Subgroups — C₁₃×#62582 #15748921

Order 3328.

1770 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3514	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#3503	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3375	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3369	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3316	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3314	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3299	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3295	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3239	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3238	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3216	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3215	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3181	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3172	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3141	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#489	C₂	1	2	yes	maximal, complemented
17	C₁₃×#2970	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₃×#559	C₂²	1	1	yes	characteristic
19	Q₈²×C₁₃	C₂²	1	2	yes	complemented
20	C₁₃×#557	—	2	1	no	—
21	C₁₃×#556	C₂²	1	1	yes	characteristic
22	C₁₃×#555	—	2	1	no	—
23	C₁₃×#554	C₂²	1	2	yes	—
24	C₁₃×#554	C₂²	1	4	yes	complemented
25	C₁₃×#551	—	2	2	no	—
26	D₄×Q₈×C₁₃	—	2	1	no	—
27	D₄×Q₈×C₁₃	—	2	2	no	—
28	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
29	C₁₃×#548	C₂²	1	2	yes	—
30	C₁₃×#546	—	2	1	no	—
31	C₁₃×#546	C₂²	1	2	yes	—
32	D₄²×C₁₃	C₂²	1	1	yes	characteristic
33	C₁₃×#544	—	2	2	no	—
34	C₁₃×#544	—	2	1	no	—
35	C₁₃×#542	—	2	1	no	—
36	C₁₃×#538	—	2	2	no	—
37	C₁₃×#533	C₂²	1	1	yes	characteristic, complemented
38	C₁₃×#533	C₂²	1	2	yes	complemented
39	C₁₃×#532	C₂²	1	1	yes	characteristic
40	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
41	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
42	C₁₃×#529	C₂²	1	1	yes	characteristic
43	C₁₃×#529	C₂²	1	2	yes	—
44	C₂×C₁₃×#124	C₂²	1	2	yes	—
45	C₁₃×#520	—	2	1	no	—
46	C₁₃×#518	—	2	1	no	—
47	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
48	C₁₃×#501	C₂²	1	1	yes	characteristic, complemented
49	C₁₃×#501	C₂²	1	2	yes	complemented
50	C₁₃×#497	C₂²	1	1	yes	characteristic
51	C₁₃×#497	C₂²	1	2	yes	complemented
52	C₁₃×#491	C₂²	1	1	yes	characteristic, complemented
53	C₁₃×#489	C₂²	1	4	yes	—
54	C₁₃×#489	C₂²	1	1	yes	characteristic
55	C₁₃×#489	C₂²	1	2	yes	—
56	C₁₃×#489	C₂²	1	4	yes	complemented
57	C₁₃×#489	C₂²	1	2	yes	complemented
58	C₁₃×#489	C₂²	1	2	yes	complemented
59	C₁₃×#489	C₂²	1	2	yes	complemented
60	C₁₃×#487	C₂²	1	2	yes	complemented
61	C₁₃×#486	C₂²	1	2	yes	—
62	C₁₃×#484	C₂²	1	4	yes	complemented
63	C₁₃×#483	C₂²	1	2	yes	complemented
64	C₁₃×#481	C₂²	1	4	yes	—
65	C₁₃×#480	C₂²	1	2	yes	—
66	C₁₃×#477	C₂²	1	2	yes	complemented
67	C₁₃×#476	C₂²	1	2	yes	—
68	C₁₃×#475	C₂²	1	4	yes	complemented
69	C₁₃×#474	C₂²	1	4	yes	complemented
70	C₁₃×#470	C₂²	1	2	yes	complemented
71	C₁₃×#468	C₂²	1	2	yes	—
72	C₁₃×#467	C₂²	1	4	yes	complemented
73	C₁₃×#465	C₂²	1	4	yes	—
74	C₁₃×#464	C₂²	1	4	yes	—
75	C₁₃×#464	C₂²	1	4	yes	complemented
76	C₁₃×#462	C₂²	1	2	yes	complemented
77	C₁₃×#460	C₂²	1	2	yes	—
78	C₁₃×#452	C₂²	1	4	yes	complemented
79	C₁₃×#451	C₂²	1	4	yes	complemented
80	C₁₃×#450	C₂²	1	4	yes	—
81	C₁₃×#446	C₂²	1	2	yes	complemented
82	C₁₃×#441	C₂²	1	4	yes	complemented
83	C₁₃×#440	C₂²	1	4	yes	complemented
84	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
85	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
86	C₁₃×#435	C₂²	1	4	yes	complemented
87	C₈×D₄×C₁₃	C₂²	1	2	yes	—
88	C₁₃×#432	C₂²	1	2	yes	complemented
89	C₁₃×#432	C₂²	1	1	yes	characteristic, complemented
90	C₁₃×#417	C₂²	1	4	yes	complemented
91	C₂×C₁₃×#103	C₂²	1	4	yes	complemented
92	C₂×C₁₃×#102	C₂²	1	4	yes	—
93	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic, complemented
94	C₂×C₁₃×#97	C₂²	1	2	yes	complemented
95	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
96	C₂×C₁₃×#41	C₂³	1	2	yes	—
97	C₂²×Q₈×C₁₃	—	2	2	no	—
98	C₂²×Q₈×C₁₃	—	2	1	no	—
99	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
100	C₂²×D₄×C₁₃	—	2	1	no	—
101	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
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×M₁₆	C₂³	1	2	yes	—
107	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
108	C₁₃×C₄⋊Q₈	—	2	1	no	—
109	C₁₃×C₄⋊Q₈	—	2	2	no	—
110	C₁₃×C₄⋊Q₈	—	2	4	no	—
111	C₁₃×C₄⋊Q₈	—	2	2	no	—
112	C₁₃×C₄⋊Q₈	—	2	1	no	—
113	C₁₃×C₄⋊Q₈	—	2	1	no	—
114	C₁₃×C₄⋊Q₈	—	2	2	no	—
115	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
116	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
117	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
118	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
119	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
120	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
121	C₁₃×#127	C₂³	1	1	yes	characteristic
122	C₁₃×#126	—	2	2	no	—
123	C₁₃×#126	—	2	2	no	—
124	C₁₃×#126	—	2	1	no	—
125	C₁₃×#125	—	2	2	no	—
126	C₁₃×#125	—	2	4	no	—
127	C₁₃×#125	—	2	2	no	—
128	C₁₃×#125	—	2	1	no	—
129	C₁₃×#125	C₂³	1	1	yes	characteristic
130	C₁₃×#124	—	2	1	no	—
131	C₁₃×#124	—	2	2	no	—
132	C₁₃×#124	—	2	2	no	—
133	C₁₃×#124	—	2	2	no	—
134	C₁₃×#124	C₂³	1	2	yes	—
135	C₁₃×#124	C₂³	1	2	yes	—
136	C₁₃×#124	C₂³	1	1	yes	characteristic
137	C₁₃×#124	C₂³	1	2	yes	—
138	C₁₃×#123	—	2	1	no	—
139	C₁₃×#123	—	2	2	no	—
140	C₁₃×#123	—	2	2	no	—
141	C₁₃×#123	—	2	2	no	—
142	C₁₃×C₂²⋊Q₈	—	2	1	no	—
143	C₁₃×C₂²⋊Q₈	—	2	2	no	—
144	C₁₃×C₂²⋊Q₈	—	2	1	no	—
145	C₁₃×C₂²⋊Q₈	—	2	2	no	—
146	C₁₃×C₂²⋊Q₈	—	2	2	no	—
147	C₁₃×C₂²⋊Q₈	—	2	4	no	—
148	C₁₃×C₂²⋊Q₈	—	2	4	no	—
149	C₁₃×C₂²⋊Q₈	—	2	4	no	—
150	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
151	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
152	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
153	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
154	C₁₃×#121	—	2	2	no	—
155	C₁₃×#121	—	2	1	no	—
156	C₁₃×#121	—	2	1	no	—
157	C₁₃×#121	—	2	1	no	—
158	C₁₃×#121	—	2	2	no	—
159	C₁₃×#121	C₂³	1	2	yes	—
160	C₁₃×#121	C₂³	1	1	yes	characteristic
161	C₁₃×#120	—	2	2	no	—
162	C₁₃×#120	—	2	2	no	—
163	C₄×Q₈×C₁₃	—	2	2	no	—
164	C₄×Q₈×C₁₃	—	2	1	no	—
165	C₄×Q₈×C₁₃	—	2	2	no	—
166	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
167	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
168	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
169	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
170	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
171	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
172	C₄×D₄×C₁₃	—	2	1	no	—
173	C₄×D₄×C₁₃	—	2	2	no	—
174	C₄×D₄×C₁₃	—	2	4	no	—
175	C₄×D₄×C₁₃	—	2	2	no	—
176	C₄×D₄×C₁₃	—	2	1	no	—
177	C₄×D₄×C₁₃	—	2	1	no	—
178	C₄×D₄×C₁₃	—	2	2	no	—
179	C₄×D₄×C₁₃	—	2	1	no	—
180	C₄×D₄×C₁₃	—	2	1	no	—
181	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
182	C₄×D₄×C₁₃	D₄	1	2	yes	—
183	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
184	C₄×D₄×C₁₃	C₂³	1	2	yes	—
185	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
186	C₄×D₄×C₁₃	C₂³	1	2	yes	—
187	C₁₃×#117	—	2	2	no	—
188	C₁₃×#117	—	2	1	no	—
189	C₁₃×#117	—	2	1	no	—
190	C₁₃×#117	—	2	1	no	—
191	C₁₃×#117	—	2	2	no	—
192	C₁₃×#117	D₄	1	2	yes	—
193	C₁₃×#117	D₄	1	1	yes	characteristic
194	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
195	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
196	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
197	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
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	C₂³	1	2	yes	—
202	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
203	C₁₃×#107	C₂³	1	2	yes	—
204	C₁₃×#107	C₂³	1	4	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×#103	C₂³	1	2	yes	—
210	C₁₃×#103	C₂³	1	4	yes	—
211	C₁₃×#103	C₂³	1	4	yes	—
212	C₁₃×#103	C₂³	1	4	yes	—
213	C₁₃×#103	C₂³	1	4	yes	—
214	C₁₃×#103	C₂³	1	2	yes	—
215	C₁₃×#103	C₂³	1	2	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	4	yes	—
222	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
223	C₁₃×#97	C₂³	1	1	yes	characteristic
224	C₁₃×#97	C₂³	1	2	yes	—
225	C₁₃×#97	C₂³	1	4	yes	—
226	C₁₃×#97	C₂³	1	1	yes	characteristic
227	C₄×C₈×C₁₃	C₂³	1	2	yes	—
228	#62582	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
229	C₂⁴×C₁₃	—	2	2	no	—
230	C₁₃×#41	—	2	4	no	—
231	C₁₃×#41	—	4	4	no	—
232	C₂×Q₈×C₁₃	—	2	1	no	—
233	C₂×Q₈×C₁₃	—	2	2	no	—
234	C₂×Q₈×C₁₃	—	2	2	no	—
235	C₂×Q₈×C₁₃	—	2	4	no	—
236	C₂×Q₈×C₁₃	—	2	2	no	—
237	C₂×Q₈×C₁₃	—	4	4	no	—
238	C₂×Q₈×C₁₃	—	8	4	no	—
239	C₂×Q₈×C₁₃	—	8	2	no	—
240	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
241	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
242	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
243	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
244	C₂×D₄×C₁₃	—	2	2	no	—
245	C₂×D₄×C₁₃	—	2	1	no	—
246	C₂×D₄×C₁₃	—	2	2	no	—
247	C₂×D₄×C₁₃	—	2	1	no	—
248	C₂×D₄×C₁₃	—	2	1	no	—
249	C₂×D₄×C₁₃	—	2	2	no	—
250	C₂×D₄×C₁₃	—	4	4	no	—
251	C₂×D₄×C₁₃	—	4	4	no	—
252	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
253	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
254	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
255	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
256	C₂²×C₄×C₁₃	—	2	2	no	—
257	C₂²×C₄×C₁₃	—	2	2	no	—
258	C₂²×C₄×C₁₃	—	2	4	no	—
259	C₂²×C₄×C₁₃	—	2	1	no	—
260	C₂²×C₄×C₁₃	—	2	2	no	—
261	C₂²×C₄×C₁₃	—	2	2	no	—
262	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
263	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
264	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
265	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
266	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
267	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
268	C₁₃×Q₁₆	—	4	4	no	—
269	C₁₃×Q₁₆	—	4	2	no	—
270	C₁₃×SD₁₆	—	4	4	no	—
271	C₁₃×SD₁₆	—	4	2	no	—
272	C₁₃×M₁₆	—	4	2	no	—
273	C₂×C₈×C₁₃	—	4	4	no	—
274	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
275	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
276	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
277	C₁₃×C₄⋊C₄	—	2	1	no	—
278	C₁₃×C₄⋊C₄	—	2	2	no	—
279	C₁₃×C₄⋊C₄	—	2	4	no	—
280	C₁₃×C₄⋊C₄	—	2	2	no	—
281	C₁₃×C₄⋊C₄	—	2	2	no	—
282	C₁₃×C₄⋊C₄	—	2	4	no	—
283	C₁₃×C₄⋊C₄	—	2	1	no	—
284	C₁₃×C₄⋊C₄	—	2	1	no	—
285	C₁₃×C₄⋊C₄	—	2	1	no	—
286	C₁₃×C₄⋊C₄	—	2	1	no	—
287	C₁₃×C₄⋊C₄	—	2	1	no	—
288	C₁₃×C₄⋊C₄	—	2	2	no	—
289	C₁₃×C₄⋊C₄	—	2	1	no	—
290	C₁₃×C₄⋊C₄	—	2	1	no	—
291	C₁₃×C₄⋊C₄	—	2	2	no	—
292	C₁₃×C₄⋊C₄	—	2	4	no	—
293	C₁₃×C₄⋊C₄	—	2	2	no	—
294	C₁₃×C₄⋊C₄	—	2	4	no	—
295	C₁₃×C₄⋊C₄	—	2	2	no	—
296	C₁₃×C₄⋊C₄	—	2	1	no	—
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	1	yes	characteristic
300	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
301	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
302	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
303	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
304	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
305	C₁₃×C₂²⋊C₄	—	2	2	no	—
306	C₁₃×C₂²⋊C₄	—	2	2	no	—
307	C₁₃×C₂²⋊C₄	—	2	4	no	—
308	C₁₃×C₂²⋊C₄	—	2	1	no	—
309	C₁₃×C₂²⋊C₄	—	2	2	no	—
310	C₁₃×C₂²⋊C₄	—	2	1	no	—
311	C₁₃×C₂²⋊C₄	—	2	1	no	—
312	C₁₃×C₂²⋊C₄	—	2	1	no	—
313	C₁₃×C₂²⋊C₄	—	2	2	no	—
314	C₁₃×C₂²⋊C₄	—	2	2	no	—
315	C₁₃×C₂²⋊C₄	—	2	2	no	—
316	C₁₃×C₂²⋊C₄	—	2	2	no	—
317	C₁₃×C₂²⋊C₄	—	2	2	no	—
318	C₁₃×C₂²⋊C₄	—	2	2	no	—
319	C₁₃×C₂²⋊C₄	—	2	1	no	—
320	C₁₃×C₂²⋊C₄	—	2	2	no	—
321	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
322	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
323	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
324	C₄²×C₁₃	—	2	2	no	—
325	C₄²×C₁₃	—	2	1	no	—
326	C₄²×C₁₃	—	2	4	no	—
327	C₄²×C₁₃	—	2	2	no	—
328	C₄²×C₁₃	C₂×D₄	1	2	yes	—
329	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
330	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
331	C₄²×C₁₃	C₂×D₄	1	2	yes	—
332	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
333	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
334	C₄²×C₁₃	C₂⁴	1	2	yes	—
335	#3514	C₂×C₁₃	1	1	yes	characteristic
336	#3503	C₂×C₁₃	1	1	yes	characteristic, complemented
337	#3375	C₂×C₁₃	1	2	yes	complemented
338	#3369	C₂×C₁₃	1	2	yes	complemented
339	#3316	C₂×C₁₃	1	4	yes	complemented
340	#3314	C₂×C₁₃	1	4	yes	complemented
341	#3299	C₂×C₁₃	1	2	yes	complemented
342	#3295	C₂×C₁₃	1	2	yes	complemented
343	#3239	C₂×C₁₃	1	2	yes	complemented
344	#3238	C₂×C₁₃	1	1	yes	characteristic, complemented
345	#3216	C₂×C₁₃	1	1	yes	characteristic, complemented
346	#3215	C₂×C₁₃	1	2	yes	complemented
347	#3181	C₂×C₁₃	1	2	yes	complemented
348	#3172	C₂×C₁₃	1	1	yes	characteristic, complemented
349	#3141	C₂×C₁₃	1	1	yes	characteristic, complemented
350	C₂×#489	C₂×C₁₃	1	2	yes	complemented
351	#2970	C₂×C₁₃	1	1	yes	characteristic, complemented
352	C₂³×C₁₃	—	2	1	no	—
353	C₂³×C₁₃	—	2	2	no	—
354	C₂³×C₁₃	—	4	4	no	—
355	C₂³×C₁₃	—	8	2	no	—
356	C₂³×C₁₃	—	8	2	no	—
357	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
358	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
359	Q₈×C₁₃	—	2	2	no	—
360	Q₈×C₁₃	—	2	2	no	—
361	Q₈×C₁₃	—	2	2	no	—
362	Q₈×C₁₃	—	2	2	no	—
363	Q₈×C₁₃	—	2	4	no	—
364	Q₈×C₁₃	—	4	2	no	—
365	Q₈×C₁₃	—	4	4	no	—
366	Q₈×C₁₃	—	8	2	no	—
367	Q₈×C₁₃	—	8	4	no	—
368	Q₈×C₁₃	—	8	2	no	—
369	D₄×C₁₃	—	2	4	no	—
370	D₄×C₁₃	—	2	2	no	—
371	D₄×C₁₃	—	2	4	no	—
372	D₄×C₁₃	—	4	4	no	—
373	D₄×C₁₃	—	4	2	no	—
374	D₄×C₁₃	—	8	1	no	—
375	D₄×C₁₃	—	8	2	no	—
376	D₄×C₁₃	—	8	1	no	—
377	D₄×C₁₃	—	8	2	no	—
378	D₄×C₁₃	#137	1	4	yes	—
379	C₂×C₄×C₁₃	—	2	4	no	—
380	C₂×C₄×C₁₃	—	2	2	no	—
381	C₂×C₄×C₁₃	—	2	4	no	—
382	C₂×C₄×C₁₃	—	2	2	no	—
383	C₂×C₄×C₁₃	—	2	2	no	—
384	C₂×C₄×C₁₃	—	2	1	no	—
385	C₂×C₄×C₁₃	—	2	1	no	—
386	C₂×C₄×C₁₃	—	2	1	no	—
387	C₂×C₄×C₁₃	—	2	2	no	—
388	C₂×C₄×C₁₃	—	2	4	no	—
389	C₂×C₄×C₁₃	—	2	2	no	—
390	C₂×C₄×C₁₃	—	4	2	no	—
391	C₂×C₄×C₁₃	—	4	1	no	—
392	C₂×C₄×C₁₃	—	4	2	no	—
393	C₂×C₄×C₁₃	—	8	2	no	—
394	C₂×C₄×C₁₃	—	8	2	no	—
395	C₂×C₄×C₁₃	—	8	2	no	—
396	C₂×C₄×C₁₃	—	8	4	no	—
397	C₂×C₄×C₁₃	—	8	2	no	—
398	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
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	1	yes	characteristic
402	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
403	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
404	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
405	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
406	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
407	C₈×C₁₃	—	2	2	no	—
408	C₈×C₁₃	—	2	4	no	—
409	C₈×C₁₃	—	2	2	no	—
410	#559	C₂²×C₁₃	1	1	yes	characteristic
411	Q₈²	C₂²×C₁₃	1	2	yes	complemented
412	#557	—	2	1	no	—
413	#556	C₂²×C₁₃	1	1	yes	characteristic
414	#555	—	2	1	no	—
415	#554	C₂²×C₁₃	1	2	yes	—
416	#554	C₂²×C₁₃	1	4	yes	complemented
417	#551	—	2	2	no	—
418	D₄×Q₈	—	2	1	no	—
419	D₄×Q₈	—	2	2	no	—
420	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
421	#548	C₂²×C₁₃	1	2	yes	—
422	#546	—	2	1	no	—
423	#546	C₂²×C₁₃	1	2	yes	—
424	D₄²	C₂²×C₁₃	1	1	yes	characteristic
425	#544	—	2	2	no	—
426	#544	—	2	1	no	—
427	#542	—	2	1	no	—
428	#538	—	2	2	no	—
429	#533	C₂²×C₁₃	1	1	yes	characteristic, complemented
430	#533	C₂²×C₁₃	1	2	yes	complemented
431	#532	C₂²×C₁₃	1	1	yes	characteristic
432	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
433	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
434	#529	C₂²×C₁₃	1	1	yes	characteristic
435	#529	C₂²×C₁₃	1	2	yes	—
436	C₂×#124	C₂²×C₁₃	1	2	yes	—
437	#520	—	2	1	no	—
438	#518	—	2	1	no	—
439	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
440	#501	C₂²×C₁₃	1	1	yes	characteristic, complemented
441	#501	C₂²×C₁₃	1	2	yes	complemented
442	#497	C₂²×C₁₃	1	1	yes	characteristic
443	#497	C₂²×C₁₃	1	2	yes	complemented
444	#491	C₂²×C₁₃	1	1	yes	characteristic, complemented
445	#489	C₂²×C₁₃	1	4	yes	—
446	#489	C₂²×C₁₃	1	1	yes	characteristic
447	#489	C₂²×C₁₃	1	2	yes	—
448	#489	C₂²×C₁₃	1	4	yes	complemented
449	#489	C₂²×C₁₃	1	2	yes	complemented
450	#489	C₂²×C₁₃	1	2	yes	complemented
451	#489	C₂²×C₁₃	1	2	yes	complemented
452	#487	C₂²×C₁₃	1	2	yes	complemented
453	#486	C₂²×C₁₃	1	2	yes	—
454	#484	C₂²×C₁₃	1	4	yes	complemented
455	#483	C₂²×C₁₃	1	2	yes	complemented
456	#481	C₂²×C₁₃	1	4	yes	—
457	#480	C₂²×C₁₃	1	2	yes	—
458	#477	C₂²×C₁₃	1	2	yes	complemented
459	#476	C₂²×C₁₃	1	2	yes	—
460	#475	C₂²×C₁₃	1	4	yes	complemented
461	#474	C₂²×C₁₃	1	4	yes	complemented
462	#470	C₂²×C₁₃	1	2	yes	complemented
463	#468	C₂²×C₁₃	1	2	yes	—
464	#467	C₂²×C₁₃	1	4	yes	complemented
465	#465	C₂²×C₁₃	1	4	yes	—
466	#464	C₂²×C₁₃	1	4	yes	—
467	#464	C₂²×C₁₃	1	4	yes	complemented
468	#462	C₂²×C₁₃	1	2	yes	complemented
469	#460	C₂²×C₁₃	1	2	yes	—
470	#452	C₂²×C₁₃	1	4	yes	complemented
471	#451	C₂²×C₁₃	1	4	yes	complemented
472	#450	C₂²×C₁₃	1	4	yes	—
473	#446	C₂²×C₁₃	1	2	yes	complemented
474	#441	C₂²×C₁₃	1	4	yes	complemented
475	#440	C₂²×C₁₃	1	4	yes	complemented
476	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
477	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
478	#435	C₂²×C₁₃	1	4	yes	complemented
479	C₈×D₄	C₂²×C₁₃	1	2	yes	—
480	#432	C₂²×C₁₃	1	2	yes	complemented
481	#432	C₂²×C₁₃	1	1	yes	characteristic, complemented
482	#417	C₂²×C₁₃	1	4	yes	complemented
483	C₂×#103	C₂²×C₁₃	1	4	yes	complemented
484	C₂×#102	C₂²×C₁₃	1	4	yes	—
485	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
486	C₂×#97	C₂²×C₁₃	1	2	yes	complemented
487	C₂²×C₁₃	—	2	2	no	—
488	C₂²×C₁₃	—	2	2	no	—
489	C₂²×C₁₃	—	2	1	no	—
490	C₂²×C₁₃	—	2	1	no	—
491	C₂²×C₁₃	—	2	1	no	—
492	C₂²×C₁₃	—	4	2	no	—
493	C₂²×C₁₃	—	4	1	no	—
494	C₂²×C₁₃	—	4	2	no	—
495	C₂²×C₁₃	—	4	1	no	—
496	C₂²×C₁₃	—	4	1	no	—
497	C₂²×C₁₃	—	4	2	no	—
498	C₂²×C₁₃	—	16	4	no	—
499	C₂²×C₁₃	C₂×#137	1	4	yes	—
500	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
501	C₄×C₁₃	—	2	1	no	—
502	C₄×C₁₃	—	2	2	no	—
503	C₄×C₁₃	—	2	1	no	—
504	C₄×C₁₃	—	2	1	no	—
505	C₄×C₁₃	—	2	2	no	—
506	C₄×C₁₃	—	2	1	no	—
507	C₄×C₁₃	—	2	2	no	—
508	C₄×C₁₃	—	4	1	no	—
509	C₄×C₁₃	—	4	2	no	—
510	C₄×C₁₃	—	4	4	no	—
511	C₄×C₁₃	—	4	2	no	—
512	C₄×C₁₃	—	4	1	no	—
513	C₄×C₁₃	—	4	2	no	—
514	C₄×C₁₃	—	4	1	no	—
515	C₄×C₁₃	C₂×#137	1	2	yes	—
516	C₄×C₁₃	#585	1	2	yes	—
517	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
518	C₂×#41	C₂³×C₁₃	1	2	yes	—
519	C₂²×Q₈	—	2	2	no	—
520	C₂²×Q₈	—	2	1	no	—
521	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
522	C₂²×D₄	—	2	1	no	—
523	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
524	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
525	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
526	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
527	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
528	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
529	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
530	C₄⋊Q₈	—	2	1	no	—
531	C₄⋊Q₈	—	2	2	no	—
532	C₄⋊Q₈	—	2	4	no	—
533	C₄⋊Q₈	—	2	2	no	—
534	C₄⋊Q₈	—	2	1	no	—
535	C₄⋊Q₈	—	2	1	no	—
536	C₄⋊Q₈	—	2	2	no	—
537	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
538	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
539	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
540	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
541	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
542	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
543	#127	C₂³×C₁₃	1	1	yes	characteristic
544	#126	—	2	2	no	—
545	#126	—	2	2	no	—
546	#126	—	2	1	no	—
547	#125	—	2	2	no	—
548	#125	—	2	4	no	—
549	#125	—	2	2	no	—
550	#125	—	2	1	no	—
551	#125	C₂³×C₁₃	1	1	yes	characteristic
552	#124	—	2	1	no	—
553	#124	—	2	2	no	—
554	#124	—	2	2	no	—
555	#124	—	2	2	no	—
556	#124	C₂³×C₁₃	1	1	yes	characteristic
557	#124	C₂³×C₁₃	1	2	yes	—
558	#124	C₂³×C₁₃	1	2	yes	—
559	#124	C₂³×C₁₃	1	2	yes	—
560	#123	—	2	1	no	—
561	#123	—	2	2	no	—
562	#123	—	2	2	no	—
563	#123	—	2	2	no	—
564	C₂²⋊Q₈	—	2	1	no	—
565	C₂²⋊Q₈	—	2	2	no	—
566	C₂²⋊Q₈	—	2	1	no	—
567	C₂²⋊Q₈	—	2	2	no	—
568	C₂²⋊Q₈	—	2	2	no	—
569	C₂²⋊Q₈	—	2	4	no	—
570	C₂²⋊Q₈	—	2	4	no	—
571	C₂²⋊Q₈	—	2	4	no	—
572	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
573	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
574	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
575	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
576	#121	—	2	2	no	—
577	#121	—	2	1	no	—
578	#121	—	2	1	no	—
579	#121	—	2	1	no	—
580	#121	—	2	2	no	—
581	#121	C₂³×C₁₃	1	2	yes	—
582	#121	C₂³×C₁₃	1	1	yes	characteristic
583	#120	—	2	2	no	—
584	#120	—	2	2	no	—
585	C₄×Q₈	—	2	2	no	—
586	C₄×Q₈	—	2	1	no	—
587	C₄×Q₈	—	2	2	no	—
588	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
589	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
590	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
591	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
592	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
593	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
594	C₄×D₄	—	2	1	no	—
595	C₄×D₄	—	2	2	no	—
596	C₄×D₄	—	2	4	no	—
597	C₄×D₄	—	2	2	no	—
598	C₄×D₄	—	2	1	no	—
599	C₄×D₄	—	2	1	no	—
600	C₄×D₄	—	2	2	no	—
601	C₄×D₄	—	2	1	no	—
602	C₄×D₄	—	2	1	no	—
603	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
604	C₄×D₄	D₄×C₁₃	1	2	yes	—
605	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
606	C₄×D₄	C₂³×C₁₃	1	2	yes	—
607	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
608	C₄×D₄	C₂³×C₁₃	1	2	yes	—
609	#117	—	2	2	no	—
610	#117	—	2	1	no	—
611	#117	—	2	1	no	—
612	#117	—	2	1	no	—
613	#117	—	2	2	no	—
614	#117	D₄×C₁₃	1	2	yes	—
615	#117	D₄×C₁₃	1	1	yes	characteristic
616	C₂×C₄⋊C₄	—	2	2	no	—
617	C₂×C₄⋊C₄	—	2	1	no	—
618	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
619	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
620	C₂×C₂²⋊C₄	—	2	2	no	—
621	C₂×C₂²⋊C₄	—	2	2	no	—
622	C₂×C₂²⋊C₄	—	2	2	no	—
623	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
624	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
625	#107	C₂³×C₁₃	1	2	yes	—
626	#107	C₂³×C₁₃	1	4	yes	—
627	#106	C₂³×C₁₃	1	2	yes	—
628	#106	C₂³×C₁₃	1	4	yes	—
629	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
630	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
631	#103	C₂³×C₁₃	1	2	yes	—
632	#103	C₂³×C₁₃	1	4	yes	—
633	#103	C₂³×C₁₃	1	4	yes	—
634	#103	C₂³×C₁₃	1	4	yes	—
635	#103	C₂³×C₁₃	1	4	yes	—
636	#103	C₂³×C₁₃	1	2	yes	—
637	#103	C₂³×C₁₃	1	2	yes	—
638	#102	C₂³×C₁₃	1	2	yes	—
639	#102	C₂³×C₁₃	1	4	yes	—
640	#102	C₂³×C₁₃	1	4	yes	—
641	#102	C₂³×C₁₃	1	4	yes	—
642	#102	C₂³×C₁₃	1	4	yes	—
643	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
644	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
645	#97	C₂³×C₁₃	1	1	yes	characteristic
646	#97	C₂³×C₁₃	1	2	yes	—
647	#97	C₂³×C₁₃	1	4	yes	—
648	#97	C₂³×C₁₃	1	1	yes	characteristic
649	C₄×C₈	C₂³×C₁₃	1	2	yes	—
650	C₂×C₁₃	—	2	4	no	—
651	C₂×C₁₃	—	4	1	no	—
652	C₂×C₁₃	—	8	2	no	—
653	C₂×C₁₃	—	8	1	no	—
654	C₂×C₁₃	#3500	1	1	yes	characteristic
655	C₂×C₁₃	C₂²×#137	1	1	yes	characteristic
656	C₂×C₁₃	#3585	1	1	yes	characteristic
657	C₂⁴	—	2	2	no	—
658	#41	—	2	4	no	—
659	#41	—	4	4	no	—
660	C₂×Q₈	—	2	1	no	—
661	C₂×Q₈	—	2	2	no	—
662	C₂×Q₈	—	2	2	no	—
663	C₂×Q₈	—	2	4	no	—
664	C₂×Q₈	—	2	2	no	—
665	C₂×Q₈	—	4	4	no	—
666	C₂×Q₈	—	8	4	no	—
667	C₂×Q₈	—	8	2	no	—
668	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
669	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
670	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
671	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
672	C₂×D₄	—	2	2	no	—
673	C₂×D₄	—	2	1	no	—
674	C₂×D₄	—	2	2	no	—
675	C₂×D₄	—	2	1	no	—
676	C₂×D₄	—	2	1	no	—
677	C₂×D₄	—	2	2	no	—
678	C₂×D₄	—	4	4	no	—
679	C₂×D₄	—	4	4	no	—
680	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
681	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
682	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
683	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
684	C₂²×C₄	—	2	2	no	—
685	C₂²×C₄	—	2	2	no	—
686	C₂²×C₄	—	2	4	no	—
687	C₂²×C₄	—	2	1	no	—
688	C₂²×C₄	—	2	2	no	—
689	C₂²×C₄	—	2	2	no	—
690	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
691	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
692	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
693	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
694	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
695	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
696	Q₁₆	—	4	4	no	—
697	Q₁₆	—	4	2	no	—
698	SD₁₆	—	4	4	no	—
699	SD₁₆	—	4	2	no	—
700	M₁₆	—	4	2	no	—
701	C₂×C₈	—	4	4	no	—
702	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
703	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
704	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
705	C₄⋊C₄	—	2	1	no	—
706	C₄⋊C₄	—	2	2	no	—
707	C₄⋊C₄	—	2	4	no	—
708	C₄⋊C₄	—	2	2	no	—
709	C₄⋊C₄	—	2	2	no	—
710	C₄⋊C₄	—	2	4	no	—
711	C₄⋊C₄	—	2	1	no	—
712	C₄⋊C₄	—	2	1	no	—
713	C₄⋊C₄	—	2	1	no	—
714	C₄⋊C₄	—	2	1	no	—
715	C₄⋊C₄	—	2	1	no	—
716	C₄⋊C₄	—	2	2	no	—
717	C₄⋊C₄	—	2	1	no	—
718	C₄⋊C₄	—	2	1	no	—
719	C₄⋊C₄	—	2	2	no	—
720	C₄⋊C₄	—	2	4	no	—
721	C₄⋊C₄	—	2	2	no	—
722	C₄⋊C₄	—	2	4	no	—
723	C₄⋊C₄	—	2	2	no	—
724	C₄⋊C₄	—	2	1	no	—
725	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
726	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
727	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
728	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
729	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
730	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
731	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
732	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
733	C₂²⋊C₄	—	2	2	no	—
734	C₂²⋊C₄	—	2	2	no	—
735	C₂²⋊C₄	—	2	4	no	—
736	C₂²⋊C₄	—	2	1	no	—
737	C₂²⋊C₄	—	2	2	no	—
738	C₂²⋊C₄	—	2	1	no	—
739	C₂²⋊C₄	—	2	1	no	—
740	C₂²⋊C₄	—	2	1	no	—
741	C₂²⋊C₄	—	2	2	no	—
742	C₂²⋊C₄	—	2	2	no	—
743	C₂²⋊C₄	—	2	2	no	—
744	C₂²⋊C₄	—	2	2	no	—
745	C₂²⋊C₄	—	2	2	no	—
746	C₂²⋊C₄	—	2	2	no	—
747	C₂²⋊C₄	—	2	1	no	—
748	C₂²⋊C₄	—	2	2	no	—
749	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
750	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
751	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
752	C₄²	—	2	2	no	—
753	C₄²	—	2	1	no	—
754	C₄²	—	2	4	no	—
755	C₄²	—	2	2	no	—
756	C₄²	C₂×D₄×C₁₃	1	2	yes	—
757	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
758	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
759	C₄²	C₂×D₄×C₁₃	1	2	yes	—
760	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
761	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
762	C₄²	C₂⁴×C₁₃	1	2	yes	—
763	C₁₃	#62582	1	1	yes	characteristic, direct product factor, Sylow
764	C₂³	—	2	1	no	—
765	C₂³	—	2	2	no	—
766	C₂³	—	4	4	no	—
767	C₂³	—	8	2	no	—
768	C₂³	—	8	2	no	—
769	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
770	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
771	Q₈	—	2	2	no	—
772	Q₈	—	2	2	no	—
773	Q₈	—	2	2	no	—
774	Q₈	—	2	2	no	—
775	Q₈	—	2	4	no	—
776	Q₈	—	4	2	no	—
777	Q₈	—	4	4	no	—
778	Q₈	—	8	2	no	—
779	Q₈	—	8	4	no	—
780	Q₈	—	8	2	no	—
781	D₄	—	2	4	no	—
782	D₄	—	2	2	no	—
783	D₄	—	2	4	no	—
784	D₄	—	4	4	no	—
785	D₄	—	4	2	no	—
786	D₄	—	8	2	no	—
787	D₄	—	8	1	no	—
788	D₄	—	8	1	no	—
789	D₄	—	8	2	no	—
790	D₄	C₁₃×#137	1	4	yes	—
791	C₂×C₄	—	2	4	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	4	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	1	no	—
797	C₂×C₄	—	2	1	no	—
798	C₂×C₄	—	2	1	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	4	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	4	2	no	—
803	C₂×C₄	—	4	1	no	—
804	C₂×C₄	—	4	2	no	—
805	C₂×C₄	—	8	2	no	—
806	C₂×C₄	—	8	2	no	—
807	C₂×C₄	—	8	2	no	—
808	C₂×C₄	—	8	4	no	—
809	C₂×C₄	—	8	2	no	—
810	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
811	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
812	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
813	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
814	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
815	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
816	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
817	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
818	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
819	C₈	—	2	2	no	—
820	C₈	—	2	4	no	—
821	C₈	—	2	2	no	—
822	C₂²	—	2	2	no	—
823	C₂²	—	2	2	no	—
824	C₂²	—	2	1	no	—
825	C₂²	—	2	1	no	—
826	C₂²	—	2	1	no	—
827	C₂²	—	4	1	no	—
828	C₂²	—	4	2	no	—
829	C₂²	—	4	2	no	—
830	C₂²	—	4	1	no	—
831	C₂²	—	4	2	no	—
832	C₂²	—	4	1	no	—
833	C₂²	—	16	4	no	—
834	C₂²	C₂×C₁₃×#137	1	4	yes	—
835	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
836	C₄	—	2	1	no	—
837	C₄	—	2	2	no	—
838	C₄	—	2	1	no	—
839	C₄	—	2	2	no	—
840	C₄	—	2	1	no	—
841	C₄	—	2	1	no	—
842	C₄	—	2	2	no	—
843	C₄	—	4	1	no	—
844	C₄	—	4	1	no	—
845	C₄	—	4	2	no	—
846	C₄	—	4	4	no	—
847	C₄	—	4	2	no	—
848	C₄	—	4	1	no	—
849	C₄	—	4	2	no	—
850	C₄	C₂×C₁₃×#137	1	2	yes	—
851	C₄	C₁₃×#585	1	2	yes	—
852	C₂	—	2	4	no	—
853	C₂	—	4	1	no	—
854	C₂	—	8	1	no	—
855	C₂	—	8	2	no	—
856	C₂	C₁₃×#3500	1	1	yes	characteristic
857	C₂	C₂²×C₁₃×#137	1	1	yes	characteristic
858	C₂	C₁₃×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3514	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₄×C₁₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#3503	C₂	semidirect
3. C₁₃×#3375	C₂	semidirect
4. C₁₃×#3369	C₂	semidirect
5. C₁₃×#3316	C₂	semidirect
6. C₁₃×#3314	C₂	semidirect
7. C₁₃×#3299	C₂	semidirect
8. C₁₃×#3295	C₂	semidirect
9. C₁₃×#3239	C₂	semidirect
10. C₁₃×#3238	C₂	semidirect
11. C₁₃×#3216	C₂	semidirect
12. C₁₃×#3215	C₂	semidirect
13. C₁₃×#3181	C₂	semidirect
14. C₁₃×#3172	C₂	semidirect
15. C₁₃×#3141	C₂	semidirect
16. C₂×C₁₃×#489	C₂	semidirect
17. C₁₃×#2970	C₂	semidirect
19. Q₈²×C₁₃	C₂²	semidirect
24. C₁₃×#554	C₂²	semidirect
37. C₁₃×#533	C₂²	semidirect
38. C₁₃×#533	C₂²	semidirect
40. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
41. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
48. C₁₃×#501	C₂²	semidirect
49. C₁₃×#501	C₂²	semidirect
51. C₁₃×#497	C₂²	semidirect
52. C₁₃×#491	C₂²	semidirect
56. C₁₃×#489	C₂²	semidirect
57. C₁₃×#489	C₂²	semidirect
58. C₁₃×#489	C₂²	semidirect
59. C₁₃×#489	C₂²	semidirect
60. C₁₃×#487	C₂²	semidirect
62. C₁₃×#484	C₂²	semidirect
63. C₁₃×#483	C₂²	semidirect
66. C₁₃×#477	C₂²	semidirect
68. C₁₃×#475	C₂²	semidirect
69. C₁₃×#474	C₂²	semidirect
70. C₁₃×#470	C₂²	semidirect
72. C₁₃×#467	C₂²	semidirect
75. C₁₃×#464	C₂²	semidirect
76. C₁₃×#462	C₂²	semidirect
78. C₁₃×#452	C₂²	semidirect
79. C₁₃×#451	C₂²	semidirect
81. C₁₃×#446	C₂²	semidirect
82. C₁₃×#441	C₂²	semidirect
83. C₁₃×#440	C₂²	semidirect
84. C₄×C₁₃×Q₁₆	C₂²	semidirect
86. C₁₃×#435	C₂²	semidirect
88. C₁₃×#432	C₂²	semidirect
89. C₁₃×#432	C₂²	semidirect
90. C₁₃×#417	C₂²	semidirect
91. C₂×C₁₃×#103	C₂²	semidirect
93. C₄×C₁₃×M₁₆	C₂²	semidirect
94. C₂×C₁₃×#97	C₂²	semidirect
228. #62582	C₁₃	direct (N × H)
336. #3503	C₂×C₁₃	semidirect
337. #3375	C₂×C₁₃	semidirect
338. #3369	C₂×C₁₃	semidirect
339. #3316	C₂×C₁₃	semidirect
340. #3314	C₂×C₁₃	semidirect
341. #3299	C₂×C₁₃	semidirect
342. #3295	C₂×C₁₃	semidirect
343. #3239	C₂×C₁₃	semidirect
344. #3238	C₂×C₁₃	semidirect
345. #3216	C₂×C₁₃	semidirect
346. #3215	C₂×C₁₃	semidirect
347. #3181	C₂×C₁₃	semidirect
348. #3172	C₂×C₁₃	semidirect
349. #3141	C₂×C₁₃	semidirect
350. C₂×#489	C₂×C₁₃	semidirect
351. #2970	C₂×C₁₃	semidirect
411. Q₈²	C₂²×C₁₃	semidirect
416. #554	C₂²×C₁₃	semidirect
429. #533	C₂²×C₁₃	semidirect
430. #533	C₂²×C₁₃	semidirect
432. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
433. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
440. #501	C₂²×C₁₃	semidirect
441. #501	C₂²×C₁₃	semidirect
443. #497	C₂²×C₁₃	semidirect
444. #491	C₂²×C₁₃	semidirect
448. #489	C₂²×C₁₃	semidirect
449. #489	C₂²×C₁₃	semidirect
450. #489	C₂²×C₁₃	semidirect
451. #489	C₂²×C₁₃	semidirect
452. #487	C₂²×C₁₃	semidirect
454. #484	C₂²×C₁₃	semidirect
455. #483	C₂²×C₁₃	semidirect
458. #477	C₂²×C₁₃	semidirect
460. #475	C₂²×C₁₃	semidirect
461. #474	C₂²×C₁₃	semidirect
462. #470	C₂²×C₁₃	semidirect
464. #467	C₂²×C₁₃	semidirect
467. #464	C₂²×C₁₃	semidirect
468. #462	C₂²×C₁₃	semidirect
470. #452	C₂²×C₁₃	semidirect
471. #451	C₂²×C₁₃	semidirect
473. #446	C₂²×C₁₃	semidirect
474. #441	C₂²×C₁₃	semidirect
475. #440	C₂²×C₁₃	semidirect
476. C₄×Q₁₆	C₂²×C₁₃	semidirect
478. #435	C₂²×C₁₃	semidirect
480. #432	C₂²×C₁₃	semidirect
481. #432	C₂²×C₁₃	semidirect
482. #417	C₂²×C₁₃	semidirect
483. C₂×#103	C₂²×C₁₃	semidirect
485. C₄×M₁₆	C₂²×C₁₃	semidirect
486. C₂×#97	C₂²×C₁₃	semidirect
763. C₁₃	#62582	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×#3514	2
C₁₃×#3503	2
C₁₃×#3375	2
C₁₃×#3369	2
C₁₃×#3316	2
C₁₃×#3314	2
C₁₃×#3299	2
C₁₃×#3295	2
C₁₃×#3239	2
C₁₃×#3238	2
C₁₃×#3216	2
C₁₃×#3215	2
C₁₃×#3181	2
C₁₃×#3172	2
C₁₃×#3141	2
C₂×C₁₃×#489	2
C₁₃×#2970	2
#62582	13

Subgroups — C13×#62582 #15748921

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62582 #15748921