Subgroups — C₁₃×#61593 #15747932

Order 3328.

2148 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3519	C₂	1	1	yes	maximal, characteristic
2	C₂×D₄×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3329	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3320	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3299	C₂	1	2	yes	maximal, complemented
6	D₄×C₁₃×SD₁₆	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3278	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3266	C₂	1	4	yes	maximal, complemented
9	C₁₃×#3218	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3206	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3193	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3190	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3112	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3108	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3004	C₂	1	2	yes	maximal, complemented
16	C₂×C₁₃×#448	C₂	1	2	yes	maximal, complemented
17	C₁₃×#2974	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂³×Q₈×C₁₃	C₂²	1	2	yes	complemented
19	C₂×C₁₃×#137	C₂²	1	4	yes	complemented
20	C₂²×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
21	C₁₃×#555	C₂²	1	1	yes	characteristic
22	C₁₃×#554	C₂²	1	1	yes	characteristic
23	C₁₃×#553	—	2	1	no	—
24	C₁₃×#553	C₂²	1	2	yes	—
25	C₁₃×#550	C₂²	1	1	yes	characteristic
26	D₄×Q₈×C₁₃	—	2	1	no	—
27	D₄×Q₈×C₁₃	—	2	2	no	—
28	D₄×Q₈×C₁₃	—	2	1	no	—
29	D₄×Q₈×C₁₃	C₂²	1	2	yes	—
30	D₄×Q₈×C₁₃	C₂²	1	4	yes	complemented
31	D₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
32	C₁₃×#546	—	2	2	no	—
33	C₁₃×#546	C₂²	1	2	yes	—
34	D₄²×C₁₃	—	2	1	no	—
35	D₄²×C₁₃	C₂²	1	1	yes	characteristic
36	C₁₃×#540	—	2	1	no	—
37	C₁₃×#538	—	2	2	no	—
38	C₁₃×#532	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
40	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
41	C₁₃×#529	C₂²	1	1	yes	characteristic
42	C₁₃×#525	C₂²	1	2	yes	—
43	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
44	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
45	C₂×C₁₃×#121	C₂²	1	2	yes	—
46	C₁₃×#518	—	2	1	no	—
47	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
48	C₂×C₄×D₄×C₁₃	—	2	1	no	—
49	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
50	C₁₃×#497	C₂²	1	2	yes	complemented
51	C₁₃×#492	C₂²	1	2	yes	complemented
52	C₁₃×#491	C₂²	1	2	yes	complemented
53	C₁₃×#487	C₂²	1	2	yes	complemented
54	C₁₃×#485	C₂²	1	4	yes	complemented
55	C₁₃×#484	C₂²	1	4	yes	complemented
56	C₁₃×#483	C₂²	1	1	yes	characteristic, complemented
57	C₁₃×#480	C₂²	1	1	yes	characteristic
58	C₁₃×#480	C₂²	1	2	yes	complemented
59	C₁₃×#479	C₂²	1	2	yes	complemented
60	C₁₃×#477	C₂²	1	2	yes	complemented
61	C₁₃×#468	C₂²	1	4	yes	complemented
62	C₁₃×#468	C₂²	1	4	yes	complemented
63	C₁₃×#467	C₂²	1	4	yes	complemented
64	C₁₃×#465	C₂²	1	4	yes	complemented
65	C₁₃×#464	C₂²	1	2	yes	complemented
66	C₁₃×#462	C₂²	1	2	yes	complemented
67	C₁₃×#461	C₂²	1	4	yes	complemented
68	C₁₃×#461	C₂²	1	2	yes	complemented
69	C₁₃×#460	C₂²	1	2	yes	complemented
70	C₁₃×#452	C₂²	1	4	yes	complemented
71	C₁₃×#451	C₂²	1	4	yes	complemented
72	C₁₃×#451	C₂²	1	1	yes	characteristic, complemented
73	C₁₃×#451	C₂²	1	2	yes	complemented
74	C₁₃×#450	C₂²	1	4	yes	complemented
75	C₁₃×#448	C₂²	1	1	yes	characteristic
76	C₁₃×#448	C₂²	1	2	yes	—
77	C₁₃×#448	C₂²	1	4	yes	complemented
78	C₁₃×#448	C₂²	1	4	yes	complemented
79	C₁₃×#448	C₂²	1	4	yes	complemented
80	C₁₃×#448	C₂²	1	2	yes	complemented
81	C₁₃×#448	C₂²	1	2	yes	complemented
82	C₁₃×#448	C₂²	1	2	yes	complemented
83	C₁₃×#440	C₂²	1	4	yes	complemented
84	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
85	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
86	C₁₃×#436	C₂²	1	2	yes	complemented
87	C₁₃×#435	C₂²	1	4	yes	complemented
88	C₈×D₄×C₁₃	C₂²	1	2	yes	—
89	C₁₃×#432	C₂²	1	1	yes	characteristic, complemented
90	C₁₃×#431	C₂²	1	1	yes	characteristic, complemented
91	C₁₃×#419	C₂²	1	4	yes	complemented
92	C₂×C₁₃×#103	C₂²	1	4	yes	complemented
93	C₁₃×#407	C₂²	1	2	yes	complemented
94	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	complemented
95	C₂×C₁₃×#41	—	2	1	no	—
96	C₂×C₁₃×#41	C₂³	1	2	yes	—
97	C₂²×Q₈×C₁₃	—	2	2	no	—
98	C₂²×Q₈×C₁₃	—	2	2	no	—
99	C₂²×Q₈×C₁₃	—	2	2	no	—
100	C₂²×Q₈×C₁₃	—	4	8	no	—
101	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
102	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
103	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
104	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
105	C₂²×D₄×C₁₃	—	2	2	no	—
106	C₂²×D₄×C₁₃	—	2	1	no	—
107	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
108	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
109	C₂³×C₄×C₁₃	—	2	2	no	—
110	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
111	C₁₃×#137	—	4	8	no	—
112	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
113	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
114	C₂×C₁₃×SD₁₆	—	4	8	no	—
115	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
116	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
117	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
118	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
119	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
120	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
121	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
122	C₁₃×C₄⋊Q₈	—	2	2	no	—
123	C₁₃×C₄⋊Q₈	—	2	2	no	—
124	C₁₃×C₄⋊Q₈	—	2	4	no	—
125	C₁₃×C₄⋊Q₈	—	2	1	no	—
126	C₁₃×C₄⋊Q₈	—	2	1	no	—
127	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
128	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
129	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
130	C₁₃×#127	—	2	1	no	—
131	C₁₃×#127	C₂³	1	1	yes	characteristic
132	C₁₃×#126	—	2	2	no	—
133	C₁₃×#126	—	2	1	no	—
134	C₁₃×#125	—	2	1	no	—
135	C₁₃×#125	C₂³	1	1	yes	characteristic
136	C₁₃×#124	—	2	2	no	—
137	C₁₃×#124	—	2	1	no	—
138	C₁₃×#124	C₂³	1	1	yes	characteristic
139	C₁₃×#123	—	2	2	no	—
140	C₁₃×#123	—	2	1	no	—
141	C₁₃×#123	—	2	2	no	—
142	C₁₃×#123	—	2	2	no	—
143	C₁₃×C₂²⋊Q₈	—	2	2	no	—
144	C₁₃×C₂²⋊Q₈	—	2	2	no	—
145	C₁₃×C₂²⋊Q₈	—	2	4	no	—
146	C₁₃×C₂²⋊Q₈	—	2	4	no	—
147	C₁₃×C₂²⋊Q₈	—	2	4	no	—
148	C₁₃×C₂²⋊Q₈	—	2	4	no	—
149	C₁₃×C₂²⋊Q₈	—	2	2	no	—
150	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
151	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
152	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
153	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
154	C₁₃×#121	—	2	2	no	—
155	C₁₃×#121	—	2	1	no	—
156	C₁₃×#121	—	2	2	no	—
157	C₁₃×#121	—	2	2	no	—
158	C₁₃×#121	—	2	1	no	—
159	C₁₃×#121	—	2	1	no	—
160	C₁₃×#121	—	2	2	no	—
161	C₁₃×#121	—	2	2	no	—
162	C₁₃×#121	C₂³	1	1	yes	characteristic
163	C₁₃×#121	C₂³	1	2	yes	—
164	C₁₃×#121	C₂³	1	2	yes	—
165	C₁₃×#121	C₂³	1	2	yes	—
166	C₁₃×#121	C₂³	1	2	yes	—
167	C₁₃×#120	—	2	2	no	—
168	C₁₃×#120	—	2	2	no	—
169	C₁₃×#120	—	2	2	no	—
170	C₄×Q₈×C₁₃	—	2	1	no	—
171	C₄×Q₈×C₁₃	—	2	1	no	—
172	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
173	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
174	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
175	C₄×D₄×C₁₃	—	2	2	no	—
176	C₄×D₄×C₁₃	—	2	4	no	—
177	C₄×D₄×C₁₃	—	2	2	no	—
178	C₄×D₄×C₁₃	—	2	1	no	—
179	C₄×D₄×C₁₃	—	2	2	no	—
180	C₄×D₄×C₁₃	—	2	2	no	—
181	C₄×D₄×C₁₃	—	2	1	no	—
182	C₄×D₄×C₁₃	—	2	1	no	—
183	C₄×D₄×C₁₃	—	2	2	no	—
184	C₄×D₄×C₁₃	—	2	1	no	—
185	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
186	C₄×D₄×C₁₃	D₄	1	2	yes	—
187	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
188	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
189	C₄×D₄×C₁₃	C₂³	1	2	yes	—
190	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
191	C₄×D₄×C₁₃	C₂³	1	2	yes	—
192	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
193	C₁₃×#117	—	2	1	no	—
194	C₁₃×#117	—	2	1	no	—
195	C₁₃×#117	C₂³	1	2	yes	—
196	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
197	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
198	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
199	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
200	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
201	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
202	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
203	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
204	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
205	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
206	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
207	C₂×C₄²×C₁₃	—	2	1	no	—
208	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
209	C₁₃×#107	C₂³	1	2	yes	—
210	C₁₃×#107	C₂³	1	4	yes	—
211	C₁₃×#106	C₂³	1	2	yes	—
212	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
213	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
214	C₁₃×#103	C₂³	1	2	yes	—
215	C₁₃×#103	C₂³	1	4	yes	—
216	C₁₃×#103	C₂³	1	4	yes	—
217	C₁₃×#103	C₂³	1	4	yes	—
218	C₁₃×#103	C₂³	1	2	yes	—
219	C₁₃×#103	C₂³	1	4	yes	—
220	C₁₃×#103	C₂³	1	4	yes	—
221	C₁₃×#103	C₂³	1	2	yes	—
222	C₁₃×#102	C₂³	1	2	yes	—
223	C₁₃×#102	C₂³	1	4	yes	—
224	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
225	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
226	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
227	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
228	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
229	C₁₃×#97	C₂³	1	2	yes	—
230	C₄×C₈×C₁₃	C₂³	1	2	yes	—
231	#61593	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
232	C₂⁴×C₁₃	—	2	2	no	—
233	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
234	C₁₃×#41	—	4	4	no	—
235	C₁₃×#41	—	8	2	no	—
236	C₂×Q₈×C₁₃	—	2	4	no	—
237	C₂×Q₈×C₁₃	—	2	1	no	—
238	C₂×Q₈×C₁₃	—	2	4	no	—
239	C₂×Q₈×C₁₃	—	2	4	no	—
240	C₂×Q₈×C₁₃	—	2	2	no	—
241	C₂×Q₈×C₁₃	—	2	1	no	—
242	C₂×Q₈×C₁₃	—	2	8	no	—
243	C₂×Q₈×C₁₃	—	2	8	no	—
244	C₂×Q₈×C₁₃	—	4	4	no	—
245	C₂×Q₈×C₁₃	—	4	4	no	—
246	C₂×Q₈×C₁₃	—	4	4	no	—
247	C₂×Q₈×C₁₃	—	4	8	no	—
248	C₂×Q₈×C₁₃	—	4	8	no	—
249	C₂×Q₈×C₁₃	—	4	8	no	—
250	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
251	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
252	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
253	C₂×D₄×C₁₃	—	2	4	no	—
254	C₂×D₄×C₁₃	—	2	2	no	—
255	C₂×D₄×C₁₃	—	2	2	no	—
256	C₂×D₄×C₁₃	—	2	1	no	—
257	C₂×D₄×C₁₃	—	2	2	no	—
258	C₂×D₄×C₁₃	—	2	2	no	—
259	C₂×D₄×C₁₃	—	2	2	no	—
260	C₂×D₄×C₁₃	—	2	1	no	—
261	C₂×D₄×C₁₃	—	2	1	no	—
262	C₂×D₄×C₁₃	—	2	2	no	—
263	C₂×D₄×C₁₃	—	4	4	no	—
264	C₂×D₄×C₁₃	—	4	4	no	—
265	C₂×D₄×C₁₃	—	8	4	no	—
266	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
267	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
268	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
269	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
270	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
271	C₂²×C₄×C₁₃	—	2	1	no	—
272	C₂²×C₄×C₁₃	—	2	1	no	—
273	C₂²×C₄×C₁₃	—	2	2	no	—
274	C₂²×C₄×C₁₃	—	2	4	no	—
275	C₂²×C₄×C₁₃	—	2	4	no	—
276	C₂²×C₄×C₁₃	—	2	2	no	—
277	C₂²×C₄×C₁₃	—	2	1	no	—
278	C₂²×C₄×C₁₃	—	2	2	no	—
279	C₂²×C₄×C₁₃	—	2	2	no	—
280	C₂²×C₄×C₁₃	—	4	4	no	—
281	C₂²×C₄×C₁₃	—	4	8	no	—
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	2	yes	—
285	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
286	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
287	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
288	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
289	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
290	C₁₃×Q₁₆	—	2	4	no	—
291	C₁₃×Q₁₆	—	4	4	no	—
292	C₁₃×SD₁₆	—	2	4	no	—
293	C₁₃×SD₁₆	—	2	8	no	—
294	C₁₃×SD₁₆	—	4	4	no	—
295	C₁₃×SD₁₆	—	4	4	no	—
296	C₁₃×SD₁₆	—	4	4	no	—
297	C₁₃×M₁₆	—	4	4	no	—
298	C₂×C₈×C₁₃	—	4	4	no	—
299	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
300	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
301	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
302	C₁₃×C₄⋊C₄	—	2	2	no	—
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	2	no	—
308	C₁₃×C₄⋊C₄	—	2	4	no	—
309	C₁₃×C₄⋊C₄	—	2	4	no	—
310	C₁₃×C₄⋊C₄	—	2	1	no	—
311	C₁₃×C₄⋊C₄	—	2	2	no	—
312	C₁₃×C₄⋊C₄	—	2	1	no	—
313	C₁₃×C₄⋊C₄	—	2	1	no	—
314	C₁₃×C₄⋊C₄	—	2	1	no	—
315	C₁₃×C₄⋊C₄	—	2	1	no	—
316	C₁₃×C₄⋊C₄	—	2	2	no	—
317	C₁₃×C₄⋊C₄	—	2	1	no	—
318	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
319	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
320	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
321	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
322	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
323	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
324	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
325	C₁₃×C₂²⋊C₄	—	2	2	no	—
326	C₁₃×C₂²⋊C₄	—	2	4	no	—
327	C₁₃×C₂²⋊C₄	—	2	4	no	—
328	C₁₃×C₂²⋊C₄	—	2	2	no	—
329	C₁₃×C₂²⋊C₄	—	2	1	no	—
330	C₁₃×C₂²⋊C₄	—	2	1	no	—
331	C₁₃×C₂²⋊C₄	—	2	1	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	—	2	1	no	—
336	C₁₃×C₂²⋊C₄	—	2	2	no	—
337	C₁₃×C₂²⋊C₄	—	2	1	no	—
338	C₁₃×C₂²⋊C₄	—	2	2	no	—
339	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
340	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
341	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
342	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
343	C₄²×C₁₃	—	2	2	no	—
344	C₄²×C₁₃	—	2	2	no	—
345	C₄²×C₁₃	—	2	2	no	—
346	C₄²×C₁₃	—	2	1	no	—
347	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
348	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
349	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
350	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
351	#3519	C₂×C₁₃	1	1	yes	characteristic
352	C₂×D₄×Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
353	#3329	C₂×C₁₃	1	2	yes	complemented
354	#3320	C₂×C₁₃	1	4	yes	complemented
355	#3299	C₂×C₁₃	1	2	yes	complemented
356	D₄×SD₁₆	C₂×C₁₃	1	2	yes	complemented
357	#3278	C₂×C₁₃	1	2	yes	complemented
358	#3266	C₂×C₁₃	1	4	yes	complemented
359	#3218	C₂×C₁₃	1	1	yes	characteristic, complemented
360	#3206	C₂×C₁₃	1	1	yes	characteristic, complemented
361	#3193	C₂×C₁₃	1	2	yes	complemented
362	#3190	C₂×C₁₃	1	2	yes	complemented
363	#3112	C₂×C₁₃	1	1	yes	characteristic, complemented
364	#3108	C₂×C₁₃	1	1	yes	characteristic, complemented
365	#3004	C₂×C₁₃	1	2	yes	complemented
366	C₂×#448	C₂×C₁₃	1	2	yes	complemented
367	#2974	C₂×C₁₃	1	1	yes	characteristic, complemented
368	C₂³×C₁₃	—	2	4	no	—
369	C₂³×C₁₃	—	2	4	no	—
370	C₂³×C₁₃	—	2	1	no	—
371	C₂³×C₁₃	—	2	2	no	—
372	C₂³×C₁₃	—	4	2	no	—
373	C₂³×C₁₃	—	4	4	no	—
374	C₂³×C₁₃	—	8	2	no	—
375	C₂³×C₁₃	—	8	2	no	—
376	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
377	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
378	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
379	Q₈×C₁₃	—	2	4	no	—
380	Q₈×C₁₃	—	2	2	no	—
381	Q₈×C₁₃	—	2	4	no	—
382	Q₈×C₁₃	—	2	4	no	—
383	Q₈×C₁₃	—	2	2	no	—
384	Q₈×C₁₃	—	4	8	no	—
385	Q₈×C₁₃	—	4	8	no	—
386	Q₈×C₁₃	—	4	4	no	—
387	Q₈×C₁₃	—	8	1	no	—
388	Q₈×C₁₃	H(5,𝔽₂)	1	4	yes	—
389	D₄×C₁₃	—	2	4	no	—
390	D₄×C₁₃	—	2	2	no	—
391	D₄×C₁₃	—	2	2	no	—
392	D₄×C₁₃	—	2	4	no	—
393	D₄×C₁₃	—	4	4	no	—
394	D₄×C₁₃	—	4	2	no	—
395	D₄×C₁₃	—	4	4	no	—
396	D₄×C₁₃	—	4	2	no	—
397	D₄×C₁₃	—	8	2	no	—
398	D₄×C₁₃	—	8	1	no	—
399	D₄×C₁₃	—	8	2	no	—
400	D₄×C₁₃	—	8	2	no	—
401	D₄×C₁₃	—	8	2	no	—
402	D₄×C₁₃	#137	1	4	yes	complemented
403	C₂×C₄×C₁₃	—	2	4	no	—
404	C₂×C₄×C₁₃	—	2	2	no	—
405	C₂×C₄×C₁₃	—	2	2	no	—
406	C₂×C₄×C₁₃	—	2	2	no	—
407	C₂×C₄×C₁₃	—	2	4	no	—
408	C₂×C₄×C₁₃	—	2	4	no	—
409	C₂×C₄×C₁₃	—	2	2	no	—
410	C₂×C₄×C₁₃	—	2	1	no	—
411	C₂×C₄×C₁₃	—	2	2	no	—
412	C₂×C₄×C₁₃	—	2	1	no	—
413	C₂×C₄×C₁₃	—	2	2	no	—
414	C₂×C₄×C₁₃	—	2	1	no	—
415	C₂×C₄×C₁₃	—	2	4	no	—
416	C₂×C₄×C₁₃	—	4	2	no	—
417	C₂×C₄×C₁₃	—	4	2	no	—
418	C₂×C₄×C₁₃	—	4	2	no	—
419	C₂×C₄×C₁₃	—	4	8	no	—
420	C₂×C₄×C₁₃	—	4	8	no	—
421	C₂×C₄×C₁₃	—	4	4	no	—
422	C₂×C₄×C₁₃	—	4	2	no	—
423	C₂×C₄×C₁₃	—	4	2	no	—
424	C₂×C₄×C₁₃	—	8	2	no	—
425	C₂×C₄×C₁₃	—	8	2	no	—
426	C₂×C₄×C₁₃	—	8	2	no	—
427	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
428	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
429	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
430	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
431	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
432	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
433	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
434	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
435	C₈×C₁₃	—	2	2	no	—
436	C₈×C₁₃	—	2	4	no	—
437	C₈×C₁₃	—	2	2	no	—
438	C₂³×Q₈	C₂²×C₁₃	1	2	yes	complemented
439	C₂×#137	C₂²×C₁₃	1	4	yes	complemented
440	C₂²×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
441	#555	C₂²×C₁₃	1	1	yes	characteristic
442	#554	C₂²×C₁₃	1	1	yes	characteristic
443	#553	—	2	1	no	—
444	#553	C₂²×C₁₃	1	2	yes	—
445	#550	C₂²×C₁₃	1	1	yes	characteristic
446	D₄×Q₈	—	2	1	no	—
447	D₄×Q₈	—	2	2	no	—
448	D₄×Q₈	—	2	1	no	—
449	D₄×Q₈	C₂²×C₁₃	1	2	yes	—
450	D₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
451	D₄×Q₈	C₂²×C₁₃	1	4	yes	complemented
452	#546	—	2	2	no	—
453	#546	C₂²×C₁₃	1	2	yes	—
454	D₄²	—	2	1	no	—
455	D₄²	C₂²×C₁₃	1	1	yes	characteristic
456	#540	—	2	1	no	—
457	#538	—	2	2	no	—
458	#532	C₂²×C₁₃	1	1	yes	characteristic
459	C₂×C₄⋊Q₈	—	2	1	no	—
460	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
461	#529	C₂²×C₁₃	1	1	yes	characteristic
462	#525	C₂²×C₁₃	1	2	yes	—
463	C₂×C₂²⋊Q₈	—	2	2	no	—
464	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
465	C₂×#121	C₂²×C₁₃	1	2	yes	—
466	#518	—	2	1	no	—
467	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
468	C₂×C₄×D₄	—	2	1	no	—
469	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
470	#497	C₂²×C₁₃	1	2	yes	complemented
471	#492	C₂²×C₁₃	1	2	yes	complemented
472	#491	C₂²×C₁₃	1	2	yes	complemented
473	#487	C₂²×C₁₃	1	2	yes	complemented
474	#485	C₂²×C₁₃	1	4	yes	complemented
475	#484	C₂²×C₁₃	1	4	yes	complemented
476	#483	C₂²×C₁₃	1	1	yes	characteristic, complemented
477	#480	C₂²×C₁₃	1	1	yes	characteristic
478	#480	C₂²×C₁₃	1	2	yes	complemented
479	#479	C₂²×C₁₃	1	2	yes	complemented
480	#477	C₂²×C₁₃	1	2	yes	complemented
481	#468	C₂²×C₁₃	1	4	yes	complemented
482	#468	C₂²×C₁₃	1	4	yes	complemented
483	#467	C₂²×C₁₃	1	4	yes	complemented
484	#465	C₂²×C₁₃	1	4	yes	complemented
485	#464	C₂²×C₁₃	1	2	yes	complemented
486	#462	C₂²×C₁₃	1	2	yes	complemented
487	#461	C₂²×C₁₃	1	2	yes	complemented
488	#461	C₂²×C₁₃	1	4	yes	complemented
489	#460	C₂²×C₁₃	1	2	yes	complemented
490	#452	C₂²×C₁₃	1	4	yes	complemented
491	#451	C₂²×C₁₃	1	1	yes	characteristic, complemented
492	#451	C₂²×C₁₃	1	2	yes	complemented
493	#451	C₂²×C₁₃	1	4	yes	complemented
494	#450	C₂²×C₁₃	1	4	yes	complemented
495	#448	C₂²×C₁₃	1	1	yes	characteristic
496	#448	C₂²×C₁₃	1	2	yes	—
497	#448	C₂²×C₁₃	1	4	yes	complemented
498	#448	C₂²×C₁₃	1	2	yes	complemented
499	#448	C₂²×C₁₃	1	2	yes	complemented
500	#448	C₂²×C₁₃	1	2	yes	complemented
501	#448	C₂²×C₁₃	1	4	yes	complemented
502	#448	C₂²×C₁₃	1	4	yes	complemented
503	#440	C₂²×C₁₃	1	4	yes	complemented
504	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
505	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
506	#436	C₂²×C₁₃	1	2	yes	complemented
507	#435	C₂²×C₁₃	1	4	yes	complemented
508	C₈×D₄	C₂²×C₁₃	1	2	yes	—
509	#432	C₂²×C₁₃	1	1	yes	characteristic, complemented
510	#431	C₂²×C₁₃	1	1	yes	characteristic, complemented
511	#419	C₂²×C₁₃	1	4	yes	complemented
512	C₂×#103	C₂²×C₁₃	1	4	yes	complemented
513	#407	C₂²×C₁₃	1	2	yes	complemented
514	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	complemented
515	C₂²×C₁₃	—	2	1	no	—
516	C₂²×C₁₃	—	2	2	no	—
517	C₂²×C₁₃	—	2	1	no	—
518	C₂²×C₁₃	—	2	2	no	—
519	C₂²×C₁₃	—	2	2	no	—
520	C₂²×C₁₃	—	2	2	no	—
521	C₂²×C₁₃	—	2	2	no	—
522	C₂²×C₁₃	—	4	8	no	—
523	C₂²×C₁₃	—	4	2	no	—
524	C₂²×C₁₃	—	4	1	no	—
525	C₂²×C₁₃	—	4	1	no	—
526	C₂²×C₁₃	—	4	2	no	—
527	C₂²×C₁₃	—	4	2	no	—
528	C₂²×C₁₃	—	4	1	no	—
529	C₂²×C₁₃	—	16	4	no	—
530	C₂²×C₁₃	C₂×#137	1	4	yes	—
531	C₂²×C₁₃	#577	1	2	yes	—
532	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
533	C₄×C₁₃	—	2	4	no	—
534	C₄×C₁₃	—	2	1	no	—
535	C₄×C₁₃	—	2	2	no	—
536	C₄×C₁₃	—	2	2	no	—
537	C₄×C₁₃	—	2	1	no	—
538	C₄×C₁₃	—	2	1	no	—
539	C₄×C₁₃	—	2	1	no	—
540	C₄×C₁₃	—	4	4	no	—
541	C₄×C₁₃	—	4	1	no	—
542	C₄×C₁₃	—	4	1	no	—
543	C₄×C₁₃	—	4	2	no	—
544	C₄×C₁₃	—	4	1	no	—
545	C₄×C₁₃	—	4	2	no	—
546	C₄×C₁₃	C₂×#137	1	2	yes	—
547	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
548	C₂×#41	—	2	1	no	—
549	C₂×#41	C₂³×C₁₃	1	2	yes	—
550	C₂²×Q₈	—	2	2	no	—
551	C₂²×Q₈	—	2	2	no	—
552	C₂²×Q₈	—	2	2	no	—
553	C₂²×Q₈	—	4	8	no	—
554	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
555	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
556	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
557	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
558	C₂²×D₄	—	2	2	no	—
559	C₂²×D₄	—	2	1	no	—
560	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
561	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
562	C₂³×C₄	—	2	2	no	—
563	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
564	#137	—	4	8	no	—
565	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
566	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
567	C₂×SD₁₆	—	4	8	no	—
568	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
569	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
570	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
571	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
572	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
573	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
574	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
575	C₄⋊Q₈	—	2	2	no	—
576	C₄⋊Q₈	—	2	2	no	—
577	C₄⋊Q₈	—	2	4	no	—
578	C₄⋊Q₈	—	2	1	no	—
579	C₄⋊Q₈	—	2	1	no	—
580	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
581	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
582	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
583	#127	—	2	1	no	—
584	#127	C₂³×C₁₃	1	1	yes	characteristic
585	#126	—	2	2	no	—
586	#126	—	2	1	no	—
587	#125	—	2	1	no	—
588	#125	C₂³×C₁₃	1	1	yes	characteristic
589	#124	—	2	2	no	—
590	#124	—	2	1	no	—
591	#124	C₂³×C₁₃	1	1	yes	characteristic
592	#123	—	2	2	no	—
593	#123	—	2	1	no	—
594	#123	—	2	2	no	—
595	#123	—	2	2	no	—
596	C₂²⋊Q₈	—	2	2	no	—
597	C₂²⋊Q₈	—	2	2	no	—
598	C₂²⋊Q₈	—	2	4	no	—
599	C₂²⋊Q₈	—	2	4	no	—
600	C₂²⋊Q₈	—	2	4	no	—
601	C₂²⋊Q₈	—	2	4	no	—
602	C₂²⋊Q₈	—	2	2	no	—
603	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
604	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
605	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
606	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
607	#121	—	2	2	no	—
608	#121	—	2	1	no	—
609	#121	—	2	2	no	—
610	#121	—	2	2	no	—
611	#121	—	2	1	no	—
612	#121	—	2	1	no	—
613	#121	—	2	2	no	—
614	#121	—	2	2	no	—
615	#121	C₂³×C₁₃	1	1	yes	characteristic
616	#121	C₂³×C₁₃	1	2	yes	—
617	#121	C₂³×C₁₃	1	2	yes	—
618	#121	C₂³×C₁₃	1	2	yes	—
619	#121	C₂³×C₁₃	1	2	yes	—
620	#120	—	2	2	no	—
621	#120	—	2	2	no	—
622	#120	—	2	2	no	—
623	C₄×Q₈	—	2	1	no	—
624	C₄×Q₈	—	2	1	no	—
625	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
626	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
627	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
628	C₄×D₄	—	2	2	no	—
629	C₄×D₄	—	2	4	no	—
630	C₄×D₄	—	2	2	no	—
631	C₄×D₄	—	2	1	no	—
632	C₄×D₄	—	2	2	no	—
633	C₄×D₄	—	2	2	no	—
634	C₄×D₄	—	2	1	no	—
635	C₄×D₄	—	2	1	no	—
636	C₄×D₄	—	2	2	no	—
637	C₄×D₄	—	2	1	no	—
638	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
639	C₄×D₄	D₄×C₁₃	1	2	yes	—
640	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
641	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
642	C₄×D₄	C₂³×C₁₃	1	2	yes	—
643	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
644	C₄×D₄	C₂³×C₁₃	1	2	yes	—
645	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
646	#117	—	2	1	no	—
647	#117	—	2	1	no	—
648	#117	C₂³×C₁₃	1	2	yes	—
649	C₂×C₄⋊C₄	—	2	1	no	—
650	C₂×C₄⋊C₄	—	2	1	no	—
651	C₂×C₄⋊C₄	—	2	1	no	—
652	C₂×C₄⋊C₄	—	2	2	no	—
653	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
654	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
655	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
656	C₂×C₂²⋊C₄	—	2	2	no	—
657	C₂×C₂²⋊C₄	—	2	2	no	—
658	C₂×C₂²⋊C₄	—	2	2	no	—
659	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
660	C₂×C₄²	—	2	1	no	—
661	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
662	#107	C₂³×C₁₃	1	2	yes	—
663	#107	C₂³×C₁₃	1	4	yes	—
664	#106	C₂³×C₁₃	1	2	yes	—
665	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
666	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
667	#103	C₂³×C₁₃	1	2	yes	—
668	#103	C₂³×C₁₃	1	4	yes	—
669	#103	C₂³×C₁₃	1	4	yes	—
670	#103	C₂³×C₁₃	1	4	yes	—
671	#103	C₂³×C₁₃	1	2	yes	—
672	#103	C₂³×C₁₃	1	4	yes	—
673	#103	C₂³×C₁₃	1	4	yes	—
674	#103	C₂³×C₁₃	1	2	yes	—
675	#102	C₂³×C₁₃	1	2	yes	—
676	#102	C₂³×C₁₃	1	4	yes	—
677	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
678	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
679	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
680	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
681	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
682	#97	C₂³×C₁₃	1	2	yes	—
683	C₄×C₈	C₂³×C₁₃	1	2	yes	—
684	C₂×C₁₃	—	2	2	no	—
685	C₂×C₁₃	—	2	4	no	—
686	C₂×C₁₃	—	4	2	no	—
687	C₂×C₁₃	—	8	2	no	—
688	C₂×C₁₃	—	8	1	no	—
689	C₂×C₁₃	#3484	1	1	yes	characteristic
690	C₂×C₁₃	C₂²×#137	1	1	yes	characteristic
691	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
692	C₂⁴	—	2	2	no	—
693	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
694	#41	—	4	4	no	—
695	#41	—	8	2	no	—
696	C₂×Q₈	—	2	4	no	—
697	C₂×Q₈	—	2	1	no	—
698	C₂×Q₈	—	2	4	no	—
699	C₂×Q₈	—	2	4	no	—
700	C₂×Q₈	—	2	2	no	—
701	C₂×Q₈	—	2	1	no	—
702	C₂×Q₈	—	2	8	no	—
703	C₂×Q₈	—	2	8	no	—
704	C₂×Q₈	—	4	4	no	—
705	C₂×Q₈	—	4	4	no	—
706	C₂×Q₈	—	4	4	no	—
707	C₂×Q₈	—	4	8	no	—
708	C₂×Q₈	—	4	8	no	—
709	C₂×Q₈	—	4	8	no	—
710	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
711	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
712	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
713	C₂×D₄	—	2	4	no	—
714	C₂×D₄	—	2	2	no	—
715	C₂×D₄	—	2	2	no	—
716	C₂×D₄	—	2	1	no	—
717	C₂×D₄	—	2	2	no	—
718	C₂×D₄	—	2	2	no	—
719	C₂×D₄	—	2	2	no	—
720	C₂×D₄	—	2	1	no	—
721	C₂×D₄	—	2	1	no	—
722	C₂×D₄	—	2	2	no	—
723	C₂×D₄	—	4	4	no	—
724	C₂×D₄	—	4	4	no	—
725	C₂×D₄	—	8	4	no	—
726	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
727	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
728	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
729	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
730	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
731	C₂²×C₄	—	2	1	no	—
732	C₂²×C₄	—	2	1	no	—
733	C₂²×C₄	—	2	2	no	—
734	C₂²×C₄	—	2	4	no	—
735	C₂²×C₄	—	2	4	no	—
736	C₂²×C₄	—	2	2	no	—
737	C₂²×C₄	—	2	1	no	—
738	C₂²×C₄	—	2	2	no	—
739	C₂²×C₄	—	2	2	no	—
740	C₂²×C₄	—	4	4	no	—
741	C₂²×C₄	—	4	8	no	—
742	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
743	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
744	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
745	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
746	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
747	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
748	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
749	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
750	Q₁₆	—	2	4	no	—
751	Q₁₆	—	4	4	no	—
752	SD₁₆	—	2	4	no	—
753	SD₁₆	—	2	8	no	—
754	SD₁₆	—	4	4	no	—
755	SD₁₆	—	4	4	no	—
756	SD₁₆	—	4	4	no	—
757	M₁₆	—	4	4	no	—
758	C₂×C₈	—	4	4	no	—
759	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
760	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
761	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
762	C₄⋊C₄	—	2	2	no	—
763	C₄⋊C₄	—	2	2	no	—
764	C₄⋊C₄	—	2	2	no	—
765	C₄⋊C₄	—	2	2	no	—
766	C₄⋊C₄	—	2	2	no	—
767	C₄⋊C₄	—	2	2	no	—
768	C₄⋊C₄	—	2	4	no	—
769	C₄⋊C₄	—	2	4	no	—
770	C₄⋊C₄	—	2	1	no	—
771	C₄⋊C₄	—	2	2	no	—
772	C₄⋊C₄	—	2	1	no	—
773	C₄⋊C₄	—	2	1	no	—
774	C₄⋊C₄	—	2	1	no	—
775	C₄⋊C₄	—	2	1	no	—
776	C₄⋊C₄	—	2	2	no	—
777	C₄⋊C₄	—	2	1	no	—
778	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
779	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
780	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
781	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
782	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
783	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
784	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
785	C₂²⋊C₄	—	2	2	no	—
786	C₂²⋊C₄	—	2	4	no	—
787	C₂²⋊C₄	—	2	4	no	—
788	C₂²⋊C₄	—	2	2	no	—
789	C₂²⋊C₄	—	2	1	no	—
790	C₂²⋊C₄	—	2	1	no	—
791	C₂²⋊C₄	—	2	1	no	—
792	C₂²⋊C₄	—	2	2	no	—
793	C₂²⋊C₄	—	2	2	no	—
794	C₂²⋊C₄	—	2	2	no	—
795	C₂²⋊C₄	—	2	1	no	—
796	C₂²⋊C₄	—	2	2	no	—
797	C₂²⋊C₄	—	2	1	no	—
798	C₂²⋊C₄	—	2	2	no	—
799	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
800	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
801	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
802	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
803	C₄²	—	2	2	no	—
804	C₄²	—	2	2	no	—
805	C₄²	—	2	2	no	—
806	C₄²	—	2	1	no	—
807	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
808	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
809	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
810	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
811	C₁₃	#61593	1	1	yes	characteristic, direct product factor, Sylow
812	C₂³	—	2	4	no	—
813	C₂³	—	2	4	no	—
814	C₂³	—	2	1	no	—
815	C₂³	—	2	2	no	—
816	C₂³	—	4	2	no	—
817	C₂³	—	4	4	no	—
818	C₂³	—	8	2	no	—
819	C₂³	—	8	2	no	—
820	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
821	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
822	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
823	Q₈	—	2	4	no	—
824	Q₈	—	2	2	no	—
825	Q₈	—	2	4	no	—
826	Q₈	—	2	4	no	—
827	Q₈	—	2	2	no	—
828	Q₈	—	4	8	no	—
829	Q₈	—	4	8	no	—
830	Q₈	—	4	4	no	—
831	Q₈	—	8	1	no	—
832	Q₈	C₁₃×H(5,𝔽₂)	1	4	yes	—
833	D₄	—	2	4	no	—
834	D₄	—	2	2	no	—
835	D₄	—	2	2	no	—
836	D₄	—	2	4	no	—
837	D₄	—	4	4	no	—
838	D₄	—	4	2	no	—
839	D₄	—	4	4	no	—
840	D₄	—	4	2	no	—
841	D₄	—	8	2	no	—
842	D₄	—	8	1	no	—
843	D₄	—	8	2	no	—
844	D₄	—	8	2	no	—
845	D₄	—	8	2	no	—
846	D₄	C₁₃×#137	1	4	yes	complemented
847	C₂×C₄	—	2	4	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	2	4	no	—
852	C₂×C₄	—	2	4	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	2	1	no	—
855	C₂×C₄	—	2	2	no	—
856	C₂×C₄	—	2	1	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	2	1	no	—
859	C₂×C₄	—	2	4	no	—
860	C₂×C₄	—	4	2	no	—
861	C₂×C₄	—	4	2	no	—
862	C₂×C₄	—	4	2	no	—
863	C₂×C₄	—	4	8	no	—
864	C₂×C₄	—	4	8	no	—
865	C₂×C₄	—	4	4	no	—
866	C₂×C₄	—	4	2	no	—
867	C₂×C₄	—	4	2	no	—
868	C₂×C₄	—	8	2	no	—
869	C₂×C₄	—	8	2	no	—
870	C₂×C₄	—	8	2	no	—
871	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
872	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
873	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
874	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
875	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
876	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
877	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
878	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
879	C₈	—	2	2	no	—
880	C₈	—	2	4	no	—
881	C₈	—	2	2	no	—
882	C₂²	—	2	1	no	—
883	C₂²	—	2	2	no	—
884	C₂²	—	2	1	no	—
885	C₂²	—	2	2	no	—
886	C₂²	—	2	2	no	—
887	C₂²	—	2	2	no	—
888	C₂²	—	2	2	no	—
889	C₂²	—	4	8	no	—
890	C₂²	—	4	1	no	—
891	C₂²	—	4	2	no	—
892	C₂²	—	4	2	no	—
893	C₂²	—	4	1	no	—
894	C₂²	—	4	2	no	—
895	C₂²	—	4	1	no	—
896	C₂²	—	16	4	no	—
897	C₂²	C₂×C₁₃×#137	1	4	yes	—
898	C₂²	C₁₃×#577	1	2	yes	—
899	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
900	C₄	—	2	1	no	—
901	C₄	—	2	1	no	—
902	C₄	—	2	1	no	—
903	C₄	—	2	4	no	—
904	C₄	—	2	1	no	—
905	C₄	—	2	2	no	—
906	C₄	—	2	2	no	—
907	C₄	—	4	1	no	—
908	C₄	—	4	2	no	—
909	C₄	—	4	1	no	—
910	C₄	—	4	2	no	—
911	C₄	—	4	4	no	—
912	C₄	—	4	1	no	—
913	C₄	C₂×C₁₃×#137	1	2	yes	—
914	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
915	C₂	—	2	2	no	—
916	C₂	—	2	4	no	—
917	C₂	—	4	2	no	—
918	C₂	—	8	1	no	—
919	C₂	—	8	2	no	—
920	C₂	C₁₃×#3484	1	1	yes	characteristic
921	C₂	C₂²×C₁₃×#137	1	1	yes	characteristic
922	C₂	C₂×C₁₃×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3519	C₂
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
2. C₂×D₄×Q₈×C₁₃	C₂	semidirect
3. C₁₃×#3329	C₂	semidirect
4. C₁₃×#3320	C₂	semidirect
5. C₁₃×#3299	C₂	semidirect
6. D₄×C₁₃×SD₁₆	C₂	semidirect
7. C₁₃×#3278	C₂	semidirect
8. C₁₃×#3266	C₂	semidirect
9. C₁₃×#3218	C₂	semidirect
10. C₁₃×#3206	C₂	semidirect
11. C₁₃×#3193	C₂	semidirect
12. C₁₃×#3190	C₂	semidirect
13. C₁₃×#3112	C₂	semidirect
14. C₁₃×#3108	C₂	semidirect
15. C₁₃×#3004	C₂	semidirect
16. C₂×C₁₃×#448	C₂	semidirect
17. C₁₃×#2974	C₂	semidirect
18. C₂³×Q₈×C₁₃	C₂²	semidirect
19. C₂×C₁₃×#137	C₂²	semidirect
20. C₂²×C₁₃×SD₁₆	C₂²	semidirect
30. D₄×Q₈×C₁₃	C₂²	semidirect
31. D₄×Q₈×C₁₃	C₂²	semidirect
40. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
44. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
47. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
50. C₁₃×#497	C₂²	semidirect
51. C₁₃×#492	C₂²	semidirect
52. C₁₃×#491	C₂²	semidirect
53. C₁₃×#487	C₂²	semidirect
54. C₁₃×#485	C₂²	semidirect
55. C₁₃×#484	C₂²	semidirect
56. C₁₃×#483	C₂²	semidirect
58. C₁₃×#480	C₂²	semidirect
59. C₁₃×#479	C₂²	semidirect
60. C₁₃×#477	C₂²	semidirect
61. C₁₃×#468	C₂²	semidirect
62. C₁₃×#468	C₂²	semidirect
63. C₁₃×#467	C₂²	semidirect
64. C₁₃×#465	C₂²	semidirect
65. C₁₃×#464	C₂²	semidirect
66. C₁₃×#462	C₂²	semidirect
67. C₁₃×#461	C₂²	semidirect
68. C₁₃×#461	C₂²	semidirect
69. C₁₃×#460	C₂²	semidirect
70. C₁₃×#452	C₂²	semidirect
71. C₁₃×#451	C₂²	semidirect
72. C₁₃×#451	C₂²	semidirect
73. C₁₃×#451	C₂²	semidirect
74. C₁₃×#450	C₂²	semidirect
77. C₁₃×#448	C₂²	semidirect
78. C₁₃×#448	C₂²	semidirect
79. C₁₃×#448	C₂²	semidirect
80. C₁₃×#448	C₂²	semidirect
81. C₁₃×#448	C₂²	semidirect
82. C₁₃×#448	C₂²	semidirect
83. C₁₃×#440	C₂²	semidirect
84. C₄×C₁₃×Q₁₆	C₂²	semidirect
85. C₄×C₁₃×SD₁₆	C₂²	semidirect
86. C₁₃×#436	C₂²	semidirect
87. C₁₃×#435	C₂²	semidirect
89. C₁₃×#432	C₂²	semidirect
90. C₁₃×#431	C₂²	semidirect
91. C₁₃×#419	C₂²	semidirect
92. C₂×C₁₃×#103	C₂²	semidirect
93. C₁₃×#407	C₂²	semidirect
94. C₂×C₁₃×C₂²⋊C₈	C₂²	semidirect
231. #61593	C₁₃	direct (N × H)
352. C₂×D₄×Q₈	C₂×C₁₃	semidirect
353. #3329	C₂×C₁₃	semidirect
354. #3320	C₂×C₁₃	semidirect
355. #3299	C₂×C₁₃	semidirect
356. D₄×SD₁₆	C₂×C₁₃	semidirect
357. #3278	C₂×C₁₃	semidirect
358. #3266	C₂×C₁₃	semidirect
359. #3218	C₂×C₁₃	semidirect
360. #3206	C₂×C₁₃	semidirect
361. #3193	C₂×C₁₃	semidirect
362. #3190	C₂×C₁₃	semidirect
363. #3112	C₂×C₁₃	semidirect
364. #3108	C₂×C₁₃	semidirect
365. #3004	C₂×C₁₃	semidirect
366. C₂×#448	C₂×C₁₃	semidirect
367. #2974	C₂×C₁₃	semidirect
402. D₄×C₁₃	#137	semidirect
438. C₂³×Q₈	C₂²×C₁₃	semidirect
439. C₂×#137	C₂²×C₁₃	semidirect
440. C₂²×SD₁₆	C₂²×C₁₃	semidirect
450. D₄×Q₈	C₂²×C₁₃	semidirect
451. D₄×Q₈	C₂²×C₁₃	semidirect
460. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
464. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
467. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
470. #497	C₂²×C₁₃	semidirect
471. #492	C₂²×C₁₃	semidirect
472. #491	C₂²×C₁₃	semidirect
473. #487	C₂²×C₁₃	semidirect
474. #485	C₂²×C₁₃	semidirect
475. #484	C₂²×C₁₃	semidirect
476. #483	C₂²×C₁₃	semidirect
478. #480	C₂²×C₁₃	semidirect
479. #479	C₂²×C₁₃	semidirect
480. #477	C₂²×C₁₃	semidirect
481. #468	C₂²×C₁₃	semidirect
482. #468	C₂²×C₁₃	semidirect
483. #467	C₂²×C₁₃	semidirect
484. #465	C₂²×C₁₃	semidirect
485. #464	C₂²×C₁₃	semidirect
486. #462	C₂²×C₁₃	semidirect
487. #461	C₂²×C₁₃	semidirect
488. #461	C₂²×C₁₃	semidirect
489. #460	C₂²×C₁₃	semidirect
490. #452	C₂²×C₁₃	semidirect
491. #451	C₂²×C₁₃	semidirect
492. #451	C₂²×C₁₃	semidirect
493. #451	C₂²×C₁₃	semidirect
494. #450	C₂²×C₁₃	semidirect
497. #448	C₂²×C₁₃	semidirect
498. #448	C₂²×C₁₃	semidirect
499. #448	C₂²×C₁₃	semidirect
500. #448	C₂²×C₁₃	semidirect
501. #448	C₂²×C₁₃	semidirect
502. #448	C₂²×C₁₃	semidirect
503. #440	C₂²×C₁₃	semidirect
504. C₄×Q₁₆	C₂²×C₁₃	semidirect
505. C₄×SD₁₆	C₂²×C₁₃	semidirect
506. #436	C₂²×C₁₃	semidirect
507. #435	C₂²×C₁₃	semidirect
509. #432	C₂²×C₁₃	semidirect
510. #431	C₂²×C₁₃	semidirect
511. #419	C₂²×C₁₃	semidirect
512. C₂×#103	C₂²×C₁₃	semidirect
513. #407	C₂²×C₁₃	semidirect
514. C₂×C₂²⋊C₈	C₂²×C₁₃	semidirect
811. C₁₃	#61593	direct (N × H)
846. D₄	C₁₃×#137	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#3519	2
C₂×D₄×Q₈×C₁₃	2
C₁₃×#3329	2
C₁₃×#3320	2
C₁₃×#3299	2
D₄×C₁₃×SD₁₆	2
C₁₃×#3278	2
C₁₃×#3266	2
C₁₃×#3218	2
C₁₃×#3206	2
C₁₃×#3193	2
C₁₃×#3190	2
C₁₃×#3112	2
C₁₃×#3108	2
C₁₃×#3004	2
C₂×C₁₃×#448	2
C₁₃×#2974	2
#61593	13

Subgroups — C13×#61593 #15747932

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61593 #15747932