Subgroups — C₁₃×#61330 #15747669

Order 3328.

1776 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3509	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3503	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3374	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3372	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3369	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3367	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3364	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3363	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3360	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3359	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3137	C₂	1	2	yes	maximal, complemented
12	C₂×C₁₃×#487	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3082	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3079	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3046	C₂	1	2	yes	maximal
16	C₁₃×#3039	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#2960	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₃×#2947	C₂	1	2	yes	maximal, complemented
19	C₄×C₁₃×#135	C₂	1	1	yes	maximal, characteristic
20	C₂×C₁₃×#137	C₂²	1	2	yes	—
21	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
22	Q₈²×C₁₃	C₂²	1	2	yes	—
23	C₁₃×#557	C₂²	1	2	yes	—
24	C₁₃×#557	C₂²	1	2	yes	—
25	C₁₃×#557	C₂²	1	2	yes	—
26	C₁₃×#556	C₂²	1	2	yes	—
27	C₁₃×#556	C₂²	1	2	yes	—
28	C₁₃×#554	—	2	2	no	—
29	C₁₃×#554	C₂²	1	2	yes	—
30	C₁₃×#552	—	2	2	no	—
31	C₁₃×#552	—	2	2	no	—
32	D₄×Q₈×C₁₃	—	2	2	no	—
33	D₄×Q₈×C₁₃	C₂²	1	2	yes	—
34	C₁₃×#544	—	2	2	no	—
35	C₁₃×#544	C₂²	1	2	yes	—
36	C₁₃×#541	—	2	2	no	—
37	C₁₃×#536	C₂²	1	2	yes	—
38	C₁₃×#533	—	2	1	no	—
39	C₁₃×#533	—	2	1	no	—
40	C₁₃×#533	—	2	1	no	—
41	C₁₃×#533	C₂²	1	1	yes	characteristic
42	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
43	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
44	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
45	C₁₃×#520	C₂²	1	2	yes	—
46	C₁₃×#519	C₂²	1	2	yes	—
47	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
48	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
49	C₁₃×#491	C₂²	1	4	yes	—
50	C₁₃×#489	C₂²	1	4	yes	—
51	C₁₃×#488	C₂²	1	4	yes	—
52	C₁₃×#487	C₂²	1	4	yes	—
53	C₁₃×#487	C₂²	1	2	yes	—
54	C₁₃×#487	C₂²	1	2	yes	—
55	C₁₃×#487	C₂²	1	2	yes	—
56	C₁₃×#487	C₂²	1	2	yes	—
57	C₁₃×#479	C₂²	1	4	yes	—
58	C₁₃×#479	C₂²	1	4	yes	—
59	C₁₃×#477	C₂²	1	2	yes	—
60	C₁₃×#477	C₂²	1	4	yes	—
61	C₁₃×#476	C₂²	1	2	yes	—
62	C₁₃×#475	C₂²	1	2	yes	—
63	C₁₃×#475	C₂²	1	4	yes	—
64	C₁₃×#474	C₂²	1	2	yes	—
65	C₁₃×#464	C₂²	1	4	yes	—
66	C₁₃×#463	C₂²	1	4	yes	—
67	C₁₃×#462	C₂²	1	2	yes	—
68	C₁₃×#462	C₂²	1	2	yes	—
69	C₁₃×#462	C₂²	1	4	yes	—
70	C₁₃×#461	C₂²	1	2	yes	—
71	C₁₃×#461	C₂²	1	2	yes	—
72	C₁₃×#461	C₂²	1	4	yes	—
73	C₁₃×#446	C₂²	1	2	yes	—
74	C₁₃×#446	C₂²	1	2	yes	—
75	C₈×Q₈×C₁₃	C₂²	1	2	yes	—
76	C₈×Q₈×C₁₃	C₂²	1	2	yes	—
77	C₁₃×#441	C₂²	1	4	yes	—
78	C₁₃×#440	C₂²	1	4	yes	—
79	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
80	C₄×C₁₃×Q₁₆	C₂²	1	4	yes	—
81	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
82	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
83	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	—
84	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
85	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
86	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
87	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
88	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
89	C₁₃×#428	C₂²	1	2	yes	—
90	C₁₃×#427	C₂²	1	1	yes	characteristic
91	C₁₃×#424	C₂²	1	2	yes	—
92	C₁₃×#423	C₂²	1	1	yes	characteristic
93	C₁₃×#419	C₂²	1	2	yes	—
94	C₁₃×#417	C₂²	1	2	yes	—
95	C₁₃×#416	C₂²	1	1	yes	characteristic
96	C₁₃×#416	C₂²	1	1	yes	characteristic
97	C₂×C₁₃×#103	C₂²	1	2	yes	—
98	C₂×C₁₃×#103	C₂²	1	2	yes	—
99	C₁₃×#405	C₂²	1	2	yes	—
100	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
101	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
102	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
103	C₂²×Q₈×C₁₃	—	2	2	no	—
104	C₂²×Q₈×C₁₃	—	2	1	no	—
105	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
106	C₁₃×#137	—	2	8	no	—
107	C₁₃×#135	—	2	4	no	—
108	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
109	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
110	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
111	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
112	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
113	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
114	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
115	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
116	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
117	C₁₃×C₄⋊Q₈	—	2	2	no	—
118	C₁₃×C₄⋊Q₈	—	2	2	no	—
119	C₁₃×C₄⋊Q₈	—	2	2	no	—
120	C₁₃×C₄⋊Q₈	—	2	4	no	—
121	C₁₃×C₄⋊Q₈	—	2	1	no	—
122	C₁₃×C₄⋊Q₈	—	2	1	no	—
123	C₁₃×C₄⋊Q₈	—	2	1	no	—
124	C₁₃×C₄⋊Q₈	—	2	1	no	—
125	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
126	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
127	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
128	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
129	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
130	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
131	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
132	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
133	C₁₃×#126	—	2	4	no	—
134	C₁₃×#126	—	2	4	no	—
135	C₁₃×#125	—	2	2	no	—
136	C₁₃×#125	—	2	2	no	—
137	C₁₃×#125	—	2	2	no	—
138	C₁₃×#125	—	2	4	no	—
139	C₁₃×#125	—	2	4	no	—
140	C₁₃×#125	—	2	4	no	—
141	C₁₃×#125	D₄	1	2	yes	—
142	C₁₃×#125	C₂³	1	4	yes	—
143	C₁₃×#124	C₂³	1	4	yes	—
144	C₁₃×#123	—	2	4	no	—
145	C₁₃×C₂²⋊Q₈	—	2	2	no	—
146	C₁₃×C₂²⋊Q₈	—	2	2	no	—
147	C₁₃×C₂²⋊Q₈	—	2	2	no	—
148	C₁₃×C₂²⋊Q₈	—	2	2	no	—
149	C₁₃×C₂²⋊Q₈	—	2	2	no	—
150	C₁₃×C₂²⋊Q₈	—	2	2	no	—
151	C₁₃×C₂²⋊Q₈	—	2	4	no	—
152	C₁₃×C₂²⋊Q₈	—	2	4	no	—
153	C₁₃×C₂²⋊Q₈	—	2	4	no	—
154	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
155	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
156	C₄×Q₈×C₁₃	—	2	2	no	—
157	C₄×Q₈×C₁₃	—	2	2	no	—
158	C₄×Q₈×C₁₃	—	2	2	no	—
159	C₄×Q₈×C₁₃	—	2	2	no	—
160	C₄×Q₈×C₁₃	—	2	2	no	—
161	C₄×Q₈×C₁₃	—	2	2	no	—
162	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
163	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
164	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
165	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
166	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
167	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
168	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
169	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
170	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
171	C₄×D₄×C₁₃	—	2	1	no	—
172	C₄×D₄×C₁₃	—	2	1	no	—
173	C₄×D₄×C₁₃	—	2	1	no	—
174	C₄×D₄×C₁₃	—	2	1	no	—
175	C₄×D₄×C₁₃	—	2	4	no	—
176	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
177	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
178	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
179	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
180	C₄×D₄×C₁₃	C₂³	1	4	yes	—
181	C₁₃×#117	—	2	2	no	—
182	C₁₃×#117	—	2	2	no	—
183	C₁₃×#117	—	2	2	no	—
184	C₁₃×#117	—	2	4	no	—
185	C₁₃×#117	—	2	1	no	—
186	C₁₃×#117	—	2	1	no	—
187	C₁₃×#117	C₂³	1	1	yes	characteristic
188	C₁₃×#117	C₂³	1	1	yes	characteristic
189	C₁₃×#117	C₂³	1	2	yes	—
190	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
191	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
192	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
193	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
194	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
195	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
196	C₂×C₄²×C₁₃	—	2	1	no	—
197	C₂×C₄²×C₁₃	—	2	1	no	—
198	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
199	C₁₃×#107	C₂³	1	1	yes	characteristic
200	C₁₃×#107	C₂³	1	1	yes	characteristic
201	C₁₃×#107	C₂³	1	4	yes	—
202	C₁₃×#106	C₂³	1	1	yes	characteristic
203	C₁₃×#106	C₂³	1	1	yes	characteristic
204	C₁₃×#106	C₂³	1	4	yes	—
205	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
206	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
207	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
208	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
209	C₁₃×#103	C₂³	1	4	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	1	yes	characteristic
214	C₁₃×#103	C₂³	1	1	yes	characteristic
215	C₁₃×#103	C₂³	1	1	yes	characteristic
216	C₁₃×#103	C₂³	1	1	yes	characteristic
217	C₁₃×#103	C₂³	1	4	yes	—
218	C₁₃×#103	C₂³	1	4	yes	—
219	C₁₃×#103	C₂³	1	4	yes	—
220	C₁₃×#102	C₂³	1	1	yes	characteristic
221	C₁₃×#102	C₂³	1	1	yes	characteristic
222	C₁₃×#102	C₂³	1	1	yes	characteristic
223	C₁₃×#102	C₂³	1	1	yes	characteristic
224	C₁₃×#102	C₂³	1	4	yes	—
225	C₁₃×#97	C₂³	1	4	yes	—
226	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
227	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
228	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
229	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
230	C₄×C₈×C₁₃	C₂³	1	4	yes	—
231	#61330	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
232	C₁₃×#41	—	2	2	no	—
233	C₁₃×#41	—	2	2	no	—
234	C₁₃×#41	—	2	2	no	—
235	C₁₃×#41	#41	1	4	yes	—
236	C₂×Q₈×C₁₃	—	2	2	no	—
237	C₂×Q₈×C₁₃	—	2	2	no	—
238	C₂×Q₈×C₁₃	—	2	4	no	—
239	C₂×Q₈×C₁₃	—	2	2	no	—
240	C₂×Q₈×C₁₃	—	2	4	no	—
241	C₂×Q₈×C₁₃	—	2	4	no	—
242	C₂×Q₈×C₁₃	—	8	2	no	—
243	C₂×Q₈×C₁₃	—	8	4	no	—
244	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
245	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
246	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
247	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
248	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
249	C₂×D₄×C₁₃	—	2	1	no	—
250	C₂×D₄×C₁₃	—	2	1	no	—
251	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
252	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
253	C₂²×C₄×C₁₃	—	2	1	no	—
254	C₂²×C₄×C₁₃	—	2	2	no	—
255	C₂²×C₄×C₁₃	—	2	2	no	—
256	C₂²×C₄×C₁₃	—	2	1	no	—
257	C₂²×C₄×C₁₃	—	2	1	no	—
258	C₂²×C₄×C₁₃	—	2	1	no	—
259	C₂²×C₄×C₁₃	—	2	1	no	—
260	C₂²×C₄×C₁₃	—	2	1	no	—
261	C₂²×C₄×C₁₃	—	2	4	no	—
262	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
263	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
264	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
265	C₁₃×Q₁₆	—	2	2	no	—
266	C₁₃×Q₁₆	—	2	8	no	—
267	C₁₃×SD₁₆	—	2	2	no	—
268	C₁₃×SD₁₆	—	2	2	no	—
269	C₁₃×SD₁₆	—	2	8	no	—
270	C₁₃×D₈	—	2	2	no	—
271	C₁₃×M₁₆	—	2	4	no	—
272	C₂×C₈×C₁₃	—	2	2	no	—
273	C₂×C₈×C₁₃	—	2	2	no	—
274	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
275	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
276	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
277	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
278	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
279	C₁₃×C₄⋊C₄	—	2	2	no	—
280	C₁₃×C₄⋊C₄	—	2	2	no	—
281	C₁₃×C₄⋊C₄	—	2	2	no	—
282	C₁₃×C₄⋊C₄	—	2	2	no	—
283	C₁₃×C₄⋊C₄	—	2	4	no	—
284	C₁₃×C₄⋊C₄	—	2	2	no	—
285	C₁₃×C₄⋊C₄	—	2	4	no	—
286	C₁₃×C₄⋊C₄	—	2	2	no	—
287	C₁₃×C₄⋊C₄	—	2	2	no	—
288	C₁₃×C₄⋊C₄	—	2	1	no	—
289	C₁₃×C₄⋊C₄	—	2	1	no	—
290	C₁₃×C₄⋊C₄	—	2	1	no	—
291	C₁₃×C₄⋊C₄	—	2	1	no	—
292	C₁₃×C₄⋊C₄	—	2	4	no	—
293	C₁₃×C₄⋊C₄	—	2	4	no	—
294	C₁₃×C₄⋊C₄	—	2	4	no	—
295	C₁₃×C₄⋊C₄	—	2	4	no	—
296	C₁₃×C₄⋊C₄	—	2	4	no	—
297	C₁₃×C₄⋊C₄	—	2	4	no	—
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	C₂×D₄	1	4	yes	—
303	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
304	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
305	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
306	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
307	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
308	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
309	C₁₃×C₂²⋊C₄	—	2	1	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	4	no	—
314	C₁₃×C₂²⋊C₄	—	2	1	no	—
315	C₁₃×C₂²⋊C₄	—	2	1	no	—
316	C₁₃×C₂²⋊C₄	—	2	4	no	—
317	C₁₃×C₂²⋊C₄	—	2	4	no	—
318	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
319	C₄²×C₁₃	—	2	1	no	—
320	C₄²×C₁₃	—	2	1	no	—
321	C₄²×C₁₃	—	2	1	no	—
322	C₄²×C₁₃	—	2	1	no	—
323	C₄²×C₁₃	—	2	1	no	—
324	C₄²×C₁₃	—	2	1	no	—
325	C₄²×C₁₃	—	2	4	no	—
326	C₄²×C₁₃	—	2	4	no	—
327	C₄²×C₁₃	—	2	4	no	—
328	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
329	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
330	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
331	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
332	C₄²×C₁₃	C₂⁴	1	4	yes	—
333	#3509	C₂×C₁₃	1	1	yes	characteristic, complemented
334	#3503	C₂×C₁₃	1	1	yes	characteristic, complemented
335	#3374	C₂×C₁₃	1	2	yes	complemented
336	#3372	C₂×C₁₃	1	2	yes	complemented
337	#3369	C₂×C₁₃	1	2	yes	complemented
338	#3367	C₂×C₁₃	1	2	yes	complemented
339	#3364	C₂×C₁₃	1	2	yes	complemented
340	#3363	C₂×C₁₃	1	2	yes	complemented
341	#3360	C₂×C₁₃	1	2	yes	complemented
342	#3359	C₂×C₁₃	1	2	yes	complemented
343	#3137	C₂×C₁₃	1	2	yes	complemented
344	C₂×#487	C₂×C₁₃	1	1	yes	characteristic, complemented
345	#3082	C₂×C₁₃	1	2	yes	complemented
346	#3079	C₂×C₁₃	1	1	yes	characteristic, complemented
347	#3046	C₂×C₁₃	1	2	yes	—
348	#3039	C₂×C₁₃	1	1	yes	characteristic, complemented
349	#2960	C₂×C₁₃	1	1	yes	characteristic, complemented
350	#2947	C₂×C₁₃	1	2	yes	complemented
351	C₄×#135	C₂×C₁₃	1	1	yes	characteristic
352	C₂³×C₁₃	—	2	1	no	—
353	C₂³×C₁₃	—	2	1	no	—
354	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
355	Q₈×C₁₃	—	2	4	no	—
356	Q₈×C₁₃	—	2	4	no	—
357	Q₈×C₁₃	—	2	1	no	—
358	Q₈×C₁₃	—	2	4	no	—
359	Q₈×C₁₃	—	2	1	no	—
360	Q₈×C₁₃	—	2	4	no	—
361	Q₈×C₁₃	—	2	1	no	—
362	Q₈×C₁₃	—	4	4	no	—
363	Q₈×C₁₃	—	4	4	no	—
364	Q₈×C₁₃	—	8	2	no	—
365	Q₈×C₁₃	—	8	4	no	—
366	Q₈×C₁₃	C₂×#41	1	2	yes	—
367	D₄×C₁₃	—	2	4	no	—
368	D₄×C₁₃	—	2	1	no	—
369	D₄×C₁₃	—	2	1	no	—
370	D₄×C₁₃	—	2	1	no	—
371	D₄×C₁₃	—	4	2	no	—
372	D₄×C₁₃	C₂×#41	1	2	yes	—
373	C₂×C₄×C₁₃	—	2	1	no	—
374	C₂×C₄×C₁₃	—	2	4	no	—
375	C₂×C₄×C₁₃	—	2	2	no	—
376	C₂×C₄×C₁₃	—	2	2	no	—
377	C₂×C₄×C₁₃	—	2	1	no	—
378	C₂×C₄×C₁₃	—	2	1	no	—
379	C₂×C₄×C₁₃	—	2	1	no	—
380	C₂×C₄×C₁₃	—	2	4	no	—
381	C₂×C₄×C₁₃	—	2	1	no	—
382	C₂×C₄×C₁₃	—	2	1	no	—
383	C₂×C₄×C₁₃	—	2	4	no	—
384	C₂×C₄×C₁₃	—	4	4	no	—
385	C₂×C₄×C₁₃	—	4	2	no	—
386	C₂×C₄×C₁₃	—	4	2	no	—
387	C₂×C₄×C₁₃	—	4	2	no	—
388	C₂×C₄×C₁₃	—	4	2	no	—
389	C₂×C₄×C₁₃	—	4	2	no	—
390	C₂×C₄×C₁₃	—	8	4	no	—
391	C₂×C₄×C₁₃	—	8	2	no	—
392	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
393	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
394	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
395	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
396	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
397	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
398	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
399	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
400	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
401	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
402	C₈×C₁₃	—	2	1	no	—
403	C₈×C₁₃	—	2	1	no	—
404	C₈×C₁₃	—	2	4	no	—
405	C₈×C₁₃	—	2	1	no	—
406	C₈×C₁₃	—	2	1	no	—
407	C₂×#137	C₂²×C₁₃	1	2	yes	—
408	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
409	Q₈²	C₂²×C₁₃	1	2	yes	—
410	#557	C₂²×C₁₃	1	2	yes	—
411	#557	C₂²×C₁₃	1	2	yes	—
412	#557	C₂²×C₁₃	1	2	yes	—
413	#556	C₂²×C₁₃	1	2	yes	—
414	#556	C₂²×C₁₃	1	2	yes	—
415	#554	—	2	2	no	—
416	#554	C₂²×C₁₃	1	2	yes	—
417	#552	—	2	2	no	—
418	#552	—	2	2	no	—
419	D₄×Q₈	—	2	2	no	—
420	D₄×Q₈	C₂²×C₁₃	1	2	yes	—
421	#544	—	2	2	no	—
422	#544	C₂²×C₁₃	1	2	yes	—
423	#541	—	2	2	no	—
424	#536	C₂²×C₁₃	1	2	yes	—
425	#533	—	2	1	no	—
426	#533	—	2	1	no	—
427	#533	—	2	1	no	—
428	#533	C₂²×C₁₃	1	1	yes	characteristic
429	C₂×C₄⋊Q₈	—	2	1	no	—
430	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
431	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
432	#520	C₂²×C₁₃	1	2	yes	—
433	#519	C₂²×C₁₃	1	2	yes	—
434	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
435	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
436	#491	C₂²×C₁₃	1	4	yes	—
437	#489	C₂²×C₁₃	1	4	yes	—
438	#488	C₂²×C₁₃	1	4	yes	—
439	#487	C₂²×C₁₃	1	4	yes	—
440	#487	C₂²×C₁₃	1	2	yes	—
441	#487	C₂²×C₁₃	1	2	yes	—
442	#487	C₂²×C₁₃	1	2	yes	—
443	#487	C₂²×C₁₃	1	2	yes	—
444	#479	C₂²×C₁₃	1	4	yes	—
445	#479	C₂²×C₁₃	1	4	yes	—
446	#477	C₂²×C₁₃	1	2	yes	—
447	#477	C₂²×C₁₃	1	4	yes	—
448	#476	C₂²×C₁₃	1	2	yes	—
449	#475	C₂²×C₁₃	1	2	yes	—
450	#475	C₂²×C₁₃	1	4	yes	—
451	#474	C₂²×C₁₃	1	2	yes	—
452	#464	C₂²×C₁₃	1	4	yes	—
453	#463	C₂²×C₁₃	1	4	yes	—
454	#462	C₂²×C₁₃	1	2	yes	—
455	#462	C₂²×C₁₃	1	4	yes	—
456	#462	C₂²×C₁₃	1	2	yes	—
457	#461	C₂²×C₁₃	1	2	yes	—
458	#461	C₂²×C₁₃	1	4	yes	—
459	#461	C₂²×C₁₃	1	2	yes	—
460	#446	C₂²×C₁₃	1	2	yes	—
461	#446	C₂²×C₁₃	1	2	yes	—
462	C₈×Q₈	C₂²×C₁₃	1	2	yes	—
463	C₈×Q₈	C₂²×C₁₃	1	2	yes	—
464	#441	C₂²×C₁₃	1	4	yes	—
465	#440	C₂²×C₁₃	1	4	yes	—
466	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
467	C₄×Q₁₆	C₂²×C₁₃	1	4	yes	—
468	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
469	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
470	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	—
471	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
472	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
473	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
474	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
475	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
476	#428	C₂²×C₁₃	1	2	yes	—
477	#427	C₂²×C₁₃	1	1	yes	characteristic
478	#424	C₂²×C₁₃	1	2	yes	—
479	#423	C₂²×C₁₃	1	1	yes	characteristic
480	#419	C₂²×C₁₃	1	2	yes	—
481	#417	C₂²×C₁₃	1	2	yes	—
482	#416	C₂²×C₁₃	1	1	yes	characteristic
483	#416	C₂²×C₁₃	1	1	yes	characteristic
484	C₂×#103	C₂²×C₁₃	1	2	yes	—
485	C₂×#103	C₂²×C₁₃	1	2	yes	—
486	#405	C₂²×C₁₃	1	2	yes	—
487	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
488	C₂²×C₁₃	—	2	1	no	—
489	C₂²×C₁₃	—	2	1	no	—
490	C₂²×C₁₃	—	2	2	no	—
491	C₂²×C₁₃	—	4	1	no	—
492	C₂²×C₁₃	—	4	1	no	—
493	C₂²×C₁₃	—	4	1	no	—
494	C₂²×C₁₃	—	4	1	no	—
495	C₂²×C₁₃	—	4	1	no	—
496	C₂²×C₁₃	#548	1	2	yes	—
497	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
498	C₄×C₁₃	—	2	2	no	—
499	C₄×C₁₃	—	2	1	no	—
500	C₄×C₁₃	—	2	4	no	—
501	C₄×C₁₃	—	2	1	no	—
502	C₄×C₁₃	—	2	4	no	—
503	C₄×C₁₃	—	4	1	no	—
504	C₄×C₁₃	—	4	4	no	—
505	C₄×C₁₃	—	4	1	no	—
506	C₄×C₁₃	—	4	1	no	—
507	C₄×C₁₃	—	4	4	no	—
508	C₄×C₁₃	—	4	1	no	—
509	C₄×C₁₃	—	4	1	no	—
510	C₄×C₁₃	#548	1	2	yes	—
511	C₄×C₁₃	#577	1	2	yes	—
512	C₄×C₁₃	#578	1	2	yes	—
513	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
514	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
515	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
516	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
517	C₂²×Q₈	—	2	2	no	—
518	C₂²×Q₈	—	2	1	no	—
519	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
520	#137	—	2	8	no	—
521	#135	—	2	4	no	—
522	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
523	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
524	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
525	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
526	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
527	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
528	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
529	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
530	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
531	C₄⋊Q₈	—	2	2	no	—
532	C₄⋊Q₈	—	2	2	no	—
533	C₄⋊Q₈	—	2	2	no	—
534	C₄⋊Q₈	—	2	4	no	—
535	C₄⋊Q₈	—	2	1	no	—
536	C₄⋊Q₈	—	2	1	no	—
537	C₄⋊Q₈	—	2	1	no	—
538	C₄⋊Q₈	—	2	1	no	—
539	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
540	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
541	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
542	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
543	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
544	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
545	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
546	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
547	#126	—	2	4	no	—
548	#126	—	2	4	no	—
549	#125	—	2	2	no	—
550	#125	—	2	2	no	—
551	#125	—	2	2	no	—
552	#125	—	2	4	no	—
553	#125	—	2	4	no	—
554	#125	—	2	4	no	—
555	#125	D₄×C₁₃	1	2	yes	—
556	#125	C₂³×C₁₃	1	4	yes	—
557	#124	C₂³×C₁₃	1	4	yes	—
558	#123	—	2	4	no	—
559	C₂²⋊Q₈	—	2	2	no	—
560	C₂²⋊Q₈	—	2	2	no	—
561	C₂²⋊Q₈	—	2	2	no	—
562	C₂²⋊Q₈	—	2	2	no	—
563	C₂²⋊Q₈	—	2	2	no	—
564	C₂²⋊Q₈	—	2	2	no	—
565	C₂²⋊Q₈	—	2	4	no	—
566	C₂²⋊Q₈	—	2	4	no	—
567	C₂²⋊Q₈	—	2	4	no	—
568	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
569	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
570	C₄×Q₈	—	2	2	no	—
571	C₄×Q₈	—	2	2	no	—
572	C₄×Q₈	—	2	2	no	—
573	C₄×Q₈	—	2	2	no	—
574	C₄×Q₈	—	2	2	no	—
575	C₄×Q₈	—	2	2	no	—
576	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
577	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
578	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
579	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
580	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
581	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
582	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
583	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
584	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
585	C₄×D₄	—	2	1	no	—
586	C₄×D₄	—	2	1	no	—
587	C₄×D₄	—	2	1	no	—
588	C₄×D₄	—	2	1	no	—
589	C₄×D₄	—	2	4	no	—
590	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
591	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
592	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
593	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
594	C₄×D₄	C₂³×C₁₃	1	4	yes	—
595	#117	—	2	2	no	—
596	#117	—	2	2	no	—
597	#117	—	2	2	no	—
598	#117	—	2	4	no	—
599	#117	—	2	1	no	—
600	#117	—	2	1	no	—
601	#117	C₂³×C₁₃	1	1	yes	characteristic
602	#117	C₂³×C₁₃	1	1	yes	characteristic
603	#117	C₂³×C₁₃	1	2	yes	—
604	C₂×C₄⋊C₄	—	2	1	no	—
605	C₂×C₄⋊C₄	—	2	1	no	—
606	C₂×C₄⋊C₄	—	2	1	no	—
607	C₂×C₄⋊C₄	—	2	2	no	—
608	C₂×C₄⋊C₄	—	2	2	no	—
609	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
610	C₂×C₄²	—	2	1	no	—
611	C₂×C₄²	—	2	1	no	—
612	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
613	#107	C₂³×C₁₃	1	1	yes	characteristic
614	#107	C₂³×C₁₃	1	1	yes	characteristic
615	#107	C₂³×C₁₃	1	4	yes	—
616	#106	C₂³×C₁₃	1	1	yes	characteristic
617	#106	C₂³×C₁₃	1	1	yes	characteristic
618	#106	C₂³×C₁₃	1	4	yes	—
619	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
620	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
621	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
622	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
623	#103	C₂³×C₁₃	1	4	yes	—
624	#103	C₂³×C₁₃	1	4	yes	—
625	#103	C₂³×C₁₃	1	4	yes	—
626	#103	C₂³×C₁₃	1	4	yes	—
627	#103	C₂³×C₁₃	1	1	yes	characteristic
628	#103	C₂³×C₁₃	1	1	yes	characteristic
629	#103	C₂³×C₁₃	1	1	yes	characteristic
630	#103	C₂³×C₁₃	1	1	yes	characteristic
631	#103	C₂³×C₁₃	1	4	yes	—
632	#103	C₂³×C₁₃	1	4	yes	—
633	#103	C₂³×C₁₃	1	4	yes	—
634	#102	C₂³×C₁₃	1	1	yes	characteristic
635	#102	C₂³×C₁₃	1	1	yes	characteristic
636	#102	C₂³×C₁₃	1	1	yes	characteristic
637	#102	C₂³×C₁₃	1	1	yes	characteristic
638	#102	C₂³×C₁₃	1	4	yes	—
639	#97	C₂³×C₁₃	1	4	yes	—
640	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
641	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
642	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
643	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
644	C₄×C₈	C₂³×C₁₃	1	4	yes	—
645	C₂×C₁₃	—	2	2	no	—
646	C₂×C₁₃	—	4	2	no	—
647	C₂×C₁₃	—	8	1	no	—
648	C₂×C₁₃	C₂×#548	1	1	yes	characteristic
649	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
650	C₂×C₁₃	C₂×#578	1	1	yes	characteristic
651	#41	—	2	2	no	—
652	#41	—	2	2	no	—
653	#41	—	2	2	no	—
654	#41	C₁₃×#41	1	4	yes	—
655	C₂×Q₈	—	2	2	no	—
656	C₂×Q₈	—	2	2	no	—
657	C₂×Q₈	—	2	4	no	—
658	C₂×Q₈	—	2	2	no	—
659	C₂×Q₈	—	2	4	no	—
660	C₂×Q₈	—	2	4	no	—
661	C₂×Q₈	—	8	2	no	—
662	C₂×Q₈	—	8	4	no	—
663	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
664	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
665	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
666	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
667	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
668	C₂×D₄	—	2	1	no	—
669	C₂×D₄	—	2	1	no	—
670	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
671	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
672	C₂²×C₄	—	2	1	no	—
673	C₂²×C₄	—	2	2	no	—
674	C₂²×C₄	—	2	2	no	—
675	C₂²×C₄	—	2	1	no	—
676	C₂²×C₄	—	2	1	no	—
677	C₂²×C₄	—	2	1	no	—
678	C₂²×C₄	—	2	1	no	—
679	C₂²×C₄	—	2	1	no	—
680	C₂²×C₄	—	2	4	no	—
681	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
682	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
683	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
684	Q₁₆	—	2	2	no	—
685	Q₁₆	—	2	8	no	—
686	SD₁₆	—	2	2	no	—
687	SD₁₆	—	2	2	no	—
688	SD₁₆	—	2	8	no	—
689	D₈	—	2	2	no	—
690	M₁₆	—	2	4	no	—
691	C₂×C₈	—	2	2	no	—
692	C₂×C₈	—	2	2	no	—
693	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
694	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
695	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
696	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
697	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
698	C₄⋊C₄	—	2	2	no	—
699	C₄⋊C₄	—	2	2	no	—
700	C₄⋊C₄	—	2	2	no	—
701	C₄⋊C₄	—	2	2	no	—
702	C₄⋊C₄	—	2	4	no	—
703	C₄⋊C₄	—	2	2	no	—
704	C₄⋊C₄	—	2	4	no	—
705	C₄⋊C₄	—	2	2	no	—
706	C₄⋊C₄	—	2	2	no	—
707	C₄⋊C₄	—	2	1	no	—
708	C₄⋊C₄	—	2	1	no	—
709	C₄⋊C₄	—	2	1	no	—
710	C₄⋊C₄	—	2	1	no	—
711	C₄⋊C₄	—	2	4	no	—
712	C₄⋊C₄	—	2	4	no	—
713	C₄⋊C₄	—	2	4	no	—
714	C₄⋊C₄	—	2	4	no	—
715	C₄⋊C₄	—	2	4	no	—
716	C₄⋊C₄	—	2	4	no	—
717	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
718	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
719	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
720	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
721	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
722	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
723	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
724	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
725	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
726	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
727	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
728	C₂²⋊C₄	—	2	1	no	—
729	C₂²⋊C₄	—	2	1	no	—
730	C₂²⋊C₄	—	2	1	no	—
731	C₂²⋊C₄	—	2	1	no	—
732	C₂²⋊C₄	—	2	4	no	—
733	C₂²⋊C₄	—	2	1	no	—
734	C₂²⋊C₄	—	2	1	no	—
735	C₂²⋊C₄	—	2	4	no	—
736	C₂²⋊C₄	—	2	4	no	—
737	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
738	C₄²	—	2	1	no	—
739	C₄²	—	2	1	no	—
740	C₄²	—	2	1	no	—
741	C₄²	—	2	1	no	—
742	C₄²	—	2	1	no	—
743	C₄²	—	2	1	no	—
744	C₄²	—	2	4	no	—
745	C₄²	—	2	4	no	—
746	C₄²	—	2	4	no	—
747	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
748	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
749	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
750	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
751	C₄²	C₂⁴×C₁₃	1	4	yes	—
752	C₁₃	#61330	1	1	yes	characteristic, direct product factor, Sylow
753	C₂³	—	2	1	no	—
754	C₂³	—	2	1	no	—
755	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
756	Q₈	—	2	4	no	—
757	Q₈	—	2	4	no	—
758	Q₈	—	2	1	no	—
759	Q₈	—	2	4	no	—
760	Q₈	—	2	1	no	—
761	Q₈	—	2	4	no	—
762	Q₈	—	2	1	no	—
763	Q₈	—	4	4	no	—
764	Q₈	—	4	4	no	—
765	Q₈	—	8	2	no	—
766	Q₈	—	8	4	no	—
767	Q₈	C₂×C₁₃×#41	1	2	yes	—
768	D₄	—	2	4	no	—
769	D₄	—	2	1	no	—
770	D₄	—	2	1	no	—
771	D₄	—	2	1	no	—
772	D₄	—	4	2	no	—
773	D₄	C₂×C₁₃×#41	1	2	yes	—
774	C₂×C₄	—	2	1	no	—
775	C₂×C₄	—	2	4	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	2	1	no	—
779	C₂×C₄	—	2	1	no	—
780	C₂×C₄	—	2	1	no	—
781	C₂×C₄	—	2	4	no	—
782	C₂×C₄	—	2	1	no	—
783	C₂×C₄	—	2	1	no	—
784	C₂×C₄	—	2	4	no	—
785	C₂×C₄	—	4	4	no	—
786	C₂×C₄	—	4	2	no	—
787	C₂×C₄	—	4	2	no	—
788	C₂×C₄	—	4	2	no	—
789	C₂×C₄	—	4	2	no	—
790	C₂×C₄	—	4	2	no	—
791	C₂×C₄	—	8	4	no	—
792	C₂×C₄	—	8	2	no	—
793	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
794	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
795	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
796	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
797	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
798	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
799	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
800	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
801	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
802	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
803	C₈	—	2	1	no	—
804	C₈	—	2	1	no	—
805	C₈	—	2	4	no	—
806	C₈	—	2	1	no	—
807	C₈	—	2	1	no	—
808	C₂²	—	2	1	no	—
809	C₂²	—	2	1	no	—
810	C₂²	—	2	2	no	—
811	C₂²	—	4	1	no	—
812	C₂²	—	4	1	no	—
813	C₂²	—	4	1	no	—
814	C₂²	—	4	1	no	—
815	C₂²	—	4	1	no	—
816	C₂²	C₁₃×#548	1	2	yes	—
817	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
818	C₄	—	2	1	no	—
819	C₄	—	2	4	no	—
820	C₄	—	2	1	no	—
821	C₄	—	2	4	no	—
822	C₄	—	2	2	no	—
823	C₄	—	4	1	no	—
824	C₄	—	4	1	no	—
825	C₄	—	4	4	no	—
826	C₄	—	4	1	no	—
827	C₄	—	4	1	no	—
828	C₄	—	4	1	no	—
829	C₄	—	4	4	no	—
830	C₄	C₁₃×#548	1	2	yes	—
831	C₄	C₁₃×#577	1	2	yes	—
832	C₄	C₁₃×#578	1	2	yes	—
833	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
834	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
835	C₂	—	2	2	no	—
836	C₂	—	4	2	no	—
837	C₂	—	8	1	no	—
838	C₂	C₂×C₁₃×#548	1	1	yes	characteristic
839	C₂	C₂×C₁₃×#577	1	1	yes	characteristic
840	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×#3509	C₂	semidirect
2. C₁₃×#3503	C₂	semidirect
3. C₁₃×#3374	C₂	semidirect
4. C₁₃×#3372	C₂	semidirect
5. C₁₃×#3369	C₂	semidirect
6. C₁₃×#3367	C₂	semidirect
7. C₁₃×#3364	C₂	semidirect
8. C₁₃×#3363	C₂	semidirect
9. C₁₃×#3360	C₂	semidirect
10. C₁₃×#3359	C₂	semidirect
11. C₁₃×#3137	C₂	semidirect
12. C₂×C₁₃×#487	C₂	semidirect
13. C₁₃×#3082	C₂	semidirect
14. C₁₃×#3079	C₂	semidirect
16. C₁₃×#3039	C₂	semidirect
17. C₁₃×#2960	C₂	semidirect
18. C₁₃×#2947	C₂	semidirect
231. #61330	C₁₃	direct (N × H)
333. #3509	C₂×C₁₃	semidirect
334. #3503	C₂×C₁₃	semidirect
335. #3374	C₂×C₁₃	semidirect
336. #3372	C₂×C₁₃	semidirect
337. #3369	C₂×C₁₃	semidirect
338. #3367	C₂×C₁₃	semidirect
339. #3364	C₂×C₁₃	semidirect
340. #3363	C₂×C₁₃	semidirect
341. #3360	C₂×C₁₃	semidirect
342. #3359	C₂×C₁₃	semidirect
343. #3137	C₂×C₁₃	semidirect
344. C₂×#487	C₂×C₁₃	semidirect
345. #3082	C₂×C₁₃	semidirect
346. #3079	C₂×C₁₃	semidirect
348. #3039	C₂×C₁₃	semidirect
349. #2960	C₂×C₁₃	semidirect
350. #2947	C₂×C₁₃	semidirect
752. C₁₃	#61330	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×#3509	2
C₁₃×#3503	2
C₁₃×#3374	2
C₁₃×#3372	2
C₁₃×#3369	2
C₁₃×#3367	2
C₁₃×#3364	2
C₁₃×#3363	2
C₁₃×#3360	2
C₁₃×#3359	2
C₁₃×#3137	2
C₂×C₁₃×#487	2
C₁₃×#3082	2
C₁₃×#3079	2
C₁₃×#3046	2
C₁₃×#3039	2
C₁₃×#2960	2
C₁₃×#2947	2
C₄×C₁₃×#135	2
#61330	13

Subgroups — C13×#61330 #15747669

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61330 #15747669