Subgroups — C₁₃×#62127 #15748466

Order 3328.

1810 conjugacy classes of subgroups.

The subgroup lattice has 880 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×#3481	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3385	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3375	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3346	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3338	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3314	C₂	1	4	yes	maximal, complemented
8	C₁₃×#3295	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3254	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3248	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3239	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3226	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3110	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3107	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3079	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#474	C₂	1	2	yes	maximal, complemented
17	C₁₃×#2990	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×#554	C₂²	1	1	yes	characteristic
22	C₁₃×#554	C₂²	1	2	yes	—
23	C₁₃×#554	C₂²	1	1	yes	characteristic
24	C₁₃×#554	C₂²	1	4	yes	complemented
25	C₁₃×#553	—	2	1	no	—
26	C₁₃×#553	C₂²	1	2	yes	—
27	C₁₃×#551	—	2	2	no	—
28	D₄×Q₈×C₁₃	—	2	1	no	—
29	D₄×Q₈×C₁₃	—	2	2	no	—
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×#533	C₂²	1	1	yes	characteristic, complemented
36	C₁₃×#533	C₂²	1	2	yes	complemented
37	C₁₃×#532	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
39	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
40	C₁₃×#529	—	2	1	no	—
41	C₁₃×#529	C₂²	1	2	yes	—
42	C₁₃×#525	—	2	2	no	—
43	C₁₃×#520	—	2	1	no	—
44	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
45	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₁₃	—	2	1	no	—
47	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
48	C₁₃×#501	C₂²	1	4	yes	complemented
49	C₁₃×#500	C₂²	1	2	yes	complemented
50	C₁₃×#489	C₂²	1	4	yes	complemented
51	C₁₃×#486	C₂²	1	2	yes	—
52	C₁₃×#485	C₂²	1	2	yes	complemented
53	C₁₃×#484	C₂²	1	4	yes	complemented
54	C₁₃×#484	C₂²	1	4	yes	complemented
55	C₁₃×#481	C₂²	1	4	yes	—
56	C₁₃×#480	C₂²	1	4	yes	complemented
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×#476	C₂²	1	2	yes	—
61	C₁₃×#475	C₂²	1	2	yes	complemented
62	C₁₃×#475	C₂²	1	1	yes	characteristic, complemented
63	C₁₃×#474	C₂²	1	4	yes	—
64	C₁₃×#474	C₂²	1	1	yes	characteristic
65	C₁₃×#474	C₂²	1	2	yes	—
66	C₁₃×#474	C₂²	1	4	yes	complemented
67	C₁₃×#474	C₂²	1	2	yes	complemented
68	C₁₃×#474	C₂²	1	2	yes	complemented
69	C₁₃×#474	C₂²	1	2	yes	complemented
70	C₁₃×#468	C₂²	1	4	yes	complemented
71	C₁₃×#467	C₂²	1	4	yes	complemented
72	C₁₃×#465	C₂²	1	4	yes	—
73	C₁₃×#464	C₂²	1	4	yes	complemented
74	C₁₃×#462	C₂²	1	1	yes	characteristic, complemented
75	C₁₃×#461	C₂²	1	1	yes	characteristic
76	C₁₃×#461	C₂²	1	2	yes	complemented
77	C₁₃×#460	C₂²	1	2	yes	—
78	C₁₃×#452	C₂²	1	2	yes	—
79	C₁₃×#450	C₂²	1	4	yes	—
80	C₁₃×#446	C₂²	1	2	yes	complemented
81	C₁₃×#440	C₂²	1	4	yes	—
82	C₁₃×#440	C₂²	1	4	yes	complemented
83	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
84	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
85	C₁₃×#435	C₂²	1	4	yes	complemented
86	C₈×D₄×C₁₃	C₂²	1	2	yes	—
87	C₁₃×#432	C₂²	1	2	yes	complemented
88	C₁₃×#431	C₂²	1	1	yes	characteristic, complemented
89	C₁₃×#428	C₂²	1	2	yes	complemented
90	C₂×C₁₃×#107	C₂²	1	4	yes	complemented
91	C₁₃×#423	C₂²	1	1	yes	characteristic, complemented
92	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	complemented
93	C₁₃×#417	C₂²	1	2	yes	—
94	C₂×C₁₃×#102	C₂²	1	4	yes	—
95	C₂×C₁₃×#41	—	2	1	no	—
96	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
97	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
98	C₂²×Q₈×C₁₃	—	2	2	no	—
99	C₂²×Q₈×C₁₃	—	2	1	no	—
100	C₂²×D₄×C₁₃	—	2	1	no	—
101	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
102	C₂³×C₄×C₁₃	—	2	2	no	—
103	C₂×C₁₃×Q₁₆	C₂³	1	2	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	2	no	—
109	C₁₃×C₄⋊Q₈	—	2	4	no	—
110	C₁₃×C₄⋊Q₈	—	2	1	no	—
111	C₁₃×C₄⋊Q₈	—	2	2	no	—
112	C₁₃×C₄⋊Q₈	—	2	1	no	—
113	C₁₃×C₄⋊Q₈	—	2	2	no	—
114	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
115	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
116	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
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×#127	C₂³	1	1	yes	characteristic
121	C₁₃×#126	—	2	2	no	—
122	C₁₃×#126	—	2	2	no	—
123	C₁₃×#125	—	2	1	no	—
124	C₁₃×#125	—	2	2	no	—
125	C₁₃×#125	—	2	4	no	—
126	C₁₃×#125	—	2	1	no	—
127	C₁₃×#125	—	2	2	no	—
128	C₁₃×#125	C₂³	1	2	yes	—
129	C₁₃×#124	—	2	1	no	—
130	C₁₃×#124	—	2	1	no	—
131	C₁₃×#124	C₂³	1	2	yes	—
132	C₁₃×#123	—	2	2	no	—
133	C₁₃×#123	—	2	2	no	—
134	C₁₃×#123	—	2	2	no	—
135	C₁₃×#123	—	2	2	no	—
136	C₁₃×C₂²⋊Q₈	—	2	1	no	—
137	C₁₃×C₂²⋊Q₈	—	2	2	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	4	yes	—
145	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
146	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
147	C₁₃×#121	—	2	2	no	—
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×#121	C₂³	1	2	yes	—
153	C₁₃×#120	—	2	2	no	—
154	C₁₃×#120	—	2	2	no	—
155	C₄×Q₈×C₁₃	—	2	2	no	—
156	C₄×Q₈×C₁₃	—	2	1	no	—
157	C₄×Q₈×C₁₃	—	2	2	no	—
158	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
159	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
160	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
161	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
162	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
163	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
164	C₄×D₄×C₁₃	—	2	1	no	—
165	C₄×D₄×C₁₃	—	2	2	no	—
166	C₄×D₄×C₁₃	—	2	4	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	—	2	1	no	—
171	C₄×D₄×C₁₃	—	2	2	no	—
172	C₄×D₄×C₁₃	—	2	1	no	—
173	C₄×D₄×C₁₃	—	2	2	no	—
174	C₄×D₄×C₁₃	—	2	2	no	—
175	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
176	C₄×D₄×C₁₃	D₄	1	2	yes	—
177	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
178	C₄×D₄×C₁₃	C₂³	1	2	yes	—
179	C₄×D₄×C₁₃	C₂³	1	2	yes	—
180	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
181	C₄×D₄×C₁₃	C₂³	1	2	yes	—
182	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
183	C₄×D₄×C₁₃	C₂³	1	2	yes	—
184	C₁₃×#117	—	2	2	no	—
185	C₁₃×#117	—	2	1	no	—
186	C₁₃×#117	—	2	1	no	—
187	C₁₃×#117	—	2	2	no	—
188	C₁₃×#117	D₄	1	2	yes	—
189	C₁₃×#117	D₄	1	1	yes	characteristic
190	C₁₃×#117	C₂³	1	1	yes	characteristic
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	4	yes	—
195	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
196	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
197	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
198	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
199	C₂×C₄²×C₁₃	—	2	1	no	—
200	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
201	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
202	C₁₃×#107	C₂³	1	2	yes	—
203	C₁₃×#107	C₂³	1	4	yes	—
204	C₁₃×#107	C₂³	1	4	yes	—
205	C₁₃×#107	C₂³	1	4	yes	—
206	C₁₃×#107	C₂³	1	4	yes	—
207	C₁₃×#106	C₂³	1	4	yes	—
208	C₁₃×#106	C₂³	1	2	yes	—
209	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
210	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
211	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
212	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
213	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
214	C₁₃×#103	C₂³	1	4	yes	—
215	C₁₃×#103	C₂³	1	2	yes	—
216	C₁₃×#103	C₂³	1	2	yes	—
217	C₁₃×#103	C₂³	1	2	yes	—
218	C₁₃×#103	C₂³	1	4	yes	—
219	C₁₃×#102	C₂³	1	2	yes	—
220	C₁₃×#102	C₂³	1	4	yes	—
221	C₁₃×#102	C₂³	1	4	yes	—
222	C₁₃×#102	C₂³	1	4	yes	—
223	C₁₃×#102	C₂³	1	4	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	#62127	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	—	2	2	no	—
232	C₁₃×#41	—	4	1	no	—
233	C₁₃×#41	—	8	2	no	—
234	C₂×Q₈×C₁₃	—	2	1	no	—
235	C₂×Q₈×C₁₃	—	2	2	no	—
236	C₂×Q₈×C₁₃	—	2	1	no	—
237	C₂×Q₈×C₁₃	—	2	4	no	—
238	C₂×Q₈×C₁₃	—	2	2	no	—
239	C₂×Q₈×C₁₃	—	8	4	no	—
240	C₂×Q₈×C₁₃	—	8	2	no	—
241	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
242	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
243	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
244	C₂×D₄×C₁₃	—	2	4	no	—
245	C₂×D₄×C₁₃	—	2	1	no	—
246	C₂×D₄×C₁₃	—	2	2	no	—
247	C₂×D₄×C₁₃	—	2	2	no	—
248	C₂×D₄×C₁₃	—	2	2	no	—
249	C₂×D₄×C₁₃	—	2	1	no	—
250	C₂×D₄×C₁₃	—	2	1	no	—
251	C₂×D₄×C₁₃	—	4	2	no	—
252	C₂×D₄×C₁₃	—	4	4	no	—
253	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
254	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
255	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
256	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
257	C₂²×C₄×C₁₃	—	2	2	no	—
258	C₂²×C₄×C₁₃	—	2	2	no	—
259	C₂²×C₄×C₁₃	—	2	4	no	—
260	C₂²×C₄×C₁₃	—	2	1	no	—
261	C₂²×C₄×C₁₃	—	2	1	no	—
262	C₂²×C₄×C₁₃	—	2	1	no	—
263	C₂²×C₄×C₁₃	—	2	2	no	—
264	C₂²×C₄×C₁₃	—	2	2	no	—
265	C₂²×C₄×C₁₃	—	2	2	no	—
266	C₂²×C₄×C₁₃	—	8	4	no	—
267	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
268	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
269	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
270	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
271	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
272	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
273	C₁₃×Q₁₆	—	4	2	no	—
274	C₁₃×SD₁₆	—	2	4	no	—
275	C₁₃×SD₁₆	—	4	4	no	—
276	C₁₃×M₁₆	—	4	2	no	—
277	C₂×C₈×C₁₃	—	4	4	no	—
278	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
279	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
280	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
281	C₁₃×C₄⋊C₄	—	2	1	no	—
282	C₁₃×C₄⋊C₄	—	2	2	no	—
283	C₁₃×C₄⋊C₄	—	2	1	no	—
284	C₁₃×C₄⋊C₄	—	2	2	no	—
285	C₁₃×C₄⋊C₄	—	2	4	no	—
286	C₁₃×C₄⋊C₄	—	2	2	no	—
287	C₁₃×C₄⋊C₄	—	2	2	no	—
288	C₁₃×C₄⋊C₄	—	2	2	no	—
289	C₁₃×C₄⋊C₄	—	2	4	no	—
290	C₁₃×C₄⋊C₄	—	2	1	no	—
291	C₁₃×C₄⋊C₄	—	2	1	no	—
292	C₁₃×C₄⋊C₄	—	2	1	no	—
293	C₁₃×C₄⋊C₄	—	2	2	no	—
294	C₁₃×C₄⋊C₄	—	2	2	no	—
295	C₁₃×C₄⋊C₄	—	2	1	no	—
296	C₁₃×C₄⋊C₄	—	2	2	no	—
297	C₁₃×C₄⋊C₄	—	2	4	no	—
298	C₁₃×C₄⋊C₄	—	2	4	no	—
299	C₁₃×C₄⋊C₄	—	2	2	no	—
300	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
301	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
302	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
303	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
304	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
305	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
306	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
307	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
308	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
309	C₁₃×C₂²⋊C₄	—	2	2	no	—
310	C₁₃×C₂²⋊C₄	—	2	2	no	—
311	C₁₃×C₂²⋊C₄	—	2	4	no	—
312	C₁₃×C₂²⋊C₄	—	2	1	no	—
313	C₁₃×C₂²⋊C₄	—	2	1	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	—	2	2	no	—
322	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
323	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
324	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
325	C₄²×C₁₃	—	2	1	no	—
326	C₄²×C₁₃	—	2	1	no	—
327	C₄²×C₁₃	—	2	1	no	—
328	C₄²×C₁₃	—	2	4	no	—
329	C₄²×C₁₃	—	2	2	no	—
330	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
331	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
332	C₄²×C₁₃	C₂×D₄	1	2	yes	—
333	C₄²×C₁₃	C₂×D₄	1	2	yes	—
334	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
335	C₄²×C₁₃	C₂⁴	1	2	yes	—
336	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
337	#3503	C₂×C₁₃	1	1	yes	characteristic, complemented
338	#3481	C₂×C₁₃	1	1	yes	characteristic
339	#3385	C₂×C₁₃	1	2	yes	complemented
340	#3375	C₂×C₁₃	1	2	yes	complemented
341	#3346	C₂×C₁₃	1	4	yes	complemented
342	#3338	C₂×C₁₃	1	2	yes	complemented
343	#3314	C₂×C₁₃	1	4	yes	complemented
344	#3295	C₂×C₁₃	1	2	yes	complemented
345	#3254	C₂×C₁₃	1	1	yes	characteristic, complemented
346	#3248	C₂×C₁₃	1	2	yes	complemented
347	#3239	C₂×C₁₃	1	2	yes	complemented
348	#3226	C₂×C₁₃	1	1	yes	characteristic, complemented
349	#3110	C₂×C₁₃	1	2	yes	complemented
350	#3107	C₂×C₁₃	1	1	yes	characteristic, complemented
351	#3079	C₂×C₁₃	1	1	yes	characteristic, complemented
352	C₂×#474	C₂×C₁₃	1	2	yes	complemented
353	#2990	C₂×C₁₃	1	1	yes	characteristic, complemented
354	C₂³×C₁₃	—	2	1	no	—
355	C₂³×C₁₃	—	2	2	no	—
356	C₂³×C₁₃	—	4	4	no	—
357	C₂³×C₁₃	—	4	4	no	—
358	C₂³×C₁₃	—	8	2	no	—
359	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
360	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
361	Q₈×C₁₃	—	2	2	no	—
362	Q₈×C₁₃	—	2	2	no	—
363	Q₈×C₁₃	—	2	1	no	—
364	Q₈×C₁₃	—	2	2	no	—
365	Q₈×C₁₃	—	2	1	no	—
366	Q₈×C₁₃	—	4	2	no	—
367	Q₈×C₁₃	—	4	4	no	—
368	Q₈×C₁₃	—	8	4	no	—
369	Q₈×C₁₃	—	8	2	no	—
370	Q₈×C₁₃	—	8	1	no	—
371	D₄×C₁₃	—	2	4	no	—
372	D₄×C₁₃	—	2	2	no	—
373	D₄×C₁₃	—	2	1	no	—
374	D₄×C₁₃	—	2	2	no	—
375	D₄×C₁₃	—	4	4	no	—
376	D₄×C₁₃	—	4	2	no	—
377	D₄×C₁₃	—	4	4	no	—
378	D₄×C₁₃	—	4	2	no	—
379	D₄×C₁₃	—	8	1	no	—
380	D₄×C₁₃	—	8	2	no	—
381	D₄×C₁₃	#137	1	4	yes	—
382	D₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
383	C₂×C₄×C₁₃	—	2	4	no	—
384	C₂×C₄×C₁₃	—	2	2	no	—
385	C₂×C₄×C₁₃	—	2	4	no	—
386	C₂×C₄×C₁₃	—	2	2	no	—
387	C₂×C₄×C₁₃	—	2	2	no	—
388	C₂×C₄×C₁₃	—	2	1	no	—
389	C₂×C₄×C₁₃	—	2	2	no	—
390	C₂×C₄×C₁₃	—	2	1	no	—
391	C₂×C₄×C₁₃	—	2	2	no	—
392	C₂×C₄×C₁₃	—	2	1	no	—
393	C₂×C₄×C₁₃	—	2	1	no	—
394	C₂×C₄×C₁₃	—	2	1	no	—
395	C₂×C₄×C₁₃	—	2	4	no	—
396	C₂×C₄×C₁₃	—	2	2	no	—
397	C₂×C₄×C₁₃	—	2	2	no	—
398	C₂×C₄×C₁₃	—	4	2	no	—
399	C₂×C₄×C₁₃	—	4	2	no	—
400	C₂×C₄×C₁₃	—	4	2	no	—
401	C₂×C₄×C₁₃	—	4	4	no	—
402	C₂×C₄×C₁₃	—	8	2	no	—
403	C₂×C₄×C₁₃	—	8	2	no	—
404	C₂×C₄×C₁₃	—	8	2	no	—
405	C₂×C₄×C₁₃	—	8	4	no	—
406	C₂×C₄×C₁₃	—	8	2	no	—
407	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
408	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
409	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
410	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
411	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
412	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
413	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
414	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
415	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
416	C₈×C₁₃	—	2	2	no	—
417	C₈×C₁₃	—	2	2	no	—
418	C₈×C₁₃	—	2	4	no	—
419	#559	C₂²×C₁₃	1	1	yes	characteristic
420	Q₈²	C₂²×C₁₃	1	2	yes	complemented
421	#557	—	2	1	no	—
422	#554	C₂²×C₁₃	1	1	yes	characteristic
423	#554	C₂²×C₁₃	1	1	yes	characteristic
424	#554	C₂²×C₁₃	1	2	yes	—
425	#554	C₂²×C₁₃	1	4	yes	complemented
426	#553	—	2	1	no	—
427	#553	C₂²×C₁₃	1	2	yes	—
428	#551	—	2	2	no	—
429	D₄×Q₈	—	2	1	no	—
430	D₄×Q₈	—	2	2	no	—
431	#546	—	2	1	no	—
432	#546	C₂²×C₁₃	1	2	yes	—
433	D₄²	C₂²×C₁₃	1	1	yes	characteristic
434	#544	—	2	2	no	—
435	#544	—	2	1	no	—
436	#533	C₂²×C₁₃	1	1	yes	characteristic, complemented
437	#533	C₂²×C₁₃	1	2	yes	complemented
438	#532	C₂²×C₁₃	1	1	yes	characteristic
439	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
440	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
441	#529	—	2	1	no	—
442	#529	C₂²×C₁₃	1	2	yes	—
443	#525	—	2	2	no	—
444	#520	—	2	1	no	—
445	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
446	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
447	C₂×C₄×D₄	—	2	1	no	—
448	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
449	#501	C₂²×C₁₃	1	4	yes	complemented
450	#500	C₂²×C₁₃	1	2	yes	complemented
451	#489	C₂²×C₁₃	1	4	yes	complemented
452	#486	C₂²×C₁₃	1	2	yes	—
453	#485	C₂²×C₁₃	1	2	yes	complemented
454	#484	C₂²×C₁₃	1	4	yes	complemented
455	#484	C₂²×C₁₃	1	4	yes	complemented
456	#481	C₂²×C₁₃	1	4	yes	—
457	#480	C₂²×C₁₃	1	4	yes	complemented
458	#479	C₂²×C₁₃	1	4	yes	complemented
459	#477	C₂²×C₁₃	1	2	yes	complemented
460	#477	C₂²×C₁₃	1	2	yes	complemented
461	#476	C₂²×C₁₃	1	2	yes	—
462	#475	C₂²×C₁₃	1	2	yes	complemented
463	#475	C₂²×C₁₃	1	1	yes	characteristic, complemented
464	#474	C₂²×C₁₃	1	2	yes	—
465	#474	C₂²×C₁₃	1	1	yes	characteristic
466	#474	C₂²×C₁₃	1	4	yes	—
467	#474	C₂²×C₁₃	1	4	yes	complemented
468	#474	C₂²×C₁₃	1	2	yes	complemented
469	#474	C₂²×C₁₃	1	2	yes	complemented
470	#474	C₂²×C₁₃	1	2	yes	complemented
471	#468	C₂²×C₁₃	1	4	yes	complemented
472	#467	C₂²×C₁₃	1	4	yes	complemented
473	#465	C₂²×C₁₃	1	4	yes	—
474	#464	C₂²×C₁₃	1	4	yes	complemented
475	#462	C₂²×C₁₃	1	1	yes	characteristic, complemented
476	#461	C₂²×C₁₃	1	1	yes	characteristic
477	#461	C₂²×C₁₃	1	2	yes	complemented
478	#460	C₂²×C₁₃	1	2	yes	—
479	#452	C₂²×C₁₃	1	2	yes	—
480	#450	C₂²×C₁₃	1	4	yes	—
481	#446	C₂²×C₁₃	1	2	yes	complemented
482	#440	C₂²×C₁₃	1	4	yes	—
483	#440	C₂²×C₁₃	1	4	yes	complemented
484	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
485	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
486	#435	C₂²×C₁₃	1	4	yes	complemented
487	C₈×D₄	C₂²×C₁₃	1	2	yes	—
488	#432	C₂²×C₁₃	1	2	yes	complemented
489	#431	C₂²×C₁₃	1	1	yes	characteristic, complemented
490	#428	C₂²×C₁₃	1	2	yes	complemented
491	C₂×#107	C₂²×C₁₃	1	4	yes	complemented
492	#423	C₂²×C₁₃	1	1	yes	characteristic, complemented
493	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	complemented
494	#417	C₂²×C₁₃	1	2	yes	—
495	C₂×#102	C₂²×C₁₃	1	4	yes	—
496	C₂²×C₁₃	—	2	2	no	—
497	C₂²×C₁₃	—	2	2	no	—
498	C₂²×C₁₃	—	2	1	no	—
499	C₂²×C₁₃	—	2	2	no	—
500	C₂²×C₁₃	—	2	1	no	—
501	C₂²×C₁₃	—	2	1	no	—
502	C₂²×C₁₃	—	4	1	no	—
503	C₂²×C₁₃	—	4	1	no	—
504	C₂²×C₁₃	—	4	2	no	—
505	C₂²×C₁₃	—	4	2	no	—
506	C₂²×C₁₃	—	4	2	no	—
507	C₂²×C₁₃	—	8	8	no	—
508	C₂²×C₁₃	C₂×#137	1	4	yes	—
509	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
510	C₄×C₁₃	—	2	1	no	—
511	C₄×C₁₃	—	2	2	no	—
512	C₄×C₁₃	—	2	1	no	—
513	C₄×C₁₃	—	2	2	no	—
514	C₄×C₁₃	—	2	2	no	—
515	C₄×C₁₃	—	2	1	no	—
516	C₄×C₁₃	—	4	1	no	—
517	C₄×C₁₃	—	4	2	no	—
518	C₄×C₁₃	—	4	1	no	—
519	C₄×C₁₃	—	4	1	no	—
520	C₄×C₁₃	—	4	2	no	—
521	C₄×C₁₃	—	4	2	no	—
522	C₄×C₁₃	—	4	4	no	—
523	C₄×C₁₃	C₂×#137	1	2	yes	—
524	C₄×C₁₃	#576	1	2	yes	—
525	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
526	C₄×C₁₃	#585	1	1	yes	characteristic
527	C₂×#41	—	2	1	no	—
528	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
529	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
530	C₂²×Q₈	—	2	2	no	—
531	C₂²×Q₈	—	2	1	no	—
532	C₂²×D₄	—	2	1	no	—
533	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
534	C₂³×C₄	—	2	2	no	—
535	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
536	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
537	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
538	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
539	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
540	C₄⋊Q₈	—	2	2	no	—
541	C₄⋊Q₈	—	2	4	no	—
542	C₄⋊Q₈	—	2	1	no	—
543	C₄⋊Q₈	—	2	2	no	—
544	C₄⋊Q₈	—	2	1	no	—
545	C₄⋊Q₈	—	2	2	no	—
546	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
547	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
548	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
549	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
550	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
551	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
552	#127	C₂³×C₁₃	1	1	yes	characteristic
553	#126	—	2	2	no	—
554	#126	—	2	2	no	—
555	#125	—	2	1	no	—
556	#125	—	2	2	no	—
557	#125	—	2	4	no	—
558	#125	—	2	1	no	—
559	#125	—	2	2	no	—
560	#125	C₂³×C₁₃	1	2	yes	—
561	#124	—	2	1	no	—
562	#124	—	2	1	no	—
563	#124	C₂³×C₁₃	1	2	yes	—
564	#123	—	2	2	no	—
565	#123	—	2	2	no	—
566	#123	—	2	2	no	—
567	#123	—	2	2	no	—
568	C₂²⋊Q₈	—	2	1	no	—
569	C₂²⋊Q₈	—	2	2	no	—
570	C₂²⋊Q₈	—	2	1	no	—
571	C₂²⋊Q₈	—	2	2	no	—
572	C₂²⋊Q₈	—	2	2	no	—
573	C₂²⋊Q₈	—	2	4	no	—
574	C₂²⋊Q₈	—	2	4	no	—
575	C₂²⋊Q₈	—	2	4	no	—
576	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
577	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
578	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
579	#121	—	2	2	no	—
580	#121	—	2	1	no	—
581	#121	—	2	1	no	—
582	#121	—	2	2	no	—
583	#121	C₂³×C₁₃	1	2	yes	—
584	#121	C₂³×C₁₃	1	2	yes	—
585	#120	—	2	2	no	—
586	#120	—	2	2	no	—
587	C₄×Q₈	—	2	2	no	—
588	C₄×Q₈	—	2	1	no	—
589	C₄×Q₈	—	2	2	no	—
590	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
591	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
592	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
593	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
594	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
595	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
596	C₄×D₄	—	2	1	no	—
597	C₄×D₄	—	2	2	no	—
598	C₄×D₄	—	2	4	no	—
599	C₄×D₄	—	2	2	no	—
600	C₄×D₄	—	2	1	no	—
601	C₄×D₄	—	2	1	no	—
602	C₄×D₄	—	2	1	no	—
603	C₄×D₄	—	2	2	no	—
604	C₄×D₄	—	2	1	no	—
605	C₄×D₄	—	2	2	no	—
606	C₄×D₄	—	2	2	no	—
607	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
608	C₄×D₄	D₄×C₁₃	1	2	yes	—
609	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
610	C₄×D₄	C₂³×C₁₃	1	2	yes	—
611	C₄×D₄	C₂³×C₁₃	1	2	yes	—
612	C₄×D₄	C₂³×C₁₃	1	2	yes	—
613	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
614	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
615	C₄×D₄	C₂³×C₁₃	1	2	yes	—
616	#117	—	2	2	no	—
617	#117	—	2	1	no	—
618	#117	—	2	1	no	—
619	#117	—	2	2	no	—
620	#117	D₄×C₁₃	1	2	yes	—
621	#117	D₄×C₁₃	1	1	yes	characteristic
622	#117	C₂³×C₁₃	1	1	yes	characteristic
623	C₂×C₄⋊C₄	—	2	2	no	—
624	C₂×C₄⋊C₄	—	2	1	no	—
625	C₂×C₄⋊C₄	—	2	1	no	—
626	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
627	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
628	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
629	C₂×C₂²⋊C₄	—	2	2	no	—
630	C₂×C₂²⋊C₄	—	2	2	no	—
631	C₂×C₄²	—	2	1	no	—
632	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
633	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
634	#107	C₂³×C₁₃	1	2	yes	—
635	#107	C₂³×C₁₃	1	4	yes	—
636	#107	C₂³×C₁₃	1	4	yes	—
637	#107	C₂³×C₁₃	1	4	yes	—
638	#107	C₂³×C₁₃	1	4	yes	—
639	#106	C₂³×C₁₃	1	4	yes	—
640	#106	C₂³×C₁₃	1	2	yes	—
641	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
642	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
643	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
644	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
645	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
646	#103	C₂³×C₁₃	1	4	yes	—
647	#103	C₂³×C₁₃	1	2	yes	—
648	#103	C₂³×C₁₃	1	2	yes	—
649	#103	C₂³×C₁₃	1	2	yes	—
650	#103	C₂³×C₁₃	1	4	yes	—
651	#102	C₂³×C₁₃	1	2	yes	—
652	#102	C₂³×C₁₃	1	4	yes	—
653	#102	C₂³×C₁₃	1	4	yes	—
654	#102	C₂³×C₁₃	1	4	yes	—
655	#102	C₂³×C₁₃	1	4	yes	—
656	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
657	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
658	#97	C₂³×C₁₃	1	4	yes	—
659	C₄×C₈	C₂³×C₁₃	1	2	yes	—
660	C₂×C₁₃	—	2	4	no	—
661	C₂×C₁₃	—	4	1	no	—
662	C₂×C₁₃	—	4	2	no	—
663	C₂×C₁₃	—	8	2	no	—
664	C₂×C₁₃	#3489	1	1	yes	characteristic
665	C₂×C₁₃	C₂²×#137	1	1	yes	characteristic
666	C₂×C₁₃	C₂×#576	1	1	yes	characteristic
667	C₂⁴	—	2	2	no	—
668	#41	—	2	4	no	—
669	#41	—	2	2	no	—
670	#41	—	4	1	no	—
671	#41	—	8	2	no	—
672	C₂×Q₈	—	2	1	no	—
673	C₂×Q₈	—	2	2	no	—
674	C₂×Q₈	—	2	1	no	—
675	C₂×Q₈	—	2	4	no	—
676	C₂×Q₈	—	2	2	no	—
677	C₂×Q₈	—	8	4	no	—
678	C₂×Q₈	—	8	2	no	—
679	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
680	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
681	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
682	C₂×D₄	—	2	4	no	—
683	C₂×D₄	—	2	1	no	—
684	C₂×D₄	—	2	2	no	—
685	C₂×D₄	—	2	2	no	—
686	C₂×D₄	—	2	2	no	—
687	C₂×D₄	—	2	1	no	—
688	C₂×D₄	—	2	1	no	—
689	C₂×D₄	—	4	2	no	—
690	C₂×D₄	—	4	4	no	—
691	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
692	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
693	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
694	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
695	C₂²×C₄	—	2	2	no	—
696	C₂²×C₄	—	2	2	no	—
697	C₂²×C₄	—	2	4	no	—
698	C₂²×C₄	—	2	1	no	—
699	C₂²×C₄	—	2	1	no	—
700	C₂²×C₄	—	2	1	no	—
701	C₂²×C₄	—	2	2	no	—
702	C₂²×C₄	—	2	2	no	—
703	C₂²×C₄	—	2	2	no	—
704	C₂²×C₄	—	8	4	no	—
705	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
706	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
707	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
708	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
709	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
710	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
711	Q₁₆	—	4	2	no	—
712	SD₁₆	—	2	4	no	—
713	SD₁₆	—	4	4	no	—
714	M₁₆	—	4	2	no	—
715	C₂×C₈	—	4	4	no	—
716	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
717	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
718	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
719	C₄⋊C₄	—	2	1	no	—
720	C₄⋊C₄	—	2	2	no	—
721	C₄⋊C₄	—	2	1	no	—
722	C₄⋊C₄	—	2	2	no	—
723	C₄⋊C₄	—	2	4	no	—
724	C₄⋊C₄	—	2	2	no	—
725	C₄⋊C₄	—	2	2	no	—
726	C₄⋊C₄	—	2	2	no	—
727	C₄⋊C₄	—	2	4	no	—
728	C₄⋊C₄	—	2	1	no	—
729	C₄⋊C₄	—	2	1	no	—
730	C₄⋊C₄	—	2	1	no	—
731	C₄⋊C₄	—	2	2	no	—
732	C₄⋊C₄	—	2	2	no	—
733	C₄⋊C₄	—	2	1	no	—
734	C₄⋊C₄	—	2	2	no	—
735	C₄⋊C₄	—	2	4	no	—
736	C₄⋊C₄	—	2	4	no	—
737	C₄⋊C₄	—	2	2	no	—
738	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
739	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
740	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
741	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
742	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
743	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
744	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
745	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
746	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
747	C₂²⋊C₄	—	2	2	no	—
748	C₂²⋊C₄	—	2	2	no	—
749	C₂²⋊C₄	—	2	4	no	—
750	C₂²⋊C₄	—	2	1	no	—
751	C₂²⋊C₄	—	2	1	no	—
752	C₂²⋊C₄	—	2	2	no	—
753	C₂²⋊C₄	—	2	2	no	—
754	C₂²⋊C₄	—	2	2	no	—
755	C₂²⋊C₄	—	2	2	no	—
756	C₂²⋊C₄	—	2	2	no	—
757	C₂²⋊C₄	—	2	1	no	—
758	C₂²⋊C₄	—	2	2	no	—
759	C₂²⋊C₄	—	2	2	no	—
760	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
761	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
762	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
763	C₄²	—	2	1	no	—
764	C₄²	—	2	1	no	—
765	C₄²	—	2	1	no	—
766	C₄²	—	2	4	no	—
767	C₄²	—	2	2	no	—
768	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
769	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
770	C₄²	C₂×D₄×C₁₃	1	2	yes	—
771	C₄²	C₂×D₄×C₁₃	1	2	yes	—
772	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
773	C₄²	C₂⁴×C₁₃	1	2	yes	—
774	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
775	C₁₃	#62127	1	1	yes	characteristic, direct product factor, Sylow
776	C₂³	—	2	1	no	—
777	C₂³	—	2	2	no	—
778	C₂³	—	4	4	no	—
779	C₂³	—	4	4	no	—
780	C₂³	—	8	2	no	—
781	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
782	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
783	Q₈	—	2	2	no	—
784	Q₈	—	2	2	no	—
785	Q₈	—	2	1	no	—
786	Q₈	—	2	2	no	—
787	Q₈	—	2	1	no	—
788	Q₈	—	4	2	no	—
789	Q₈	—	4	4	no	—
790	Q₈	—	8	4	no	—
791	Q₈	—	8	2	no	—
792	Q₈	—	8	1	no	—
793	D₄	—	2	4	no	—
794	D₄	—	2	2	no	—
795	D₄	—	2	1	no	—
796	D₄	—	2	2	no	—
797	D₄	—	4	4	no	—
798	D₄	—	4	2	no	—
799	D₄	—	4	4	no	—
800	D₄	—	4	2	no	—
801	D₄	—	8	1	no	—
802	D₄	—	8	2	no	—
803	D₄	C₁₃×#137	1	4	yes	—
804	D₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
805	C₂×C₄	—	2	4	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	4	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	1	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	1	no	—
815	C₂×C₄	—	2	1	no	—
816	C₂×C₄	—	2	1	no	—
817	C₂×C₄	—	2	4	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	4	2	no	—
821	C₂×C₄	—	4	2	no	—
822	C₂×C₄	—	4	2	no	—
823	C₂×C₄	—	4	4	no	—
824	C₂×C₄	—	8	2	no	—
825	C₂×C₄	—	8	2	no	—
826	C₂×C₄	—	8	2	no	—
827	C₂×C₄	—	8	4	no	—
828	C₂×C₄	—	8	2	no	—
829	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
830	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
831	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
832	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
833	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
834	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
835	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
836	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
837	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
838	C₈	—	2	2	no	—
839	C₈	—	2	2	no	—
840	C₈	—	2	4	no	—
841	C₂²	—	2	2	no	—
842	C₂²	—	2	2	no	—
843	C₂²	—	2	1	no	—
844	C₂²	—	2	1	no	—
845	C₂²	—	2	1	no	—
846	C₂²	—	2	2	no	—
847	C₂²	—	4	1	no	—
848	C₂²	—	4	1	no	—
849	C₂²	—	4	2	no	—
850	C₂²	—	4	2	no	—
851	C₂²	—	4	2	no	—
852	C₂²	—	8	8	no	—
853	C₂²	C₂×C₁₃×#137	1	4	yes	—
854	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
855	C₄	—	2	1	no	—
856	C₄	—	2	2	no	—
857	C₄	—	2	2	no	—
858	C₄	—	2	1	no	—
859	C₄	—	2	1	no	—
860	C₄	—	2	2	no	—
861	C₄	—	4	1	no	—
862	C₄	—	4	1	no	—
863	C₄	—	4	2	no	—
864	C₄	—	4	2	no	—
865	C₄	—	4	4	no	—
866	C₄	—	4	1	no	—
867	C₄	—	4	2	no	—
868	C₄	C₂×C₁₃×#137	1	2	yes	—
869	C₄	C₁₃×#576	1	2	yes	—
870	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
871	C₄	C₁₃×#585	1	1	yes	characteristic
872	C₂	—	2	4	no	—
873	C₂	—	4	1	no	—
874	C₂	—	4	2	no	—
875	C₂	—	8	2	no	—
876	C₂	C₁₃×#3489	1	1	yes	characteristic
877	C₂	C₂²×C₁₃×#137	1	1	yes	characteristic
878	C₂	C₂×C₁₃×#576	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3481	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×#3375	C₂	semidirect
5. C₁₃×#3346	C₂	semidirect
6. C₁₃×#3338	C₂	semidirect
7. C₁₃×#3314	C₂	semidirect
8. C₁₃×#3295	C₂	semidirect
9. C₁₃×#3254	C₂	semidirect
10. C₁₃×#3248	C₂	semidirect
11. C₁₃×#3239	C₂	semidirect
12. C₁₃×#3226	C₂	semidirect
13. C₁₃×#3110	C₂	semidirect
14. C₁₃×#3107	C₂	semidirect
15. C₁₃×#3079	C₂	semidirect
16. C₂×C₁₃×#474	C₂	semidirect
17. C₁₃×#2990	C₂	semidirect
19. Q₈²×C₁₃	C₂²	semidirect
24. C₁₃×#554	C₂²	semidirect
35. C₁₃×#533	C₂²	semidirect
36. C₁₃×#533	C₂²	semidirect
38. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
39. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
48. C₁₃×#501	C₂²	semidirect
49. C₁₃×#500	C₂²	semidirect
50. C₁₃×#489	C₂²	semidirect
52. C₁₃×#485	C₂²	semidirect
53. C₁₃×#484	C₂²	semidirect
54. C₁₃×#484	C₂²	semidirect
56. C₁₃×#480	C₂²	semidirect
57. C₁₃×#479	C₂²	semidirect
58. C₁₃×#477	C₂²	semidirect
59. C₁₃×#477	C₂²	semidirect
61. C₁₃×#475	C₂²	semidirect
62. C₁₃×#475	C₂²	semidirect
66. C₁₃×#474	C₂²	semidirect
67. C₁₃×#474	C₂²	semidirect
68. C₁₃×#474	C₂²	semidirect
69. C₁₃×#474	C₂²	semidirect
70. C₁₃×#468	C₂²	semidirect
71. C₁₃×#467	C₂²	semidirect
73. C₁₃×#464	C₂²	semidirect
74. C₁₃×#462	C₂²	semidirect
76. C₁₃×#461	C₂²	semidirect
80. C₁₃×#446	C₂²	semidirect
82. C₁₃×#440	C₂²	semidirect
83. C₄×C₁₃×Q₁₆	C₂²	semidirect
85. C₁₃×#435	C₂²	semidirect
87. C₁₃×#432	C₂²	semidirect
88. C₁₃×#431	C₂²	semidirect
89. C₁₃×#428	C₂²	semidirect
90. C₂×C₁₃×#107	C₂²	semidirect
91. C₁₃×#423	C₂²	semidirect
92. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
228. #62127	C₁₃	direct (N × H)
337. #3503	C₂×C₁₃	semidirect
339. #3385	C₂×C₁₃	semidirect
340. #3375	C₂×C₁₃	semidirect
341. #3346	C₂×C₁₃	semidirect
342. #3338	C₂×C₁₃	semidirect
343. #3314	C₂×C₁₃	semidirect
344. #3295	C₂×C₁₃	semidirect
345. #3254	C₂×C₁₃	semidirect
346. #3248	C₂×C₁₃	semidirect
347. #3239	C₂×C₁₃	semidirect
348. #3226	C₂×C₁₃	semidirect
349. #3110	C₂×C₁₃	semidirect
350. #3107	C₂×C₁₃	semidirect
351. #3079	C₂×C₁₃	semidirect
352. C₂×#474	C₂×C₁₃	semidirect
353. #2990	C₂×C₁₃	semidirect
420. Q₈²	C₂²×C₁₃	semidirect
425. #554	C₂²×C₁₃	semidirect
436. #533	C₂²×C₁₃	semidirect
437. #533	C₂²×C₁₃	semidirect
439. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
440. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
449. #501	C₂²×C₁₃	semidirect
450. #500	C₂²×C₁₃	semidirect
451. #489	C₂²×C₁₃	semidirect
453. #485	C₂²×C₁₃	semidirect
454. #484	C₂²×C₁₃	semidirect
455. #484	C₂²×C₁₃	semidirect
457. #480	C₂²×C₁₃	semidirect
458. #479	C₂²×C₁₃	semidirect
459. #477	C₂²×C₁₃	semidirect
460. #477	C₂²×C₁₃	semidirect
462. #475	C₂²×C₁₃	semidirect
463. #475	C₂²×C₁₃	semidirect
467. #474	C₂²×C₁₃	semidirect
468. #474	C₂²×C₁₃	semidirect
469. #474	C₂²×C₁₃	semidirect
470. #474	C₂²×C₁₃	semidirect
471. #468	C₂²×C₁₃	semidirect
472. #467	C₂²×C₁₃	semidirect
474. #464	C₂²×C₁₃	semidirect
475. #462	C₂²×C₁₃	semidirect
477. #461	C₂²×C₁₃	semidirect
481. #446	C₂²×C₁₃	semidirect
483. #440	C₂²×C₁₃	semidirect
484. C₄×Q₁₆	C₂²×C₁₃	semidirect
486. #435	C₂²×C₁₃	semidirect
488. #432	C₂²×C₁₃	semidirect
489. #431	C₂²×C₁₃	semidirect
490. #428	C₂²×C₁₃	semidirect
491. C₂×#107	C₂²×C₁₃	semidirect
492. #423	C₂²×C₁₃	semidirect
493. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
775. C₁₃	#62127	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×#3481	2
C₁₃×#3385	2
C₁₃×#3375	2
C₁₃×#3346	2
C₁₃×#3338	2
C₁₃×#3314	2
C₁₃×#3295	2
C₁₃×#3254	2
C₁₃×#3248	2
C₁₃×#3239	2
C₁₃×#3226	2
C₁₃×#3110	2
C₁₃×#3107	2
C₁₃×#3079	2
C₂×C₁₃×#474	2
C₁₃×#2990	2
#62127	13

Subgroups — C13×#62127 #15748466

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62127 #15748466