Subgroups — C₁₃×#61373 #15747712

Order 3328.

1778 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3503	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3386	C₂	1	4	yes	maximal, complemented
3	C₁₃×#3385	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3383	C₂	1	2	yes	maximal, complemented
5	Q₈×C₁₃×Q₁₆	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3380	C₂	1	2	yes	maximal, complemented
7	Q₈×C₁₃×D₈	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3164	C₂	1	2	yes	maximal, complemented
9	C₂×C₁₃×#500	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3083	C₂	1	4	yes	maximal, complemented
11	C₁₃×#3079	C₂	1	2	yes	maximal, complemented
12	C₁₃×#2960	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#2951	C₂	1	2	yes	maximal
14	C₄×C₁₃×#135	C₂	1	1	yes	maximal, characteristic
15	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
16	Q₈²×C₁₃	C₂²	1	4	yes	—
17	C₁₃×#557	C₂²	1	4	yes	—
18	C₁₃×#554	—	2	4	no	—
19	C₁₃×#554	C₂²	1	4	yes	—
20	D₄×Q₈×C₁₃	—	2	4	no	—
21	D₄×Q₈×C₁₃	C₂²	1	4	yes	—
22	C₁₃×#544	—	2	4	no	—
23	C₁₃×#544	C₂²	1	4	yes	—
24	C₁₃×#533	—	2	2	no	—
25	C₁₃×#533	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×C₄⋊Q₈	—	2	2	no	—
27	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
28	C₁₃×#520	C₂²	1	4	yes	—
29	C₄×C₁₃×#41	C₂²	1	2	yes	—
30	C₁₃×#501	C₂²	1	8	yes	—
31	C₁₃×#500	C₂²	1	4	yes	—
32	C₁₃×#500	C₂²	1	2	yes	—
33	C₁₃×#500	C₂²	1	2	yes	—
34	C₁₃×#500	C₂²	1	2	yes	—
35	C₁₃×#500	C₂²	1	2	yes	—
36	C₁₃×#499	C₂²	1	4	yes	—
37	C₁₃×#479	C₂²	1	8	yes	—
38	C₁₃×#478	C₂²	1	8	yes	—
39	C₁₃×#477	C₂²	1	4	yes	—
40	C₁₃×#477	C₂²	1	8	yes	—
41	C₁₃×#476	C₂²	1	4	yes	—
42	C₁₃×#475	C₂²	1	4	yes	—
43	C₁₃×#474	C₂²	1	4	yes	—
44	C₁₃×#474	C₂²	1	8	yes	—
45	C₁₃×#446	C₂²	1	2	yes	—
46	C₁₃×#446	C₂²	1	2	yes	—
47	C₈×Q₈×C₁₃	C₂²	1	2	yes	—
48	C₈×Q₈×C₁₃	C₂²	1	2	yes	—
49	C₁₃×#440	C₂²	1	8	yes	—
50	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
51	C₄×C₁₃×Q₁₆	C₂²	1	4	yes	—
52	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
53	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
54	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
55	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
56	C₄×C₁₃×D₈	C₂²	1	4	yes	—
57	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
58	C₁₃×#428	C₂²	1	4	yes	—
59	C₁₃×#427	C₂²	1	1	yes	characteristic
60	C₂×C₁₃×#107	C₂²	1	2	yes	—
61	C₂×C₁₃×#107	C₂²	1	2	yes	—
62	C₁₃×#424	C₂²	1	2	yes	—
63	C₁₃×#423	C₂²	1	1	yes	characteristic
64	C₁₃×#417	C₂²	1	4	yes	—
65	C₁₃×#416	C₂²	1	2	yes	—
66	C₁₃×#405	C₂²	1	2	yes	—
67	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
68	C₂×C₁₃×#41	C₂³	1	2	yes	—
69	C₂²×Q₈×C₁₃	—	2	4	no	—
70	C₂²×Q₈×C₁₃	—	2	2	no	—
71	C₁₃×#135	Q₈	1	8	yes	complemented
72	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
73	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
74	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
75	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
76	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
77	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
78	C₁₃×C₄⋊Q₈	—	2	4	no	—
79	C₁₃×C₄⋊Q₈	—	2	4	no	—
80	C₁₃×C₄⋊Q₈	—	2	4	no	—
81	C₁₃×C₄⋊Q₈	—	2	8	no	—
82	C₁₃×C₄⋊Q₈	—	2	2	no	—
83	C₁₃×C₄⋊Q₈	—	2	2	no	—
84	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
85	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
86	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
87	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	—
88	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
89	C₁₃×#125	—	2	4	no	—
90	C₁₃×#125	—	2	8	no	—
91	C₁₃×#125	D₄	1	2	yes	—
92	C₁₃×#125	C₂³	1	8	yes	—
93	C₁₃×C₂²⋊Q₈	—	2	4	no	—
94	C₁₃×C₂²⋊Q₈	—	2	4	no	—
95	C₁₃×C₂²⋊Q₈	—	2	8	no	—
96	C₁₃×C₂²⋊Q₈	—	2	8	no	—
97	C₁₃×C₂²⋊Q₈	—	2	8	no	—
98	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
99	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
100	C₄×Q₈×C₁₃	—	2	4	no	—
101	C₄×Q₈×C₁₃	—	2	4	no	—
102	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
103	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
104	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
105	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
106	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
107	C₄×D₄×C₁₃	—	2	2	no	—
108	C₄×D₄×C₁₃	—	2	2	no	—
109	C₄×D₄×C₁₃	—	2	8	no	—
110	C₄×D₄×C₁₃	C₂³	1	2	yes	—
111	C₄×D₄×C₁₃	C₂³	1	2	yes	—
112	C₄×D₄×C₁₃	C₂³	1	8	yes	—
113	C₁₃×#117	—	2	4	no	—
114	C₁₃×#117	—	2	2	no	—
115	C₁₃×#117	C₂³	1	2	yes	—
116	C₁₃×#117	C₂³	1	2	yes	—
117	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
118	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
119	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
120	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
121	C₂×C₄²×C₁₃	—	2	2	no	—
122	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
123	C₁₃×#107	C₂³	1	4	yes	—
124	C₁₃×#107	C₂³	1	4	yes	—
125	C₁₃×#107	C₂³	1	4	yes	—
126	C₁₃×#107	C₂³	1	4	yes	—
127	C₁₃×#107	C₂³	1	1	yes	characteristic
128	C₁₃×#107	C₂³	1	1	yes	characteristic
129	C₁₃×#107	C₂³	1	8	yes	—
130	C₁₃×#106	C₂³	1	2	yes	—
131	C₁₃×#106	C₂³	1	8	yes	—
132	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
133	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
134	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
135	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
136	C₁₃×#103	C₂³	1	2	yes	—
137	C₁₃×#103	C₂³	1	2	yes	—
138	C₁₃×#103	C₂³	1	8	yes	—
139	C₁₃×#102	C₂³	1	2	yes	—
140	C₁₃×#102	C₂³	1	2	yes	—
141	C₁₃×#102	C₂³	1	8	yes	—
142	C₁₃×#97	C₂³	1	4	yes	—
143	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
144	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
145	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
146	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
147	C₄×C₈×C₁₃	C₂³	1	4	yes	—
148	#61373	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
149	C₁₃×#41	—	2	4	no	—
150	C₁₃×#41	C₂×Q₈	1	8	yes	complemented
151	C₂×Q₈×C₁₃	—	2	4	no	—
152	C₂×Q₈×C₁₃	—	2	8	no	—
153	C₂×Q₈×C₁₃	—	2	4	no	—
154	C₂×Q₈×C₁₃	—	8	4	no	—
155	C₂×Q₈×C₁₃	—	8	8	no	—
156	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
157	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
158	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
159	C₂×D₄×C₁₃	—	2	2	no	—
160	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
161	C₂²×C₄×C₁₃	—	2	2	no	—
162	C₂²×C₄×C₁₃	—	2	4	no	—
163	C₂²×C₄×C₁₃	—	2	2	no	—
164	C₂²×C₄×C₁₃	—	2	2	no	—
165	C₂²×C₄×C₁₃	—	2	8	no	—
166	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
169	C₁₃×Q₁₆	C₂×Q₈	1	4	yes	complemented
170	C₁₃×SD₁₆	C₂×Q₈	1	8	yes	complemented
171	C₁₃×D₈	C₂×Q₈	1	4	yes	complemented
172	C₁₃×M₁₆	—	2	4	no	—
173	C₂×C₈×C₁₃	—	2	2	no	—
174	C₂×C₈×C₁₃	C₂×Q₈	1	4	yes	complemented
175	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
176	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
177	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
178	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
179	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
180	C₁₃×C₄⋊C₄	—	2	4	no	—
181	C₁₃×C₄⋊C₄	—	2	4	no	—
182	C₁₃×C₄⋊C₄	—	2	8	no	—
183	C₁₃×C₄⋊C₄	—	2	4	no	—
184	C₁₃×C₄⋊C₄	—	2	8	no	—
185	C₁₃×C₄⋊C₄	—	2	2	no	—
186	C₁₃×C₄⋊C₄	—	2	2	no	—
187	C₁₃×C₄⋊C₄	—	2	8	no	—
188	C₁₃×C₄⋊C₄	—	2	8	no	—
189	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
190	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
191	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
192	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
193	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
194	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
195	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
196	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
197	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
198	C₁₃×C₂²⋊C₄	—	2	2	no	—
199	C₁₃×C₂²⋊C₄	—	2	2	no	—
200	C₁₃×C₂²⋊C₄	—	2	2	no	—
201	C₁₃×C₂²⋊C₄	—	2	8	no	—
202	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
203	C₄²×C₁₃	—	2	2	no	—
204	C₄²×C₁₃	—	2	2	no	—
205	C₄²×C₁₃	—	2	2	no	—
206	C₄²×C₁₃	—	2	8	no	—
207	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
208	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
209	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
210	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
211	C₄²×C₁₃	C₂⁴	1	4	yes	—
212	#3503	C₂×C₁₃	1	2	yes	complemented
213	#3386	C₂×C₁₃	1	4	yes	complemented
214	#3385	C₂×C₁₃	1	4	yes	complemented
215	#3383	C₂×C₁₃	1	2	yes	complemented
216	Q₈×Q₁₆	C₂×C₁₃	1	2	yes	complemented
217	#3380	C₂×C₁₃	1	2	yes	complemented
218	Q₈×D₈	C₂×C₁₃	1	2	yes	complemented
219	#3164	C₂×C₁₃	1	2	yes	complemented
220	C₂×#500	C₂×C₁₃	1	1	yes	characteristic, complemented
221	#3083	C₂×C₁₃	1	4	yes	complemented
222	#3079	C₂×C₁₃	1	2	yes	complemented
223	#2960	C₂×C₁₃	1	1	yes	characteristic, complemented
224	#2951	C₂×C₁₃	1	2	yes	—
225	C₄×#135	C₂×C₁₃	1	1	yes	characteristic
226	C₂³×C₁₃	—	2	2	no	—
227	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
228	Q₈×C₁₃	—	2	4	no	—
229	Q₈×C₁₃	—	2	4	no	—
230	Q₈×C₁₃	—	2	2	no	—
231	Q₈×C₁₃	—	4	8	no	—
232	Q₈×C₁₃	—	8	4	no	—
233	Q₈×C₁₃	—	8	8	no	—
234	Q₈×C₁₃	C₂²×Q₈	1	4	yes	—
235	D₄×C₁₃	—	2	8	no	—
236	D₄×C₁₃	—	2	2	no	—
237	D₄×C₁₃	C₂²×Q₈	1	4	yes	—
238	C₂×C₄×C₁₃	—	2	2	no	—
239	C₂×C₄×C₁₃	—	2	8	no	—
240	C₂×C₄×C₁₃	—	2	2	no	—
241	C₂×C₄×C₁₃	—	2	2	no	—
242	C₂×C₄×C₁₃	—	2	2	no	—
243	C₂×C₄×C₁₃	—	2	2	no	—
244	C₂×C₄×C₁₃	—	2	8	no	—
245	C₂×C₄×C₁₃	—	4	4	no	—
246	C₂×C₄×C₁₃	—	4	4	no	—
247	C₂×C₄×C₁₃	—	8	8	no	—
248	C₂×C₄×C₁₃	—	8	4	no	—
249	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
250	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
251	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
252	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
253	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
254	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
255	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
256	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
257	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
258	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
259	C₈×C₁₃	—	2	1	no	—
260	C₈×C₁₃	—	2	1	no	—
261	C₈×C₁₃	—	2	4	no	—
262	C₈×C₁₃	C₂²×Q₈	1	2	yes	—
263	C₈×C₁₃	C₂²×Q₈	1	2	yes	—
264	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
265	Q₈²	C₂²×C₁₃	1	4	yes	—
266	#557	C₂²×C₁₃	1	4	yes	—
267	#554	—	2	4	no	—
268	#554	C₂²×C₁₃	1	4	yes	—
269	D₄×Q₈	—	2	4	no	—
270	D₄×Q₈	C₂²×C₁₃	1	4	yes	—
271	#544	—	2	4	no	—
272	#544	C₂²×C₁₃	1	4	yes	—
273	#533	—	2	2	no	—
274	#533	C₂²×C₁₃	1	1	yes	characteristic
275	C₂×C₄⋊Q₈	—	2	2	no	—
276	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
277	#520	C₂²×C₁₃	1	4	yes	—
278	C₄×#41	C₂²×C₁₃	1	2	yes	—
279	#501	C₂²×C₁₃	1	8	yes	—
280	#500	C₂²×C₁₃	1	4	yes	—
281	#500	C₂²×C₁₃	1	2	yes	—
282	#500	C₂²×C₁₃	1	2	yes	—
283	#500	C₂²×C₁₃	1	2	yes	—
284	#500	C₂²×C₁₃	1	2	yes	—
285	#499	C₂²×C₁₃	1	4	yes	—
286	#479	C₂²×C₁₃	1	8	yes	—
287	#478	C₂²×C₁₃	1	8	yes	—
288	#477	C₂²×C₁₃	1	4	yes	—
289	#477	C₂²×C₁₃	1	8	yes	—
290	#476	C₂²×C₁₃	1	4	yes	—
291	#475	C₂²×C₁₃	1	4	yes	—
292	#474	C₂²×C₁₃	1	4	yes	—
293	#474	C₂²×C₁₃	1	8	yes	—
294	#446	C₂²×C₁₃	1	2	yes	—
295	#446	C₂²×C₁₃	1	2	yes	—
296	C₈×Q₈	C₂²×C₁₃	1	2	yes	—
297	C₈×Q₈	C₂²×C₁₃	1	2	yes	—
298	#440	C₂²×C₁₃	1	8	yes	—
299	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
300	C₄×Q₁₆	C₂²×C₁₃	1	4	yes	—
301	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
302	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
303	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
304	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
305	C₄×D₈	C₂²×C₁₃	1	4	yes	—
306	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
307	#428	C₂²×C₁₃	1	4	yes	—
308	#427	C₂²×C₁₃	1	1	yes	characteristic
309	C₂×#107	C₂²×C₁₃	1	2	yes	—
310	C₂×#107	C₂²×C₁₃	1	2	yes	—
311	#424	C₂²×C₁₃	1	2	yes	—
312	#423	C₂²×C₁₃	1	1	yes	characteristic
313	#417	C₂²×C₁₃	1	4	yes	—
314	#416	C₂²×C₁₃	1	2	yes	—
315	#405	C₂²×C₁₃	1	2	yes	—
316	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
317	C₂²×C₁₃	—	2	1	no	—
318	C₂²×C₁₃	—	2	1	no	—
319	C₂²×C₁₃	—	2	4	no	—
320	C₂²×C₁₃	—	4	2	no	—
321	C₂²×C₁₃	—	4	2	no	—
322	C₂²×C₁₃	D₄×Q₈	1	2	yes	—
323	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
324	C₄×C₁₃	—	2	4	no	—
325	C₄×C₁₃	—	2	1	no	—
326	C₄×C₁₃	—	2	4	no	—
327	C₄×C₁₃	—	2	1	no	—
328	C₄×C₁₃	—	2	4	no	—
329	C₄×C₁₃	—	4	2	no	—
330	C₄×C₁₃	—	4	8	no	—
331	C₄×C₁₃	—	4	2	no	—
332	C₄×C₁₃	D₄×Q₈	1	2	yes	—
333	C₄×C₁₃	#576	1	2	yes	—
334	C₄×C₁₃	#578	1	2	yes	—
335	C₄×C₁₃	C₂³×Q₈	1	1	yes	characteristic
336	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
337	C₂×#41	C₂³×C₁₃	1	2	yes	—
338	C₂²×Q₈	—	2	4	no	—
339	C₂²×Q₈	—	2	2	no	—
340	#135	Q₈×C₁₃	1	8	yes	complemented
341	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
342	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
343	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
344	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
345	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
346	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
347	C₄⋊Q₈	—	2	4	no	—
348	C₄⋊Q₈	—	2	4	no	—
349	C₄⋊Q₈	—	2	4	no	—
350	C₄⋊Q₈	—	2	8	no	—
351	C₄⋊Q₈	—	2	2	no	—
352	C₄⋊Q₈	—	2	2	no	—
353	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
354	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
355	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
356	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
357	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	—
358	#125	—	2	4	no	—
359	#125	—	2	8	no	—
360	#125	D₄×C₁₃	1	2	yes	—
361	#125	C₂³×C₁₃	1	8	yes	—
362	C₂²⋊Q₈	—	2	4	no	—
363	C₂²⋊Q₈	—	2	4	no	—
364	C₂²⋊Q₈	—	2	8	no	—
365	C₂²⋊Q₈	—	2	8	no	—
366	C₂²⋊Q₈	—	2	8	no	—
367	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
368	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
369	C₄×Q₈	—	2	4	no	—
370	C₄×Q₈	—	2	4	no	—
371	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
372	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
373	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
374	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
375	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
376	C₄×D₄	—	2	2	no	—
377	C₄×D₄	—	2	2	no	—
378	C₄×D₄	—	2	8	no	—
379	C₄×D₄	C₂³×C₁₃	1	2	yes	—
380	C₄×D₄	C₂³×C₁₃	1	2	yes	—
381	C₄×D₄	C₂³×C₁₃	1	8	yes	—
382	#117	—	2	4	no	—
383	#117	—	2	2	no	—
384	#117	C₂³×C₁₃	1	2	yes	—
385	#117	C₂³×C₁₃	1	2	yes	—
386	C₂×C₄⋊C₄	—	2	2	no	—
387	C₂×C₄⋊C₄	—	2	4	no	—
388	C₂×C₄⋊C₄	—	2	4	no	—
389	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
390	C₂×C₄²	—	2	2	no	—
391	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
392	#107	C₂³×C₁₃	1	4	yes	—
393	#107	C₂³×C₁₃	1	4	yes	—
394	#107	C₂³×C₁₃	1	4	yes	—
395	#107	C₂³×C₁₃	1	4	yes	—
396	#107	C₂³×C₁₃	1	1	yes	characteristic
397	#107	C₂³×C₁₃	1	1	yes	characteristic
398	#107	C₂³×C₁₃	1	8	yes	—
399	#106	C₂³×C₁₃	1	2	yes	—
400	#106	C₂³×C₁₃	1	8	yes	—
401	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
402	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
403	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
404	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
405	#103	C₂³×C₁₃	1	2	yes	—
406	#103	C₂³×C₁₃	1	2	yes	—
407	#103	C₂³×C₁₃	1	8	yes	—
408	#102	C₂³×C₁₃	1	2	yes	—
409	#102	C₂³×C₁₃	1	2	yes	—
410	#102	C₂³×C₁₃	1	8	yes	—
411	#97	C₂³×C₁₃	1	4	yes	—
412	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
413	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
414	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
415	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
416	C₄×C₈	C₂³×C₁₃	1	4	yes	—
417	C₂×C₁₃	—	2	2	no	—
418	C₂×C₁₃	—	4	4	no	—
419	C₂×C₁₃	C₂×D₄×Q₈	1	1	yes	characteristic
420	C₂×C₁₃	C₂×#576	1	1	yes	characteristic
421	C₂×C₁₃	C₂×#578	1	1	yes	characteristic
422	#41	—	2	4	no	—
423	#41	C₂×Q₈×C₁₃	1	8	yes	complemented
424	C₂×Q₈	—	2	4	no	—
425	C₂×Q₈	—	2	8	no	—
426	C₂×Q₈	—	2	4	no	—
427	C₂×Q₈	—	8	4	no	—
428	C₂×Q₈	—	8	8	no	—
429	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
430	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
431	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
432	C₂×D₄	—	2	2	no	—
433	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
434	C₂²×C₄	—	2	2	no	—
435	C₂²×C₄	—	2	4	no	—
436	C₂²×C₄	—	2	2	no	—
437	C₂²×C₄	—	2	2	no	—
438	C₂²×C₄	—	2	8	no	—
439	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
440	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
441	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
442	Q₁₆	C₂×Q₈×C₁₃	1	4	yes	complemented
443	SD₁₆	C₂×Q₈×C₁₃	1	8	yes	complemented
444	D₈	C₂×Q₈×C₁₃	1	4	yes	complemented
445	M₁₆	—	2	4	no	—
446	C₂×C₈	—	2	2	no	—
447	C₂×C₈	C₂×Q₈×C₁₃	1	4	yes	complemented
448	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
449	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
450	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
451	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
452	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
453	C₄⋊C₄	—	2	4	no	—
454	C₄⋊C₄	—	2	4	no	—
455	C₄⋊C₄	—	2	8	no	—
456	C₄⋊C₄	—	2	4	no	—
457	C₄⋊C₄	—	2	8	no	—
458	C₄⋊C₄	—	2	2	no	—
459	C₄⋊C₄	—	2	2	no	—
460	C₄⋊C₄	—	2	8	no	—
461	C₄⋊C₄	—	2	8	no	—
462	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
463	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
464	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
465	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
466	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
467	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
468	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
469	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
470	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
471	C₂²⋊C₄	—	2	2	no	—
472	C₂²⋊C₄	—	2	2	no	—
473	C₂²⋊C₄	—	2	2	no	—
474	C₂²⋊C₄	—	2	8	no	—
475	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
476	C₄²	—	2	2	no	—
477	C₄²	—	2	2	no	—
478	C₄²	—	2	2	no	—
479	C₄²	—	2	8	no	—
480	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
481	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
482	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
483	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
484	C₄²	C₂⁴×C₁₃	1	4	yes	—
485	C₁₃	#61373	1	1	yes	characteristic, direct product factor, Sylow
486	C₂³	—	2	2	no	—
487	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
488	Q₈	—	2	4	no	—
489	Q₈	—	2	4	no	—
490	Q₈	—	2	2	no	—
491	Q₈	—	4	8	no	—
492	Q₈	—	8	4	no	—
493	Q₈	—	8	8	no	—
494	Q₈	C₂²×Q₈×C₁₃	1	4	yes	—
495	D₄	—	2	8	no	—
496	D₄	—	2	2	no	—
497	D₄	C₂²×Q₈×C₁₃	1	4	yes	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	8	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	2	2	no	—
504	C₂×C₄	—	2	8	no	—
505	C₂×C₄	—	4	4	no	—
506	C₂×C₄	—	4	4	no	—
507	C₂×C₄	—	8	8	no	—
508	C₂×C₄	—	8	4	no	—
509	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
510	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
511	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
512	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
513	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
514	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
515	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
516	C₂×C₄	C₂²×Q₈×C₁₃	1	2	yes	—
517	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
518	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
519	C₈	—	2	1	no	—
520	C₈	—	2	1	no	—
521	C₈	—	2	4	no	—
522	C₈	C₂²×Q₈×C₁₃	1	2	yes	—
523	C₈	C₂²×Q₈×C₁₃	1	2	yes	—
524	C₂²	—	2	1	no	—
525	C₂²	—	2	1	no	—
526	C₂²	—	2	4	no	—
527	C₂²	—	4	2	no	—
528	C₂²	—	4	2	no	—
529	C₂²	D₄×Q₈×C₁₃	1	2	yes	—
530	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
531	C₄	—	2	1	no	—
532	C₄	—	2	4	no	—
533	C₄	—	2	1	no	—
534	C₄	—	2	4	no	—
535	C₄	—	2	4	no	—
536	C₄	—	4	2	no	—
537	C₄	—	4	8	no	—
538	C₄	—	4	2	no	—
539	C₄	D₄×Q₈×C₁₃	1	2	yes	—
540	C₄	C₁₃×#576	1	2	yes	—
541	C₄	C₁₃×#578	1	2	yes	—
542	C₄	C₂³×Q₈×C₁₃	1	1	yes	characteristic
543	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
544	C₂	—	2	2	no	—
545	C₂	—	4	4	no	—
546	C₂	C₂×D₄×Q₈×C₁₃	1	1	yes	characteristic
547	C₂	C₂×C₁₃×#576	1	1	yes	characteristic
548	C₂	C₂×C₁₃×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₂×C₁₃×#135	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₁₃×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3503	C₂	semidirect
2. C₁₃×#3386	C₂	semidirect
3. C₁₃×#3385	C₂	semidirect
4. C₁₃×#3383	C₂	semidirect
5. Q₈×C₁₃×Q₁₆	C₂	semidirect
6. C₁₃×#3380	C₂	semidirect
7. Q₈×C₁₃×D₈	C₂	semidirect
8. C₁₃×#3164	C₂	semidirect
9. C₂×C₁₃×#500	C₂	semidirect
10. C₁₃×#3083	C₂	semidirect
11. C₁₃×#3079	C₂	semidirect
12. C₁₃×#2960	C₂	semidirect
71. C₁₃×#135	Q₈	semidirect
148. #61373	C₁₃	direct (N × H)
150. C₁₃×#41	C₂×Q₈	semidirect
169. C₁₃×Q₁₆	C₂×Q₈	semidirect
170. C₁₃×SD₁₆	C₂×Q₈	semidirect
171. C₁₃×D₈	C₂×Q₈	semidirect
174. C₂×C₈×C₁₃	C₂×Q₈	semidirect
212. #3503	C₂×C₁₃	semidirect
213. #3386	C₂×C₁₃	semidirect
214. #3385	C₂×C₁₃	semidirect
215. #3383	C₂×C₁₃	semidirect
216. Q₈×Q₁₆	C₂×C₁₃	semidirect
217. #3380	C₂×C₁₃	semidirect
218. Q₈×D₈	C₂×C₁₃	semidirect
219. #3164	C₂×C₁₃	semidirect
220. C₂×#500	C₂×C₁₃	semidirect
221. #3083	C₂×C₁₃	semidirect
222. #3079	C₂×C₁₃	semidirect
223. #2960	C₂×C₁₃	semidirect
340. #135	Q₈×C₁₃	semidirect
423. #41	C₂×Q₈×C₁₃	semidirect
442. Q₁₆	C₂×Q₈×C₁₃	semidirect
443. SD₁₆	C₂×Q₈×C₁₃	semidirect
444. D₈	C₂×Q₈×C₁₃	semidirect
447. C₂×C₈	C₂×Q₈×C₁₃	semidirect
485. C₁₃	#61373	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#3503	2
C₁₃×#3386	2
C₁₃×#3385	2
C₁₃×#3383	2
Q₈×C₁₃×Q₁₆	2
C₁₃×#3380	2
Q₈×C₁₃×D₈	2
C₁₃×#3164	2
C₂×C₁₃×#500	2
C₁₃×#3083	2
C₁₃×#3079	2
C₁₃×#2960	2
C₁₃×#2951	2
C₄×C₁₃×#135	2
#61373	13

Subgroups — C13×#61373 #15747712

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61373 #15747712