Subgroups — C₁₃×#61162 #15747501

Order 3328.

2162 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#554	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×C₁₃×#41	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3333	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3331	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3316	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3314	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3299	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3295	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3141	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3092	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3079	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3056	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3037	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3007	C₂	1	2	yes	maximal, complemented
15	C₄×C₁₃×#137	C₂	1	1	yes	maximal, characteristic, complemented
16	D₄×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₁₃×#417	C₂	1	2	yes	maximal, complemented
18	C₂²×C₁₃×#41	C₂²	1	2	yes	—
19	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#137	C₂²	1	2	yes	complemented
21	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	complemented
22	C₁₃×#554	—	2	1	no	—
23	C₁₃×#554	—	2	2	no	—
24	C₁₃×#554	—	2	1	no	—
25	C₁₃×#554	C₂²	1	2	yes	—
26	C₁₃×#554	C₂²	1	4	yes	complemented
27	C₁₃×#554	C₂²	1	2	yes	complemented
28	C₁₃×#550	C₂²	1	1	yes	characteristic
29	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
30	C₁₃×#548	C₂²	1	2	yes	—
31	C₁₃×#547	—	2	1	no	—
32	C₁₃×#547	C₂²	1	1	yes	characteristic
33	C₁₃×#546	—	2	2	no	—
34	C₁₃×#546	C₂²	1	2	yes	—
35	D₄²×C₁₃	—	2	1	no	—
36	D₄²×C₁₃	C₂²	1	1	yes	characteristic
37	C₁₃×#532	—	2	1	no	—
38	C₁₃×#532	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₁₃×#125	—	2	1	no	—
41	C₁₃×#525	—	2	2	no	—
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	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
46	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
47	C₂×C₄×D₄×C₁₃	—	2	1	no	—
48	C₂×C₄×D₄×C₁₃	—	2	1	no	—
49	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
50	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
51	C₁₃×#489	C₂²	1	4	yes	complemented
52	C₁₃×#487	C₂²	1	2	yes	complemented
53	C₁₃×#486	C₂²	1	2	yes	complemented
54	C₁₃×#484	C₂²	1	4	yes	complemented
55	C₁₃×#483	C₂²	1	4	yes	complemented
56	C₁₃×#481	C₂²	1	4	yes	complemented
57	C₁₃×#480	C₂²	1	4	yes	complemented
58	C₁₃×#477	C₂²	1	2	yes	complemented
59	C₁₃×#476	C₂²	1	2	yes	complemented
60	C₁₃×#475	C₂²	1	2	yes	complemented
61	C₁₃×#474	C₂²	1	2	yes	complemented
62	C₁₃×#470	C₂²	1	4	yes	complemented
63	C₁₃×#468	C₂²	1	4	yes	complemented
64	C₁₃×#467	C₂²	1	4	yes	complemented
65	C₁₃×#465	C₂²	1	4	yes	complemented
66	C₁₃×#464	C₂²	1	4	yes	complemented
67	C₁₃×#462	C₂²	1	2	yes	complemented
68	C₁₃×#460	C₂²	1	2	yes	complemented
69	C₁₃×#452	C₂²	1	4	yes	complemented
70	C₁₃×#452	C₂²	1	4	yes	complemented
71	C₁₃×#451	C₂²	1	4	yes	complemented
72	C₁₃×#450	C₂²	1	4	yes	complemented
73	C₁₃×#441	C₂²	1	2	yes	complemented
74	C₁₃×#440	C₂²	1	2	yes	complemented
75	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
76	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
77	C₁₃×#436	C₂²	1	2	yes	complemented
78	C₁₃×#435	C₂²	1	4	yes	complemented
79	C₈×D₄×C₁₃	C₂²	1	2	yes	—
80	C₁₃×#428	C₂²	1	2	yes	complemented
81	C₁₃×#428	C₂²	1	1	yes	characteristic, complemented
82	C₁₃×#423	C₂²	1	1	yes	characteristic, complemented
83	C₁₃×#419	C₂²	1	1	yes	characteristic, complemented
84	C₁₃×#417	C₂²	1	2	yes	—
85	C₁₃×#417	C₂²	1	1	yes	characteristic
86	C₁₃×#417	C₂²	1	2	yes	complemented
87	C₁₃×#417	C₂²	1	2	yes	complemented
88	C₁₃×#417	C₂²	1	2	yes	complemented
89	C₁₃×#417	C₂²	1	4	yes	complemented
90	C₁₃×#417	C₂²	1	4	yes	complemented
91	C₂×C₁₃×#103	C₂²	1	4	yes	complemented
92	C₂×C₁₃×#102	C₂²	1	4	yes	complemented
93	C₁₃×#407	C₂²	1	2	yes	complemented
94	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic, complemented
95	C₂×C₁₃×#41	—	2	2	no	—
96	C₂×C₁₃×#41	—	2	2	no	—
97	C₂×C₁₃×#41	—	2	8	no	—
98	C₂×C₁₃×#41	—	4	4	no	—
99	C₂×C₁₃×#41	C₂³	1	2	yes	—
100	C₂×C₁₃×#41	C₂³	1	2	yes	—
101	C₂×C₁₃×#41	C₂³	1	2	yes	—
102	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
103	C₂²×Q₈×C₁₃	—	2	1	no	—
104	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
105	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
106	C₂²×D₄×C₁₃	—	2	2	no	—
107	C₂²×D₄×C₁₃	—	2	1	no	—
108	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
109	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
110	C₂³×C₄×C₁₃	—	2	2	no	—
111	C₂³×C₄×C₁₃	—	2	2	no	—
112	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
113	C₁₃×#137	—	2	4	no	—
114	C₁₃×#137	—	4	4	no	—
115	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
116	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
117	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
118	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
119	C₂×C₁₃×M₁₆	—	4	4	no	—
120	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
121	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
122	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
123	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
124	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
125	C₁₃×C₄⋊Q₈	—	2	1	no	—
126	C₁₃×C₄⋊Q₈	—	2	1	no	—
127	C₁₃×C₄⋊Q₈	—	2	1	no	—
128	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
129	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
130	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
131	C₁₃×#127	—	2	1	no	—
132	C₁₃×#127	C₂³	1	1	yes	characteristic
133	C₁₃×#125	—	2	2	no	—
134	C₁₃×#125	—	2	2	no	—
135	C₁₃×#125	—	2	4	no	—
136	C₁₃×#124	—	2	2	no	—
137	C₁₃×#124	C₂³	1	2	yes	—
138	C₁₃×#123	—	2	2	no	—
139	C₁₃×#123	—	2	2	no	—
140	C₁₃×#123	—	2	2	no	—
141	C₁₃×C₂²⋊Q₈	—	2	2	no	—
142	C₁₃×C₂²⋊Q₈	—	2	2	no	—
143	C₁₃×C₂²⋊Q₈	—	2	2	no	—
144	C₁₃×C₂²⋊Q₈	—	2	4	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	2	no	—
149	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
150	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
151	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
152	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
153	C₁₃×#121	—	2	2	no	—
154	C₁₃×#121	—	2	1	no	—
155	C₁₃×#121	—	2	1	no	—
156	C₁₃×#121	—	2	1	no	—
157	C₁₃×#121	—	2	1	no	—
158	C₁₃×#121	—	2	2	no	—
159	C₁₃×#121	—	2	2	no	—
160	C₁₃×#121	C₂³	1	2	yes	—
161	C₁₃×#121	C₂³	1	2	yes	—
162	C₁₃×#120	—	2	2	no	—
163	C₁₃×#120	—	2	2	no	—
164	C₁₃×#120	—	2	2	no	—
165	C₄×Q₈×C₁₃	—	2	1	no	—
166	C₄×Q₈×C₁₃	—	2	1	no	—
167	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
168	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
169	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
170	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
171	C₄×D₄×C₁₃	—	2	1	no	—
172	C₄×D₄×C₁₃	—	2	2	no	—
173	C₄×D₄×C₁₃	—	2	4	no	—
174	C₄×D₄×C₁₃	—	2	2	no	—
175	C₄×D₄×C₁₃	—	2	2	no	—
176	C₄×D₄×C₁₃	—	2	1	no	—
177	C₄×D₄×C₁₃	—	2	1	no	—
178	C₄×D₄×C₁₃	—	2	2	no	—
179	C₄×D₄×C₁₃	—	2	1	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	D₄	1	1	yes	characteristic
184	C₄×D₄×C₁₃	D₄	1	2	yes	—
185	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
186	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
187	C₄×D₄×C₁₃	C₂³	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	C₁₃×#117	—	2	1	no	—
192	C₁₃×#117	C₂³	1	1	yes	characteristic
193	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
194	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
195	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
196	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
197	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
198	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
199	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
200	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
201	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
202	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
203	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
204	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
205	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
206	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
207	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
208	C₂×C₄²×C₁₃	—	2	1	no	—
209	C₂×C₄²×C₁₃	—	2	1	no	—
210	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
211	C₁₃×#107	C₂³	1	2	yes	—
212	C₁₃×#107	C₂³	1	4	yes	—
213	C₁₃×#106	C₂³	1	2	yes	—
214	C₁₃×#106	C₂³	1	4	yes	—
215	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
216	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
217	C₁₃×#103	C₂³	1	2	yes	—
218	C₁₃×#103	C₂³	1	4	yes	—
219	C₁₃×#103	C₂³	1	4	yes	—
220	C₁₃×#103	C₂³	1	4	yes	—
221	C₁₃×#103	C₂³	1	4	yes	—
222	C₁₃×#103	C₂³	1	2	yes	—
223	C₁₃×#103	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×#102	C₂³	1	4	yes	—
228	C₁₃×#102	C₂³	1	4	yes	—
229	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
230	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
231	C₁₃×#97	C₂³	1	2	yes	—
232	C₄×C₈×C₁₃	C₂³	1	2	yes	—
233	#61162	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
234	C₂⁴×C₁₃	—	2	2	no	—
235	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
236	C₁₃×#41	—	2	2	no	—
237	C₁₃×#41	—	2	4	no	—
238	C₁₃×#41	—	2	4	no	—
239	C₁₃×#41	—	2	4	no	—
240	C₁₃×#41	—	2	4	no	—
241	C₁₃×#41	—	4	8	no	—
242	C₁₃×#41	—	4	2	no	—
243	C₁₃×#41	—	4	2	no	—
244	C₁₃×#41	—	4	8	no	—
245	C₁₃×#41	#41	1	4	yes	—
246	C₂×Q₈×C₁₃	—	2	1	no	—
247	C₂×Q₈×C₁₃	—	2	2	no	—
248	C₂×Q₈×C₁₃	—	2	2	no	—
249	C₂×Q₈×C₁₃	—	2	2	no	—
250	C₂×Q₈×C₁₃	—	2	4	no	—
251	C₂×Q₈×C₁₃	—	2	2	no	—
252	C₂×Q₈×C₁₃	—	2	2	no	—
253	C₂×Q₈×C₁₃	—	4	2	no	—
254	C₂×Q₈×C₁₃	—	8	2	no	—
255	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
256	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
257	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
258	C₂×D₄×C₁₃	—	2	1	no	—
259	C₂×D₄×C₁₃	—	2	4	no	—
260	C₂×D₄×C₁₃	—	2	4	no	—
261	C₂×D₄×C₁₃	—	2	2	no	—
262	C₂×D₄×C₁₃	—	2	2	no	—
263	C₂×D₄×C₁₃	—	2	2	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	1	no	—
269	C₂×D₄×C₁₃	—	4	2	no	—
270	C₂×D₄×C₁₃	—	4	8	no	—
271	C₂×D₄×C₁₃	—	4	4	no	—
272	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
273	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
274	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
275	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
276	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
277	C₂²×C₄×C₁₃	—	2	1	no	—
278	C₂²×C₄×C₁₃	—	2	4	no	—
279	C₂²×C₄×C₁₃	—	2	4	no	—
280	C₂²×C₄×C₁₃	—	2	1	no	—
281	C₂²×C₄×C₁₃	—	2	1	no	—
282	C₂²×C₄×C₁₃	—	2	2	no	—
283	C₂²×C₄×C₁₃	—	2	2	no	—
284	C₂²×C₄×C₁₃	—	2	4	no	—
285	C₂²×C₄×C₁₃	—	2	4	no	—
286	C₂²×C₄×C₁₃	—	2	1	no	—
287	C₂²×C₄×C₁₃	—	2	2	no	—
288	C₂²×C₄×C₁₃	—	2	2	no	—
289	C₂²×C₄×C₁₃	—	2	2	no	—
290	C₂²×C₄×C₁₃	—	2	1	no	—
291	C₂²×C₄×C₁₃	—	4	8	no	—
292	C₂²×C₄×C₁₃	—	8	4	no	—
293	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
294	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
295	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
296	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
297	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
298	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
299	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
300	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
301	C₁₃×Q₁₆	—	2	4	no	—
302	C₁₃×Q₁₆	—	4	4	no	—
303	C₁₃×SD₁₆	—	2	4	no	—
304	C₁₃×SD₁₆	—	4	4	no	—
305	C₁₃×M₁₆	—	2	2	no	—
306	C₁₃×M₁₆	—	2	2	no	—
307	C₁₃×M₁₆	—	2	4	no	—
308	C₁₃×M₁₆	—	4	4	no	—
309	C₂×C₈×C₁₃	—	4	4	no	—
310	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
311	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
312	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
313	C₁₃×C₄⋊C₄	—	2	1	no	—
314	C₁₃×C₄⋊C₄	—	2	4	no	—
315	C₁₃×C₄⋊C₄	—	2	4	no	—
316	C₁₃×C₄⋊C₄	—	2	2	no	—
317	C₁₃×C₄⋊C₄	—	2	1	no	—
318	C₁₃×C₄⋊C₄	—	2	2	no	—
319	C₁₃×C₄⋊C₄	—	2	2	no	—
320	C₁₃×C₄⋊C₄	—	2	2	no	—
321	C₁₃×C₄⋊C₄	—	2	2	no	—
322	C₁₃×C₄⋊C₄	—	2	2	no	—
323	C₁₃×C₄⋊C₄	—	2	4	no	—
324	C₁₃×C₄⋊C₄	—	2	4	no	—
325	C₁₃×C₄⋊C₄	—	2	1	no	—
326	C₁₃×C₄⋊C₄	—	2	1	no	—
327	C₁₃×C₄⋊C₄	—	2	1	no	—
328	C₁₃×C₄⋊C₄	—	2	2	no	—
329	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
330	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
331	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
332	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
333	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
334	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
335	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
336	C₁₃×C₂²⋊C₄	—	2	2	no	—
337	C₁₃×C₂²⋊C₄	—	2	4	no	—
338	C₁₃×C₂²⋊C₄	—	2	4	no	—
339	C₁₃×C₂²⋊C₄	—	2	1	no	—
340	C₁₃×C₂²⋊C₄	—	2	2	no	—
341	C₁₃×C₂²⋊C₄	—	2	2	no	—
342	C₁₃×C₂²⋊C₄	—	2	2	no	—
343	C₁₃×C₂²⋊C₄	—	2	1	no	—
344	C₁₃×C₂²⋊C₄	—	2	1	no	—
345	C₁₃×C₂²⋊C₄	—	2	2	no	—
346	C₁₃×C₂²⋊C₄	—	2	2	no	—
347	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
348	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
349	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
350	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
351	C₄²×C₁₃	—	2	1	no	—
352	C₄²×C₁₃	—	2	1	no	—
353	C₄²×C₁₃	—	2	1	no	—
354	C₄²×C₁₃	—	2	2	no	—
355	C₄²×C₁₃	—	2	2	no	—
356	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
357	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
358	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
359	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
360	C₂×#554	C₂×C₁₃	1	1	yes	characteristic, complemented
361	D₄×#41	C₂×C₁₃	1	1	yes	characteristic
362	#3333	C₂×C₁₃	1	2	yes	complemented
363	#3331	C₂×C₁₃	1	2	yes	complemented
364	#3316	C₂×C₁₃	1	4	yes	complemented
365	#3314	C₂×C₁₃	1	4	yes	complemented
366	#3299	C₂×C₁₃	1	2	yes	complemented
367	#3295	C₂×C₁₃	1	2	yes	complemented
368	#3141	C₂×C₁₃	1	1	yes	characteristic, complemented
369	#3092	C₂×C₁₃	1	2	yes	complemented
370	#3079	C₂×C₁₃	1	1	yes	characteristic, complemented
371	#3056	C₂×C₁₃	1	2	yes	complemented
372	#3037	C₂×C₁₃	1	1	yes	characteristic, complemented
373	#3007	C₂×C₁₃	1	2	yes	complemented
374	C₄×#137	C₂×C₁₃	1	1	yes	characteristic, complemented
375	D₄×M₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
376	C₂×#417	C₂×C₁₃	1	2	yes	complemented
377	C₂³×C₁₃	—	2	4	no	—
378	C₂³×C₁₃	—	2	4	no	—
379	C₂³×C₁₃	—	2	1	no	—
380	C₂³×C₁₃	—	2	2	no	—
381	C₂³×C₁₃	—	4	2	no	—
382	C₂³×C₁₃	—	4	4	no	—
383	C₂³×C₁₃	—	4	4	no	—
384	C₂³×C₁₃	—	8	2	no	—
385	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
386	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
387	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
388	Q₈×C₁₃	—	2	1	no	—
389	Q₈×C₁₃	—	2	2	no	—
390	Q₈×C₁₃	—	2	2	no	—
391	Q₈×C₁₃	—	2	2	no	—
392	Q₈×C₁₃	—	2	2	no	—
393	Q₈×C₁₃	—	4	4	no	—
394	Q₈×C₁₃	—	4	2	no	—
395	Q₈×C₁₃	—	8	2	no	—
396	Q₈×C₁₃	—	8	2	no	—
397	Q₈×C₁₃	C₂×#41	1	2	yes	—
398	D₄×C₁₃	—	2	4	no	—
399	D₄×C₁₃	—	2	4	no	—
400	D₄×C₁₃	—	2	2	no	—
401	D₄×C₁₃	—	2	2	no	—
402	D₄×C₁₃	—	2	1	no	—
403	D₄×C₁₃	—	2	2	no	—
404	D₄×C₁₃	—	4	4	no	—
405	D₄×C₁₃	—	4	4	no	—
406	D₄×C₁₃	—	4	4	no	—
407	D₄×C₁₃	—	4	4	no	—
408	D₄×C₁₃	—	4	4	no	—
409	D₄×C₁₃	—	4	2	no	—
410	D₄×C₁₃	—	8	1	no	—
411	D₄×C₁₃	—	8	2	no	—
412	D₄×C₁₃	#137	1	4	yes	complemented
413	D₄×C₁₃	C₂×#41	1	2	yes	—
414	C₂×C₄×C₁₃	—	2	4	no	—
415	C₂×C₄×C₁₃	—	2	1	no	—
416	C₂×C₄×C₁₃	—	2	4	no	—
417	C₂×C₄×C₁₃	—	2	4	no	—
418	C₂×C₄×C₁₃	—	2	4	no	—
419	C₂×C₄×C₁₃	—	2	2	no	—
420	C₂×C₄×C₁₃	—	2	2	no	—
421	C₂×C₄×C₁₃	—	2	2	no	—
422	C₂×C₄×C₁₃	—	2	2	no	—
423	C₂×C₄×C₁₃	—	2	2	no	—
424	C₂×C₄×C₁₃	—	2	1	no	—
425	C₂×C₄×C₁₃	—	2	1	no	—
426	C₂×C₄×C₁₃	—	2	2	no	—
427	C₂×C₄×C₁₃	—	2	2	no	—
428	C₂×C₄×C₁₃	—	2	2	no	—
429	C₂×C₄×C₁₃	—	2	4	no	—
430	C₂×C₄×C₁₃	—	4	1	no	—
431	C₂×C₄×C₁₃	—	4	4	no	—
432	C₂×C₄×C₁₃	—	4	4	no	—
433	C₂×C₄×C₁₃	—	4	4	no	—
434	C₂×C₄×C₁₃	—	4	2	no	—
435	C₂×C₄×C₁₃	—	4	4	no	—
436	C₂×C₄×C₁₃	—	4	2	no	—
437	C₂×C₄×C₁₃	—	4	4	no	—
438	C₂×C₄×C₁₃	—	4	2	no	—
439	C₂×C₄×C₁₃	—	8	1	no	—
440	C₂×C₄×C₁₃	—	8	4	no	—
441	C₂×C₄×C₁₃	—	8	4	no	—
442	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
443	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
444	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
445	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
446	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
447	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
448	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
449	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
450	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
451	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
452	C₈×C₁₃	—	2	2	no	—
453	C₈×C₁₃	—	2	2	no	—
454	C₈×C₁₃	—	2	4	no	—
455	C₂²×#41	C₂²×C₁₃	1	2	yes	—
456	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
457	C₂×#137	C₂²×C₁₃	1	2	yes	complemented
458	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	complemented
459	#554	—	2	1	no	—
460	#554	—	2	2	no	—
461	#554	—	2	1	no	—
462	#554	C₂²×C₁₃	1	2	yes	—
463	#554	C₂²×C₁₃	1	2	yes	complemented
464	#554	C₂²×C₁₃	1	4	yes	complemented
465	#550	C₂²×C₁₃	1	1	yes	characteristic
466	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
467	#548	C₂²×C₁₃	1	2	yes	—
468	#547	—	2	1	no	—
469	#547	C₂²×C₁₃	1	1	yes	characteristic
470	#546	—	2	2	no	—
471	#546	C₂²×C₁₃	1	2	yes	—
472	D₄²	—	2	1	no	—
473	D₄²	C₂²×C₁₃	1	1	yes	characteristic
474	#532	—	2	1	no	—
475	#532	C₂²×C₁₃	1	1	yes	characteristic
476	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
477	C₂×#125	—	2	1	no	—
478	#525	—	2	2	no	—
479	#525	C₂²×C₁₃	1	2	yes	—
480	C₂×C₂²⋊Q₈	—	2	2	no	—
481	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
482	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
483	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
484	C₂×C₄×D₄	—	2	1	no	—
485	C₂×C₄×D₄	—	2	1	no	—
486	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
487	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
488	#489	C₂²×C₁₃	1	4	yes	complemented
489	#487	C₂²×C₁₃	1	2	yes	complemented
490	#486	C₂²×C₁₃	1	2	yes	complemented
491	#484	C₂²×C₁₃	1	4	yes	complemented
492	#483	C₂²×C₁₃	1	4	yes	complemented
493	#481	C₂²×C₁₃	1	4	yes	complemented
494	#480	C₂²×C₁₃	1	4	yes	complemented
495	#477	C₂²×C₁₃	1	2	yes	complemented
496	#476	C₂²×C₁₃	1	2	yes	complemented
497	#475	C₂²×C₁₃	1	2	yes	complemented
498	#474	C₂²×C₁₃	1	2	yes	complemented
499	#470	C₂²×C₁₃	1	4	yes	complemented
500	#468	C₂²×C₁₃	1	4	yes	complemented
501	#467	C₂²×C₁₃	1	4	yes	complemented
502	#465	C₂²×C₁₃	1	4	yes	complemented
503	#464	C₂²×C₁₃	1	4	yes	complemented
504	#462	C₂²×C₁₃	1	2	yes	complemented
505	#460	C₂²×C₁₃	1	2	yes	complemented
506	#452	C₂²×C₁₃	1	4	yes	complemented
507	#452	C₂²×C₁₃	1	4	yes	complemented
508	#451	C₂²×C₁₃	1	4	yes	complemented
509	#450	C₂²×C₁₃	1	4	yes	complemented
510	#441	C₂²×C₁₃	1	2	yes	complemented
511	#440	C₂²×C₁₃	1	2	yes	complemented
512	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
513	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
514	#436	C₂²×C₁₃	1	2	yes	complemented
515	#435	C₂²×C₁₃	1	4	yes	complemented
516	C₈×D₄	C₂²×C₁₃	1	2	yes	—
517	#428	C₂²×C₁₃	1	2	yes	complemented
518	#428	C₂²×C₁₃	1	1	yes	characteristic, complemented
519	#423	C₂²×C₁₃	1	1	yes	characteristic, complemented
520	#419	C₂²×C₁₃	1	1	yes	characteristic, complemented
521	#417	C₂²×C₁₃	1	2	yes	—
522	#417	C₂²×C₁₃	1	1	yes	characteristic
523	#417	C₂²×C₁₃	1	4	yes	complemented
524	#417	C₂²×C₁₃	1	4	yes	complemented
525	#417	C₂²×C₁₃	1	2	yes	complemented
526	#417	C₂²×C₁₃	1	2	yes	complemented
527	#417	C₂²×C₁₃	1	2	yes	complemented
528	C₂×#103	C₂²×C₁₃	1	4	yes	complemented
529	C₂×#102	C₂²×C₁₃	1	4	yes	complemented
530	#407	C₂²×C₁₃	1	2	yes	complemented
531	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
532	C₂²×C₁₃	—	2	1	no	—
533	C₂²×C₁₃	—	2	2	no	—
534	C₂²×C₁₃	—	2	2	no	—
535	C₂²×C₁₃	—	2	1	no	—
536	C₂²×C₁₃	—	2	2	no	—
537	C₂²×C₁₃	—	2	2	no	—
538	C₂²×C₁₃	—	2	2	no	—
539	C₂²×C₁₃	—	2	2	no	—
540	C₂²×C₁₃	—	4	8	no	—
541	C₂²×C₁₃	—	4	1	no	—
542	C₂²×C₁₃	—	4	1	no	—
543	C₂²×C₁₃	—	4	2	no	—
544	C₂²×C₁₃	—	4	2	no	—
545	C₂²×C₁₃	—	4	2	no	—
546	C₂²×C₁₃	—	8	8	no	—
547	C₂²×C₁₃	#546	1	2	yes	—
548	C₂²×C₁₃	C₂×#137	1	4	yes	—
549	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
550	C₄×C₁₃	—	2	1	no	—
551	C₄×C₁₃	—	2	1	no	—
552	C₄×C₁₃	—	2	2	no	—
553	C₄×C₁₃	—	2	2	no	—
554	C₄×C₁₃	—	2	2	no	—
555	C₄×C₁₃	—	2	1	no	—
556	C₄×C₁₃	—	4	2	no	—
557	C₄×C₁₃	—	4	4	no	—
558	C₄×C₁₃	—	4	1	no	—
559	C₄×C₁₃	—	4	2	no	—
560	C₄×C₁₃	—	4	2	no	—
561	C₄×C₁₃	—	4	1	no	—
562	C₄×C₁₃	#546	1	2	yes	—
563	C₄×C₁₃	C₂×#137	1	2	yes	—
564	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
565	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
566	C₂×#41	—	2	2	no	—
567	C₂×#41	—	2	2	no	—
568	C₂×#41	—	2	8	no	—
569	C₂×#41	—	4	4	no	—
570	C₂×#41	C₂³×C₁₃	1	2	yes	—
571	C₂×#41	C₂³×C₁₃	1	2	yes	—
572	C₂×#41	C₂³×C₁₃	1	2	yes	—
573	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
574	C₂²×Q₈	—	2	1	no	—
575	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
576	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
577	C₂²×D₄	—	2	2	no	—
578	C₂²×D₄	—	2	1	no	—
579	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
580	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
581	C₂³×C₄	—	2	2	no	—
582	C₂³×C₄	—	2	2	no	—
583	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
584	#137	—	2	4	no	—
585	#137	—	4	4	no	—
586	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
587	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
588	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
589	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
590	C₂×M₁₆	—	4	4	no	—
591	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
592	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
593	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
594	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
595	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
596	C₄⋊Q₈	—	2	1	no	—
597	C₄⋊Q₈	—	2	1	no	—
598	C₄⋊Q₈	—	2	1	no	—
599	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
600	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
601	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
602	#127	—	2	1	no	—
603	#127	C₂³×C₁₃	1	1	yes	characteristic
604	#125	—	2	2	no	—
605	#125	—	2	2	no	—
606	#125	—	2	4	no	—
607	#124	—	2	2	no	—
608	#124	C₂³×C₁₃	1	2	yes	—
609	#123	—	2	2	no	—
610	#123	—	2	2	no	—
611	#123	—	2	2	no	—
612	C₂²⋊Q₈	—	2	2	no	—
613	C₂²⋊Q₈	—	2	2	no	—
614	C₂²⋊Q₈	—	2	2	no	—
615	C₂²⋊Q₈	—	2	4	no	—
616	C₂²⋊Q₈	—	2	4	no	—
617	C₂²⋊Q₈	—	2	4	no	—
618	C₂²⋊Q₈	—	2	4	no	—
619	C₂²⋊Q₈	—	2	2	no	—
620	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
621	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
622	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
623	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
624	#121	—	2	2	no	—
625	#121	—	2	1	no	—
626	#121	—	2	1	no	—
627	#121	—	2	1	no	—
628	#121	—	2	1	no	—
629	#121	—	2	2	no	—
630	#121	—	2	2	no	—
631	#121	C₂³×C₁₃	1	2	yes	—
632	#121	C₂³×C₁₃	1	2	yes	—
633	#120	—	2	2	no	—
634	#120	—	2	2	no	—
635	#120	—	2	2	no	—
636	C₄×Q₈	—	2	1	no	—
637	C₄×Q₈	—	2	1	no	—
638	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
639	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
640	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
641	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
642	C₄×D₄	—	2	1	no	—
643	C₄×D₄	—	2	2	no	—
644	C₄×D₄	—	2	4	no	—
645	C₄×D₄	—	2	2	no	—
646	C₄×D₄	—	2	2	no	—
647	C₄×D₄	—	2	1	no	—
648	C₄×D₄	—	2	1	no	—
649	C₄×D₄	—	2	2	no	—
650	C₄×D₄	—	2	1	no	—
651	C₄×D₄	—	2	2	no	—
652	C₄×D₄	—	2	1	no	—
653	C₄×D₄	—	2	1	no	—
654	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
655	C₄×D₄	D₄×C₁₃	1	2	yes	—
656	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
657	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
658	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
659	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
660	C₄×D₄	C₂³×C₁₃	1	2	yes	—
661	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
662	#117	—	2	1	no	—
663	#117	C₂³×C₁₃	1	1	yes	characteristic
664	C₂×C₄⋊C₄	—	2	2	no	—
665	C₂×C₄⋊C₄	—	2	2	no	—
666	C₂×C₄⋊C₄	—	2	2	no	—
667	C₂×C₄⋊C₄	—	2	1	no	—
668	C₂×C₄⋊C₄	—	2	1	no	—
669	C₂×C₄⋊C₄	—	2	2	no	—
670	C₂×C₄⋊C₄	—	2	1	no	—
671	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
672	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
673	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
674	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
675	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
676	C₂×C₂²⋊C₄	—	2	2	no	—
677	C₂×C₂²⋊C₄	—	2	2	no	—
678	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
679	C₂×C₄²	—	2	1	no	—
680	C₂×C₄²	—	2	1	no	—
681	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
682	#107	C₂³×C₁₃	1	2	yes	—
683	#107	C₂³×C₁₃	1	4	yes	—
684	#106	C₂³×C₁₃	1	2	yes	—
685	#106	C₂³×C₁₃	1	4	yes	—
686	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
687	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
688	#103	C₂³×C₁₃	1	2	yes	—
689	#103	C₂³×C₁₃	1	4	yes	—
690	#103	C₂³×C₁₃	1	4	yes	—
691	#103	C₂³×C₁₃	1	4	yes	—
692	#103	C₂³×C₁₃	1	4	yes	—
693	#103	C₂³×C₁₃	1	2	yes	—
694	#103	C₂³×C₁₃	1	2	yes	—
695	#102	C₂³×C₁₃	1	2	yes	—
696	#102	C₂³×C₁₃	1	4	yes	—
697	#102	C₂³×C₁₃	1	4	yes	—
698	#102	C₂³×C₁₃	1	4	yes	—
699	#102	C₂³×C₁₃	1	4	yes	—
700	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
701	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
702	#97	C₂³×C₁₃	1	2	yes	—
703	C₄×C₈	C₂³×C₁₃	1	2	yes	—
704	C₂×C₁₃	—	2	2	no	—
705	C₂×C₁₃	—	2	4	no	—
706	C₂×C₁₃	—	4	2	no	—
707	C₂×C₁₃	—	4	2	no	—
708	C₂×C₁₃	—	8	2	no	—
709	C₂×C₁₃	C₂×#546	1	1	yes	characteristic
710	C₂×C₁₃	C₂²×#137	1	1	yes	characteristic
711	C₂×C₁₃	#3585	1	1	yes	characteristic
712	C₂⁴	—	2	2	no	—
713	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
714	#41	—	2	2	no	—
715	#41	—	2	4	no	—
716	#41	—	2	4	no	—
717	#41	—	2	4	no	—
718	#41	—	2	4	no	—
719	#41	—	4	8	no	—
720	#41	—	4	2	no	—
721	#41	—	4	2	no	—
722	#41	—	4	8	no	—
723	#41	C₁₃×#41	1	4	yes	—
724	C₂×Q₈	—	2	1	no	—
725	C₂×Q₈	—	2	2	no	—
726	C₂×Q₈	—	2	2	no	—
727	C₂×Q₈	—	2	2	no	—
728	C₂×Q₈	—	2	4	no	—
729	C₂×Q₈	—	2	2	no	—
730	C₂×Q₈	—	2	2	no	—
731	C₂×Q₈	—	4	2	no	—
732	C₂×Q₈	—	8	2	no	—
733	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
734	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
735	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
736	C₂×D₄	—	2	1	no	—
737	C₂×D₄	—	2	4	no	—
738	C₂×D₄	—	2	4	no	—
739	C₂×D₄	—	2	2	no	—
740	C₂×D₄	—	2	2	no	—
741	C₂×D₄	—	2	2	no	—
742	C₂×D₄	—	2	2	no	—
743	C₂×D₄	—	2	2	no	—
744	C₂×D₄	—	2	1	no	—
745	C₂×D₄	—	2	2	no	—
746	C₂×D₄	—	2	1	no	—
747	C₂×D₄	—	4	2	no	—
748	C₂×D₄	—	4	8	no	—
749	C₂×D₄	—	4	4	no	—
750	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
751	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
752	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
753	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
754	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
755	C₂²×C₄	—	2	1	no	—
756	C₂²×C₄	—	2	4	no	—
757	C₂²×C₄	—	2	4	no	—
758	C₂²×C₄	—	2	1	no	—
759	C₂²×C₄	—	2	1	no	—
760	C₂²×C₄	—	2	2	no	—
761	C₂²×C₄	—	2	2	no	—
762	C₂²×C₄	—	2	4	no	—
763	C₂²×C₄	—	2	4	no	—
764	C₂²×C₄	—	2	1	no	—
765	C₂²×C₄	—	2	2	no	—
766	C₂²×C₄	—	2	2	no	—
767	C₂²×C₄	—	2	2	no	—
768	C₂²×C₄	—	2	1	no	—
769	C₂²×C₄	—	4	8	no	—
770	C₂²×C₄	—	8	4	no	—
771	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
772	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
773	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
774	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
775	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
776	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
777	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
778	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
779	Q₁₆	—	2	4	no	—
780	Q₁₆	—	4	4	no	—
781	SD₁₆	—	2	4	no	—
782	SD₁₆	—	4	4	no	—
783	M₁₆	—	2	2	no	—
784	M₁₆	—	2	2	no	—
785	M₁₆	—	2	4	no	—
786	M₁₆	—	4	4	no	—
787	C₂×C₈	—	4	4	no	—
788	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
789	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
790	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
791	C₄⋊C₄	—	2	1	no	—
792	C₄⋊C₄	—	2	4	no	—
793	C₄⋊C₄	—	2	4	no	—
794	C₄⋊C₄	—	2	2	no	—
795	C₄⋊C₄	—	2	1	no	—
796	C₄⋊C₄	—	2	2	no	—
797	C₄⋊C₄	—	2	2	no	—
798	C₄⋊C₄	—	2	2	no	—
799	C₄⋊C₄	—	2	2	no	—
800	C₄⋊C₄	—	2	2	no	—
801	C₄⋊C₄	—	2	4	no	—
802	C₄⋊C₄	—	2	4	no	—
803	C₄⋊C₄	—	2	1	no	—
804	C₄⋊C₄	—	2	1	no	—
805	C₄⋊C₄	—	2	1	no	—
806	C₄⋊C₄	—	2	2	no	—
807	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
808	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
809	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
810	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
811	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
812	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
813	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
814	C₂²⋊C₄	—	2	2	no	—
815	C₂²⋊C₄	—	2	4	no	—
816	C₂²⋊C₄	—	2	4	no	—
817	C₂²⋊C₄	—	2	1	no	—
818	C₂²⋊C₄	—	2	2	no	—
819	C₂²⋊C₄	—	2	2	no	—
820	C₂²⋊C₄	—	2	2	no	—
821	C₂²⋊C₄	—	2	1	no	—
822	C₂²⋊C₄	—	2	1	no	—
823	C₂²⋊C₄	—	2	2	no	—
824	C₂²⋊C₄	—	2	2	no	—
825	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
826	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
827	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
828	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
829	C₄²	—	2	1	no	—
830	C₄²	—	2	1	no	—
831	C₄²	—	2	1	no	—
832	C₄²	—	2	2	no	—
833	C₄²	—	2	2	no	—
834	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
835	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
836	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
837	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
838	C₁₃	#61162	1	1	yes	characteristic, direct product factor, Sylow
839	C₂³	—	2	4	no	—
840	C₂³	—	2	4	no	—
841	C₂³	—	2	1	no	—
842	C₂³	—	2	2	no	—
843	C₂³	—	4	2	no	—
844	C₂³	—	4	4	no	—
845	C₂³	—	4	4	no	—
846	C₂³	—	8	2	no	—
847	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
848	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
849	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
850	Q₈	—	2	1	no	—
851	Q₈	—	2	2	no	—
852	Q₈	—	2	2	no	—
853	Q₈	—	2	2	no	—
854	Q₈	—	2	2	no	—
855	Q₈	—	4	4	no	—
856	Q₈	—	4	2	no	—
857	Q₈	—	8	2	no	—
858	Q₈	—	8	2	no	—
859	Q₈	C₂×C₁₃×#41	1	2	yes	—
860	D₄	—	2	4	no	—
861	D₄	—	2	4	no	—
862	D₄	—	2	2	no	—
863	D₄	—	2	2	no	—
864	D₄	—	2	1	no	—
865	D₄	—	2	2	no	—
866	D₄	—	4	4	no	—
867	D₄	—	4	4	no	—
868	D₄	—	4	4	no	—
869	D₄	—	4	4	no	—
870	D₄	—	4	4	no	—
871	D₄	—	4	2	no	—
872	D₄	—	8	1	no	—
873	D₄	—	8	2	no	—
874	D₄	C₁₃×#137	1	4	yes	complemented
875	D₄	C₂×C₁₃×#41	1	2	yes	—
876	C₂×C₄	—	2	4	no	—
877	C₂×C₄	—	2	1	no	—
878	C₂×C₄	—	2	4	no	—
879	C₂×C₄	—	2	4	no	—
880	C₂×C₄	—	2	4	no	—
881	C₂×C₄	—	2	2	no	—
882	C₂×C₄	—	2	2	no	—
883	C₂×C₄	—	2	2	no	—
884	C₂×C₄	—	2	2	no	—
885	C₂×C₄	—	2	2	no	—
886	C₂×C₄	—	2	1	no	—
887	C₂×C₄	—	2	1	no	—
888	C₂×C₄	—	2	2	no	—
889	C₂×C₄	—	2	2	no	—
890	C₂×C₄	—	2	2	no	—
891	C₂×C₄	—	2	4	no	—
892	C₂×C₄	—	4	1	no	—
893	C₂×C₄	—	4	4	no	—
894	C₂×C₄	—	4	4	no	—
895	C₂×C₄	—	4	4	no	—
896	C₂×C₄	—	4	2	no	—
897	C₂×C₄	—	4	4	no	—
898	C₂×C₄	—	4	2	no	—
899	C₂×C₄	—	4	4	no	—
900	C₂×C₄	—	4	2	no	—
901	C₂×C₄	—	8	1	no	—
902	C₂×C₄	—	8	4	no	—
903	C₂×C₄	—	8	4	no	—
904	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
905	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
906	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
907	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
908	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
909	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
910	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
911	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
912	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
913	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
914	C₈	—	2	2	no	—
915	C₈	—	2	2	no	—
916	C₈	—	2	4	no	—
917	C₂²	—	2	1	no	—
918	C₂²	—	2	1	no	—
919	C₂²	—	2	2	no	—
920	C₂²	—	2	2	no	—
921	C₂²	—	2	2	no	—
922	C₂²	—	2	2	no	—
923	C₂²	—	2	2	no	—
924	C₂²	—	2	2	no	—
925	C₂²	—	4	8	no	—
926	C₂²	—	4	1	no	—
927	C₂²	—	4	1	no	—
928	C₂²	—	4	2	no	—
929	C₂²	—	4	2	no	—
930	C₂²	—	4	2	no	—
931	C₂²	—	8	8	no	—
932	C₂²	C₁₃×#546	1	2	yes	—
933	C₂²	C₂×C₁₃×#137	1	4	yes	—
934	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
935	C₄	—	2	1	no	—
936	C₄	—	2	1	no	—
937	C₄	—	2	1	no	—
938	C₄	—	2	2	no	—
939	C₄	—	2	2	no	—
940	C₄	—	2	2	no	—
941	C₄	—	4	1	no	—
942	C₄	—	4	2	no	—
943	C₄	—	4	4	no	—
944	C₄	—	4	1	no	—
945	C₄	—	4	2	no	—
946	C₄	—	4	2	no	—
947	C₄	C₁₃×#546	1	2	yes	—
948	C₄	C₂×C₁₃×#137	1	2	yes	—
949	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
950	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
951	C₂	—	2	2	no	—
952	C₂	—	2	4	no	—
953	C₂	—	4	2	no	—
954	C₂	—	4	2	no	—
955	C₂	—	8	2	no	—
956	C₂	C₂×C₁₃×#546	1	1	yes	characteristic
957	C₂	C₂²×C₁₃×#137	1	1	yes	characteristic
958	C₂	C₁₃×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	D₄×C₁₃×#41	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
1. C₂×C₁₃×#554	C₂	semidirect
3. C₁₃×#3333	C₂	semidirect
4. C₁₃×#3331	C₂	semidirect
5. C₁₃×#3316	C₂	semidirect
6. C₁₃×#3314	C₂	semidirect
7. C₁₃×#3299	C₂	semidirect
8. C₁₃×#3295	C₂	semidirect
9. C₁₃×#3141	C₂	semidirect
10. C₁₃×#3092	C₂	semidirect
11. C₁₃×#3079	C₂	semidirect
12. C₁₃×#3056	C₂	semidirect
13. C₁₃×#3037	C₂	semidirect
14. C₁₃×#3007	C₂	semidirect
15. C₄×C₁₃×#137	C₂	semidirect
16. D₄×C₁₃×M₁₆	C₂	semidirect
17. C₂×C₁₃×#417	C₂	semidirect
20. C₂×C₁₃×#137	C₂²	semidirect
21. C₂²×C₁₃×M₁₆	C₂²	semidirect
26. C₁₃×#554	C₂²	semidirect
27. C₁₃×#554	C₂²	semidirect
39. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
44. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
46. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
50. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
51. C₁₃×#489	C₂²	semidirect
52. C₁₃×#487	C₂²	semidirect
53. C₁₃×#486	C₂²	semidirect
54. C₁₃×#484	C₂²	semidirect
55. C₁₃×#483	C₂²	semidirect
56. C₁₃×#481	C₂²	semidirect
57. C₁₃×#480	C₂²	semidirect
58. C₁₃×#477	C₂²	semidirect
59. C₁₃×#476	C₂²	semidirect
60. C₁₃×#475	C₂²	semidirect
61. C₁₃×#474	C₂²	semidirect
62. C₁₃×#470	C₂²	semidirect
63. C₁₃×#468	C₂²	semidirect
64. C₁₃×#467	C₂²	semidirect
65. C₁₃×#465	C₂²	semidirect
66. C₁₃×#464	C₂²	semidirect
67. C₁₃×#462	C₂²	semidirect
68. C₁₃×#460	C₂²	semidirect
69. C₁₃×#452	C₂²	semidirect
70. C₁₃×#452	C₂²	semidirect
71. C₁₃×#451	C₂²	semidirect
72. C₁₃×#450	C₂²	semidirect
73. C₁₃×#441	C₂²	semidirect
74. C₁₃×#440	C₂²	semidirect
75. C₄×C₁₃×Q₁₆	C₂²	semidirect
76. C₄×C₁₃×SD₁₆	C₂²	semidirect
77. C₁₃×#436	C₂²	semidirect
78. C₁₃×#435	C₂²	semidirect
80. C₁₃×#428	C₂²	semidirect
81. C₁₃×#428	C₂²	semidirect
82. C₁₃×#423	C₂²	semidirect
83. C₁₃×#419	C₂²	semidirect
86. C₁₃×#417	C₂²	semidirect
87. C₁₃×#417	C₂²	semidirect
88. C₁₃×#417	C₂²	semidirect
89. C₁₃×#417	C₂²	semidirect
90. C₁₃×#417	C₂²	semidirect
91. C₂×C₁₃×#103	C₂²	semidirect
92. C₂×C₁₃×#102	C₂²	semidirect
93. C₁₃×#407	C₂²	semidirect
94. C₄×C₁₃×M₁₆	C₂²	semidirect
233. #61162	C₁₃	direct (N × H)
360. C₂×#554	C₂×C₁₃	semidirect
362. #3333	C₂×C₁₃	semidirect
363. #3331	C₂×C₁₃	semidirect
364. #3316	C₂×C₁₃	semidirect
365. #3314	C₂×C₁₃	semidirect
366. #3299	C₂×C₁₃	semidirect
367. #3295	C₂×C₁₃	semidirect
368. #3141	C₂×C₁₃	semidirect
369. #3092	C₂×C₁₃	semidirect
370. #3079	C₂×C₁₃	semidirect
371. #3056	C₂×C₁₃	semidirect
372. #3037	C₂×C₁₃	semidirect
373. #3007	C₂×C₁₃	semidirect
374. C₄×#137	C₂×C₁₃	semidirect
375. D₄×M₁₆	C₂×C₁₃	semidirect
376. C₂×#417	C₂×C₁₃	semidirect
412. D₄×C₁₃	#137	semidirect
457. C₂×#137	C₂²×C₁₃	semidirect
458. C₂²×M₁₆	C₂²×C₁₃	semidirect
463. #554	C₂²×C₁₃	semidirect
464. #554	C₂²×C₁₃	semidirect
476. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
481. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
483. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
487. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
488. #489	C₂²×C₁₃	semidirect
489. #487	C₂²×C₁₃	semidirect
490. #486	C₂²×C₁₃	semidirect
491. #484	C₂²×C₁₃	semidirect
492. #483	C₂²×C₁₃	semidirect
493. #481	C₂²×C₁₃	semidirect
494. #480	C₂²×C₁₃	semidirect
495. #477	C₂²×C₁₃	semidirect
496. #476	C₂²×C₁₃	semidirect
497. #475	C₂²×C₁₃	semidirect
498. #474	C₂²×C₁₃	semidirect
499. #470	C₂²×C₁₃	semidirect
500. #468	C₂²×C₁₃	semidirect
501. #467	C₂²×C₁₃	semidirect
502. #465	C₂²×C₁₃	semidirect
503. #464	C₂²×C₁₃	semidirect
504. #462	C₂²×C₁₃	semidirect
505. #460	C₂²×C₁₃	semidirect
506. #452	C₂²×C₁₃	semidirect
507. #452	C₂²×C₁₃	semidirect
508. #451	C₂²×C₁₃	semidirect
509. #450	C₂²×C₁₃	semidirect
510. #441	C₂²×C₁₃	semidirect
511. #440	C₂²×C₁₃	semidirect
512. C₄×Q₁₆	C₂²×C₁₃	semidirect
513. C₄×SD₁₆	C₂²×C₁₃	semidirect
514. #436	C₂²×C₁₃	semidirect
515. #435	C₂²×C₁₃	semidirect
517. #428	C₂²×C₁₃	semidirect
518. #428	C₂²×C₁₃	semidirect
519. #423	C₂²×C₁₃	semidirect
520. #419	C₂²×C₁₃	semidirect
523. #417	C₂²×C₁₃	semidirect
524. #417	C₂²×C₁₃	semidirect
525. #417	C₂²×C₁₃	semidirect
526. #417	C₂²×C₁₃	semidirect
527. #417	C₂²×C₁₃	semidirect
528. C₂×#103	C₂²×C₁₃	semidirect
529. C₂×#102	C₂²×C₁₃	semidirect
530. #407	C₂²×C₁₃	semidirect
531. C₄×M₁₆	C₂²×C₁₃	semidirect
838. C₁₃	#61162	direct (N × H)
874. 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
C₂×C₁₃×#554	2
D₄×C₁₃×#41	2
C₁₃×#3333	2
C₁₃×#3331	2
C₁₃×#3316	2
C₁₃×#3314	2
C₁₃×#3299	2
C₁₃×#3295	2
C₁₃×#3141	2
C₁₃×#3092	2
C₁₃×#3079	2
C₁₃×#3056	2
C₁₃×#3037	2
C₁₃×#3007	2
C₄×C₁₃×#137	2
D₄×C₁₃×M₁₆	2
C₂×C₁₃×#417	2
#61162	13

Subgroups — C13×#61162 #15747501

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61162 #15747501