Subgroups — C₁₃×#62108 #15748447

Order 3328.

1750 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3503	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3475	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3385	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3369	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3357	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3344	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3331	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3314	C₂	1	4	yes	maximal, complemented
9	C₁₃×#3252	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3249	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3238	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3230	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3116	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3101	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3079	C₂	1	2	yes	maximal, complemented
16	C₂×C₁₃×#476	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#2989	C₂	1	1	yes	maximal, characteristic, complemented
18	Q₈²×C₁₃	C₂²	1	2	yes	complemented
19	C₁₃×#557	—	2	1	no	—
20	C₁₃×#556	C₂²	1	1	yes	characteristic
21	C₁₃×#555	C₂²	1	1	yes	characteristic
22	C₁₃×#554	C₂²	1	1	yes	characteristic
23	C₁₃×#554	C₂²	1	4	yes	—
24	C₁₃×#554	C₂²	1	2	yes	complemented
25	C₁₃×#553	—	2	1	no	—
26	C₁₃×#552	—	2	1	no	—
27	C₁₃×#552	C₂²	1	2	yes	—
28	C₁₃×#551	—	2	2	no	—
29	D₄×Q₈×C₁₃	—	2	2	no	—
30	D₄×Q₈×C₁₃	—	2	1	no	—
31	C₁₃×#547	C₂²	1	1	yes	characteristic
32	C₁₃×#546	C₂²	1	2	yes	—
33	C₁₃×#544	—	2	1	no	—
34	C₁₃×#544	—	2	2	no	—
35	C₁₃×#533	C₂²	1	1	yes	characteristic
36	C₁₃×#533	C₂²	1	1	yes	characteristic
37	C₁₃×#533	C₂²	1	2	yes	complemented
38	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
40	C₁₃×#529	—	2	2	no	—
41	C₁₃×#529	C₂²	1	2	yes	—
42	C₁₃×#525	—	2	1	no	—
43	C₁₃×#520	—	2	1	no	—
44	C₄×C₁₃×#41	C₂²	1	2	yes	—
45	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
47	C₂×C₁₃×#117	—	2	1	no	—
48	C₁₃×#501	C₂²	1	4	yes	complemented
49	C₁₃×#500	C₂²	1	2	yes	complemented
50	C₁₃×#489	C₂²	1	4	yes	—
51	C₁₃×#487	C₂²	1	2	yes	complemented
52	C₁₃×#485	C₂²	1	4	yes	complemented
53	C₁₃×#484	C₂²	1	4	yes	—
54	C₁₃×#483	C₂²	1	2	yes	—
55	C₁₃×#483	C₂²	1	4	yes	complemented
56	C₁₃×#480	C₂²	1	4	yes	—
57	C₁₃×#479	C₂²	1	4	yes	complemented
58	C₁₃×#477	C₂²	1	2	yes	complemented
59	C₁₃×#477	C₂²	1	2	yes	complemented
60	C₁₃×#477	C₂²	1	2	yes	complemented
61	C₁₃×#477	C₂²	1	2	yes	complemented
62	C₁₃×#476	C₂²	1	2	yes	—
63	C₁₃×#476	C₂²	1	2	yes	—
64	C₁₃×#476	C₂²	1	2	yes	—
65	C₁₃×#476	C₂²	1	2	yes	—
66	C₁₃×#476	C₂²	1	1	yes	characteristic
67	C₁₃×#476	C₂²	1	1	yes	characteristic
68	C₁₃×#475	C₂²	1	4	yes	complemented
69	C₁₃×#474	C₂²	1	4	yes	—
70	C₁₃×#470	C₂²	1	4	yes	complemented
71	C₁₃×#468	C₂²	1	4	yes	—
72	C₁₃×#467	C₂²	1	4	yes	—
73	C₁₃×#464	C₂²	1	4	yes	—
74	C₁₃×#462	C₂²	1	2	yes	complemented
75	C₁₃×#462	C₂²	1	2	yes	complemented
76	C₁₃×#461	C₂²	1	1	yes	characteristic
77	C₁₃×#461	C₂²	1	1	yes	characteristic
78	C₁₃×#452	C₂²	1	4	yes	—
79	C₁₃×#450	C₂²	1	2	yes	—
80	C₁₃×#446	C₂²	1	2	yes	complemented
81	C₁₃×#441	C₂²	1	4	yes	complemented
82	C₁₃×#440	C₂²	1	4	yes	—
83	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
84	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
85	C₁₃×#436	C₂²	1	2	yes	complemented
86	C₁₃×#435	C₂²	1	4	yes	—
87	C₁₃×#432	C₂²	1	2	yes	complemented
88	C₁₃×#431	C₂²	1	1	yes	characteristic
89	C₁₃×#428	C₂²	1	4	yes	complemented
90	C₂×C₁₃×#106	C₂²	1	2	yes	—
91	C₁₃×#423	C₂²	1	2	yes	complemented
92	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
93	C₁₃×#417	C₂²	1	4	yes	—
94	C₂×C₁₃×#102	C₂²	1	2	yes	—
95	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
96	C₂×C₁₃×#41	C₂³	1	2	yes	—
97	C₂²×Q₈×C₁₃	—	2	1	no	—
98	C₂²×Q₈×C₁₃	—	2	2	no	—
99	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
100	C₂³×C₄×C₁₃	—	2	1	no	—
101	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
102	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
103	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
104	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
105	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
106	C₁₃×C₄⋊Q₈	—	2	2	no	—
107	C₁₃×C₄⋊Q₈	—	2	4	no	—
108	C₁₃×C₄⋊Q₈	—	2	1	no	—
109	C₁₃×C₄⋊Q₈	—	2	1	no	—
110	C₁₃×C₄⋊Q₈	—	2	2	no	—
111	C₁₃×C₄⋊Q₈	—	2	2	no	—
112	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
113	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
114	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
115	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
116	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
117	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
118	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
119	C₁₃×#126	—	2	2	no	—
120	C₁₃×#126	—	2	2	no	—
121	C₁₃×#126	—	2	2	no	—
122	C₁₃×#125	—	2	2	no	—
123	C₁₃×#125	—	2	4	no	—
124	C₁₃×#125	—	2	2	no	—
125	C₁₃×#125	—	2	1	no	—
126	C₁₃×#125	—	2	1	no	—
127	C₁₃×#125	—	2	2	no	—
128	C₁₃×#125	C₂³	1	2	yes	—
129	C₁₃×#124	—	2	2	no	—
130	C₁₃×#124	C₂³	1	2	yes	—
131	C₁₃×#123	—	2	2	no	—
132	C₁₃×#123	—	2	2	no	—
133	C₁₃×#123	—	2	2	no	—
134	C₁₃×#123	—	2	2	no	—
135	C₁₃×C₂²⋊Q₈	—	2	1	no	—
136	C₁₃×C₂²⋊Q₈	—	2	1	no	—
137	C₁₃×C₂²⋊Q₈	—	2	1	no	—
138	C₁₃×C₂²⋊Q₈	—	2	1	no	—
139	C₁₃×C₂²⋊Q₈	—	2	2	no	—
140	C₁₃×C₂²⋊Q₈	—	2	2	no	—
141	C₁₃×C₂²⋊Q₈	—	2	4	no	—
142	C₁₃×C₂²⋊Q₈	—	2	4	no	—
143	C₁₃×C₂²⋊Q₈	—	2	4	no	—
144	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
145	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
146	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
147	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
148	C₁₃×#121	—	2	1	no	—
149	C₁₃×#121	—	2	1	no	—
150	C₁₃×#121	—	2	2	no	—
151	C₁₃×#121	C₂³	1	2	yes	—
152	C₁₃×#120	—	2	2	no	—
153	C₄×Q₈×C₁₃	—	2	2	no	—
154	C₄×Q₈×C₁₃	—	2	1	no	—
155	C₄×Q₈×C₁₃	—	2	1	no	—
156	C₄×Q₈×C₁₃	—	2	2	no	—
157	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
158	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
159	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
160	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
161	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
162	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
163	C₄×D₄×C₁₃	—	2	4	no	—
164	C₄×D₄×C₁₃	—	2	2	no	—
165	C₄×D₄×C₁₃	—	2	2	no	—
166	C₄×D₄×C₁₃	—	2	2	no	—
167	C₄×D₄×C₁₃	—	2	2	no	—
168	C₄×D₄×C₁₃	—	2	1	no	—
169	C₄×D₄×C₁₃	—	2	1	no	—
170	C₄×D₄×C₁₃	D₄	1	2	yes	—
171	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
172	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
173	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
174	C₄×D₄×C₁₃	C₂³	1	2	yes	—
175	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
176	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
177	C₄×D₄×C₁₃	C₂³	1	2	yes	—
178	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
179	C₁₃×#117	—	2	1	no	—
180	C₁₃×#117	—	2	1	no	—
181	C₁₃×#117	—	2	2	no	—
182	C₁₃×#117	—	2	1	no	—
183	C₁₃×#117	—	2	1	no	—
184	C₁₃×#117	—	2	2	no	—
185	C₁₃×#117	—	2	2	no	—
186	C₁₃×#117	—	2	2	no	—
187	C₁₃×#117	D₄	1	1	yes	characteristic
188	C₁₃×#117	D₄	1	2	yes	—
189	C₁₃×#117	C₂³	1	2	yes	—
190	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
191	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
192	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
193	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
194	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
195	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
196	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
197	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
198	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
199	C₂×C₄²×C₁₃	—	2	2	no	—
200	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
202	C₁₃×#107	C₂³	1	4	yes	—
203	C₁₃×#107	C₂³	1	4	yes	—
204	C₁₃×#107	C₂³	1	4	yes	—
205	C₁₃×#106	C₂³	1	4	yes	—
206	C₁₃×#106	C₂³	1	4	yes	—
207	C₁₃×#106	C₂³	1	2	yes	—
208	C₁₃×#106	C₂³	1	2	yes	—
209	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
210	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
211	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
212	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
213	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
214	C₁₃×#103	C₂³	1	4	yes	—
215	C₁₃×#103	C₂³	1	4	yes	—
216	C₁₃×#103	C₂³	1	2	yes	—
217	C₁₃×#103	C₂³	1	2	yes	—
218	C₁₃×#103	C₂³	1	4	yes	—
219	C₁₃×#103	C₂³	1	4	yes	—
220	C₁₃×#102	C₂³	1	4	yes	—
221	C₁₃×#102	C₂³	1	4	yes	—
222	C₁₃×#102	C₂³	1	2	yes	—
223	C₁₃×#102	C₂³	1	2	yes	—
224	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
225	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
226	C₁₃×#97	C₂³	1	4	yes	—
227	C₄×C₈×C₁₃	C₂³	1	2	yes	—
228	#62108	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
229	C₂⁴×C₁₃	—	2	1	no	—
230	C₁₃×#41	—	2	4	no	—
231	C₁₃×#41	—	2	4	no	—
232	C₁₃×#41	—	4	2	no	—
233	C₂×Q₈×C₁₃	—	2	1	no	—
234	C₂×Q₈×C₁₃	—	2	2	no	—
235	C₂×Q₈×C₁₃	—	2	1	no	—
236	C₂×Q₈×C₁₃	—	2	4	no	—
237	C₂×Q₈×C₁₃	—	2	2	no	—
238	C₂×Q₈×C₁₃	—	8	2	no	—
239	C₂×Q₈×C₁₃	—	8	4	no	—
240	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
241	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
242	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
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	1	no	—
247	C₂×D₄×C₁₃	—	4	1	no	—
248	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
249	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
250	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
251	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
252	C₂²×C₄×C₁₃	—	2	1	no	—
253	C₂²×C₄×C₁₃	—	2	4	no	—
254	C₂²×C₄×C₁₃	—	2	2	no	—
255	C₂²×C₄×C₁₃	—	2	1	no	—
256	C₂²×C₄×C₁₃	—	2	2	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	2	no	—
261	C₂²×C₄×C₁₃	—	4	4	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	1	yes	characteristic
267	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
268	C₁₃×Q₁₆	—	4	4	no	—
269	C₁₃×SD₁₆	—	2	4	no	—
270	C₁₃×SD₁₆	—	4	2	no	—
271	C₁₃×M₁₆	—	4	4	no	—
272	C₂×C₈×C₁₃	—	4	2	no	—
273	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
274	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
275	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
276	C₁₃×C₄⋊C₄	—	2	2	no	—
277	C₁₃×C₄⋊C₄	—	2	1	no	—
278	C₁₃×C₄⋊C₄	—	2	1	no	—
279	C₁₃×C₄⋊C₄	—	2	1	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	2	no	—
284	C₁₃×C₄⋊C₄	—	2	1	no	—
285	C₁₃×C₄⋊C₄	—	2	4	no	—
286	C₁₃×C₄⋊C₄	—	2	2	no	—
287	C₁₃×C₄⋊C₄	—	2	1	no	—
288	C₁₃×C₄⋊C₄	—	2	2	no	—
289	C₁₃×C₄⋊C₄	—	2	2	no	—
290	C₁₃×C₄⋊C₄	—	2	2	no	—
291	C₁₃×C₄⋊C₄	—	2	1	no	—
292	C₁₃×C₄⋊C₄	—	2	2	no	—
293	C₁₃×C₄⋊C₄	—	2	4	no	—
294	C₁₃×C₄⋊C₄	—	2	2	no	—
295	C₁₃×C₄⋊C₄	—	2	1	no	—
296	C₁₃×C₄⋊C₄	—	2	4	no	—
297	C₁₃×C₄⋊C₄	—	2	2	no	—
298	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
299	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
300	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
301	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
302	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
303	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
304	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
305	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
306	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
307	C₁₃×C₂²⋊C₄	—	2	2	no	—
308	C₁₃×C₂²⋊C₄	—	2	4	no	—
309	C₁₃×C₂²⋊C₄	—	2	2	no	—
310	C₁₃×C₂²⋊C₄	—	2	2	no	—
311	C₁₃×C₂²⋊C₄	—	2	2	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	1	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	C₂×D₄	1	2	yes	—
321	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
322	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
323	C₄²×C₁₃	—	2	2	no	—
324	C₄²×C₁₃	—	2	2	no	—
325	C₄²×C₁₃	—	2	2	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	2	yes	—
330	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
331	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
332	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
333	C₄²×C₁₃	C₂⁴	1	2	yes	—
334	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
335	#3503	C₂×C₁₃	1	1	yes	characteristic, complemented
336	#3475	C₂×C₁₃	1	1	yes	characteristic
337	#3385	C₂×C₁₃	1	2	yes	complemented
338	#3369	C₂×C₁₃	1	2	yes	complemented
339	#3357	C₂×C₁₃	1	2	yes	complemented
340	#3344	C₂×C₁₃	1	4	yes	complemented
341	#3331	C₂×C₁₃	1	2	yes	complemented
342	#3314	C₂×C₁₃	1	4	yes	complemented
343	#3252	C₂×C₁₃	1	2	yes	complemented
344	#3249	C₂×C₁₃	1	1	yes	characteristic, complemented
345	#3238	C₂×C₁₃	1	2	yes	complemented
346	#3230	C₂×C₁₃	1	1	yes	characteristic, complemented
347	#3116	C₂×C₁₃	1	2	yes	complemented
348	#3101	C₂×C₁₃	1	1	yes	characteristic, complemented
349	#3079	C₂×C₁₃	1	2	yes	complemented
350	C₂×#476	C₂×C₁₃	1	1	yes	characteristic, complemented
351	#2989	C₂×C₁₃	1	1	yes	characteristic, complemented
352	C₂³×C₁₃	—	2	1	no	—
353	C₂³×C₁₃	—	2	1	no	—
354	C₂³×C₁₃	—	4	2	no	—
355	C₂³×C₁₃	—	4	2	no	—
356	C₂³×C₁₃	—	8	1	no	—
357	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
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	2	no	—
363	Q₈×C₁₃	—	2	2	no	—
364	Q₈×C₁₃	—	4	2	no	—
365	Q₈×C₁₃	—	4	4	no	—
366	Q₈×C₁₃	—	8	1	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	1	no	—
372	D₄×C₁₃	—	2	1	no	—
373	D₄×C₁₃	—	2	1	no	—
374	D₄×C₁₃	—	4	2	no	—
375	D₄×C₁₃	—	4	4	no	—
376	D₄×C₁₃	—	8	2	no	—
377	D₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
378	C₂×C₄×C₁₃	—	2	4	no	—
379	C₂×C₄×C₁₃	—	2	1	no	—
380	C₂×C₄×C₁₃	—	2	2	no	—
381	C₂×C₄×C₁₃	—	2	1	no	—
382	C₂×C₄×C₁₃	—	2	2	no	—
383	C₂×C₄×C₁₃	—	2	1	no	—
384	C₂×C₄×C₁₃	—	2	2	no	—
385	C₂×C₄×C₁₃	—	2	2	no	—
386	C₂×C₄×C₁₃	—	2	2	no	—
387	C₂×C₄×C₁₃	—	2	4	no	—
388	C₂×C₄×C₁₃	—	2	2	no	—
389	C₂×C₄×C₁₃	—	2	1	no	—
390	C₂×C₄×C₁₃	—	4	2	no	—
391	C₂×C₄×C₁₃	—	4	1	no	—
392	C₂×C₄×C₁₃	—	4	4	no	—
393	C₂×C₄×C₁₃	—	4	2	no	—
394	C₂×C₄×C₁₃	—	4	2	no	—
395	C₂×C₄×C₁₃	—	4	2	no	—
396	C₂×C₄×C₁₃	—	4	2	no	—
397	C₂×C₄×C₁₃	—	4	2	no	—
398	C₂×C₄×C₁₃	—	8	2	no	—
399	C₂×C₄×C₁₃	—	8	2	no	—
400	C₂×C₄×C₁₃	—	8	4	no	—
401	C₂×C₄×C₁₃	#137	1	4	yes	—
402	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
403	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
404	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
405	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
406	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
407	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
408	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
409	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
410	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
411	C₈×C₁₃	—	2	2	no	—
412	C₈×C₁₃	—	2	4	no	—
413	C₈×C₁₃	—	2	2	no	—
414	Q₈²	C₂²×C₁₃	1	2	yes	complemented
415	#557	—	2	1	no	—
416	#556	C₂²×C₁₃	1	1	yes	characteristic
417	#555	C₂²×C₁₃	1	1	yes	characteristic
418	#554	C₂²×C₁₃	1	1	yes	characteristic
419	#554	C₂²×C₁₃	1	4	yes	—
420	#554	C₂²×C₁₃	1	2	yes	complemented
421	#553	—	2	1	no	—
422	#552	—	2	1	no	—
423	#552	C₂²×C₁₃	1	2	yes	—
424	#551	—	2	2	no	—
425	D₄×Q₈	—	2	2	no	—
426	D₄×Q₈	—	2	1	no	—
427	#547	C₂²×C₁₃	1	1	yes	characteristic
428	#546	C₂²×C₁₃	1	2	yes	—
429	#544	—	2	1	no	—
430	#544	—	2	2	no	—
431	#533	C₂²×C₁₃	1	1	yes	characteristic
432	#533	C₂²×C₁₃	1	1	yes	characteristic
433	#533	C₂²×C₁₃	1	2	yes	complemented
434	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
435	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
436	#529	—	2	2	no	—
437	#529	C₂²×C₁₃	1	2	yes	—
438	#525	—	2	1	no	—
439	#520	—	2	1	no	—
440	C₄×#41	C₂²×C₁₃	1	2	yes	—
441	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
442	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
443	C₂×#117	—	2	1	no	—
444	#501	C₂²×C₁₃	1	4	yes	complemented
445	#500	C₂²×C₁₃	1	2	yes	complemented
446	#489	C₂²×C₁₃	1	4	yes	—
447	#487	C₂²×C₁₃	1	2	yes	complemented
448	#485	C₂²×C₁₃	1	4	yes	complemented
449	#484	C₂²×C₁₃	1	4	yes	—
450	#483	C₂²×C₁₃	1	2	yes	—
451	#483	C₂²×C₁₃	1	4	yes	complemented
452	#480	C₂²×C₁₃	1	4	yes	—
453	#479	C₂²×C₁₃	1	4	yes	complemented
454	#477	C₂²×C₁₃	1	2	yes	complemented
455	#477	C₂²×C₁₃	1	2	yes	complemented
456	#477	C₂²×C₁₃	1	2	yes	complemented
457	#477	C₂²×C₁₃	1	2	yes	complemented
458	#476	C₂²×C₁₃	1	2	yes	—
459	#476	C₂²×C₁₃	1	1	yes	characteristic
460	#476	C₂²×C₁₃	1	2	yes	—
461	#476	C₂²×C₁₃	1	1	yes	characteristic
462	#476	C₂²×C₁₃	1	2	yes	—
463	#476	C₂²×C₁₃	1	2	yes	—
464	#475	C₂²×C₁₃	1	4	yes	complemented
465	#474	C₂²×C₁₃	1	4	yes	—
466	#470	C₂²×C₁₃	1	4	yes	complemented
467	#468	C₂²×C₁₃	1	4	yes	—
468	#467	C₂²×C₁₃	1	4	yes	—
469	#464	C₂²×C₁₃	1	4	yes	—
470	#462	C₂²×C₁₃	1	2	yes	complemented
471	#462	C₂²×C₁₃	1	2	yes	complemented
472	#461	C₂²×C₁₃	1	1	yes	characteristic
473	#461	C₂²×C₁₃	1	1	yes	characteristic
474	#452	C₂²×C₁₃	1	4	yes	—
475	#450	C₂²×C₁₃	1	2	yes	—
476	#446	C₂²×C₁₃	1	2	yes	complemented
477	#441	C₂²×C₁₃	1	4	yes	complemented
478	#440	C₂²×C₁₃	1	4	yes	—
479	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
480	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
481	#436	C₂²×C₁₃	1	2	yes	complemented
482	#435	C₂²×C₁₃	1	4	yes	—
483	#432	C₂²×C₁₃	1	2	yes	complemented
484	#431	C₂²×C₁₃	1	1	yes	characteristic
485	#428	C₂²×C₁₃	1	4	yes	complemented
486	C₂×#106	C₂²×C₁₃	1	2	yes	—
487	#423	C₂²×C₁₃	1	2	yes	complemented
488	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
489	#417	C₂²×C₁₃	1	4	yes	—
490	C₂×#102	C₂²×C₁₃	1	2	yes	—
491	C₂²×C₁₃	—	2	1	no	—
492	C₂²×C₁₃	—	2	1	no	—
493	C₂²×C₁₃	—	2	2	no	—
494	C₂²×C₁₃	—	2	2	no	—
495	C₂²×C₁₃	—	2	2	no	—
496	C₂²×C₁₃	—	2	2	no	—
497	C₂²×C₁₃	—	4	1	no	—
498	C₂²×C₁₃	—	4	1	no	—
499	C₂²×C₁₃	—	4	1	no	—
500	C₂²×C₁₃	—	4	1	no	—
501	C₂²×C₁₃	—	4	1	no	—
502	C₂²×C₁₃	—	8	4	no	—
503	C₂²×C₁₃	C₂×#137	1	2	yes	—
504	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
505	C₄×C₁₃	—	2	1	no	—
506	C₄×C₁₃	—	2	2	no	—
507	C₄×C₁₃	—	2	1	no	—
508	C₄×C₁₃	—	2	2	no	—
509	C₄×C₁₃	—	2	1	no	—
510	C₄×C₁₃	—	2	2	no	—
511	C₄×C₁₃	—	4	4	no	—
512	C₄×C₁₃	—	4	2	no	—
513	C₄×C₁₃	—	4	2	no	—
514	C₄×C₁₃	—	4	2	no	—
515	C₄×C₁₃	—	4	2	no	—
516	C₄×C₁₃	—	4	1	no	—
517	C₄×C₁₃	—	4	1	no	—
518	C₄×C₁₃	C₂×#137	1	2	yes	—
519	C₄×C₁₃	C₂×#137	1	2	yes	—
520	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
521	C₄×C₁₃	#585	1	1	yes	characteristic
522	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
523	C₂×#41	C₂³×C₁₃	1	2	yes	—
524	C₂²×Q₈	—	2	1	no	—
525	C₂²×Q₈	—	2	2	no	—
526	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
527	C₂³×C₄	—	2	1	no	—
528	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
529	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
530	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
531	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
532	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
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	2	no	—
538	C₄⋊Q₈	—	2	2	no	—
539	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
540	C₄⋊Q₈	C₂³×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	1	yes	characteristic
544	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
545	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
546	#126	—	2	2	no	—
547	#126	—	2	2	no	—
548	#126	—	2	2	no	—
549	#125	—	2	2	no	—
550	#125	—	2	4	no	—
551	#125	—	2	2	no	—
552	#125	—	2	1	no	—
553	#125	—	2	1	no	—
554	#125	—	2	2	no	—
555	#125	C₂³×C₁₃	1	2	yes	—
556	#124	—	2	2	no	—
557	#124	C₂³×C₁₃	1	2	yes	—
558	#123	—	2	2	no	—
559	#123	—	2	2	no	—
560	#123	—	2	2	no	—
561	#123	—	2	2	no	—
562	C₂²⋊Q₈	—	2	1	no	—
563	C₂²⋊Q₈	—	2	1	no	—
564	C₂²⋊Q₈	—	2	1	no	—
565	C₂²⋊Q₈	—	2	1	no	—
566	C₂²⋊Q₈	—	2	2	no	—
567	C₂²⋊Q₈	—	2	2	no	—
568	C₂²⋊Q₈	—	2	4	no	—
569	C₂²⋊Q₈	—	2	4	no	—
570	C₂²⋊Q₈	—	2	4	no	—
571	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
572	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
573	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
574	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
575	#121	—	2	1	no	—
576	#121	—	2	1	no	—
577	#121	—	2	2	no	—
578	#121	C₂³×C₁₃	1	2	yes	—
579	#120	—	2	2	no	—
580	C₄×Q₈	—	2	2	no	—
581	C₄×Q₈	—	2	1	no	—
582	C₄×Q₈	—	2	1	no	—
583	C₄×Q₈	—	2	2	no	—
584	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
585	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
586	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
587	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
588	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
589	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
590	C₄×D₄	—	2	4	no	—
591	C₄×D₄	—	2	2	no	—
592	C₄×D₄	—	2	2	no	—
593	C₄×D₄	—	2	2	no	—
594	C₄×D₄	—	2	2	no	—
595	C₄×D₄	—	2	1	no	—
596	C₄×D₄	—	2	1	no	—
597	C₄×D₄	D₄×C₁₃	1	2	yes	—
598	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
599	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
600	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
601	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
602	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
603	C₄×D₄	C₂³×C₁₃	1	2	yes	—
604	C₄×D₄	C₂³×C₁₃	1	2	yes	—
605	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
606	#117	—	2	1	no	—
607	#117	—	2	1	no	—
608	#117	—	2	2	no	—
609	#117	—	2	1	no	—
610	#117	—	2	1	no	—
611	#117	—	2	2	no	—
612	#117	—	2	2	no	—
613	#117	—	2	2	no	—
614	#117	D₄×C₁₃	1	1	yes	characteristic
615	#117	D₄×C₁₃	1	2	yes	—
616	#117	C₂³×C₁₃	1	2	yes	—
617	C₂×C₄⋊C₄	—	2	1	no	—
618	C₂×C₄⋊C₄	—	2	2	no	—
619	C₂×C₄⋊C₄	—	2	1	no	—
620	C₂×C₄⋊C₄	—	2	1	no	—
621	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
622	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
623	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
624	C₂×C₂²⋊C₄	—	2	1	no	—
625	C₂×C₂²⋊C₄	—	2	2	no	—
626	C₂×C₄²	—	2	2	no	—
627	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
628	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
629	#107	C₂³×C₁₃	1	4	yes	—
630	#107	C₂³×C₁₃	1	4	yes	—
631	#107	C₂³×C₁₃	1	4	yes	—
632	#106	C₂³×C₁₃	1	4	yes	—
633	#106	C₂³×C₁₃	1	4	yes	—
634	#106	C₂³×C₁₃	1	2	yes	—
635	#106	C₂³×C₁₃	1	2	yes	—
636	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
637	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
638	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
639	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
640	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
641	#103	C₂³×C₁₃	1	4	yes	—
642	#103	C₂³×C₁₃	1	4	yes	—
643	#103	C₂³×C₁₃	1	2	yes	—
644	#103	C₂³×C₁₃	1	2	yes	—
645	#103	C₂³×C₁₃	1	4	yes	—
646	#103	C₂³×C₁₃	1	4	yes	—
647	#102	C₂³×C₁₃	1	4	yes	—
648	#102	C₂³×C₁₃	1	4	yes	—
649	#102	C₂³×C₁₃	1	2	yes	—
650	#102	C₂³×C₁₃	1	2	yes	—
651	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
652	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
653	#97	C₂³×C₁₃	1	4	yes	—
654	C₄×C₈	C₂³×C₁₃	1	2	yes	—
655	C₂×C₁₃	—	2	2	no	—
656	C₂×C₁₃	—	4	2	no	—
657	C₂×C₁₃	—	4	2	no	—
658	C₂×C₁₃	—	8	1	no	—
659	C₂×C₁₃	#3489	1	1	yes	characteristic
660	C₂×C₁₃	C₂²×#137	1	1	yes	characteristic
661	C₂×C₁₃	#3585	1	1	yes	characteristic
662	C₂⁴	—	2	1	no	—
663	#41	—	2	4	no	—
664	#41	—	2	4	no	—
665	#41	—	4	2	no	—
666	C₂×Q₈	—	2	1	no	—
667	C₂×Q₈	—	2	2	no	—
668	C₂×Q₈	—	2	1	no	—
669	C₂×Q₈	—	2	4	no	—
670	C₂×Q₈	—	2	2	no	—
671	C₂×Q₈	—	8	2	no	—
672	C₂×Q₈	—	8	4	no	—
673	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
674	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
675	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
676	C₂×D₄	—	2	2	no	—
677	C₂×D₄	—	2	2	no	—
678	C₂×D₄	—	2	2	no	—
679	C₂×D₄	—	2	1	no	—
680	C₂×D₄	—	4	1	no	—
681	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
682	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
683	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
684	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
685	C₂²×C₄	—	2	1	no	—
686	C₂²×C₄	—	2	4	no	—
687	C₂²×C₄	—	2	2	no	—
688	C₂²×C₄	—	2	1	no	—
689	C₂²×C₄	—	2	2	no	—
690	C₂²×C₄	—	2	1	no	—
691	C₂²×C₄	—	2	1	no	—
692	C₂²×C₄	—	2	1	no	—
693	C₂²×C₄	—	2	2	no	—
694	C₂²×C₄	—	4	4	no	—
695	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
696	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
697	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
698	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
699	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
700	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
701	Q₁₆	—	4	4	no	—
702	SD₁₆	—	2	4	no	—
703	SD₁₆	—	4	2	no	—
704	M₁₆	—	4	4	no	—
705	C₂×C₈	—	4	2	no	—
706	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
707	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
708	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
709	C₄⋊C₄	—	2	2	no	—
710	C₄⋊C₄	—	2	1	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	4	no	—
716	C₄⋊C₄	—	2	2	no	—
717	C₄⋊C₄	—	2	1	no	—
718	C₄⋊C₄	—	2	4	no	—
719	C₄⋊C₄	—	2	2	no	—
720	C₄⋊C₄	—	2	1	no	—
721	C₄⋊C₄	—	2	2	no	—
722	C₄⋊C₄	—	2	2	no	—
723	C₄⋊C₄	—	2	2	no	—
724	C₄⋊C₄	—	2	1	no	—
725	C₄⋊C₄	—	2	2	no	—
726	C₄⋊C₄	—	2	4	no	—
727	C₄⋊C₄	—	2	2	no	—
728	C₄⋊C₄	—	2	1	no	—
729	C₄⋊C₄	—	2	4	no	—
730	C₄⋊C₄	—	2	2	no	—
731	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
732	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
733	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
734	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
735	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
736	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
737	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
738	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
739	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
740	C₂²⋊C₄	—	2	2	no	—
741	C₂²⋊C₄	—	2	4	no	—
742	C₂²⋊C₄	—	2	2	no	—
743	C₂²⋊C₄	—	2	2	no	—
744	C₂²⋊C₄	—	2	2	no	—
745	C₂²⋊C₄	—	2	1	no	—
746	C₂²⋊C₄	—	2	2	no	—
747	C₂²⋊C₄	—	2	2	no	—
748	C₂²⋊C₄	—	2	1	no	—
749	C₂²⋊C₄	—	2	1	no	—
750	C₂²⋊C₄	—	2	1	no	—
751	C₂²⋊C₄	—	2	2	no	—
752	C₂²⋊C₄	—	2	2	no	—
753	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
754	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
755	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
756	C₄²	—	2	2	no	—
757	C₄²	—	2	2	no	—
758	C₄²	—	2	2	no	—
759	C₄²	—	2	4	no	—
760	C₄²	—	2	2	no	—
761	C₄²	C₂×D₄×C₁₃	1	2	yes	—
762	C₄²	C₂×D₄×C₁₃	1	2	yes	—
763	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
764	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
765	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
766	C₄²	C₂⁴×C₁₃	1	2	yes	—
767	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
768	C₁₃	#62108	1	1	yes	characteristic, direct product factor, Sylow
769	C₂³	—	2	1	no	—
770	C₂³	—	2	1	no	—
771	C₂³	—	4	2	no	—
772	C₂³	—	4	2	no	—
773	C₂³	—	8	1	no	—
774	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
775	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
776	Q₈	—	2	2	no	—
777	Q₈	—	2	2	no	—
778	Q₈	—	2	2	no	—
779	Q₈	—	2	2	no	—
780	Q₈	—	2	2	no	—
781	Q₈	—	4	2	no	—
782	Q₈	—	4	4	no	—
783	Q₈	—	8	4	no	—
784	Q₈	—	8	2	no	—
785	Q₈	—	8	1	no	—
786	D₄	—	2	4	no	—
787	D₄	—	2	2	no	—
788	D₄	—	2	1	no	—
789	D₄	—	2	1	no	—
790	D₄	—	2	1	no	—
791	D₄	—	4	2	no	—
792	D₄	—	4	4	no	—
793	D₄	—	8	2	no	—
794	D₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
795	C₂×C₄	—	2	4	no	—
796	C₂×C₄	—	2	1	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	1	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	1	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	2	4	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	1	no	—
807	C₂×C₄	—	4	2	no	—
808	C₂×C₄	—	4	1	no	—
809	C₂×C₄	—	4	4	no	—
810	C₂×C₄	—	4	2	no	—
811	C₂×C₄	—	4	2	no	—
812	C₂×C₄	—	4	2	no	—
813	C₂×C₄	—	4	2	no	—
814	C₂×C₄	—	4	2	no	—
815	C₂×C₄	—	8	2	no	—
816	C₂×C₄	—	8	2	no	—
817	C₂×C₄	—	8	4	no	—
818	C₂×C₄	C₁₃×#137	1	4	yes	—
819	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
820	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
821	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
822	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
823	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
824	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
825	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
826	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
827	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
828	C₈	—	2	2	no	—
829	C₈	—	2	4	no	—
830	C₈	—	2	2	no	—
831	C₂²	—	2	1	no	—
832	C₂²	—	2	1	no	—
833	C₂²	—	2	2	no	—
834	C₂²	—	2	2	no	—
835	C₂²	—	2	2	no	—
836	C₂²	—	2	2	no	—
837	C₂²	—	4	1	no	—
838	C₂²	—	4	1	no	—
839	C₂²	—	4	1	no	—
840	C₂²	—	4	1	no	—
841	C₂²	—	4	1	no	—
842	C₂²	—	8	4	no	—
843	C₂²	C₂×C₁₃×#137	1	2	yes	—
844	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
845	C₄	—	2	2	no	—
846	C₄	—	2	1	no	—
847	C₄	—	2	2	no	—
848	C₄	—	2	1	no	—
849	C₄	—	2	2	no	—
850	C₄	—	2	1	no	—
851	C₄	—	4	1	no	—
852	C₄	—	4	1	no	—
853	C₄	—	4	4	no	—
854	C₄	—	4	2	no	—
855	C₄	—	4	2	no	—
856	C₄	—	4	2	no	—
857	C₄	—	4	2	no	—
858	C₄	C₂×C₁₃×#137	1	2	yes	—
859	C₄	C₂×C₁₃×#137	1	2	yes	—
860	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
861	C₄	C₁₃×#585	1	1	yes	characteristic
862	C₂	—	2	2	no	—
863	C₂	—	4	2	no	—
864	C₂	—	4	2	no	—
865	C₂	—	8	1	no	—
866	C₂	C₁₃×#3489	1	1	yes	characteristic
867	C₂	C₂²×C₁₃×#137	1	1	yes	characteristic
868	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×#3475	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
1. C₁₃×#3503	C₂	semidirect
3. C₁₃×#3385	C₂	semidirect
4. C₁₃×#3369	C₂	semidirect
5. C₁₃×#3357	C₂	semidirect
6. C₁₃×#3344	C₂	semidirect
7. C₁₃×#3331	C₂	semidirect
8. C₁₃×#3314	C₂	semidirect
9. C₁₃×#3252	C₂	semidirect
10. C₁₃×#3249	C₂	semidirect
11. C₁₃×#3238	C₂	semidirect
12. C₁₃×#3230	C₂	semidirect
13. C₁₃×#3116	C₂	semidirect
14. C₁₃×#3101	C₂	semidirect
15. C₁₃×#3079	C₂	semidirect
16. C₂×C₁₃×#476	C₂	semidirect
17. C₁₃×#2989	C₂	semidirect
18. Q₈²×C₁₃	C₂²	semidirect
24. C₁₃×#554	C₂²	semidirect
37. C₁₃×#533	C₂²	semidirect
39. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
48. C₁₃×#501	C₂²	semidirect
49. C₁₃×#500	C₂²	semidirect
51. C₁₃×#487	C₂²	semidirect
52. C₁₃×#485	C₂²	semidirect
55. C₁₃×#483	C₂²	semidirect
57. C₁₃×#479	C₂²	semidirect
58. C₁₃×#477	C₂²	semidirect
59. C₁₃×#477	C₂²	semidirect
60. C₁₃×#477	C₂²	semidirect
61. C₁₃×#477	C₂²	semidirect
68. C₁₃×#475	C₂²	semidirect
70. C₁₃×#470	C₂²	semidirect
74. C₁₃×#462	C₂²	semidirect
75. C₁₃×#462	C₂²	semidirect
80. C₁₃×#446	C₂²	semidirect
81. C₁₃×#441	C₂²	semidirect
85. C₁₃×#436	C₂²	semidirect
87. C₁₃×#432	C₂²	semidirect
89. C₁₃×#428	C₂²	semidirect
91. C₁₃×#423	C₂²	semidirect
228. #62108	C₁₃	direct (N × H)
335. #3503	C₂×C₁₃	semidirect
337. #3385	C₂×C₁₃	semidirect
338. #3369	C₂×C₁₃	semidirect
339. #3357	C₂×C₁₃	semidirect
340. #3344	C₂×C₁₃	semidirect
341. #3331	C₂×C₁₃	semidirect
342. #3314	C₂×C₁₃	semidirect
343. #3252	C₂×C₁₃	semidirect
344. #3249	C₂×C₁₃	semidirect
345. #3238	C₂×C₁₃	semidirect
346. #3230	C₂×C₁₃	semidirect
347. #3116	C₂×C₁₃	semidirect
348. #3101	C₂×C₁₃	semidirect
349. #3079	C₂×C₁₃	semidirect
350. C₂×#476	C₂×C₁₃	semidirect
351. #2989	C₂×C₁₃	semidirect
414. Q₈²	C₂²×C₁₃	semidirect
420. #554	C₂²×C₁₃	semidirect
433. #533	C₂²×C₁₃	semidirect
435. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
444. #501	C₂²×C₁₃	semidirect
445. #500	C₂²×C₁₃	semidirect
447. #487	C₂²×C₁₃	semidirect
448. #485	C₂²×C₁₃	semidirect
451. #483	C₂²×C₁₃	semidirect
453. #479	C₂²×C₁₃	semidirect
454. #477	C₂²×C₁₃	semidirect
455. #477	C₂²×C₁₃	semidirect
456. #477	C₂²×C₁₃	semidirect
457. #477	C₂²×C₁₃	semidirect
464. #475	C₂²×C₁₃	semidirect
466. #470	C₂²×C₁₃	semidirect
470. #462	C₂²×C₁₃	semidirect
471. #462	C₂²×C₁₃	semidirect
476. #446	C₂²×C₁₃	semidirect
477. #441	C₂²×C₁₃	semidirect
481. #436	C₂²×C₁₃	semidirect
483. #432	C₂²×C₁₃	semidirect
485. #428	C₂²×C₁₃	semidirect
487. #423	C₂²×C₁₃	semidirect
768. C₁₃	#62108	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×#3503	2
C₁₃×#3475	2
C₁₃×#3385	2
C₁₃×#3369	2
C₁₃×#3357	2
C₁₃×#3344	2
C₁₃×#3331	2
C₁₃×#3314	2
C₁₃×#3252	2
C₁₃×#3249	2
C₁₃×#3238	2
C₁₃×#3230	2
C₁₃×#3116	2
C₁₃×#3101	2
C₁₃×#3079	2
C₂×C₁₃×#476	2
C₁₃×#2989	2
#62108	13

Subgroups — C13×#62108 #15748447

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62108 #15748447