Subgroups — C₁₃×#61108 #15747447

Order 3328.

2592 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3586	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3584	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#578	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3293	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3290	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3289	C₂	1	8	yes	maximal, complemented
7	C₁₃×#3156	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#3069	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3067	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×#473	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3022	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3020	C₂	1	2	yes	maximal, complemented
13	C₁₃×#2957	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#2955	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#585	C₂²	1	2	yes	—
16	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	2	yes	complemented
17	C₁₃×#578	—	2	4	no	—
18	C₁₃×#578	—	2	2	no	—
19	C₁₃×#578	—	2	2	no	—
20	C₁₃×#578	—	2	1	no	—
21	C₁₃×#578	C₂²	1	4	yes	complemented
22	C₁₃×#578	C₂²	1	8	yes	complemented
23	C₁₃×#578	C₂²	1	4	yes	complemented
24	C₁₃×#578	C₂²	1	2	yes	complemented
25	C₁₃×#577	—	2	4	no	—
26	C₁₃×#577	—	2	2	no	—
27	C₁₃×#577	C₂²	1	4	yes	complemented
28	C₁₃×#577	C₂²	1	8	yes	complemented
29	C₁₃×#576	—	2	1	no	—
30	C₁₃×#576	C₂²	1	2	yes	complemented
31	C₁₃×#575	—	2	4	no	—
32	C₁₃×#575	—	2	2	no	—
33	C₁₃×#575	C₂²	1	2	yes	—
34	C₁₃×#575	C₂²	1	1	yes	characteristic
35	C₁₃×#575	C₂²	1	2	yes	complemented
36	C₂×C₁₃×#137	—	2	4	no	—
37	C₂×C₁₃×#137	—	2	2	no	—
38	C₂×C₁₃×#137	C₂²	1	2	yes	—
39	C₂×C₁₃×#137	C₂²	1	2	yes	complemented
40	C₂×C₁₃×#137	C₂²	1	2	yes	complemented
41	C₂×C₁₃×#135	—	2	2	no	—
42	C₂×C₁₃×#135	—	2	1	no	—
43	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
44	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
45	C₂²×C₁₃×Q₁₆	—	2	1	no	—
46	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
47	C₁₃×#568	C₂²	1	2	yes	complemented
48	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
49	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic, complemented
50	C₁₃×#536	C₂²	1	2	yes	complemented
51	C₁₃×#497	C₂²	1	4	yes	complemented
52	C₁₃×#495	C₂²	1	2	yes	complemented
53	C₁₃×#494	C₂²	1	2	yes	complemented
54	C₁₃×#473	C₂²	1	4	yes	complemented
55	C₁₃×#473	C₂²	1	8	yes	complemented
56	C₁₃×#473	C₂²	1	4	yes	complemented
57	C₁₃×#473	C₂²	1	2	yes	complemented
58	C₁₃×#472	C₂²	1	2	yes	complemented
59	C₁₃×#471	C₂²	1	4	yes	complemented
60	C₁₃×#471	C₂²	1	8	yes	complemented
61	C₁₃×#456	C₂²	1	8	yes	complemented
62	C₁₃×#456	C₂²	1	8	yes	complemented
63	C₁₃×#455	C₂²	1	8	yes	complemented
64	C₁₃×#454	C₂²	1	8	yes	complemented
65	C₁₃×#444	C₂²	1	4	yes	complemented
66	C₁₃×#444	C₂²	1	4	yes	complemented
67	C₁₃×#443	C₂²	1	4	yes	complemented
68	C₁₃×#443	C₂²	1	4	yes	complemented
69	C₁₃×#430	C₂²	1	1	yes	characteristic, complemented
70	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic, complemented
71	C₁₃×#421	C₂²	1	1	yes	characteristic
72	C₁₃×#421	C₂²	1	1	yes	characteristic, complemented
73	C₁₃×#421	C₂²	1	2	yes	complemented
74	C₁₃×#413	C₂²	1	2	yes	complemented
75	C₂×C₁₃×#101	C₂²	1	2	yes	complemented
76	C₁₃×#405	C₂²	1	1	yes	characteristic, complemented
77	C₁₃×2₋¹⁺⁴	—	2	4	no	—
78	C₁₃×2₋¹⁺⁴	—	2	4	no	—
79	C₁₃×2₋¹⁺⁴	—	2	2	no	—
80	C₁₃×2₋¹⁺⁴	—	2	2	no	—
81	C₁₃×2₋¹⁺⁴	—	4	2	no	—
82	C₁₃×2₋¹⁺⁴	C₂³	1	8	yes	—
83	C₁₃×2₋¹⁺⁴	C₂³	1	4	yes	—
84	C₁₃×H(5,𝔽₂)	—	2	2	no	—
85	C₁₃×H(5,𝔽₂)	—	2	2	no	—
86	C₁₃×H(5,𝔽₂)	—	4	2	no	—
87	C₁₃×H(5,𝔽₂)	C₂³	1	4	yes	—
88	C₂×C₁₃×#41	—	2	4	no	—
89	C₂×C₁₃×#41	—	2	4	no	—
90	C₂×C₁₃×#41	—	2	2	no	—
91	C₂×C₁₃×#41	—	2	2	no	—
92	C₂×C₁₃×#41	—	4	2	no	—
93	C₂×C₁₃×#41	—	4	2	no	—
94	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
95	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
96	C₂×C₁₃×#41	C₂³	1	2	yes	—
97	C₂×C₁₃×#41	C₂³	1	2	yes	—
98	C₂²×Q₈×C₁₃	—	2	2	no	—
99	C₂²×Q₈×C₁₃	—	2	2	no	—
100	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
101	C₁₃×#137	—	2	4	no	—
102	C₁₃×#137	—	2	4	no	—
103	C₁₃×#137	—	2	2	no	—
104	C₁₃×#137	—	2	2	no	—
105	C₁₃×#137	—	2	8	no	—
106	C₁₃×#137	—	2	4	no	—
107	C₁₃×#137	—	2	8	no	—
108	C₁₃×#137	—	2	8	no	—
109	C₁₃×#137	—	2	8	no	—
110	C₁₃×#137	—	2	4	no	—
111	C₁₃×#137	—	2	8	no	—
112	C₁₃×#137	—	2	4	no	—
113	C₁₃×#137	—	2	4	no	—
114	C₁₃×#137	D₄	1	2	yes	—
115	C₁₃×#137	D₄	1	2	yes	—
116	C₁₃×#137	C₂³	1	8	yes	—
117	C₁₃×#137	C₂³	1	8	yes	—
118	C₁₃×#137	C₂³	1	4	yes	—
119	C₁₃×#137	C₂³	1	4	yes	—
120	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
121	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
122	C₁₃×AGL(1,ℤ/8)	—	2	4	no	—
123	C₁₃×AGL(1,ℤ/8)	—	2	4	no	—
124	C₁₃×AGL(1,ℤ/8)	—	2	8	no	—
125	C₁₃×AGL(1,ℤ/8)	D₄	1	2	yes	—
126	C₁₃×AGL(1,ℤ/8)	D₄	1	2	yes	—
127	C₁₃×AGL(1,ℤ/8)	C₂³	1	4	yes	—
128	C₁₃×AGL(1,ℤ/8)	C₂³	1	4	yes	—
129	C₁₃×#135	—	2	4	no	—
130	C₁₃×#135	—	2	4	no	—
131	C₁₃×#135	—	2	2	no	—
132	C₁₃×#135	—	2	4	no	—
133	C₁₃×#135	—	2	8	no	—
134	C₁₃×#135	—	2	2	no	—
135	C₁₃×#135	—	2	4	no	—
136	C₁₃×#135	—	2	4	no	—
137	C₁₃×#135	—	2	8	no	—
138	C₁₃×#135	—	2	1	no	—
139	C₁₃×#135	—	2	1	no	—
140	C₁₃×#135	—	2	1	no	—
141	C₁₃×#135	—	2	1	no	—
142	C₁₃×#135	D₄	1	2	yes	—
143	C₁₃×#135	D₄	1	2	yes	—
144	C₁₃×#135	C₂³	1	2	yes	—
145	C₁₃×#135	C₂³	1	4	yes	—
146	C₁₃×#135	C₂³	1	2	yes	—
147	C₂×C₁₃×Q₁₆	—	2	2	no	—
148	C₂×C₁₃×Q₁₆	—	2	2	no	—
149	C₂×C₁₃×Q₁₆	—	2	4	no	—
150	C₂×C₁₃×Q₁₆	—	2	4	no	—
151	C₂×C₁₃×Q₁₆	—	2	2	no	—
152	C₂×C₁₃×Q₁₆	—	2	8	no	—
153	C₂×C₁₃×Q₁₆	—	2	1	no	—
154	C₂×C₁₃×Q₁₆	—	2	1	no	—
155	C₂×C₁₃×Q₁₆	—	2	1	no	—
156	C₂×C₁₃×Q₁₆	—	2	1	no	—
157	C₂×C₁₃×Q₁₆	D₄	1	1	yes	characteristic
158	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
159	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
160	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
161	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
162	C₂×C₁₃×SD₁₆	—	2	2	no	—
163	C₂×C₁₃×SD₁₆	—	2	2	no	—
164	C₂×C₁₃×SD₁₆	—	2	4	no	—
165	C₂×C₁₃×SD₁₆	—	2	8	no	—
166	C₂×C₁₃×SD₁₆	D₄	1	2	yes	—
167	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
168	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
169	C₂×C₁₃×D₈	—	2	2	no	—
170	C₂×C₁₃×D₈	D₄	1	1	yes	characteristic
171	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
172	C₁₃×#131	—	2	4	no	—
173	C₁₃×#131	—	2	1	no	—
174	C₁₃×#131	—	2	1	no	—
175	C₁₃×#131	—	2	1	no	—
176	C₁₃×#131	—	2	1	no	—
177	C₁₃×#131	C₂³	1	2	yes	—
178	C₁₃×#131	C₂³	1	2	yes	—
179	C₁₃×#131	C₂³	1	8	yes	—
180	C₁₃×#131	C₂³	1	2	yes	—
181	C₁₃×#131	C₂³	1	2	yes	—
182	C₂×C₁₃×M₁₆	—	2	4	no	—
183	C₂×C₁₃×M₁₆	—	2	1	no	—
184	C₂×C₁₃×M₁₆	—	2	1	no	—
185	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
186	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
187	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
188	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
189	C₂²×C₈×C₁₃	—	2	1	no	—
190	C₂²×C₈×C₁₃	—	2	1	no	—
191	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
192	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
193	C₁₃×#124	C₂³	1	4	yes	—
194	C₁₃×#123	—	4	2	no	—
195	C₁₃×C₂²⋊Q₈	—	4	2	no	—
196	C₁₃×#117	C₂³	1	1	yes	characteristic
197	C₁₃×#108	C₂³	1	2	yes	—
198	C₁₃×#108	C₂³	1	2	yes	—
199	C₁₃×#108	C₂³	1	4	yes	—
200	C₁₃×#104	C₂³	1	4	yes	—
201	C₁₃×#104	C₂³	1	4	yes	—
202	C₁₃×#104	C₂³	1	8	yes	—
203	C₁₃×#101	C₂³	1	8	yes	—
204	C₁₃×#101	C₂³	1	4	yes	—
205	C₁₃×#100	C₂³	1	4	yes	—
206	C₁₃×#97	C₂³	1	2	yes	—
207	C₄×C₈×C₁₃	C₂³	1	2	yes	—
208	#61108	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
209	C₁₃×#41	—	2	1	no	—
210	C₁₃×#41	—	2	2	no	—
211	C₁₃×#41	—	2	1	no	—
212	C₁₃×#41	—	2	1	no	—
213	C₁₃×#41	—	2	2	no	—
214	C₁₃×#41	—	2	1	no	—
215	C₁₃×#41	—	2	4	no	—
216	C₁₃×#41	—	2	4	no	—
217	C₁₃×#41	—	2	4	no	—
218	C₁₃×#41	—	2	8	no	—
219	C₁₃×#41	—	2	4	no	—
220	C₁₃×#41	—	2	8	no	—
221	C₁₃×#41	—	2	2	no	—
222	C₁₃×#41	—	2	2	no	—
223	C₁₃×#41	—	2	2	no	—
224	C₁₃×#41	—	2	2	no	—
225	C₁₃×#41	—	4	4	no	—
226	C₁₃×#41	—	4	4	no	—
227	C₁₃×#41	—	4	8	no	—
228	C₁₃×#41	—	4	4	no	—
229	C₁₃×#41	—	4	4	no	—
230	C₁₃×#41	—	4	4	no	—
231	C₁₃×#41	—	4	4	no	—
232	C₁₃×#41	—	4	8	no	—
233	C₁₃×#41	—	4	2	no	—
234	C₁₃×#41	—	4	2	no	—
235	C₁₃×#41	C₂×D₄	1	2	yes	—
236	C₁₃×#41	C₂×D₄	1	4	yes	—
237	C₁₃×#41	C₂×D₄	1	2	yes	—
238	C₁₃×#41	C₂⁴	1	2	yes	—
239	C₁₃×#41	C₂⁴	1	4	yes	—
240	C₁₃×#41	C₂⁴	1	2	yes	—
241	C₂×Q₈×C₁₃	—	2	2	no	—
242	C₂×Q₈×C₁₃	—	2	8	no	—
243	C₂×Q₈×C₁₃	—	2	4	no	—
244	C₂×Q₈×C₁₃	—	2	8	no	—
245	C₂×Q₈×C₁₃	—	2	4	no	—
246	C₂×Q₈×C₁₃	—	2	2	no	—
247	C₂×Q₈×C₁₃	—	2	2	no	—
248	C₂×Q₈×C₁₃	—	2	2	no	—
249	C₂×Q₈×C₁₃	—	2	2	no	—
250	C₂×Q₈×C₁₃	—	4	2	no	—
251	C₂×Q₈×C₁₃	—	4	4	no	—
252	C₂×Q₈×C₁₃	—	4	4	no	—
253	C₂×Q₈×C₁₃	—	4	2	no	—
254	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
255	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
256	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
257	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
258	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
259	C₂×D₄×C₁₃	—	2	1	no	—
260	C₂×D₄×C₁₃	—	2	2	no	—
261	C₂×D₄×C₁₃	—	2	1	no	—
262	C₂×D₄×C₁₃	—	2	4	no	—
263	C₂×D₄×C₁₃	—	2	4	no	—
264	C₂×D₄×C₁₃	—	2	2	no	—
265	C₂×D₄×C₁₃	—	4	4	no	—
266	C₂×D₄×C₁₃	—	4	2	no	—
267	C₂×D₄×C₁₃	—	4	4	no	—
268	C₂×D₄×C₁₃	—	4	4	no	—
269	C₂×D₄×C₁₃	—	4	2	no	—
270	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
271	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
272	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
273	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
274	C₂²×C₄×C₁₃	—	2	1	no	—
275	C₂²×C₄×C₁₃	—	2	1	no	—
276	C₂²×C₄×C₁₃	—	2	2	no	—
277	C₂²×C₄×C₁₃	—	2	2	no	—
278	C₂²×C₄×C₁₃	—	2	2	no	—
279	C₂²×C₄×C₁₃	—	4	4	no	—
280	C₂²×C₄×C₁₃	—	4	2	no	—
281	C₂²×C₄×C₁₃	—	4	2	no	—
282	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
283	C₁₃×Q₁₆	—	2	8	no	—
284	C₁₃×Q₁₆	—	2	8	no	—
285	C₁₃×Q₁₆	—	2	4	no	—
286	C₁₃×Q₁₆	—	2	4	no	—
287	C₁₃×Q₁₆	—	2	2	no	—
288	C₁₃×Q₁₆	—	2	2	no	—
289	C₁₃×Q₁₆	—	2	1	no	—
290	C₁₃×Q₁₆	—	2	2	no	—
291	C₁₃×Q₁₆	—	2	2	no	—
292	C₁₃×Q₁₆	—	2	8	no	—
293	C₁₃×Q₁₆	—	2	1	no	—
294	C₁₃×Q₁₆	C₂×D₄	1	2	yes	—
295	C₁₃×Q₁₆	C₂×D₄	1	2	yes	—
296	C₁₃×Q₁₆	C₂×D₄	1	4	yes	—
297	C₁₃×SD₁₆	—	2	4	no	—
298	C₁₃×SD₁₆	—	2	4	no	—
299	C₁₃×SD₁₆	—	2	8	no	—
300	C₁₃×SD₁₆	—	2	4	no	—
301	C₁₃×SD₁₆	—	2	8	no	—
302	C₁₃×SD₁₆	—	2	4	no	—
303	C₁₃×SD₁₆	—	2	2	no	—
304	C₁₃×SD₁₆	—	2	8	no	—
305	C₁₃×SD₁₆	—	2	2	no	—
306	C₁₃×SD₁₆	C₂×D₄	1	4	yes	—
307	C₁₃×SD₁₆	C₂×D₄	1	4	yes	—
308	C₁₃×SD₁₆	C₂×D₄	1	4	yes	—
309	C₁₃×SD₁₆	C₂×D₄	1	4	yes	—
310	C₁₃×D₈	—	2	4	no	—
311	C₁₃×D₈	—	2	4	no	—
312	C₁₃×D₈	—	2	1	no	—
313	C₁₃×D₈	—	2	1	no	—
314	C₁₃×D₈	C₂×D₄	1	2	yes	—
315	C₁₃×D₈	C₂×D₄	1	2	yes	—
316	C₁₃×D₈	C₂×D₄	1	4	yes	—
317	C₁₃×M₁₆	—	2	2	no	—
318	C₁₃×M₁₆	—	2	1	no	—
319	C₁₃×M₁₆	—	2	1	no	—
320	C₁₃×M₁₆	—	2	2	no	—
321	C₁₃×M₁₆	—	2	2	no	—
322	C₁₃×M₁₆	—	2	8	no	—
323	C₁₃×M₁₆	—	2	2	no	—
324	C₁₃×M₁₆	—	2	2	no	—
325	C₁₃×M₁₆	C₂×D₄	1	2	yes	—
326	C₁₃×M₁₆	C₂×D₄	1	2	yes	—
327	C₁₃×M₁₆	C₂⁴	1	2	yes	—
328	C₁₃×M₁₆	C₂⁴	1	4	yes	—
329	C₁₃×M₁₆	C₂⁴	1	2	yes	—
330	C₂×C₈×C₁₃	—	2	1	no	—
331	C₂×C₈×C₁₃	—	2	1	no	—
332	C₂×C₈×C₁₃	—	2	2	no	—
333	C₂×C₈×C₁₃	—	2	2	no	—
334	C₂×C₈×C₁₃	—	2	2	no	—
335	C₂×C₈×C₁₃	—	2	2	no	—
336	C₂×C₈×C₁₃	—	2	2	no	—
337	C₂×C₈×C₁₃	—	2	8	no	—
338	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
339	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
340	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
341	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
342	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
343	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
344	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
345	C₁₃×C₄⋊C₄	—	2	1	no	—
346	C₁₃×C₄⋊C₄	—	4	4	no	—
347	C₁₃×C₂²⋊C₄	—	2	1	no	—
348	C₁₃×C₂²⋊C₄	—	4	4	no	—
349	C₄²×C₁₃	C₂⁴	1	2	yes	—
350	#3586	C₂×C₁₃	1	2	yes	complemented
351	#3584	C₂×C₁₃	1	1	yes	characteristic, complemented
352	C₂×#578	C₂×C₁₃	1	1	yes	characteristic, complemented
353	#3293	C₂×C₁₃	1	4	yes	complemented
354	#3290	C₂×C₁₃	1	4	yes	complemented
355	#3289	C₂×C₁₃	1	8	yes	complemented
356	#3156	C₂×C₁₃	1	1	yes	characteristic, complemented
357	#3069	C₂×C₁₃	1	2	yes	complemented
358	#3067	C₂×C₁₃	1	1	yes	characteristic, complemented
359	C₂×#473	C₂×C₁₃	1	1	yes	characteristic, complemented
360	#3022	C₂×C₁₃	1	2	yes	complemented
361	#3020	C₂×C₁₃	1	2	yes	complemented
362	#2957	C₂×C₁₃	1	1	yes	characteristic, complemented
363	#2955	C₂×C₁₃	1	1	yes	characteristic, complemented
364	C₂³×C₁₃	—	2	1	no	—
365	C₂³×C₁₃	—	2	2	no	—
366	C₂³×C₁₃	—	2	1	no	—
367	C₂³×C₁₃	—	2	2	no	—
368	C₂³×C₁₃	—	4	4	no	—
369	C₂³×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
370	Q₈×C₁₃	—	2	1	no	—
371	Q₈×C₁₃	—	2	2	no	—
372	Q₈×C₁₃	—	2	1	no	—
373	Q₈×C₁₃	—	2	4	no	—
374	Q₈×C₁₃	—	2	2	no	—
375	Q₈×C₁₃	—	2	4	no	—
376	Q₈×C₁₃	—	2	2	no	—
377	Q₈×C₁₃	—	4	8	no	—
378	Q₈×C₁₃	—	4	4	no	—
379	Q₈×C₁₃	—	4	2	no	—
380	Q₈×C₁₃	—	4	2	no	—
381	Q₈×C₁₃	C₂²×D₄	1	2	yes	—
382	Q₈×C₁₃	C₂²×D₄	1	4	yes	—
383	Q₈×C₁₃	C₂²×D₄	1	2	yes	—
384	D₄×C₁₃	—	2	2	no	—
385	D₄×C₁₃	—	2	4	no	—
386	D₄×C₁₃	—	2	2	no	—
387	D₄×C₁₃	—	2	2	no	—
388	D₄×C₁₃	—	2	4	no	—
389	D₄×C₁₃	—	2	2	no	—
390	D₄×C₁₃	—	2	1	no	—
391	D₄×C₁₃	—	2	2	no	—
392	D₄×C₁₃	—	2	1	no	—
393	D₄×C₁₃	—	2	2	no	—
394	D₄×C₁₃	—	2	2	no	—
395	D₄×C₁₃	—	4	4	no	—
396	D₄×C₁₃	—	4	4	no	—
397	D₄×C₁₃	—	4	4	no	—
398	D₄×C₁₃	—	4	8	no	—
399	D₄×C₁₃	—	4	2	no	—
400	D₄×C₁₃	—	4	2	no	—
401	D₄×C₁₃	C₂²×D₄	1	2	yes	—
402	D₄×C₁₃	C₂²×D₄	1	4	yes	—
403	D₄×C₁₃	C₂²×D₄	1	2	yes	—
404	C₂×C₄×C₁₃	—	2	1	no	—
405	C₂×C₄×C₁₃	—	2	2	no	—
406	C₂×C₄×C₁₃	—	2	1	no	—
407	C₂×C₄×C₁₃	—	2	2	no	—
408	C₂×C₄×C₁₃	—	2	4	no	—
409	C₂×C₄×C₁₃	—	2	2	no	—
410	C₂×C₄×C₁₃	—	2	2	no	—
411	C₂×C₄×C₁₃	—	2	4	no	—
412	C₂×C₄×C₁₃	—	2	2	no	—
413	C₂×C₄×C₁₃	—	2	2	no	—
414	C₂×C₄×C₁₃	—	2	4	no	—
415	C₂×C₄×C₁₃	—	2	2	no	—
416	C₂×C₄×C₁₃	—	4	4	no	—
417	C₂×C₄×C₁₃	—	4	4	no	—
418	C₂×C₄×C₁₃	—	4	4	no	—
419	C₂×C₄×C₁₃	—	4	8	no	—
420	C₂×C₄×C₁₃	—	4	8	no	—
421	C₂×C₄×C₁₃	—	4	2	no	—
422	C₂×C₄×C₁₃	—	4	2	no	—
423	C₂×C₄×C₁₃	—	4	2	no	—
424	C₂×C₄×C₁₃	—	4	2	no	—
425	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
426	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
427	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
428	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
429	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
430	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
431	C₈×C₁₃	—	2	2	no	—
432	C₈×C₁₃	—	2	4	no	—
433	C₈×C₁₃	—	2	2	no	—
434	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
435	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
436	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
437	C₈×C₁₃	C₂²×D₄	1	4	yes	—
438	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
439	#585	C₂²×C₁₃	1	2	yes	—
440	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	2	yes	complemented
441	#578	—	2	4	no	—
442	#578	—	2	2	no	—
443	#578	—	2	2	no	—
444	#578	—	2	1	no	—
445	#578	C₂²×C₁₃	1	2	yes	complemented
446	#578	C₂²×C₁₃	1	8	yes	complemented
447	#578	C₂²×C₁₃	1	4	yes	complemented
448	#578	C₂²×C₁₃	1	4	yes	complemented
449	#577	—	2	4	no	—
450	#577	—	2	2	no	—
451	#577	C₂²×C₁₃	1	4	yes	complemented
452	#577	C₂²×C₁₃	1	8	yes	complemented
453	#576	—	2	1	no	—
454	#576	C₂²×C₁₃	1	2	yes	complemented
455	#575	—	2	4	no	—
456	#575	—	2	2	no	—
457	#575	C₂²×C₁₃	1	2	yes	—
458	#575	C₂²×C₁₃	1	1	yes	characteristic
459	#575	C₂²×C₁₃	1	2	yes	complemented
460	C₂×#137	—	2	4	no	—
461	C₂×#137	—	2	2	no	—
462	C₂×#137	C₂²×C₁₃	1	2	yes	—
463	C₂×#137	C₂²×C₁₃	1	2	yes	complemented
464	C₂×#137	C₂²×C₁₃	1	2	yes	complemented
465	C₂×#135	—	2	2	no	—
466	C₂×#135	—	2	1	no	—
467	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
468	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
469	C₂²×Q₁₆	—	2	1	no	—
470	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
471	#568	C₂²×C₁₃	1	2	yes	complemented
472	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
473	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic, complemented
474	#536	C₂²×C₁₃	1	2	yes	complemented
475	#497	C₂²×C₁₃	1	4	yes	complemented
476	#495	C₂²×C₁₃	1	2	yes	complemented
477	#494	C₂²×C₁₃	1	2	yes	complemented
478	#473	C₂²×C₁₃	1	4	yes	complemented
479	#473	C₂²×C₁₃	1	8	yes	complemented
480	#473	C₂²×C₁₃	1	4	yes	complemented
481	#473	C₂²×C₁₃	1	2	yes	complemented
482	#472	C₂²×C₁₃	1	2	yes	complemented
483	#471	C₂²×C₁₃	1	4	yes	complemented
484	#471	C₂²×C₁₃	1	8	yes	complemented
485	#456	C₂²×C₁₃	1	8	yes	complemented
486	#456	C₂²×C₁₃	1	8	yes	complemented
487	#455	C₂²×C₁₃	1	8	yes	complemented
488	#454	C₂²×C₁₃	1	8	yes	complemented
489	#444	C₂²×C₁₃	1	4	yes	complemented
490	#444	C₂²×C₁₃	1	4	yes	complemented
491	#443	C₂²×C₁₃	1	4	yes	complemented
492	#443	C₂²×C₁₃	1	4	yes	complemented
493	#430	C₂²×C₁₃	1	1	yes	characteristic, complemented
494	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic, complemented
495	#421	C₂²×C₁₃	1	1	yes	characteristic
496	#421	C₂²×C₁₃	1	1	yes	characteristic, complemented
497	#421	C₂²×C₁₃	1	2	yes	complemented
498	#413	C₂²×C₁₃	1	2	yes	complemented
499	C₂×#101	C₂²×C₁₃	1	2	yes	complemented
500	#405	C₂²×C₁₃	1	1	yes	characteristic, complemented
501	C₂²×C₁₃	—	2	2	no	—
502	C₂²×C₁₃	—	2	4	no	—
503	C₂²×C₁₃	—	2	2	no	—
504	C₂²×C₁₃	—	4	1	no	—
505	C₂²×C₁₃	—	4	2	no	—
506	C₂²×C₁₃	—	4	2	no	—
507	C₂²×C₁₃	—	8	2	no	—
508	C₂²×C₁₃	—	8	1	no	—
509	C₂²×C₁₃	—	8	2	no	—
510	C₂²×C₁₃	—	16	4	no	—
511	C₂²×C₁₃	D₄²	1	1	yes	characteristic
512	C₂²×C₁₃	D₄²	1	1	yes	characteristic
513	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
514	C₄×C₁₃	—	2	2	no	—
515	C₄×C₁₃	—	2	4	no	—
516	C₄×C₁₃	—	2	2	no	—
517	C₄×C₁₃	—	4	2	no	—
518	C₄×C₁₃	—	4	2	no	—
519	C₄×C₁₃	—	4	4	no	—
520	C₄×C₁₃	D₄²	1	1	yes	characteristic
521	C₄×C₁₃	D₄²	1	1	yes	characteristic
522	C₄×C₁₃	C₂³×D₄	1	1	yes	characteristic
523	C₄×C₁₃	C₂³×D₄	1	1	yes	characteristic
524	2₋¹⁺⁴	—	2	4	no	—
525	2₋¹⁺⁴	—	2	4	no	—
526	2₋¹⁺⁴	—	2	2	no	—
527	2₋¹⁺⁴	—	2	2	no	—
528	2₋¹⁺⁴	—	4	2	no	—
529	2₋¹⁺⁴	C₂³×C₁₃	1	8	yes	—
530	2₋¹⁺⁴	C₂³×C₁₃	1	4	yes	—
531	H(5,𝔽₂)	—	2	2	no	—
532	H(5,𝔽₂)	—	2	2	no	—
533	H(5,𝔽₂)	—	4	2	no	—
534	H(5,𝔽₂)	C₂³×C₁₃	1	4	yes	—
535	C₂×#41	—	2	4	no	—
536	C₂×#41	—	2	4	no	—
537	C₂×#41	—	2	2	no	—
538	C₂×#41	—	2	2	no	—
539	C₂×#41	—	4	2	no	—
540	C₂×#41	—	4	2	no	—
541	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
542	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
543	C₂×#41	C₂³×C₁₃	1	2	yes	—
544	C₂×#41	C₂³×C₁₃	1	2	yes	—
545	C₂²×Q₈	—	2	2	no	—
546	C₂²×Q₈	—	2	2	no	—
547	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
548	#137	—	2	4	no	—
549	#137	—	2	4	no	—
550	#137	—	2	2	no	—
551	#137	—	2	2	no	—
552	#137	—	2	8	no	—
553	#137	—	2	4	no	—
554	#137	—	2	8	no	—
555	#137	—	2	8	no	—
556	#137	—	2	8	no	—
557	#137	—	2	4	no	—
558	#137	—	2	8	no	—
559	#137	—	2	4	no	—
560	#137	—	2	4	no	—
561	#137	D₄×C₁₃	1	2	yes	—
562	#137	D₄×C₁₃	1	2	yes	—
563	#137	C₂³×C₁₃	1	8	yes	—
564	#137	C₂³×C₁₃	1	8	yes	—
565	#137	C₂³×C₁₃	1	4	yes	—
566	#137	C₂³×C₁₃	1	4	yes	—
567	AGL(1,ℤ/8)	—	2	2	no	—
568	AGL(1,ℤ/8)	—	2	2	no	—
569	AGL(1,ℤ/8)	—	2	4	no	—
570	AGL(1,ℤ/8)	—	2	4	no	—
571	AGL(1,ℤ/8)	—	2	8	no	—
572	AGL(1,ℤ/8)	D₄×C₁₃	1	2	yes	—
573	AGL(1,ℤ/8)	D₄×C₁₃	1	2	yes	—
574	AGL(1,ℤ/8)	C₂³×C₁₃	1	4	yes	—
575	AGL(1,ℤ/8)	C₂³×C₁₃	1	4	yes	—
576	#135	—	2	4	no	—
577	#135	—	2	4	no	—
578	#135	—	2	2	no	—
579	#135	—	2	4	no	—
580	#135	—	2	8	no	—
581	#135	—	2	2	no	—
582	#135	—	2	4	no	—
583	#135	—	2	4	no	—
584	#135	—	2	8	no	—
585	#135	—	2	1	no	—
586	#135	—	2	1	no	—
587	#135	—	2	1	no	—
588	#135	—	2	1	no	—
589	#135	D₄×C₁₃	1	2	yes	—
590	#135	D₄×C₁₃	1	2	yes	—
591	#135	C₂³×C₁₃	1	2	yes	—
592	#135	C₂³×C₁₃	1	2	yes	—
593	#135	C₂³×C₁₃	1	4	yes	—
594	C₂×Q₁₆	—	2	2	no	—
595	C₂×Q₁₆	—	2	2	no	—
596	C₂×Q₁₆	—	2	4	no	—
597	C₂×Q₁₆	—	2	4	no	—
598	C₂×Q₁₆	—	2	2	no	—
599	C₂×Q₁₆	—	2	8	no	—
600	C₂×Q₁₆	—	2	1	no	—
601	C₂×Q₁₆	—	2	1	no	—
602	C₂×Q₁₆	—	2	1	no	—
603	C₂×Q₁₆	—	2	1	no	—
604	C₂×Q₁₆	D₄×C₁₃	1	1	yes	characteristic
605	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
606	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
607	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
608	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
609	C₂×SD₁₆	—	2	2	no	—
610	C₂×SD₁₆	—	2	2	no	—
611	C₂×SD₁₆	—	2	4	no	—
612	C₂×SD₁₆	—	2	8	no	—
613	C₂×SD₁₆	D₄×C₁₃	1	2	yes	—
614	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
615	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
616	C₂×D₈	—	2	2	no	—
617	C₂×D₈	D₄×C₁₃	1	1	yes	characteristic
618	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
619	#131	—	2	4	no	—
620	#131	—	2	1	no	—
621	#131	—	2	1	no	—
622	#131	—	2	1	no	—
623	#131	—	2	1	no	—
624	#131	C₂³×C₁₃	1	2	yes	—
625	#131	C₂³×C₁₃	1	2	yes	—
626	#131	C₂³×C₁₃	1	2	yes	—
627	#131	C₂³×C₁₃	1	2	yes	—
628	#131	C₂³×C₁₃	1	8	yes	—
629	C₂×M₁₆	—	2	4	no	—
630	C₂×M₁₆	—	2	1	no	—
631	C₂×M₁₆	—	2	1	no	—
632	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
633	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
634	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
635	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
636	C₂²×C₈	—	2	1	no	—
637	C₂²×C₈	—	2	1	no	—
638	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
639	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
640	#124	C₂³×C₁₃	1	4	yes	—
641	#123	—	4	2	no	—
642	C₂²⋊Q₈	—	4	2	no	—
643	#117	C₂³×C₁₃	1	1	yes	characteristic
644	#108	C₂³×C₁₃	1	2	yes	—
645	#108	C₂³×C₁₃	1	2	yes	—
646	#108	C₂³×C₁₃	1	4	yes	—
647	#104	C₂³×C₁₃	1	4	yes	—
648	#104	C₂³×C₁₃	1	4	yes	—
649	#104	C₂³×C₁₃	1	8	yes	—
650	#101	C₂³×C₁₃	1	8	yes	—
651	#101	C₂³×C₁₃	1	4	yes	—
652	#100	C₂³×C₁₃	1	4	yes	—
653	#97	C₂³×C₁₃	1	2	yes	—
654	C₄×C₈	C₂³×C₁₃	1	2	yes	—
655	C₂×C₁₃	—	2	1	no	—
656	C₂×C₁₃	—	2	1	no	—
657	C₂×C₁₃	—	2	1	no	—
658	C₂×C₁₃	—	4	2	no	—
659	C₂×C₁₃	—	4	4	no	—
660	C₂×C₁₃	—	4	2	no	—
661	C₂×C₁₃	—	8	2	no	—
662	C₂×C₁₃	C₂×D₄²	1	1	yes	characteristic
663	#41	—	2	1	no	—
664	#41	—	2	2	no	—
665	#41	—	2	1	no	—
666	#41	—	2	1	no	—
667	#41	—	2	2	no	—
668	#41	—	2	1	no	—
669	#41	—	2	4	no	—
670	#41	—	2	4	no	—
671	#41	—	2	4	no	—
672	#41	—	2	8	no	—
673	#41	—	2	4	no	—
674	#41	—	2	8	no	—
675	#41	—	2	2	no	—
676	#41	—	2	2	no	—
677	#41	—	2	2	no	—
678	#41	—	2	2	no	—
679	#41	—	4	4	no	—
680	#41	—	4	4	no	—
681	#41	—	4	8	no	—
682	#41	—	4	4	no	—
683	#41	—	4	4	no	—
684	#41	—	4	4	no	—
685	#41	—	4	4	no	—
686	#41	—	4	8	no	—
687	#41	—	4	2	no	—
688	#41	—	4	2	no	—
689	#41	C₂×D₄×C₁₃	1	2	yes	—
690	#41	C₂×D₄×C₁₃	1	4	yes	—
691	#41	C₂×D₄×C₁₃	1	2	yes	—
692	#41	C₂⁴×C₁₃	1	2	yes	—
693	#41	C₂⁴×C₁₃	1	4	yes	—
694	#41	C₂⁴×C₁₃	1	2	yes	—
695	C₂×Q₈	—	2	2	no	—
696	C₂×Q₈	—	2	8	no	—
697	C₂×Q₈	—	2	4	no	—
698	C₂×Q₈	—	2	8	no	—
699	C₂×Q₈	—	2	4	no	—
700	C₂×Q₈	—	2	2	no	—
701	C₂×Q₈	—	2	2	no	—
702	C₂×Q₈	—	2	2	no	—
703	C₂×Q₈	—	2	2	no	—
704	C₂×Q₈	—	4	2	no	—
705	C₂×Q₈	—	4	4	no	—
706	C₂×Q₈	—	4	4	no	—
707	C₂×Q₈	—	4	2	no	—
708	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
709	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
710	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
711	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
712	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
713	C₂×D₄	—	2	1	no	—
714	C₂×D₄	—	2	2	no	—
715	C₂×D₄	—	2	1	no	—
716	C₂×D₄	—	2	4	no	—
717	C₂×D₄	—	2	4	no	—
718	C₂×D₄	—	2	2	no	—
719	C₂×D₄	—	4	4	no	—
720	C₂×D₄	—	4	2	no	—
721	C₂×D₄	—	4	4	no	—
722	C₂×D₄	—	4	4	no	—
723	C₂×D₄	—	4	2	no	—
724	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
725	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
726	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
727	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
728	C₂²×C₄	—	2	1	no	—
729	C₂²×C₄	—	2	1	no	—
730	C₂²×C₄	—	2	2	no	—
731	C₂²×C₄	—	2	2	no	—
732	C₂²×C₄	—	2	2	no	—
733	C₂²×C₄	—	4	4	no	—
734	C₂²×C₄	—	4	2	no	—
735	C₂²×C₄	—	4	2	no	—
736	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
737	Q₁₆	—	2	8	no	—
738	Q₁₆	—	2	8	no	—
739	Q₁₆	—	2	4	no	—
740	Q₁₆	—	2	4	no	—
741	Q₁₆	—	2	2	no	—
742	Q₁₆	—	2	2	no	—
743	Q₁₆	—	2	1	no	—
744	Q₁₆	—	2	2	no	—
745	Q₁₆	—	2	2	no	—
746	Q₁₆	—	2	8	no	—
747	Q₁₆	—	2	1	no	—
748	Q₁₆	C₂×D₄×C₁₃	1	2	yes	—
749	Q₁₆	C₂×D₄×C₁₃	1	2	yes	—
750	Q₁₆	C₂×D₄×C₁₃	1	4	yes	—
751	SD₁₆	—	2	4	no	—
752	SD₁₆	—	2	4	no	—
753	SD₁₆	—	2	8	no	—
754	SD₁₆	—	2	4	no	—
755	SD₁₆	—	2	8	no	—
756	SD₁₆	—	2	4	no	—
757	SD₁₆	—	2	2	no	—
758	SD₁₆	—	2	8	no	—
759	SD₁₆	—	2	2	no	—
760	SD₁₆	C₂×D₄×C₁₃	1	4	yes	—
761	SD₁₆	C₂×D₄×C₁₃	1	4	yes	—
762	SD₁₆	C₂×D₄×C₁₃	1	4	yes	—
763	SD₁₆	C₂×D₄×C₁₃	1	4	yes	—
764	D₈	—	2	4	no	—
765	D₈	—	2	4	no	—
766	D₈	—	2	1	no	—
767	D₈	—	2	1	no	—
768	D₈	C₂×D₄×C₁₃	1	2	yes	—
769	D₈	C₂×D₄×C₁₃	1	2	yes	—
770	D₈	C₂×D₄×C₁₃	1	4	yes	—
771	M₁₆	—	2	2	no	—
772	M₁₆	—	2	1	no	—
773	M₁₆	—	2	1	no	—
774	M₁₆	—	2	2	no	—
775	M₁₆	—	2	2	no	—
776	M₁₆	—	2	8	no	—
777	M₁₆	—	2	2	no	—
778	M₁₆	—	2	2	no	—
779	M₁₆	C₂×D₄×C₁₃	1	2	yes	—
780	M₁₆	C₂×D₄×C₁₃	1	2	yes	—
781	M₁₆	C₂⁴×C₁₃	1	2	yes	—
782	M₁₆	C₂⁴×C₁₃	1	4	yes	—
783	M₁₆	C₂⁴×C₁₃	1	2	yes	—
784	C₂×C₈	—	2	1	no	—
785	C₂×C₈	—	2	1	no	—
786	C₂×C₈	—	2	2	no	—
787	C₂×C₈	—	2	2	no	—
788	C₂×C₈	—	2	2	no	—
789	C₂×C₈	—	2	2	no	—
790	C₂×C₈	—	2	2	no	—
791	C₂×C₈	—	2	8	no	—
792	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
793	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
794	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
795	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
796	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
797	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
798	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
799	C₄⋊C₄	—	2	1	no	—
800	C₄⋊C₄	—	4	4	no	—
801	C₂²⋊C₄	—	2	1	no	—
802	C₂²⋊C₄	—	4	4	no	—
803	C₄²	C₂⁴×C₁₃	1	2	yes	—
804	C₁₃	#61108	1	1	yes	characteristic, direct product factor, Sylow
805	C₂³	—	2	1	no	—
806	C₂³	—	2	2	no	—
807	C₂³	—	2	1	no	—
808	C₂³	—	2	2	no	—
809	C₂³	—	4	4	no	—
810	C₂³	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
811	Q₈	—	2	1	no	—
812	Q₈	—	2	2	no	—
813	Q₈	—	2	1	no	—
814	Q₈	—	2	4	no	—
815	Q₈	—	2	2	no	—
816	Q₈	—	2	4	no	—
817	Q₈	—	2	2	no	—
818	Q₈	—	4	8	no	—
819	Q₈	—	4	4	no	—
820	Q₈	—	4	2	no	—
821	Q₈	—	4	2	no	—
822	Q₈	C₂²×D₄×C₁₃	1	2	yes	—
823	Q₈	C₂²×D₄×C₁₃	1	4	yes	—
824	Q₈	C₂²×D₄×C₁₃	1	2	yes	—
825	D₄	—	2	2	no	—
826	D₄	—	2	4	no	—
827	D₄	—	2	2	no	—
828	D₄	—	2	2	no	—
829	D₄	—	2	4	no	—
830	D₄	—	2	2	no	—
831	D₄	—	2	1	no	—
832	D₄	—	2	2	no	—
833	D₄	—	2	1	no	—
834	D₄	—	2	2	no	—
835	D₄	—	2	2	no	—
836	D₄	—	4	4	no	—
837	D₄	—	4	4	no	—
838	D₄	—	4	4	no	—
839	D₄	—	4	8	no	—
840	D₄	—	4	2	no	—
841	D₄	—	4	2	no	—
842	D₄	C₂²×D₄×C₁₃	1	2	yes	—
843	D₄	C₂²×D₄×C₁₃	1	4	yes	—
844	D₄	C₂²×D₄×C₁₃	1	2	yes	—
845	C₂×C₄	—	2	1	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	1	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	2	4	no	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	2	2	no	—
852	C₂×C₄	—	2	4	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	4	no	—
856	C₂×C₄	—	2	2	no	—
857	C₂×C₄	—	4	4	no	—
858	C₂×C₄	—	4	4	no	—
859	C₂×C₄	—	4	4	no	—
860	C₂×C₄	—	4	8	no	—
861	C₂×C₄	—	4	8	no	—
862	C₂×C₄	—	4	2	no	—
863	C₂×C₄	—	4	2	no	—
864	C₂×C₄	—	4	2	no	—
865	C₂×C₄	—	4	2	no	—
866	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
867	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
868	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
869	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
870	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
871	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
872	C₈	—	2	2	no	—
873	C₈	—	2	4	no	—
874	C₈	—	2	2	no	—
875	C₈	C₂²×D₄×C₁₃	1	1	yes	characteristic
876	C₈	C₂²×D₄×C₁₃	1	1	yes	characteristic
877	C₈	C₂²×D₄×C₁₃	1	1	yes	characteristic
878	C₈	C₂²×D₄×C₁₃	1	4	yes	—
879	C₈	C₂²×D₄×C₁₃	1	1	yes	characteristic
880	C₂²	—	2	2	no	—
881	C₂²	—	2	4	no	—
882	C₂²	—	2	2	no	—
883	C₂²	—	4	1	no	—
884	C₂²	—	4	2	no	—
885	C₂²	—	4	2	no	—
886	C₂²	—	8	2	no	—
887	C₂²	—	8	1	no	—
888	C₂²	—	8	2	no	—
889	C₂²	—	16	4	no	—
890	C₂²	D₄²×C₁₃	1	1	yes	characteristic
891	C₂²	D₄²×C₁₃	1	1	yes	characteristic
892	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
893	C₄	—	2	2	no	—
894	C₄	—	2	4	no	—
895	C₄	—	2	2	no	—
896	C₄	—	4	2	no	—
897	C₄	—	4	2	no	—
898	C₄	—	4	4	no	—
899	C₄	D₄²×C₁₃	1	1	yes	characteristic
900	C₄	D₄²×C₁₃	1	1	yes	characteristic
901	C₄	C₂³×D₄×C₁₃	1	1	yes	characteristic
902	C₄	C₂³×D₄×C₁₃	1	1	yes	characteristic
903	C₂	—	2	1	no	—
904	C₂	—	2	1	no	—
905	C₂	—	2	1	no	—
906	C₂	—	4	2	no	—
907	C₂	—	4	2	no	—
908	C₂	—	4	4	no	—
909	C₂	—	8	2	no	—
910	C₂	C₂×D₄²×C₁₃	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₃	C₂×D₄²
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3586	C₂	semidirect
2. C₁₃×#3584	C₂	semidirect
3. C₂×C₁₃×#578	C₂	semidirect
4. C₁₃×#3293	C₂	semidirect
5. C₁₃×#3290	C₂	semidirect
6. C₁₃×#3289	C₂	semidirect
7. C₁₃×#3156	C₂	semidirect
8. C₁₃×#3069	C₂	semidirect
9. C₁₃×#3067	C₂	semidirect
10. C₂×C₁₃×#473	C₂	semidirect
11. C₁₃×#3022	C₂	semidirect
12. C₁₃×#3020	C₂	semidirect
13. C₁₃×#2957	C₂	semidirect
14. C₁₃×#2955	C₂	semidirect
16. C₂×C₁₃×2₋¹⁺⁴	C₂²	semidirect
21. C₁₃×#578	C₂²	semidirect
22. C₁₃×#578	C₂²	semidirect
23. C₁₃×#578	C₂²	semidirect
24. C₁₃×#578	C₂²	semidirect
27. C₁₃×#577	C₂²	semidirect
28. C₁₃×#577	C₂²	semidirect
30. C₁₃×#576	C₂²	semidirect
35. C₁₃×#575	C₂²	semidirect
39. C₂×C₁₃×#137	C₂²	semidirect
40. C₂×C₁₃×#137	C₂²	semidirect
46. C₂²×C₁₃×Q₁₆	C₂²	semidirect
47. C₁₃×#568	C₂²	semidirect
49. C₂×C₁₃×#131	C₂²	semidirect
50. C₁₃×#536	C₂²	semidirect
51. C₁₃×#497	C₂²	semidirect
52. C₁₃×#495	C₂²	semidirect
53. C₁₃×#494	C₂²	semidirect
54. C₁₃×#473	C₂²	semidirect
55. C₁₃×#473	C₂²	semidirect
56. C₁₃×#473	C₂²	semidirect
57. C₁₃×#473	C₂²	semidirect
58. C₁₃×#472	C₂²	semidirect
59. C₁₃×#471	C₂²	semidirect
60. C₁₃×#471	C₂²	semidirect
61. C₁₃×#456	C₂²	semidirect
62. C₁₃×#456	C₂²	semidirect
63. C₁₃×#455	C₂²	semidirect
64. C₁₃×#454	C₂²	semidirect
65. C₁₃×#444	C₂²	semidirect
66. C₁₃×#444	C₂²	semidirect
67. C₁₃×#443	C₂²	semidirect
68. C₁₃×#443	C₂²	semidirect
69. C₁₃×#430	C₂²	semidirect
70. C₂×C₁₃×#108	C₂²	semidirect
72. C₁₃×#421	C₂²	semidirect
73. C₁₃×#421	C₂²	semidirect
74. C₁₃×#413	C₂²	semidirect
75. C₂×C₁₃×#101	C₂²	semidirect
76. C₁₃×#405	C₂²	semidirect
208. #61108	C₁₃	direct (N × H)
350. #3586	C₂×C₁₃	semidirect
351. #3584	C₂×C₁₃	semidirect
352. C₂×#578	C₂×C₁₃	semidirect
353. #3293	C₂×C₁₃	semidirect
354. #3290	C₂×C₁₃	semidirect
355. #3289	C₂×C₁₃	semidirect
356. #3156	C₂×C₁₃	semidirect
357. #3069	C₂×C₁₃	semidirect
358. #3067	C₂×C₁₃	semidirect
359. C₂×#473	C₂×C₁₃	semidirect
360. #3022	C₂×C₁₃	semidirect
361. #3020	C₂×C₁₃	semidirect
362. #2957	C₂×C₁₃	semidirect
363. #2955	C₂×C₁₃	semidirect
440. C₂×2₋¹⁺⁴	C₂²×C₁₃	semidirect
445. #578	C₂²×C₁₃	semidirect
446. #578	C₂²×C₁₃	semidirect
447. #578	C₂²×C₁₃	semidirect
448. #578	C₂²×C₁₃	semidirect
451. #577	C₂²×C₁₃	semidirect
452. #577	C₂²×C₁₃	semidirect
454. #576	C₂²×C₁₃	semidirect
459. #575	C₂²×C₁₃	semidirect
463. C₂×#137	C₂²×C₁₃	semidirect
464. C₂×#137	C₂²×C₁₃	semidirect
470. C₂²×Q₁₆	C₂²×C₁₃	semidirect
471. #568	C₂²×C₁₃	semidirect
473. C₂×#131	C₂²×C₁₃	semidirect
474. #536	C₂²×C₁₃	semidirect
475. #497	C₂²×C₁₃	semidirect
476. #495	C₂²×C₁₃	semidirect
477. #494	C₂²×C₁₃	semidirect
478. #473	C₂²×C₁₃	semidirect
479. #473	C₂²×C₁₃	semidirect
480. #473	C₂²×C₁₃	semidirect
481. #473	C₂²×C₁₃	semidirect
482. #472	C₂²×C₁₃	semidirect
483. #471	C₂²×C₁₃	semidirect
484. #471	C₂²×C₁₃	semidirect
485. #456	C₂²×C₁₃	semidirect
486. #456	C₂²×C₁₃	semidirect
487. #455	C₂²×C₁₃	semidirect
488. #454	C₂²×C₁₃	semidirect
489. #444	C₂²×C₁₃	semidirect
490. #444	C₂²×C₁₃	semidirect
491. #443	C₂²×C₁₃	semidirect
492. #443	C₂²×C₁₃	semidirect
493. #430	C₂²×C₁₃	semidirect
494. C₂×#108	C₂²×C₁₃	semidirect
496. #421	C₂²×C₁₃	semidirect
497. #421	C₂²×C₁₃	semidirect
498. #413	C₂²×C₁₃	semidirect
499. C₂×#101	C₂²×C₁₃	semidirect
500. #405	C₂²×C₁₃	semidirect
804. C₁₃	#61108	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×#3586	2
C₁₃×#3584	2
C₂×C₁₃×#578	2
C₁₃×#3293	2
C₁₃×#3290	2
C₁₃×#3289	2
C₁₃×#3156	2
C₁₃×#3069	2
C₁₃×#3067	2
C₂×C₁₃×#473	2
C₁₃×#3022	2
C₁₃×#3020	2
C₁₃×#2957	2
C₁₃×#2955	2
#61108	13

Subgroups — C13×#61108 #15747447

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61108 #15747447