Subgroups — C₁₃×#61585 #15747924

Order 3328.

2378 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3496	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#547	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3330	C₂	1	8	yes	maximal, complemented
4	C₁₃×#3272	C₂	1	8	yes	maximal, complemented
5	C₁₃×#3206	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3193	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3100	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3006	C₂	1	4	yes	maximal, complemented
9	C₁₃×#2975	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×H(5,𝔽₂)	—	2	1	no	—
11	C₂²×C₁₃×#41	C₂²	1	2	yes	complemented
12	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	8	yes	complemented
13	C₁₃×#547	—	2	4	no	—
14	C₁₃×#547	C₂²	1	8	yes	complemented
15	C₁₃×#547	C₂²	1	4	yes	complemented
16	C₁₃×#546	—	2	4	no	—
17	D₄²×C₁₃	C₂²	1	4	yes	complemented
18	C₁₃×#537	—	2	1	no	—
19	C₁₃×#534	—	2	2	no	—
20	C₁₃×#532	C₂²	1	2	yes	—
21	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₁₃×#123	—	2	2	no	—
23	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
24	C₂×C₁₃×#121	—	2	1	no	—
25	C₂×C₁₃×#121	C₂²	1	4	yes	—
26	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
28	C₂²×C₁₃×C₄⋊C₄	—	2	1	no	—
29	C₁₃×#492	C₂²	1	4	yes	complemented
30	C₁₃×#487	C₂²	1	4	yes	complemented
31	C₁₃×#484	C₂²	1	8	yes	complemented
32	C₁₃×#480	C₂²	1	4	yes	complemented
33	C₁₃×#474	C₂²	1	4	yes	complemented
34	C₁₃×#468	C₂²	1	16	yes	complemented
35	C₁₃×#461	C₂²	1	8	yes	complemented
36	C₁₃×#459	C₂²	1	4	yes	complemented
37	C₁₃×#450	C₂²	1	8	yes	complemented
38	C₁₃×#449	C₂²	1	16	yes	complemented
39	C₁₃×#448	C₂²	1	8	yes	complemented
40	C₁₃×#447	C₂²	1	4	yes	complemented
41	C₄×C₁₃×D₈	C₂²	1	8	yes	complemented
42	C₁₃×#436	C₂²	1	8	yes	complemented
43	C₁₃×#431	C₂²	1	2	yes	complemented
44	C₁₃×#417	C₂²	1	8	yes	complemented
45	C₁₃×#407	C₂²	1	4	yes	complemented
46	C₁₃×H(5,𝔽₂)	—	4	8	no	—
47	C₂×C₁₃×#41	—	2	4	no	—
48	C₂×C₁₃×#41	—	2	2	no	—
49	C₂×C₁₃×#41	—	2	4	no	—
50	C₂×C₁₃×#41	—	4	8	no	—
51	C₂×C₁₃×#41	C₂³	1	8	yes	—
52	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
53	C₂²×D₄×C₁₃	—	2	2	no	—
54	C₂²×D₄×C₁₃	—	2	4	no	—
55	C₂²×D₄×C₁₃	—	2	4	no	—
56	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
57	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
58	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
59	C₂³×C₄×C₁₃	—	2	1	no	—
60	C₂³×C₄×C₁₃	—	2	2	no	—
61	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
62	C₁₃×AGL(1,ℤ/8)	—	4	16	no	—
63	C₂×C₁₃×SD₁₆	C₂³	1	16	yes	—
64	C₂×C₁₃×D₈	C₂³	1	8	yes	—
65	C₂×C₁₃×M₁₆	C₂³	1	8	yes	—
66	C₁₃×C₄⋊Q₈	—	2	2	no	—
67	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
68	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
69	C₁₃×#127	C₂³	1	2	yes	—
70	C₁₃×#124	—	2	2	no	—
71	C₁₃×#123	—	2	16	no	—
72	C₁₃×#123	—	2	8	no	—
73	C₁₃×C₂²⋊Q₈	—	2	4	no	—
74	C₁₃×C₂²⋊Q₈	—	2	4	no	—
75	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
76	C₁₃×#121	—	2	8	no	—
77	C₁₃×#121	—	2	4	no	—
78	C₁₃×#121	—	2	4	no	—
79	C₁₃×#121	—	2	2	no	—
80	C₁₃×#121	—	2	4	no	—
81	C₁₃×#121	C₂³	1	4	yes	—
82	C₁₃×#121	C₂³	1	8	yes	—
83	C₁₃×#120	—	2	8	no	—
84	C₄×D₄×C₁₃	—	2	2	no	—
85	C₄×D₄×C₁₃	—	2	2	no	—
86	C₄×D₄×C₁₃	D₄	1	4	yes	—
87	C₄×D₄×C₁₃	C₂³	1	4	yes	—
88	C₄×D₄×C₁₃	C₂³	1	4	yes	—
89	C₄×D₄×C₁₃	C₂³	1	4	yes	—
90	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
91	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
92	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
93	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
94	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
95	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
96	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
97	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
98	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
99	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
100	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
101	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
102	C₁₃×#107	C₂³	1	8	yes	—
103	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
104	C₁₃×#103	C₂³	1	16	yes	—
105	C₁₃×#102	C₂³	1	8	yes	—
106	C₁₃×#102	C₂³	1	8	yes	—
107	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
108	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	—
109	C₄×C₈×C₁₃	C₂³	1	4	yes	—
110	#61585	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
111	C₂⁴×C₁₃	—	2	1	no	—
112	C₂⁴×C₁₃	—	2	4	no	—
113	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
114	C₁₃×#41	—	2	16	no	—
115	C₁₃×#41	—	4	8	no	—
116	C₁₃×#41	—	4	16	no	—
117	C₁₃×#41	—	4	16	no	—
118	C₁₃×#41	—	4	8	no	—
119	C₂×Q₈×C₁₃	—	2	2	no	—
120	C₂×Q₈×C₁₃	—	2	2	no	—
121	C₂×Q₈×C₁₃	—	4	4	no	—
122	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
123	C₂×D₄×C₁₃	—	2	4	no	—
124	C₂×D₄×C₁₃	—	2	8	no	—
125	C₂×D₄×C₁₃	—	2	4	no	—
126	C₂×D₄×C₁₃	—	2	8	no	—
127	C₂×D₄×C₁₃	—	2	4	no	—
128	C₂×D₄×C₁₃	—	2	1	no	—
129	C₂×D₄×C₁₃	—	2	2	no	—
130	C₂×D₄×C₁₃	—	2	2	no	—
131	C₂×D₄×C₁₃	—	2	4	no	—
132	C₂×D₄×C₁₃	—	4	8	no	—
133	C₂×D₄×C₁₃	—	4	16	no	—
134	C₂×D₄×C₁₃	—	4	8	no	—
135	C₂×D₄×C₁₃	—	4	16	no	—
136	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
137	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
138	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
139	C₂²×C₄×C₁₃	—	2	1	no	—
140	C₂²×C₄×C₁₃	—	2	2	no	—
141	C₂²×C₄×C₁₃	—	2	4	no	—
142	C₂²×C₄×C₁₃	—	2	4	no	—
143	C₂²×C₄×C₁₃	—	2	8	no	—
144	C₂²×C₄×C₁₃	—	2	4	no	—
145	C₂²×C₄×C₁₃	—	4	4	no	—
146	C₂²×C₄×C₁₃	—	4	8	no	—
147	C₂²×C₄×C₁₃	—	4	4	no	—
148	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
150	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
151	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
153	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
154	C₁₃×SD₁₆	—	4	16	no	—
155	C₁₃×D₈	—	2	16	no	—
156	C₁₃×M₁₆	—	4	8	no	—
157	C₂×C₈×C₁₃	C₂⁴	1	8	yes	—
158	C₁₃×C₄⋊C₄	—	2	4	no	—
159	C₁₃×C₄⋊C₄	—	2	8	no	—
160	C₁₃×C₄⋊C₄	—	2	4	no	—
161	C₁₃×C₄⋊C₄	—	2	1	no	—
162	C₁₃×C₄⋊C₄	—	2	4	no	—
163	C₁₃×C₄⋊C₄	—	2	2	no	—
164	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
165	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
166	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
167	C₁₃×C₂²⋊C₄	—	2	8	no	—
168	C₁₃×C₂²⋊C₄	—	2	4	no	—
169	C₁₃×C₂²⋊C₄	—	2	4	no	—
170	C₁₃×C₂²⋊C₄	—	2	8	no	—
171	C₁₃×C₂²⋊C₄	—	2	4	no	—
172	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
173	C₄²×C₁₃	C₂×D₄	1	2	yes	—
174	C₄²×C₁₃	C₂⁴	1	2	yes	—
175	#3496	C₂×C₁₃	1	1	yes	characteristic, complemented
176	C₂×#547	C₂×C₁₃	1	1	yes	characteristic, complemented
177	#3330	C₂×C₁₃	1	8	yes	complemented
178	#3272	C₂×C₁₃	1	8	yes	complemented
179	#3206	C₂×C₁₃	1	2	yes	complemented
180	#3193	C₂×C₁₃	1	4	yes	complemented
181	#3100	C₂×C₁₃	1	2	yes	complemented
182	#3006	C₂×C₁₃	1	4	yes	complemented
183	#2975	C₂×C₁₃	1	1	yes	characteristic, complemented
184	C₂³×C₁₃	—	2	4	no	—
185	C₂³×C₁₃	—	2	2	no	—
186	C₂³×C₁₃	—	2	4	no	—
187	C₂³×C₁₃	—	2	4	no	—
188	C₂³×C₁₃	—	4	2	no	—
189	C₂³×C₁₃	—	4	2	no	—
190	C₂³×C₁₃	—	4	2	no	—
191	C₂³×C₁₃	—	4	8	no	—
192	C₂³×C₁₃	—	4	2	no	—
193	C₂³×C₁₃	—	8	4	no	—
194	C₂³×C₁₃	—	8	4	no	—
195	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
196	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
197	Q₈×C₁₃	—	2	8	no	—
198	Q₈×C₁₃	—	4	4	no	—
199	Q₈×C₁₃	—	4	4	no	—
200	D₄×C₁₃	—	2	4	no	—
201	D₄×C₁₃	—	2	8	no	—
202	D₄×C₁₃	—	2	2	no	—
203	D₄×C₁₃	—	2	8	no	—
204	D₄×C₁₃	—	4	16	no	—
205	D₄×C₁₃	—	4	16	no	—
206	D₄×C₁₃	—	4	8	no	—
207	D₄×C₁₃	—	4	4	no	—
208	D₄×C₁₃	—	8	2	no	—
209	D₄×C₁₃	—	8	4	no	—
210	D₄×C₁₃	H(5,𝔽₂)	1	4	yes	complemented
211	C₂×C₄×C₁₃	—	2	8	no	—
212	C₂×C₄×C₁₃	—	2	2	no	—
213	C₂×C₄×C₁₃	—	2	2	no	—
214	C₂×C₄×C₁₃	—	2	4	no	—
215	C₂×C₄×C₁₃	—	2	4	no	—
216	C₂×C₄×C₁₃	—	4	2	no	—
217	C₂×C₄×C₁₃	—	4	4	no	—
218	C₂×C₄×C₁₃	—	4	1	no	—
219	C₂×C₄×C₁₃	—	4	16	no	—
220	C₂×C₄×C₁₃	—	4	4	no	—
221	C₂×C₄×C₁₃	—	4	8	no	—
222	C₂×C₄×C₁₃	—	4	2	no	—
223	C₂×C₄×C₁₃	—	4	8	no	—
224	C₂×C₄×C₁₃	—	4	8	no	—
225	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	4	yes	complemented
226	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
227	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
228	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
229	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
230	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
231	C₈×C₁₃	—	2	8	no	—
232	C₂×H(5,𝔽₂)	—	2	1	no	—
233	C₂²×#41	C₂²×C₁₃	1	2	yes	complemented
234	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	8	yes	complemented
235	#547	—	2	4	no	—
236	#547	C₂²×C₁₃	1	8	yes	complemented
237	#547	C₂²×C₁₃	1	4	yes	complemented
238	#546	—	2	4	no	—
239	D₄²	C₂²×C₁₃	1	4	yes	complemented
240	#537	—	2	1	no	—
241	#534	—	2	2	no	—
242	#532	C₂²×C₁₃	1	2	yes	—
243	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
244	C₂×#123	—	2	2	no	—
245	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
246	C₂×#121	—	2	1	no	—
247	C₂×#121	C₂²×C₁₃	1	4	yes	—
248	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
249	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
250	C₂²×C₄⋊C₄	—	2	1	no	—
251	#492	C₂²×C₁₃	1	4	yes	complemented
252	#487	C₂²×C₁₃	1	4	yes	complemented
253	#484	C₂²×C₁₃	1	8	yes	complemented
254	#480	C₂²×C₁₃	1	4	yes	complemented
255	#474	C₂²×C₁₃	1	4	yes	complemented
256	#468	C₂²×C₁₃	1	16	yes	complemented
257	#461	C₂²×C₁₃	1	8	yes	complemented
258	#459	C₂²×C₁₃	1	4	yes	complemented
259	#450	C₂²×C₁₃	1	8	yes	complemented
260	#449	C₂²×C₁₃	1	16	yes	complemented
261	#448	C₂²×C₁₃	1	8	yes	complemented
262	#447	C₂²×C₁₃	1	4	yes	complemented
263	C₄×D₈	C₂²×C₁₃	1	8	yes	complemented
264	#436	C₂²×C₁₃	1	8	yes	complemented
265	#431	C₂²×C₁₃	1	2	yes	complemented
266	#417	C₂²×C₁₃	1	8	yes	complemented
267	#407	C₂²×C₁₃	1	4	yes	complemented
268	C₂²×C₁₃	—	2	1	no	—
269	C₂²×C₁₃	—	2	1	no	—
270	C₂²×C₁₃	—	2	4	no	—
271	C₂²×C₁₃	—	2	4	no	—
272	C₂²×C₁₃	—	2	4	no	—
273	C₂²×C₁₃	—	2	4	no	—
274	C₂²×C₁₃	—	4	8	no	—
275	C₂²×C₁₃	—	4	2	no	—
276	C₂²×C₁₃	—	4	2	no	—
277	C₂²×C₁₃	—	4	4	no	—
278	C₂²×C₁₃	—	4	4	no	—
279	C₂²×C₁₃	—	4	4	no	—
280	C₂²×C₁₃	—	8	4	no	—
281	C₂²×C₁₃	—	16	8	no	—
282	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
283	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
284	C₄×C₁₃	—	2	2	no	—
285	C₄×C₁₃	—	2	4	no	—
286	C₄×C₁₃	—	2	1	no	—
287	C₄×C₁₃	—	4	4	no	—
288	C₄×C₁₃	—	4	2	no	—
289	C₄×C₁₃	—	4	4	no	—
290	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	4	yes	—
291	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
292	H(5,𝔽₂)	—	4	8	no	—
293	C₂×#41	—	2	4	no	—
294	C₂×#41	—	2	2	no	—
295	C₂×#41	—	2	4	no	—
296	C₂×#41	—	4	8	no	—
297	C₂×#41	C₂³×C₁₃	1	8	yes	—
298	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
299	C₂²×D₄	—	2	2	no	—
300	C₂²×D₄	—	2	4	no	—
301	C₂²×D₄	—	2	4	no	—
302	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
303	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
304	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
305	C₂³×C₄	—	2	1	no	—
306	C₂³×C₄	—	2	2	no	—
307	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
308	AGL(1,ℤ/8)	—	4	16	no	—
309	C₂×SD₁₆	C₂³×C₁₃	1	16	yes	—
310	C₂×D₈	C₂³×C₁₃	1	8	yes	—
311	C₂×M₁₆	C₂³×C₁₃	1	8	yes	—
312	C₄⋊Q₈	—	2	2	no	—
313	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
314	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
315	#127	C₂³×C₁₃	1	2	yes	—
316	#124	—	2	2	no	—
317	#123	—	2	16	no	—
318	#123	—	2	8	no	—
319	C₂²⋊Q₈	—	2	4	no	—
320	C₂²⋊Q₈	—	2	4	no	—
321	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
322	#121	—	2	8	no	—
323	#121	—	2	4	no	—
324	#121	—	2	4	no	—
325	#121	—	2	2	no	—
326	#121	—	2	4	no	—
327	#121	C₂³×C₁₃	1	4	yes	—
328	#121	C₂³×C₁₃	1	8	yes	—
329	#120	—	2	8	no	—
330	C₄×D₄	—	2	2	no	—
331	C₄×D₄	—	2	2	no	—
332	C₄×D₄	D₄×C₁₃	1	4	yes	—
333	C₄×D₄	C₂³×C₁₃	1	4	yes	—
334	C₄×D₄	C₂³×C₁₃	1	4	yes	—
335	C₄×D₄	C₂³×C₁₃	1	4	yes	—
336	C₂×C₄⋊C₄	—	2	1	no	—
337	C₂×C₄⋊C₄	—	2	2	no	—
338	C₂×C₄⋊C₄	—	2	1	no	—
339	C₂×C₄⋊C₄	—	2	8	no	—
340	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
341	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
342	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
343	C₂×C₂²⋊C₄	—	2	2	no	—
344	C₂×C₂²⋊C₄	—	2	1	no	—
345	C₂×C₂²⋊C₄	—	2	4	no	—
346	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
347	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
348	#107	C₂³×C₁₃	1	8	yes	—
349	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
350	#103	C₂³×C₁₃	1	16	yes	—
351	#102	C₂³×C₁₃	1	8	yes	—
352	#102	C₂³×C₁₃	1	8	yes	—
353	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
354	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	—
355	C₄×C₈	C₂³×C₁₃	1	4	yes	—
356	C₂×C₁₃	—	2	2	no	—
357	C₂×C₁₃	—	4	4	no	—
358	C₂×C₁₃	—	4	4	no	—
359	C₂×C₁₃	—	8	4	no	—
360	C₂×C₁₃	#3484	1	1	yes	characteristic
361	C₂×C₁₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
362	C₂×C₁₃	#3586	1	1	yes	characteristic
363	C₂⁴	—	2	1	no	—
364	C₂⁴	—	2	4	no	—
365	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
366	#41	—	2	16	no	—
367	#41	—	4	8	no	—
368	#41	—	4	16	no	—
369	#41	—	4	16	no	—
370	#41	—	4	8	no	—
371	C₂×Q₈	—	2	2	no	—
372	C₂×Q₈	—	2	2	no	—
373	C₂×Q₈	—	4	4	no	—
374	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
375	C₂×D₄	—	2	4	no	—
376	C₂×D₄	—	2	8	no	—
377	C₂×D₄	—	2	4	no	—
378	C₂×D₄	—	2	8	no	—
379	C₂×D₄	—	2	4	no	—
380	C₂×D₄	—	2	1	no	—
381	C₂×D₄	—	2	2	no	—
382	C₂×D₄	—	2	2	no	—
383	C₂×D₄	—	2	4	no	—
384	C₂×D₄	—	4	8	no	—
385	C₂×D₄	—	4	16	no	—
386	C₂×D₄	—	4	8	no	—
387	C₂×D₄	—	4	16	no	—
388	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
389	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
390	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
391	C₂²×C₄	—	2	1	no	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	—	2	4	no	—
394	C₂²×C₄	—	2	4	no	—
395	C₂²×C₄	—	2	8	no	—
396	C₂²×C₄	—	2	4	no	—
397	C₂²×C₄	—	4	4	no	—
398	C₂²×C₄	—	4	8	no	—
399	C₂²×C₄	—	4	4	no	—
400	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
401	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
402	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
403	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
404	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
405	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
406	SD₁₆	—	4	16	no	—
407	D₈	—	2	16	no	—
408	M₁₆	—	4	8	no	—
409	C₂×C₈	C₂⁴×C₁₃	1	8	yes	—
410	C₄⋊C₄	—	2	4	no	—
411	C₄⋊C₄	—	2	8	no	—
412	C₄⋊C₄	—	2	4	no	—
413	C₄⋊C₄	—	2	1	no	—
414	C₄⋊C₄	—	2	4	no	—
415	C₄⋊C₄	—	2	2	no	—
416	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
417	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
418	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
419	C₂²⋊C₄	—	2	8	no	—
420	C₂²⋊C₄	—	2	4	no	—
421	C₂²⋊C₄	—	2	4	no	—
422	C₂²⋊C₄	—	2	8	no	—
423	C₂²⋊C₄	—	2	4	no	—
424	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
425	C₄²	C₂×D₄×C₁₃	1	2	yes	—
426	C₄²	C₂⁴×C₁₃	1	2	yes	—
427	C₁₃	#61585	1	1	yes	characteristic, direct product factor, Sylow
428	C₂³	—	2	4	no	—
429	C₂³	—	2	2	no	—
430	C₂³	—	2	4	no	—
431	C₂³	—	2	4	no	—
432	C₂³	—	4	2	no	—
433	C₂³	—	4	2	no	—
434	C₂³	—	4	2	no	—
435	C₂³	—	4	8	no	—
436	C₂³	—	4	2	no	—
437	C₂³	—	8	4	no	—
438	C₂³	—	8	4	no	—
439	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
440	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
441	Q₈	—	2	8	no	—
442	Q₈	—	4	4	no	—
443	Q₈	—	4	4	no	—
444	D₄	—	2	4	no	—
445	D₄	—	2	8	no	—
446	D₄	—	2	2	no	—
447	D₄	—	2	8	no	—
448	D₄	—	4	16	no	—
449	D₄	—	4	16	no	—
450	D₄	—	4	8	no	—
451	D₄	—	4	4	no	—
452	D₄	—	8	4	no	—
453	D₄	—	8	2	no	—
454	D₄	C₁₃×H(5,𝔽₂)	1	4	yes	complemented
455	C₂×C₄	—	2	8	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	4	no	—
459	C₂×C₄	—	2	4	no	—
460	C₂×C₄	—	4	2	no	—
461	C₂×C₄	—	4	4	no	—
462	C₂×C₄	—	4	1	no	—
463	C₂×C₄	—	4	16	no	—
464	C₂×C₄	—	4	4	no	—
465	C₂×C₄	—	4	8	no	—
466	C₂×C₄	—	4	2	no	—
467	C₂×C₄	—	4	8	no	—
468	C₂×C₄	—	4	8	no	—
469	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	4	yes	complemented
470	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
471	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
472	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
473	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
474	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
475	C₈	—	2	8	no	—
476	C₂²	—	2	1	no	—
477	C₂²	—	2	1	no	—
478	C₂²	—	2	4	no	—
479	C₂²	—	2	4	no	—
480	C₂²	—	2	4	no	—
481	C₂²	—	2	4	no	—
482	C₂²	—	4	8	no	—
483	C₂²	—	4	2	no	—
484	C₂²	—	4	2	no	—
485	C₂²	—	4	4	no	—
486	C₂²	—	4	4	no	—
487	C₂²	—	4	4	no	—
488	C₂²	—	8	4	no	—
489	C₂²	—	16	8	no	—
490	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
491	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
492	C₄	—	2	2	no	—
493	C₄	—	2	4	no	—
494	C₄	—	2	1	no	—
495	C₄	—	4	2	no	—
496	C₄	—	4	4	no	—
497	C₄	—	4	4	no	—
498	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	4	yes	—
499	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
500	C₂	—	2	2	no	—
501	C₂	—	4	4	no	—
502	C₂	—	4	4	no	—
503	C₂	—	8	4	no	—
504	C₂	C₁₃×#3484	1	1	yes	characteristic
505	C₂	C₂²×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
506	C₂	C₁₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄×D₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3496	C₂	semidirect
2. C₂×C₁₃×#547	C₂	semidirect
3. C₁₃×#3330	C₂	semidirect
4. C₁₃×#3272	C₂	semidirect
5. C₁₃×#3206	C₂	semidirect
6. C₁₃×#3193	C₂	semidirect
7. C₁₃×#3100	C₂	semidirect
8. C₁₃×#3006	C₂	semidirect
9. C₁₃×#2975	C₂	semidirect
11. C₂²×C₁₃×#41	C₂²	semidirect
12. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
14. C₁₃×#547	C₂²	semidirect
15. C₁₃×#547	C₂²	semidirect
17. D₄²×C₁₃	C₂²	semidirect
21. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
23. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
27. C₂×C₄×D₄×C₁₃	C₂²	semidirect
29. C₁₃×#492	C₂²	semidirect
30. C₁₃×#487	C₂²	semidirect
31. C₁₃×#484	C₂²	semidirect
32. C₁₃×#480	C₂²	semidirect
33. C₁₃×#474	C₂²	semidirect
34. C₁₃×#468	C₂²	semidirect
35. C₁₃×#461	C₂²	semidirect
36. C₁₃×#459	C₂²	semidirect
37. C₁₃×#450	C₂²	semidirect
38. C₁₃×#449	C₂²	semidirect
39. C₁₃×#448	C₂²	semidirect
40. C₁₃×#447	C₂²	semidirect
41. C₄×C₁₃×D₈	C₂²	semidirect
42. C₁₃×#436	C₂²	semidirect
43. C₁₃×#431	C₂²	semidirect
44. C₁₃×#417	C₂²	semidirect
45. C₁₃×#407	C₂²	semidirect
110. #61585	C₁₃	direct (N × H)
175. #3496	C₂×C₁₃	semidirect
176. C₂×#547	C₂×C₁₃	semidirect
177. #3330	C₂×C₁₃	semidirect
178. #3272	C₂×C₁₃	semidirect
179. #3206	C₂×C₁₃	semidirect
180. #3193	C₂×C₁₃	semidirect
181. #3100	C₂×C₁₃	semidirect
182. #3006	C₂×C₁₃	semidirect
183. #2975	C₂×C₁₃	semidirect
210. D₄×C₁₃	H(5,𝔽₂)	semidirect
225. C₂×C₄×C₁₃	AGL(1,ℤ/8)	semidirect
233. C₂²×#41	C₂²×C₁₃	semidirect
234. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
236. #547	C₂²×C₁₃	semidirect
237. #547	C₂²×C₁₃	semidirect
239. D₄²	C₂²×C₁₃	semidirect
243. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
245. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
249. C₂×C₄×D₄	C₂²×C₁₃	semidirect
251. #492	C₂²×C₁₃	semidirect
252. #487	C₂²×C₁₃	semidirect
253. #484	C₂²×C₁₃	semidirect
254. #480	C₂²×C₁₃	semidirect
255. #474	C₂²×C₁₃	semidirect
256. #468	C₂²×C₁₃	semidirect
257. #461	C₂²×C₁₃	semidirect
258. #459	C₂²×C₁₃	semidirect
259. #450	C₂²×C₁₃	semidirect
260. #449	C₂²×C₁₃	semidirect
261. #448	C₂²×C₁₃	semidirect
262. #447	C₂²×C₁₃	semidirect
263. C₄×D₈	C₂²×C₁₃	semidirect
264. #436	C₂²×C₁₃	semidirect
265. #431	C₂²×C₁₃	semidirect
266. #417	C₂²×C₁₃	semidirect
267. #407	C₂²×C₁₃	semidirect
427. C₁₃	#61585	direct (N × H)
454. D₄	C₁₃×H(5,𝔽₂)	semidirect
469. C₂×C₄	C₁₃×AGL(1,ℤ/8)	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#3496	2
C₂×C₁₃×#547	2
C₁₃×#3330	2
C₁₃×#3272	2
C₁₃×#3206	2
C₁₃×#3193	2
C₁₃×#3100	2
C₁₃×#3006	2
C₁₃×#2975	2
#61585	13

Subgroups — C13×#61585 #15747924

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61585 #15747924