Subgroups — C₁₃×#61005 #15747344

Order 3328.

1672 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×#3495	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3256	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3255	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3252	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3244	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3242	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3225	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3223	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3197	C₂	1	1	yes	maximal, characteristic
10	C₁₃×#3196	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3195	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3185	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3183	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3172	C₂	1	2	yes	maximal, complemented
15	C₁₃×#3127	C₂	1	2	yes	maximal, complemented
16	C₁₃×#3125	C₂	1	2	yes	maximal, complemented
17	C₁₃×#3121	C₂	1	2	yes	maximal, complemented
18	C₁₃×#3120	C₂	1	2	yes	maximal, complemented
19	C₁₃×#2921	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₃×#556	—	2	2	no	—
21	C₁₃×#554	—	2	2	no	—
22	C₁₃×#552	—	2	2	no	—
23	C₁₃×#552	—	2	2	no	—
24	C₁₃×#552	—	2	2	no	—
25	C₁₃×#552	—	2	2	no	—
26	C₁₃×#551	—	2	2	no	—
27	C₁₃×#551	—	2	2	no	—
28	C₁₃×#544	C₂²	1	2	yes	—
29	C₁₃×#542	C₂²	1	2	yes	—
30	C₁₃×#542	C₂²	1	2	yes	—
31	C₁₃×#541	C₂²	1	2	yes	—
32	C₁₃×#541	C₂²	1	2	yes	—
33	C₁₃×#536	C₂²	1	2	yes	—
34	C₁₃×#533	C₂²	1	2	yes	—
35	C₁₃×#533	C₂²	1	2	yes	—
36	C₁₃×#529	C₂²	1	2	yes	—
37	C₁₃×#529	C₂²	1	2	yes	—
38	C₁₃×#525	C₂²	1	2	yes	—
39	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
40	C₁₃×#520	C₂²	1	2	yes	—
41	C₁₃×#519	C₂²	1	2	yes	—
42	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
43	C₁₃×#501	C₂²	1	2	yes	complemented
44	C₁₃×#499	C₂²	1	1	yes	characteristic, complemented
45	C₁₃×#498	C₂²	1	1	yes	characteristic, complemented
46	C₁₃×#497	C₂²	1	2	yes	complemented
47	C₁₃×#495	C₂²	1	1	yes	characteristic, complemented
48	C₁₃×#494	C₂²	1	1	yes	characteristic, complemented
49	C₁₃×#491	C₂²	1	2	yes	complemented
50	C₁₃×#489	C₂²	1	2	yes	complemented
51	C₁₃×#488	C₂²	1	2	yes	complemented
52	C₁₃×#487	C₂²	1	2	yes	complemented
53	C₁₃×#485	C₂²	1	2	yes	—
54	C₁₃×#485	C₂²	1	2	yes	—
55	C₁₃×#485	C₂²	1	2	yes	—
56	C₁₃×#484	C₂²	1	2	yes	—
57	C₁₃×#483	C₂²	1	2	yes	—
58	C₁₃×#483	C₂²	1	2	yes	—
59	C₁₃×#482	C₂²	1	2	yes	—
60	C₁₃×#481	C₂²	1	2	yes	—
61	C₁₃×#479	C₂²	1	2	yes	complemented
62	C₁₃×#479	C₂²	1	2	yes	complemented
63	C₁₃×#479	C₂²	1	2	yes	complemented
64	C₁₃×#478	C₂²	1	2	yes	complemented
65	C₁₃×#477	C₂²	1	2	yes	complemented
66	C₁₃×#476	C₂²	1	2	yes	complemented
67	C₁₃×#475	C₂²	1	2	yes	complemented
68	C₁₃×#475	C₂²	1	2	yes	complemented
69	C₁₃×#470	C₂²	1	2	yes	—
70	C₁₃×#470	C₂²	1	2	yes	—
71	C₁₃×#470	C₂²	1	1	yes	characteristic
72	C₁₃×#470	C₂²	1	1	yes	characteristic
73	C₁₃×#470	C₂²	1	2	yes	—
74	C₁₃×#470	C₂²	1	1	yes	characteristic
75	C₁₃×#469	C₂²	1	1	yes	characteristic
76	C₁₃×#468	C₂²	1	2	yes	—
77	C₁₃×#468	C₂²	1	2	yes	—
78	C₁₃×#468	C₂²	1	2	yes	—
79	C₁₃×#464	C₂²	1	2	yes	complemented
80	C₁₃×#464	C₂²	1	2	yes	complemented
81	C₁₃×#464	C₂²	1	2	yes	complemented
82	C₁₃×#463	C₂²	1	2	yes	complemented
83	C₁₃×#462	C₂²	1	2	yes	complemented
84	C₁₃×#462	C₂²	1	2	yes	complemented
85	C₁₃×#462	C₂²	1	2	yes	complemented
86	C₁₃×#461	C₂²	1	2	yes	complemented
87	C₁₃×#452	C₂²	1	2	yes	—
88	C₁₃×#452	C₂²	1	2	yes	—
89	C₁₃×#452	C₂²	1	2	yes	—
90	C₁₃×#451	C₂²	1	2	yes	—
91	C₁₃×#451	C₂²	1	2	yes	—
92	C₁₃×#451	C₂²	1	2	yes	—
93	C₁₃×#449	C₂²	1	2	yes	—
94	C₁₃×#448	C₂²	1	2	yes	—
95	C₁₃×#442	C₂²	1	1	yes	characteristic, complemented
96	C₁₃×#441	C₂²	1	1	yes	characteristic, complemented
97	C₁₃×#441	C₂²	1	1	yes	characteristic, complemented
98	C₁₃×#441	C₂²	1	2	yes	complemented
99	C₁₃×#441	C₂²	1	1	yes	characteristic, complemented
100	C₁₃×#440	C₂²	1	2	yes	complemented
101	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
102	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
103	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
104	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
105	C₁₃×#433	C₂²	1	2	yes	—
106	C₁₃×#433	C₂²	1	2	yes	—
107	C₁₃×#433	C₂²	1	2	yes	—
108	C₁₃×#433	C₂²	1	2	yes	—
109	C₁₃×#423	C₂²	1	1	yes	characteristic
110	C₁₃×#423	C₂²	1	1	yes	characteristic
111	C₁₃×#407	C₂²	1	1	yes	characteristic
112	C₁₃×#407	C₂²	1	1	yes	characteristic
113	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
114	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
115	C₂×C₁₃×#41	C₂³	1	2	yes	—
116	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
117	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
118	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
119	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
120	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
121	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
122	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
123	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
124	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
125	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
126	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
127	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
128	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
129	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
130	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
131	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
132	C₁₃×C₄⋊Q₈	—	2	2	no	—
133	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
134	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
135	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
136	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
137	C₁₃×#126	—	2	2	no	—
138	C₁₃×#126	—	2	2	no	—
139	C₁₃×#126	—	2	2	no	—
140	C₁₃×#126	—	2	2	no	—
141	C₁₃×#126	—	2	2	no	—
142	C₁₃×#126	—	2	2	no	—
143	C₁₃×#126	—	2	2	no	—
144	C₁₃×#126	—	2	2	no	—
145	C₁₃×#125	—	2	2	no	—
146	C₁₃×#125	—	2	2	no	—
147	C₁₃×#125	—	2	2	no	—
148	C₁₃×#125	—	2	2	no	—
149	C₁₃×#125	—	2	2	no	—
150	C₁₃×#125	—	2	2	no	—
151	C₁₃×#125	—	2	2	no	—
152	C₁₃×#125	C₂³	1	2	yes	—
153	C₁₃×#125	C₂³	1	2	yes	—
154	C₁₃×#124	—	2	2	no	—
155	C₁₃×#124	—	2	2	no	—
156	C₁₃×#124	C₂³	1	2	yes	—
157	C₁₃×#124	C₂³	1	2	yes	—
158	C₁₃×#123	—	2	2	no	—
159	C₁₃×#123	—	2	2	no	—
160	C₁₃×#123	—	2	2	no	—
161	C₁₃×#123	—	2	2	no	—
162	C₁₃×#123	—	2	2	no	—
163	C₁₃×#123	—	2	2	no	—
164	C₁₃×#123	—	2	2	no	—
165	C₁₃×C₂²⋊Q₈	—	2	2	no	—
166	C₁₃×C₂²⋊Q₈	—	2	2	no	—
167	C₁₃×C₂²⋊Q₈	—	2	2	no	—
168	C₁₃×C₂²⋊Q₈	—	2	2	no	—
169	C₁₃×C₂²⋊Q₈	—	2	2	no	—
170	C₁₃×C₂²⋊Q₈	—	2	2	no	—
171	C₁₃×C₂²⋊Q₈	—	2	2	no	—
172	C₁₃×C₂²⋊Q₈	—	2	2	no	—
173	C₁₃×C₂²⋊Q₈	—	2	2	no	—
174	C₁₃×C₂²⋊Q₈	—	2	2	no	—
175	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
176	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
177	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
178	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
179	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
180	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
181	C₁₃×#121	C₂³	1	2	yes	—
182	C₁₃×#121	C₂³	1	2	yes	—
183	C₁₃×#120	—	2	2	no	—
184	C₄×Q₈×C₁₃	—	2	2	no	—
185	C₄×Q₈×C₁₃	—	2	2	no	—
186	C₄×Q₈×C₁₃	—	2	2	no	—
187	C₄×Q₈×C₁₃	—	2	2	no	—
188	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
189	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
190	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
191	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
192	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
193	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
194	C₄×D₄×C₁₃	—	2	2	no	—
195	C₄×D₄×C₁₃	—	2	2	no	—
196	C₄×D₄×C₁₃	—	2	2	no	—
197	C₄×D₄×C₁₃	—	2	2	no	—
198	C₄×D₄×C₁₃	—	2	2	no	—
199	C₄×D₄×C₁₃	—	2	2	no	—
200	C₄×D₄×C₁₃	C₂³	1	2	yes	—
201	C₄×D₄×C₁₃	C₂³	1	2	yes	—
202	C₁₃×#117	—	2	2	no	—
203	C₁₃×#117	—	2	2	no	—
204	C₁₃×#117	—	2	2	no	—
205	C₁₃×#117	—	2	2	no	—
206	C₁₃×#117	—	2	2	no	—
207	C₁₃×#117	—	2	2	no	—
208	C₁₃×#117	—	2	2	no	—
209	C₁₃×#117	D₄	1	2	yes	—
210	C₁₃×#117	D₄	1	2	yes	—
211	C₁₃×#117	C₂³	1	2	yes	—
212	C₁₃×#117	C₂³	1	2	yes	—
213	C₁₃×#117	C₂³	1	2	yes	—
214	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
215	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
216	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
217	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
218	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
219	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
220	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
221	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
222	C₁₃×#107	C₂³	1	2	yes	—
223	C₁₃×#107	C₂³	1	2	yes	—
224	C₁₃×#107	C₂³	1	2	yes	—
225	C₁₃×#106	C₂³	1	2	yes	—
226	C₁₃×#106	C₂³	1	2	yes	—
227	C₁₃×#106	C₂³	1	1	yes	characteristic
228	C₁₃×#106	C₂³	1	1	yes	characteristic
229	C₁₃×#106	C₂³	1	2	yes	—
230	C₁₃×#106	C₂³	1	1	yes	characteristic
231	C₁₃×#106	C₂³	1	1	yes	characteristic
232	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
233	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
234	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
235	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
236	C₁₃×#103	C₂³	1	2	yes	—
237	C₁₃×#103	C₂³	1	2	yes	—
238	C₁₃×#103	C₂³	1	2	yes	—
239	C₁₃×#103	C₂³	1	2	yes	—
240	C₁₃×#103	C₂³	1	2	yes	—
241	C₁₃×#103	C₂³	1	2	yes	—
242	C₁₃×#103	C₂³	1	2	yes	—
243	C₁₃×#103	C₂³	1	2	yes	—
244	C₁₃×#103	C₂³	1	2	yes	—
245	C₁₃×#103	C₂³	1	2	yes	—
246	C₁₃×#103	C₂³	1	2	yes	—
247	C₁₃×#103	C₂³	1	2	yes	—
248	C₁₃×#102	C₂³	1	2	yes	—
249	C₁₃×#102	C₂³	1	2	yes	—
250	C₁₃×#102	C₂³	1	2	yes	—
251	C₁₃×#102	C₂³	1	2	yes	—
252	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
253	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
254	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
255	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
256	C₁₃×#97	C₂³	1	1	yes	characteristic
257	C₁₃×#97	C₂³	1	1	yes	characteristic
258	C₁₃×#97	C₂³	1	2	yes	—
259	C₄×C₈×C₁₃	C₂³	1	2	yes	—
260	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
261	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
262	#61005	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
263	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
264	C₁₃×#41	—	4	2	no	—
265	C₁₃×#41	—	4	2	no	—
266	C₂×Q₈×C₁₃	—	2	2	no	—
267	C₂×Q₈×C₁₃	—	2	2	no	—
268	C₂×Q₈×C₁₃	—	2	2	no	—
269	C₂×Q₈×C₁₃	—	4	2	no	—
270	C₂×Q₈×C₁₃	—	4	2	no	—
271	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
272	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
273	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
274	C₂×D₄×C₁₃	—	2	2	no	—
275	C₂×D₄×C₁₃	—	2	2	no	—
276	C₂×D₄×C₁₃	—	2	2	no	—
277	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
278	C₂²×C₄×C₁₃	—	2	2	no	—
279	C₂²×C₄×C₁₃	—	2	2	no	—
280	C₂²×C₄×C₁₃	—	2	2	no	—
281	C₂²×C₄×C₁₃	—	2	2	no	—
282	C₂²×C₄×C₁₃	—	2	2	no	—
283	C₂²×C₄×C₁₃	—	4	1	no	—
284	C₂²×C₄×C₁₃	—	4	1	no	—
285	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
286	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
287	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
288	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
289	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
290	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
291	C₁₃×Q₁₆	—	4	1	no	—
292	C₁₃×Q₁₆	—	4	2	no	—
293	C₁₃×Q₁₆	—	4	2	no	—
294	C₁₃×Q₁₆	—	4	1	no	—
295	C₁₃×Q₁₆	—	4	2	no	—
296	C₁₃×Q₁₆	—	4	1	no	—
297	C₁₃×SD₁₆	—	4	2	no	—
298	C₁₃×SD₁₆	—	4	2	no	—
299	C₁₃×SD₁₆	—	4	2	no	—
300	C₁₃×D₈	—	4	1	no	—
301	C₁₃×M₁₆	—	4	1	no	—
302	C₁₃×M₁₆	—	4	1	no	—
303	C₁₃×M₁₆	—	4	1	no	—
304	C₁₃×M₁₆	—	4	1	no	—
305	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
306	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
307	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
308	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
309	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
310	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
311	C₁₃×C₄⋊C₄	—	2	2	no	—
312	C₁₃×C₄⋊C₄	—	2	2	no	—
313	C₁₃×C₄⋊C₄	—	2	2	no	—
314	C₁₃×C₄⋊C₄	—	2	2	no	—
315	C₁₃×C₄⋊C₄	—	2	2	no	—
316	C₁₃×C₄⋊C₄	—	2	2	no	—
317	C₁₃×C₄⋊C₄	—	2	2	no	—
318	C₁₃×C₄⋊C₄	—	2	2	no	—
319	C₁₃×C₄⋊C₄	—	2	2	no	—
320	C₁₃×C₄⋊C₄	—	2	2	no	—
321	C₁₃×C₄⋊C₄	—	2	2	no	—
322	C₁₃×C₄⋊C₄	—	2	2	no	—
323	C₁₃×C₄⋊C₄	—	2	2	no	—
324	C₁₃×C₄⋊C₄	—	2	2	no	—
325	C₁₃×C₄⋊C₄	—	2	2	no	—
326	C₁₃×C₄⋊C₄	—	2	2	no	—
327	C₁₃×C₄⋊C₄	—	2	2	no	—
328	C₁₃×C₄⋊C₄	—	2	2	no	—
329	C₁₃×C₄⋊C₄	—	2	2	no	—
330	C₁₃×C₄⋊C₄	—	2	2	no	—
331	C₁₃×C₄⋊C₄	—	2	2	no	—
332	C₁₃×C₄⋊C₄	—	2	2	no	—
333	C₁₃×C₄⋊C₄	—	2	2	no	—
334	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
335	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
336	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
337	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
338	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
339	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
340	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
341	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
342	C₁₃×C₂²⋊C₄	—	2	2	no	—
343	C₁₃×C₂²⋊C₄	—	2	2	no	—
344	C₁₃×C₂²⋊C₄	—	2	2	no	—
345	C₁₃×C₂²⋊C₄	—	2	2	no	—
346	C₁₃×C₂²⋊C₄	—	2	2	no	—
347	C₁₃×C₂²⋊C₄	—	2	2	no	—
348	C₁₃×C₂²⋊C₄	—	2	2	no	—
349	C₁₃×C₂²⋊C₄	—	2	2	no	—
350	C₁₃×C₂²⋊C₄	—	2	2	no	—
351	C₁₃×C₂²⋊C₄	—	2	2	no	—
352	C₁₃×C₂²⋊C₄	—	2	2	no	—
353	C₁₃×C₂²⋊C₄	—	2	2	no	—
354	C₁₃×C₂²⋊C₄	—	2	2	no	—
355	C₁₃×C₂²⋊C₄	—	2	2	no	—
356	C₁₃×C₂²⋊C₄	—	2	2	no	—
357	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
358	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
359	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
360	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
361	C₄²×C₁₃	—	2	2	no	—
362	C₄²×C₁₃	—	2	2	no	—
363	C₄²×C₁₃	—	2	2	no	—
364	C₄²×C₁₃	—	2	2	no	—
365	C₄²×C₁₃	—	2	2	no	—
366	C₄²×C₁₃	—	2	2	no	—
367	C₄²×C₁₃	—	2	2	no	—
368	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
369	C₄²×C₁₃	C₂×D₄	1	2	yes	—
370	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
371	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
372	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
373	C₄²×C₁₃	C₂⁴	1	2	yes	—
374	#3495	C₂×C₁₃	1	2	yes	complemented
375	#3256	C₂×C₁₃	1	1	yes	characteristic, complemented
376	#3255	C₂×C₁₃	1	1	yes	characteristic, complemented
377	#3252	C₂×C₁₃	1	2	yes	complemented
378	#3244	C₂×C₁₃	1	2	yes	complemented
379	#3242	C₂×C₁₃	1	2	yes	complemented
380	#3225	C₂×C₁₃	1	2	yes	complemented
381	#3223	C₂×C₁₃	1	2	yes	complemented
382	#3197	C₂×C₁₃	1	1	yes	characteristic
383	#3196	C₂×C₁₃	1	2	yes	complemented
384	#3195	C₂×C₁₃	1	1	yes	characteristic, complemented
385	#3185	C₂×C₁₃	1	1	yes	characteristic, complemented
386	#3183	C₂×C₁₃	1	1	yes	characteristic, complemented
387	#3172	C₂×C₁₃	1	2	yes	complemented
388	#3127	C₂×C₁₃	1	2	yes	complemented
389	#3125	C₂×C₁₃	1	2	yes	complemented
390	#3121	C₂×C₁₃	1	2	yes	complemented
391	#3120	C₂×C₁₃	1	2	yes	complemented
392	#2921	C₂×C₁₃	1	1	yes	characteristic, complemented
393	C₂³×C₁₃	—	2	2	no	—
394	C₂³×C₁₃	—	4	1	no	—
395	C₂³×C₁₃	—	4	2	no	—
396	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
397	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
398	Q₈×C₁₃	—	2	2	no	—
399	Q₈×C₁₃	—	2	2	no	—
400	Q₈×C₁₃	—	2	2	no	—
401	Q₈×C₁₃	—	2	2	no	—
402	Q₈×C₁₃	—	2	2	no	—
403	Q₈×C₁₃	—	2	2	no	—
404	Q₈×C₁₃	—	4	4	no	—
405	Q₈×C₁₃	—	8	2	no	—
406	Q₈×C₁₃	—	8	2	no	—
407	D₄×C₁₃	—	2	2	no	—
408	D₄×C₁₃	—	2	2	no	—
409	D₄×C₁₃	—	4	4	no	—
410	D₄×C₁₃	—	4	4	no	—
411	D₄×C₁₃	—	8	2	no	—
412	C₂×C₄×C₁₃	—	2	1	no	—
413	C₂×C₄×C₁₃	—	2	1	no	—
414	C₂×C₄×C₁₃	—	2	2	no	—
415	C₂×C₄×C₁₃	—	2	2	no	—
416	C₂×C₄×C₁₃	—	2	2	no	—
417	C₂×C₄×C₁₃	—	2	2	no	—
418	C₂×C₄×C₁₃	—	2	2	no	—
419	C₂×C₄×C₁₃	—	2	2	no	—
420	C₂×C₄×C₁₃	—	2	2	no	—
421	C₂×C₄×C₁₃	—	2	2	no	—
422	C₂×C₄×C₁₃	—	2	2	no	—
423	C₂×C₄×C₁₃	—	4	1	no	—
424	C₂×C₄×C₁₃	—	4	2	no	—
425	C₂×C₄×C₁₃	—	4	2	no	—
426	C₂×C₄×C₁₃	—	4	2	no	—
427	C₂×C₄×C₁₃	—	4	4	no	—
428	C₂×C₄×C₁₃	—	4	4	no	—
429	C₂×C₄×C₁₃	—	8	2	no	—
430	C₂×C₄×C₁₃	—	8	2	no	—
431	C₂×C₄×C₁₃	—	8	2	no	—
432	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
433	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
434	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
435	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
436	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
437	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
438	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
439	C₈×C₁₃	—	2	1	no	—
440	C₈×C₁₃	—	2	1	no	—
441	C₈×C₁₃	—	2	2	no	—
442	C₈×C₁₃	—	2	2	no	—
443	C₈×C₁₃	—	2	1	no	—
444	C₈×C₁₃	—	2	1	no	—
445	#556	—	2	2	no	—
446	#554	—	2	2	no	—
447	#552	—	2	2	no	—
448	#552	—	2	2	no	—
449	#552	—	2	2	no	—
450	#552	—	2	2	no	—
451	#551	—	2	2	no	—
452	#551	—	2	2	no	—
453	#544	C₂²×C₁₃	1	2	yes	—
454	#542	C₂²×C₁₃	1	2	yes	—
455	#542	C₂²×C₁₃	1	2	yes	—
456	#541	C₂²×C₁₃	1	2	yes	—
457	#541	C₂²×C₁₃	1	2	yes	—
458	#536	C₂²×C₁₃	1	2	yes	—
459	#533	C₂²×C₁₃	1	2	yes	—
460	#533	C₂²×C₁₃	1	2	yes	—
461	#529	C₂²×C₁₃	1	2	yes	—
462	#529	C₂²×C₁₃	1	2	yes	—
463	#525	C₂²×C₁₃	1	2	yes	—
464	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
465	#520	C₂²×C₁₃	1	2	yes	—
466	#519	C₂²×C₁₃	1	2	yes	—
467	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
468	#501	C₂²×C₁₃	1	2	yes	complemented
469	#499	C₂²×C₁₃	1	1	yes	characteristic, complemented
470	#498	C₂²×C₁₃	1	1	yes	characteristic, complemented
471	#497	C₂²×C₁₃	1	2	yes	complemented
472	#495	C₂²×C₁₃	1	1	yes	characteristic, complemented
473	#494	C₂²×C₁₃	1	1	yes	characteristic, complemented
474	#491	C₂²×C₁₃	1	2	yes	complemented
475	#489	C₂²×C₁₃	1	2	yes	complemented
476	#488	C₂²×C₁₃	1	2	yes	complemented
477	#487	C₂²×C₁₃	1	2	yes	complemented
478	#485	C₂²×C₁₃	1	2	yes	—
479	#485	C₂²×C₁₃	1	2	yes	—
480	#485	C₂²×C₁₃	1	2	yes	—
481	#484	C₂²×C₁₃	1	2	yes	—
482	#483	C₂²×C₁₃	1	2	yes	—
483	#483	C₂²×C₁₃	1	2	yes	—
484	#482	C₂²×C₁₃	1	2	yes	—
485	#481	C₂²×C₁₃	1	2	yes	—
486	#479	C₂²×C₁₃	1	2	yes	complemented
487	#479	C₂²×C₁₃	1	2	yes	complemented
488	#479	C₂²×C₁₃	1	2	yes	complemented
489	#478	C₂²×C₁₃	1	2	yes	complemented
490	#477	C₂²×C₁₃	1	2	yes	complemented
491	#476	C₂²×C₁₃	1	2	yes	complemented
492	#475	C₂²×C₁₃	1	2	yes	complemented
493	#475	C₂²×C₁₃	1	2	yes	complemented
494	#470	C₂²×C₁₃	1	2	yes	—
495	#470	C₂²×C₁₃	1	2	yes	—
496	#470	C₂²×C₁₃	1	1	yes	characteristic
497	#470	C₂²×C₁₃	1	1	yes	characteristic
498	#470	C₂²×C₁₃	1	2	yes	—
499	#470	C₂²×C₁₃	1	1	yes	characteristic
500	#469	C₂²×C₁₃	1	1	yes	characteristic
501	#468	C₂²×C₁₃	1	2	yes	—
502	#468	C₂²×C₁₃	1	2	yes	—
503	#468	C₂²×C₁₃	1	2	yes	—
504	#464	C₂²×C₁₃	1	2	yes	complemented
505	#464	C₂²×C₁₃	1	2	yes	complemented
506	#464	C₂²×C₁₃	1	2	yes	complemented
507	#463	C₂²×C₁₃	1	2	yes	complemented
508	#462	C₂²×C₁₃	1	2	yes	complemented
509	#462	C₂²×C₁₃	1	2	yes	complemented
510	#462	C₂²×C₁₃	1	2	yes	complemented
511	#461	C₂²×C₁₃	1	2	yes	complemented
512	#452	C₂²×C₁₃	1	2	yes	—
513	#452	C₂²×C₁₃	1	2	yes	—
514	#452	C₂²×C₁₃	1	2	yes	—
515	#451	C₂²×C₁₃	1	2	yes	—
516	#451	C₂²×C₁₃	1	2	yes	—
517	#451	C₂²×C₁₃	1	2	yes	—
518	#449	C₂²×C₁₃	1	2	yes	—
519	#448	C₂²×C₁₃	1	2	yes	—
520	#442	C₂²×C₁₃	1	1	yes	characteristic, complemented
521	#441	C₂²×C₁₃	1	1	yes	characteristic, complemented
522	#441	C₂²×C₁₃	1	1	yes	characteristic, complemented
523	#441	C₂²×C₁₃	1	2	yes	complemented
524	#441	C₂²×C₁₃	1	1	yes	characteristic, complemented
525	#440	C₂²×C₁₃	1	2	yes	complemented
526	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
527	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
528	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
529	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
530	#433	C₂²×C₁₃	1	2	yes	—
531	#433	C₂²×C₁₃	1	2	yes	—
532	#433	C₂²×C₁₃	1	2	yes	—
533	#433	C₂²×C₁₃	1	2	yes	—
534	#423	C₂²×C₁₃	1	1	yes	characteristic
535	#423	C₂²×C₁₃	1	1	yes	characteristic
536	#407	C₂²×C₁₃	1	1	yes	characteristic
537	#407	C₂²×C₁₃	1	1	yes	characteristic
538	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
539	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
540	C₂²×C₁₃	—	2	2	no	—
541	C₂²×C₁₃	—	2	2	no	—
542	C₂²×C₁₃	—	2	2	no	—
543	C₂²×C₁₃	—	2	2	no	—
544	C₂²×C₁₃	—	2	1	no	—
545	C₂²×C₁₃	—	4	2	no	—
546	C₂²×C₁₃	—	4	2	no	—
547	C₂²×C₁₃	—	4	2	no	—
548	C₂²×C₁₃	—	8	2	no	—
549	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
550	C₄×C₁₃	—	2	2	no	—
551	C₄×C₁₃	—	2	2	no	—
552	C₄×C₁₃	—	2	2	no	—
553	C₄×C₁₃	—	2	2	no	—
554	C₄×C₁₃	—	2	2	no	—
555	C₄×C₁₃	—	2	1	no	—
556	C₄×C₁₃	—	4	2	no	—
557	C₄×C₁₃	—	4	2	no	—
558	C₄×C₁₃	—	4	2	no	—
559	C₄×C₁₃	—	4	2	no	—
560	C₄×C₁₃	—	4	2	no	—
561	C₄×C₁₃	—	4	2	no	—
562	C₄×C₁₃	—	4	2	no	—
563	C₄×C₁₃	#585	1	1	yes	characteristic
564	C₄×C₁₃	#585	1	1	yes	characteristic
565	C₂×#41	C₂³×C₁₃	1	2	yes	—
566	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
567	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
568	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
569	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
570	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
571	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
572	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
573	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
574	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
575	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
576	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
577	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
578	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
579	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
580	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
581	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
582	C₄⋊Q₈	—	2	2	no	—
583	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
584	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
585	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
586	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
587	#126	—	2	2	no	—
588	#126	—	2	2	no	—
589	#126	—	2	2	no	—
590	#126	—	2	2	no	—
591	#126	—	2	2	no	—
592	#126	—	2	2	no	—
593	#126	—	2	2	no	—
594	#126	—	2	2	no	—
595	#125	—	2	2	no	—
596	#125	—	2	2	no	—
597	#125	—	2	2	no	—
598	#125	—	2	2	no	—
599	#125	—	2	2	no	—
600	#125	—	2	2	no	—
601	#125	—	2	2	no	—
602	#125	C₂³×C₁₃	1	2	yes	—
603	#125	C₂³×C₁₃	1	2	yes	—
604	#124	—	2	2	no	—
605	#124	—	2	2	no	—
606	#124	C₂³×C₁₃	1	2	yes	—
607	#124	C₂³×C₁₃	1	2	yes	—
608	#123	—	2	2	no	—
609	#123	—	2	2	no	—
610	#123	—	2	2	no	—
611	#123	—	2	2	no	—
612	#123	—	2	2	no	—
613	#123	—	2	2	no	—
614	#123	—	2	2	no	—
615	C₂²⋊Q₈	—	2	2	no	—
616	C₂²⋊Q₈	—	2	2	no	—
617	C₂²⋊Q₈	—	2	2	no	—
618	C₂²⋊Q₈	—	2	2	no	—
619	C₂²⋊Q₈	—	2	2	no	—
620	C₂²⋊Q₈	—	2	2	no	—
621	C₂²⋊Q₈	—	2	2	no	—
622	C₂²⋊Q₈	—	2	2	no	—
623	C₂²⋊Q₈	—	2	2	no	—
624	C₂²⋊Q₈	—	2	2	no	—
625	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
626	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
627	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
628	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
629	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
630	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
631	#121	C₂³×C₁₃	1	2	yes	—
632	#121	C₂³×C₁₃	1	2	yes	—
633	#120	—	2	2	no	—
634	C₄×Q₈	—	2	2	no	—
635	C₄×Q₈	—	2	2	no	—
636	C₄×Q₈	—	2	2	no	—
637	C₄×Q₈	—	2	2	no	—
638	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
639	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
640	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
641	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
642	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
643	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
644	C₄×D₄	—	2	2	no	—
645	C₄×D₄	—	2	2	no	—
646	C₄×D₄	—	2	2	no	—
647	C₄×D₄	—	2	2	no	—
648	C₄×D₄	—	2	2	no	—
649	C₄×D₄	—	2	2	no	—
650	C₄×D₄	C₂³×C₁₃	1	2	yes	—
651	C₄×D₄	C₂³×C₁₃	1	2	yes	—
652	#117	—	2	2	no	—
653	#117	—	2	2	no	—
654	#117	—	2	2	no	—
655	#117	—	2	2	no	—
656	#117	—	2	2	no	—
657	#117	—	2	2	no	—
658	#117	—	2	2	no	—
659	#117	D₄×C₁₃	1	2	yes	—
660	#117	D₄×C₁₃	1	2	yes	—
661	#117	C₂³×C₁₃	1	2	yes	—
662	#117	C₂³×C₁₃	1	2	yes	—
663	#117	C₂³×C₁₃	1	2	yes	—
664	C₂×C₄⋊C₄	—	2	2	no	—
665	C₂×C₄⋊C₄	—	2	2	no	—
666	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
667	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
668	C₂×C₂²⋊C₄	—	2	2	no	—
669	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
670	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
671	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
672	#107	C₂³×C₁₃	1	2	yes	—
673	#107	C₂³×C₁₃	1	2	yes	—
674	#107	C₂³×C₁₃	1	2	yes	—
675	#106	C₂³×C₁₃	1	2	yes	—
676	#106	C₂³×C₁₃	1	2	yes	—
677	#106	C₂³×C₁₃	1	1	yes	characteristic
678	#106	C₂³×C₁₃	1	1	yes	characteristic
679	#106	C₂³×C₁₃	1	2	yes	—
680	#106	C₂³×C₁₃	1	1	yes	characteristic
681	#106	C₂³×C₁₃	1	1	yes	characteristic
682	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
683	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
684	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
685	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
686	#103	C₂³×C₁₃	1	2	yes	—
687	#103	C₂³×C₁₃	1	2	yes	—
688	#103	C₂³×C₁₃	1	2	yes	—
689	#103	C₂³×C₁₃	1	2	yes	—
690	#103	C₂³×C₁₃	1	2	yes	—
691	#103	C₂³×C₁₃	1	2	yes	—
692	#103	C₂³×C₁₃	1	2	yes	—
693	#103	C₂³×C₁₃	1	2	yes	—
694	#103	C₂³×C₁₃	1	2	yes	—
695	#103	C₂³×C₁₃	1	2	yes	—
696	#103	C₂³×C₁₃	1	2	yes	—
697	#103	C₂³×C₁₃	1	2	yes	—
698	#102	C₂³×C₁₃	1	2	yes	—
699	#102	C₂³×C₁₃	1	2	yes	—
700	#102	C₂³×C₁₃	1	2	yes	—
701	#102	C₂³×C₁₃	1	2	yes	—
702	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
703	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
704	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
705	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
706	#97	C₂³×C₁₃	1	1	yes	characteristic
707	#97	C₂³×C₁₃	1	1	yes	characteristic
708	#97	C₂³×C₁₃	1	2	yes	—
709	C₄×C₈	C₂³×C₁₃	1	2	yes	—
710	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
711	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
712	C₂×C₁₃	—	4	1	no	—
713	C₂×C₁₃	—	4	2	no	—
714	C₂×C₁₃	—	8	2	no	—
715	C₂×C₁₃	#3449	1	1	yes	characteristic
716	C₂×C₁₃	#3586	1	2	yes	—
717	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
718	#41	—	4	2	no	—
719	#41	—	4	2	no	—
720	C₂×Q₈	—	2	2	no	—
721	C₂×Q₈	—	2	2	no	—
722	C₂×Q₈	—	2	2	no	—
723	C₂×Q₈	—	4	2	no	—
724	C₂×Q₈	—	4	2	no	—
725	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
726	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
727	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
728	C₂×D₄	—	2	2	no	—
729	C₂×D₄	—	2	2	no	—
730	C₂×D₄	—	2	2	no	—
731	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
732	C₂²×C₄	—	2	2	no	—
733	C₂²×C₄	—	2	2	no	—
734	C₂²×C₄	—	2	2	no	—
735	C₂²×C₄	—	2	2	no	—
736	C₂²×C₄	—	2	2	no	—
737	C₂²×C₄	—	4	1	no	—
738	C₂²×C₄	—	4	1	no	—
739	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
740	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
741	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
742	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
743	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
744	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
745	Q₁₆	—	4	1	no	—
746	Q₁₆	—	4	2	no	—
747	Q₁₆	—	4	2	no	—
748	Q₁₆	—	4	1	no	—
749	Q₁₆	—	4	2	no	—
750	Q₁₆	—	4	1	no	—
751	SD₁₆	—	4	2	no	—
752	SD₁₆	—	4	2	no	—
753	SD₁₆	—	4	2	no	—
754	D₈	—	4	1	no	—
755	M₁₆	—	4	1	no	—
756	M₁₆	—	4	1	no	—
757	M₁₆	—	4	1	no	—
758	M₁₆	—	4	1	no	—
759	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
760	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
761	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
762	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
763	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
764	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
765	C₄⋊C₄	—	2	2	no	—
766	C₄⋊C₄	—	2	2	no	—
767	C₄⋊C₄	—	2	2	no	—
768	C₄⋊C₄	—	2	2	no	—
769	C₄⋊C₄	—	2	2	no	—
770	C₄⋊C₄	—	2	2	no	—
771	C₄⋊C₄	—	2	2	no	—
772	C₄⋊C₄	—	2	2	no	—
773	C₄⋊C₄	—	2	2	no	—
774	C₄⋊C₄	—	2	2	no	—
775	C₄⋊C₄	—	2	2	no	—
776	C₄⋊C₄	—	2	2	no	—
777	C₄⋊C₄	—	2	2	no	—
778	C₄⋊C₄	—	2	2	no	—
779	C₄⋊C₄	—	2	2	no	—
780	C₄⋊C₄	—	2	2	no	—
781	C₄⋊C₄	—	2	2	no	—
782	C₄⋊C₄	—	2	2	no	—
783	C₄⋊C₄	—	2	2	no	—
784	C₄⋊C₄	—	2	2	no	—
785	C₄⋊C₄	—	2	2	no	—
786	C₄⋊C₄	—	2	2	no	—
787	C₄⋊C₄	—	2	2	no	—
788	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
789	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
790	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
791	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
792	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
793	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
794	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
795	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
796	C₂²⋊C₄	—	2	2	no	—
797	C₂²⋊C₄	—	2	2	no	—
798	C₂²⋊C₄	—	2	2	no	—
799	C₂²⋊C₄	—	2	2	no	—
800	C₂²⋊C₄	—	2	2	no	—
801	C₂²⋊C₄	—	2	2	no	—
802	C₂²⋊C₄	—	2	2	no	—
803	C₂²⋊C₄	—	2	2	no	—
804	C₂²⋊C₄	—	2	2	no	—
805	C₂²⋊C₄	—	2	2	no	—
806	C₂²⋊C₄	—	2	2	no	—
807	C₂²⋊C₄	—	2	2	no	—
808	C₂²⋊C₄	—	2	2	no	—
809	C₂²⋊C₄	—	2	2	no	—
810	C₂²⋊C₄	—	2	2	no	—
811	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
812	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
813	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
814	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
815	C₄²	—	2	2	no	—
816	C₄²	—	2	2	no	—
817	C₄²	—	2	2	no	—
818	C₄²	—	2	2	no	—
819	C₄²	—	2	2	no	—
820	C₄²	—	2	2	no	—
821	C₄²	—	2	2	no	—
822	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
823	C₄²	C₂×D₄×C₁₃	1	2	yes	—
824	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
825	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
826	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
827	C₄²	C₂⁴×C₁₃	1	2	yes	—
828	C₁₃	#61005	1	1	yes	characteristic, direct product factor, Sylow
829	C₂³	—	2	2	no	—
830	C₂³	—	4	1	no	—
831	C₂³	—	4	2	no	—
832	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
833	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
834	Q₈	—	2	2	no	—
835	Q₈	—	2	2	no	—
836	Q₈	—	2	2	no	—
837	Q₈	—	2	2	no	—
838	Q₈	—	2	2	no	—
839	Q₈	—	2	2	no	—
840	Q₈	—	4	4	no	—
841	Q₈	—	8	2	no	—
842	Q₈	—	8	2	no	—
843	D₄	—	2	2	no	—
844	D₄	—	2	2	no	—
845	D₄	—	4	4	no	—
846	D₄	—	4	4	no	—
847	D₄	—	8	2	no	—
848	C₂×C₄	—	2	1	no	—
849	C₂×C₄	—	2	1	no	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	2	2	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	2	no	—
856	C₂×C₄	—	2	2	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	4	1	no	—
860	C₂×C₄	—	4	2	no	—
861	C₂×C₄	—	4	2	no	—
862	C₂×C₄	—	4	2	no	—
863	C₂×C₄	—	4	4	no	—
864	C₂×C₄	—	4	4	no	—
865	C₂×C₄	—	8	2	no	—
866	C₂×C₄	—	8	2	no	—
867	C₂×C₄	—	8	2	no	—
868	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
869	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
870	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
871	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
872	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
873	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
874	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
875	C₈	—	2	1	no	—
876	C₈	—	2	1	no	—
877	C₈	—	2	2	no	—
878	C₈	—	2	2	no	—
879	C₈	—	2	1	no	—
880	C₈	—	2	1	no	—
881	C₂²	—	2	2	no	—
882	C₂²	—	2	2	no	—
883	C₂²	—	2	2	no	—
884	C₂²	—	2	2	no	—
885	C₂²	—	2	1	no	—
886	C₂²	—	4	2	no	—
887	C₂²	—	4	2	no	—
888	C₂²	—	4	2	no	—
889	C₂²	—	8	2	no	—
890	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
891	C₄	—	2	2	no	—
892	C₄	—	2	2	no	—
893	C₄	—	2	2	no	—
894	C₄	—	2	2	no	—
895	C₄	—	2	2	no	—
896	C₄	—	2	1	no	—
897	C₄	—	4	2	no	—
898	C₄	—	4	2	no	—
899	C₄	—	4	2	no	—
900	C₄	—	4	2	no	—
901	C₄	—	4	2	no	—
902	C₄	—	4	2	no	—
903	C₄	—	4	2	no	—
904	C₄	C₁₃×#585	1	1	yes	characteristic
905	C₄	C₁₃×#585	1	1	yes	characteristic
906	C₂	—	4	1	no	—
907	C₂	—	4	2	no	—
908	C₂	—	8	2	no	—
909	C₂	C₁₃×#3449	1	1	yes	characteristic
910	C₂	C₁₃×#3586	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3197	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₁₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3495	C₂	semidirect
2. C₁₃×#3256	C₂	semidirect
3. C₁₃×#3255	C₂	semidirect
4. C₁₃×#3252	C₂	semidirect
5. C₁₃×#3244	C₂	semidirect
6. C₁₃×#3242	C₂	semidirect
7. C₁₃×#3225	C₂	semidirect
8. C₁₃×#3223	C₂	semidirect
10. C₁₃×#3196	C₂	semidirect
11. C₁₃×#3195	C₂	semidirect
12. C₁₃×#3185	C₂	semidirect
13. C₁₃×#3183	C₂	semidirect
14. C₁₃×#3172	C₂	semidirect
15. C₁₃×#3127	C₂	semidirect
16. C₁₃×#3125	C₂	semidirect
17. C₁₃×#3121	C₂	semidirect
18. C₁₃×#3120	C₂	semidirect
19. C₁₃×#2921	C₂	semidirect
43. C₁₃×#501	C₂²	semidirect
44. C₁₃×#499	C₂²	semidirect
45. C₁₃×#498	C₂²	semidirect
46. C₁₃×#497	C₂²	semidirect
47. C₁₃×#495	C₂²	semidirect
48. C₁₃×#494	C₂²	semidirect
49. C₁₃×#491	C₂²	semidirect
50. C₁₃×#489	C₂²	semidirect
51. C₁₃×#488	C₂²	semidirect
52. C₁₃×#487	C₂²	semidirect
61. C₁₃×#479	C₂²	semidirect
62. C₁₃×#479	C₂²	semidirect
63. C₁₃×#479	C₂²	semidirect
64. C₁₃×#478	C₂²	semidirect
65. C₁₃×#477	C₂²	semidirect
66. C₁₃×#476	C₂²	semidirect
67. C₁₃×#475	C₂²	semidirect
68. C₁₃×#475	C₂²	semidirect
79. C₁₃×#464	C₂²	semidirect
80. C₁₃×#464	C₂²	semidirect
81. C₁₃×#464	C₂²	semidirect
82. C₁₃×#463	C₂²	semidirect
83. C₁₃×#462	C₂²	semidirect
84. C₁₃×#462	C₂²	semidirect
85. C₁₃×#462	C₂²	semidirect
86. C₁₃×#461	C₂²	semidirect
95. C₁₃×#442	C₂²	semidirect
96. C₁₃×#441	C₂²	semidirect
97. C₁₃×#441	C₂²	semidirect
98. C₁₃×#441	C₂²	semidirect
99. C₁₃×#441	C₂²	semidirect
100. C₁₃×#440	C₂²	semidirect
101. C₄×C₁₃×Q₁₆	C₂²	semidirect
102. C₄×C₁₃×Q₁₆	C₂²	semidirect
103. C₄×C₁₃×SD₁₆	C₂²	semidirect
104. C₄×C₁₃×SD₁₆	C₂²	semidirect
262. #61005	C₁₃	direct (N × H)
374. #3495	C₂×C₁₃	semidirect
375. #3256	C₂×C₁₃	semidirect
376. #3255	C₂×C₁₃	semidirect
377. #3252	C₂×C₁₃	semidirect
378. #3244	C₂×C₁₃	semidirect
379. #3242	C₂×C₁₃	semidirect
380. #3225	C₂×C₁₃	semidirect
381. #3223	C₂×C₁₃	semidirect
383. #3196	C₂×C₁₃	semidirect
384. #3195	C₂×C₁₃	semidirect
385. #3185	C₂×C₁₃	semidirect
386. #3183	C₂×C₁₃	semidirect
387. #3172	C₂×C₁₃	semidirect
388. #3127	C₂×C₁₃	semidirect
389. #3125	C₂×C₁₃	semidirect
390. #3121	C₂×C₁₃	semidirect
391. #3120	C₂×C₁₃	semidirect
392. #2921	C₂×C₁₃	semidirect
468. #501	C₂²×C₁₃	semidirect
469. #499	C₂²×C₁₃	semidirect
470. #498	C₂²×C₁₃	semidirect
471. #497	C₂²×C₁₃	semidirect
472. #495	C₂²×C₁₃	semidirect
473. #494	C₂²×C₁₃	semidirect
474. #491	C₂²×C₁₃	semidirect
475. #489	C₂²×C₁₃	semidirect
476. #488	C₂²×C₁₃	semidirect
477. #487	C₂²×C₁₃	semidirect
486. #479	C₂²×C₁₃	semidirect
487. #479	C₂²×C₁₃	semidirect
488. #479	C₂²×C₁₃	semidirect
489. #478	C₂²×C₁₃	semidirect
490. #477	C₂²×C₁₃	semidirect
491. #476	C₂²×C₁₃	semidirect
492. #475	C₂²×C₁₃	semidirect
493. #475	C₂²×C₁₃	semidirect
504. #464	C₂²×C₁₃	semidirect
505. #464	C₂²×C₁₃	semidirect
506. #464	C₂²×C₁₃	semidirect
507. #463	C₂²×C₁₃	semidirect
508. #462	C₂²×C₁₃	semidirect
509. #462	C₂²×C₁₃	semidirect
510. #462	C₂²×C₁₃	semidirect
511. #461	C₂²×C₁₃	semidirect
520. #442	C₂²×C₁₃	semidirect
521. #441	C₂²×C₁₃	semidirect
522. #441	C₂²×C₁₃	semidirect
523. #441	C₂²×C₁₃	semidirect
524. #441	C₂²×C₁₃	semidirect
525. #440	C₂²×C₁₃	semidirect
526. C₄×Q₁₆	C₂²×C₁₃	semidirect
527. C₄×Q₁₆	C₂²×C₁₃	semidirect
528. C₄×SD₁₆	C₂²×C₁₃	semidirect
529. C₄×SD₁₆	C₂²×C₁₃	semidirect
828. C₁₃	#61005	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×#3495	2
C₁₃×#3256	2
C₁₃×#3255	2
C₁₃×#3252	2
C₁₃×#3244	2
C₁₃×#3242	2
C₁₃×#3225	2
C₁₃×#3223	2
C₁₃×#3197	2
C₁₃×#3196	2
C₁₃×#3195	2
C₁₃×#3185	2
C₁₃×#3183	2
C₁₃×#3172	2
C₁₃×#3127	2
C₁₃×#3125	2
C₁₃×#3121	2
C₁₃×#3120	2
C₁₃×#2921	2
#61005	13

Subgroups — C13×#61005 #15747344

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61005 #15747344