Subgroups — C₁₃×#61680 #15748019

Order 3328.

2096 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3550	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3496	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3324	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3311	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3302	C₂	1	2	yes	maximal, complemented
6	D₄×C₁₃×SD₁₆	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3276	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3266	C₂	1	4	yes	maximal, complemented
9	C₁₃×#3216	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3210	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3201	C₂	1	4	yes	maximal, complemented
12	C₁₃×#3110	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3101	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3009	C₂	1	4	yes	maximal, complemented
15	C₁₃×#2981	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	2	yes	—
17	C₂×C₁₃×#137	C₂²	1	4	yes	complemented
18	C₂²×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
19	C₁₃×#563	—	2	2	no	—
20	C₁₃×#559	—	2	1	no	—
21	Q₈²×C₁₃	—	2	1	no	—
22	C₁₃×#556	C₂²	1	2	yes	complemented
23	C₁₃×#556	C₂²	1	2	yes	complemented
24	D₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
25	D₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
26	C₁₃×#547	—	2	1	no	—
27	C₁₃×#547	C₂²	1	2	yes	—
28	C₁₃×#546	—	2	2	no	—
29	C₁₃×#546	C₂²	1	4	yes	—
30	D₄²×C₁₃	—	2	1	no	—
31	D₄²×C₁₃	C₂²	1	2	yes	—
32	C₁₃×#542	—	2	2	no	—
33	C₁₃×#542	—	2	2	no	—
34	C₁₃×#537	C₂²	1	2	yes	—
35	C₁₃×#536	C₂²	1	4	yes	complemented
36	C₁₃×#534	—	2	2	no	—
37	C₁₃×#533	C₂²	1	1	yes	characteristic, complemented
38	C₁₃×#533	C₂²	1	1	yes	characteristic, complemented
39	C₁₃×#532	C₂²	1	1	yes	characteristic
40	C₁₃×#532	C₂²	1	1	yes	characteristic
41	C₂×C₁₃×#121	—	2	2	no	—
42	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
43	C₁₃×#497	C₂²	1	2	yes	complemented
44	C₁₃×#494	C₂²	1	1	yes	characteristic, complemented
45	C₁₃×#492	C₂²	1	1	yes	characteristic, complemented
46	C₁₃×#489	C₂²	1	2	yes	complemented
47	C₁₃×#487	C₂²	1	1	yes	characteristic, complemented
48	C₁₃×#486	C₂²	1	1	yes	characteristic, complemented
49	C₁₃×#485	C₂²	1	4	yes	complemented
50	C₁₃×#484	C₂²	1	2	yes	complemented
51	C₁₃×#483	C₂²	1	2	yes	complemented
52	C₁₃×#482	C₂²	1	4	yes	complemented
53	C₁₃×#476	C₂²	1	2	yes	complemented
54	C₁₃×#474	C₂²	1	2	yes	complemented
55	C₁₃×#470	C₂²	1	4	yes	complemented
56	C₁₃×#468	C₂²	1	4	yes	complemented
57	C₁₃×#467	C₂²	1	4	yes	complemented
58	C₁₃×#465	C₂²	1	4	yes	complemented
59	C₁₃×#464	C₂²	1	4	yes	complemented
60	C₁₃×#462	C₂²	1	2	yes	complemented
61	C₁₃×#461	C₂²	1	2	yes	complemented
62	C₁₃×#461	C₂²	1	2	yes	complemented
63	C₁₃×#460	C₂²	1	2	yes	complemented
64	C₁₃×#452	C₂²	1	4	yes	complemented
65	C₁₃×#452	C₂²	1	4	yes	complemented
66	C₁₃×#452	C₂²	1	4	yes	complemented
67	C₁₃×#452	C₂²	1	4	yes	complemented
68	C₁₃×#451	C₂²	1	4	yes	complemented
69	C₁₃×#450	C₂²	1	2	yes	—
70	C₁₃×#450	C₂²	1	2	yes	—
71	C₁₃×#450	C₂²	1	4	yes	complemented
72	C₁₃×#450	C₂²	1	4	yes	complemented
73	C₁₃×#448	C₂²	1	4	yes	complemented
74	C₁₃×#440	C₂²	1	4	yes	complemented
75	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
76	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
77	C₁₃×#436	C₂²	1	2	yes	complemented
78	C₁₃×#435	C₂²	1	4	yes	complemented
79	C₈×D₄×C₁₃	C₂²	1	2	yes	complemented
80	C₁₃×#432	C₂²	1	1	yes	characteristic, complemented
81	C₁₃×#431	C₂²	1	1	yes	characteristic, complemented
82	C₁₃×#418	C₂²	1	4	yes	complemented
83	C₁₃×#416	C₂²	1	4	yes	complemented
84	C₁₃×#408	C₂²	1	4	yes	complemented
85	C₁₃×H(5,𝔽₂)	—	4	8	no	—
86	C₂×C₁₃×#41	—	2	2	no	—
87	C₂×C₁₃×#41	C₂³	1	4	yes	—
88	C₂×C₁₃×#41	C₂³	1	2	yes	—
89	C₂×C₁₃×#41	C₂³	1	2	yes	—
90	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
91	C₂²×D₄×C₁₃	—	2	4	no	—
92	C₂²×D₄×C₁₃	—	2	2	no	—
93	C₂²×D₄×C₁₃	—	2	2	no	—
94	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
95	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
96	C₂³×C₄×C₁₃	—	2	1	no	—
97	C₁₃×#137	—	4	8	no	—
98	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
99	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
100	C₂×C₁₃×SD₁₆	—	4	8	no	—
101	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
102	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
103	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
104	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
105	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
106	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
107	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
108	C₁₃×C₄⋊Q₈	—	2	4	no	—
109	C₁₃×C₄⋊Q₈	—	2	2	no	—
110	C₁₃×C₄⋊Q₈	—	2	2	no	—
111	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
112	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
113	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
114	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
115	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
116	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
117	C₁₃×#127	D₄	1	1	yes	characteristic
118	C₁₃×#127	C₂³	1	1	yes	characteristic
119	C₁₃×#126	—	2	4	no	—
120	C₁₃×#126	—	2	4	no	—
121	C₁₃×#125	—	2	1	no	—
122	C₁₃×#125	—	2	1	no	—
123	C₁₃×#124	—	2	4	no	—
124	C₁₃×#124	—	2	2	no	—
125	C₁₃×#124	—	2	2	no	—
126	C₁₃×#124	D₄	1	2	yes	—
127	C₁₃×#124	C₂³	1	2	yes	—
128	C₁₃×#123	—	2	4	no	—
129	C₁₃×#123	—	2	4	no	—
130	C₁₃×#123	—	2	4	no	—
131	C₁₃×#123	—	2	4	no	—
132	C₁₃×C₂²⋊Q₈	—	2	2	no	—
133	C₁₃×C₂²⋊Q₈	—	2	1	no	—
134	C₁₃×C₂²⋊Q₈	—	2	1	no	—
135	C₁₃×C₂²⋊Q₈	—	2	4	no	—
136	C₁₃×C₂²⋊Q₈	—	2	4	no	—
137	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
138	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
139	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
140	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
141	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
142	C₁₃×#121	—	2	4	no	—
143	C₁₃×#121	—	2	2	no	—
144	C₁₃×#121	—	2	2	no	—
145	C₁₃×#121	—	2	1	no	—
146	C₁₃×#121	—	2	1	no	—
147	C₁₃×#121	—	2	2	no	—
148	C₁₃×#121	—	2	4	no	—
149	C₁₃×#121	D₄	1	2	yes	—
150	C₁₃×#121	D₄	1	2	yes	—
151	C₁₃×#121	C₂³	1	4	yes	—
152	C₁₃×#120	—	2	4	no	—
153	C₁₃×#120	—	2	4	no	—
154	C₄×Q₈×C₁₃	—	2	2	no	—
155	C₄×Q₈×C₁₃	—	2	2	no	—
156	C₄×Q₈×C₁₃	—	2	1	no	—
157	C₄×Q₈×C₁₃	—	2	1	no	—
158	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
159	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
160	C₄×D₄×C₁₃	—	2	2	no	—
161	C₄×D₄×C₁₃	—	2	2	no	—
162	C₄×D₄×C₁₃	—	2	1	no	—
163	C₄×D₄×C₁₃	—	2	1	no	—
164	C₄×D₄×C₁₃	—	2	1	no	—
165	C₄×D₄×C₁₃	—	2	1	no	—
166	C₄×D₄×C₁₃	C₂³	1	2	yes	—
167	C₄×D₄×C₁₃	C₂³	1	2	yes	—
168	C₄×D₄×C₁₃	C₂³	1	2	yes	—
169	C₄×D₄×C₁₃	C₂³	1	2	yes	—
170	C₁₃×#117	—	2	1	no	—
171	C₁₃×#117	—	2	1	no	—
172	C₁₃×#117	C₂³	1	4	yes	—
173	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
174	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
175	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
176	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
177	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
178	C₁₃×#107	C₂³	1	4	yes	—
179	C₁₃×#106	C₂³	1	2	yes	—
180	C₁₃×#106	C₂³	1	2	yes	—
181	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
182	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
183	C₁₃×#103	C₂³	1	4	yes	—
184	C₁₃×#103	C₂³	1	4	yes	—
185	C₁₃×#103	C₂³	1	2	yes	—
186	C₁₃×#103	C₂³	1	2	yes	—
187	C₁₃×#103	C₂³	1	4	yes	—
188	C₁₃×#102	C₂³	1	2	yes	—
189	C₁₃×#102	C₂³	1	4	yes	—
190	C₁₃×#102	C₂³	1	2	yes	—
191	C₁₃×#102	C₂³	1	4	yes	—
192	C₁₃×#102	C₂³	1	4	yes	—
193	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
194	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
195	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
196	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
197	C₁₃×#97	C₂³	1	2	yes	—
198	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
199	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
200	#61680	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
201	C₂⁴×C₁₃	—	2	1	no	—
202	C₂⁴×C₁₃	—	2	4	no	—
203	C₁₃×#41	—	2	8	no	—
204	C₁₃×#41	—	4	4	no	—
205	C₁₃×#41	—	4	4	no	—
206	C₁₃×#41	—	4	4	no	—
207	C₁₃×#41	—	4	8	no	—
208	C₂×Q₈×C₁₃	—	2	1	no	—
209	C₂×Q₈×C₁₃	—	2	1	no	—
210	C₂×Q₈×C₁₃	—	2	4	no	—
211	C₂×Q₈×C₁₃	—	4	4	no	—
212	C₂×Q₈×C₁₃	—	4	4	no	—
213	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
214	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
215	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
216	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
217	C₂×D₄×C₁₃	—	2	4	no	—
218	C₂×D₄×C₁₃	—	2	8	no	—
219	C₂×D₄×C₁₃	—	2	4	no	—
220	C₂×D₄×C₁₃	—	2	2	no	—
221	C₂×D₄×C₁₃	—	2	4	no	—
222	C₂×D₄×C₁₃	—	2	1	no	—
223	C₂×D₄×C₁₃	—	2	1	no	—
224	C₂×D₄×C₁₃	—	2	4	no	—
225	C₂×D₄×C₁₃	—	2	1	no	—
226	C₂×D₄×C₁₃	—	4	4	no	—
227	C₂×D₄×C₁₃	—	4	8	no	—
228	C₂×D₄×C₁₃	—	4	16	no	—
229	C₂×D₄×C₁₃	—	8	4	no	—
230	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
231	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
232	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
233	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
234	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
235	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
236	C₂²×C₄×C₁₃	—	2	1	no	—
237	C₂²×C₄×C₁₃	—	2	4	no	—
238	C₂²×C₄×C₁₃	—	2	4	no	—
239	C₂²×C₄×C₁₃	—	2	2	no	—
240	C₂²×C₄×C₁₃	—	2	2	no	—
241	C₂²×C₄×C₁₃	—	2	2	no	—
242	C₂²×C₄×C₁₃	—	8	2	no	—
243	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
244	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
245	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
246	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
247	C₁₃×Q₁₆	—	4	4	no	—
248	C₁₃×Q₁₆	—	4	4	no	—
249	C₁₃×SD₁₆	—	2	4	no	—
250	C₁₃×SD₁₆	—	2	8	no	—
251	C₁₃×SD₁₆	—	2	4	no	—
252	C₁₃×SD₁₆	—	4	4	no	—
253	C₁₃×SD₁₆	—	4	4	no	—
254	C₁₃×M₁₆	—	4	4	no	—
255	C₂×C₈×C₁₃	—	4	4	no	—
256	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
257	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
258	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
259	C₁₃×C₄⋊C₄	—	2	1	no	—
260	C₁₃×C₄⋊C₄	—	2	4	no	—
261	C₁₃×C₄⋊C₄	—	2	1	no	—
262	C₁₃×C₄⋊C₄	—	2	1	no	—
263	C₁₃×C₄⋊C₄	—	2	1	no	—
264	C₁₃×C₄⋊C₄	—	2	1	no	—
265	C₁₃×C₄⋊C₄	—	2	1	no	—
266	C₁₃×C₄⋊C₄	—	2	1	no	—
267	C₁₃×C₄⋊C₄	—	2	1	no	—
268	C₁₃×C₄⋊C₄	—	2	1	no	—
269	C₁₃×C₄⋊C₄	—	2	4	no	—
270	C₁₃×C₄⋊C₄	—	2	4	no	—
271	C₁₃×C₄⋊C₄	—	2	2	no	—
272	C₁₃×C₄⋊C₄	—	2	2	no	—
273	C₁₃×C₄⋊C₄	—	2	2	no	—
274	C₁₃×C₄⋊C₄	—	2	2	no	—
275	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
276	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
277	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
278	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
279	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
280	C₁₃×C₂²⋊C₄	—	2	4	no	—
281	C₁₃×C₂²⋊C₄	—	2	2	no	—
282	C₁₃×C₂²⋊C₄	—	2	2	no	—
283	C₁₃×C₂²⋊C₄	—	2	4	no	—
284	C₁₃×C₂²⋊C₄	—	2	4	no	—
285	C₁₃×C₂²⋊C₄	—	2	4	no	—
286	C₁₃×C₂²⋊C₄	—	2	2	no	—
287	C₁₃×C₂²⋊C₄	—	2	2	no	—
288	C₁₃×C₂²⋊C₄	—	2	2	no	—
289	C₁₃×C₂²⋊C₄	—	2	4	no	—
290	C₁₃×C₂²⋊C₄	—	2	2	no	—
291	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
292	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
293	C₄²×C₁₃	—	2	2	no	—
294	C₄²×C₁₃	—	2	2	no	—
295	C₄²×C₁₃	—	2	4	no	—
296	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
297	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
298	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
299	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
300	#3550	C₂×C₁₃	1	1	yes	characteristic, complemented
301	#3496	C₂×C₁₃	1	1	yes	characteristic
302	#3324	C₂×C₁₃	1	2	yes	complemented
303	#3311	C₂×C₁₃	1	4	yes	complemented
304	#3302	C₂×C₁₃	1	2	yes	complemented
305	D₄×SD₁₆	C₂×C₁₃	1	2	yes	complemented
306	#3276	C₂×C₁₃	1	2	yes	complemented
307	#3266	C₂×C₁₃	1	4	yes	complemented
308	#3216	C₂×C₁₃	1	1	yes	characteristic, complemented
309	#3210	C₂×C₁₃	1	1	yes	characteristic, complemented
310	#3201	C₂×C₁₃	1	4	yes	complemented
311	#3110	C₂×C₁₃	1	1	yes	characteristic, complemented
312	#3101	C₂×C₁₃	1	1	yes	characteristic, complemented
313	#3009	C₂×C₁₃	1	4	yes	complemented
314	#2981	C₂×C₁₃	1	1	yes	characteristic, complemented
315	C₂³×C₁₃	—	2	4	no	—
316	C₂³×C₁₃	—	2	2	no	—
317	C₂³×C₁₃	—	2	2	no	—
318	C₂³×C₁₃	—	4	8	no	—
319	C₂³×C₁₃	—	8	1	no	—
320	C₂³×C₁₃	—	8	1	no	—
321	C₂³×C₁₃	—	8	4	no	—
322	C₂³×C₁₃	—	8	4	no	—
323	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
324	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
325	Q₈×C₁₃	—	2	2	no	—
326	Q₈×C₁₃	—	2	4	no	—
327	Q₈×C₁₃	—	2	2	no	—
328	Q₈×C₁₃	—	2	4	no	—
329	Q₈×C₁₃	—	4	2	no	—
330	Q₈×C₁₃	—	4	2	no	—
331	Q₈×C₁₃	—	4	2	no	—
332	Q₈×C₁₃	—	8	4	no	—
333	D₄×C₁₃	—	2	4	no	—
334	D₄×C₁₃	—	2	4	no	—
335	D₄×C₁₃	—	2	2	no	—
336	D₄×C₁₃	—	2	4	no	—
337	D₄×C₁₃	—	4	2	no	—
338	D₄×C₁₃	—	4	4	no	—
339	D₄×C₁₃	—	4	2	no	—
340	D₄×C₁₃	—	4	8	no	—
341	D₄×C₁₃	—	4	8	no	—
342	D₄×C₁₃	—	4	4	no	—
343	D₄×C₁₃	—	4	2	no	—
344	D₄×C₁₃	—	8	1	no	—
345	D₄×C₁₃	—	8	4	no	—
346	D₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
347	C₂×C₄×C₁₃	—	2	2	no	—
348	C₂×C₄×C₁₃	—	2	4	no	—
349	C₂×C₄×C₁₃	—	2	4	no	—
350	C₂×C₄×C₁₃	—	2	2	no	—
351	C₂×C₄×C₁₃	—	2	2	no	—
352	C₂×C₄×C₁₃	—	2	2	no	—
353	C₂×C₄×C₁₃	—	2	2	no	—
354	C₂×C₄×C₁₃	—	2	2	no	—
355	C₂×C₄×C₁₃	—	2	2	no	—
356	C₂×C₄×C₁₃	—	2	2	no	—
357	C₂×C₄×C₁₃	—	4	1	no	—
358	C₂×C₄×C₁₃	—	4	8	no	—
359	C₂×C₄×C₁₃	—	4	4	no	—
360	C₂×C₄×C₁₃	—	4	4	no	—
361	C₂×C₄×C₁₃	—	8	2	no	—
362	C₂×C₄×C₁₃	—	8	1	no	—
363	C₂×C₄×C₁₃	—	8	4	no	—
364	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
365	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
366	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
367	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
368	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
369	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
370	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
371	C₈×C₁₃	—	2	2	no	—
372	C₈×C₁₃	—	2	4	no	—
373	C₈×C₁₃	—	2	2	no	—
374	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	2	yes	—
375	C₂×#137	C₂²×C₁₃	1	4	yes	complemented
376	C₂²×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
377	#563	—	2	2	no	—
378	#559	—	2	1	no	—
379	Q₈²	—	2	1	no	—
380	#556	C₂²×C₁₃	1	2	yes	complemented
381	#556	C₂²×C₁₃	1	2	yes	complemented
382	D₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
383	D₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
384	#547	—	2	1	no	—
385	#547	C₂²×C₁₃	1	2	yes	—
386	#546	—	2	2	no	—
387	#546	C₂²×C₁₃	1	4	yes	—
388	D₄²	—	2	1	no	—
389	D₄²	C₂²×C₁₃	1	2	yes	—
390	#542	—	2	2	no	—
391	#542	—	2	2	no	—
392	#537	C₂²×C₁₃	1	2	yes	—
393	#536	C₂²×C₁₃	1	4	yes	complemented
394	#534	—	2	2	no	—
395	#533	C₂²×C₁₃	1	1	yes	characteristic, complemented
396	#533	C₂²×C₁₃	1	1	yes	characteristic, complemented
397	#532	C₂²×C₁₃	1	1	yes	characteristic
398	#532	C₂²×C₁₃	1	1	yes	characteristic
399	C₂×#121	—	2	2	no	—
400	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
401	#497	C₂²×C₁₃	1	2	yes	complemented
402	#494	C₂²×C₁₃	1	1	yes	characteristic, complemented
403	#492	C₂²×C₁₃	1	1	yes	characteristic, complemented
404	#489	C₂²×C₁₃	1	2	yes	complemented
405	#487	C₂²×C₁₃	1	1	yes	characteristic, complemented
406	#486	C₂²×C₁₃	1	1	yes	characteristic, complemented
407	#485	C₂²×C₁₃	1	4	yes	complemented
408	#484	C₂²×C₁₃	1	2	yes	complemented
409	#483	C₂²×C₁₃	1	2	yes	complemented
410	#482	C₂²×C₁₃	1	4	yes	complemented
411	#476	C₂²×C₁₃	1	2	yes	complemented
412	#474	C₂²×C₁₃	1	2	yes	complemented
413	#470	C₂²×C₁₃	1	4	yes	complemented
414	#468	C₂²×C₁₃	1	4	yes	complemented
415	#467	C₂²×C₁₃	1	4	yes	complemented
416	#465	C₂²×C₁₃	1	4	yes	complemented
417	#464	C₂²×C₁₃	1	4	yes	complemented
418	#462	C₂²×C₁₃	1	2	yes	complemented
419	#461	C₂²×C₁₃	1	2	yes	complemented
420	#461	C₂²×C₁₃	1	2	yes	complemented
421	#460	C₂²×C₁₃	1	2	yes	complemented
422	#452	C₂²×C₁₃	1	4	yes	complemented
423	#452	C₂²×C₁₃	1	4	yes	complemented
424	#452	C₂²×C₁₃	1	4	yes	complemented
425	#452	C₂²×C₁₃	1	4	yes	complemented
426	#451	C₂²×C₁₃	1	4	yes	complemented
427	#450	C₂²×C₁₃	1	2	yes	—
428	#450	C₂²×C₁₃	1	2	yes	—
429	#450	C₂²×C₁₃	1	4	yes	complemented
430	#450	C₂²×C₁₃	1	4	yes	complemented
431	#448	C₂²×C₁₃	1	4	yes	complemented
432	#440	C₂²×C₁₃	1	4	yes	complemented
433	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
434	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
435	#436	C₂²×C₁₃	1	2	yes	complemented
436	#435	C₂²×C₁₃	1	4	yes	complemented
437	C₈×D₄	C₂²×C₁₃	1	2	yes	complemented
438	#432	C₂²×C₁₃	1	1	yes	characteristic, complemented
439	#431	C₂²×C₁₃	1	1	yes	characteristic, complemented
440	#418	C₂²×C₁₃	1	4	yes	complemented
441	#416	C₂²×C₁₃	1	4	yes	complemented
442	#408	C₂²×C₁₃	1	4	yes	complemented
443	C₂²×C₁₃	—	2	1	no	—
444	C₂²×C₁₃	—	2	4	no	—
445	C₂²×C₁₃	—	2	4	no	—
446	C₂²×C₁₃	—	2	1	no	—
447	C₂²×C₁₃	—	2	4	no	—
448	C₂²×C₁₃	—	2	1	no	—
449	C₂²×C₁₃	—	2	4	no	—
450	C₂²×C₁₃	—	4	2	no	—
451	C₂²×C₁₃	—	4	2	no	—
452	C₂²×C₁₃	—	4	2	no	—
453	C₂²×C₁₃	—	4	2	no	—
454	C₂²×C₁₃	—	4	2	no	—
455	C₂²×C₁₃	—	8	4	no	—
456	C₂²×C₁₃	—	16	8	no	—
457	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
458	C₄×C₁₃	—	2	1	no	—
459	C₄×C₁₃	—	2	1	no	—
460	C₄×C₁₃	—	2	1	no	—
461	C₄×C₁₃	—	2	4	no	—
462	C₄×C₁₃	—	2	1	no	—
463	C₄×C₁₃	—	4	2	no	—
464	C₄×C₁₃	—	4	2	no	—
465	C₄×C₁₃	—	4	2	no	—
466	C₄×C₁₃	—	4	2	no	—
467	C₄×C₁₃	—	4	2	no	—
468	C₄×C₁₃	—	4	2	no	—
469	C₄×C₁₃	#577	1	2	yes	—
470	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
471	H(5,𝔽₂)	—	4	8	no	—
472	C₂×#41	—	2	2	no	—
473	C₂×#41	C₂³×C₁₃	1	4	yes	—
474	C₂×#41	C₂³×C₁₃	1	2	yes	—
475	C₂×#41	C₂³×C₁₃	1	2	yes	—
476	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
477	C₂²×D₄	—	2	4	no	—
478	C₂²×D₄	—	2	2	no	—
479	C₂²×D₄	—	2	2	no	—
480	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
481	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
482	C₂³×C₄	—	2	1	no	—
483	#137	—	4	8	no	—
484	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
485	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
486	C₂×SD₁₆	—	4	8	no	—
487	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
488	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
489	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
490	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
491	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
492	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
493	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
494	C₄⋊Q₈	—	2	4	no	—
495	C₄⋊Q₈	—	2	2	no	—
496	C₄⋊Q₈	—	2	2	no	—
497	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
498	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
499	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
500	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
501	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
502	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
503	#127	D₄×C₁₃	1	1	yes	characteristic
504	#127	C₂³×C₁₃	1	1	yes	characteristic
505	#126	—	2	4	no	—
506	#126	—	2	4	no	—
507	#125	—	2	1	no	—
508	#125	—	2	1	no	—
509	#124	—	2	4	no	—
510	#124	—	2	2	no	—
511	#124	—	2	2	no	—
512	#124	D₄×C₁₃	1	2	yes	—
513	#124	C₂³×C₁₃	1	2	yes	—
514	#123	—	2	4	no	—
515	#123	—	2	4	no	—
516	#123	—	2	4	no	—
517	#123	—	2	4	no	—
518	C₂²⋊Q₈	—	2	2	no	—
519	C₂²⋊Q₈	—	2	1	no	—
520	C₂²⋊Q₈	—	2	1	no	—
521	C₂²⋊Q₈	—	2	4	no	—
522	C₂²⋊Q₈	—	2	4	no	—
523	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
524	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
525	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
526	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
527	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
528	#121	—	2	4	no	—
529	#121	—	2	2	no	—
530	#121	—	2	2	no	—
531	#121	—	2	1	no	—
532	#121	—	2	1	no	—
533	#121	—	2	2	no	—
534	#121	—	2	4	no	—
535	#121	D₄×C₁₃	1	2	yes	—
536	#121	D₄×C₁₃	1	2	yes	—
537	#121	C₂³×C₁₃	1	4	yes	—
538	#120	—	2	4	no	—
539	#120	—	2	4	no	—
540	C₄×Q₈	—	2	2	no	—
541	C₄×Q₈	—	2	2	no	—
542	C₄×Q₈	—	2	1	no	—
543	C₄×Q₈	—	2	1	no	—
544	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
545	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
546	C₄×D₄	—	2	2	no	—
547	C₄×D₄	—	2	2	no	—
548	C₄×D₄	—	2	1	no	—
549	C₄×D₄	—	2	1	no	—
550	C₄×D₄	—	2	1	no	—
551	C₄×D₄	—	2	1	no	—
552	C₄×D₄	C₂³×C₁₃	1	2	yes	—
553	C₄×D₄	C₂³×C₁₃	1	2	yes	—
554	C₄×D₄	C₂³×C₁₃	1	2	yes	—
555	C₄×D₄	C₂³×C₁₃	1	2	yes	—
556	#117	—	2	1	no	—
557	#117	—	2	1	no	—
558	#117	C₂³×C₁₃	1	4	yes	—
559	C₂×C₄⋊C₄	—	2	2	no	—
560	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
561	C₂×C₂²⋊C₄	—	2	1	no	—
562	C₂×C₂²⋊C₄	—	2	4	no	—
563	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
564	#107	C₂³×C₁₃	1	4	yes	—
565	#106	C₂³×C₁₃	1	2	yes	—
566	#106	C₂³×C₁₃	1	2	yes	—
567	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
568	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
569	#103	C₂³×C₁₃	1	4	yes	—
570	#103	C₂³×C₁₃	1	4	yes	—
571	#103	C₂³×C₁₃	1	2	yes	—
572	#103	C₂³×C₁₃	1	2	yes	—
573	#103	C₂³×C₁₃	1	4	yes	—
574	#102	C₂³×C₁₃	1	2	yes	—
575	#102	C₂³×C₁₃	1	4	yes	—
576	#102	C₂³×C₁₃	1	2	yes	—
577	#102	C₂³×C₁₃	1	4	yes	—
578	#102	C₂³×C₁₃	1	4	yes	—
579	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
580	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
581	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
582	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
583	#97	C₂³×C₁₃	1	2	yes	—
584	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
585	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
586	C₂×C₁₃	—	4	1	no	—
587	C₂×C₁₃	—	4	4	no	—
588	C₂×C₁₃	—	4	4	no	—
589	C₂×C₁₃	—	8	2	no	—
590	C₂×C₁₃	#3484	1	1	yes	characteristic
591	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
592	C₂×C₁₃	#3586	1	1	yes	characteristic
593	C₂⁴	—	2	1	no	—
594	C₂⁴	—	2	4	no	—
595	#41	—	2	8	no	—
596	#41	—	4	4	no	—
597	#41	—	4	4	no	—
598	#41	—	4	4	no	—
599	#41	—	4	8	no	—
600	C₂×Q₈	—	2	1	no	—
601	C₂×Q₈	—	2	1	no	—
602	C₂×Q₈	—	2	4	no	—
603	C₂×Q₈	—	4	4	no	—
604	C₂×Q₈	—	4	4	no	—
605	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
606	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
607	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
608	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
609	C₂×D₄	—	2	4	no	—
610	C₂×D₄	—	2	8	no	—
611	C₂×D₄	—	2	4	no	—
612	C₂×D₄	—	2	2	no	—
613	C₂×D₄	—	2	4	no	—
614	C₂×D₄	—	2	1	no	—
615	C₂×D₄	—	2	1	no	—
616	C₂×D₄	—	2	4	no	—
617	C₂×D₄	—	2	1	no	—
618	C₂×D₄	—	4	4	no	—
619	C₂×D₄	—	4	8	no	—
620	C₂×D₄	—	4	16	no	—
621	C₂×D₄	—	8	4	no	—
622	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
623	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
624	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
625	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
626	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
627	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
628	C₂²×C₄	—	2	1	no	—
629	C₂²×C₄	—	2	4	no	—
630	C₂²×C₄	—	2	4	no	—
631	C₂²×C₄	—	2	2	no	—
632	C₂²×C₄	—	2	2	no	—
633	C₂²×C₄	—	2	2	no	—
634	C₂²×C₄	—	8	2	no	—
635	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
636	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
637	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
638	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
639	Q₁₆	—	4	4	no	—
640	Q₁₆	—	4	4	no	—
641	SD₁₆	—	2	4	no	—
642	SD₁₆	—	2	8	no	—
643	SD₁₆	—	2	4	no	—
644	SD₁₆	—	4	4	no	—
645	SD₁₆	—	4	4	no	—
646	M₁₆	—	4	4	no	—
647	C₂×C₈	—	4	4	no	—
648	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
649	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
650	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
651	C₄⋊C₄	—	2	1	no	—
652	C₄⋊C₄	—	2	4	no	—
653	C₄⋊C₄	—	2	1	no	—
654	C₄⋊C₄	—	2	1	no	—
655	C₄⋊C₄	—	2	1	no	—
656	C₄⋊C₄	—	2	1	no	—
657	C₄⋊C₄	—	2	1	no	—
658	C₄⋊C₄	—	2	1	no	—
659	C₄⋊C₄	—	2	1	no	—
660	C₄⋊C₄	—	2	1	no	—
661	C₄⋊C₄	—	2	4	no	—
662	C₄⋊C₄	—	2	4	no	—
663	C₄⋊C₄	—	2	2	no	—
664	C₄⋊C₄	—	2	2	no	—
665	C₄⋊C₄	—	2	2	no	—
666	C₄⋊C₄	—	2	2	no	—
667	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
668	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
669	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
670	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
671	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
672	C₂²⋊C₄	—	2	4	no	—
673	C₂²⋊C₄	—	2	2	no	—
674	C₂²⋊C₄	—	2	2	no	—
675	C₂²⋊C₄	—	2	4	no	—
676	C₂²⋊C₄	—	2	4	no	—
677	C₂²⋊C₄	—	2	4	no	—
678	C₂²⋊C₄	—	2	2	no	—
679	C₂²⋊C₄	—	2	2	no	—
680	C₂²⋊C₄	—	2	2	no	—
681	C₂²⋊C₄	—	2	4	no	—
682	C₂²⋊C₄	—	2	2	no	—
683	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
684	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
685	C₄²	—	2	2	no	—
686	C₄²	—	2	2	no	—
687	C₄²	—	2	4	no	—
688	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
689	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
690	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
691	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
692	C₁₃	#61680	1	1	yes	characteristic, direct product factor, Sylow
693	C₂³	—	2	4	no	—
694	C₂³	—	2	2	no	—
695	C₂³	—	2	2	no	—
696	C₂³	—	4	8	no	—
697	C₂³	—	8	1	no	—
698	C₂³	—	8	1	no	—
699	C₂³	—	8	4	no	—
700	C₂³	—	8	4	no	—
701	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
702	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
703	Q₈	—	2	2	no	—
704	Q₈	—	2	4	no	—
705	Q₈	—	2	2	no	—
706	Q₈	—	2	4	no	—
707	Q₈	—	4	2	no	—
708	Q₈	—	4	2	no	—
709	Q₈	—	4	2	no	—
710	Q₈	—	8	4	no	—
711	D₄	—	2	4	no	—
712	D₄	—	2	4	no	—
713	D₄	—	2	2	no	—
714	D₄	—	2	4	no	—
715	D₄	—	4	2	no	—
716	D₄	—	4	4	no	—
717	D₄	—	4	2	no	—
718	D₄	—	4	8	no	—
719	D₄	—	4	8	no	—
720	D₄	—	4	4	no	—
721	D₄	—	4	2	no	—
722	D₄	—	8	1	no	—
723	D₄	—	8	4	no	—
724	D₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	4	no	—
727	C₂×C₄	—	2	4	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	4	1	no	—
736	C₂×C₄	—	4	8	no	—
737	C₂×C₄	—	4	4	no	—
738	C₂×C₄	—	4	4	no	—
739	C₂×C₄	—	8	2	no	—
740	C₂×C₄	—	8	1	no	—
741	C₂×C₄	—	8	4	no	—
742	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
743	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
744	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
745	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
746	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
747	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
748	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
749	C₈	—	2	2	no	—
750	C₈	—	2	4	no	—
751	C₈	—	2	2	no	—
752	C₂²	—	2	1	no	—
753	C₂²	—	2	4	no	—
754	C₂²	—	2	1	no	—
755	C₂²	—	2	4	no	—
756	C₂²	—	2	4	no	—
757	C₂²	—	2	1	no	—
758	C₂²	—	2	4	no	—
759	C₂²	—	4	2	no	—
760	C₂²	—	4	2	no	—
761	C₂²	—	4	2	no	—
762	C₂²	—	4	2	no	—
763	C₂²	—	4	2	no	—
764	C₂²	—	8	4	no	—
765	C₂²	—	16	8	no	—
766	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
767	C₄	—	2	1	no	—
768	C₄	—	2	1	no	—
769	C₄	—	2	1	no	—
770	C₄	—	2	1	no	—
771	C₄	—	2	4	no	—
772	C₄	—	4	2	no	—
773	C₄	—	4	2	no	—
774	C₄	—	4	2	no	—
775	C₄	—	4	2	no	—
776	C₄	—	4	2	no	—
777	C₄	—	4	2	no	—
778	C₄	C₁₃×#577	1	2	yes	—
779	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
780	C₂	—	4	1	no	—
781	C₂	—	4	4	no	—
782	C₂	—	4	4	no	—
783	C₂	—	8	2	no	—
784	C₂	C₁₃×#3484	1	1	yes	characteristic
785	C₂	C₂×C₁₃×#577	1	1	yes	characteristic
786	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×#3496	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₁₃×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3550	C₂	semidirect
3. C₁₃×#3324	C₂	semidirect
4. C₁₃×#3311	C₂	semidirect
5. C₁₃×#3302	C₂	semidirect
6. D₄×C₁₃×SD₁₆	C₂	semidirect
7. C₁₃×#3276	C₂	semidirect
8. C₁₃×#3266	C₂	semidirect
9. C₁₃×#3216	C₂	semidirect
10. C₁₃×#3210	C₂	semidirect
11. C₁₃×#3201	C₂	semidirect
12. C₁₃×#3110	C₂	semidirect
13. C₁₃×#3101	C₂	semidirect
14. C₁₃×#3009	C₂	semidirect
15. C₁₃×#2981	C₂	semidirect
17. C₂×C₁₃×#137	C₂²	semidirect
18. C₂²×C₁₃×SD₁₆	C₂²	semidirect
22. C₁₃×#556	C₂²	semidirect
23. C₁₃×#556	C₂²	semidirect
24. D₄×Q₈×C₁₃	C₂²	semidirect
25. D₄×Q₈×C₁₃	C₂²	semidirect
35. C₁₃×#536	C₂²	semidirect
37. C₁₃×#533	C₂²	semidirect
38. C₁₃×#533	C₂²	semidirect
43. C₁₃×#497	C₂²	semidirect
44. C₁₃×#494	C₂²	semidirect
45. C₁₃×#492	C₂²	semidirect
46. C₁₃×#489	C₂²	semidirect
47. C₁₃×#487	C₂²	semidirect
48. C₁₃×#486	C₂²	semidirect
49. C₁₃×#485	C₂²	semidirect
50. C₁₃×#484	C₂²	semidirect
51. C₁₃×#483	C₂²	semidirect
52. C₁₃×#482	C₂²	semidirect
53. C₁₃×#476	C₂²	semidirect
54. C₁₃×#474	C₂²	semidirect
55. C₁₃×#470	C₂²	semidirect
56. C₁₃×#468	C₂²	semidirect
57. C₁₃×#467	C₂²	semidirect
58. C₁₃×#465	C₂²	semidirect
59. C₁₃×#464	C₂²	semidirect
60. C₁₃×#462	C₂²	semidirect
61. C₁₃×#461	C₂²	semidirect
62. C₁₃×#461	C₂²	semidirect
63. C₁₃×#460	C₂²	semidirect
64. C₁₃×#452	C₂²	semidirect
65. C₁₃×#452	C₂²	semidirect
66. C₁₃×#452	C₂²	semidirect
67. C₁₃×#452	C₂²	semidirect
68. C₁₃×#451	C₂²	semidirect
71. C₁₃×#450	C₂²	semidirect
72. C₁₃×#450	C₂²	semidirect
73. C₁₃×#448	C₂²	semidirect
74. C₁₃×#440	C₂²	semidirect
75. C₄×C₁₃×SD₁₆	C₂²	semidirect
76. C₄×C₁₃×SD₁₆	C₂²	semidirect
77. C₁₃×#436	C₂²	semidirect
78. C₁₃×#435	C₂²	semidirect
79. C₈×D₄×C₁₃	C₂²	semidirect
80. C₁₃×#432	C₂²	semidirect
81. C₁₃×#431	C₂²	semidirect
82. C₁₃×#418	C₂²	semidirect
83. C₁₃×#416	C₂²	semidirect
84. C₁₃×#408	C₂²	semidirect
200. #61680	C₁₃	direct (N × H)
300. #3550	C₂×C₁₃	semidirect
302. #3324	C₂×C₁₃	semidirect
303. #3311	C₂×C₁₃	semidirect
304. #3302	C₂×C₁₃	semidirect
305. D₄×SD₁₆	C₂×C₁₃	semidirect
306. #3276	C₂×C₁₃	semidirect
307. #3266	C₂×C₁₃	semidirect
308. #3216	C₂×C₁₃	semidirect
309. #3210	C₂×C₁₃	semidirect
310. #3201	C₂×C₁₃	semidirect
311. #3110	C₂×C₁₃	semidirect
312. #3101	C₂×C₁₃	semidirect
313. #3009	C₂×C₁₃	semidirect
314. #2981	C₂×C₁₃	semidirect
375. C₂×#137	C₂²×C₁₃	semidirect
376. C₂²×SD₁₆	C₂²×C₁₃	semidirect
380. #556	C₂²×C₁₃	semidirect
381. #556	C₂²×C₁₃	semidirect
382. D₄×Q₈	C₂²×C₁₃	semidirect
383. D₄×Q₈	C₂²×C₁₃	semidirect
393. #536	C₂²×C₁₃	semidirect
395. #533	C₂²×C₁₃	semidirect
396. #533	C₂²×C₁₃	semidirect
401. #497	C₂²×C₁₃	semidirect
402. #494	C₂²×C₁₃	semidirect
403. #492	C₂²×C₁₃	semidirect
404. #489	C₂²×C₁₃	semidirect
405. #487	C₂²×C₁₃	semidirect
406. #486	C₂²×C₁₃	semidirect
407. #485	C₂²×C₁₃	semidirect
408. #484	C₂²×C₁₃	semidirect
409. #483	C₂²×C₁₃	semidirect
410. #482	C₂²×C₁₃	semidirect
411. #476	C₂²×C₁₃	semidirect
412. #474	C₂²×C₁₃	semidirect
413. #470	C₂²×C₁₃	semidirect
414. #468	C₂²×C₁₃	semidirect
415. #467	C₂²×C₁₃	semidirect
416. #465	C₂²×C₁₃	semidirect
417. #464	C₂²×C₁₃	semidirect
418. #462	C₂²×C₁₃	semidirect
419. #461	C₂²×C₁₃	semidirect
420. #461	C₂²×C₁₃	semidirect
421. #460	C₂²×C₁₃	semidirect
422. #452	C₂²×C₁₃	semidirect
423. #452	C₂²×C₁₃	semidirect
424. #452	C₂²×C₁₃	semidirect
425. #452	C₂²×C₁₃	semidirect
426. #451	C₂²×C₁₃	semidirect
429. #450	C₂²×C₁₃	semidirect
430. #450	C₂²×C₁₃	semidirect
431. #448	C₂²×C₁₃	semidirect
432. #440	C₂²×C₁₃	semidirect
433. C₄×SD₁₆	C₂²×C₁₃	semidirect
434. C₄×SD₁₆	C₂²×C₁₃	semidirect
435. #436	C₂²×C₁₃	semidirect
436. #435	C₂²×C₁₃	semidirect
437. C₈×D₄	C₂²×C₁₃	semidirect
438. #432	C₂²×C₁₃	semidirect
439. #431	C₂²×C₁₃	semidirect
440. #418	C₂²×C₁₃	semidirect
441. #416	C₂²×C₁₃	semidirect
442. #408	C₂²×C₁₃	semidirect
692. C₁₃	#61680	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×#3550	2
C₁₃×#3496	2
C₁₃×#3324	2
C₁₃×#3311	2
C₁₃×#3302	2
D₄×C₁₃×SD₁₆	2
C₁₃×#3276	2
C₁₃×#3266	2
C₁₃×#3216	2
C₁₃×#3210	2
C₁₃×#3201	2
C₁₃×#3110	2
C₁₃×#3101	2
C₁₃×#3009	2
C₁₃×#2981	2
#61680	13

Subgroups — C13×#61680 #15748019

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61680 #15748019