Subgroups — C₁₃×#61561 #15747900

Order 3328.

2282 conjugacy classes of subgroups.

The subgroup lattice has 958 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3505	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#546	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3297	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3296	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3282	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3280	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3211	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3189	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3188	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3187	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3105	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3002	C₂	1	2	yes	maximal, complemented
13	C₂×C₁₃×#450	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₁₃×#447	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#2972	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic, complemented
17	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#135	C₂²	1	4	yes	complemented
19	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
20	C₂²×C₁₃×D₈	C₂²	1	2	yes	complemented
21	C₁₃×#553	—	2	2	no	—
22	C₁₃×#553	C₂²	1	2	yes	complemented
23	C₁₃×#552	C₂²	1	2	yes	complemented
24	C₁₃×#551	—	2	2	no	—
25	C₁₃×#548	C₂²	1	2	yes	complemented
26	C₁₃×#546	—	2	2	no	—
27	C₁₃×#546	—	2	2	no	—
28	C₁₃×#546	C₂²	1	4	yes	—
29	C₁₃×#546	C₂²	1	4	yes	complemented
30	C₁₃×#546	C₂²	1	2	yes	complemented
31	C₁₃×#539	—	2	1	no	—
32	C₁₃×#538	—	2	1	no	—
33	C₁₃×#534	—	2	1	no	—
34	C₁₃×#529	C₂²	1	2	yes	complemented
35	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic, complemented
36	C₁₃×#525	C₂²	1	2	yes	complemented
37	C₂×C₁₃×#123	—	2	1	no	—
38	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
40	C₂×C₁₃×#121	—	2	1	no	—
41	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
42	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₁₃×#120	—	2	1	no	—
44	C₁₃×#518	—	2	1	no	—
45	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
47	C₂²×C₁₃×C₂²⋊C₄	—	2	1	no	—
48	C₁₃×#495	C₂²	1	4	yes	complemented
49	C₁₃×#488	C₂²	1	4	yes	complemented
50	C₁₃×#484	C₂²	1	2	yes	complemented
51	C₁₃×#484	C₂²	1	2	yes	complemented
52	C₁₃×#483	C₂²	1	2	yes	complemented
53	C₁₃×#482	C₂²	1	4	yes	complemented
54	C₁₃×#481	C₂²	1	2	yes	complemented
55	C₁₃×#478	C₂²	1	4	yes	complemented
56	C₁₃×#467	C₂²	1	4	yes	complemented
57	C₁₃×#466	C₂²	1	4	yes	complemented
58	C₁₃×#465	C₂²	1	4	yes	complemented
59	C₁₃×#465	C₂²	1	4	yes	complemented
60	C₁₃×#464	C₂²	1	4	yes	complemented
61	C₁₃×#463	C₂²	1	4	yes	complemented
62	C₁₃×#463	C₂²	1	4	yes	complemented
63	C₁₃×#452	C₂²	1	4	yes	complemented
64	C₁₃×#451	C₂²	1	2	yes	complemented
65	C₁₃×#451	C₂²	1	2	yes	complemented
66	C₁₃×#450	C₂²	1	4	yes	complemented
67	C₁₃×#450	C₂²	1	2	yes	complemented
68	C₁₃×#450	C₂²	1	2	yes	complemented
69	C₁₃×#450	C₂²	1	2	yes	complemented
70	C₁₃×#449	C₂²	1	4	yes	complemented
71	C₁₃×#449	C₂²	1	4	yes	complemented
72	C₁₃×#448	C₂²	1	2	yes	complemented
73	C₁₃×#447	C₂²	1	2	yes	—
74	C₁₃×#447	C₂²	1	2	yes	—
75	C₁₃×#447	C₂²	1	4	yes	complemented
76	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
77	C₄×C₁₃×D₈	C₂²	1	4	yes	complemented
78	C₈×D₄×C₁₃	C₂²	1	4	yes	complemented
79	C₈×D₄×C₁₃	C₂²	1	4	yes	complemented
80	C₁₃×#431	C₂²	1	2	yes	complemented
81	C₁₃×#416	C₂²	1	4	yes	complemented
82	C₂×C₁₃×#102	C₂²	1	2	yes	complemented
83	C₂×C₁₃×#102	C₂²	1	2	yes	complemented
84	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
85	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
86	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	complemented
87	C₂⁵×C₁₃	—	2	1	no	—
88	C₂×C₁₃×#41	—	2	2	no	—
89	C₂×C₁₃×#41	—	4	4	no	—
90	C₂×C₁₃×#41	C₂³	1	4	yes	—
91	C₂×C₁₃×#41	C₂³	1	2	yes	complemented
92	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
93	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
94	C₂²×D₄×C₁₃	—	2	1	no	—
95	C₂²×D₄×C₁₃	—	2	1	no	—
96	C₂²×D₄×C₁₃	—	2	1	no	—
97	C₂²×D₄×C₁₃	—	2	1	no	—
98	C₂²×D₄×C₁₃	—	2	1	no	—
99	C₂²×D₄×C₁₃	—	2	1	no	—
100	C₂²×D₄×C₁₃	—	4	4	no	—
101	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
102	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
103	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
104	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
105	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
106	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
107	C₂³×C₄×C₁₃	—	2	1	no	—
108	C₂³×C₄×C₁₃	—	2	1	no	—
109	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
110	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
111	C₁₃×#135	—	4	8	no	—
112	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	complemented
113	C₂×C₁₃×SD₁₆	—	4	4	no	—
114	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
115	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
116	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	complemented
117	C₂×C₁₃×D₈	—	4	4	no	—
118	C₂×C₁₃×D₈	C₂³	1	4	yes	—
119	C₂×C₁₃×D₈	C₂³	1	4	yes	—
120	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
121	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
122	C₂²×C₈×C₁₃	C₂³	1	4	yes	complemented
123	C₁₃×#126	—	2	2	no	—
124	C₁₃×#126	—	2	2	no	—
125	C₁₃×#126	—	2	2	no	—
126	C₁₃×#125	—	2	2	no	—
127	C₁₃×#125	C₂³	1	2	yes	complemented
128	C₁₃×#124	—	2	2	no	—
129	C₁₃×#124	—	2	2	no	—
130	C₁₃×#124	C₂³	1	4	yes	—
131	C₁₃×#124	C₂³	1	2	yes	complemented
132	C₁₃×#123	—	2	2	no	—
133	C₁₃×#123	—	2	2	no	—
134	C₁₃×#123	—	2	2	no	—
135	C₁₃×#123	—	2	4	no	—
136	C₁₃×#123	—	2	4	no	—
137	C₁₃×#123	—	2	2	no	—
138	C₁₃×#123	—	2	2	no	—
139	C₁₃×C₂²⋊Q₈	—	2	1	no	—
140	C₁₃×C₂²⋊Q₈	—	2	1	no	—
141	C₁₃×C₂²⋊Q₈	—	2	1	no	—
142	C₁₃×C₂²⋊Q₈	—	2	1	no	—
143	C₁₃×C₂²⋊Q₈	—	2	2	no	—
144	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
145	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
146	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
147	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
148	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	complemented
149	C₁₃×#121	—	2	2	no	—
150	C₁₃×#121	—	2	2	no	—
151	C₁₃×#121	—	2	1	no	—
152	C₁₃×#121	—	2	1	no	—
153	C₁₃×#121	—	2	2	no	—
154	C₁₃×#121	—	2	4	no	—
155	C₁₃×#121	—	2	4	no	—
156	C₁₃×#121	—	2	2	no	—
157	C₁₃×#121	C₂³	1	2	yes	—
158	C₁₃×#121	C₂³	1	2	yes	—
159	C₁₃×#121	C₂³	1	4	yes	—
160	C₁₃×#121	C₂³	1	2	yes	complemented
161	C₁₃×#120	—	2	2	no	—
162	C₁₃×#120	—	2	4	no	—
163	C₁₃×#120	—	2	4	no	—
164	C₁₃×#120	—	2	2	no	—
165	C₄×Q₈×C₁₃	C₂³	1	2	yes	complemented
166	C₄×D₄×C₁₃	—	2	2	no	—
167	C₄×D₄×C₁₃	—	2	2	no	—
168	C₄×D₄×C₁₃	—	2	2	no	—
169	C₄×D₄×C₁₃	—	2	2	no	—
170	C₄×D₄×C₁₃	—	2	2	no	—
171	C₄×D₄×C₁₃	—	2	2	no	—
172	C₄×D₄×C₁₃	D₄	1	2	yes	—
173	C₄×D₄×C₁₃	D₄	1	2	yes	—
174	C₄×D₄×C₁₃	C₂³	1	4	yes	—
175	C₄×D₄×C₁₃	C₂³	1	2	yes	—
176	C₄×D₄×C₁₃	C₂³	1	2	yes	—
177	C₄×D₄×C₁₃	C₂³	1	2	yes	complemented
178	C₁₃×#117	—	2	2	no	—
179	C₁₃×#117	—	2	2	no	—
180	C₁₃×#117	C₂³	1	2	yes	complemented
181	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
182	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
183	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
184	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
185	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
186	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
187	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
188	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
189	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
190	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
191	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
192	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
193	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
194	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
195	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
196	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
197	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
198	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
199	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
200	C₁₃×#107	C₂³	1	4	yes	complemented
201	C₁₃×#106	C₂³	1	4	yes	complemented
202	C₁₃×C₄⋊C₈	C₂³	1	4	yes	complemented
203	C₁₃×#103	C₂³	1	4	yes	complemented
204	C₁₃×#103	C₂³	1	4	yes	complemented
205	C₁₃×#103	C₂³	1	4	yes	complemented
206	C₁₃×#102	C₂³	1	4	yes	—
207	C₁₃×#102	C₂³	1	4	yes	—
208	C₁₃×#102	C₂³	1	4	yes	—
209	C₁₃×#102	C₂³	1	4	yes	—
210	C₁₃×#102	C₂³	1	4	yes	complemented
211	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
212	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
213	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
214	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
215	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	complemented
216	C₄×C₈×C₁₃	C₂³	1	4	yes	complemented
217	#61561	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
218	C₂⁴×C₁₃	—	2	1	no	—
219	C₂⁴×C₁₃	—	2	1	no	—
220	C₂⁴×C₁₃	—	2	2	no	—
221	C₂⁴×C₁₃	—	2	2	no	—
222	C₂⁴×C₁₃	—	2	1	no	—
223	C₂⁴×C₁₃	—	4	4	no	—
224	C₂⁴×C₁₃	—	4	4	no	—
225	C₂⁴×C₁₃	—	8	2	no	—
226	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
227	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
228	C₁₃×#41	—	2	8	no	—
229	C₁₃×#41	—	4	4	no	—
230	C₁₃×#41	—	4	4	no	—
231	C₁₃×#41	—	4	8	no	—
232	C₂×Q₈×C₁₃	—	2	1	no	—
233	C₂×Q₈×C₁₃	—	2	1	no	—
234	C₂×Q₈×C₁₃	—	4	2	no	—
235	C₂×Q₈×C₁₃	—	4	2	no	—
236	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
237	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
238	C₂×D₄×C₁₃	—	2	4	no	—
239	C₂×D₄×C₁₃	—	2	4	no	—
240	C₂×D₄×C₁₃	—	2	4	no	—
241	C₂×D₄×C₁₃	—	2	4	no	—
242	C₂×D₄×C₁₃	—	2	2	no	—
243	C₂×D₄×C₁₃	—	2	2	no	—
244	C₂×D₄×C₁₃	—	2	4	no	—
245	C₂×D₄×C₁₃	—	2	2	no	—
246	C₂×D₄×C₁₃	—	2	4	no	—
247	C₂×D₄×C₁₃	—	2	2	no	—
248	C₂×D₄×C₁₃	—	2	1	no	—
249	C₂×D₄×C₁₃	—	2	2	no	—
250	C₂×D₄×C₁₃	—	2	2	no	—
251	C₂×D₄×C₁₃	—	2	1	no	—
252	C₂×D₄×C₁₃	—	2	1	no	—
253	C₂×D₄×C₁₃	—	4	2	no	—
254	C₂×D₄×C₁₃	—	4	2	no	—
255	C₂×D₄×C₁₃	—	4	2	no	—
256	C₂×D₄×C₁₃	—	4	2	no	—
257	C₂×D₄×C₁₃	—	4	4	no	—
258	C₂×D₄×C₁₃	—	4	4	no	—
259	C₂×D₄×C₁₃	—	4	4	no	—
260	C₂×D₄×C₁₃	—	4	4	no	—
261	C₂×D₄×C₁₃	—	4	4	no	—
262	C₂×D₄×C₁₃	—	8	2	no	—
263	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
264	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
265	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
266	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
267	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
268	C₂²×C₄×C₁₃	—	2	1	no	—
269	C₂²×C₄×C₁₃	—	2	1	no	—
270	C₂²×C₄×C₁₃	—	2	1	no	—
271	C₂²×C₄×C₁₃	—	2	1	no	—
272	C₂²×C₄×C₁₃	—	2	1	no	—
273	C₂²×C₄×C₁₃	—	2	4	no	—
274	C₂²×C₄×C₁₃	—	2	4	no	—
275	C₂²×C₄×C₁₃	—	2	2	no	—
276	C₂²×C₄×C₁₃	—	2	2	no	—
277	C₂²×C₄×C₁₃	—	4	2	no	—
278	C₂²×C₄×C₁₃	—	4	2	no	—
279	C₂²×C₄×C₁₃	—	4	4	no	—
280	C₂²×C₄×C₁₃	—	8	2	no	—
281	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
282	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
283	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
284	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
285	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
286	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
287	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
288	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
289	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
290	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
291	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
292	C₁₃×Q₁₆	—	4	4	no	—
293	C₁₃×SD₁₆	—	2	8	no	—
294	C₁₃×SD₁₆	—	4	4	no	—
295	C₁₃×SD₁₆	—	4	4	no	—
296	C₁₃×D₈	—	2	8	no	—
297	C₁₃×D₈	—	4	4	no	—
298	C₂×C₈×C₁₃	—	4	2	no	—
299	C₂×C₈×C₁₃	—	4	2	no	—
300	C₂×C₈×C₁₃	—	4	4	no	—
301	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
302	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
303	C₁₃×C₄⋊C₄	—	2	2	no	—
304	C₁₃×C₄⋊C₄	—	2	2	no	—
305	C₁₃×C₄⋊C₄	—	2	2	no	—
306	C₁₃×C₄⋊C₄	—	2	2	no	—
307	C₁₃×C₄⋊C₄	—	2	1	no	—
308	C₁₃×C₄⋊C₄	—	2	1	no	—
309	C₁₃×C₄⋊C₄	—	2	1	no	—
310	C₁₃×C₄⋊C₄	—	2	2	no	—
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	C₂×D₄	1	2	yes	—
315	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
316	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
317	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
318	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
319	C₁₃×C₂²⋊C₄	—	2	2	no	—
320	C₁₃×C₂²⋊C₄	—	2	2	no	—
321	C₁₃×C₂²⋊C₄	—	2	2	no	—
322	C₁₃×C₂²⋊C₄	—	2	2	no	—
323	C₁₃×C₂²⋊C₄	—	2	2	no	—
324	C₁₃×C₂²⋊C₄	—	2	2	no	—
325	C₁₃×C₂²⋊C₄	—	2	4	no	—
326	C₁₃×C₂²⋊C₄	—	2	4	no	—
327	C₁₃×C₂²⋊C₄	—	2	2	no	—
328	C₁₃×C₂²⋊C₄	—	2	2	no	—
329	C₁₃×C₂²⋊C₄	—	2	2	no	—
330	C₁₃×C₂²⋊C₄	—	2	4	no	—
331	C₁₃×C₂²⋊C₄	—	2	4	no	—
332	C₁₃×C₂²⋊C₄	—	2	2	no	—
333	C₁₃×C₂²⋊C₄	—	2	2	no	—
334	C₁₃×C₂²⋊C₄	—	2	2	no	—
335	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
336	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
337	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
338	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
339	C₄²×C₁₃	—	2	2	no	—
340	C₄²×C₁₃	—	2	2	no	—
341	C₄²×C₁₃	C₂×D₄	1	2	yes	—
342	C₄²×C₁₃	C₂⁴	1	2	yes	—
343	#3505	C₂×C₁₃	1	1	yes	characteristic, complemented
344	C₂×#546	C₂×C₁₃	1	1	yes	characteristic, complemented
345	#3297	C₂×C₁₃	1	4	yes	complemented
346	#3296	C₂×C₁₃	1	4	yes	complemented
347	#3282	C₂×C₁₃	1	4	yes	complemented
348	#3280	C₂×C₁₃	1	4	yes	complemented
349	#3211	C₂×C₁₃	1	2	yes	complemented
350	#3189	C₂×C₁₃	1	1	yes	characteristic, complemented
351	#3188	C₂×C₁₃	1	2	yes	complemented
352	#3187	C₂×C₁₃	1	1	yes	characteristic, complemented
353	#3105	C₂×C₁₃	1	2	yes	complemented
354	#3002	C₂×C₁₃	1	2	yes	complemented
355	C₂×#450	C₂×C₁₃	1	1	yes	characteristic, complemented
356	C₂×#447	C₂×C₁₃	1	1	yes	characteristic, complemented
357	#2972	C₂×C₁₃	1	1	yes	characteristic, complemented
358	C₂³×C₁₃	—	2	4	no	—
359	C₂³×C₁₃	—	2	2	no	—
360	C₂³×C₁₃	—	2	2	no	—
361	C₂³×C₁₃	—	2	2	no	—
362	C₂³×C₁₃	—	2	2	no	—
363	C₂³×C₁₃	—	4	1	no	—
364	C₂³×C₁₃	—	4	1	no	—
365	C₂³×C₁₃	—	4	1	no	—
366	C₂³×C₁₃	—	4	1	no	—
367	C₂³×C₁₃	—	4	4	no	—
368	C₂³×C₁₃	—	4	4	no	—
369	C₂³×C₁₃	—	4	2	no	—
370	C₂³×C₁₃	—	4	2	no	—
371	C₂³×C₁₃	—	4	2	no	—
372	C₂³×C₁₃	—	4	2	no	—
373	C₂³×C₁₃	—	4	4	no	—
374	C₂³×C₁₃	—	4	4	no	—
375	C₂³×C₁₃	—	4	2	no	—
376	C₂³×C₁₃	—	4	2	no	—
377	C₂³×C₁₃	—	8	2	no	—
378	C₂³×C₁₃	—	8	2	no	—
379	C₂³×C₁₃	—	8	1	no	—
380	C₂³×C₁₃	—	8	1	no	—
381	C₂³×C₁₃	—	8	16	no	—
382	C₂³×C₁₃	#135	1	4	yes	complemented
383	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
384	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
385	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
386	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
387	Q₈×C₁₃	—	2	4	no	—
388	Q₈×C₁₃	—	2	4	no	—
389	Q₈×C₁₃	—	4	2	no	—
390	Q₈×C₁₃	—	8	1	no	—
391	D₄×C₁₃	—	2	4	no	—
392	D₄×C₁₃	—	2	4	no	—
393	D₄×C₁₃	—	2	4	no	—
394	D₄×C₁₃	—	2	2	no	—
395	D₄×C₁₃	—	2	4	no	—
396	D₄×C₁₃	—	2	2	no	—
397	D₄×C₁₃	—	2	2	no	—
398	D₄×C₁₃	—	4	4	no	—
399	D₄×C₁₃	—	4	4	no	—
400	D₄×C₁₃	—	4	2	no	—
401	D₄×C₁₃	—	4	8	no	—
402	D₄×C₁₃	—	4	4	no	—
403	D₄×C₁₃	—	4	4	no	—
404	D₄×C₁₃	—	8	1	no	—
405	D₄×C₁₃	—	8	2	no	—
406	D₄×C₁₃	—	8	4	no	—
407	D₄×C₁₃	—	8	2	no	—
408	D₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
409	C₂×C₄×C₁₃	—	2	2	no	—
410	C₂×C₄×C₁₃	—	2	2	no	—
411	C₂×C₄×C₁₃	—	2	2	no	—
412	C₂×C₄×C₁₃	—	2	4	no	—
413	C₂×C₄×C₁₃	—	2	2	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	—	4	1	no	—
420	C₂×C₄×C₁₃	—	4	1	no	—
421	C₂×C₄×C₁₃	—	4	1	no	—
422	C₂×C₄×C₁₃	—	4	1	no	—
423	C₂×C₄×C₁₃	—	4	2	no	—
424	C₂×C₄×C₁₃	—	4	1	no	—
425	C₂×C₄×C₁₃	—	4	8	no	—
426	C₂×C₄×C₁₃	—	4	2	no	—
427	C₂×C₄×C₁₃	—	4	2	no	—
428	C₂×C₄×C₁₃	—	4	2	no	—
429	C₂×C₄×C₁₃	—	8	2	no	—
430	C₂×C₄×C₁₃	—	8	4	no	—
431	C₂×C₄×C₁₃	—	8	2	no	—
432	C₂×C₄×C₁₃	—	8	1	no	—
433	C₂×C₄×C₁₃	—	8	1	no	—
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	C₂²×D₄	1	1	yes	characteristic
439	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
440	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
441	C₈×C₁₃	—	2	4	no	—
442	C₈×C₁₃	—	2	4	no	—
443	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic, complemented
444	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
445	C₂×#135	C₂²×C₁₃	1	4	yes	complemented
446	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
447	C₂²×D₈	C₂²×C₁₃	1	2	yes	complemented
448	#553	—	2	2	no	—
449	#553	C₂²×C₁₃	1	2	yes	complemented
450	#552	C₂²×C₁₃	1	2	yes	complemented
451	#551	—	2	2	no	—
452	#548	C₂²×C₁₃	1	2	yes	complemented
453	#546	—	2	2	no	—
454	#546	—	2	2	no	—
455	#546	C₂²×C₁₃	1	4	yes	—
456	#546	C₂²×C₁₃	1	4	yes	complemented
457	#546	C₂²×C₁₃	1	2	yes	complemented
458	#539	—	2	1	no	—
459	#538	—	2	1	no	—
460	#534	—	2	1	no	—
461	#529	C₂²×C₁₃	1	2	yes	complemented
462	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic, complemented
463	#525	C₂²×C₁₃	1	2	yes	complemented
464	C₂×#123	—	2	1	no	—
465	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
466	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
467	C₂×#121	—	2	1	no	—
468	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
469	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic, complemented
470	C₂×#120	—	2	1	no	—
471	#518	—	2	1	no	—
472	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
473	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
474	C₂²×C₂²⋊C₄	—	2	1	no	—
475	#495	C₂²×C₁₃	1	4	yes	complemented
476	#488	C₂²×C₁₃	1	4	yes	complemented
477	#484	C₂²×C₁₃	1	2	yes	complemented
478	#484	C₂²×C₁₃	1	2	yes	complemented
479	#483	C₂²×C₁₃	1	2	yes	complemented
480	#482	C₂²×C₁₃	1	4	yes	complemented
481	#481	C₂²×C₁₃	1	2	yes	complemented
482	#478	C₂²×C₁₃	1	4	yes	complemented
483	#467	C₂²×C₁₃	1	4	yes	complemented
484	#466	C₂²×C₁₃	1	4	yes	complemented
485	#465	C₂²×C₁₃	1	4	yes	complemented
486	#465	C₂²×C₁₃	1	4	yes	complemented
487	#464	C₂²×C₁₃	1	4	yes	complemented
488	#463	C₂²×C₁₃	1	4	yes	complemented
489	#463	C₂²×C₁₃	1	4	yes	complemented
490	#452	C₂²×C₁₃	1	4	yes	complemented
491	#451	C₂²×C₁₃	1	2	yes	complemented
492	#451	C₂²×C₁₃	1	2	yes	complemented
493	#450	C₂²×C₁₃	1	2	yes	complemented
494	#450	C₂²×C₁₃	1	2	yes	complemented
495	#450	C₂²×C₁₃	1	4	yes	complemented
496	#450	C₂²×C₁₃	1	2	yes	complemented
497	#449	C₂²×C₁₃	1	4	yes	complemented
498	#449	C₂²×C₁₃	1	4	yes	complemented
499	#448	C₂²×C₁₃	1	2	yes	complemented
500	#447	C₂²×C₁₃	1	2	yes	—
501	#447	C₂²×C₁₃	1	2	yes	—
502	#447	C₂²×C₁₃	1	4	yes	complemented
503	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
504	C₄×D₈	C₂²×C₁₃	1	4	yes	complemented
505	C₈×D₄	C₂²×C₁₃	1	4	yes	complemented
506	C₈×D₄	C₂²×C₁₃	1	4	yes	complemented
507	#431	C₂²×C₁₃	1	2	yes	complemented
508	#416	C₂²×C₁₃	1	4	yes	complemented
509	C₂×#102	C₂²×C₁₃	1	2	yes	complemented
510	C₂×#102	C₂²×C₁₃	1	2	yes	complemented
511	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
512	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
513	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	complemented
514	C₂²×C₁₃	—	2	1	no	—
515	C₂²×C₁₃	—	2	1	no	—
516	C₂²×C₁₃	—	2	1	no	—
517	C₂²×C₁₃	—	2	1	no	—
518	C₂²×C₁₃	—	2	1	no	—
519	C₂²×C₁₃	—	2	1	no	—
520	C₂²×C₁₃	—	2	2	no	—
521	C₂²×C₁₃	—	2	2	no	—
522	C₂²×C₁₃	—	2	4	no	—
523	C₂²×C₁₃	—	2	2	no	—
524	C₂²×C₁₃	—	4	4	no	—
525	C₂²×C₁₃	—	4	8	no	—
526	C₂²×C₁₃	—	4	2	no	—
527	C₂²×C₁₃	—	4	2	no	—
528	C₂²×C₁₃	—	4	2	no	—
529	C₂²×C₁₃	—	4	2	no	—
530	C₂²×C₁₃	—	4	2	no	—
531	C₂²×C₁₃	—	4	2	no	—
532	C₂²×C₁₃	—	4	2	no	—
533	C₂²×C₁₃	—	4	2	no	—
534	C₂²×C₁₃	—	8	2	no	—
535	C₂²×C₁₃	—	8	8	no	—
536	C₂²×C₁₃	—	8	8	no	—
537	C₂²×C₁₃	—	8	4	no	—
538	C₂²×C₁₃	—	16	2	no	—
539	C₂²×C₁₃	C₂×#135	1	2	yes	—
540	C₂²×C₁₃	C₂×#135	1	2	yes	—
541	C₂²×C₁₃	C₂×#135	1	2	yes	—
542	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
543	C₄×C₁₃	—	2	2	no	—
544	C₄×C₁₃	—	2	2	no	—
545	C₄×C₁₃	—	2	1	no	—
546	C₄×C₁₃	—	2	1	no	—
547	C₄×C₁₃	—	2	1	no	—
548	C₄×C₁₃	—	2	2	no	—
549	C₄×C₁₃	—	4	2	no	—
550	C₄×C₁₃	—	4	2	no	—
551	C₄×C₁₃	—	4	2	no	—
552	C₄×C₁₃	—	4	2	no	—
553	C₄×C₁₃	—	4	2	no	—
554	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
555	C₂⁵	—	2	1	no	—
556	C₂×#41	—	2	2	no	—
557	C₂×#41	—	4	4	no	—
558	C₂×#41	C₂³×C₁₃	1	4	yes	—
559	C₂×#41	C₂³×C₁₃	1	2	yes	complemented
560	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
561	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
562	C₂²×D₄	—	2	1	no	—
563	C₂²×D₄	—	2	1	no	—
564	C₂²×D₄	—	2	1	no	—
565	C₂²×D₄	—	2	1	no	—
566	C₂²×D₄	—	2	1	no	—
567	C₂²×D₄	—	2	1	no	—
568	C₂²×D₄	—	4	4	no	—
569	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
570	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
571	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
572	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
573	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
574	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
575	C₂³×C₄	—	2	1	no	—
576	C₂³×C₄	—	2	1	no	—
577	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
578	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
579	#135	—	4	8	no	—
580	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	complemented
581	C₂×SD₁₆	—	4	4	no	—
582	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
583	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
584	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	complemented
585	C₂×D₈	—	4	4	no	—
586	C₂×D₈	C₂³×C₁₃	1	4	yes	—
587	C₂×D₈	C₂³×C₁₃	1	4	yes	—
588	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
589	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
590	C₂²×C₈	C₂³×C₁₃	1	4	yes	complemented
591	#126	—	2	2	no	—
592	#126	—	2	2	no	—
593	#126	—	2	2	no	—
594	#125	—	2	2	no	—
595	#125	C₂³×C₁₃	1	2	yes	complemented
596	#124	—	2	2	no	—
597	#124	—	2	2	no	—
598	#124	C₂³×C₁₃	1	4	yes	—
599	#124	C₂³×C₁₃	1	2	yes	complemented
600	#123	—	2	2	no	—
601	#123	—	2	2	no	—
602	#123	—	2	2	no	—
603	#123	—	2	4	no	—
604	#123	—	2	4	no	—
605	#123	—	2	2	no	—
606	#123	—	2	2	no	—
607	C₂²⋊Q₈	—	2	1	no	—
608	C₂²⋊Q₈	—	2	1	no	—
609	C₂²⋊Q₈	—	2	1	no	—
610	C₂²⋊Q₈	—	2	1	no	—
611	C₂²⋊Q₈	—	2	2	no	—
612	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
613	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
614	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
615	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
616	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	complemented
617	#121	—	2	2	no	—
618	#121	—	2	2	no	—
619	#121	—	2	1	no	—
620	#121	—	2	1	no	—
621	#121	—	2	2	no	—
622	#121	—	2	4	no	—
623	#121	—	2	4	no	—
624	#121	—	2	2	no	—
625	#121	C₂³×C₁₃	1	2	yes	—
626	#121	C₂³×C₁₃	1	2	yes	—
627	#121	C₂³×C₁₃	1	4	yes	—
628	#121	C₂³×C₁₃	1	2	yes	complemented
629	#120	—	2	2	no	—
630	#120	—	2	4	no	—
631	#120	—	2	4	no	—
632	#120	—	2	2	no	—
633	C₄×Q₈	C₂³×C₁₃	1	2	yes	complemented
634	C₄×D₄	—	2	2	no	—
635	C₄×D₄	—	2	2	no	—
636	C₄×D₄	—	2	2	no	—
637	C₄×D₄	—	2	2	no	—
638	C₄×D₄	—	2	2	no	—
639	C₄×D₄	—	2	2	no	—
640	C₄×D₄	D₄×C₁₃	1	2	yes	—
641	C₄×D₄	D₄×C₁₃	1	2	yes	—
642	C₄×D₄	C₂³×C₁₃	1	4	yes	—
643	C₄×D₄	C₂³×C₁₃	1	2	yes	—
644	C₄×D₄	C₂³×C₁₃	1	2	yes	—
645	C₄×D₄	C₂³×C₁₃	1	2	yes	complemented
646	#117	—	2	2	no	—
647	#117	—	2	2	no	—
648	#117	C₂³×C₁₃	1	2	yes	complemented
649	C₂×C₄⋊C₄	—	2	1	no	—
650	C₂×C₄⋊C₄	—	2	1	no	—
651	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
652	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
653	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
654	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
655	C₂×C₂²⋊C₄	—	2	1	no	—
656	C₂×C₂²⋊C₄	—	2	1	no	—
657	C₂×C₂²⋊C₄	—	2	1	no	—
658	C₂×C₂²⋊C₄	—	2	1	no	—
659	C₂×C₂²⋊C₄	—	2	1	no	—
660	C₂×C₂²⋊C₄	—	2	1	no	—
661	C₂×C₂²⋊C₄	—	2	1	no	—
662	C₂×C₂²⋊C₄	—	2	4	no	—
663	C₂×C₂²⋊C₄	—	2	4	no	—
664	C₂×C₂²⋊C₄	—	2	2	no	—
665	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
666	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
667	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
668	#107	C₂³×C₁₃	1	4	yes	complemented
669	#106	C₂³×C₁₃	1	4	yes	complemented
670	C₄⋊C₈	C₂³×C₁₃	1	4	yes	complemented
671	#103	C₂³×C₁₃	1	4	yes	complemented
672	#103	C₂³×C₁₃	1	4	yes	complemented
673	#103	C₂³×C₁₃	1	4	yes	complemented
674	#102	C₂³×C₁₃	1	4	yes	—
675	#102	C₂³×C₁₃	1	4	yes	—
676	#102	C₂³×C₁₃	1	4	yes	—
677	#102	C₂³×C₁₃	1	4	yes	—
678	#102	C₂³×C₁₃	1	4	yes	complemented
679	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
680	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
681	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
682	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
683	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	complemented
684	C₄×C₈	C₂³×C₁₃	1	4	yes	complemented
685	C₂×C₁₃	—	2	2	no	—
686	C₂×C₁₃	—	2	2	no	—
687	C₂×C₁₃	—	2	2	no	—
688	C₂×C₁₃	—	4	2	no	—
689	C₂×C₁₃	—	4	4	no	—
690	C₂×C₁₃	—	8	2	no	—
691	C₂×C₁₃	—	8	2	no	—
692	C₂×C₁₃	#3484	1	1	yes	characteristic
693	C₂×C₁₃	C₂²×#135	1	1	yes	characteristic
694	C₂×C₁₃	#3585	1	1	yes	characteristic
695	C₂⁴	—	2	1	no	—
696	C₂⁴	—	2	1	no	—
697	C₂⁴	—	2	2	no	—
698	C₂⁴	—	2	2	no	—
699	C₂⁴	—	2	1	no	—
700	C₂⁴	—	4	4	no	—
701	C₂⁴	—	4	4	no	—
702	C₂⁴	—	8	2	no	—
703	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
704	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
705	#41	—	2	8	no	—
706	#41	—	4	4	no	—
707	#41	—	4	4	no	—
708	#41	—	4	8	no	—
709	C₂×Q₈	—	2	1	no	—
710	C₂×Q₈	—	2	1	no	—
711	C₂×Q₈	—	4	2	no	—
712	C₂×Q₈	—	4	2	no	—
713	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
714	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
715	C₂×D₄	—	2	4	no	—
716	C₂×D₄	—	2	4	no	—
717	C₂×D₄	—	2	4	no	—
718	C₂×D₄	—	2	4	no	—
719	C₂×D₄	—	2	2	no	—
720	C₂×D₄	—	2	2	no	—
721	C₂×D₄	—	2	4	no	—
722	C₂×D₄	—	2	2	no	—
723	C₂×D₄	—	2	4	no	—
724	C₂×D₄	—	2	2	no	—
725	C₂×D₄	—	2	1	no	—
726	C₂×D₄	—	2	2	no	—
727	C₂×D₄	—	2	2	no	—
728	C₂×D₄	—	2	1	no	—
729	C₂×D₄	—	2	1	no	—
730	C₂×D₄	—	4	2	no	—
731	C₂×D₄	—	4	2	no	—
732	C₂×D₄	—	4	2	no	—
733	C₂×D₄	—	4	2	no	—
734	C₂×D₄	—	4	4	no	—
735	C₂×D₄	—	4	4	no	—
736	C₂×D₄	—	4	4	no	—
737	C₂×D₄	—	4	4	no	—
738	C₂×D₄	—	4	4	no	—
739	C₂×D₄	—	8	2	no	—
740	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
741	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
742	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
743	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
744	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
745	C₂²×C₄	—	2	1	no	—
746	C₂²×C₄	—	2	1	no	—
747	C₂²×C₄	—	2	1	no	—
748	C₂²×C₄	—	2	1	no	—
749	C₂²×C₄	—	2	1	no	—
750	C₂²×C₄	—	2	4	no	—
751	C₂²×C₄	—	2	4	no	—
752	C₂²×C₄	—	2	2	no	—
753	C₂²×C₄	—	2	2	no	—
754	C₂²×C₄	—	4	2	no	—
755	C₂²×C₄	—	4	2	no	—
756	C₂²×C₄	—	4	4	no	—
757	C₂²×C₄	—	8	2	no	—
758	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
759	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
760	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
761	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
762	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
763	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
764	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
765	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
766	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
767	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
768	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
769	Q₁₆	—	4	4	no	—
770	SD₁₆	—	2	8	no	—
771	SD₁₆	—	4	4	no	—
772	SD₁₆	—	4	4	no	—
773	D₈	—	2	8	no	—
774	D₈	—	4	4	no	—
775	C₂×C₈	—	4	2	no	—
776	C₂×C₈	—	4	2	no	—
777	C₂×C₈	—	4	4	no	—
778	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
779	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
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	1	no	—
785	C₄⋊C₄	—	2	1	no	—
786	C₄⋊C₄	—	2	1	no	—
787	C₄⋊C₄	—	2	2	no	—
788	C₄⋊C₄	—	2	2	no	—
789	C₄⋊C₄	—	2	2	no	—
790	C₄⋊C₄	—	2	2	no	—
791	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
792	C₄⋊C₄	C₂×D₄×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	4	no	—
803	C₂²⋊C₄	—	2	4	no	—
804	C₂²⋊C₄	—	2	2	no	—
805	C₂²⋊C₄	—	2	2	no	—
806	C₂²⋊C₄	—	2	2	no	—
807	C₂²⋊C₄	—	2	4	no	—
808	C₂²⋊C₄	—	2	4	no	—
809	C₂²⋊C₄	—	2	2	no	—
810	C₂²⋊C₄	—	2	2	no	—
811	C₂²⋊C₄	—	2	2	no	—
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	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
816	C₄²	—	2	2	no	—
817	C₄²	—	2	2	no	—
818	C₄²	C₂×D₄×C₁₃	1	2	yes	—
819	C₄²	C₂⁴×C₁₃	1	2	yes	—
820	C₁₃	#61561	1	1	yes	characteristic, direct product factor, Sylow
821	C₂³	—	2	4	no	—
822	C₂³	—	2	2	no	—
823	C₂³	—	2	2	no	—
824	C₂³	—	2	2	no	—
825	C₂³	—	2	2	no	—
826	C₂³	—	4	1	no	—
827	C₂³	—	4	1	no	—
828	C₂³	—	4	1	no	—
829	C₂³	—	4	1	no	—
830	C₂³	—	4	4	no	—
831	C₂³	—	4	4	no	—
832	C₂³	—	4	2	no	—
833	C₂³	—	4	2	no	—
834	C₂³	—	4	2	no	—
835	C₂³	—	4	2	no	—
836	C₂³	—	4	4	no	—
837	C₂³	—	4	4	no	—
838	C₂³	—	4	2	no	—
839	C₂³	—	4	2	no	—
840	C₂³	—	8	2	no	—
841	C₂³	—	8	2	no	—
842	C₂³	—	8	1	no	—
843	C₂³	—	8	1	no	—
844	C₂³	—	8	16	no	—
845	C₂³	C₁₃×#135	1	4	yes	complemented
846	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
847	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
848	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
849	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
850	Q₈	—	2	4	no	—
851	Q₈	—	2	4	no	—
852	Q₈	—	4	2	no	—
853	Q₈	—	8	1	no	—
854	D₄	—	2	4	no	—
855	D₄	—	2	4	no	—
856	D₄	—	2	4	no	—
857	D₄	—	2	2	no	—
858	D₄	—	2	4	no	—
859	D₄	—	2	2	no	—
860	D₄	—	2	2	no	—
861	D₄	—	4	4	no	—
862	D₄	—	4	4	no	—
863	D₄	—	4	2	no	—
864	D₄	—	4	8	no	—
865	D₄	—	4	4	no	—
866	D₄	—	4	4	no	—
867	D₄	—	8	1	no	—
868	D₄	—	8	4	no	—
869	D₄	—	8	2	no	—
870	D₄	—	8	2	no	—
871	D₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
872	C₂×C₄	—	2	2	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	4	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	2	2	no	—
878	C₂×C₄	—	2	2	no	—
879	C₂×C₄	—	2	2	no	—
880	C₂×C₄	—	2	2	no	—
881	C₂×C₄	—	2	2	no	—
882	C₂×C₄	—	4	1	no	—
883	C₂×C₄	—	4	1	no	—
884	C₂×C₄	—	4	1	no	—
885	C₂×C₄	—	4	1	no	—
886	C₂×C₄	—	4	2	no	—
887	C₂×C₄	—	4	1	no	—
888	C₂×C₄	—	4	8	no	—
889	C₂×C₄	—	4	2	no	—
890	C₂×C₄	—	4	2	no	—
891	C₂×C₄	—	4	2	no	—
892	C₂×C₄	—	8	4	no	—
893	C₂×C₄	—	8	2	no	—
894	C₂×C₄	—	8	2	no	—
895	C₂×C₄	—	8	1	no	—
896	C₂×C₄	—	8	1	no	—
897	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
898	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
899	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
900	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
901	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
902	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
903	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
904	C₈	—	2	4	no	—
905	C₈	—	2	4	no	—
906	C₂²	—	2	1	no	—
907	C₂²	—	2	1	no	—
908	C₂²	—	2	1	no	—
909	C₂²	—	2	1	no	—
910	C₂²	—	2	1	no	—
911	C₂²	—	2	1	no	—
912	C₂²	—	2	2	no	—
913	C₂²	—	2	2	no	—
914	C₂²	—	2	2	no	—
915	C₂²	—	2	4	no	—
916	C₂²	—	4	4	no	—
917	C₂²	—	4	8	no	—
918	C₂²	—	4	2	no	—
919	C₂²	—	4	2	no	—
920	C₂²	—	4	2	no	—
921	C₂²	—	4	2	no	—
922	C₂²	—	4	2	no	—
923	C₂²	—	4	2	no	—
924	C₂²	—	4	2	no	—
925	C₂²	—	4	2	no	—
926	C₂²	—	8	2	no	—
927	C₂²	—	8	8	no	—
928	C₂²	—	8	8	no	—
929	C₂²	—	8	4	no	—
930	C₂²	—	16	2	no	—
931	C₂²	C₂×C₁₃×#135	1	2	yes	—
932	C₂²	C₂×C₁₃×#135	1	2	yes	—
933	C₂²	C₂×C₁₃×#135	1	2	yes	—
934	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
935	C₄	—	2	2	no	—
936	C₄	—	2	2	no	—
937	C₄	—	2	2	no	—
938	C₄	—	2	1	no	—
939	C₄	—	2	1	no	—
940	C₄	—	2	1	no	—
941	C₄	—	4	2	no	—
942	C₄	—	4	2	no	—
943	C₄	—	4	2	no	—
944	C₄	—	4	2	no	—
945	C₄	—	4	2	no	—
946	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
947	C₂	—	2	2	no	—
948	C₂	—	2	2	no	—
949	C₂	—	2	2	no	—
950	C₂	—	4	2	no	—
951	C₂	—	4	4	no	—
952	C₂	—	8	2	no	—
953	C₂	—	8	2	no	—
954	C₂	C₁₃×#3484	1	1	yes	characteristic
955	C₂	C₂²×C₁₃×#135	1	1	yes	characteristic
956	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 ◁ C₂×C₄×D₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3505	C₂	semidirect
2. C₂×C₁₃×#546	C₂	semidirect
3. C₁₃×#3297	C₂	semidirect
4. C₁₃×#3296	C₂	semidirect
5. C₁₃×#3282	C₂	semidirect
6. C₁₃×#3280	C₂	semidirect
7. C₁₃×#3211	C₂	semidirect
8. C₁₃×#3189	C₂	semidirect
9. C₁₃×#3188	C₂	semidirect
10. C₁₃×#3187	C₂	semidirect
11. C₁₃×#3105	C₂	semidirect
12. C₁₃×#3002	C₂	semidirect
13. C₂×C₁₃×#450	C₂	semidirect
14. C₂×C₁₃×#447	C₂	semidirect
15. C₁₃×#2972	C₂	semidirect
16. C₂²×C₁₃×#41	C₂²	semidirect
18. C₂×C₁₃×#135	C₂²	semidirect
19. C₂²×C₁₃×SD₁₆	C₂²	semidirect
20. C₂²×C₁₃×D₈	C₂²	semidirect
22. C₁₃×#553	C₂²	semidirect
23. C₁₃×#552	C₂²	semidirect
25. C₁₃×#548	C₂²	semidirect
29. C₁₃×#546	C₂²	semidirect
30. C₁₃×#546	C₂²	semidirect
34. C₁₃×#529	C₂²	semidirect
35. C₂×C₁₃×#124	C₂²	semidirect
36. C₁₃×#525	C₂²	semidirect
42. C₂×C₁₃×#121	C₂²	semidirect
46. C₂×C₄×D₄×C₁₃	C₂²	semidirect
48. C₁₃×#495	C₂²	semidirect
49. C₁₃×#488	C₂²	semidirect
50. C₁₃×#484	C₂²	semidirect
51. C₁₃×#484	C₂²	semidirect
52. C₁₃×#483	C₂²	semidirect
53. C₁₃×#482	C₂²	semidirect
54. C₁₃×#481	C₂²	semidirect
55. C₁₃×#478	C₂²	semidirect
56. C₁₃×#467	C₂²	semidirect
57. C₁₃×#466	C₂²	semidirect
58. C₁₃×#465	C₂²	semidirect
59. C₁₃×#465	C₂²	semidirect
60. C₁₃×#464	C₂²	semidirect
61. C₁₃×#463	C₂²	semidirect
62. C₁₃×#463	C₂²	semidirect
63. C₁₃×#452	C₂²	semidirect
64. C₁₃×#451	C₂²	semidirect
65. C₁₃×#451	C₂²	semidirect
66. C₁₃×#450	C₂²	semidirect
67. C₁₃×#450	C₂²	semidirect
68. C₁₃×#450	C₂²	semidirect
69. C₁₃×#450	C₂²	semidirect
70. C₁₃×#449	C₂²	semidirect
71. C₁₃×#449	C₂²	semidirect
72. C₁₃×#448	C₂²	semidirect
75. C₁₃×#447	C₂²	semidirect
76. C₄×C₁₃×SD₁₆	C₂²	semidirect
77. C₄×C₁₃×D₈	C₂²	semidirect
78. C₈×D₄×C₁₃	C₂²	semidirect
79. C₈×D₄×C₁₃	C₂²	semidirect
80. C₁₃×#431	C₂²	semidirect
81. C₁₃×#416	C₂²	semidirect
82. C₂×C₁₃×#102	C₂²	semidirect
83. C₂×C₁₃×#102	C₂²	semidirect
86. C₂×C₁₃×C₂²⋊C₈	C₂²	semidirect
91. C₂×C₁₃×#41	C₂³	semidirect
112. C₂×C₁₃×Q₁₆	C₂³	semidirect
116. C₂×C₁₃×SD₁₆	C₂³	semidirect
122. C₂²×C₈×C₁₃	C₂³	semidirect
127. C₁₃×#125	C₂³	semidirect
131. C₁₃×#124	C₂³	semidirect
148. C₁₃×C₂²⋊Q₈	C₂³	semidirect
160. C₁₃×#121	C₂³	semidirect
165. C₄×Q₈×C₁₃	C₂³	semidirect
177. C₄×D₄×C₁₃	C₂³	semidirect
180. C₁₃×#117	C₂³	semidirect
200. C₁₃×#107	C₂³	semidirect
201. C₁₃×#106	C₂³	semidirect
202. C₁₃×C₄⋊C₈	C₂³	semidirect
203. C₁₃×#103	C₂³	semidirect
204. C₁₃×#103	C₂³	semidirect
205. C₁₃×#103	C₂³	semidirect
210. C₁₃×#102	C₂³	semidirect
215. C₁₃×C₂²⋊C₈	C₂³	semidirect
216. C₄×C₈×C₁₃	C₂³	semidirect
217. #61561	C₁₃	direct (N × H)
343. #3505	C₂×C₁₃	semidirect
344. C₂×#546	C₂×C₁₃	semidirect
345. #3297	C₂×C₁₃	semidirect
346. #3296	C₂×C₁₃	semidirect
347. #3282	C₂×C₁₃	semidirect
348. #3280	C₂×C₁₃	semidirect
349. #3211	C₂×C₁₃	semidirect
350. #3189	C₂×C₁₃	semidirect
351. #3188	C₂×C₁₃	semidirect
352. #3187	C₂×C₁₃	semidirect
353. #3105	C₂×C₁₃	semidirect
354. #3002	C₂×C₁₃	semidirect
355. C₂×#450	C₂×C₁₃	semidirect
356. C₂×#447	C₂×C₁₃	semidirect
357. #2972	C₂×C₁₃	semidirect
382. C₂³×C₁₃	#135	semidirect
443. C₂²×#41	C₂²×C₁₃	semidirect
445. C₂×#135	C₂²×C₁₃	semidirect
446. C₂²×SD₁₆	C₂²×C₁₃	semidirect
447. C₂²×D₈	C₂²×C₁₃	semidirect
449. #553	C₂²×C₁₃	semidirect
450. #552	C₂²×C₁₃	semidirect
452. #548	C₂²×C₁₃	semidirect
456. #546	C₂²×C₁₃	semidirect
457. #546	C₂²×C₁₃	semidirect
461. #529	C₂²×C₁₃	semidirect
462. C₂×#124	C₂²×C₁₃	semidirect
463. #525	C₂²×C₁₃	semidirect
469. C₂×#121	C₂²×C₁₃	semidirect
473. C₂×C₄×D₄	C₂²×C₁₃	semidirect
475. #495	C₂²×C₁₃	semidirect
476. #488	C₂²×C₁₃	semidirect
477. #484	C₂²×C₁₃	semidirect
478. #484	C₂²×C₁₃	semidirect
479. #483	C₂²×C₁₃	semidirect
480. #482	C₂²×C₁₃	semidirect
481. #481	C₂²×C₁₃	semidirect
482. #478	C₂²×C₁₃	semidirect
483. #467	C₂²×C₁₃	semidirect
484. #466	C₂²×C₁₃	semidirect
485. #465	C₂²×C₁₃	semidirect
486. #465	C₂²×C₁₃	semidirect
487. #464	C₂²×C₁₃	semidirect
488. #463	C₂²×C₁₃	semidirect
489. #463	C₂²×C₁₃	semidirect
490. #452	C₂²×C₁₃	semidirect
491. #451	C₂²×C₁₃	semidirect
492. #451	C₂²×C₁₃	semidirect
493. #450	C₂²×C₁₃	semidirect
494. #450	C₂²×C₁₃	semidirect
495. #450	C₂²×C₁₃	semidirect
496. #450	C₂²×C₁₃	semidirect
497. #449	C₂²×C₁₃	semidirect
498. #449	C₂²×C₁₃	semidirect
499. #448	C₂²×C₁₃	semidirect
502. #447	C₂²×C₁₃	semidirect
503. C₄×SD₁₆	C₂²×C₁₃	semidirect
504. C₄×D₈	C₂²×C₁₃	semidirect
505. C₈×D₄	C₂²×C₁₃	semidirect
506. C₈×D₄	C₂²×C₁₃	semidirect
507. #431	C₂²×C₁₃	semidirect
508. #416	C₂²×C₁₃	semidirect
509. C₂×#102	C₂²×C₁₃	semidirect
510. C₂×#102	C₂²×C₁₃	semidirect
513. C₂×C₂²⋊C₈	C₂²×C₁₃	semidirect
559. C₂×#41	C₂³×C₁₃	semidirect
580. C₂×Q₁₆	C₂³×C₁₃	semidirect
584. C₂×SD₁₆	C₂³×C₁₃	semidirect
590. C₂²×C₈	C₂³×C₁₃	semidirect
595. #125	C₂³×C₁₃	semidirect
599. #124	C₂³×C₁₃	semidirect
616. C₂²⋊Q₈	C₂³×C₁₃	semidirect
628. #121	C₂³×C₁₃	semidirect
633. C₄×Q₈	C₂³×C₁₃	semidirect
645. C₄×D₄	C₂³×C₁₃	semidirect
648. #117	C₂³×C₁₃	semidirect
668. #107	C₂³×C₁₃	semidirect
669. #106	C₂³×C₁₃	semidirect
670. C₄⋊C₈	C₂³×C₁₃	semidirect
671. #103	C₂³×C₁₃	semidirect
672. #103	C₂³×C₁₃	semidirect
673. #103	C₂³×C₁₃	semidirect
678. #102	C₂³×C₁₃	semidirect
683. C₂²⋊C₈	C₂³×C₁₃	semidirect
684. C₄×C₈	C₂³×C₁₃	semidirect
820. C₁₃	#61561	direct (N × H)
845. C₂³	C₁₃×#135	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₃×#3505	2
C₂×C₁₃×#546	2
C₁₃×#3297	2
C₁₃×#3296	2
C₁₃×#3282	2
C₁₃×#3280	2
C₁₃×#3211	2
C₁₃×#3189	2
C₁₃×#3188	2
C₁₃×#3187	2
C₁₃×#3105	2
C₁₃×#3002	2
C₂×C₁₃×#450	2
C₂×C₁₃×#447	2
C₁₃×#2972	2
#61561	13

Subgroups — C13×#61561 #15747900

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61561 #15747900