Subgroups — C₁₃×#60765 #15747104

Order 3328.

2250 conjugacy classes of subgroups.

The subgroup lattice has 1032 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3488	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#537	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3204	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3198	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3196	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3192	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3188	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3187	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3099	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3092	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×#481	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3062	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3060	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3012	C₂	1	2	yes	maximal, complemented
15	C₁₃×#3006	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#3002	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#2880	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	1	yes	characteristic, complemented
19	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
20	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
22	C₂×C₁₃×#135	C₂²	1	2	yes	complemented
23	C₂×C₁₃×#131	C₂²	1	2	yes	complemented
24	C₁₃×#550	—	2	1	no	—
25	C₁₃×#548	—	2	1	no	—
26	C₁₃×#546	—	2	2	no	—
27	C₁₃×#546	—	2	1	no	—
28	D₄²×C₁₃	—	2	1	no	—
29	D₄²×C₁₃	—	2	2	no	—
30	C₁₃×#537	—	2	2	no	—
31	C₁₃×#537	—	2	1	no	—
32	C₁₃×#537	—	2	1	no	—
33	C₁₃×#537	C₂²	1	2	yes	—
34	C₁₃×#537	C₂²	1	1	yes	characteristic, complemented
35	C₁₃×#537	C₂²	1	2	yes	complemented
36	C₁₃×#537	C₂²	1	4	yes	complemented
37	C₁₃×#537	C₂²	1	2	yes	complemented
38	C₁₃×#535	C₂²	1	1	yes	characteristic, complemented
39	C₁₃×#535	C₂²	1	2	yes	complemented
40	C₁₃×#525	C₂²	1	1	yes	characteristic
41	C₁₃×#525	C₂²	1	2	yes	—
42	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
43	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
44	C₂×C₁₃×#121	—	2	1	no	—
45	C₂×C₁₃×#121	—	2	2	no	—
46	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
47	C₂×C₁₃×#121	C₂²	1	2	yes	—
48	C₂×C₁₃×#121	C₂²	1	2	yes	complemented
49	C₁₃×#520	C₂²	1	1	yes	characteristic, complemented
50	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
51	C₁₃×#485	C₂²	1	4	yes	complemented
52	C₁₃×#484	C₂²	1	2	yes	complemented
53	C₁₃×#483	C₂²	1	2	yes	complemented
54	C₁₃×#483	C₂²	1	4	yes	complemented
55	C₁₃×#482	C₂²	1	4	yes	complemented
56	C₁₃×#481	C₂²	1	2	yes	complemented
57	C₁₃×#481	C₂²	1	2	yes	complemented
58	C₁₃×#481	C₂²	1	4	yes	complemented
59	C₁₃×#481	C₂²	1	2	yes	complemented
60	C₁₃×#481	C₂²	1	4	yes	complemented
61	C₁₃×#480	C₂²	1	2	yes	complemented
62	C₁₃×#470	C₂²	1	4	yes	complemented
63	C₁₃×#469	C₂²	1	4	yes	complemented
64	C₁₃×#469	C₂²	1	4	yes	complemented
65	C₁₃×#468	C₂²	1	4	yes	complemented
66	C₁₃×#466	C₂²	1	4	yes	complemented
67	C₁₃×#465	C₂²	1	4	yes	complemented
68	C₁₃×#465	C₂²	1	4	yes	complemented
69	C₁₃×#465	C₂²	1	4	yes	complemented
70	C₁₃×#452	C₂²	1	4	yes	complemented
71	C₁₃×#452	C₂²	1	2	yes	complemented
72	C₁₃×#451	C₂²	1	1	yes	characteristic, complemented
73	C₁₃×#450	C₂²	1	4	yes	complemented
74	C₁₃×#450	C₂²	1	1	yes	characteristic, complemented
75	C₁₃×#449	C₂²	1	4	yes	complemented
76	C₁₃×#449	C₂²	1	4	yes	complemented
77	C₁₃×#449	C₂²	1	2	yes	complemented
78	C₁₃×#448	C₂²	1	2	yes	complemented
79	C₁₃×#448	C₂²	1	1	yes	characteristic, complemented
80	C₁₃×#447	C₂²	1	2	yes	complemented
81	C₁₃×#447	C₂²	1	4	yes	complemented
82	C₁₃×#447	C₂²	1	1	yes	characteristic, complemented
83	C₁₃×#428	C₂²	1	2	yes	complemented
84	C₂×C₁₃×#106	C₂²	1	2	yes	complemented
85	C₁₃×#417	C₂²	1	2	yes	complemented
86	C₁₃×#417	C₂²	1	2	yes	complemented
87	C₁₃×#416	C₂²	1	2	yes	complemented
88	C₂×C₁₃×#102	C₂²	1	2	yes	complemented
89	C₁₃×#408	C₂²	1	2	yes	complemented
90	C₁₃×#408	C₂²	1	4	yes	complemented
91	C₁₃×#407	C₂²	1	1	yes	characteristic, complemented
92	C₁₃×#407	C₂²	1	2	yes	complemented
93	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
94	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	complemented
95	C₁₃×H(5,𝔽₂)	—	4	4	no	—
96	C₂×C₁₃×#41	—	2	1	no	—
97	C₂×C₁₃×#41	—	2	1	no	—
98	C₂×C₁₃×#41	—	2	1	no	—
99	C₂×C₁₃×#41	—	4	4	no	—
100	C₂×C₁₃×#41	—	4	4	no	—
101	C₂×C₁₃×#41	D₄	1	2	yes	—
102	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
103	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
104	C₂×C₁₃×#41	C₂³	1	2	yes	—
105	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
106	C₂×C₁₃×#41	C₂³	1	2	yes	—
107	C₂×C₁₃×#41	C₂³	1	2	yes	—
108	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
109	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
110	C₂×C₁₃×#41	C₂³	1	2	yes	—
111	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
112	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
113	C₂²×D₄×C₁₃	—	2	1	no	—
114	C₂²×D₄×C₁₃	—	2	2	no	—
115	C₂²×D₄×C₁₃	—	2	1	no	—
116	C₂²×D₄×C₁₃	—	2	2	no	—
117	C₂²×D₄×C₁₃	—	2	2	no	—
118	C₂²×D₄×C₁₃	—	2	1	no	—
119	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
120	C₂²×D₄×C₁₃	D₄	1	2	yes	—
121	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
122	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
123	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
124	C₂³×C₄×C₁₃	—	2	1	no	—
125	C₂³×C₄×C₁₃	—	2	1	no	—
126	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
127	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
128	C₁₃×AGL(1,ℤ/8)	—	4	4	no	—
129	C₁₃×#135	—	4	4	no	—
130	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
131	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
132	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
133	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
134	C₂×C₁₃×D₈	C₂³	1	2	yes	—
135	C₂×C₁₃×D₈	C₂³	1	4	yes	—
136	C₁₃×#131	—	4	4	no	—
137	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
138	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
139	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
140	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
141	C₁₃×#127	—	2	1	no	—
142	C₁₃×#127	—	2	2	no	—
143	C₁₃×#124	—	2	1	no	—
144	C₁₃×#124	—	2	2	no	—
145	C₁₃×#123	—	2	1	no	—
146	C₁₃×#123	—	2	2	no	—
147	C₁₃×C₂²⋊Q₈	—	2	2	no	—
148	C₁₃×C₂²⋊Q₈	—	2	2	no	—
149	C₁₃×C₂²⋊Q₈	—	2	4	no	—
150	C₁₃×C₂²⋊Q₈	—	2	1	no	—
151	C₁₃×C₂²⋊Q₈	—	2	2	no	—
152	C₁₃×C₂²⋊Q₈	—	2	2	no	—
153	C₁₃×C₂²⋊Q₈	—	2	2	no	—
154	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
155	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
156	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
157	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
158	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
159	C₁₃×#121	—	2	2	no	—
160	C₁₃×#121	—	2	4	no	—
161	C₁₃×#121	—	2	2	no	—
162	C₁₃×#121	—	2	4	no	—
163	C₁₃×#121	—	2	4	no	—
164	C₁₃×#121	—	2	4	no	—
165	C₁₃×#121	—	2	4	no	—
166	C₁₃×#121	—	2	2	no	—
167	C₁₃×#121	—	2	2	no	—
168	C₁₃×#121	—	2	2	no	—
169	C₁₃×#121	—	2	1	no	—
170	C₁₃×#121	—	2	2	no	—
171	C₁₃×#121	—	2	1	no	—
172	C₁₃×#121	—	2	2	no	—
173	C₁₃×#121	—	2	1	no	—
174	C₁₃×#121	—	2	2	no	—
175	C₁₃×#121	—	2	2	no	—
176	C₁₃×#121	—	2	2	no	—
177	C₁₃×#121	C₂³	1	2	yes	—
178	C₁₃×#121	C₂³	1	1	yes	characteristic
179	C₁₃×#121	C₂³	1	4	yes	—
180	C₁₃×#121	C₂³	1	1	yes	characteristic
181	C₁₃×#121	C₂³	1	2	yes	—
182	C₁₃×#121	C₂³	1	2	yes	—
183	C₁₃×#121	C₂³	1	2	yes	—
184	C₁₃×#121	C₂³	1	4	yes	—
185	C₁₃×#121	C₂³	1	2	yes	—
186	C₁₃×#120	—	2	1	no	—
187	C₁₃×#120	—	2	2	no	—
188	C₁₃×#120	—	2	2	no	—
189	C₁₃×#120	—	2	2	no	—
190	C₁₃×#120	—	2	2	no	—
191	C₄×Q₈×C₁₃	—	2	1	no	—
192	C₄×D₄×C₁₃	—	2	2	no	—
193	C₄×D₄×C₁₃	—	2	1	no	—
194	C₄×D₄×C₁₃	—	2	1	no	—
195	C₄×D₄×C₁₃	—	2	2	no	—
196	C₄×D₄×C₁₃	—	2	1	no	—
197	C₄×D₄×C₁₃	—	2	2	no	—
198	C₁₃×#117	C₂³	1	1	yes	characteristic
199	C₁₃×#117	C₂³	1	2	yes	—
200	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
201	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
202	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
203	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
204	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
205	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
206	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
207	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
208	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
209	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
210	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
211	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
212	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
213	C₁₃×#107	C₂³	1	4	yes	—
214	C₁₃×#106	C₂³	1	4	yes	—
215	C₁₃×#106	C₂³	1	4	yes	—
216	C₁₃×#106	C₂³	1	4	yes	—
217	C₁₃×#103	C₂³	1	2	yes	—
218	C₁₃×#103	C₂³	1	2	yes	—
219	C₁₃×#103	C₂³	1	4	yes	—
220	C₁₃×#103	C₂³	1	4	yes	—
221	C₁₃×#102	C₂³	1	4	yes	—
222	C₁₃×#102	C₂³	1	4	yes	—
223	C₁₃×#102	C₂³	1	2	yes	—
224	C₁₃×#102	C₂³	1	2	yes	—
225	C₁₃×#102	C₂³	1	4	yes	—
226	C₁₃×#102	C₂³	1	4	yes	—
227	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
228	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
229	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
230	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
231	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
232	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
233	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
234	#60765	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
235	C₂⁴×C₁₃	—	2	1	no	—
236	C₂⁴×C₁₃	—	2	2	no	—
237	C₂⁴×C₁₃	—	2	1	no	—
238	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
239	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
240	C₁₃×#41	—	2	4	no	—
241	C₁₃×#41	—	2	4	no	—
242	C₁₃×#41	—	2	4	no	—
243	C₁₃×#41	—	2	4	no	—
244	C₁₃×#41	—	2	4	no	—
245	C₁₃×#41	—	4	4	no	—
246	C₁₃×#41	—	4	4	no	—
247	C₁₃×#41	—	4	2	no	—
248	C₁₃×#41	—	4	2	no	—
249	C₁₃×#41	—	4	2	no	—
250	C₁₃×#41	—	4	2	no	—
251	C₁₃×#41	—	4	4	no	—
252	C₁₃×#41	—	4	4	no	—
253	C₁₃×#41	—	4	4	no	—
254	C₁₃×#41	—	4	4	no	—
255	C₂×Q₈×C₁₃	—	2	1	no	—
256	C₂×Q₈×C₁₃	—	4	2	no	—
257	C₂×Q₈×C₁₃	—	4	2	no	—
258	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
259	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
260	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
261	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
262	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
263	C₂×D₄×C₁₃	—	2	1	no	—
264	C₂×D₄×C₁₃	—	2	2	no	—
265	C₂×D₄×C₁₃	—	2	2	no	—
266	C₂×D₄×C₁₃	—	2	1	no	—
267	C₂×D₄×C₁₃	—	2	2	no	—
268	C₂×D₄×C₁₃	—	2	2	no	—
269	C₂×D₄×C₁₃	—	2	2	no	—
270	C₂×D₄×C₁₃	—	2	1	no	—
271	C₂×D₄×C₁₃	—	2	2	no	—
272	C₂×D₄×C₁₃	—	2	2	no	—
273	C₂×D₄×C₁₃	—	2	2	no	—
274	C₂×D₄×C₁₃	—	2	4	no	—
275	C₂×D₄×C₁₃	—	2	4	no	—
276	C₂×D₄×C₁₃	—	2	1	no	—
277	C₂×D₄×C₁₃	—	2	2	no	—
278	C₂×D₄×C₁₃	—	2	1	no	—
279	C₂×D₄×C₁₃	—	2	4	no	—
280	C₂×D₄×C₁₃	—	4	2	no	—
281	C₂×D₄×C₁₃	—	4	2	no	—
282	C₂×D₄×C₁₃	—	4	4	no	—
283	C₂×D₄×C₁₃	—	4	4	no	—
284	C₂×D₄×C₁₃	—	4	8	no	—
285	C₂×D₄×C₁₃	—	4	4	no	—
286	C₂×D₄×C₁₃	—	4	4	no	—
287	C₂×D₄×C₁₃	—	8	4	no	—
288	C₂×D₄×C₁₃	—	8	2	no	—
289	C₂×D₄×C₁₃	—	8	4	no	—
290	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
291	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
292	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
293	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
294	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
295	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
296	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
297	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
298	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
299	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
300	C₂²×C₄×C₁₃	—	2	4	no	—
301	C₂²×C₄×C₁₃	—	2	2	no	—
302	C₂²×C₄×C₁₃	—	2	1	no	—
303	C₂²×C₄×C₁₃	—	2	2	no	—
304	C₂²×C₄×C₁₃	—	2	1	no	—
305	C₂²×C₄×C₁₃	—	2	2	no	—
306	C₂²×C₄×C₁₃	—	2	2	no	—
307	C₂²×C₄×C₁₃	—	2	2	no	—
308	C₂²×C₄×C₁₃	—	2	1	no	—
309	C₂²×C₄×C₁₃	—	2	2	no	—
310	C₂²×C₄×C₁₃	—	2	2	no	—
311	C₂²×C₄×C₁₃	—	4	4	no	—
312	C₂²×C₄×C₁₃	—	4	4	no	—
313	C₂²×C₄×C₁₃	—	8	2	no	—
314	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
315	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
316	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
317	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
318	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
319	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
320	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
321	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
322	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
323	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
324	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
325	C₁₃×Q₁₆	—	4	2	no	—
326	C₁₃×SD₁₆	—	4	2	no	—
327	C₁₃×SD₁₆	—	4	2	no	—
328	C₁₃×SD₁₆	—	4	4	no	—
329	C₁₃×D₈	—	4	2	no	—
330	C₁₃×D₈	—	4	4	no	—
331	C₁₃×M₁₆	—	2	4	no	—
332	C₁₃×M₁₆	—	4	4	no	—
333	C₂×C₈×C₁₃	—	2	4	no	—
334	C₂×C₈×C₁₃	—	4	4	no	—
335	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
336	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
337	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
338	C₁₃×C₄⋊C₄	—	2	2	no	—
339	C₁₃×C₄⋊C₄	—	2	2	no	—
340	C₁₃×C₄⋊C₄	—	2	2	no	—
341	C₁₃×C₄⋊C₄	—	2	4	no	—
342	C₁₃×C₄⋊C₄	—	2	4	no	—
343	C₁₃×C₄⋊C₄	—	2	2	no	—
344	C₁₃×C₄⋊C₄	—	2	1	no	—
345	C₁₃×C₄⋊C₄	—	2	1	no	—
346	C₁₃×C₄⋊C₄	—	2	2	no	—
347	C₁₃×C₄⋊C₄	—	2	1	no	—
348	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
349	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
350	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
351	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
352	C₁₃×C₂²⋊C₄	—	2	4	no	—
353	C₁₃×C₂²⋊C₄	—	2	4	no	—
354	C₁₃×C₂²⋊C₄	—	2	2	no	—
355	C₁₃×C₂²⋊C₄	—	2	1	no	—
356	C₁₃×C₂²⋊C₄	—	2	1	no	—
357	C₁₃×C₂²⋊C₄	—	2	2	no	—
358	C₁₃×C₂²⋊C₄	—	2	1	no	—
359	C₁₃×C₂²⋊C₄	—	2	2	no	—
360	C₁₃×C₂²⋊C₄	—	2	1	no	—
361	C₁₃×C₂²⋊C₄	—	2	2	no	—
362	C₁₃×C₂²⋊C₄	—	2	2	no	—
363	C₁₃×C₂²⋊C₄	—	2	2	no	—
364	C₁₃×C₂²⋊C₄	—	2	4	no	—
365	C₁₃×C₂²⋊C₄	—	2	4	no	—
366	C₁₃×C₂²⋊C₄	—	2	2	no	—
367	C₁₃×C₂²⋊C₄	—	2	1	no	—
368	C₄²×C₁₃	—	2	2	no	—
369	C₄²×C₁₃	—	2	1	no	—
370	#3488	C₂×C₁₃	1	1	yes	characteristic, complemented
371	C₂×#537	C₂×C₁₃	1	1	yes	characteristic, complemented
372	#3204	C₂×C₁₃	1	4	yes	complemented
373	#3198	C₂×C₁₃	1	4	yes	complemented
374	#3196	C₂×C₁₃	1	2	yes	complemented
375	#3192	C₂×C₁₃	1	2	yes	complemented
376	#3188	C₂×C₁₃	1	2	yes	complemented
377	#3187	C₂×C₁₃	1	2	yes	complemented
378	#3099	C₂×C₁₃	1	2	yes	complemented
379	#3092	C₂×C₁₃	1	1	yes	characteristic, complemented
380	C₂×#481	C₂×C₁₃	1	1	yes	characteristic, complemented
381	#3062	C₂×C₁₃	1	2	yes	complemented
382	#3060	C₂×C₁₃	1	2	yes	complemented
383	#3012	C₂×C₁₃	1	2	yes	complemented
384	#3006	C₂×C₁₃	1	1	yes	characteristic, complemented
385	#3002	C₂×C₁₃	1	1	yes	characteristic, complemented
386	#2880	C₂×C₁₃	1	1	yes	characteristic, complemented
387	C₂³×C₁₃	—	2	2	no	—
388	C₂³×C₁₃	—	2	2	no	—
389	C₂³×C₁₃	—	2	4	no	—
390	C₂³×C₁₃	—	2	2	no	—
391	C₂³×C₁₃	—	2	2	no	—
392	C₂³×C₁₃	—	2	1	no	—
393	C₂³×C₁₃	—	4	1	no	—
394	C₂³×C₁₃	—	4	2	no	—
395	C₂³×C₁₃	—	4	2	no	—
396	C₂³×C₁₃	—	4	2	no	—
397	C₂³×C₁₃	—	4	2	no	—
398	C₂³×C₁₃	—	4	4	no	—
399	C₂³×C₁₃	—	4	2	no	—
400	C₂³×C₁₃	—	4	2	no	—
401	C₂³×C₁₃	—	8	1	no	—
402	C₂³×C₁₃	—	8	2	no	—
403	C₂³×C₁₃	—	8	1	no	—
404	C₂³×C₁₃	—	8	2	no	—
405	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
406	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
407	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
408	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
409	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
410	Q₈×C₁₃	—	2	2	no	—
411	Q₈×C₁₃	—	2	2	no	—
412	Q₈×C₁₃	—	2	2	no	—
413	Q₈×C₁₃	—	2	2	no	—
414	Q₈×C₁₃	—	2	2	no	—
415	Q₈×C₁₃	—	4	2	no	—
416	Q₈×C₁₃	—	4	2	no	—
417	D₄×C₁₃	—	2	4	no	—
418	D₄×C₁₃	—	2	4	no	—
419	D₄×C₁₃	—	2	2	no	—
420	D₄×C₁₃	—	2	2	no	—
421	D₄×C₁₃	—	2	2	no	—
422	D₄×C₁₃	—	2	4	no	—
423	D₄×C₁₃	—	2	2	no	—
424	D₄×C₁₃	—	2	2	no	—
425	D₄×C₁₃	—	4	2	no	—
426	D₄×C₁₃	—	4	2	no	—
427	D₄×C₁₃	—	4	2	no	—
428	D₄×C₁₃	—	4	4	no	—
429	D₄×C₁₃	—	4	2	no	—
430	D₄×C₁₃	—	4	4	no	—
431	D₄×C₁₃	—	4	4	no	—
432	D₄×C₁₃	—	4	2	no	—
433	D₄×C₁₃	—	4	4	no	—
434	D₄×C₁₃	—	4	4	no	—
435	D₄×C₁₃	—	4	2	no	—
436	D₄×C₁₃	—	4	2	no	—
437	D₄×C₁₃	—	8	1	no	—
438	D₄×C₁₃	—	8	2	no	—
439	D₄×C₁₃	—	8	4	no	—
440	D₄×C₁₃	—	8	4	no	—
441	D₄×C₁₃	—	8	2	no	—
442	D₄×C₁₃	—	8	2	no	—
443	D₄×C₁₃	—	8	2	no	—
444	C₂×C₄×C₁₃	—	2	2	no	—
445	C₂×C₄×C₁₃	—	2	2	no	—
446	C₂×C₄×C₁₃	—	2	2	no	—
447	C₂×C₄×C₁₃	—	2	4	no	—
448	C₂×C₄×C₁₃	—	2	2	no	—
449	C₂×C₄×C₁₃	—	2	2	no	—
450	C₂×C₄×C₁₃	—	2	4	no	—
451	C₂×C₄×C₁₃	—	2	1	no	—
452	C₂×C₄×C₁₃	—	2	2	no	—
453	C₂×C₄×C₁₃	—	2	1	no	—
454	C₂×C₄×C₁₃	—	2	4	no	—
455	C₂×C₄×C₁₃	—	2	1	no	—
456	C₂×C₄×C₁₃	—	2	2	no	—
457	C₂×C₄×C₁₃	—	4	2	no	—
458	C₂×C₄×C₁₃	—	4	2	no	—
459	C₂×C₄×C₁₃	—	4	2	no	—
460	C₂×C₄×C₁₃	—	4	4	no	—
461	C₂×C₄×C₁₃	—	4	4	no	—
462	C₂×C₄×C₁₃	—	4	2	no	—
463	C₂×C₄×C₁₃	—	4	4	no	—
464	C₂×C₄×C₁₃	—	4	4	no	—
465	C₂×C₄×C₁₃	—	4	2	no	—
466	C₂×C₄×C₁₃	—	8	2	no	—
467	C₂×C₄×C₁₃	—	8	2	no	—
468	C₂×C₄×C₁₃	—	8	1	no	—
469	C₂×C₄×C₁₃	—	8	2	no	—
470	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
471	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
472	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
473	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
474	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
475	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
476	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
477	C₈×C₁₃	—	2	2	no	—
478	C₈×C₁₃	—	2	2	no	—
479	C₈×C₁₃	—	2	4	no	—
480	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	1	yes	characteristic, complemented
481	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
482	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic, complemented
483	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	complemented
484	C₂×#135	C₂²×C₁₃	1	2	yes	complemented
485	C₂×#131	C₂²×C₁₃	1	2	yes	complemented
486	#550	—	2	1	no	—
487	#548	—	2	1	no	—
488	#546	—	2	2	no	—
489	#546	—	2	1	no	—
490	D₄²	—	2	1	no	—
491	D₄²	—	2	2	no	—
492	#537	—	2	2	no	—
493	#537	—	2	1	no	—
494	#537	—	2	1	no	—
495	#537	C₂²×C₁₃	1	2	yes	—
496	#537	C₂²×C₁₃	1	4	yes	complemented
497	#537	C₂²×C₁₃	1	2	yes	complemented
498	#537	C₂²×C₁₃	1	2	yes	complemented
499	#537	C₂²×C₁₃	1	1	yes	characteristic, complemented
500	#535	C₂²×C₁₃	1	2	yes	complemented
501	#535	C₂²×C₁₃	1	1	yes	characteristic, complemented
502	#525	C₂²×C₁₃	1	1	yes	characteristic
503	#525	C₂²×C₁₃	1	2	yes	—
504	C₂×C₂²⋊Q₈	—	2	1	no	—
505	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
506	C₂×#121	—	2	1	no	—
507	C₂×#121	—	2	2	no	—
508	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
509	C₂×#121	C₂²×C₁₃	1	2	yes	—
510	C₂×#121	C₂²×C₁₃	1	2	yes	complemented
511	#520	C₂²×C₁₃	1	1	yes	characteristic, complemented
512	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
513	#485	C₂²×C₁₃	1	4	yes	complemented
514	#484	C₂²×C₁₃	1	2	yes	complemented
515	#483	C₂²×C₁₃	1	2	yes	complemented
516	#483	C₂²×C₁₃	1	4	yes	complemented
517	#482	C₂²×C₁₃	1	4	yes	complemented
518	#481	C₂²×C₁₃	1	2	yes	complemented
519	#481	C₂²×C₁₃	1	2	yes	complemented
520	#481	C₂²×C₁₃	1	4	yes	complemented
521	#481	C₂²×C₁₃	1	2	yes	complemented
522	#481	C₂²×C₁₃	1	4	yes	complemented
523	#480	C₂²×C₁₃	1	2	yes	complemented
524	#470	C₂²×C₁₃	1	4	yes	complemented
525	#469	C₂²×C₁₃	1	4	yes	complemented
526	#469	C₂²×C₁₃	1	4	yes	complemented
527	#468	C₂²×C₁₃	1	4	yes	complemented
528	#466	C₂²×C₁₃	1	4	yes	complemented
529	#465	C₂²×C₁₃	1	4	yes	complemented
530	#465	C₂²×C₁₃	1	4	yes	complemented
531	#465	C₂²×C₁₃	1	4	yes	complemented
532	#452	C₂²×C₁₃	1	4	yes	complemented
533	#452	C₂²×C₁₃	1	2	yes	complemented
534	#451	C₂²×C₁₃	1	1	yes	characteristic, complemented
535	#450	C₂²×C₁₃	1	4	yes	complemented
536	#450	C₂²×C₁₃	1	1	yes	characteristic, complemented
537	#449	C₂²×C₁₃	1	4	yes	complemented
538	#449	C₂²×C₁₃	1	2	yes	complemented
539	#449	C₂²×C₁₃	1	4	yes	complemented
540	#448	C₂²×C₁₃	1	1	yes	characteristic, complemented
541	#448	C₂²×C₁₃	1	2	yes	complemented
542	#447	C₂²×C₁₃	1	2	yes	complemented
543	#447	C₂²×C₁₃	1	1	yes	characteristic, complemented
544	#447	C₂²×C₁₃	1	4	yes	complemented
545	#428	C₂²×C₁₃	1	2	yes	complemented
546	C₂×#106	C₂²×C₁₃	1	2	yes	complemented
547	#417	C₂²×C₁₃	1	2	yes	complemented
548	#417	C₂²×C₁₃	1	2	yes	complemented
549	#416	C₂²×C₁₃	1	2	yes	complemented
550	C₂×#102	C₂²×C₁₃	1	2	yes	complemented
551	#408	C₂²×C₁₃	1	2	yes	complemented
552	#408	C₂²×C₁₃	1	4	yes	complemented
553	#407	C₂²×C₁₃	1	1	yes	characteristic, complemented
554	#407	C₂²×C₁₃	1	2	yes	complemented
555	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
556	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	complemented
557	C₂²×C₁₃	—	2	1	no	—
558	C₂²×C₁₃	—	2	1	no	—
559	C₂²×C₁₃	—	2	1	no	—
560	C₂²×C₁₃	—	2	1	no	—
561	C₂²×C₁₃	—	2	1	no	—
562	C₂²×C₁₃	—	2	2	no	—
563	C₂²×C₁₃	—	2	2	no	—
564	C₂²×C₁₃	—	2	1	no	—
565	C₂²×C₁₃	—	2	2	no	—
566	C₂²×C₁₃	—	2	2	no	—
567	C₂²×C₁₃	—	2	2	no	—
568	C₂²×C₁₃	—	2	1	no	—
569	C₂²×C₁₃	—	2	2	no	—
570	C₂²×C₁₃	—	4	4	no	—
571	C₂²×C₁₃	—	4	2	no	—
572	C₂²×C₁₃	—	4	2	no	—
573	C₂²×C₁₃	—	4	1	no	—
574	C₂²×C₁₃	—	4	2	no	—
575	C₂²×C₁₃	—	4	2	no	—
576	C₂²×C₁₃	—	4	1	no	—
577	C₂²×C₁₃	—	4	2	no	—
578	C₂²×C₁₃	—	4	1	no	—
579	C₂²×C₁₃	—	4	2	no	—
580	C₂²×C₁₃	—	8	4	no	—
581	C₂²×C₁₃	—	8	4	no	—
582	C₂²×C₁₃	—	16	2	no	—
583	C₂²×C₁₃	—	16	4	no	—
584	C₂²×C₁₃	#534	1	2	yes	—
585	C₂²×C₁₃	#577	1	2	yes	—
586	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
587	C₄×C₁₃	—	2	1	no	—
588	C₄×C₁₃	—	2	1	no	—
589	C₄×C₁₃	—	2	2	no	—
590	C₄×C₁₃	—	2	2	no	—
591	C₄×C₁₃	—	4	4	no	—
592	C₄×C₁₃	—	4	1	no	—
593	C₄×C₁₃	—	4	1	no	—
594	C₄×C₁₃	—	4	2	no	—
595	C₄×C₁₃	—	4	2	no	—
596	C₄×C₁₃	—	4	1	no	—
597	C₄×C₁₃	#534	1	2	yes	—
598	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
599	H(5,𝔽₂)	—	4	4	no	—
600	C₂×#41	—	2	1	no	—
601	C₂×#41	—	2	1	no	—
602	C₂×#41	—	2	1	no	—
603	C₂×#41	—	4	4	no	—
604	C₂×#41	—	4	4	no	—
605	C₂×#41	D₄×C₁₃	1	2	yes	—
606	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
607	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
608	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
609	C₂×#41	C₂³×C₁₃	1	2	yes	—
610	C₂×#41	C₂³×C₁₃	1	2	yes	—
611	C₂×#41	C₂³×C₁₃	1	2	yes	—
612	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
613	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
614	C₂×#41	C₂³×C₁₃	1	2	yes	—
615	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
616	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
617	C₂²×D₄	—	2	1	no	—
618	C₂²×D₄	—	2	2	no	—
619	C₂²×D₄	—	2	1	no	—
620	C₂²×D₄	—	2	2	no	—
621	C₂²×D₄	—	2	2	no	—
622	C₂²×D₄	—	2	1	no	—
623	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
624	C₂²×D₄	D₄×C₁₃	1	2	yes	—
625	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
626	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
627	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
628	C₂³×C₄	—	2	1	no	—
629	C₂³×C₄	—	2	1	no	—
630	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
631	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
632	AGL(1,ℤ/8)	—	4	4	no	—
633	#135	—	4	4	no	—
634	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
635	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
636	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
637	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
638	C₂×D₈	C₂³×C₁₃	1	2	yes	—
639	C₂×D₈	C₂³×C₁₃	1	4	yes	—
640	#131	—	4	4	no	—
641	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
642	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
643	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
644	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
645	#127	—	2	1	no	—
646	#127	—	2	2	no	—
647	#124	—	2	1	no	—
648	#124	—	2	2	no	—
649	#123	—	2	1	no	—
650	#123	—	2	2	no	—
651	C₂²⋊Q₈	—	2	2	no	—
652	C₂²⋊Q₈	—	2	2	no	—
653	C₂²⋊Q₈	—	2	4	no	—
654	C₂²⋊Q₈	—	2	1	no	—
655	C₂²⋊Q₈	—	2	2	no	—
656	C₂²⋊Q₈	—	2	2	no	—
657	C₂²⋊Q₈	—	2	2	no	—
658	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
659	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
660	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
661	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
662	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
663	#121	—	2	2	no	—
664	#121	—	2	4	no	—
665	#121	—	2	2	no	—
666	#121	—	2	4	no	—
667	#121	—	2	4	no	—
668	#121	—	2	4	no	—
669	#121	—	2	4	no	—
670	#121	—	2	2	no	—
671	#121	—	2	2	no	—
672	#121	—	2	2	no	—
673	#121	—	2	1	no	—
674	#121	—	2	2	no	—
675	#121	—	2	1	no	—
676	#121	—	2	2	no	—
677	#121	—	2	1	no	—
678	#121	—	2	2	no	—
679	#121	—	2	2	no	—
680	#121	—	2	2	no	—
681	#121	C₂³×C₁₃	1	2	yes	—
682	#121	C₂³×C₁₃	1	1	yes	characteristic
683	#121	C₂³×C₁₃	1	2	yes	—
684	#121	C₂³×C₁₃	1	2	yes	—
685	#121	C₂³×C₁₃	1	2	yes	—
686	#121	C₂³×C₁₃	1	4	yes	—
687	#121	C₂³×C₁₃	1	4	yes	—
688	#121	C₂³×C₁₃	1	1	yes	characteristic
689	#121	C₂³×C₁₃	1	2	yes	—
690	#120	—	2	1	no	—
691	#120	—	2	2	no	—
692	#120	—	2	2	no	—
693	#120	—	2	2	no	—
694	#120	—	2	2	no	—
695	C₄×Q₈	—	2	1	no	—
696	C₄×D₄	—	2	2	no	—
697	C₄×D₄	—	2	1	no	—
698	C₄×D₄	—	2	1	no	—
699	C₄×D₄	—	2	2	no	—
700	C₄×D₄	—	2	1	no	—
701	C₄×D₄	—	2	2	no	—
702	#117	C₂³×C₁₃	1	1	yes	characteristic
703	#117	C₂³×C₁₃	1	2	yes	—
704	C₂×C₄⋊C₄	—	2	1	no	—
705	C₂×C₄⋊C₄	—	2	1	no	—
706	C₂×C₄⋊C₄	—	2	1	no	—
707	C₂×C₄⋊C₄	—	2	2	no	—
708	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
709	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
710	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
711	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
712	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
713	C₂×C₂²⋊C₄	—	2	2	no	—
714	C₂×C₂²⋊C₄	—	2	2	no	—
715	C₂×C₂²⋊C₄	—	2	1	no	—
716	C₂×C₂²⋊C₄	—	2	2	no	—
717	#107	C₂³×C₁₃	1	4	yes	—
718	#106	C₂³×C₁₃	1	4	yes	—
719	#106	C₂³×C₁₃	1	4	yes	—
720	#106	C₂³×C₁₃	1	4	yes	—
721	#103	C₂³×C₁₃	1	2	yes	—
722	#103	C₂³×C₁₃	1	2	yes	—
723	#103	C₂³×C₁₃	1	4	yes	—
724	#103	C₂³×C₁₃	1	4	yes	—
725	#102	C₂³×C₁₃	1	4	yes	—
726	#102	C₂³×C₁₃	1	4	yes	—
727	#102	C₂³×C₁₃	1	2	yes	—
728	#102	C₂³×C₁₃	1	2	yes	—
729	#102	C₂³×C₁₃	1	4	yes	—
730	#102	C₂³×C₁₃	1	4	yes	—
731	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
732	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
733	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
734	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
735	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
736	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
737	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
738	C₂×C₁₃	—	2	2	no	—
739	C₂×C₁₃	—	2	2	no	—
740	C₂×C₁₃	—	4	1	no	—
741	C₂×C₁₃	—	4	2	no	—
742	C₂×C₁₃	—	4	2	no	—
743	C₂×C₁₃	—	8	2	no	—
744	C₂×C₁₃	—	8	2	no	—
745	C₂×C₁₃	—	8	1	no	—
746	C₂×C₁₃	C₂×#534	1	1	yes	characteristic
747	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
748	C₂×C₁₃	#3585	1	1	yes	characteristic
749	C₂⁴	—	2	1	no	—
750	C₂⁴	—	2	2	no	—
751	C₂⁴	—	2	1	no	—
752	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
753	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
754	#41	—	2	4	no	—
755	#41	—	2	4	no	—
756	#41	—	2	4	no	—
757	#41	—	2	4	no	—
758	#41	—	2	4	no	—
759	#41	—	4	4	no	—
760	#41	—	4	4	no	—
761	#41	—	4	2	no	—
762	#41	—	4	2	no	—
763	#41	—	4	2	no	—
764	#41	—	4	2	no	—
765	#41	—	4	4	no	—
766	#41	—	4	4	no	—
767	#41	—	4	4	no	—
768	#41	—	4	4	no	—
769	C₂×Q₈	—	2	1	no	—
770	C₂×Q₈	—	4	2	no	—
771	C₂×Q₈	—	4	2	no	—
772	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
773	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
774	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
775	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
776	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
777	C₂×D₄	—	2	1	no	—
778	C₂×D₄	—	2	2	no	—
779	C₂×D₄	—	2	2	no	—
780	C₂×D₄	—	2	1	no	—
781	C₂×D₄	—	2	2	no	—
782	C₂×D₄	—	2	2	no	—
783	C₂×D₄	—	2	2	no	—
784	C₂×D₄	—	2	1	no	—
785	C₂×D₄	—	2	2	no	—
786	C₂×D₄	—	2	2	no	—
787	C₂×D₄	—	2	2	no	—
788	C₂×D₄	—	2	4	no	—
789	C₂×D₄	—	2	4	no	—
790	C₂×D₄	—	2	1	no	—
791	C₂×D₄	—	2	2	no	—
792	C₂×D₄	—	2	1	no	—
793	C₂×D₄	—	2	4	no	—
794	C₂×D₄	—	4	2	no	—
795	C₂×D₄	—	4	2	no	—
796	C₂×D₄	—	4	4	no	—
797	C₂×D₄	—	4	4	no	—
798	C₂×D₄	—	4	8	no	—
799	C₂×D₄	—	4	4	no	—
800	C₂×D₄	—	4	4	no	—
801	C₂×D₄	—	8	4	no	—
802	C₂×D₄	—	8	2	no	—
803	C₂×D₄	—	8	4	no	—
804	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
805	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
806	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
807	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
808	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
809	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
810	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
811	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
812	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
813	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
814	C₂²×C₄	—	2	4	no	—
815	C₂²×C₄	—	2	2	no	—
816	C₂²×C₄	—	2	1	no	—
817	C₂²×C₄	—	2	2	no	—
818	C₂²×C₄	—	2	1	no	—
819	C₂²×C₄	—	2	2	no	—
820	C₂²×C₄	—	2	2	no	—
821	C₂²×C₄	—	2	2	no	—
822	C₂²×C₄	—	2	1	no	—
823	C₂²×C₄	—	2	2	no	—
824	C₂²×C₄	—	2	2	no	—
825	C₂²×C₄	—	4	4	no	—
826	C₂²×C₄	—	4	4	no	—
827	C₂²×C₄	—	8	2	no	—
828	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
829	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
830	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
831	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
832	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
833	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
834	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
835	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
836	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
837	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
838	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
839	Q₁₆	—	4	2	no	—
840	SD₁₆	—	4	2	no	—
841	SD₁₆	—	4	2	no	—
842	SD₁₆	—	4	4	no	—
843	D₈	—	4	2	no	—
844	D₈	—	4	4	no	—
845	M₁₆	—	2	4	no	—
846	M₁₆	—	4	4	no	—
847	C₂×C₈	—	2	4	no	—
848	C₂×C₈	—	4	4	no	—
849	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
850	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
851	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
852	C₄⋊C₄	—	2	2	no	—
853	C₄⋊C₄	—	2	2	no	—
854	C₄⋊C₄	—	2	2	no	—
855	C₄⋊C₄	—	2	4	no	—
856	C₄⋊C₄	—	2	4	no	—
857	C₄⋊C₄	—	2	2	no	—
858	C₄⋊C₄	—	2	1	no	—
859	C₄⋊C₄	—	2	1	no	—
860	C₄⋊C₄	—	2	2	no	—
861	C₄⋊C₄	—	2	1	no	—
862	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
863	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
864	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
865	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
866	C₂²⋊C₄	—	2	4	no	—
867	C₂²⋊C₄	—	2	4	no	—
868	C₂²⋊C₄	—	2	2	no	—
869	C₂²⋊C₄	—	2	1	no	—
870	C₂²⋊C₄	—	2	1	no	—
871	C₂²⋊C₄	—	2	2	no	—
872	C₂²⋊C₄	—	2	1	no	—
873	C₂²⋊C₄	—	2	2	no	—
874	C₂²⋊C₄	—	2	1	no	—
875	C₂²⋊C₄	—	2	2	no	—
876	C₂²⋊C₄	—	2	2	no	—
877	C₂²⋊C₄	—	2	2	no	—
878	C₂²⋊C₄	—	2	4	no	—
879	C₂²⋊C₄	—	2	4	no	—
880	C₂²⋊C₄	—	2	2	no	—
881	C₂²⋊C₄	—	2	1	no	—
882	C₄²	—	2	2	no	—
883	C₄²	—	2	1	no	—
884	C₁₃	#60765	1	1	yes	characteristic, direct product factor, Sylow
885	C₂³	—	2	2	no	—
886	C₂³	—	2	2	no	—
887	C₂³	—	2	4	no	—
888	C₂³	—	2	2	no	—
889	C₂³	—	2	2	no	—
890	C₂³	—	2	1	no	—
891	C₂³	—	4	1	no	—
892	C₂³	—	4	2	no	—
893	C₂³	—	4	2	no	—
894	C₂³	—	4	2	no	—
895	C₂³	—	4	2	no	—
896	C₂³	—	4	4	no	—
897	C₂³	—	4	2	no	—
898	C₂³	—	4	2	no	—
899	C₂³	—	8	1	no	—
900	C₂³	—	8	2	no	—
901	C₂³	—	8	1	no	—
902	C₂³	—	8	2	no	—
903	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
904	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
905	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
906	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
907	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
908	Q₈	—	2	2	no	—
909	Q₈	—	2	2	no	—
910	Q₈	—	2	2	no	—
911	Q₈	—	2	2	no	—
912	Q₈	—	2	2	no	—
913	Q₈	—	4	2	no	—
914	Q₈	—	4	2	no	—
915	D₄	—	2	4	no	—
916	D₄	—	2	4	no	—
917	D₄	—	2	2	no	—
918	D₄	—	2	2	no	—
919	D₄	—	2	2	no	—
920	D₄	—	2	4	no	—
921	D₄	—	2	2	no	—
922	D₄	—	2	2	no	—
923	D₄	—	4	2	no	—
924	D₄	—	4	2	no	—
925	D₄	—	4	2	no	—
926	D₄	—	4	4	no	—
927	D₄	—	4	2	no	—
928	D₄	—	4	4	no	—
929	D₄	—	4	4	no	—
930	D₄	—	4	2	no	—
931	D₄	—	4	4	no	—
932	D₄	—	4	4	no	—
933	D₄	—	4	2	no	—
934	D₄	—	4	2	no	—
935	D₄	—	8	2	no	—
936	D₄	—	8	2	no	—
937	D₄	—	8	2	no	—
938	D₄	—	8	4	no	—
939	D₄	—	8	4	no	—
940	D₄	—	8	1	no	—
941	D₄	—	8	2	no	—
942	C₂×C₄	—	2	2	no	—
943	C₂×C₄	—	2	2	no	—
944	C₂×C₄	—	2	2	no	—
945	C₂×C₄	—	2	4	no	—
946	C₂×C₄	—	2	2	no	—
947	C₂×C₄	—	2	2	no	—
948	C₂×C₄	—	2	4	no	—
949	C₂×C₄	—	2	1	no	—
950	C₂×C₄	—	2	2	no	—
951	C₂×C₄	—	2	1	no	—
952	C₂×C₄	—	2	4	no	—
953	C₂×C₄	—	2	1	no	—
954	C₂×C₄	—	2	2	no	—
955	C₂×C₄	—	4	2	no	—
956	C₂×C₄	—	4	2	no	—
957	C₂×C₄	—	4	2	no	—
958	C₂×C₄	—	4	4	no	—
959	C₂×C₄	—	4	4	no	—
960	C₂×C₄	—	4	2	no	—
961	C₂×C₄	—	4	4	no	—
962	C₂×C₄	—	4	4	no	—
963	C₂×C₄	—	4	2	no	—
964	C₂×C₄	—	8	2	no	—
965	C₂×C₄	—	8	2	no	—
966	C₂×C₄	—	8	1	no	—
967	C₂×C₄	—	8	2	no	—
968	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
969	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
970	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
971	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
972	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
973	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
974	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
975	C₈	—	2	2	no	—
976	C₈	—	2	2	no	—
977	C₈	—	2	4	no	—
978	C₂²	—	2	1	no	—
979	C₂²	—	2	1	no	—
980	C₂²	—	2	1	no	—
981	C₂²	—	2	1	no	—
982	C₂²	—	2	2	no	—
983	C₂²	—	2	1	no	—
984	C₂²	—	2	2	no	—
985	C₂²	—	2	1	no	—
986	C₂²	—	2	2	no	—
987	C₂²	—	2	2	no	—
988	C₂²	—	2	1	no	—
989	C₂²	—	2	2	no	—
990	C₂²	—	2	2	no	—
991	C₂²	—	4	4	no	—
992	C₂²	—	4	2	no	—
993	C₂²	—	4	1	no	—
994	C₂²	—	4	2	no	—
995	C₂²	—	4	2	no	—
996	C₂²	—	4	2	no	—
997	C₂²	—	4	1	no	—
998	C₂²	—	4	2	no	—
999	C₂²	—	4	2	no	—
1000	C₂²	—	4	1	no	—
1001	C₂²	—	8	4	no	—
1002	C₂²	—	8	4	no	—
1003	C₂²	—	16	2	no	—
1004	C₂²	—	16	4	no	—
1005	C₂²	C₁₃×#534	1	2	yes	—
1006	C₂²	C₁₃×#577	1	2	yes	—
1007	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
1008	C₄	—	2	1	no	—
1009	C₄	—	2	1	no	—
1010	C₄	—	2	2	no	—
1011	C₄	—	2	2	no	—
1012	C₄	—	4	2	no	—
1013	C₄	—	4	1	no	—
1014	C₄	—	4	4	no	—
1015	C₄	—	4	1	no	—
1016	C₄	—	4	1	no	—
1017	C₄	—	4	2	no	—
1018	C₄	C₁₃×#534	1	2	yes	—
1019	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
1020	C₂	—	2	2	no	—
1021	C₂	—	2	2	no	—
1022	C₂	—	4	1	no	—
1023	C₂	—	4	2	no	—
1024	C₂	—	4	2	no	—
1025	C₂	—	8	2	no	—
1026	C₂	—	8	2	no	—
1027	C₂	—	8	1	no	—
1028	C₂	C₂×C₁₃×#534	1	1	yes	characteristic
1029	C₂	C₂×C₁₃×#577	1	1	yes	characteristic
1030	C₂	C₁₃×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂²×C₁₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3488	C₂	semidirect
2. C₂×C₁₃×#537	C₂	semidirect
3. C₁₃×#3204	C₂	semidirect
4. C₁₃×#3198	C₂	semidirect
5. C₁₃×#3196	C₂	semidirect
6. C₁₃×#3192	C₂	semidirect
7. C₁₃×#3188	C₂	semidirect
8. C₁₃×#3187	C₂	semidirect
9. C₁₃×#3099	C₂	semidirect
10. C₁₃×#3092	C₂	semidirect
11. C₂×C₁₃×#481	C₂	semidirect
12. C₁₃×#3062	C₂	semidirect
13. C₁₃×#3060	C₂	semidirect
14. C₁₃×#3012	C₂	semidirect
15. C₁₃×#3006	C₂	semidirect
16. C₁₃×#3002	C₂	semidirect
17. C₁₃×#2880	C₂	semidirect
18. C₂×C₁₃×H(5,𝔽₂)	C₂²	semidirect
20. C₂²×C₁₃×#41	C₂²	semidirect
21. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
22. C₂×C₁₃×#135	C₂²	semidirect
23. C₂×C₁₃×#131	C₂²	semidirect
34. C₁₃×#537	C₂²	semidirect
35. C₁₃×#537	C₂²	semidirect
36. C₁₃×#537	C₂²	semidirect
37. C₁₃×#537	C₂²	semidirect
38. C₁₃×#535	C₂²	semidirect
39. C₁₃×#535	C₂²	semidirect
43. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
48. C₂×C₁₃×#121	C₂²	semidirect
49. C₁₃×#520	C₂²	semidirect
50. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
51. C₁₃×#485	C₂²	semidirect
52. C₁₃×#484	C₂²	semidirect
53. C₁₃×#483	C₂²	semidirect
54. C₁₃×#483	C₂²	semidirect
55. C₁₃×#482	C₂²	semidirect
56. C₁₃×#481	C₂²	semidirect
57. C₁₃×#481	C₂²	semidirect
58. C₁₃×#481	C₂²	semidirect
59. C₁₃×#481	C₂²	semidirect
60. C₁₃×#481	C₂²	semidirect
61. C₁₃×#480	C₂²	semidirect
62. C₁₃×#470	C₂²	semidirect
63. C₁₃×#469	C₂²	semidirect
64. C₁₃×#469	C₂²	semidirect
65. C₁₃×#468	C₂²	semidirect
66. C₁₃×#466	C₂²	semidirect
67. C₁₃×#465	C₂²	semidirect
68. C₁₃×#465	C₂²	semidirect
69. C₁₃×#465	C₂²	semidirect
70. C₁₃×#452	C₂²	semidirect
71. C₁₃×#452	C₂²	semidirect
72. C₁₃×#451	C₂²	semidirect
73. C₁₃×#450	C₂²	semidirect
74. C₁₃×#450	C₂²	semidirect
75. C₁₃×#449	C₂²	semidirect
76. C₁₃×#449	C₂²	semidirect
77. C₁₃×#449	C₂²	semidirect
78. C₁₃×#448	C₂²	semidirect
79. C₁₃×#448	C₂²	semidirect
80. C₁₃×#447	C₂²	semidirect
81. C₁₃×#447	C₂²	semidirect
82. C₁₃×#447	C₂²	semidirect
83. C₁₃×#428	C₂²	semidirect
84. C₂×C₁₃×#106	C₂²	semidirect
85. C₁₃×#417	C₂²	semidirect
86. C₁₃×#417	C₂²	semidirect
87. C₁₃×#416	C₂²	semidirect
88. C₂×C₁₃×#102	C₂²	semidirect
89. C₁₃×#408	C₂²	semidirect
90. C₁₃×#408	C₂²	semidirect
91. C₁₃×#407	C₂²	semidirect
92. C₁₃×#407	C₂²	semidirect
93. C₂×C₁₃×C₂²⋊C₈	C₂²	semidirect
94. C₂×C₁₃×C₂²⋊C₈	C₂²	semidirect
234. #60765	C₁₃	direct (N × H)
370. #3488	C₂×C₁₃	semidirect
371. C₂×#537	C₂×C₁₃	semidirect
372. #3204	C₂×C₁₃	semidirect
373. #3198	C₂×C₁₃	semidirect
374. #3196	C₂×C₁₃	semidirect
375. #3192	C₂×C₁₃	semidirect
376. #3188	C₂×C₁₃	semidirect
377. #3187	C₂×C₁₃	semidirect
378. #3099	C₂×C₁₃	semidirect
379. #3092	C₂×C₁₃	semidirect
380. C₂×#481	C₂×C₁₃	semidirect
381. #3062	C₂×C₁₃	semidirect
382. #3060	C₂×C₁₃	semidirect
383. #3012	C₂×C₁₃	semidirect
384. #3006	C₂×C₁₃	semidirect
385. #3002	C₂×C₁₃	semidirect
386. #2880	C₂×C₁₃	semidirect
480. C₂×H(5,𝔽₂)	C₂²×C₁₃	semidirect
482. C₂²×#41	C₂²×C₁₃	semidirect
483. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
484. C₂×#135	C₂²×C₁₃	semidirect
485. C₂×#131	C₂²×C₁₃	semidirect
496. #537	C₂²×C₁₃	semidirect
497. #537	C₂²×C₁₃	semidirect
498. #537	C₂²×C₁₃	semidirect
499. #537	C₂²×C₁₃	semidirect
500. #535	C₂²×C₁₃	semidirect
501. #535	C₂²×C₁₃	semidirect
505. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
510. C₂×#121	C₂²×C₁₃	semidirect
511. #520	C₂²×C₁₃	semidirect
512. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
513. #485	C₂²×C₁₃	semidirect
514. #484	C₂²×C₁₃	semidirect
515. #483	C₂²×C₁₃	semidirect
516. #483	C₂²×C₁₃	semidirect
517. #482	C₂²×C₁₃	semidirect
518. #481	C₂²×C₁₃	semidirect
519. #481	C₂²×C₁₃	semidirect
520. #481	C₂²×C₁₃	semidirect
521. #481	C₂²×C₁₃	semidirect
522. #481	C₂²×C₁₃	semidirect
523. #480	C₂²×C₁₃	semidirect
524. #470	C₂²×C₁₃	semidirect
525. #469	C₂²×C₁₃	semidirect
526. #469	C₂²×C₁₃	semidirect
527. #468	C₂²×C₁₃	semidirect
528. #466	C₂²×C₁₃	semidirect
529. #465	C₂²×C₁₃	semidirect
530. #465	C₂²×C₁₃	semidirect
531. #465	C₂²×C₁₃	semidirect
532. #452	C₂²×C₁₃	semidirect
533. #452	C₂²×C₁₃	semidirect
534. #451	C₂²×C₁₃	semidirect
535. #450	C₂²×C₁₃	semidirect
536. #450	C₂²×C₁₃	semidirect
537. #449	C₂²×C₁₃	semidirect
538. #449	C₂²×C₁₃	semidirect
539. #449	C₂²×C₁₃	semidirect
540. #448	C₂²×C₁₃	semidirect
541. #448	C₂²×C₁₃	semidirect
542. #447	C₂²×C₁₃	semidirect
543. #447	C₂²×C₁₃	semidirect
544. #447	C₂²×C₁₃	semidirect
545. #428	C₂²×C₁₃	semidirect
546. C₂×#106	C₂²×C₁₃	semidirect
547. #417	C₂²×C₁₃	semidirect
548. #417	C₂²×C₁₃	semidirect
549. #416	C₂²×C₁₃	semidirect
550. C₂×#102	C₂²×C₁₃	semidirect
551. #408	C₂²×C₁₃	semidirect
552. #408	C₂²×C₁₃	semidirect
553. #407	C₂²×C₁₃	semidirect
554. #407	C₂²×C₁₃	semidirect
555. C₂×C₂²⋊C₈	C₂²×C₁₃	semidirect
556. C₂×C₂²⋊C₈	C₂²×C₁₃	semidirect
884. C₁₃	#60765	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×#3488	2
C₂×C₁₃×#537	2
C₁₃×#3204	2
C₁₃×#3198	2
C₁₃×#3196	2
C₁₃×#3192	2
C₁₃×#3188	2
C₁₃×#3187	2
C₁₃×#3099	2
C₁₃×#3092	2
C₂×C₁₃×#481	2
C₁₃×#3062	2
C₁₃×#3060	2
C₁₃×#3012	2
C₁₃×#3006	2
C₁₃×#3002	2
C₁₃×#2880	2
#60765	13

Subgroups — C13×#60765 #15747104

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60765 #15747104