Subgroups — C₁₃×#61584 #15747923

Order 3328.

2086 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3506	C₂	1	1	yes	maximal, characteristic
2	C₂×D₄×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3329	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3328	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3278	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3276	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3209	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#3206	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3196	C₂	1	4	yes	maximal, complemented
10	C₁₃×#3104	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3103	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3004	C₂	1	4	yes	maximal, complemented
13	C₁₃×#2975	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂³×Q₈×C₁₃	C₂²	1	2	yes	—
15	C₂×C₁₃×#137	C₂²	1	8	yes	complemented
16	C₁₃×#559	—	2	2	no	—
17	C₁₃×#556	C₂²	1	2	yes	—
18	C₁₃×#555	C₂²	1	2	yes	—
19	C₁₃×#553	—	2	2	no	—
20	C₁₃×#550	C₂²	1	2	yes	—
21	D₄×Q₈×C₁₃	—	2	2	no	—
22	D₄×Q₈×C₁₃	—	2	2	no	—
23	D₄×Q₈×C₁₃	C₂²	1	4	yes	—
24	D₄×Q₈×C₁₃	C₂²	1	4	yes	—
25	C₁₃×#547	C₂²	1	2	yes	—
26	C₁₃×#538	—	2	2	no	—
27	C₁₃×#535	—	2	1	no	—
28	C₁₃×#533	C₂²	1	1	yes	characteristic
29	C₁₃×#532	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
31	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
32	C₁₃×#525	C₂²	1	4	yes	—
33	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
34	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
35	C₁₃×#520	—	2	1	no	—
36	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₁₃	—	2	1	no	—
38	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
39	C₁₃×#494	C₂²	1	2	yes	complemented
40	C₁₃×#492	C₂²	1	2	yes	complemented
41	C₁₃×#487	C₂²	1	2	yes	complemented
42	C₁₃×#487	C₂²	1	2	yes	complemented
43	C₁₃×#485	C₂²	1	8	yes	complemented
44	C₁₃×#484	C₂²	1	2	yes	—
45	C₁₃×#481	C₂²	1	2	yes	—
46	C₁₃×#477	C₂²	1	2	yes	complemented
47	C₁₃×#475	C₂²	1	2	yes	complemented
48	C₁₃×#470	C₂²	1	8	yes	complemented
49	C₁₃×#468	C₂²	1	8	yes	complemented
50	C₁₃×#462	C₂²	1	2	yes	complemented
51	C₁₃×#462	C₂²	1	4	yes	complemented
52	C₁₃×#461	C₂²	1	4	yes	complemented
53	C₁₃×#460	C₂²	1	2	yes	complemented
54	C₁₃×#452	C₂²	1	8	yes	complemented
55	C₁₃×#451	C₂²	1	2	yes	—
56	C₁₃×#451	C₂²	1	4	yes	—
57	C₁₃×#451	C₂²	1	8	yes	complemented
58	C₁₃×#448	C₂²	1	2	yes	—
59	C₁₃×#448	C₂²	1	4	yes	—
60	C₁₃×#448	C₂²	1	8	yes	complemented
61	C₄×C₁₃×Q₁₆	C₂²	1	4	yes	complemented
62	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
63	C₁₃×#436	C₂²	1	4	yes	—
64	C₁₃×#436	C₂²	1	4	yes	—
65	C₁₃×#431	C₂²	1	1	yes	characteristic
66	C₁₃×#431	C₂²	1	1	yes	characteristic
67	C₁₃×#419	C₂²	1	8	yes	complemented
68	C₁₃×#407	C₂²	1	4	yes	—
69	C₂×C₁₃×#41	—	2	1	no	—
70	C₂×C₁₃×#41	C₂³	1	4	yes	—
71	C₂²×Q₈×C₁₃	—	2	2	no	—
72	C₂²×Q₈×C₁₃	—	2	4	no	—
73	C₂²×Q₈×C₁₃	—	4	8	no	—
74	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
75	C₂²×Q₈×C₁₃	C₂³	1	8	yes	—
76	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
77	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
78	C₂³×C₄×C₁₃	—	2	2	no	—
79	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
80	C₁₃×#137	—	4	16	no	—
81	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
82	C₂×C₁₃×Q₁₆	C₂³	1	8	yes	—
83	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
84	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
85	C₂×C₁₃×M₁₆	C₂³	1	8	yes	—
86	C₁₃×C₄⋊Q₈	—	2	4	no	—
87	C₁₃×C₄⋊Q₈	—	2	4	no	—
88	C₁₃×C₄⋊Q₈	—	2	1	no	—
89	C₁₃×C₄⋊Q₈	—	2	1	no	—
90	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
91	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
92	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
93	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
94	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
95	C₁₃×#127	—	2	2	no	—
96	C₁₃×#127	C₂³	1	1	yes	characteristic
97	C₁₃×#126	—	2	4	no	—
98	C₁₃×#125	—	2	1	no	—
99	C₁₃×#124	—	2	2	no	—
100	C₁₃×#124	—	2	4	no	—
101	C₁₃×#124	—	2	1	no	—
102	C₁₃×#123	—	2	4	no	—
103	C₁₃×#123	—	2	4	no	—
104	C₁₃×C₂²⋊Q₈	—	2	4	no	—
105	C₁₃×C₂²⋊Q₈	—	2	1	no	—
106	C₁₃×C₂²⋊Q₈	—	2	8	no	—
107	C₁₃×C₂²⋊Q₈	—	2	8	no	—
108	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
109	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
110	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
111	C₁₃×#121	—	2	2	no	—
112	C₁₃×#121	—	2	2	no	—
113	C₁₃×#121	—	2	1	no	—
114	C₁₃×#121	—	2	4	no	—
115	C₁₃×#121	C₂³	1	2	yes	—
116	C₁₃×#121	C₂³	1	4	yes	—
117	C₁₃×#120	—	2	4	no	—
118	C₄×Q₈×C₁₃	—	2	2	no	—
119	C₄×Q₈×C₁₃	—	2	1	no	—
120	C₄×Q₈×C₁₃	—	2	1	no	—
121	C₄×Q₈×C₁₃	—	2	1	no	—
122	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
123	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
124	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
125	C₄×D₄×C₁₃	—	2	4	no	—
126	C₄×D₄×C₁₃	—	2	4	no	—
127	C₄×D₄×C₁₃	—	2	4	no	—
128	C₄×D₄×C₁₃	—	2	4	no	—
129	C₄×D₄×C₁₃	—	2	2	no	—
130	C₄×D₄×C₁₃	—	2	1	no	—
131	C₄×D₄×C₁₃	D₄	1	2	yes	—
132	C₄×D₄×C₁₃	D₄	1	2	yes	—
133	C₄×D₄×C₁₃	C₂³	1	2	yes	—
134	C₄×D₄×C₁₃	C₂³	1	2	yes	—
135	C₄×D₄×C₁₃	C₂³	1	2	yes	—
136	C₁₃×#117	—	2	1	no	—
137	C₁₃×#117	—	2	2	no	—
138	C₁₃×#117	C₂³	1	4	yes	—
139	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
140	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
141	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
142	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
143	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
144	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
145	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
146	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
147	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
148	C₂×C₄²×C₁₃	—	2	1	no	—
149	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
150	C₁₃×#107	C₂³	1	4	yes	—
151	C₁₃×#106	C₂³	1	4	yes	—
152	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
153	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
154	C₁₃×#103	C₂³	1	4	yes	—
155	C₁₃×#103	C₂³	1	4	yes	—
156	C₁₃×#103	C₂³	1	8	yes	—
157	C₁₃×#103	C₂³	1	8	yes	—
158	C₁₃×#103	C₂³	1	4	yes	—
159	C₁₃×#102	C₂³	1	4	yes	—
160	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
161	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
162	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	—
163	C₄×C₈×C₁₃	C₂³	1	2	yes	—
164	C₄×C₈×C₁₃	C₂³	1	2	yes	—
165	#61584	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
166	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
167	C₁₃×#41	—	4	8	no	—
168	C₁₃×#41	—	4	4	no	—
169	C₂×Q₈×C₁₃	—	2	4	no	—
170	C₂×Q₈×C₁₃	—	2	1	no	—
171	C₂×Q₈×C₁₃	—	2	1	no	—
172	C₂×Q₈×C₁₃	—	2	8	no	—
173	C₂×Q₈×C₁₃	—	2	2	no	—
174	C₂×Q₈×C₁₃	—	2	1	no	—
175	C₂×Q₈×C₁₃	—	2	16	no	—
176	C₂×Q₈×C₁₃	—	4	8	no	—
177	C₂×Q₈×C₁₃	—	4	4	no	—
178	C₂×Q₈×C₁₃	—	4	8	no	—
179	C₂×Q₈×C₁₃	—	4	16	no	—
180	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
181	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
182	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
183	C₂×D₄×C₁₃	—	2	2	no	—
184	C₂×D₄×C₁₃	—	2	4	no	—
185	C₂×D₄×C₁₃	—	2	4	no	—
186	C₂×D₄×C₁₃	—	2	4	no	—
187	C₂×D₄×C₁₃	—	2	1	no	—
188	C₂×D₄×C₁₃	—	2	1	no	—
189	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
190	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
191	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
192	C₂²×C₄×C₁₃	—	2	1	no	—
193	C₂²×C₄×C₁₃	—	2	1	no	—
194	C₂²×C₄×C₁₃	—	2	2	no	—
195	C₂²×C₄×C₁₃	—	2	8	no	—
196	C₂²×C₄×C₁₃	—	2	2	no	—
197	C₂²×C₄×C₁₃	—	2	4	no	—
198	C₂²×C₄×C₁₃	—	4	4	no	—
199	C₂²×C₄×C₁₃	—	4	8	no	—
200	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
201	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
202	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
203	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
204	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
205	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
206	C₁₃×Q₁₆	—	2	8	no	—
207	C₁₃×Q₁₆	—	4	8	no	—
208	C₁₃×SD₁₆	—	2	8	no	—
209	C₁₃×SD₁₆	—	4	8	no	—
210	C₁₃×M₁₆	—	4	8	no	—
211	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
212	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
213	C₁₃×C₄⋊C₄	—	2	1	no	—
214	C₁₃×C₄⋊C₄	—	2	2	no	—
215	C₁₃×C₄⋊C₄	—	2	2	no	—
216	C₁₃×C₄⋊C₄	—	2	4	no	—
217	C₁₃×C₄⋊C₄	—	2	2	no	—
218	C₁₃×C₄⋊C₄	—	2	2	no	—
219	C₁₃×C₄⋊C₄	—	2	2	no	—
220	C₁₃×C₄⋊C₄	—	2	2	no	—
221	C₁₃×C₄⋊C₄	—	2	8	no	—
222	C₁₃×C₄⋊C₄	—	2	1	no	—
223	C₁₃×C₄⋊C₄	—	2	1	no	—
224	C₁₃×C₄⋊C₄	—	2	2	no	—
225	C₁₃×C₄⋊C₄	—	2	1	no	—
226	C₁₃×C₄⋊C₄	—	2	1	no	—
227	C₁₃×C₄⋊C₄	—	2	2	no	—
228	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
229	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
230	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
231	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
232	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
233	C₁₃×C₂²⋊C₄	—	2	8	no	—
234	C₁₃×C₂²⋊C₄	—	2	2	no	—
235	C₁₃×C₂²⋊C₄	—	2	4	no	—
236	C₁₃×C₂²⋊C₄	—	2	4	no	—
237	C₁₃×C₂²⋊C₄	—	2	4	no	—
238	C₁₃×C₂²⋊C₄	—	2	2	no	—
239	C₁₃×C₂²⋊C₄	—	2	2	no	—
240	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
241	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
242	C₄²×C₁₃	—	2	2	no	—
243	C₄²×C₁₃	—	2	2	no	—
244	C₄²×C₁₃	—	2	4	no	—
245	C₄²×C₁₃	—	2	2	no	—
246	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
247	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
248	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
249	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
250	#3506	C₂×C₁₃	1	1	yes	characteristic
251	C₂×D₄×Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
252	#3329	C₂×C₁₃	1	4	yes	complemented
253	#3328	C₂×C₁₃	1	4	yes	complemented
254	#3278	C₂×C₁₃	1	4	yes	complemented
255	#3276	C₂×C₁₃	1	4	yes	complemented
256	#3209	C₂×C₁₃	1	1	yes	characteristic, complemented
257	#3206	C₂×C₁₃	1	1	yes	characteristic, complemented
258	#3196	C₂×C₁₃	1	4	yes	complemented
259	#3104	C₂×C₁₃	1	1	yes	characteristic, complemented
260	#3103	C₂×C₁₃	1	1	yes	characteristic, complemented
261	#3004	C₂×C₁₃	1	4	yes	complemented
262	#2975	C₂×C₁₃	1	1	yes	characteristic, complemented
263	C₂³×C₁₃	—	2	4	no	—
264	C₂³×C₁₃	—	2	2	no	—
265	C₂³×C₁₃	—	4	2	no	—
266	C₂³×C₁₃	—	4	2	no	—
267	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
268	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
269	Q₈×C₁₃	—	2	4	no	—
270	Q₈×C₁₃	—	2	2	no	—
271	Q₈×C₁₃	—	2	8	no	—
272	Q₈×C₁₃	—	2	4	no	—
273	Q₈×C₁₃	—	4	16	no	—
274	Q₈×C₁₃	—	4	4	no	—
275	Q₈×C₁₃	—	4	2	no	—
276	Q₈×C₁₃	—	8	1	no	—
277	Q₈×C₁₃	H(5,𝔽₂)	1	4	yes	—
278	D₄×C₁₃	—	2	4	no	—
279	D₄×C₁₃	—	2	4	no	—
280	D₄×C₁₃	—	2	4	no	—
281	D₄×C₁₃	—	4	4	no	—
282	D₄×C₁₃	—	4	2	no	—
283	D₄×C₁₃	—	8	1	no	—
284	D₄×C₁₃	—	8	4	no	—
285	D₄×C₁₃	—	8	4	no	—
286	C₂×C₄×C₁₃	—	2	4	no	—
287	C₂×C₄×C₁₃	—	2	2	no	—
288	C₂×C₄×C₁₃	—	2	8	no	—
289	C₂×C₄×C₁₃	—	2	2	no	—
290	C₂×C₄×C₁₃	—	2	2	no	—
291	C₂×C₄×C₁₃	—	2	2	no	—
292	C₂×C₄×C₁₃	—	2	2	no	—
293	C₂×C₄×C₁₃	—	2	2	no	—
294	C₂×C₄×C₁₃	—	2	4	no	—
295	C₂×C₄×C₁₃	—	4	4	no	—
296	C₂×C₄×C₁₃	—	4	2	no	—
297	C₂×C₄×C₁₃	—	4	1	no	—
298	C₂×C₄×C₁₃	—	4	16	no	—
299	C₂×C₄×C₁₃	—	4	2	no	—
300	C₂×C₄×C₁₃	—	4	4	no	—
301	C₂×C₄×C₁₃	—	4	4	no	—
302	C₂×C₄×C₁₃	—	8	4	no	—
303	C₂×C₄×C₁₃	#137	1	4	yes	complemented
304	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
305	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
306	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
307	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
308	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
309	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
310	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
311	C₈×C₁₃	—	2	4	no	—
312	C₈×C₁₃	—	2	4	no	—
313	C₂³×Q₈	C₂²×C₁₃	1	2	yes	—
314	C₂×#137	C₂²×C₁₃	1	8	yes	complemented
315	#559	—	2	2	no	—
316	#556	C₂²×C₁₃	1	2	yes	—
317	#555	C₂²×C₁₃	1	2	yes	—
318	#553	—	2	2	no	—
319	#550	C₂²×C₁₃	1	2	yes	—
320	D₄×Q₈	—	2	2	no	—
321	D₄×Q₈	—	2	2	no	—
322	D₄×Q₈	C₂²×C₁₃	1	4	yes	—
323	D₄×Q₈	C₂²×C₁₃	1	4	yes	—
324	#547	C₂²×C₁₃	1	2	yes	—
325	#538	—	2	2	no	—
326	#535	—	2	1	no	—
327	#533	C₂²×C₁₃	1	1	yes	characteristic
328	#532	C₂²×C₁₃	1	1	yes	characteristic
329	C₂×C₄⋊Q₈	—	2	1	no	—
330	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
331	#525	C₂²×C₁₃	1	4	yes	—
332	C₂×C₂²⋊Q₈	—	2	2	no	—
333	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
334	#520	—	2	1	no	—
335	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
336	C₂×C₄×D₄	—	2	1	no	—
337	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
338	#494	C₂²×C₁₃	1	2	yes	complemented
339	#492	C₂²×C₁₃	1	2	yes	complemented
340	#487	C₂²×C₁₃	1	2	yes	complemented
341	#487	C₂²×C₁₃	1	2	yes	complemented
342	#485	C₂²×C₁₃	1	8	yes	complemented
343	#484	C₂²×C₁₃	1	2	yes	—
344	#481	C₂²×C₁₃	1	2	yes	—
345	#477	C₂²×C₁₃	1	2	yes	complemented
346	#475	C₂²×C₁₃	1	2	yes	complemented
347	#470	C₂²×C₁₃	1	8	yes	complemented
348	#468	C₂²×C₁₃	1	8	yes	complemented
349	#462	C₂²×C₁₃	1	4	yes	complemented
350	#462	C₂²×C₁₃	1	2	yes	complemented
351	#461	C₂²×C₁₃	1	4	yes	complemented
352	#460	C₂²×C₁₃	1	2	yes	complemented
353	#452	C₂²×C₁₃	1	8	yes	complemented
354	#451	C₂²×C₁₃	1	2	yes	—
355	#451	C₂²×C₁₃	1	4	yes	—
356	#451	C₂²×C₁₃	1	8	yes	complemented
357	#448	C₂²×C₁₃	1	2	yes	—
358	#448	C₂²×C₁₃	1	4	yes	—
359	#448	C₂²×C₁₃	1	8	yes	complemented
360	C₄×Q₁₆	C₂²×C₁₃	1	4	yes	complemented
361	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
362	#436	C₂²×C₁₃	1	4	yes	—
363	#436	C₂²×C₁₃	1	4	yes	—
364	#431	C₂²×C₁₃	1	1	yes	characteristic
365	#431	C₂²×C₁₃	1	1	yes	characteristic
366	#419	C₂²×C₁₃	1	8	yes	complemented
367	#407	C₂²×C₁₃	1	4	yes	—
368	C₂²×C₁₃	—	2	1	no	—
369	C₂²×C₁₃	—	2	1	no	—
370	C₂²×C₁₃	—	2	4	no	—
371	C₂²×C₁₃	—	2	4	no	—
372	C₂²×C₁₃	—	2	4	no	—
373	C₂²×C₁₃	—	4	8	no	—
374	C₂²×C₁₃	—	4	2	no	—
375	C₂²×C₁₃	—	4	2	no	—
376	C₂²×C₁₃	—	4	2	no	—
377	C₂²×C₁₃	C₂×#137	1	2	yes	—
378	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
379	C₄×C₁₃	—	2	1	no	—
380	C₄×C₁₃	—	2	1	no	—
381	C₄×C₁₃	—	2	4	no	—
382	C₄×C₁₃	—	2	1	no	—
383	C₄×C₁₃	—	2	4	no	—
384	C₄×C₁₃	—	4	2	no	—
385	C₄×C₁₃	—	4	2	no	—
386	C₄×C₁₃	—	4	4	no	—
387	C₄×C₁₃	—	4	2	no	—
388	C₄×C₁₃	—	4	2	no	—
389	C₄×C₁₃	C₂×#137	1	2	yes	—
390	C₄×C₁₃	C₂×#137	1	2	yes	—
391	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
392	C₂×#41	—	2	1	no	—
393	C₂×#41	C₂³×C₁₃	1	4	yes	—
394	C₂²×Q₈	—	2	2	no	—
395	C₂²×Q₈	—	2	4	no	—
396	C₂²×Q₈	—	4	8	no	—
397	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
398	C₂²×Q₈	C₂³×C₁₃	1	8	yes	—
399	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
400	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
401	C₂³×C₄	—	2	2	no	—
402	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
403	#137	—	4	16	no	—
404	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
405	C₂×Q₁₆	C₂³×C₁₃	1	8	yes	—
406	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
407	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
408	C₂×M₁₆	C₂³×C₁₃	1	8	yes	—
409	C₄⋊Q₈	—	2	4	no	—
410	C₄⋊Q₈	—	2	4	no	—
411	C₄⋊Q₈	—	2	1	no	—
412	C₄⋊Q₈	—	2	1	no	—
413	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
414	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
415	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
416	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
417	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
418	#127	—	2	2	no	—
419	#127	C₂³×C₁₃	1	1	yes	characteristic
420	#126	—	2	4	no	—
421	#125	—	2	1	no	—
422	#124	—	2	2	no	—
423	#124	—	2	4	no	—
424	#124	—	2	1	no	—
425	#123	—	2	4	no	—
426	#123	—	2	4	no	—
427	C₂²⋊Q₈	—	2	4	no	—
428	C₂²⋊Q₈	—	2	1	no	—
429	C₂²⋊Q₈	—	2	8	no	—
430	C₂²⋊Q₈	—	2	8	no	—
431	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
432	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
433	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
434	#121	—	2	2	no	—
435	#121	—	2	2	no	—
436	#121	—	2	1	no	—
437	#121	—	2	4	no	—
438	#121	C₂³×C₁₃	1	2	yes	—
439	#121	C₂³×C₁₃	1	4	yes	—
440	#120	—	2	4	no	—
441	C₄×Q₈	—	2	2	no	—
442	C₄×Q₈	—	2	1	no	—
443	C₄×Q₈	—	2	1	no	—
444	C₄×Q₈	—	2	1	no	—
445	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
446	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
447	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
448	C₄×D₄	—	2	4	no	—
449	C₄×D₄	—	2	4	no	—
450	C₄×D₄	—	2	4	no	—
451	C₄×D₄	—	2	4	no	—
452	C₄×D₄	—	2	2	no	—
453	C₄×D₄	—	2	1	no	—
454	C₄×D₄	D₄×C₁₃	1	2	yes	—
455	C₄×D₄	D₄×C₁₃	1	2	yes	—
456	C₄×D₄	C₂³×C₁₃	1	2	yes	—
457	C₄×D₄	C₂³×C₁₃	1	2	yes	—
458	C₄×D₄	C₂³×C₁₃	1	2	yes	—
459	#117	—	2	1	no	—
460	#117	—	2	2	no	—
461	#117	C₂³×C₁₃	1	4	yes	—
462	C₂×C₄⋊C₄	—	2	1	no	—
463	C₂×C₄⋊C₄	—	2	1	no	—
464	C₂×C₄⋊C₄	—	2	1	no	—
465	C₂×C₄⋊C₄	—	2	2	no	—
466	C₂×C₄⋊C₄	—	2	2	no	—
467	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
468	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
469	C₂×C₂²⋊C₄	—	2	2	no	—
470	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
471	C₂×C₄²	—	2	1	no	—
472	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
473	#107	C₂³×C₁₃	1	4	yes	—
474	#106	C₂³×C₁₃	1	4	yes	—
475	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
476	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
477	#103	C₂³×C₁₃	1	4	yes	—
478	#103	C₂³×C₁₃	1	4	yes	—
479	#103	C₂³×C₁₃	1	8	yes	—
480	#103	C₂³×C₁₃	1	8	yes	—
481	#103	C₂³×C₁₃	1	4	yes	—
482	#102	C₂³×C₁₃	1	4	yes	—
483	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
484	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
485	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	—
486	C₄×C₈	C₂³×C₁₃	1	2	yes	—
487	C₄×C₈	C₂³×C₁₃	1	2	yes	—
488	C₂×C₁₃	—	2	2	no	—
489	C₂×C₁₃	—	4	4	no	—
490	C₂×C₁₃	—	8	2	no	—
491	C₂×C₁₃	#3484	1	1	yes	characteristic
492	C₂×C₁₃	C₂²×#137	1	1	yes	characteristic
493	C₂×C₁₃	#3586	1	1	yes	characteristic
494	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
495	#41	—	4	8	no	—
496	#41	—	4	4	no	—
497	C₂×Q₈	—	2	4	no	—
498	C₂×Q₈	—	2	1	no	—
499	C₂×Q₈	—	2	1	no	—
500	C₂×Q₈	—	2	8	no	—
501	C₂×Q₈	—	2	2	no	—
502	C₂×Q₈	—	2	1	no	—
503	C₂×Q₈	—	2	16	no	—
504	C₂×Q₈	—	4	8	no	—
505	C₂×Q₈	—	4	4	no	—
506	C₂×Q₈	—	4	8	no	—
507	C₂×Q₈	—	4	16	no	—
508	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
509	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
510	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
511	C₂×D₄	—	2	2	no	—
512	C₂×D₄	—	2	4	no	—
513	C₂×D₄	—	2	4	no	—
514	C₂×D₄	—	2	4	no	—
515	C₂×D₄	—	2	1	no	—
516	C₂×D₄	—	2	1	no	—
517	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
518	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
519	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
520	C₂²×C₄	—	2	1	no	—
521	C₂²×C₄	—	2	1	no	—
522	C₂²×C₄	—	2	2	no	—
523	C₂²×C₄	—	2	8	no	—
524	C₂²×C₄	—	2	2	no	—
525	C₂²×C₄	—	2	4	no	—
526	C₂²×C₄	—	4	4	no	—
527	C₂²×C₄	—	4	8	no	—
528	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
529	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
530	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
531	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
532	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
533	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
534	Q₁₆	—	2	8	no	—
535	Q₁₆	—	4	8	no	—
536	SD₁₆	—	2	8	no	—
537	SD₁₆	—	4	8	no	—
538	M₁₆	—	4	8	no	—
539	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
540	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
541	C₄⋊C₄	—	2	1	no	—
542	C₄⋊C₄	—	2	2	no	—
543	C₄⋊C₄	—	2	2	no	—
544	C₄⋊C₄	—	2	4	no	—
545	C₄⋊C₄	—	2	2	no	—
546	C₄⋊C₄	—	2	2	no	—
547	C₄⋊C₄	—	2	2	no	—
548	C₄⋊C₄	—	2	2	no	—
549	C₄⋊C₄	—	2	8	no	—
550	C₄⋊C₄	—	2	1	no	—
551	C₄⋊C₄	—	2	1	no	—
552	C₄⋊C₄	—	2	2	no	—
553	C₄⋊C₄	—	2	1	no	—
554	C₄⋊C₄	—	2	1	no	—
555	C₄⋊C₄	—	2	2	no	—
556	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
557	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
558	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
559	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
560	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
561	C₂²⋊C₄	—	2	8	no	—
562	C₂²⋊C₄	—	2	2	no	—
563	C₂²⋊C₄	—	2	4	no	—
564	C₂²⋊C₄	—	2	4	no	—
565	C₂²⋊C₄	—	2	4	no	—
566	C₂²⋊C₄	—	2	2	no	—
567	C₂²⋊C₄	—	2	2	no	—
568	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
569	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
570	C₄²	—	2	2	no	—
571	C₄²	—	2	2	no	—
572	C₄²	—	2	4	no	—
573	C₄²	—	2	2	no	—
574	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
575	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
576	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
577	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
578	C₁₃	#61584	1	1	yes	characteristic, direct product factor, Sylow
579	C₂³	—	2	4	no	—
580	C₂³	—	2	2	no	—
581	C₂³	—	4	2	no	—
582	C₂³	—	4	2	no	—
583	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
584	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
585	Q₈	—	2	4	no	—
586	Q₈	—	2	2	no	—
587	Q₈	—	2	8	no	—
588	Q₈	—	2	4	no	—
589	Q₈	—	4	16	no	—
590	Q₈	—	4	4	no	—
591	Q₈	—	4	2	no	—
592	Q₈	—	8	1	no	—
593	Q₈	C₁₃×H(5,𝔽₂)	1	4	yes	—
594	D₄	—	2	4	no	—
595	D₄	—	2	4	no	—
596	D₄	—	2	4	no	—
597	D₄	—	4	4	no	—
598	D₄	—	4	2	no	—
599	D₄	—	8	1	no	—
600	D₄	—	8	4	no	—
601	D₄	—	8	4	no	—
602	C₂×C₄	—	2	4	no	—
603	C₂×C₄	—	2	2	no	—
604	C₂×C₄	—	2	8	no	—
605	C₂×C₄	—	2	2	no	—
606	C₂×C₄	—	2	2	no	—
607	C₂×C₄	—	2	2	no	—
608	C₂×C₄	—	2	2	no	—
609	C₂×C₄	—	2	2	no	—
610	C₂×C₄	—	2	4	no	—
611	C₂×C₄	—	4	4	no	—
612	C₂×C₄	—	4	2	no	—
613	C₂×C₄	—	4	1	no	—
614	C₂×C₄	—	4	16	no	—
615	C₂×C₄	—	4	4	no	—
616	C₂×C₄	—	4	2	no	—
617	C₂×C₄	—	4	4	no	—
618	C₂×C₄	—	8	4	no	—
619	C₂×C₄	C₁₃×#137	1	4	yes	complemented
620	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
621	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
622	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
623	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
624	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
625	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
626	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
627	C₈	—	2	4	no	—
628	C₈	—	2	4	no	—
629	C₂²	—	2	1	no	—
630	C₂²	—	2	1	no	—
631	C₂²	—	2	4	no	—
632	C₂²	—	2	4	no	—
633	C₂²	—	2	4	no	—
634	C₂²	—	4	8	no	—
635	C₂²	—	4	2	no	—
636	C₂²	—	4	2	no	—
637	C₂²	—	4	2	no	—
638	C₂²	C₂×C₁₃×#137	1	2	yes	—
639	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
640	C₄	—	2	1	no	—
641	C₄	—	2	1	no	—
642	C₄	—	2	4	no	—
643	C₄	—	2	1	no	—
644	C₄	—	2	4	no	—
645	C₄	—	4	2	no	—
646	C₄	—	4	2	no	—
647	C₄	—	4	2	no	—
648	C₄	—	4	4	no	—
649	C₄	—	4	2	no	—
650	C₄	C₂×C₁₃×#137	1	2	yes	—
651	C₄	C₂×C₁₃×#137	1	2	yes	—
652	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
653	C₂	—	2	2	no	—
654	C₂	—	4	4	no	—
655	C₂	—	8	2	no	—
656	C₂	C₁₃×#3484	1	1	yes	characteristic
657	C₂	C₂²×C₁₃×#137	1	1	yes	characteristic
658	C₂	C₁₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3506	C₂
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
2. C₂×D₄×Q₈×C₁₃	C₂	semidirect
3. C₁₃×#3329	C₂	semidirect
4. C₁₃×#3328	C₂	semidirect
5. C₁₃×#3278	C₂	semidirect
6. C₁₃×#3276	C₂	semidirect
7. C₁₃×#3209	C₂	semidirect
8. C₁₃×#3206	C₂	semidirect
9. C₁₃×#3196	C₂	semidirect
10. C₁₃×#3104	C₂	semidirect
11. C₁₃×#3103	C₂	semidirect
12. C₁₃×#3004	C₂	semidirect
13. C₁₃×#2975	C₂	semidirect
15. C₂×C₁₃×#137	C₂²	semidirect
39. C₁₃×#494	C₂²	semidirect
40. C₁₃×#492	C₂²	semidirect
41. C₁₃×#487	C₂²	semidirect
42. C₁₃×#487	C₂²	semidirect
43. C₁₃×#485	C₂²	semidirect
46. C₁₃×#477	C₂²	semidirect
47. C₁₃×#475	C₂²	semidirect
48. C₁₃×#470	C₂²	semidirect
49. C₁₃×#468	C₂²	semidirect
50. C₁₃×#462	C₂²	semidirect
51. C₁₃×#462	C₂²	semidirect
52. C₁₃×#461	C₂²	semidirect
53. C₁₃×#460	C₂²	semidirect
54. C₁₃×#452	C₂²	semidirect
57. C₁₃×#451	C₂²	semidirect
60. C₁₃×#448	C₂²	semidirect
61. C₄×C₁₃×Q₁₆	C₂²	semidirect
62. C₄×C₁₃×SD₁₆	C₂²	semidirect
67. C₁₃×#419	C₂²	semidirect
165. #61584	C₁₃	direct (N × H)
251. C₂×D₄×Q₈	C₂×C₁₃	semidirect
252. #3329	C₂×C₁₃	semidirect
253. #3328	C₂×C₁₃	semidirect
254. #3278	C₂×C₁₃	semidirect
255. #3276	C₂×C₁₃	semidirect
256. #3209	C₂×C₁₃	semidirect
257. #3206	C₂×C₁₃	semidirect
258. #3196	C₂×C₁₃	semidirect
259. #3104	C₂×C₁₃	semidirect
260. #3103	C₂×C₁₃	semidirect
261. #3004	C₂×C₁₃	semidirect
262. #2975	C₂×C₁₃	semidirect
303. C₂×C₄×C₁₃	#137	semidirect
314. C₂×#137	C₂²×C₁₃	semidirect
338. #494	C₂²×C₁₃	semidirect
339. #492	C₂²×C₁₃	semidirect
340. #487	C₂²×C₁₃	semidirect
341. #487	C₂²×C₁₃	semidirect
342. #485	C₂²×C₁₃	semidirect
345. #477	C₂²×C₁₃	semidirect
346. #475	C₂²×C₁₃	semidirect
347. #470	C₂²×C₁₃	semidirect
348. #468	C₂²×C₁₃	semidirect
349. #462	C₂²×C₁₃	semidirect
350. #462	C₂²×C₁₃	semidirect
351. #461	C₂²×C₁₃	semidirect
352. #460	C₂²×C₁₃	semidirect
353. #452	C₂²×C₁₃	semidirect
356. #451	C₂²×C₁₃	semidirect
359. #448	C₂²×C₁₃	semidirect
360. C₄×Q₁₆	C₂²×C₁₃	semidirect
361. C₄×SD₁₆	C₂²×C₁₃	semidirect
366. #419	C₂²×C₁₃	semidirect
578. C₁₃	#61584	direct (N × H)
619. C₂×C₄	C₁₃×#137	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#3506	2
C₂×D₄×Q₈×C₁₃	2
C₁₃×#3329	2
C₁₃×#3328	2
C₁₃×#3278	2
C₁₃×#3276	2
C₁₃×#3209	2
C₁₃×#3206	2
C₁₃×#3196	2
C₁₃×#3104	2
C₁₃×#3103	2
C₁₃×#3004	2
C₁₃×#2975	2
#61584	13

Subgroups — C13×#61584 #15747923

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61584 #15747923