×#336	C₂×C₁₃	1	1	yes	characteristic, complemented
129	C₂³×C₁₃	—	2	4	no	—
130	C₂³×C₁₃	—	4	2	no	—
131	C₂³×C₁₃	—	4	2	no	—
132	C₂³×C₁₃	—	4	2	no	—
133	C₂³×C₁₃	—	4	2	no	—
134	C₂³×C₁₃	—	4	2	no	—
135	C₂³×C₁₃	—	4	2	no	—
136	C₂³×C₁₃	—	4	8	no	—
137	C₂³×C₁₃	—	4	8	no	—
138	C₂³×C₁₃	—	4	8	no	—
139	C₂³×C₁₃	—	8	4	no	—
140	C₂³×C₁₃	—	8	4	no	—
141	C₂³×C₁₃	—	8	4	no	—
142	C₂³×C₁₃	—	8	4	no	—
143	C₂³×C₁₃	#120	1	2	yes	—
144	C₂³×C₁₃	C₂²⋊Q₈	1	2	yes	—
145	C₂³×C₁₃	#124	1	2	yes	—
146	C₂³×C₁₃	C₂×D₈	1	2	yes	—
147	C₂³×C₁₃	C₂×SD₁₆	1	2	yes	—
148	C₂³×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
149	C₂³×C₁₃	#137	1	2	yes	—
150	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
151	Q₈×C₁₃	—	4	32	no	—
152	D₄×C₁₃	—	2	8	no	—
153	D₄×C₁₃	—	4	4	no	—
154	D₄×C₁₃	—	4	8	no	—
155	C₂×C₄×C₁₃	—	2	2	no	—
156	C₂×C₄×C₁₃	—	2	2	no	—
157	C₂×C₄×C₁₃	—	2	2	no	—
158	C₂×C₄×C₁₃	—	2	2	no	—
159	C₂×C₄×C₁₃	—	2	8	no	—
160	C₂×C₄×C₁₃	—	2	8	no	—
161	C₂×C₄×C₁₃	—	2	8	no	—
162	C₂×C₄×C₁₃	—	4	4	no	—
163	C₂×C₄×C₁₃	—	4	4	no	—
164	C₂×C₄×C₁₃	—	4	16	no	—
165	C₂×C₄×C₁₃	—	4	2	no	—
166	C₂×C₄×C₁₃	—	4	2	no	—
167	C₂×C₄×C₁₃	—	4	2	no	—
168	C₂×C₄×C₁₃	—	8	4	no	—
169	C₂×C₄×C₁₃	#120	1	2	yes	—
170	C₂×C₄×C₁₃	C₂²⋊Q₈	1	8	yes	—
171	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
172	C₂×C₄×C₁₃	#124	1	8	yes	—
173	C₂×C₄×C₁₃	#124	1	2	yes	—
174	C₂×C₄×C₁₃	C₂×D₈	1	4	yes	—
175	C₂×C₄×C₁₃	C₂×SD₁₆	1	4	yes	—
176	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
177	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
178	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
179	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
180	C₈×C₁₃	—	4	4	no	—
181	C₂³×Q₈	—	2	1	no	—
182	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
183	C₂³×C₈	C₂²×C₁₃	1	2	yes	—
184	C₂×C₄⋊Q₈	—	2	8	no	—
185	C₂×C₄⋊Q₈	—	2	2	no	—
186	C₂×C₄⋊Q₈	C₂²×C₁₃	1	4	yes	complemented
187	C₂²×C₄⋊C₄	—	2	1	no	—
188	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
189	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
190	C₂²×C₂²⋊C₄	—	2	1	no	—
191	C₂²×C₂²⋊C₄	—	2	1	no	—
192	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
193	C₂×#102	—	2	8	no	—
194	C₂×#102	C₂²×C₁₃	1	8	yes	—
195	#390	—	2	2	no	—
196	#390	C₂²×C₁₃	1	4	yes	—
197	#340	C₂²×C₁₃	1	8	yes	complemented
198	#336	C₂²×C₁₃	1	4	yes	complemented
199	C₂²×C₁₃	—	4	4	no	—
200	C₂²×C₁₃	—	4	4	no	—
201	C₂²×C₁₃	—	4	4	no	—
202	C₂²×C₁₃	—	8	2	no	—
203	C₂²×C₁₃	—	8	2	no	—
204	C₂²×C₁₃	—	8	2	no	—
205	C₂²×C₁₃	—	8	2	no	—
206	C₂²×C₁₃	—	8	16	no	—
207	C₂²×C₁₃	#393	1	4	yes	—
208	C₂²×C₁₃	#447	1	4	yes	—
209	C₂²×C₁₃	#448	1	4	yes	—
210	C₂²×C₁₃	#474	1	4	yes	—
211	C₂²×C₁₃	#476	1	4	yes	—
212	C₂²×C₁₃	#486	1	4	yes	—
213	C₂²×C₁₃	#489	1	4	yes	—
214	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
215	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
216	C₂²×C₁₃	C₂×#124	1	1	yes	characteristic
217	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
218	C₂²×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
219	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
220	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
221	C₄×C₁₃	—	2	4	no	—
222	C₄×C₁₃	—	2	4	no	—
223	C₄×C₁₃	—	4	8	no	—
224	C₄×C₁₃	—	8	2	no	—
225	C₄×C₁₃	#393	1	4	yes	—
226	C₄×C₁₃	C₂×C₂²⋊Q₈	1	2	yes	—
227	C₄×C₁₃	C₂×#124	1	2	yes	—
228	C₂⁵	—	2	1	no	—
229	C₂²×Q₈	—	2	8	no	—
230	C₂²×Q₈	—	2	4	no	—
231	C₂²×Q₈	—	4	4	no	—
232	C₂²×Q₈	—	4	4	no	—
233	C₂²×D₄	—	2	4	no	—
234	C₂²×D₄	—	2	1	no	—
235	C₂²×D₄	—	2	4	no	—
236	C₂²×D₄	—	2	2	no	—
237	C₂²×D₄	Q₈×C₁₃	1	4	yes	complemented
238	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
239	C₂³×C₄	—	2	2	no	—
240	C₂³×C₄	—	2	1	no	—
241	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
242	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
243	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
244	C₂²×C₈	—	2	4	no	—
245	C₂²×C₈	—	2	4	no	—
246	C₂²×C₈	—	2	4	no	—
247	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
248	C₄⋊Q₈	—	2	16	no	—
249	C₄⋊Q₈	—	2	16	no	—
250	C₂×C₄⋊C₄	—	2	8	no	—
251	C₂×C₄⋊C₄	—	2	4	no	—
252	C₂×C₄⋊C₄	—	2	2	no	—
253	C₂×C₄⋊C₄	—	2	4	no	—
254	C₂×C₄⋊C₄	—	2	4	no	—
255	C₂×C₄⋊C₄	—	2	1	no	—
256	C₂×C₄⋊C₄	D₄×C₁₃	1	8	yes	—
257	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
258	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
259	C₂×C₂²⋊C₄	—	2	4	no	—
260	C₂×C₂²⋊C₄	—	2	4	no	—
261	C₂×C₂²⋊C₄	—	4	4	no	—
262	C₂×C₂²⋊C₄	—	4	4	no	—
263	C₂×C₄²	—	2	4	no	—
264	C₂×C₄²	D₄×C₁₃	1	2	yes	—
265	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
266	#102	—	2	16	no	—
267	C₂×C₁₃	—	8	4	no	—
268	C₂×C₁₃	#2023	1	8	yes	direct product factor
269	C₂×C₁₃	C₂×#393	1	1	yes	characteristic
270	C₂×C₁₃	C₂×#447	1	1	yes	characteristic
271	C₂×C₁₃	C₂×#448	1	1	yes	characteristic
272	C₂×C₁₃	C₂×#474	1	1	yes	characteristic
273	C₂×C₁₃	C₂×#476	1	1	yes	characteristic
274	C₂×C₁₃	C₂×#486	1	1	yes	characteristic
275	C₂×C₁₃	C₂×#489	1	1	yes	characteristic
276	C₂⁴	—	2	4	no	—
277	C₂⁴	—	2	2	no	—
278	C₂⁴	—	4	2	no	—
279	C₂⁴	—	4	2	no	—
280	C₂⁴	—	4	2	no	—
281	C₂⁴	—	4	2	no	—
282	C₂⁴	—	4	2	no	—
283	C₂⁴	—	4	2	no	—
284	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
285	C₂×Q₈	—	2	16	no	—
286	C₂×Q₈	—	4	32	no	—
287	C₂×Q₈	—	4	8	no	—
288	C₂×Q₈	—	4	8	no	—
289	C₂×D₄	—	2	16	no	—
290	C₂×D₄	—	2	4	no	—
291	C₂×D₄	—	2	4	no	—
292	C₂×D₄	—	2	4	no	—
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	—	4	2	no	—
295	C₂×D₄	—	4	2	no	—
296	C₂×D₄	—	4	8	no	—
297	C₂×D₄	C₂×Q₈×C₁₃	1	4	yes	complemented
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	8	no	—
303	C₂²×C₄	—	2	4	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	4	4	no	—
306	C₂²×C₄	—	4	4	no	—
307	C₂²×C₄	—	4	2	no	—
308	C₂²×C₄	—	4	2	no	—
309	C₂²×C₄	—	4	2	no	—
310	C₂²×C₄	C₁₃×D₈	1	4	yes	—
311	C₂²×C₄	C₁₃×SD₁₆	1	4	yes	—
312	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
313	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
314	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
315	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
316	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
317	C₂²×C₄	C₁₃×#41	1	4	yes	—
318	C₂²×C₄	C₁₃×#41	1	2	yes	—
319	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
320	C₂×C₈	—	2	4	no	—
321	C₂×C₈	—	2	4	no	—
322	C₂×C₈	—	2	4	no	—
323	C₂×C₈	—	4	8	no	—
324	C₄⋊C₄	—	2	16	no	—
325	C₄⋊C₄	—	2	8	no	—
326	C₄⋊C₄	—	2	4	no	—
327	C₄⋊C₄	—	2	4	no	—
328	C₄⋊C₄	—	4	2	no	—
329	C₄⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
330	C₂²⋊C₄	—	4	8	no	—
331	C₂²⋊C₄	—	4	8	no	—
332	C₄²	—	2	4	no	—
333	C₄²	—	2	4	no	—
334	C₁₃	C₂×#2023	1	1	yes	characteristic, direct product factor, Sylow
335	C₂³	—	2	4	no	—
336	C₂³	—	4	8	no	—
337	C₂³	—	4	8	no	—
338	C₂³	—	4	8	no	—
339	C₂³	—	4	2	no	—
340	C₂³	—	4	2	no	—
341	C₂³	—	4	2	no	—
342	C₂³	—	4	2	no	—
343	C₂³	—	4	2	no	—
344	C₂³	—	4	2	no	—
345	C₂³	—	8	4	no	—
346	C₂³	—	8	4	no	—
347	C₂³	—	8	4	no	—
348	C₂³	—	8	4	no	—
349	C₂³	C₁₃×#120	1	2	yes	—
350	C₂³	C₁₃×C₂²⋊Q₈	1	2	yes	—
351	C₂³	C₁₃×#124	1	2	yes	—
352	C₂³	C₂×C₁₃×D₈	1	2	yes	—
353	C₂³	C₂×C₁₃×SD₁₆	1	2	yes	—
354	C₂³	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
355	C₂³	C₁₃×#137	1	2	yes	—
356	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
357	Q₈	—	4	32	no	—
358	D₄	—	2	8	no	—
359	D₄	—	4	8	no	—
360	D₄	—	4	4	no	—
361	C₂×C₄	—	2	8	no	—
362	C₂×C₄	—	2	8	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	8	no	—
368	C₂×C₄	—	4	16	no	—
369	C₂×C₄	—	4	4	no	—
370	C₂×C₄	—	4	4	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	8	4	no	—
375	C₂×C₄	C₁₃×#120	1	2	yes	—
376	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
377	C₂×C₄	C₁₃×C₂²⋊Q₈	1	8	yes	—
378	C₂×C₄	C₁₃×#124	1	2	yes	—
379	C₂×C₄	C₁₃×#124	1	8	yes	—
380	C₂×C₄	C₂×C₁₃×D₈	1	4	yes	—
381	C₂×C₄	C₂×C₁₃×SD₁₆	1	4	yes	—
382	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
383	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
384	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
385	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
386	C₈	—	4	4	no	—
387	C₂²	—	4	4	no	—
388	C₂²	—	4	4	no	—
389	C₂²	—	4	4	no	—
390	C₂²	—	8	16	no	—
391	C₂²	—	8	2	no	—
392	C₂²	—	8	2	no	—
393	C₂²	—	8	2	no	—
394	C₂²	—	8	2	no	—
395	C₂²	C₁₃×#393	1	4	yes	—
396	C₂²	C₁₃×#447	1	4	yes	—
397	C₂²	C₁₃×#448	1	4	yes	—
398	C₂²	C₁₃×#474	1	4	yes	—
399	C₂²	C₁₃×#476	1	4	yes	—
400	C₂²	C₁₃×#486	1	4	yes	—
401	C₂²	C₁₃×#489	1	4	yes	—
402	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
403	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
404	C₂²	C₂×C₁₃×#124	1	1	yes	characteristic
405	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
406	C₂²	C₂²×C₁₃×SD₁₆	1	1	yes	characteristic
407	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
408	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
409	C₄	—	2	4	no	—
410	C₄	—	2	4	no	—
411	C₄	—	4	8	no	—
412	C₄	—	8	2	no	—
413	C₄	C₁₃×#393	1	4	yes	—
414	C₄	C₂×C₁₃×C₂²⋊Q₈	1	2	yes	—
415	C₄	C₂×C₁₃×#124	1	2	yes	—
416	C₂	—	8	4	no	—
417	C₂	C₁₃×#2023	1	8	yes	direct product factor
418	C₂	C₂×C₁₃×#393	1	1	yes	characteristic
419	C₂	C₂×C₁₃×#447	1	1	yes	characteristic
420	C₂	C₂×C₁₃×#448	1	1	yes	characteristic
421	C₂	C₂×C₁₃×#474	1	1	yes	characteristic
422	C₂	C₂×C₁₃×#476	1	1	yes	characteristic
423	C₂	C₂×C₁₃×#486	1	1	yes	characteristic
424	C₂	C₂×C₁₃×#489	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₁₃	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂³×D₄×C₁₃	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₃×C₄⋊Q₈	C₂	semidirect
4. C₁₃×#2023	C₂	direct (N × H)
5. C₂×C₁₃×#340	C₂	semidirect
6. C₂×C₁₃×#336	C₂	semidirect
12. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
23. C₁₃×#340	C₂²	semidirect
24. C₁₃×#336	C₂²	semidirect
34. C₂²×D₄×C₁₃	Q₈	semidirect
64. C₂×#2023	C₁₃	direct (N × H)
86. C₂×D₄×C₁₃	C₂×Q₈	semidirect
123. C₂²×C₄⋊Q₈	C₂×C₁₃	semidirect
126. #2023	C₂×C₁₃	direct (N × H)
127. C₂×#340	C₂×C₁₃	semidirect
128. C₂×#336	C₂×C₁₃	semidirect
186. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
197. #340	C₂²×C₁₃	semidirect
198. #336	C₂²×C₁₃	semidirect
237. C₂²×D₄	Q₈×C₁₃	semidirect
268. C₂×C₁₃	#2023	direct (N × H)
297. C₂×D₄	C₂×Q₈×C₁₃	semidirect
334. C₁₃	C₂×#2023	direct (N × H)
417. C₂	C₁₃×#2023	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×C₄⋊Q₈	2
C₂²×C₁₃×#102	2
C₂×C₁₃×#390	2
C₁₃×#2023	2
C₂×C₁₃×#340	2
C₂×C₁₃×#336	2
C₂×#2023	13

Subgroups — C2×C13×#2023 #15709786

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2023 #15709786