Subgroups — C₁₃×#25894 #15712233

Order 3328.

1260 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#491	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#479	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2562	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2036	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2035	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1981	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1955	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#1787	C₂	1	2	yes	maximal, complemented
10	C₁₃×#1787	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1763	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×Q₈×C₁₃	C₂²	1	2	yes	—
13	D₄×Q₈×C₁₃	—	2	4	no	—
14	D₄×Q₈×C₁₃	—	2	4	no	—
15	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
16	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
19	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
20	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₁₃	—	2	1	no	—
22	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
23	C₁₃×#491	—	2	4	no	—
24	C₁₃×#479	—	2	4	no	—
25	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#103	C₂²	1	2	yes	—
29	C₂×C₁₃×#103	C₂²	1	2	yes	—
30	C₂×C₁₃×#103	C₂²	1	2	yes	—
31	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×#103	C₂²	1	2	yes	—
34	C₂×C₁₃×#103	C₂²	1	2	yes	—
35	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
36	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
37	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
38	C₁₃×#400	—	2	1	no	—
39	C₁₃×#394	—	2	1	no	—
40	C₁₃×#388	—	2	2	no	—
41	C₁₃×#380	C₂²	1	2	yes	—
42	C₁₃×#380	C₂²	1	2	yes	—
43	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
44	C₁₃×#340	C₂²	1	2	yes	—
45	C₂²×Q₈×C₁₃	—	2	4	no	—
46	C₂²×Q₈×C₁₃	—	2	4	no	—
47	C₂²×Q₈×C₁₃	—	2	2	no	—
48	C₂²×Q₈×C₁₃	—	2	4	no	—
49	C₂²×Q₈×C₁₃	—	2	4	no	—
50	C₂²×Q₈×C₁₃	—	4	2	no	—
51	C₂²×Q₈×C₁₃	—	4	2	no	—
52	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
53	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
54	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
55	C₂³×C₄×C₁₃	—	2	2	no	—
56	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
57	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
58	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
59	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
60	C₁₃×C₄⋊Q₈	—	2	8	no	—
61	C₁₃×C₄⋊Q₈	—	2	2	no	—
62	C₁₃×C₄⋊Q₈	D₄	1	4	yes	—
63	C₁₃×#125	—	2	2	no	—
64	C₁₃×#125	—	2	2	no	—
65	C₁₃×C₂²⋊Q₈	—	2	16	no	—
66	C₁₃×C₂²⋊Q₈	—	2	4	no	—
67	C₁₃×C₂²⋊Q₈	—	2	4	no	—
68	C₄×Q₈×C₁₃	—	2	2	no	—
69	C₄×Q₈×C₁₃	D₄	1	4	yes	—
70	C₄×D₄×C₁₃	—	2	8	no	—
71	C₄×D₄×C₁₃	—	2	2	no	—
72	C₄×D₄×C₁₃	—	2	2	no	—
73	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
74	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
75	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
76	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
77	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
78	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
79	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
80	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
81	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
88	C₂×C₄²×C₁₃	—	2	1	no	—
89	C₂×C₄²×C₁₃	—	2	1	no	—
90	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
91	C₁₃×#107	—	2	2	no	—
92	C₁₃×#106	—	2	2	no	—
93	C₁₃×C₄⋊C₈	—	2	2	no	—
94	C₁₃×#103	—	2	2	no	—
95	C₁₃×#103	—	2	2	no	—
96	C₁₃×#103	—	2	4	no	—
97	C₁₃×#103	—	2	4	no	—
98	C₁₃×#103	—	2	4	no	—
99	C₁₃×#103	—	4	2	no	—
100	C₁₃×#103	—	4	2	no	—
101	C₁₃×C₂²⋊C₈	—	4	2	no	—
102	C₁₃×C₂²⋊C₈	—	4	2	no	—
103	C₁₃×#97	—	2	2	no	—
104	C₁₃×#95	—	2	1	no	—
105	C₁₃×#95	—	2	2	no	—
106	C₁₃×#95	—	2	2	no	—
107	#25894	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
108	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
109	C₂×Q₈×C₁₃	—	2	8	no	—
110	C₂×Q₈×C₁₃	—	2	1	no	—
111	C₂×Q₈×C₁₃	—	2	2	no	—
112	C₂×Q₈×C₁₃	—	2	2	no	—
113	C₂×Q₈×C₁₃	—	2	2	no	—
114	C₂×Q₈×C₁₃	—	2	2	no	—
115	C₂×Q₈×C₁₃	—	2	2	no	—
116	C₂×Q₈×C₁₃	—	2	2	no	—
117	C₂×Q₈×C₁₃	—	4	4	no	—
118	C₂×Q₈×C₁₃	—	4	4	no	—
119	C₂×Q₈×C₁₃	—	4	8	no	—
120	C₂×Q₈×C₁₃	—	4	8	no	—
121	C₂×Q₈×C₁₃	—	4	8	no	—
122	C₂×Q₈×C₁₃	—	4	8	no	—
123	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
124	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
125	C₂×Q₈×C₁₃	#41	1	4	yes	—
126	C₂×D₄×C₁₃	—	2	4	no	—
127	C₂×D₄×C₁₃	—	2	2	no	—
128	C₂²×C₄×C₁₃	—	2	1	no	—
129	C₂²×C₄×C₁₃	—	2	8	no	—
130	C₂²×C₄×C₁₃	—	2	1	no	—
131	C₂²×C₄×C₁₃	—	2	2	no	—
132	C₂²×C₄×C₁₃	—	2	2	no	—
133	C₂²×C₄×C₁₃	—	2	2	no	—
134	C₂²×C₄×C₁₃	—	2	2	no	—
135	C₂²×C₄×C₁₃	—	2	2	no	—
136	C₂²×C₄×C₁₃	—	2	2	no	—
137	C₂²×C₄×C₁₃	—	2	2	no	—
138	C₂²×C₄×C₁₃	—	2	2	no	—
139	C₂²×C₄×C₁₃	—	2	1	no	—
140	C₂²×C₄×C₁₃	—	2	1	no	—
141	C₂²×C₄×C₁₃	—	4	4	no	—
142	C₂²×C₄×C₁₃	—	4	4	no	—
143	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
144	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
147	C₂×C₈×C₁₃	—	2	2	no	—
148	C₂×C₈×C₁₃	—	2	1	no	—
149	C₂×C₈×C₁₃	—	2	1	no	—
150	C₂×C₈×C₁₃	—	2	2	no	—
151	C₂×C₈×C₁₃	—	2	2	no	—
152	C₂×C₈×C₁₃	—	2	2	no	—
153	C₂×C₈×C₁₃	—	2	2	no	—
154	C₁₃×C₄⋊C₄	—	2	8	no	—
155	C₁₃×C₄⋊C₄	—	2	4	no	—
156	C₁₃×C₄⋊C₄	—	2	4	no	—
157	C₁₃×C₄⋊C₄	—	2	4	no	—
158	C₁₃×C₄⋊C₄	—	2	2	no	—
159	C₁₃×C₄⋊C₄	—	2	1	no	—
160	C₁₃×C₄⋊C₄	—	2	1	no	—
161	C₁₃×C₄⋊C₄	—	2	1	no	—
162	C₁₃×C₄⋊C₄	—	2	1	no	—
163	C₁₃×C₄⋊C₄	—	2	1	no	—
164	C₁₃×C₄⋊C₄	—	2	2	no	—
165	C₁₃×C₄⋊C₄	—	2	2	no	—
166	C₁₃×C₄⋊C₄	—	4	2	no	—
167	C₁₃×C₄⋊C₄	—	4	2	no	—
168	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
169	C₁₃×C₂²⋊C₄	—	2	8	no	—
170	C₁₃×C₂²⋊C₄	—	2	4	no	—
171	C₁₃×C₂²⋊C₄	—	4	4	no	—
172	C₁₃×C₂²⋊C₄	—	8	2	no	—
173	C₄²×C₁₃	—	2	4	no	—
174	C₄²×C₁₃	—	8	1	no	—
175	C₄²×C₁₃	C₂×D₄	1	2	yes	—
176	C₄²×C₁₃	C₂×D₄	1	2	yes	—
177	C₂×D₄×Q₈	C₂×C₁₃	1	1	yes	characteristic
178	C₂×#491	C₂×C₁₃	1	1	yes	characteristic, complemented
179	C₂×#479	C₂×C₁₃	1	1	yes	characteristic, complemented
180	#2562	C₂×C₁₃	1	1	yes	characteristic
181	#2036	C₂×C₁₃	1	2	yes	complemented
182	#2035	C₂×C₁₃	1	2	yes	complemented
183	#1981	C₂×C₁₃	1	1	yes	characteristic, complemented
184	#1955	C₂×C₁₃	1	1	yes	characteristic
185	#1787	C₂×C₁₃	1	2	yes	complemented
186	#1787	C₂×C₁₃	1	2	yes	complemented
187	#1763	C₂×C₁₃	1	1	yes	characteristic, complemented
188	C₂³×C₁₃	—	2	2	no	—
189	C₂³×C₁₃	—	2	2	no	—
190	C₂³×C₁₃	—	2	2	no	—
191	C₂³×C₁₃	—	2	2	no	—
192	C₂³×C₁₃	—	2	2	no	—
193	C₂³×C₁₃	—	2	2	no	—
194	C₂³×C₁₃	#137	1	4	yes	—
195	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
196	Q₈×C₁₃	—	2	2	no	—
197	Q₈×C₁₃	—	2	4	no	—
198	Q₈×C₁₃	—	2	4	no	—
199	Q₈×C₁₃	—	2	4	no	—
200	Q₈×C₁₃	—	4	16	no	—
201	Q₈×C₁₃	—	4	2	no	—
202	Q₈×C₁₃	—	4	2	no	—
203	Q₈×C₁₃	#124	1	4	yes	—
204	D₄×C₁₃	—	2	8	no	—
205	C₂×C₄×C₁₃	—	2	2	no	—
206	C₂×C₄×C₁₃	—	2	4	no	—
207	C₂×C₄×C₁₃	—	2	2	no	—
208	C₂×C₄×C₁₃	—	2	1	no	—
209	C₂×C₄×C₁₃	—	2	1	no	—
210	C₂×C₄×C₁₃	—	2	2	no	—
211	C₂×C₄×C₁₃	—	2	4	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	—	4	16	no	—
216	C₂×C₄×C₁₃	—	4	2	no	—
217	C₂×C₄×C₁₃	—	4	2	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	2	no	—
222	C₂×C₄×C₁₃	—	4	2	no	—
223	C₂×C₄×C₁₃	—	4	2	no	—
224	C₂×C₄×C₁₃	—	4	1	no	—
225	C₂×C₄×C₁₃	—	4	1	no	—
226	C₂×C₄×C₁₃	—	4	2	no	—
227	C₂×C₄×C₁₃	—	4	2	no	—
228	C₂×C₄×C₁₃	—	4	2	no	—
229	C₂×C₄×C₁₃	—	4	2	no	—
230	C₂×C₄×C₁₃	—	4	1	no	—
231	C₂×C₄×C₁₃	—	4	1	no	—
232	C₂×C₄×C₁₃	#120	1	2	yes	—
233	C₂×C₄×C₁₃	#120	1	2	yes	—
234	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
235	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
236	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
237	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
238	C₈×C₁₃	—	4	1	no	—
239	C₈×C₁₃	—	4	1	no	—
240	C₈×C₁₃	—	4	2	no	—
241	C₂³×Q₈	C₂²×C₁₃	1	2	yes	—
242	D₄×Q₈	—	2	4	no	—
243	D₄×Q₈	—	2	4	no	—
244	C₂×C₄⋊Q₈	—	2	1	no	—
245	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
246	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
247	C₂×C₂²⋊Q₈	—	2	2	no	—
248	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
249	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
250	C₂×C₄×D₄	—	2	1	no	—
251	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
252	#491	—	2	4	no	—
253	#479	—	2	4	no	—
254	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
255	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
256	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
257	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
258	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
259	C₂×#103	C₂²×C₁₃	1	2	yes	—
260	C₂×#103	C₂²×C₁₃	1	2	yes	—
261	C₂×#103	C₂²×C₁₃	1	2	yes	—
262	C₂×#103	C₂²×C₁₃	1	2	yes	—
263	C₂×#103	C₂²×C₁₃	1	2	yes	—
264	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
265	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
266	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
267	#400	—	2	1	no	—
268	#394	—	2	1	no	—
269	#388	—	2	2	no	—
270	#380	C₂²×C₁₃	1	2	yes	—
271	#380	C₂²×C₁₃	1	2	yes	—
272	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
273	#340	C₂²×C₁₃	1	2	yes	—
274	C₂²×C₁₃	—	2	4	no	—
275	C₂²×C₁₃	—	2	4	no	—
276	C₂²×C₁₃	—	2	4	no	—
277	C₂²×C₁₃	—	4	2	no	—
278	C₂²×C₁₃	—	4	2	no	—
279	C₂²×C₁₃	—	4	2	no	—
280	C₂²×C₁₃	—	4	2	no	—
281	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
282	C₂²×C₁₃	#546	1	2	yes	—
283	C₂²×C₁₃	C₂×#137	1	2	yes	—
284	C₂²×C₁₃	#577	1	1	yes	characteristic
285	C₂²×C₁₃	#578	1	1	yes	characteristic
286	C₄×C₁₃	—	2	4	no	—
287	C₄×C₁₃	—	2	2	no	—
288	C₄×C₁₃	—	2	2	no	—
289	C₄×C₁₃	—	4	2	no	—
290	C₄×C₁₃	—	4	4	no	—
291	C₄×C₁₃	—	4	2	no	—
292	C₄×C₁₃	—	8	1	no	—
293	C₄×C₁₃	—	8	1	no	—
294	C₄×C₁₃	—	8	2	no	—
295	C₄×C₁₃	C₂×#124	1	1	yes	characteristic
296	C₄×C₁₃	#535	1	1	yes	characteristic
297	C₄×C₁₃	#546	1	2	yes	—
298	C₂²×Q₈	—	2	4	no	—
299	C₂²×Q₈	—	2	4	no	—
300	C₂²×Q₈	—	2	2	no	—
301	C₂²×Q₈	—	2	4	no	—
302	C₂²×Q₈	—	2	4	no	—
303	C₂²×Q₈	—	4	2	no	—
304	C₂²×Q₈	—	4	2	no	—
305	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
306	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
307	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
308	C₂³×C₄	—	2	2	no	—
309	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
310	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
311	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
312	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
313	C₄⋊Q₈	—	2	8	no	—
314	C₄⋊Q₈	—	2	2	no	—
315	C₄⋊Q₈	D₄×C₁₃	1	4	yes	—
316	#125	—	2	2	no	—
317	#125	—	2	2	no	—
318	C₂²⋊Q₈	—	2	16	no	—
319	C₂²⋊Q₈	—	2	4	no	—
320	C₂²⋊Q₈	—	2	4	no	—
321	C₄×Q₈	—	2	2	no	—
322	C₄×Q₈	D₄×C₁₃	1	4	yes	—
323	C₄×D₄	—	2	8	no	—
324	C₄×D₄	—	2	2	no	—
325	C₄×D₄	—	2	2	no	—
326	C₂×C₄⋊C₄	—	2	1	no	—
327	C₂×C₄⋊C₄	—	2	1	no	—
328	C₂×C₄⋊C₄	—	2	1	no	—
329	C₂×C₄⋊C₄	—	2	2	no	—
330	C₂×C₄⋊C₄	—	2	1	no	—
331	C₂×C₄⋊C₄	—	2	1	no	—
332	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
333	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
334	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
335	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
336	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
337	C₂×C₂²⋊C₄	—	2	2	no	—
338	C₂×C₂²⋊C₄	—	2	2	no	—
339	C₂×C₂²⋊C₄	—	2	2	no	—
340	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
341	C₂×C₄²	—	2	1	no	—
342	C₂×C₄²	—	2	1	no	—
343	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
344	#107	—	2	2	no	—
345	#106	—	2	2	no	—
346	C₄⋊C₈	—	2	2	no	—
347	#103	—	2	2	no	—
348	#103	—	2	2	no	—
349	#103	—	2	4	no	—
350	#103	—	2	4	no	—
351	#103	—	2	4	no	—
352	#103	—	4	2	no	—
353	#103	—	4	2	no	—
354	C₂²⋊C₈	—	4	2	no	—
355	C₂²⋊C₈	—	4	2	no	—
356	#97	—	2	2	no	—
357	#95	—	2	1	no	—
358	#95	—	2	2	no	—
359	#95	—	2	2	no	—
360	C₂×C₁₃	—	4	4	no	—
361	C₂×C₁₃	#2435	1	1	yes	characteristic
362	C₂×C₁₃	#3004	1	1	yes	characteristic
363	C₂×C₁₃	#3013	1	1	yes	characteristic
364	C₂×C₁₃	#3312	1	2	yes	—
365	C₂×C₁₃	#3320	1	2	yes	—
366	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
367	C₂×Q₈	—	2	8	no	—
368	C₂×Q₈	—	2	1	no	—
369	C₂×Q₈	—	2	2	no	—
370	C₂×Q₈	—	2	2	no	—
371	C₂×Q₈	—	2	2	no	—
372	C₂×Q₈	—	2	2	no	—
373	C₂×Q₈	—	2	2	no	—
374	C₂×Q₈	—	2	2	no	—
375	C₂×Q₈	—	4	4	no	—
376	C₂×Q₈	—	4	4	no	—
377	C₂×Q₈	—	4	8	no	—
378	C₂×Q₈	—	4	8	no	—
379	C₂×Q₈	—	4	8	no	—
380	C₂×Q₈	—	4	8	no	—
381	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
382	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
383	C₂×Q₈	C₁₃×#41	1	4	yes	—
384	C₂×D₄	—	2	4	no	—
385	C₂×D₄	—	2	2	no	—
386	C₂²×C₄	—	2	1	no	—
387	C₂²×C₄	—	2	8	no	—
388	C₂²×C₄	—	2	1	no	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	2	2	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	—	2	2	no	—
394	C₂²×C₄	—	2	2	no	—
395	C₂²×C₄	—	2	2	no	—
396	C₂²×C₄	—	2	2	no	—
397	C₂²×C₄	—	2	1	no	—
398	C₂²×C₄	—	2	1	no	—
399	C₂²×C₄	—	4	4	no	—
400	C₂²×C₄	—	4	4	no	—
401	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
402	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
403	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
404	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
405	C₂×C₈	—	2	2	no	—
406	C₂×C₈	—	2	1	no	—
407	C₂×C₈	—	2	1	no	—
408	C₂×C₈	—	2	2	no	—
409	C₂×C₈	—	2	2	no	—
410	C₂×C₈	—	2	2	no	—
411	C₂×C₈	—	2	2	no	—
412	C₄⋊C₄	—	2	8	no	—
413	C₄⋊C₄	—	2	4	no	—
414	C₄⋊C₄	—	2	4	no	—
415	C₄⋊C₄	—	2	4	no	—
416	C₄⋊C₄	—	2	2	no	—
417	C₄⋊C₄	—	2	1	no	—
418	C₄⋊C₄	—	2	1	no	—
419	C₄⋊C₄	—	2	1	no	—
420	C₄⋊C₄	—	2	1	no	—
421	C₄⋊C₄	—	2	1	no	—
422	C₄⋊C₄	—	2	2	no	—
423	C₄⋊C₄	—	2	2	no	—
424	C₄⋊C₄	—	4	2	no	—
425	C₄⋊C₄	—	4	2	no	—
426	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
427	C₂²⋊C₄	—	2	8	no	—
428	C₂²⋊C₄	—	2	4	no	—
429	C₂²⋊C₄	—	4	4	no	—
430	C₂²⋊C₄	—	8	2	no	—
431	C₄²	—	2	4	no	—
432	C₄²	—	8	1	no	—
433	C₄²	C₂×D₄×C₁₃	1	2	yes	—
434	C₄²	C₂×D₄×C₁₃	1	2	yes	—
435	C₁₃	#25894	1	1	yes	characteristic, direct product factor, Sylow
436	C₂³	—	2	2	no	—
437	C₂³	—	2	2	no	—
438	C₂³	—	2	2	no	—
439	C₂³	—	2	2	no	—
440	C₂³	—	2	2	no	—
441	C₂³	—	2	2	no	—
442	C₂³	C₁₃×#137	1	4	yes	—
443	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
444	Q₈	—	2	2	no	—
445	Q₈	—	2	4	no	—
446	Q₈	—	2	4	no	—
447	Q₈	—	2	4	no	—
448	Q₈	—	4	16	no	—
449	Q₈	—	4	2	no	—
450	Q₈	—	4	2	no	—
451	Q₈	C₁₃×#124	1	4	yes	—
452	D₄	—	2	8	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	4	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	1	no	—
457	C₂×C₄	—	2	1	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	4	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	4	16	no	—
464	C₂×C₄	—	4	2	no	—
465	C₂×C₄	—	4	2	no	—
466	C₂×C₄	—	4	1	no	—
467	C₂×C₄	—	4	1	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	—	4	2	no	—
470	C₂×C₄	—	4	2	no	—
471	C₂×C₄	—	4	2	no	—
472	C₂×C₄	—	4	1	no	—
473	C₂×C₄	—	4	1	no	—
474	C₂×C₄	—	4	2	no	—
475	C₂×C₄	—	4	2	no	—
476	C₂×C₄	—	4	2	no	—
477	C₂×C₄	—	4	2	no	—
478	C₂×C₄	—	4	1	no	—
479	C₂×C₄	—	4	1	no	—
480	C₂×C₄	C₁₃×#120	1	2	yes	—
481	C₂×C₄	C₁₃×#120	1	2	yes	—
482	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
483	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
484	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
485	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
486	C₈	—	4	1	no	—
487	C₈	—	4	1	no	—
488	C₈	—	4	2	no	—
489	C₂²	—	2	4	no	—
490	C₂²	—	2	4	no	—
491	C₂²	—	2	4	no	—
492	C₂²	—	4	2	no	—
493	C₂²	—	4	2	no	—
494	C₂²	—	4	2	no	—
495	C₂²	—	4	2	no	—
496	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
497	C₂²	C₁₃×#546	1	2	yes	—
498	C₂²	C₂×C₁₃×#137	1	2	yes	—
499	C₂²	C₁₃×#577	1	1	yes	characteristic
500	C₂²	C₁₃×#578	1	1	yes	characteristic
501	C₄	—	2	2	no	—
502	C₄	—	2	4	no	—
503	C₄	—	2	2	no	—
504	C₄	—	4	2	no	—
505	C₄	—	4	2	no	—
506	C₄	—	4	4	no	—
507	C₄	—	8	1	no	—
508	C₄	—	8	2	no	—
509	C₄	—	8	1	no	—
510	C₄	C₂×C₁₃×#124	1	1	yes	characteristic
511	C₄	C₁₃×#535	1	1	yes	characteristic
512	C₄	C₁₃×#546	1	2	yes	—
513	C₂	—	4	4	no	—
514	C₂	C₁₃×#2435	1	1	yes	characteristic
515	C₂	C₁₃×#3004	1	1	yes	characteristic
516	C₂	C₁₃×#3013	1	1	yes	characteristic
517	C₂	C₁₃×#3312	1	2	yes	—
518	C₂	C₁₃×#3320	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#491	C₂	semidirect
3. C₂×C₁₃×#479	C₂	semidirect
5. C₁₃×#2036	C₂	semidirect
6. C₁₃×#2035	C₂	semidirect
7. C₁₃×#1981	C₂	semidirect
9. C₁₃×#1787	C₂	semidirect
10. C₁₃×#1787	C₂	semidirect
11. C₁₃×#1763	C₂	semidirect
107. #25894	C₁₃	direct (N × H)
178. C₂×#491	C₂×C₁₃	semidirect
179. C₂×#479	C₂×C₁₃	semidirect
181. #2036	C₂×C₁₃	semidirect
182. #2035	C₂×C₁₃	semidirect
183. #1981	C₂×C₁₃	semidirect
185. #1787	C₂×C₁₃	semidirect
186. #1787	C₂×C₁₃	semidirect
187. #1763	C₂×C₁₃	semidirect
435. C₁₃	#25894	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×D₄×Q₈×C₁₃	2
C₂×C₁₃×#491	2
C₂×C₁₃×#479	2
C₁₃×#2562	2
C₁₃×#2036	2
C₁₃×#2035	2
C₁₃×#1981	2
C₁₃×#1955	2
C₁₃×#1787	2
C₁₃×#1763	2
#25894	13

Subgroups — C13×#25894 #15712233

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#25894 #15712233