Subgroups — C₁₃×#61904 #15748243

Order 3328.

1788 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3523	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#559	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3401	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3400	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3394	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3373	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3371	C₂	1	4	yes	maximal, complemented
8	C₁₃×#3365	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3217	C₂	1	1	yes	maximal, characteristic
10	C₁₃×#3215	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3211	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3208	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3114	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3113	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3108	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#3101	C₂	1	2	yes	maximal, complemented
17	C₁₃×#2984	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₃×#559	—	2	1	no	—
19	C₁₃×#559	—	2	1	no	—
20	C₁₃×#559	—	2	2	no	—
21	C₁₃×#559	C₂²	1	2	yes	—
22	C₁₃×#559	C₂²	1	4	yes	—
23	C₁₃×#559	C₂²	1	2	yes	—
24	C₁₃×#557	C₂²	1	1	yes	characteristic, complemented
25	C₁₃×#557	C₂²	1	1	yes	characteristic, complemented
26	C₁₃×#557	C₂²	1	2	yes	complemented
27	C₁₃×#556	C₂²	1	1	yes	characteristic, complemented
28	C₁₃×#556	C₂²	1	2	yes	complemented
29	C₁₃×#552	—	2	1	no	—
30	C₁₃×#552	—	2	2	no	—
31	D₄×Q₈×C₁₃	—	2	1	no	—
32	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
33	C₁₃×#541	—	2	2	no	—
34	C₁₃×#541	—	2	1	no	—
35	C₁₃×#533	C₂²	1	2	yes	—
36	C₁₃×#533	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
38	C₁₃×#529	C₂²	1	1	yes	characteristic
39	C₁₃×#529	C₂²	1	2	yes	—
40	C₂×C₁₃×#124	—	2	1	no	—
41	C₂×C₁₃×#124	C₂²	1	2	yes	—
42	C₂×C₁₃×#123	—	2	2	no	—
43	C₁₃×#519	—	2	1	no	—
44	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
45	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₁₃	—	2	1	no	—
47	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
48	C₁₃×#497	C₂²	1	4	yes	complemented
49	C₁₃×#496	C₂²	1	2	yes	—
50	C₁₃×#495	C₂²	1	4	yes	complemented
51	C₁₃×#492	C₂²	1	2	yes	—
52	C₁₃×#490	C₂²	1	2	yes	—
53	C₁₃×#489	C₂²	1	4	yes	complemented
54	C₁₃×#488	C₂²	1	4	yes	complemented
55	C₁₃×#486	C₂²	1	2	yes	—
56	C₁₃×#483	C₂²	1	1	yes	characteristic
57	C₁₃×#483	C₂²	1	2	yes	—
58	C₁₃×#480	C₂²	1	1	yes	characteristic
59	C₁₃×#479	C₂²	1	2	yes	complemented
60	C₁₃×#478	C₂²	1	4	yes	complemented
61	C₁₃×#476	C₂²	1	4	yes	complemented
62	C₁₃×#475	C₂²	1	2	yes	complemented
63	C₁₃×#464	C₂²	1	2	yes	complemented
64	C₁₃×#464	C₂²	1	4	yes	complemented
65	C₁₃×#464	C₂²	1	4	yes	complemented
66	C₁₃×#464	C₂²	1	4	yes	complemented
67	C₁₃×#463	C₂²	1	4	yes	complemented
68	C₁₃×#463	C₂²	1	4	yes	complemented
69	C₁₃×#462	C₂²	1	2	yes	complemented
70	C₁₃×#461	C₂²	1	4	yes	complemented
71	C₁₃×#460	C₂²	1	2	yes	—
72	C₁₃×#460	C₂²	1	4	yes	—
73	C₁₃×#459	C₂²	1	2	yes	—
74	C₁₃×#451	C₂²	1	1	yes	characteristic
75	C₁₃×#451	C₂²	1	2	yes	—
76	C₁₃×#450	C₂²	1	2	yes	—
77	C₁₃×#450	C₂²	1	2	yes	—
78	C₁₃×#450	C₂²	1	2	yes	—
79	C₁₃×#448	C₂²	1	1	yes	characteristic
80	C₁₃×#447	C₂²	1	2	yes	—
81	C₁₃×#446	C₂²	1	4	yes	complemented
82	C₁₃×#446	C₂²	1	2	yes	complemented
83	C₈×Q₈×C₁₃	C₂²	1	2	yes	complemented
84	C₁₃×#442	C₂²	1	4	yes	complemented
85	C₁₃×#441	C₂²	1	4	yes	complemented
86	C₁₃×#440	C₂²	1	4	yes	complemented
87	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
88	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
89	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
90	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
91	C₁₃×#432	C₂²	1	1	yes	characteristic
92	C₁₃×#432	C₂²	1	2	yes	—
93	C₁₃×#431	C₂²	1	2	yes	—
94	C₁₃×#431	C₂²	1	1	yes	characteristic
95	C₂²×Q₈×C₁₃	—	2	1	no	—
96	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
97	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
98	C₂²×D₄×C₁₃	—	2	1	no	—
99	C₂²×D₄×C₁₃	—	2	1	no	—
100	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
101	C₂³×C₄×C₁₃	—	2	2	no	—
102	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
103	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
104	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
105	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
106	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
107	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
108	C₂×C₁₃×D₈	C₂³	1	4	yes	—
109	C₁₃×C₄⋊Q₈	—	2	1	no	—
110	C₁₃×C₄⋊Q₈	—	2	2	no	—
111	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
112	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
113	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
114	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
115	C₁₃×#127	—	2	1	no	—
116	C₁₃×#127	—	2	1	no	—
117	C₁₃×#127	C₂³	1	2	yes	—
118	C₁₃×#127	C₂³	1	2	yes	—
119	C₁₃×#126	—	2	2	no	—
120	C₁₃×#126	—	2	2	no	—
121	C₁₃×#126	—	2	2	no	—
122	C₁₃×#126	—	2	2	no	—
123	C₁₃×#126	—	2	1	no	—
124	C₁₃×#125	—	2	2	no	—
125	C₁₃×#125	—	2	2	no	—
126	C₁₃×#125	—	2	2	no	—
127	C₁₃×#125	—	2	1	no	—
128	C₁₃×#125	—	2	2	no	—
129	C₁₃×#125	—	2	2	no	—
130	C₁₃×#125	—	2	1	no	—
131	C₁₃×#125	C₂³	1	2	yes	—
132	C₁₃×#125	C₂³	1	1	yes	characteristic
133	C₁₃×#124	—	2	2	no	—
134	C₁₃×#124	—	2	2	no	—
135	C₁₃×#124	—	2	4	no	—
136	C₁₃×#124	—	2	2	no	—
137	C₁₃×#124	—	2	2	no	—
138	C₁₃×#124	C₂³	1	2	yes	—
139	C₁₃×#124	C₂³	1	4	yes	—
140	C₁₃×#124	C₂³	1	4	yes	—
141	C₁₃×#124	C₂³	1	1	yes	characteristic
142	C₁₃×#123	—	2	2	no	—
143	C₁₃×#123	—	2	1	no	—
144	C₁₃×#123	—	2	4	no	—
145	C₁₃×#123	—	2	4	no	—
146	C₁₃×#123	—	2	4	no	—
147	C₁₃×#123	—	2	4	no	—
148	C₁₃×C₂²⋊Q₈	—	2	1	no	—
149	C₁₃×C₂²⋊Q₈	—	2	2	no	—
150	C₁₃×C₂²⋊Q₈	—	2	1	no	—
151	C₁₃×C₂²⋊Q₈	—	2	2	no	—
152	C₁₃×C₂²⋊Q₈	—	2	1	no	—
153	C₁₃×C₂²⋊Q₈	—	2	2	no	—
154	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
155	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
156	C₁₃×#121	C₂³	1	1	yes	characteristic
157	C₄×Q₈×C₁₃	—	2	1	no	—
158	C₄×Q₈×C₁₃	—	2	1	no	—
159	C₄×Q₈×C₁₃	—	2	2	no	—
160	C₄×Q₈×C₁₃	—	2	1	no	—
161	C₄×Q₈×C₁₃	—	2	1	no	—
162	C₄×Q₈×C₁₃	—	2	2	no	—
163	C₄×Q₈×C₁₃	—	2	1	no	—
164	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
165	C₄×Q₈×C₁₃	D₄	1	2	yes	—
166	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
167	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
168	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
169	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
170	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
171	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
172	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
173	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
174	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
175	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
176	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
177	C₄×D₄×C₁₃	—	2	1	no	—
178	C₄×D₄×C₁₃	—	2	2	no	—
179	C₄×D₄×C₁₃	—	2	2	no	—
180	C₄×D₄×C₁₃	—	2	2	no	—
181	C₄×D₄×C₁₃	—	2	4	no	—
182	C₄×D₄×C₁₃	—	2	2	no	—
183	C₄×D₄×C₁₃	—	2	2	no	—
184	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
185	C₄×D₄×C₁₃	C₂³	1	4	yes	—
186	C₄×D₄×C₁₃	C₂³	1	4	yes	—
187	C₄×D₄×C₁₃	C₂³	1	2	yes	—
188	C₁₃×#117	—	2	2	no	—
189	C₁₃×#117	—	2	1	no	—
190	C₁₃×#117	—	2	1	no	—
191	C₁₃×#117	—	2	2	no	—
192	C₁₃×#117	—	2	2	no	—
193	C₁₃×#117	—	2	1	no	—
194	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
195	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
196	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
197	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
198	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
199	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
200	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
201	C₂×C₄²×C₁₃	—	2	1	no	—
202	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
203	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
204	C₁₃×#107	C₂³	1	2	yes	—
205	C₁₃×#106	C₂³	1	2	yes	—
206	C₁₃×#106	C₂³	1	4	yes	—
207	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
208	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
209	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
210	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
211	C₁₃×#103	C₂³	1	2	yes	—
212	C₁₃×#103	C₂³	1	4	yes	—
213	C₁₃×#103	C₂³	1	2	yes	—
214	C₁₃×#103	C₂³	1	2	yes	—
215	C₁₃×#103	C₂³	1	4	yes	—
216	C₁₃×#102	C₂³	1	2	yes	—
217	C₁₃×#102	C₂³	1	4	yes	—
218	C₁₃×#102	C₂³	1	4	yes	—
219	C₁₃×#102	C₂³	1	4	yes	—
220	C₁₃×#102	C₂³	1	4	yes	—
221	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
222	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
223	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
224	C₁₃×#97	C₂³	1	4	yes	—
225	C₁₃×#97	C₂³	1	2	yes	—
226	C₄×C₈×C₁₃	C₂³	1	4	yes	—
227	C₄×C₈×C₁₃	C₂³	1	2	yes	—
228	#61904	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
229	C₂⁴×C₁₃	—	2	2	no	—
230	C₂×Q₈×C₁₃	—	2	2	no	—
231	C₂×Q₈×C₁₃	—	2	1	no	—
232	C₂×Q₈×C₁₃	—	2	1	no	—
233	C₂×Q₈×C₁₃	—	4	2	no	—
234	C₂×Q₈×C₁₃	—	4	2	no	—
235	C₂×Q₈×C₁₃	—	4	4	no	—
236	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
237	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
238	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
239	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
240	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
241	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
242	C₂×D₄×C₁₃	—	2	1	no	—
243	C₂×D₄×C₁₃	—	2	2	no	—
244	C₂×D₄×C₁₃	—	2	2	no	—
245	C₂×D₄×C₁₃	—	2	2	no	—
246	C₂×D₄×C₁₃	—	2	2	no	—
247	C₂×D₄×C₁₃	—	2	2	no	—
248	C₂×D₄×C₁₃	—	4	4	no	—
249	C₂×D₄×C₁₃	—	4	4	no	—
250	C₂×D₄×C₁₃	—	8	2	no	—
251	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
252	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
253	C₂²×C₄×C₁₃	—	2	1	no	—
254	C₂²×C₄×C₁₃	—	2	1	no	—
255	C₂²×C₄×C₁₃	—	2	2	no	—
256	C₂²×C₄×C₁₃	—	2	1	no	—
257	C₂²×C₄×C₁₃	—	2	4	no	—
258	C₂²×C₄×C₁₃	—	2	4	no	—
259	C₂²×C₄×C₁₃	—	8	4	no	—
260	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
261	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
262	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
263	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
264	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
265	C₁₃×Q₁₆	—	4	4	no	—
266	C₁₃×Q₁₆	—	4	2	no	—
267	C₁₃×SD₁₆	—	4	4	no	—
268	C₁₃×SD₁₆	—	4	2	no	—
269	C₁₃×SD₁₆	—	4	4	no	—
270	C₁₃×SD₁₆	—	4	4	no	—
271	C₁₃×D₈	—	4	4	no	—
272	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
273	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
274	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
275	C₁₃×C₄⋊C₄	—	2	2	no	—
276	C₁₃×C₄⋊C₄	—	2	2	no	—
277	C₁₃×C₄⋊C₄	—	2	1	no	—
278	C₁₃×C₄⋊C₄	—	2	2	no	—
279	C₁₃×C₄⋊C₄	—	2	1	no	—
280	C₁₃×C₄⋊C₄	—	2	2	no	—
281	C₁₃×C₄⋊C₄	—	2	1	no	—
282	C₁₃×C₄⋊C₄	—	2	2	no	—
283	C₁₃×C₄⋊C₄	—	2	1	no	—
284	C₁₃×C₄⋊C₄	—	2	2	no	—
285	C₁₃×C₄⋊C₄	—	2	1	no	—
286	C₁₃×C₄⋊C₄	—	2	2	no	—
287	C₁₃×C₄⋊C₄	—	2	1	no	—
288	C₁₃×C₄⋊C₄	—	2	1	no	—
289	C₁₃×C₄⋊C₄	—	2	2	no	—
290	C₁₃×C₄⋊C₄	—	2	2	no	—
291	C₁₃×C₄⋊C₄	—	2	2	no	—
292	C₁₃×C₄⋊C₄	—	2	2	no	—
293	C₁₃×C₄⋊C₄	—	2	2	no	—
294	C₁₃×C₄⋊C₄	—	2	1	no	—
295	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
296	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
297	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
298	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
299	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
300	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
301	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
302	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
303	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
304	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
305	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
306	C₁₃×C₂²⋊C₄	—	2	1	no	—
307	C₁₃×C₂²⋊C₄	—	2	2	no	—
308	C₁₃×C₂²⋊C₄	—	2	4	no	—
309	C₁₃×C₂²⋊C₄	—	2	4	no	—
310	C₁₃×C₂²⋊C₄	—	2	4	no	—
311	C₁₃×C₂²⋊C₄	—	2	4	no	—
312	C₁₃×C₂²⋊C₄	—	2	4	no	—
313	C₁₃×C₂²⋊C₄	—	2	4	no	—
314	C₁₃×C₂²⋊C₄	—	2	1	no	—
315	C₁₃×C₂²⋊C₄	—	2	2	no	—
316	C₁₃×C₂²⋊C₄	—	2	1	no	—
317	C₁₃×C₂²⋊C₄	—	2	1	no	—
318	C₁₃×C₂²⋊C₄	—	2	2	no	—
319	C₁₃×C₂²⋊C₄	—	2	2	no	—
320	C₁₃×C₂²⋊C₄	—	2	1	no	—
321	C₄²×C₁₃	—	2	2	no	—
322	C₄²×C₁₃	—	2	2	no	—
323	C₄²×C₁₃	—	2	2	no	—
324	C₄²×C₁₃	—	2	2	no	—
325	C₄²×C₁₃	—	2	2	no	—
326	C₄²×C₁₃	—	2	2	no	—
327	C₄²×C₁₃	—	2	1	no	—
328	C₄²×C₁₃	C₂×D₄	1	2	yes	—
329	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
330	C₄²×C₁₃	C₂×D₄	1	2	yes	—
331	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
332	C₄²×C₁₃	C₂⁴	1	2	yes	—
333	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
334	C₄²×C₁₃	C₂⁴	1	2	yes	—
335	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
336	#3523	C₂×C₁₃	1	1	yes	characteristic, complemented
337	C₂×#559	C₂×C₁₃	1	1	yes	characteristic, complemented
338	#3401	C₂×C₁₃	1	4	yes	complemented
339	#3400	C₂×C₁₃	1	2	yes	complemented
340	#3394	C₂×C₁₃	1	2	yes	complemented
341	#3373	C₂×C₁₃	1	2	yes	complemented
342	#3371	C₂×C₁₃	1	4	yes	complemented
343	#3365	C₂×C₁₃	1	2	yes	complemented
344	#3217	C₂×C₁₃	1	1	yes	characteristic
345	#3215	C₂×C₁₃	1	2	yes	complemented
346	#3211	C₂×C₁₃	1	2	yes	complemented
347	#3208	C₂×C₁₃	1	1	yes	characteristic, complemented
348	#3114	C₂×C₁₃	1	2	yes	complemented
349	#3113	C₂×C₁₃	1	1	yes	characteristic, complemented
350	#3108	C₂×C₁₃	1	1	yes	characteristic, complemented
351	#3101	C₂×C₁₃	1	2	yes	complemented
352	#2984	C₂×C₁₃	1	1	yes	characteristic, complemented
353	C₂³×C₁₃	—	2	1	no	—
354	C₂³×C₁₃	—	2	4	no	—
355	C₂³×C₁₃	—	4	4	no	—
356	C₂³×C₁₃	—	4	4	no	—
357	C₂³×C₁₃	—	4	4	no	—
358	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
359	Q₈×C₁₃	—	2	2	no	—
360	Q₈×C₁₃	—	2	2	no	—
361	Q₈×C₁₃	—	2	2	no	—
362	Q₈×C₁₃	—	2	4	no	—
363	Q₈×C₁₃	—	2	2	no	—
364	Q₈×C₁₃	—	2	2	no	—
365	Q₈×C₁₃	—	4	2	no	—
366	Q₈×C₁₃	—	4	2	no	—
367	Q₈×C₁₃	—	4	4	no	—
368	Q₈×C₁₃	—	4	2	no	—
369	D₄×C₁₃	—	2	2	no	—
370	D₄×C₁₃	—	2	4	no	—
371	D₄×C₁₃	—	2	4	no	—
372	D₄×C₁₃	—	4	4	no	—
373	D₄×C₁₃	—	4	4	no	—
374	D₄×C₁₃	—	4	2	no	—
375	D₄×C₁₃	—	4	4	no	—
376	D₄×C₁₃	—	8	2	no	—
377	D₄×C₁₃	—	8	2	no	—
378	C₂×C₄×C₁₃	—	2	4	no	—
379	C₂×C₄×C₁₃	—	2	2	no	—
380	C₂×C₄×C₁₃	—	2	2	no	—
381	C₂×C₄×C₁₃	—	2	2	no	—
382	C₂×C₄×C₁₃	—	2	1	no	—
383	C₂×C₄×C₁₃	—	2	2	no	—
384	C₂×C₄×C₁₃	—	2	1	no	—
385	C₂×C₄×C₁₃	—	2	2	no	—
386	C₂×C₄×C₁₃	—	2	2	no	—
387	C₂×C₄×C₁₃	—	2	2	no	—
388	C₂×C₄×C₁₃	—	2	1	no	—
389	C₂×C₄×C₁₃	—	4	2	no	—
390	C₂×C₄×C₁₃	—	4	4	no	—
391	C₂×C₄×C₁₃	—	4	2	no	—
392	C₂×C₄×C₁₃	—	4	2	no	—
393	C₂×C₄×C₁₃	—	4	2	no	—
394	C₂×C₄×C₁₃	—	8	4	no	—
395	C₂×C₄×C₁₃	—	8	4	no	—
396	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
397	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
398	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
399	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
400	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
401	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
402	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
403	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
404	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
405	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
406	C₈×C₁₃	—	2	4	no	—
407	C₈×C₁₃	—	2	2	no	—
408	C₈×C₁₃	—	2	2	no	—
409	#559	—	2	1	no	—
410	#559	—	2	1	no	—
411	#559	—	2	2	no	—
412	#559	C₂²×C₁₃	1	2	yes	—
413	#559	C₂²×C₁₃	1	4	yes	—
414	#559	C₂²×C₁₃	1	2	yes	—
415	#557	C₂²×C₁₃	1	1	yes	characteristic, complemented
416	#557	C₂²×C₁₃	1	1	yes	characteristic, complemented
417	#557	C₂²×C₁₃	1	2	yes	complemented
418	#556	C₂²×C₁₃	1	1	yes	characteristic, complemented
419	#556	C₂²×C₁₃	1	2	yes	complemented
420	#552	—	2	1	no	—
421	#552	—	2	2	no	—
422	D₄×Q₈	—	2	1	no	—
423	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
424	#541	—	2	2	no	—
425	#541	—	2	1	no	—
426	#533	C₂²×C₁₃	1	2	yes	—
427	#533	C₂²×C₁₃	1	1	yes	characteristic
428	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
429	#529	C₂²×C₁₃	1	1	yes	characteristic
430	#529	C₂²×C₁₃	1	2	yes	—
431	C₂×#124	—	2	1	no	—
432	C₂×#124	C₂²×C₁₃	1	2	yes	—
433	C₂×#123	—	2	2	no	—
434	#519	—	2	1	no	—
435	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
436	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
437	C₂×C₄×D₄	—	2	1	no	—
438	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
439	#497	C₂²×C₁₃	1	4	yes	complemented
440	#496	C₂²×C₁₃	1	2	yes	—
441	#495	C₂²×C₁₃	1	4	yes	complemented
442	#492	C₂²×C₁₃	1	2	yes	—
443	#490	C₂²×C₁₃	1	2	yes	—
444	#489	C₂²×C₁₃	1	4	yes	complemented
445	#488	C₂²×C₁₃	1	4	yes	complemented
446	#486	C₂²×C₁₃	1	2	yes	—
447	#483	C₂²×C₁₃	1	1	yes	characteristic
448	#483	C₂²×C₁₃	1	2	yes	—
449	#480	C₂²×C₁₃	1	1	yes	characteristic
450	#479	C₂²×C₁₃	1	2	yes	complemented
451	#478	C₂²×C₁₃	1	4	yes	complemented
452	#476	C₂²×C₁₃	1	4	yes	complemented
453	#475	C₂²×C₁₃	1	2	yes	complemented
454	#464	C₂²×C₁₃	1	2	yes	complemented
455	#464	C₂²×C₁₃	1	4	yes	complemented
456	#464	C₂²×C₁₃	1	4	yes	complemented
457	#464	C₂²×C₁₃	1	4	yes	complemented
458	#463	C₂²×C₁₃	1	4	yes	complemented
459	#463	C₂²×C₁₃	1	4	yes	complemented
460	#462	C₂²×C₁₃	1	2	yes	complemented
461	#461	C₂²×C₁₃	1	4	yes	complemented
462	#460	C₂²×C₁₃	1	2	yes	—
463	#460	C₂²×C₁₃	1	4	yes	—
464	#459	C₂²×C₁₃	1	2	yes	—
465	#451	C₂²×C₁₃	1	1	yes	characteristic
466	#451	C₂²×C₁₃	1	2	yes	—
467	#450	C₂²×C₁₃	1	2	yes	—
468	#450	C₂²×C₁₃	1	2	yes	—
469	#450	C₂²×C₁₃	1	2	yes	—
470	#448	C₂²×C₁₃	1	1	yes	characteristic
471	#447	C₂²×C₁₃	1	2	yes	—
472	#446	C₂²×C₁₃	1	4	yes	complemented
473	#446	C₂²×C₁₃	1	2	yes	complemented
474	C₈×Q₈	C₂²×C₁₃	1	2	yes	complemented
475	#442	C₂²×C₁₃	1	4	yes	complemented
476	#441	C₂²×C₁₃	1	4	yes	complemented
477	#440	C₂²×C₁₃	1	4	yes	complemented
478	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
479	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
480	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
481	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
482	#432	C₂²×C₁₃	1	1	yes	characteristic
483	#432	C₂²×C₁₃	1	2	yes	—
484	#431	C₂²×C₁₃	1	2	yes	—
485	#431	C₂²×C₁₃	1	1	yes	characteristic
486	C₂²×C₁₃	—	2	1	no	—
487	C₂²×C₁₃	—	2	1	no	—
488	C₂²×C₁₃	—	4	4	no	—
489	C₂²×C₁₃	—	4	1	no	—
490	C₂²×C₁₃	—	4	1	no	—
491	C₂²×C₁₃	—	4	4	no	—
492	C₂²×C₁₃	—	4	4	no	—
493	C₂²×C₁₃	—	4	1	no	—
494	C₂²×C₁₃	—	8	8	no	—
495	C₂²×C₁₃	#577	1	2	yes	—
496	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
497	C₄×C₁₃	—	2	1	no	—
498	C₄×C₁₃	—	2	1	no	—
499	C₄×C₁₃	—	2	2	no	—
500	C₄×C₁₃	—	2	2	no	—
501	C₄×C₁₃	—	2	2	no	—
502	C₄×C₁₃	—	2	2	no	—
503	C₄×C₁₃	—	2	1	no	—
504	C₄×C₁₃	—	2	1	no	—
505	C₄×C₁₃	—	4	2	no	—
506	C₄×C₁₃	—	4	1	no	—
507	C₄×C₁₃	—	4	2	no	—
508	C₄×C₁₃	—	4	2	no	—
509	C₄×C₁₃	—	4	1	no	—
510	C₄×C₁₃	—	4	2	no	—
511	C₄×C₁₃	—	4	1	no	—
512	C₄×C₁₃	#575	1	2	yes	—
513	C₄×C₁₃	#585	1	2	yes	—
514	C₂²×Q₈	—	2	1	no	—
515	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
516	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
517	C₂²×D₄	—	2	1	no	—
518	C₂²×D₄	—	2	1	no	—
519	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
520	C₂³×C₄	—	2	2	no	—
521	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
522	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
523	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
524	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
525	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
526	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
527	C₂×D₈	C₂³×C₁₃	1	4	yes	—
528	C₄⋊Q₈	—	2	1	no	—
529	C₄⋊Q₈	—	2	2	no	—
530	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
531	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
532	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
533	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
534	#127	—	2	1	no	—
535	#127	—	2	1	no	—
536	#127	C₂³×C₁₃	1	2	yes	—
537	#127	C₂³×C₁₃	1	2	yes	—
538	#126	—	2	2	no	—
539	#126	—	2	2	no	—
540	#126	—	2	2	no	—
541	#126	—	2	2	no	—
542	#126	—	2	1	no	—
543	#125	—	2	2	no	—
544	#125	—	2	2	no	—
545	#125	—	2	2	no	—
546	#125	—	2	1	no	—
547	#125	—	2	2	no	—
548	#125	—	2	2	no	—
549	#125	—	2	1	no	—
550	#125	C₂³×C₁₃	1	2	yes	—
551	#125	C₂³×C₁₃	1	1	yes	characteristic
552	#124	—	2	2	no	—
553	#124	—	2	2	no	—
554	#124	—	2	4	no	—
555	#124	—	2	2	no	—
556	#124	—	2	2	no	—
557	#124	C₂³×C₁₃	1	4	yes	—
558	#124	C₂³×C₁₃	1	4	yes	—
559	#124	C₂³×C₁₃	1	2	yes	—
560	#124	C₂³×C₁₃	1	1	yes	characteristic
561	#123	—	2	2	no	—
562	#123	—	2	1	no	—
563	#123	—	2	4	no	—
564	#123	—	2	4	no	—
565	#123	—	2	4	no	—
566	#123	—	2	4	no	—
567	C₂²⋊Q₈	—	2	1	no	—
568	C₂²⋊Q₈	—	2	2	no	—
569	C₂²⋊Q₈	—	2	1	no	—
570	C₂²⋊Q₈	—	2	2	no	—
571	C₂²⋊Q₈	—	2	1	no	—
572	C₂²⋊Q₈	—	2	2	no	—
573	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
574	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
575	#121	C₂³×C₁₃	1	1	yes	characteristic
576	C₄×Q₈	—	2	1	no	—
577	C₄×Q₈	—	2	1	no	—
578	C₄×Q₈	—	2	2	no	—
579	C₄×Q₈	—	2	1	no	—
580	C₄×Q₈	—	2	1	no	—
581	C₄×Q₈	—	2	2	no	—
582	C₄×Q₈	—	2	1	no	—
583	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
584	C₄×Q₈	D₄×C₁₃	1	2	yes	—
585	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
586	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
587	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
588	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
589	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
590	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
591	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
592	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
593	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
594	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
595	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
596	C₄×D₄	—	2	1	no	—
597	C₄×D₄	—	2	2	no	—
598	C₄×D₄	—	2	2	no	—
599	C₄×D₄	—	2	2	no	—
600	C₄×D₄	—	2	4	no	—
601	C₄×D₄	—	2	2	no	—
602	C₄×D₄	—	2	2	no	—
603	C₄×D₄	C₂³×C₁₃	1	4	yes	—
604	C₄×D₄	C₂³×C₁₃	1	4	yes	—
605	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
606	C₄×D₄	C₂³×C₁₃	1	2	yes	—
607	#117	—	2	2	no	—
608	#117	—	2	1	no	—
609	#117	—	2	1	no	—
610	#117	—	2	2	no	—
611	#117	—	2	2	no	—
612	#117	—	2	1	no	—
613	C₂×C₄⋊C₄	—	2	1	no	—
614	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
615	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
616	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
617	C₂×C₂²⋊C₄	—	2	2	no	—
618	C₂×C₂²⋊C₄	—	2	2	no	—
619	C₂×C₂²⋊C₄	—	2	2	no	—
620	C₂×C₄²	—	2	1	no	—
621	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
622	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
623	#107	C₂³×C₁₃	1	2	yes	—
624	#106	C₂³×C₁₃	1	2	yes	—
625	#106	C₂³×C₁₃	1	4	yes	—
626	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
627	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
628	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
629	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
630	#103	C₂³×C₁₃	1	2	yes	—
631	#103	C₂³×C₁₃	1	4	yes	—
632	#103	C₂³×C₁₃	1	2	yes	—
633	#103	C₂³×C₁₃	1	2	yes	—
634	#103	C₂³×C₁₃	1	4	yes	—
635	#102	C₂³×C₁₃	1	2	yes	—
636	#102	C₂³×C₁₃	1	4	yes	—
637	#102	C₂³×C₁₃	1	4	yes	—
638	#102	C₂³×C₁₃	1	4	yes	—
639	#102	C₂³×C₁₃	1	4	yes	—
640	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
641	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
642	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
643	#97	C₂³×C₁₃	1	4	yes	—
644	#97	C₂³×C₁₃	1	2	yes	—
645	C₄×C₈	C₂³×C₁₃	1	4	yes	—
646	C₄×C₈	C₂³×C₁₃	1	2	yes	—
647	C₂×C₁₃	—	2	2	no	—
648	C₂×C₁₃	—	8	1	no	—
649	C₂×C₁₃	—	8	4	no	—
650	C₂×C₁₃	#3487	1	1	yes	characteristic
651	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
652	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
653	C₂⁴	—	2	2	no	—
654	C₂×Q₈	—	2	2	no	—
655	C₂×Q₈	—	2	1	no	—
656	C₂×Q₈	—	2	1	no	—
657	C₂×Q₈	—	4	2	no	—
658	C₂×Q₈	—	4	2	no	—
659	C₂×Q₈	—	4	4	no	—
660	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
661	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
662	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
663	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
664	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
665	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
666	C₂×D₄	—	2	1	no	—
667	C₂×D₄	—	2	2	no	—
668	C₂×D₄	—	2	2	no	—
669	C₂×D₄	—	2	2	no	—
670	C₂×D₄	—	2	2	no	—
671	C₂×D₄	—	2	2	no	—
672	C₂×D₄	—	4	4	no	—
673	C₂×D₄	—	4	4	no	—
674	C₂×D₄	—	8	2	no	—
675	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
676	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
677	C₂²×C₄	—	2	1	no	—
678	C₂²×C₄	—	2	1	no	—
679	C₂²×C₄	—	2	2	no	—
680	C₂²×C₄	—	2	1	no	—
681	C₂²×C₄	—	2	4	no	—
682	C₂²×C₄	—	2	4	no	—
683	C₂²×C₄	—	8	4	no	—
684	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
685	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
686	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
687	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
688	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
689	Q₁₆	—	4	4	no	—
690	Q₁₆	—	4	2	no	—
691	SD₁₆	—	4	4	no	—
692	SD₁₆	—	4	2	no	—
693	SD₁₆	—	4	4	no	—
694	SD₁₆	—	4	4	no	—
695	D₈	—	4	4	no	—
696	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
697	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
698	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
699	C₄⋊C₄	—	2	2	no	—
700	C₄⋊C₄	—	2	2	no	—
701	C₄⋊C₄	—	2	1	no	—
702	C₄⋊C₄	—	2	2	no	—
703	C₄⋊C₄	—	2	1	no	—
704	C₄⋊C₄	—	2	2	no	—
705	C₄⋊C₄	—	2	1	no	—
706	C₄⋊C₄	—	2	2	no	—
707	C₄⋊C₄	—	2	1	no	—
708	C₄⋊C₄	—	2	2	no	—
709	C₄⋊C₄	—	2	1	no	—
710	C₄⋊C₄	—	2	2	no	—
711	C₄⋊C₄	—	2	1	no	—
712	C₄⋊C₄	—	2	1	no	—
713	C₄⋊C₄	—	2	2	no	—
714	C₄⋊C₄	—	2	2	no	—
715	C₄⋊C₄	—	2	2	no	—
716	C₄⋊C₄	—	2	2	no	—
717	C₄⋊C₄	—	2	2	no	—
718	C₄⋊C₄	—	2	1	no	—
719	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
720	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
721	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
722	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
723	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
724	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
725	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
726	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
727	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
728	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
729	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
730	C₂²⋊C₄	—	2	1	no	—
731	C₂²⋊C₄	—	2	2	no	—
732	C₂²⋊C₄	—	2	4	no	—
733	C₂²⋊C₄	—	2	4	no	—
734	C₂²⋊C₄	—	2	4	no	—
735	C₂²⋊C₄	—	2	4	no	—
736	C₂²⋊C₄	—	2	4	no	—
737	C₂²⋊C₄	—	2	4	no	—
738	C₂²⋊C₄	—	2	1	no	—
739	C₂²⋊C₄	—	2	2	no	—
740	C₂²⋊C₄	—	2	1	no	—
741	C₂²⋊C₄	—	2	1	no	—
742	C₂²⋊C₄	—	2	2	no	—
743	C₂²⋊C₄	—	2	2	no	—
744	C₂²⋊C₄	—	2	1	no	—
745	C₄²	—	2	2	no	—
746	C₄²	—	2	2	no	—
747	C₄²	—	2	2	no	—
748	C₄²	—	2	2	no	—
749	C₄²	—	2	2	no	—
750	C₄²	—	2	2	no	—
751	C₄²	—	2	1	no	—
752	C₄²	C₂×D₄×C₁₃	1	2	yes	—
753	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
754	C₄²	C₂×D₄×C₁₃	1	2	yes	—
755	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
756	C₄²	C₂⁴×C₁₃	1	2	yes	—
757	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
758	C₄²	C₂⁴×C₁₃	1	2	yes	—
759	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
760	C₁₃	#61904	1	1	yes	characteristic, direct product factor, Sylow
761	C₂³	—	2	1	no	—
762	C₂³	—	2	4	no	—
763	C₂³	—	4	4	no	—
764	C₂³	—	4	4	no	—
765	C₂³	—	4	4	no	—
766	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
767	Q₈	—	2	2	no	—
768	Q₈	—	2	2	no	—
769	Q₈	—	2	2	no	—
770	Q₈	—	2	4	no	—
771	Q₈	—	2	2	no	—
772	Q₈	—	2	2	no	—
773	Q₈	—	4	2	no	—
774	Q₈	—	4	4	no	—
775	Q₈	—	4	2	no	—
776	Q₈	—	4	2	no	—
777	D₄	—	2	2	no	—
778	D₄	—	2	4	no	—
779	D₄	—	2	4	no	—
780	D₄	—	4	4	no	—
781	D₄	—	4	4	no	—
782	D₄	—	4	2	no	—
783	D₄	—	4	4	no	—
784	D₄	—	8	2	no	—
785	D₄	—	8	2	no	—
786	C₂×C₄	—	2	4	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	1	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	1	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	1	no	—
797	C₂×C₄	—	4	2	no	—
798	C₂×C₄	—	4	4	no	—
799	C₂×C₄	—	4	2	no	—
800	C₂×C₄	—	4	2	no	—
801	C₂×C₄	—	4	2	no	—
802	C₂×C₄	—	8	4	no	—
803	C₂×C₄	—	8	4	no	—
804	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
805	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
806	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
807	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
808	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
809	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
810	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
811	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
812	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
813	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
814	C₈	—	2	4	no	—
815	C₈	—	2	2	no	—
816	C₈	—	2	2	no	—
817	C₂²	—	2	1	no	—
818	C₂²	—	2	1	no	—
819	C₂²	—	4	1	no	—
820	C₂²	—	4	4	no	—
821	C₂²	—	4	4	no	—
822	C₂²	—	4	1	no	—
823	C₂²	—	4	4	no	—
824	C₂²	—	4	1	no	—
825	C₂²	—	8	8	no	—
826	C₂²	C₁₃×#577	1	2	yes	—
827	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
828	C₄	—	2	1	no	—
829	C₄	—	2	2	no	—
830	C₄	—	2	2	no	—
831	C₄	—	2	2	no	—
832	C₄	—	2	2	no	—
833	C₄	—	2	1	no	—
834	C₄	—	2	1	no	—
835	C₄	—	2	1	no	—
836	C₄	—	4	2	no	—
837	C₄	—	4	1	no	—
838	C₄	—	4	2	no	—
839	C₄	—	4	1	no	—
840	C₄	—	4	2	no	—
841	C₄	—	4	1	no	—
842	C₄	—	4	2	no	—
843	C₄	C₁₃×#575	1	2	yes	—
844	C₄	C₁₃×#585	1	2	yes	—
845	C₂	—	2	2	no	—
846	C₂	—	8	4	no	—
847	C₂	—	8	1	no	—
848	C₂	C₁₃×#3487	1	1	yes	characteristic
849	C₂	C₂×C₁₃×#575	1	1	yes	characteristic
850	C₂	C₂×C₁₃×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3217	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄×Q₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3523	C₂	semidirect
2. C₂×C₁₃×#559	C₂	semidirect
3. C₁₃×#3401	C₂	semidirect
4. C₁₃×#3400	C₂	semidirect
5. C₁₃×#3394	C₂	semidirect
6. C₁₃×#3373	C₂	semidirect
7. C₁₃×#3371	C₂	semidirect
8. C₁₃×#3365	C₂	semidirect
10. C₁₃×#3215	C₂	semidirect
11. C₁₃×#3211	C₂	semidirect
12. C₁₃×#3208	C₂	semidirect
13. C₁₃×#3114	C₂	semidirect
14. C₁₃×#3113	C₂	semidirect
15. C₁₃×#3108	C₂	semidirect
16. C₁₃×#3101	C₂	semidirect
17. C₁₃×#2984	C₂	semidirect
24. C₁₃×#557	C₂²	semidirect
25. C₁₃×#557	C₂²	semidirect
26. C₁₃×#557	C₂²	semidirect
27. C₁₃×#556	C₂²	semidirect
28. C₁₃×#556	C₂²	semidirect
32. D₄×Q₈×C₁₃	C₂²	semidirect
48. C₁₃×#497	C₂²	semidirect
50. C₁₃×#495	C₂²	semidirect
53. C₁₃×#489	C₂²	semidirect
54. C₁₃×#488	C₂²	semidirect
59. C₁₃×#479	C₂²	semidirect
60. C₁₃×#478	C₂²	semidirect
61. C₁₃×#476	C₂²	semidirect
62. C₁₃×#475	C₂²	semidirect
63. C₁₃×#464	C₂²	semidirect
64. C₁₃×#464	C₂²	semidirect
65. C₁₃×#464	C₂²	semidirect
66. C₁₃×#464	C₂²	semidirect
67. C₁₃×#463	C₂²	semidirect
68. C₁₃×#463	C₂²	semidirect
69. C₁₃×#462	C₂²	semidirect
70. C₁₃×#461	C₂²	semidirect
81. C₁₃×#446	C₂²	semidirect
82. C₁₃×#446	C₂²	semidirect
83. C₈×Q₈×C₁₃	C₂²	semidirect
84. C₁₃×#442	C₂²	semidirect
85. C₁₃×#441	C₂²	semidirect
86. C₁₃×#440	C₂²	semidirect
87. C₄×C₁₃×Q₁₆	C₂²	semidirect
88. C₄×C₁₃×SD₁₆	C₂²	semidirect
89. C₄×C₁₃×SD₁₆	C₂²	semidirect
90. C₄×C₁₃×SD₁₆	C₂²	semidirect
228. #61904	C₁₃	direct (N × H)
336. #3523	C₂×C₁₃	semidirect
337. C₂×#559	C₂×C₁₃	semidirect
338. #3401	C₂×C₁₃	semidirect
339. #3400	C₂×C₁₃	semidirect
340. #3394	C₂×C₁₃	semidirect
341. #3373	C₂×C₁₃	semidirect
342. #3371	C₂×C₁₃	semidirect
343. #3365	C₂×C₁₃	semidirect
345. #3215	C₂×C₁₃	semidirect
346. #3211	C₂×C₁₃	semidirect
347. #3208	C₂×C₁₃	semidirect
348. #3114	C₂×C₁₃	semidirect
349. #3113	C₂×C₁₃	semidirect
350. #3108	C₂×C₁₃	semidirect
351. #3101	C₂×C₁₃	semidirect
352. #2984	C₂×C₁₃	semidirect
415. #557	C₂²×C₁₃	semidirect
416. #557	C₂²×C₁₃	semidirect
417. #557	C₂²×C₁₃	semidirect
418. #556	C₂²×C₁₃	semidirect
419. #556	C₂²×C₁₃	semidirect
423. D₄×Q₈	C₂²×C₁₃	semidirect
439. #497	C₂²×C₁₃	semidirect
441. #495	C₂²×C₁₃	semidirect
444. #489	C₂²×C₁₃	semidirect
445. #488	C₂²×C₁₃	semidirect
450. #479	C₂²×C₁₃	semidirect
451. #478	C₂²×C₁₃	semidirect
452. #476	C₂²×C₁₃	semidirect
453. #475	C₂²×C₁₃	semidirect
454. #464	C₂²×C₁₃	semidirect
455. #464	C₂²×C₁₃	semidirect
456. #464	C₂²×C₁₃	semidirect
457. #464	C₂²×C₁₃	semidirect
458. #463	C₂²×C₁₃	semidirect
459. #463	C₂²×C₁₃	semidirect
460. #462	C₂²×C₁₃	semidirect
461. #461	C₂²×C₁₃	semidirect
472. #446	C₂²×C₁₃	semidirect
473. #446	C₂²×C₁₃	semidirect
474. C₈×Q₈	C₂²×C₁₃	semidirect
475. #442	C₂²×C₁₃	semidirect
476. #441	C₂²×C₁₃	semidirect
477. #440	C₂²×C₁₃	semidirect
478. C₄×Q₁₆	C₂²×C₁₃	semidirect
479. C₄×SD₁₆	C₂²×C₁₃	semidirect
480. C₄×SD₁₆	C₂²×C₁₃	semidirect
481. C₄×SD₁₆	C₂²×C₁₃	semidirect
760. C₁₃	#61904	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×#3523	2
C₂×C₁₃×#559	2
C₁₃×#3401	2
C₁₃×#3400	2
C₁₃×#3394	2
C₁₃×#3373	2
C₁₃×#3371	2
C₁₃×#3365	2
C₁₃×#3217	2
C₁₃×#3215	2
C₁₃×#3211	2
C₁₃×#3208	2
C₁₃×#3114	2
C₁₃×#3113	2
C₁₃×#3108	2
C₁₃×#3101	2
C₁₃×#2984	2
#61904	13

Subgroups — C13×#61904 #15748243

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61904 #15748243