Subgroups — C₁₃×#24202 #15710541

Order 3328.

1132 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#559	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#460	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₃×#441	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2581	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2042	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2015	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1985	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1961	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#1877	C₂	1	2	yes	maximal, complemented
10	C₁₃×#1864	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1805	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
13	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
14	C₁₃×#559	—	2	4	no	—
15	C₁₃×#559	—	2	4	no	—
16	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#124	—	2	1	no	—
18	C₂×C₁₃×#124	C₂²	1	2	yes	—
19	C₂×C₁₃×#123	—	2	2	no	—
20	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
22	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₁₃	—	2	1	no	—
24	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
25	C₁₃×#460	—	2	4	no	—
26	C₁₃×#441	—	2	4	no	—
27	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#103	C₂²	1	2	yes	—
32	C₂×C₁₃×#102	C₂²	1	2	yes	—
33	C₂×C₁₃×#102	C₂²	1	2	yes	—
34	C₂×C₁₃×#102	C₂²	1	2	yes	—
35	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
36	C₁₃×#400	—	2	1	no	—
37	C₁₃×#395	—	2	1	no	—
38	C₁₃×#391	C₂²	1	2	yes	—
39	C₁₃×#389	C₂²	1	2	yes	—
40	C₁₃×#387	—	2	2	no	—
41	C₁₃×#382	C₂²	1	1	yes	characteristic
42	C₁₃×#340	C₂²	1	2	yes	—
43	C₁₃×#336	C₂²	1	2	yes	—
44	C₁₃×#336	C₂²	1	2	yes	—
45	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
46	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
47	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
48	C₂²×D₄×C₁₃	—	2	1	no	—
49	C₂²×D₄×C₁₃	—	2	1	no	—
50	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
51	C₂³×C₄×C₁₃	—	2	2	no	—
52	C₂×C₁₃×Q₁₆	—	2	2	no	—
53	C₂×C₁₃×Q₁₆	—	2	2	no	—
54	C₂×C₁₃×Q₁₆	—	2	2	no	—
55	C₂×C₁₃×SD₁₆	—	2	4	no	—
56	C₂×C₁₃×SD₁₆	—	2	4	no	—
57	C₂×C₁₃×SD₁₆	—	4	2	no	—
58	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
59	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
60	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
61	C₁₃×#127	—	2	2	no	—
62	C₁₃×#127	D₄	1	4	yes	—
63	C₁₃×#124	—	2	8	no	—
64	C₁₃×#124	—	2	4	no	—
65	C₁₃×#124	—	2	4	no	—
66	C₁₃×#123	—	2	16	no	—
67	C₄×Q₈×C₁₃	—	2	2	no	—
68	C₄×Q₈×C₁₃	—	2	2	no	—
69	C₄×Q₈×C₁₃	—	2	2	no	—
70	C₄×Q₈×C₁₃	—	2	2	no	—
71	C₄×Q₈×C₁₃	—	2	2	no	—
72	C₄×Q₈×C₁₃	D₄	1	4	yes	—
73	C₄×D₄×C₁₃	—	2	8	no	—
74	C₄×D₄×C₁₃	—	2	4	no	—
75	C₄×D₄×C₁₃	—	2	4	no	—
76	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
77	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
78	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
79	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
80	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
81	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
82	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
83	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
84	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
85	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
86	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
87	C₂×C₄²×C₁₃	—	2	1	no	—
88	C₂×C₄²×C₁₃	—	2	1	no	—
89	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
90	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
91	C₁₃×#106	—	2	2	no	—
92	C₁₃×C₄⋊C₈	—	2	2	no	—
93	C₁₃×#103	—	2	2	no	—
94	C₁₃×#103	—	2	2	no	—
95	C₁₃×#103	—	4	2	no	—
96	C₁₃×#102	—	2	4	no	—
97	C₁₃×#102	—	2	4	no	—
98	C₁₃×#102	—	4	2	no	—
99	C₁₃×#97	—	2	2	no	—
100	C₁₃×#95	—	2	1	no	—
101	C₁₃×#95	—	2	1	no	—
102	C₁₃×#95	—	2	2	no	—
103	C₁₃×#95	—	2	2	no	—
104	C₁₃×#95	—	2	2	no	—
105	#24202	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
106	C₂⁴×C₁₃	—	2	2	no	—
107	C₂×Q₈×C₁₃	—	2	2	no	—
108	C₂×Q₈×C₁₃	—	2	1	no	—
109	C₂×Q₈×C₁₃	—	2	1	no	—
110	C₂×Q₈×C₁₃	—	2	1	no	—
111	C₂×Q₈×C₁₃	—	2	1	no	—
112	C₂×Q₈×C₁₃	—	2	1	no	—
113	C₂×Q₈×C₁₃	—	2	1	no	—
114	C₂×Q₈×C₁₃	—	2	1	no	—
115	C₂×Q₈×C₁₃	—	2	1	no	—
116	C₂×Q₈×C₁₃	—	2	1	no	—
117	C₂×Q₈×C₁₃	—	2	1	no	—
118	C₂×Q₈×C₁₃	—	4	2	no	—
119	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
120	C₂×Q₈×C₁₃	#41	1	2	yes	—
121	C₂×D₄×C₁₃	—	2	4	no	—
122	C₂×D₄×C₁₃	—	2	4	no	—
123	C₂×D₄×C₁₃	—	2	2	no	—
124	C₂×D₄×C₁₃	—	2	2	no	—
125	C₂×D₄×C₁₃	—	2	2	no	—
126	C₂×D₄×C₁₃	—	2	2	no	—
127	C₂×D₄×C₁₃	—	2	2	no	—
128	C₂×D₄×C₁₃	—	4	4	no	—
129	C₂×D₄×C₁₃	—	8	2	no	—
130	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
131	C₂²×C₄×C₁₃	—	2	1	no	—
132	C₂²×C₄×C₁₃	—	2	1	no	—
133	C₂²×C₄×C₁₃	—	2	1	no	—
134	C₂²×C₄×C₁₃	—	2	8	no	—
135	C₂²×C₄×C₁₃	—	2	2	no	—
136	C₂²×C₄×C₁₃	—	2	1	no	—
137	C₂²×C₄×C₁₃	—	8	4	no	—
138	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
139	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
140	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
143	C₁₃×Q₁₆	—	2	8	no	—
144	C₁₃×SD₁₆	—	4	8	no	—
145	C₂×C₈×C₁₃	—	2	1	no	—
146	C₂×C₈×C₁₃	—	2	1	no	—
147	C₂×C₈×C₁₃	—	2	1	no	—
148	C₂×C₈×C₁₃	—	2	2	no	—
149	C₂×C₈×C₁₃	—	2	2	no	—
150	C₂×C₈×C₁₃	—	2	1	no	—
151	C₂×C₈×C₁₃	—	2	2	no	—
152	C₂×C₈×C₁₃	—	2	1	no	—
153	C₂×C₈×C₁₃	#41	1	2	yes	—
154	C₁₃×C₄⋊C₄	—	2	4	no	—
155	C₁₃×C₄⋊C₄	—	2	2	no	—
156	C₁₃×C₄⋊C₄	—	2	4	no	—
157	C₁₃×C₄⋊C₄	—	2	1	no	—
158	C₁₃×C₄⋊C₄	—	2	1	no	—
159	C₁₃×C₄⋊C₄	—	2	1	no	—
160	C₁₃×C₄⋊C₄	—	2	2	no	—
161	C₁₃×C₄⋊C₄	—	2	2	no	—
162	C₁₃×C₄⋊C₄	—	4	4	no	—
163	C₁₃×C₄⋊C₄	—	4	2	no	—
164	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
165	C₁₃×C₂²⋊C₄	—	2	8	no	—
166	C₁₃×C₂²⋊C₄	—	2	8	no	—
167	C₁₃×C₂²⋊C₄	—	2	8	no	—
168	C₄²×C₁₃	—	2	4	no	—
169	C₄²×C₁₃	—	2	2	no	—
170	C₄²×C₁₃	—	2	2	no	—
171	C₄²×C₁₃	—	4	2	no	—
172	C₄²×C₁₃	C₂×D₄	1	2	yes	—
173	C₄²×C₁₃	C₂×D₄	1	2	yes	—
174	C₂×#559	C₂×C₁₃	1	1	yes	characteristic
175	C₂×#460	C₂×C₁₃	1	1	yes	characteristic
176	C₂×#441	C₂×C₁₃	1	1	yes	characteristic, complemented
177	#2581	C₂×C₁₃	1	1	yes	characteristic, complemented
178	#2042	C₂×C₁₃	1	2	yes	complemented
179	#2015	C₂×C₁₃	1	2	yes	complemented
180	#1985	C₂×C₁₃	1	1	yes	characteristic, complemented
181	#1961	C₂×C₁₃	1	1	yes	characteristic
182	#1877	C₂×C₁₃	1	2	yes	complemented
183	#1864	C₂×C₁₃	1	2	yes	complemented
184	#1805	C₂×C₁₃	1	1	yes	characteristic, complemented
185	C₂³×C₁₃	—	2	4	no	—
186	C₂³×C₁₃	—	4	2	no	—
187	C₂³×C₁₃	—	4	2	no	—
188	C₂³×C₁₃	—	4	4	no	—
189	C₂³×C₁₃	—	4	4	no	—
190	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
191	Q₈×C₁₃	—	2	2	no	—
192	Q₈×C₁₃	—	2	2	no	—
193	Q₈×C₁₃	—	2	2	no	—
194	Q₈×C₁₃	—	2	2	no	—
195	Q₈×C₁₃	—	4	4	no	—
196	Q₈×C₁₃	—	4	1	no	—
197	Q₈×C₁₃	—	4	1	no	—
198	Q₈×C₁₃	—	4	1	no	—
199	Q₈×C₁₃	—	4	1	no	—
200	D₄×C₁₃	—	2	4	no	—
201	D₄×C₁₃	—	2	4	no	—
202	D₄×C₁₃	—	4	8	no	—
203	D₄×C₁₃	—	4	2	no	—
204	D₄×C₁₃	—	4	2	no	—
205	D₄×C₁₃	—	8	4	no	—
206	C₂×C₄×C₁₃	—	2	2	no	—
207	C₂×C₄×C₁₃	—	2	2	no	—
208	C₂×C₄×C₁₃	—	2	2	no	—
209	C₂×C₄×C₁₃	—	2	2	no	—
210	C₂×C₄×C₁₃	—	2	2	no	—
211	C₂×C₄×C₁₃	—	2	2	no	—
212	C₂×C₄×C₁₃	—	2	2	no	—
213	C₂×C₄×C₁₃	—	2	2	no	—
214	C₂×C₄×C₁₃	—	2	2	no	—
215	C₂×C₄×C₁₃	—	2	4	no	—
216	C₂×C₄×C₁₃	—	4	1	no	—
217	C₂×C₄×C₁₃	—	4	1	no	—
218	C₂×C₄×C₁₃	—	4	1	no	—
219	C₂×C₄×C₁₃	—	4	1	no	—
220	C₂×C₄×C₁₃	—	4	2	no	—
221	C₂×C₄×C₁₃	—	4	1	no	—
222	C₂×C₄×C₁₃	—	4	2	no	—
223	C₂×C₄×C₁₃	—	4	2	no	—
224	C₂×C₄×C₁₃	—	4	2	no	—
225	C₂×C₄×C₁₃	—	4	2	no	—
226	C₂×C₄×C₁₃	—	8	8	no	—
227	C₂×C₄×C₁₃	#120	1	2	yes	—
228	C₂×C₄×C₁₃	#120	1	2	yes	—
229	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
230	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
231	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
232	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
233	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
234	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
235	C₈×C₁₃	—	2	2	no	—
236	C₈×C₁₃	—	4	1	no	—
237	C₈×C₁₃	—	4	2	no	—
238	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
239	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
240	#559	—	2	4	no	—
241	#559	—	2	4	no	—
242	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
243	C₂×#124	—	2	1	no	—
244	C₂×#124	C₂²×C₁₃	1	2	yes	—
245	C₂×#123	—	2	2	no	—
246	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
247	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
248	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
249	C₂×C₄×D₄	—	2	1	no	—
250	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
251	#460	—	2	4	no	—
252	#441	—	2	4	no	—
253	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
254	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
255	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
256	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
257	C₂×#103	C₂²×C₁₃	1	2	yes	—
258	C₂×#102	C₂²×C₁₃	1	2	yes	—
259	C₂×#102	C₂²×C₁₃	1	2	yes	—
260	C₂×#102	C₂²×C₁₃	1	2	yes	—
261	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
262	#400	—	2	1	no	—
263	#395	—	2	1	no	—
264	#391	C₂²×C₁₃	1	2	yes	—
265	#389	C₂²×C₁₃	1	2	yes	—
266	#387	—	2	2	no	—
267	#382	C₂²×C₁₃	1	1	yes	characteristic
268	#340	C₂²×C₁₃	1	2	yes	—
269	#336	C₂²×C₁₃	1	2	yes	—
270	#336	C₂²×C₁₃	1	2	yes	—
271	C₂²×C₁₃	—	4	4	no	—
272	C₂²×C₁₃	—	4	4	no	—
273	C₂²×C₁₃	—	4	4	no	—
274	C₂²×C₁₃	—	8	4	no	—
275	C₂²×C₁₃	—	8	4	no	—
276	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
277	C₂²×C₁₃	#548	1	1	yes	characteristic
278	C₂²×C₁₃	#550	1	1	yes	characteristic
279	C₂²×C₁₃	#575	1	2	yes	—
280	C₂²×C₁₃	#577	1	2	yes	—
281	C₄×C₁₃	—	2	2	no	—
282	C₄×C₁₃	—	2	2	no	—
283	C₄×C₁₃	—	4	2	no	—
284	C₄×C₁₃	—	4	2	no	—
285	C₄×C₁₃	—	4	2	no	—
286	C₄×C₁₃	—	4	2	no	—
287	C₄×C₁₃	—	4	2	no	—
288	C₄×C₁₃	—	8	2	no	—
289	C₄×C₁₃	—	8	1	no	—
290	C₄×C₁₃	#525	1	1	yes	characteristic
291	C₄×C₁₃	#537	1	1	yes	characteristic
292	C₄×C₁₃	#546	1	1	yes	characteristic
293	C₄×C₁₃	#547	1	1	yes	characteristic
294	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
295	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
296	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
297	C₂²×D₄	—	2	1	no	—
298	C₂²×D₄	—	2	1	no	—
299	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
300	C₂³×C₄	—	2	2	no	—
301	C₂×Q₁₆	—	2	2	no	—
302	C₂×Q₁₆	—	2	2	no	—
303	C₂×Q₁₆	—	2	2	no	—
304	C₂×SD₁₆	—	2	4	no	—
305	C₂×SD₁₆	—	2	4	no	—
306	C₂×SD₁₆	—	4	2	no	—
307	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
308	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
309	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
310	#127	—	2	2	no	—
311	#127	D₄×C₁₃	1	4	yes	—
312	#124	—	2	8	no	—
313	#124	—	2	4	no	—
314	#124	—	2	4	no	—
315	#123	—	2	16	no	—
316	C₄×Q₈	—	2	2	no	—
317	C₄×Q₈	—	2	2	no	—
318	C₄×Q₈	—	2	2	no	—
319	C₄×Q₈	—	2	2	no	—
320	C₄×Q₈	—	2	2	no	—
321	C₄×Q₈	D₄×C₁₃	1	4	yes	—
322	C₄×D₄	—	2	8	no	—
323	C₄×D₄	—	2	4	no	—
324	C₄×D₄	—	2	4	no	—
325	C₂×C₄⋊C₄	—	2	1	no	—
326	C₂×C₄⋊C₄	—	2	1	no	—
327	C₂×C₄⋊C₄	—	2	2	no	—
328	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
329	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
330	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
331	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
332	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
333	C₂×C₂²⋊C₄	—	2	2	no	—
334	C₂×C₂²⋊C₄	—	2	2	no	—
335	C₂×C₂²⋊C₄	—	2	2	no	—
336	C₂×C₄²	—	2	1	no	—
337	C₂×C₄²	—	2	1	no	—
338	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
339	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
340	#106	—	2	2	no	—
341	C₄⋊C₈	—	2	2	no	—
342	#103	—	2	2	no	—
343	#103	—	2	2	no	—
344	#103	—	4	2	no	—
345	#102	—	2	4	no	—
346	#102	—	2	4	no	—
347	#102	—	4	2	no	—
348	#97	—	2	2	no	—
349	#95	—	2	1	no	—
350	#95	—	2	1	no	—
351	#95	—	2	2	no	—
352	#95	—	2	2	no	—
353	#95	—	2	2	no	—
354	C₂×C₁₃	—	8	4	no	—
355	C₂×C₁₃	#2407	1	1	yes	characteristic
356	C₂×C₁₃	#3005	1	1	yes	characteristic
357	C₂×C₁₃	#3009	1	1	yes	characteristic
358	C₂×C₁₃	#3371	1	2	yes	—
359	C₂×C₁₃	#3401	1	2	yes	—
360	C₂⁴	—	2	2	no	—
361	C₂×Q₈	—	2	2	no	—
362	C₂×Q₈	—	2	1	no	—
363	C₂×Q₈	—	2	1	no	—
364	C₂×Q₈	—	2	1	no	—
365	C₂×Q₈	—	2	1	no	—
366	C₂×Q₈	—	2	1	no	—
367	C₂×Q₈	—	2	1	no	—
368	C₂×Q₈	—	2	1	no	—
369	C₂×Q₈	—	2	1	no	—
370	C₂×Q₈	—	2	1	no	—
371	C₂×Q₈	—	2	1	no	—
372	C₂×Q₈	—	4	2	no	—
373	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
374	C₂×Q₈	C₁₃×#41	1	2	yes	—
375	C₂×D₄	—	2	4	no	—
376	C₂×D₄	—	2	4	no	—
377	C₂×D₄	—	2	2	no	—
378	C₂×D₄	—	2	2	no	—
379	C₂×D₄	—	2	2	no	—
380	C₂×D₄	—	2	2	no	—
381	C₂×D₄	—	2	2	no	—
382	C₂×D₄	—	4	4	no	—
383	C₂×D₄	—	8	2	no	—
384	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
385	C₂²×C₄	—	2	1	no	—
386	C₂²×C₄	—	2	1	no	—
387	C₂²×C₄	—	2	1	no	—
388	C₂²×C₄	—	2	8	no	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	2	1	no	—
391	C₂²×C₄	—	8	4	no	—
392	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
393	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
394	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
395	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
396	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
397	Q₁₆	—	2	8	no	—
398	SD₁₆	—	4	8	no	—
399	C₂×C₈	—	2	1	no	—
400	C₂×C₈	—	2	1	no	—
401	C₂×C₈	—	2	1	no	—
402	C₂×C₈	—	2	2	no	—
403	C₂×C₈	—	2	2	no	—
404	C₂×C₈	—	2	1	no	—
405	C₂×C₈	—	2	2	no	—
406	C₂×C₈	—	2	1	no	—
407	C₂×C₈	C₁₃×#41	1	2	yes	—
408	C₄⋊C₄	—	2	4	no	—
409	C₄⋊C₄	—	2	2	no	—
410	C₄⋊C₄	—	2	4	no	—
411	C₄⋊C₄	—	2	1	no	—
412	C₄⋊C₄	—	2	1	no	—
413	C₄⋊C₄	—	2	1	no	—
414	C₄⋊C₄	—	2	2	no	—
415	C₄⋊C₄	—	2	2	no	—
416	C₄⋊C₄	—	4	4	no	—
417	C₄⋊C₄	—	4	2	no	—
418	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
419	C₂²⋊C₄	—	2	8	no	—
420	C₂²⋊C₄	—	2	8	no	—
421	C₂²⋊C₄	—	2	8	no	—
422	C₄²	—	2	4	no	—
423	C₄²	—	2	2	no	—
424	C₄²	—	2	2	no	—
425	C₄²	—	4	2	no	—
426	C₄²	C₂×D₄×C₁₃	1	2	yes	—
427	C₄²	C₂×D₄×C₁₃	1	2	yes	—
428	C₁₃	#24202	1	1	yes	characteristic, direct product factor, Sylow
429	C₂³	—	2	4	no	—
430	C₂³	—	4	2	no	—
431	C₂³	—	4	2	no	—
432	C₂³	—	4	4	no	—
433	C₂³	—	4	4	no	—
434	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
435	Q₈	—	2	2	no	—
436	Q₈	—	2	2	no	—
437	Q₈	—	2	2	no	—
438	Q₈	—	2	2	no	—
439	Q₈	—	4	4	no	—
440	Q₈	—	4	1	no	—
441	Q₈	—	4	1	no	—
442	Q₈	—	4	1	no	—
443	Q₈	—	4	1	no	—
444	D₄	—	2	4	no	—
445	D₄	—	2	4	no	—
446	D₄	—	4	8	no	—
447	D₄	—	4	2	no	—
448	D₄	—	4	2	no	—
449	D₄	—	8	4	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	4	no	—
460	C₂×C₄	—	4	1	no	—
461	C₂×C₄	—	4	1	no	—
462	C₂×C₄	—	4	1	no	—
463	C₂×C₄	—	4	1	no	—
464	C₂×C₄	—	4	2	no	—
465	C₂×C₄	—	4	1	no	—
466	C₂×C₄	—	4	2	no	—
467	C₂×C₄	—	4	2	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	—	4	2	no	—
470	C₂×C₄	—	8	8	no	—
471	C₂×C₄	C₁₃×#120	1	2	yes	—
472	C₂×C₄	C₁₃×#120	1	2	yes	—
473	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
474	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
475	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
476	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
477	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
478	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
479	C₈	—	2	2	no	—
480	C₈	—	4	1	no	—
481	C₈	—	4	2	no	—
482	C₂²	—	4	4	no	—
483	C₂²	—	4	4	no	—
484	C₂²	—	4	4	no	—
485	C₂²	—	8	4	no	—
486	C₂²	—	8	4	no	—
487	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
488	C₂²	C₁₃×#548	1	1	yes	characteristic
489	C₂²	C₁₃×#550	1	1	yes	characteristic
490	C₂²	C₁₃×#575	1	2	yes	—
491	C₂²	C₁₃×#577	1	2	yes	—
492	C₄	—	2	2	no	—
493	C₄	—	2	2	no	—
494	C₄	—	4	2	no	—
495	C₄	—	4	2	no	—
496	C₄	—	4	2	no	—
497	C₄	—	4	2	no	—
498	C₄	—	4	2	no	—
499	C₄	—	8	2	no	—
500	C₄	—	8	1	no	—
501	C₄	C₁₃×#525	1	1	yes	characteristic
502	C₄	C₁₃×#537	1	1	yes	characteristic
503	C₄	C₁₃×#546	1	1	yes	characteristic
504	C₄	C₁₃×#547	1	1	yes	characteristic
505	C₂	—	8	4	no	—
506	C₂	C₁₃×#2407	1	1	yes	characteristic
507	C₂	C₁₃×#3005	1	1	yes	characteristic
508	C₂	C₁₃×#3009	1	1	yes	characteristic
509	C₂	C₁₃×#3371	1	2	yes	—
510	C₂	C₁₃×#3401	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#127	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄×Q₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₁₃×#441	C₂	semidirect
4. C₁₃×#2581	C₂	semidirect
5. C₁₃×#2042	C₂	semidirect
6. C₁₃×#2015	C₂	semidirect
7. C₁₃×#1985	C₂	semidirect
9. C₁₃×#1877	C₂	semidirect
10. C₁₃×#1864	C₂	semidirect
11. C₁₃×#1805	C₂	semidirect
105. #24202	C₁₃	direct (N × H)
176. C₂×#441	C₂×C₁₃	semidirect
177. #2581	C₂×C₁₃	semidirect
178. #2042	C₂×C₁₃	semidirect
179. #2015	C₂×C₁₃	semidirect
180. #1985	C₂×C₁₃	semidirect
182. #1877	C₂×C₁₃	semidirect
183. #1864	C₂×C₁₃	semidirect
184. #1805	C₂×C₁₃	semidirect
428. C₁₃	#24202	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#559	2
C₂×C₁₃×#460	2
C₂×C₁₃×#441	2
C₁₃×#2581	2
C₁₃×#2042	2
C₁₃×#2015	2
C₁₃×#1985	2
C₁₃×#1961	2
C₁₃×#1877	2
C₁₃×#1864	2
C₁₃×#1805	2
#24202	13

Subgroups — C13×#24202 #15710541

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24202 #15710541