Subgroups — C₁₃×#61574 #15747913

Order 3328.

2094 conjugacy classes of subgroups.

The subgroup lattice has 908 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
2	C₂×D₄×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3320	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3312	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3270	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3266	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3218	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3196	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3189	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3187	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3117	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3004	C₂	1	2	yes	maximal, complemented
13	C₂×C₁₃×#451	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₁₃×#448	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#2973	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
17	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
18	C₂×C₁₃×#137	C₂²	1	4	yes	complemented
19	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
20	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
21	C₁₃×#553	—	2	2	no	—
22	C₁₃×#553	C₂²	1	2	yes	—
23	C₁₃×#552	C₂²	1	2	yes	—
24	C₁₃×#551	—	2	2	no	—
25	D₄×Q₈×C₁₃	—	2	2	no	—
26	D₄×Q₈×C₁₃	—	2	2	no	—
27	D₄×Q₈×C₁₃	C₂²	1	4	yes	—
28	D₄×Q₈×C₁₃	C₂²	1	4	yes	complemented
29	C₁₃×#548	C₂²	1	2	yes	—
30	C₁₃×#546	C₂²	1	2	yes	—
31	C₁₃×#539	—	2	1	no	—
32	C₁₃×#538	—	2	1	no	—
33	C₁₃×#534	—	2	1	no	—
34	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
35	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
36	C₁₃×#529	C₂²	1	2	yes	—
37	C₁₃×#525	C₂²	1	2	yes	—
38	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
39	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
40	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
41	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
42	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
44	C₁₃×#518	—	2	1	no	—
45	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₄×D₄×C₁₃	—	2	1	no	—
47	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
48	C₁₃×#497	C₂²	1	4	yes	complemented
49	C₁₃×#491	C₂²	1	4	yes	complemented
50	C₁₃×#485	C₂²	1	4	yes	complemented
51	C₁₃×#484	C₂²	1	2	yes	complemented
52	C₁₃×#484	C₂²	1	2	yes	complemented
53	C₁₃×#483	C₂²	1	2	yes	complemented
54	C₁₃×#481	C₂²	1	2	yes	—
55	C₁₃×#479	C₂²	1	4	yes	complemented
56	C₁₃×#470	C₂²	1	4	yes	complemented
57	C₁₃×#468	C₂²	1	4	yes	complemented
58	C₁₃×#467	C₂²	1	4	yes	complemented
59	C₁₃×#465	C₂²	1	4	yes	complemented
60	C₁₃×#464	C₂²	1	4	yes	complemented
61	C₁₃×#462	C₂²	1	4	yes	complemented
62	C₁₃×#461	C₂²	1	4	yes	complemented
63	C₁₃×#452	C₂²	1	4	yes	complemented
64	C₁₃×#451	C₂²	1	4	yes	complemented
65	C₁₃×#451	C₂²	1	2	yes	complemented
66	C₁₃×#451	C₂²	1	4	yes	complemented
67	C₁₃×#451	C₂²	1	2	yes	complemented
68	C₁₃×#451	C₂²	1	2	yes	complemented
69	C₁₃×#451	C₂²	1	2	yes	complemented
70	C₁₃×#450	C₂²	1	2	yes	complemented
71	C₁₃×#448	C₂²	1	2	yes	—
72	C₁₃×#448	C₂²	1	2	yes	—
73	C₁₃×#448	C₂²	1	2	yes	—
74	C₁₃×#448	C₂²	1	4	yes	complemented
75	C₁₃×#448	C₂²	1	4	yes	complemented
76	C₁₃×#441	C₂²	1	4	yes	complemented
77	C₁₃×#440	C₂²	1	4	yes	complemented
78	C₁₃×#435	C₂²	1	4	yes	—
79	C₁₃×#435	C₂²	1	4	yes	complemented
80	C₁₃×#432	C₂²	1	2	yes	complemented
81	C₁₃×#419	C₂²	1	4	yes	complemented
82	C₂×C₁₃×#103	C₂²	1	2	yes	complemented
83	C₂×C₁₃×#103	C₂²	1	2	yes	complemented
84	C₁₃×#407	C₂²	1	2	yes	complemented
85	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
86	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
87	C₂×C₁₃×#41	C₂³	1	2	yes	—
88	C₂²×Q₈×C₁₃	—	2	1	no	—
89	C₂²×Q₈×C₁₃	—	2	1	no	—
90	C₂²×Q₈×C₁₃	—	2	1	no	—
91	C₂²×Q₈×C₁₃	—	2	1	no	—
92	C₂²×Q₈×C₁₃	—	2	2	no	—
93	C₂²×Q₈×C₁₃	—	4	4	no	—
94	C₂²×Q₈×C₁₃	—	4	4	no	—
95	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
96	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
97	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
98	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
99	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
100	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
101	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
102	C₂²×D₄×C₁₃	—	2	1	no	—
103	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
104	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
105	C₂³×C₄×C₁₃	—	2	1	no	—
106	C₂³×C₄×C₁₃	—	2	1	no	—
107	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
108	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
109	C₁₃×#137	—	4	8	no	—
110	C₂×C₁₃×Q₁₆	—	4	4	no	—
111	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
112	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
113	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
114	C₂×C₁₃×SD₁₆	—	4	4	no	—
115	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
116	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
117	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
118	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
119	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
120	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
121	C₁₃×C₄⋊Q₈	—	2	4	no	—
122	C₁₃×C₄⋊Q₈	—	2	4	no	—
123	C₁₃×C₄⋊Q₈	—	2	2	no	—
124	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
125	C₁₃×#126	—	2	2	no	—
126	C₁₃×#126	—	2	2	no	—
127	C₁₃×#126	—	2	2	no	—
128	C₁₃×#125	—	2	2	no	—
129	C₁₃×#125	C₂³	1	2	yes	—
130	C₁₃×#124	—	2	2	no	—
131	C₁₃×#124	C₂³	1	2	yes	—
132	C₁₃×#123	—	2	2	no	—
133	C₁₃×#123	—	2	2	no	—
134	C₁₃×#123	—	2	2	no	—
135	C₁₃×#123	—	2	2	no	—
136	C₁₃×#123	—	2	2	no	—
137	C₁₃×C₂²⋊Q₈	—	2	1	no	—
138	C₁₃×C₂²⋊Q₈	—	2	1	no	—
139	C₁₃×C₂²⋊Q₈	—	2	1	no	—
140	C₁₃×C₂²⋊Q₈	—	2	1	no	—
141	C₁₃×C₂²⋊Q₈	—	2	2	no	—
142	C₁₃×C₂²⋊Q₈	—	2	2	no	—
143	C₁₃×C₂²⋊Q₈	—	2	4	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	C₂³	1	2	yes	—
148	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
149	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
150	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
151	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
152	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
153	C₁₃×#121	—	2	2	no	—
154	C₁₃×#121	—	2	2	no	—
155	C₁₃×#121	—	2	1	no	—
156	C₁₃×#121	—	2	1	no	—
157	C₁₃×#121	—	2	2	no	—
158	C₁₃×#121	C₂³	1	2	yes	—
159	C₁₃×#121	C₂³	1	2	yes	—
160	C₁₃×#121	C₂³	1	2	yes	—
161	C₁₃×#120	—	2	2	no	—
162	C₁₃×#120	—	2	2	no	—
163	C₄×Q₈×C₁₃	—	2	2	no	—
164	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
165	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
166	C₄×D₄×C₁₃	—	2	4	no	—
167	C₄×D₄×C₁₃	—	2	4	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	—	2	2	no	—
173	C₄×D₄×C₁₃	D₄	1	2	yes	—
174	C₄×D₄×C₁₃	D₄	1	2	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	—
178	C₁₃×#117	—	2	2	no	—
179	C₁₃×#117	—	2	2	no	—
180	C₁₃×#117	C₂³	1	2	yes	—
181	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
182	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
183	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
184	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
185	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
186	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
187	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
188	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
189	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
190	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	1	no	—
195	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
196	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
197	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
198	C₂×C₄²×C₁₃	—	2	1	no	—
199	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
200	C₁₃×#107	C₂³	1	4	yes	—
201	C₁₃×#106	C₂³	1	4	yes	—
202	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
203	C₁₃×#103	C₂³	1	4	yes	—
204	C₁₃×#103	C₂³	1	4	yes	—
205	C₁₃×#103	C₂³	1	4	yes	—
206	C₁₃×#103	C₂³	1	4	yes	—
207	C₁₃×#103	C₂³	1	4	yes	—
208	C₁₃×#103	C₂³	1	4	yes	—
209	C₁₃×#103	C₂³	1	4	yes	—
210	C₁₃×#102	C₂³	1	4	yes	—
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	—
216	C₁₃×#97	C₂³	1	4	yes	—
217	#61574	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
218	C₂⁴×C₁₃	—	2	1	no	—
219	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
220	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
221	C₁₃×#41	—	4	4	no	—
222	C₂×Q₈×C₁₃	—	2	4	no	—
223	C₂×Q₈×C₁₃	—	2	1	no	—
224	C₂×Q₈×C₁₃	—	2	4	no	—
225	C₂×Q₈×C₁₃	—	2	2	no	—
226	C₂×Q₈×C₁₃	—	2	2	no	—
227	C₂×Q₈×C₁₃	—	2	1	no	—
228	C₂×Q₈×C₁₃	—	2	1	no	—
229	C₂×Q₈×C₁₃	—	2	1	no	—
230	C₂×Q₈×C₁₃	—	2	4	no	—
231	C₂×Q₈×C₁₃	—	2	4	no	—
232	C₂×Q₈×C₁₃	—	2	8	no	—
233	C₂×Q₈×C₁₃	—	4	2	no	—
234	C₂×Q₈×C₁₃	—	4	2	no	—
235	C₂×Q₈×C₁₃	—	4	4	no	—
236	C₂×Q₈×C₁₃	—	4	2	no	—
237	C₂×Q₈×C₁₃	—	4	2	no	—
238	C₂×Q₈×C₁₃	—	4	4	no	—
239	C₂×Q₈×C₁₃	—	4	4	no	—
240	C₂×Q₈×C₁₃	—	4	2	no	—
241	C₂×Q₈×C₁₃	—	4	4	no	—
242	C₂×Q₈×C₁₃	—	4	4	no	—
243	C₂×Q₈×C₁₃	—	4	8	no	—
244	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
245	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
246	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
247	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
248	C₂×D₄×C₁₃	—	2	4	no	—
249	C₂×D₄×C₁₃	—	2	2	no	—
250	C₂×D₄×C₁₃	—	2	2	no	—
251	C₂×D₄×C₁₃	—	2	2	no	—
252	C₂×D₄×C₁₃	—	2	2	no	—
253	C₂×D₄×C₁₃	—	2	1	no	—
254	C₂×D₄×C₁₃	—	4	2	no	—
255	C₂×D₄×C₁₃	—	4	4	no	—
256	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
257	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
258	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
259	C₂²×C₄×C₁₃	—	2	1	no	—
260	C₂²×C₄×C₁₃	—	2	1	no	—
261	C₂²×C₄×C₁₃	—	2	1	no	—
262	C₂²×C₄×C₁₃	—	2	1	no	—
263	C₂²×C₄×C₁₃	—	2	1	no	—
264	C₂²×C₄×C₁₃	—	2	4	no	—
265	C₂²×C₄×C₁₃	—	2	2	no	—
266	C₂²×C₄×C₁₃	—	2	2	no	—
267	C₂²×C₄×C₁₃	—	2	1	no	—
268	C₂²×C₄×C₁₃	—	2	1	no	—
269	C₂²×C₄×C₁₃	—	2	2	no	—
270	C₂²×C₄×C₁₃	—	2	2	no	—
271	C₂²×C₄×C₁₃	—	4	2	no	—
272	C₂²×C₄×C₁₃	—	4	2	no	—
273	C₂²×C₄×C₁₃	—	4	4	no	—
274	C₂²×C₄×C₁₃	—	4	4	no	—
275	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
276	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
277	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
278	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
279	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
280	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
281	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
282	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
283	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
284	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
285	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
286	C₁₃×Q₁₆	—	2	8	no	—
287	C₁₃×Q₁₆	—	4	4	no	—
288	C₁₃×Q₁₆	—	4	4	no	—
289	C₁₃×SD₁₆	—	2	8	no	—
290	C₁₃×SD₁₆	—	4	4	no	—
291	C₁₃×SD₁₆	—	4	4	no	—
292	C₁₃×M₁₆	—	4	4	no	—
293	C₂×C₈×C₁₃	—	4	2	no	—
294	C₂×C₈×C₁₃	—	4	2	no	—
295	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
296	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
297	C₁₃×C₄⋊C₄	—	2	2	no	—
298	C₁₃×C₄⋊C₄	—	2	4	no	—
299	C₁₃×C₄⋊C₄	—	2	4	no	—
300	C₁₃×C₄⋊C₄	—	2	2	no	—
301	C₁₃×C₄⋊C₄	—	2	4	no	—
302	C₁₃×C₄⋊C₄	—	2	4	no	—
303	C₁₃×C₄⋊C₄	—	2	2	no	—
304	C₁₃×C₄⋊C₄	—	2	2	no	—
305	C₁₃×C₄⋊C₄	—	2	1	no	—
306	C₁₃×C₄⋊C₄	—	2	1	no	—
307	C₁₃×C₄⋊C₄	—	2	1	no	—
308	C₁₃×C₄⋊C₄	—	2	2	no	—
309	C₁₃×C₄⋊C₄	—	2	2	no	—
310	C₁₃×C₄⋊C₄	—	2	2	no	—
311	C₁₃×C₄⋊C₄	—	2	2	no	—
312	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
313	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
314	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
315	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
316	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
317	C₁₃×C₂²⋊C₄	—	2	2	no	—
318	C₁₃×C₂²⋊C₄	—	2	2	no	—
319	C₁₃×C₂²⋊C₄	—	2	4	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	2	no	—
326	C₁₃×C₂²⋊C₄	—	2	2	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	C₂×D₄	1	2	yes	—
331	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
332	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
333	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
334	C₄²×C₁₃	—	2	4	no	—
335	C₄²×C₁₃	—	2	2	no	—
336	C₄²×C₁₃	—	2	2	no	—
337	C₄²×C₁₃	C₂×D₄	1	2	yes	—
338	C₄²×C₁₃	C₂⁴	1	2	yes	—
339	#3505	C₂×C₁₃	1	1	yes	characteristic
340	C₂×D₄×Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
341	#3320	C₂×C₁₃	1	4	yes	complemented
342	#3312	C₂×C₁₃	1	4	yes	complemented
343	#3270	C₂×C₁₃	1	4	yes	complemented
344	#3266	C₂×C₁₃	1	4	yes	complemented
345	#3218	C₂×C₁₃	1	2	yes	complemented
346	#3196	C₂×C₁₃	1	2	yes	complemented
347	#3189	C₂×C₁₃	1	1	yes	characteristic, complemented
348	#3187	C₂×C₁₃	1	1	yes	characteristic, complemented
349	#3117	C₂×C₁₃	1	2	yes	complemented
350	#3004	C₂×C₁₃	1	2	yes	complemented
351	C₂×#451	C₂×C₁₃	1	1	yes	characteristic, complemented
352	C₂×#448	C₂×C₁₃	1	1	yes	characteristic, complemented
353	#2973	C₂×C₁₃	1	1	yes	characteristic, complemented
354	C₂³×C₁₃	—	2	2	no	—
355	C₂³×C₁₃	—	2	2	no	—
356	C₂³×C₁₃	—	4	1	no	—
357	C₂³×C₁₃	—	4	1	no	—
358	C₂³×C₁₃	—	4	1	no	—
359	C₂³×C₁₃	—	4	1	no	—
360	C₂³×C₁₃	—	4	2	no	—
361	C₂³×C₁₃	—	8	1	no	—
362	C₂³×C₁₃	—	8	1	no	—
363	C₂³×C₁₃	#137	1	4	yes	complemented
364	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
365	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
366	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
367	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
368	Q₈×C₁₃	—	2	4	no	—
369	Q₈×C₁₃	—	2	2	no	—
370	Q₈×C₁₃	—	2	2	no	—
371	Q₈×C₁₃	—	2	4	no	—
372	Q₈×C₁₃	—	2	4	no	—
373	Q₈×C₁₃	—	2	2	no	—
374	Q₈×C₁₃	—	4	8	no	—
375	Q₈×C₁₃	—	4	4	no	—
376	Q₈×C₁₃	—	4	4	no	—
377	Q₈×C₁₃	—	4	2	no	—
378	Q₈×C₁₃	—	4	2	no	—
379	Q₈×C₁₃	—	8	1	no	—
380	Q₈×C₁₃	H(5,𝔽₂)	1	4	yes	—
381	D₄×C₁₃	—	2	4	no	—
382	D₄×C₁₃	—	2	4	no	—
383	D₄×C₁₃	—	2	4	no	—
384	D₄×C₁₃	—	4	4	no	—
385	D₄×C₁₃	—	4	4	no	—
386	D₄×C₁₃	—	8	1	no	—
387	D₄×C₁₃	—	8	2	no	—
388	D₄×C₁₃	—	8	2	no	—
389	C₂×C₄×C₁₃	—	2	4	no	—
390	C₂×C₄×C₁₃	—	2	2	no	—
391	C₂×C₄×C₁₃	—	2	2	no	—
392	C₂×C₄×C₁₃	—	2	2	no	—
393	C₂×C₄×C₁₃	—	2	2	no	—
394	C₂×C₄×C₁₃	—	2	4	no	—
395	C₂×C₄×C₁₃	—	2	2	no	—
396	C₂×C₄×C₁₃	—	2	2	no	—
397	C₂×C₄×C₁₃	—	2	2	no	—
398	C₂×C₄×C₁₃	—	2	2	no	—
399	C₂×C₄×C₁₃	—	2	2	no	—
400	C₂×C₄×C₁₃	—	2	2	no	—
401	C₂×C₄×C₁₃	—	2	2	no	—
402	C₂×C₄×C₁₃	—	4	2	no	—
403	C₂×C₄×C₁₃	—	4	1	no	—
404	C₂×C₄×C₁₃	—	4	1	no	—
405	C₂×C₄×C₁₃	—	4	1	no	—
406	C₂×C₄×C₁₃	—	4	1	no	—
407	C₂×C₄×C₁₃	—	4	1	no	—
408	C₂×C₄×C₁₃	—	4	4	no	—
409	C₂×C₄×C₁₃	—	4	4	no	—
410	C₂×C₄×C₁₃	—	4	8	no	—
411	C₂×C₄×C₁₃	—	4	2	no	—
412	C₂×C₄×C₁₃	—	4	2	no	—
413	C₂×C₄×C₁₃	—	4	2	no	—
414	C₂×C₄×C₁₃	—	4	2	no	—
415	C₂×C₄×C₁₃	—	8	2	no	—
416	C₂×C₄×C₁₃	—	8	2	no	—
417	C₂×C₄×C₁₃	—	8	1	no	—
418	C₂×C₄×C₁₃	—	8	1	no	—
419	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
420	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
421	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
422	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
423	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
424	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
425	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
426	C₈×C₁₃	—	2	4	no	—
427	C₈×C₁₃	—	2	4	no	—
428	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
429	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
430	C₂×#137	C₂²×C₁₃	1	4	yes	complemented
431	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
432	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
433	#553	—	2	2	no	—
434	#553	C₂²×C₁₃	1	2	yes	—
435	#552	C₂²×C₁₃	1	2	yes	—
436	#551	—	2	2	no	—
437	D₄×Q₈	—	2	2	no	—
438	D₄×Q₈	—	2	2	no	—
439	D₄×Q₈	C₂²×C₁₃	1	4	yes	—
440	D₄×Q₈	C₂²×C₁₃	1	4	yes	complemented
441	#548	C₂²×C₁₃	1	2	yes	—
442	#546	C₂²×C₁₃	1	2	yes	—
443	#539	—	2	1	no	—
444	#538	—	2	1	no	—
445	#534	—	2	1	no	—
446	C₂×C₄⋊Q₈	—	2	1	no	—
447	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
448	#529	C₂²×C₁₃	1	2	yes	—
449	#525	C₂²×C₁₃	1	2	yes	—
450	C₂×C₂²⋊Q₈	—	2	1	no	—
451	C₂×C₂²⋊Q₈	—	2	1	no	—
452	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
453	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
454	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
455	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
456	#518	—	2	1	no	—
457	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
458	C₂×C₄×D₄	—	2	1	no	—
459	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
460	#497	C₂²×C₁₃	1	4	yes	complemented
461	#491	C₂²×C₁₃	1	4	yes	complemented
462	#485	C₂²×C₁₃	1	4	yes	complemented
463	#484	C₂²×C₁₃	1	2	yes	complemented
464	#484	C₂²×C₁₃	1	2	yes	complemented
465	#483	C₂²×C₁₃	1	2	yes	complemented
466	#481	C₂²×C₁₃	1	2	yes	—
467	#479	C₂²×C₁₃	1	4	yes	complemented
468	#470	C₂²×C₁₃	1	4	yes	complemented
469	#468	C₂²×C₁₃	1	4	yes	complemented
470	#467	C₂²×C₁₃	1	4	yes	complemented
471	#465	C₂²×C₁₃	1	4	yes	complemented
472	#464	C₂²×C₁₃	1	4	yes	complemented
473	#462	C₂²×C₁₃	1	4	yes	complemented
474	#461	C₂²×C₁₃	1	4	yes	complemented
475	#452	C₂²×C₁₃	1	4	yes	complemented
476	#451	C₂²×C₁₃	1	2	yes	complemented
477	#451	C₂²×C₁₃	1	2	yes	complemented
478	#451	C₂²×C₁₃	1	2	yes	complemented
479	#451	C₂²×C₁₃	1	2	yes	complemented
480	#451	C₂²×C₁₃	1	4	yes	complemented
481	#451	C₂²×C₁₃	1	4	yes	complemented
482	#450	C₂²×C₁₃	1	2	yes	complemented
483	#448	C₂²×C₁₃	1	2	yes	—
484	#448	C₂²×C₁₃	1	2	yes	—
485	#448	C₂²×C₁₃	1	2	yes	—
486	#448	C₂²×C₁₃	1	4	yes	complemented
487	#448	C₂²×C₁₃	1	4	yes	complemented
488	#441	C₂²×C₁₃	1	4	yes	complemented
489	#440	C₂²×C₁₃	1	4	yes	complemented
490	#435	C₂²×C₁₃	1	4	yes	—
491	#435	C₂²×C₁₃	1	4	yes	complemented
492	#432	C₂²×C₁₃	1	2	yes	complemented
493	#419	C₂²×C₁₃	1	4	yes	complemented
494	C₂×#103	C₂²×C₁₃	1	2	yes	complemented
495	C₂×#103	C₂²×C₁₃	1	2	yes	complemented
496	#407	C₂²×C₁₃	1	2	yes	complemented
497	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
498	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
499	C₂²×C₁₃	—	2	1	no	—
500	C₂²×C₁₃	—	2	1	no	—
501	C₂²×C₁₃	—	2	1	no	—
502	C₂²×C₁₃	—	2	1	no	—
503	C₂²×C₁₃	—	2	1	no	—
504	C₂²×C₁₃	—	2	1	no	—
505	C₂²×C₁₃	—	2	2	no	—
506	C₂²×C₁₃	—	2	2	no	—
507	C₂²×C₁₃	—	2	2	no	—
508	C₂²×C₁₃	—	4	4	no	—
509	C₂²×C₁₃	—	4	4	no	—
510	C₂²×C₁₃	—	4	2	no	—
511	C₂²×C₁₃	—	4	2	no	—
512	C₂²×C₁₃	—	4	2	no	—
513	C₂²×C₁₃	—	16	2	no	—
514	C₂²×C₁₃	C₂×#137	1	2	yes	—
515	C₂²×C₁₃	C₂×#137	1	2	yes	—
516	C₂²×C₁₃	C₂×#137	1	2	yes	—
517	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
518	C₄×C₁₃	—	2	2	no	—
519	C₄×C₁₃	—	2	4	no	—
520	C₄×C₁₃	—	2	1	no	—
521	C₄×C₁₃	—	2	2	no	—
522	C₄×C₁₃	—	2	1	no	—
523	C₄×C₁₃	—	2	1	no	—
524	C₄×C₁₃	—	2	2	no	—
525	C₄×C₁₃	—	4	2	no	—
526	C₄×C₁₃	—	4	2	no	—
527	C₄×C₁₃	—	4	2	no	—
528	C₄×C₁₃	—	4	2	no	—
529	C₄×C₁₃	—	4	2	no	—
530	C₄×C₁₃	—	4	2	no	—
531	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
532	C₂×#41	C₂³×C₁₃	1	2	yes	—
533	C₂²×Q₈	—	2	1	no	—
534	C₂²×Q₈	—	2	1	no	—
535	C₂²×Q₈	—	2	1	no	—
536	C₂²×Q₈	—	2	1	no	—
537	C₂²×Q₈	—	2	2	no	—
538	C₂²×Q₈	—	4	4	no	—
539	C₂²×Q₈	—	4	4	no	—
540	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
541	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
542	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
543	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
544	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
545	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
546	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
547	C₂²×D₄	—	2	1	no	—
548	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
549	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
550	C₂³×C₄	—	2	1	no	—
551	C₂³×C₄	—	2	1	no	—
552	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
553	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
554	#137	—	4	8	no	—
555	C₂×Q₁₆	—	4	4	no	—
556	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
557	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
558	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
559	C₂×SD₁₆	—	4	4	no	—
560	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
561	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
562	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
563	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
564	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
565	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
566	C₄⋊Q₈	—	2	4	no	—
567	C₄⋊Q₈	—	2	4	no	—
568	C₄⋊Q₈	—	2	2	no	—
569	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
570	#126	—	2	2	no	—
571	#126	—	2	2	no	—
572	#126	—	2	2	no	—
573	#125	—	2	2	no	—
574	#125	C₂³×C₁₃	1	2	yes	—
575	#124	—	2	2	no	—
576	#124	C₂³×C₁₃	1	2	yes	—
577	#123	—	2	2	no	—
578	#123	—	2	2	no	—
579	#123	—	2	2	no	—
580	#123	—	2	2	no	—
581	#123	—	2	2	no	—
582	C₂²⋊Q₈	—	2	1	no	—
583	C₂²⋊Q₈	—	2	1	no	—
584	C₂²⋊Q₈	—	2	1	no	—
585	C₂²⋊Q₈	—	2	1	no	—
586	C₂²⋊Q₈	—	2	2	no	—
587	C₂²⋊Q₈	—	2	2	no	—
588	C₂²⋊Q₈	—	2	4	no	—
589	C₂²⋊Q₈	—	2	4	no	—
590	C₂²⋊Q₈	—	2	4	no	—
591	C₂²⋊Q₈	—	2	4	no	—
592	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
593	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
594	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
595	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
596	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
597	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
598	#121	—	2	2	no	—
599	#121	—	2	2	no	—
600	#121	—	2	1	no	—
601	#121	—	2	1	no	—
602	#121	—	2	2	no	—
603	#121	C₂³×C₁₃	1	2	yes	—
604	#121	C₂³×C₁₃	1	2	yes	—
605	#121	C₂³×C₁₃	1	2	yes	—
606	#120	—	2	2	no	—
607	#120	—	2	2	no	—
608	C₄×Q₈	—	2	2	no	—
609	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
610	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
611	C₄×D₄	—	2	4	no	—
612	C₄×D₄	—	2	4	no	—
613	C₄×D₄	—	2	2	no	—
614	C₄×D₄	—	2	2	no	—
615	C₄×D₄	—	2	2	no	—
616	C₄×D₄	—	2	2	no	—
617	C₄×D₄	—	2	2	no	—
618	C₄×D₄	D₄×C₁₃	1	2	yes	—
619	C₄×D₄	D₄×C₁₃	1	2	yes	—
620	C₄×D₄	C₂³×C₁₃	1	2	yes	—
621	C₄×D₄	C₂³×C₁₃	1	2	yes	—
622	C₄×D₄	C₂³×C₁₃	1	2	yes	—
623	#117	—	2	2	no	—
624	#117	—	2	2	no	—
625	#117	C₂³×C₁₃	1	2	yes	—
626	C₂×C₄⋊C₄	—	2	1	no	—
627	C₂×C₄⋊C₄	—	2	1	no	—
628	C₂×C₄⋊C₄	—	2	1	no	—
629	C₂×C₄⋊C₄	—	2	1	no	—
630	C₂×C₄⋊C₄	—	2	1	no	—
631	C₂×C₄⋊C₄	—	2	1	no	—
632	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
633	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
634	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
635	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
636	C₂×C₂²⋊C₄	—	2	1	no	—
637	C₂×C₂²⋊C₄	—	2	1	no	—
638	C₂×C₂²⋊C₄	—	2	1	no	—
639	C₂×C₂²⋊C₄	—	2	1	no	—
640	C₂×C₂²⋊C₄	—	2	2	no	—
641	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
642	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
643	C₂×C₄²	—	2	1	no	—
644	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
645	#107	C₂³×C₁₃	1	4	yes	—
646	#106	C₂³×C₁₃	1	4	yes	—
647	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
648	#103	C₂³×C₁₃	1	4	yes	—
649	#103	C₂³×C₁₃	1	4	yes	—
650	#103	C₂³×C₁₃	1	4	yes	—
651	#103	C₂³×C₁₃	1	4	yes	—
652	#103	C₂³×C₁₃	1	4	yes	—
653	#103	C₂³×C₁₃	1	4	yes	—
654	#103	C₂³×C₁₃	1	4	yes	—
655	#102	C₂³×C₁₃	1	4	yes	—
656	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
657	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
658	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
659	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
660	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
661	#97	C₂³×C₁₃	1	4	yes	—
662	C₂×C₁₃	—	2	2	no	—
663	C₂×C₁₃	—	2	2	no	—
664	C₂×C₁₃	—	2	2	no	—
665	C₂×C₁₃	—	4	2	no	—
666	C₂×C₁₃	—	8	2	no	—
667	C₂×C₁₃	#3484	1	1	yes	characteristic
668	C₂×C₁₃	C₂²×#137	1	1	yes	characteristic
669	C₂×C₁₃	#3586	1	1	yes	characteristic
670	C₂⁴	—	2	1	no	—
671	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
672	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
673	#41	—	4	4	no	—
674	C₂×Q₈	—	2	4	no	—
675	C₂×Q₈	—	2	1	no	—
676	C₂×Q₈	—	2	4	no	—
677	C₂×Q₈	—	2	2	no	—
678	C₂×Q₈	—	2	2	no	—
679	C₂×Q₈	—	2	1	no	—
680	C₂×Q₈	—	2	1	no	—
681	C₂×Q₈	—	2	1	no	—
682	C₂×Q₈	—	2	4	no	—
683	C₂×Q₈	—	2	4	no	—
684	C₂×Q₈	—	2	8	no	—
685	C₂×Q₈	—	4	2	no	—
686	C₂×Q₈	—	4	2	no	—
687	C₂×Q₈	—	4	4	no	—
688	C₂×Q₈	—	4	2	no	—
689	C₂×Q₈	—	4	2	no	—
690	C₂×Q₈	—	4	4	no	—
691	C₂×Q₈	—	4	4	no	—
692	C₂×Q₈	—	4	2	no	—
693	C₂×Q₈	—	4	4	no	—
694	C₂×Q₈	—	4	4	no	—
695	C₂×Q₈	—	4	8	no	—
696	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
697	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
698	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
699	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
700	C₂×D₄	—	2	4	no	—
701	C₂×D₄	—	2	2	no	—
702	C₂×D₄	—	2	2	no	—
703	C₂×D₄	—	2	2	no	—
704	C₂×D₄	—	2	2	no	—
705	C₂×D₄	—	2	1	no	—
706	C₂×D₄	—	4	2	no	—
707	C₂×D₄	—	4	4	no	—
708	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
709	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
710	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
711	C₂²×C₄	—	2	1	no	—
712	C₂²×C₄	—	2	1	no	—
713	C₂²×C₄	—	2	1	no	—
714	C₂²×C₄	—	2	1	no	—
715	C₂²×C₄	—	2	1	no	—
716	C₂²×C₄	—	2	4	no	—
717	C₂²×C₄	—	2	2	no	—
718	C₂²×C₄	—	2	2	no	—
719	C₂²×C₄	—	2	1	no	—
720	C₂²×C₄	—	2	1	no	—
721	C₂²×C₄	—	2	2	no	—
722	C₂²×C₄	—	2	2	no	—
723	C₂²×C₄	—	4	2	no	—
724	C₂²×C₄	—	4	2	no	—
725	C₂²×C₄	—	4	4	no	—
726	C₂²×C₄	—	4	4	no	—
727	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
728	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
729	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
730	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
731	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
732	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
733	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
734	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
735	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
736	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
737	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
738	Q₁₆	—	2	8	no	—
739	Q₁₆	—	4	4	no	—
740	Q₁₆	—	4	4	no	—
741	SD₁₆	—	2	8	no	—
742	SD₁₆	—	4	4	no	—
743	SD₁₆	—	4	4	no	—
744	M₁₆	—	4	4	no	—
745	C₂×C₈	—	4	2	no	—
746	C₂×C₈	—	4	2	no	—
747	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
748	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
749	C₄⋊C₄	—	2	2	no	—
750	C₄⋊C₄	—	2	4	no	—
751	C₄⋊C₄	—	2	4	no	—
752	C₄⋊C₄	—	2	2	no	—
753	C₄⋊C₄	—	2	4	no	—
754	C₄⋊C₄	—	2	4	no	—
755	C₄⋊C₄	—	2	2	no	—
756	C₄⋊C₄	—	2	2	no	—
757	C₄⋊C₄	—	2	1	no	—
758	C₄⋊C₄	—	2	1	no	—
759	C₄⋊C₄	—	2	1	no	—
760	C₄⋊C₄	—	2	2	no	—
761	C₄⋊C₄	—	2	2	no	—
762	C₄⋊C₄	—	2	2	no	—
763	C₄⋊C₄	—	2	2	no	—
764	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
765	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
766	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
767	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
768	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
769	C₂²⋊C₄	—	2	2	no	—
770	C₂²⋊C₄	—	2	2	no	—
771	C₂²⋊C₄	—	2	4	no	—
772	C₂²⋊C₄	—	2	2	no	—
773	C₂²⋊C₄	—	2	2	no	—
774	C₂²⋊C₄	—	2	2	no	—
775	C₂²⋊C₄	—	2	2	no	—
776	C₂²⋊C₄	—	2	2	no	—
777	C₂²⋊C₄	—	2	2	no	—
778	C₂²⋊C₄	—	2	2	no	—
779	C₂²⋊C₄	—	2	2	no	—
780	C₂²⋊C₄	—	2	2	no	—
781	C₂²⋊C₄	—	2	2	no	—
782	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
783	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
784	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
785	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
786	C₄²	—	2	4	no	—
787	C₄²	—	2	2	no	—
788	C₄²	—	2	2	no	—
789	C₄²	C₂×D₄×C₁₃	1	2	yes	—
790	C₄²	C₂⁴×C₁₃	1	2	yes	—
791	C₁₃	#61574	1	1	yes	characteristic, direct product factor, Sylow
792	C₂³	—	2	2	no	—
793	C₂³	—	2	2	no	—
794	C₂³	—	4	1	no	—
795	C₂³	—	4	1	no	—
796	C₂³	—	4	1	no	—
797	C₂³	—	4	1	no	—
798	C₂³	—	4	2	no	—
799	C₂³	—	8	1	no	—
800	C₂³	—	8	1	no	—
801	C₂³	C₁₃×#137	1	4	yes	complemented
802	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
803	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
804	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
805	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
806	Q₈	—	2	4	no	—
807	Q₈	—	2	2	no	—
808	Q₈	—	2	2	no	—
809	Q₈	—	2	4	no	—
810	Q₈	—	2	4	no	—
811	Q₈	—	2	2	no	—
812	Q₈	—	4	8	no	—
813	Q₈	—	4	4	no	—
814	Q₈	—	4	4	no	—
815	Q₈	—	4	2	no	—
816	Q₈	—	4	2	no	—
817	Q₈	—	8	1	no	—
818	Q₈	C₁₃×H(5,𝔽₂)	1	4	yes	—
819	D₄	—	2	4	no	—
820	D₄	—	2	4	no	—
821	D₄	—	2	4	no	—
822	D₄	—	4	4	no	—
823	D₄	—	4	4	no	—
824	D₄	—	8	1	no	—
825	D₄	—	8	2	no	—
826	D₄	—	8	2	no	—
827	C₂×C₄	—	2	4	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	2	no	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	2	4	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	2	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	2	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	4	2	no	—
841	C₂×C₄	—	4	1	no	—
842	C₂×C₄	—	4	1	no	—
843	C₂×C₄	—	4	1	no	—
844	C₂×C₄	—	4	1	no	—
845	C₂×C₄	—	4	1	no	—
846	C₂×C₄	—	4	4	no	—
847	C₂×C₄	—	4	4	no	—
848	C₂×C₄	—	4	8	no	—
849	C₂×C₄	—	4	2	no	—
850	C₂×C₄	—	4	2	no	—
851	C₂×C₄	—	4	2	no	—
852	C₂×C₄	—	4	2	no	—
853	C₂×C₄	—	8	2	no	—
854	C₂×C₄	—	8	2	no	—
855	C₂×C₄	—	8	1	no	—
856	C₂×C₄	—	8	1	no	—
857	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
858	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
859	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
860	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
861	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
862	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
863	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
864	C₈	—	2	4	no	—
865	C₈	—	2	4	no	—
866	C₂²	—	2	1	no	—
867	C₂²	—	2	1	no	—
868	C₂²	—	2	1	no	—
869	C₂²	—	2	1	no	—
870	C₂²	—	2	1	no	—
871	C₂²	—	2	1	no	—
872	C₂²	—	2	2	no	—
873	C₂²	—	2	2	no	—
874	C₂²	—	2	2	no	—
875	C₂²	—	4	4	no	—
876	C₂²	—	4	4	no	—
877	C₂²	—	4	2	no	—
878	C₂²	—	4	2	no	—
879	C₂²	—	4	2	no	—
880	C₂²	—	16	2	no	—
881	C₂²	C₂×C₁₃×#137	1	2	yes	—
882	C₂²	C₂×C₁₃×#137	1	2	yes	—
883	C₂²	C₂×C₁₃×#137	1	2	yes	—
884	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
885	C₄	—	2	2	no	—
886	C₄	—	2	2	no	—
887	C₄	—	2	4	no	—
888	C₄	—	2	1	no	—
889	C₄	—	2	2	no	—
890	C₄	—	2	1	no	—
891	C₄	—	2	1	no	—
892	C₄	—	4	2	no	—
893	C₄	—	4	2	no	—
894	C₄	—	4	2	no	—
895	C₄	—	4	2	no	—
896	C₄	—	4	2	no	—
897	C₄	—	4	2	no	—
898	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
899	C₂	—	2	2	no	—
900	C₂	—	2	2	no	—
901	C₂	—	2	2	no	—
902	C₂	—	4	2	no	—
903	C₂	—	8	2	no	—
904	C₂	C₁₃×#3484	1	1	yes	characteristic
905	C₂	C₂²×C₁₃×#137	1	1	yes	characteristic
906	C₂	C₁₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3505	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×#3320	C₂	semidirect
4. C₁₃×#3312	C₂	semidirect
5. C₁₃×#3270	C₂	semidirect
6. C₁₃×#3266	C₂	semidirect
7. C₁₃×#3218	C₂	semidirect
8. C₁₃×#3196	C₂	semidirect
9. C₁₃×#3189	C₂	semidirect
10. C₁₃×#3187	C₂	semidirect
11. C₁₃×#3117	C₂	semidirect
12. C₁₃×#3004	C₂	semidirect
13. C₂×C₁₃×#451	C₂	semidirect
14. C₂×C₁₃×#448	C₂	semidirect
15. C₁₃×#2973	C₂	semidirect
17. C₂³×Q₈×C₁₃	C₂²	semidirect
18. C₂×C₁₃×#137	C₂²	semidirect
19. C₂²×C₁₃×Q₁₆	C₂²	semidirect
20. C₂²×C₁₃×SD₁₆	C₂²	semidirect
28. D₄×Q₈×C₁₃	C₂²	semidirect
35. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
42. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
45. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
48. C₁₃×#497	C₂²	semidirect
49. C₁₃×#491	C₂²	semidirect
50. C₁₃×#485	C₂²	semidirect
51. C₁₃×#484	C₂²	semidirect
52. C₁₃×#484	C₂²	semidirect
53. C₁₃×#483	C₂²	semidirect
55. C₁₃×#479	C₂²	semidirect
56. C₁₃×#470	C₂²	semidirect
57. C₁₃×#468	C₂²	semidirect
58. C₁₃×#467	C₂²	semidirect
59. C₁₃×#465	C₂²	semidirect
60. C₁₃×#464	C₂²	semidirect
61. C₁₃×#462	C₂²	semidirect
62. C₁₃×#461	C₂²	semidirect
63. C₁₃×#452	C₂²	semidirect
64. C₁₃×#451	C₂²	semidirect
65. C₁₃×#451	C₂²	semidirect
66. C₁₃×#451	C₂²	semidirect
67. C₁₃×#451	C₂²	semidirect
68. C₁₃×#451	C₂²	semidirect
69. C₁₃×#451	C₂²	semidirect
70. C₁₃×#450	C₂²	semidirect
74. C₁₃×#448	C₂²	semidirect
75. C₁₃×#448	C₂²	semidirect
76. C₁₃×#441	C₂²	semidirect
77. C₁₃×#440	C₂²	semidirect
79. C₁₃×#435	C₂²	semidirect
80. C₁₃×#432	C₂²	semidirect
81. C₁₃×#419	C₂²	semidirect
82. C₂×C₁₃×#103	C₂²	semidirect
83. C₂×C₁₃×#103	C₂²	semidirect
84. C₁₃×#407	C₂²	semidirect
217. #61574	C₁₃	direct (N × H)
340. C₂×D₄×Q₈	C₂×C₁₃	semidirect
341. #3320	C₂×C₁₃	semidirect
342. #3312	C₂×C₁₃	semidirect
343. #3270	C₂×C₁₃	semidirect
344. #3266	C₂×C₁₃	semidirect
345. #3218	C₂×C₁₃	semidirect
346. #3196	C₂×C₁₃	semidirect
347. #3189	C₂×C₁₃	semidirect
348. #3187	C₂×C₁₃	semidirect
349. #3117	C₂×C₁₃	semidirect
350. #3004	C₂×C₁₃	semidirect
351. C₂×#451	C₂×C₁₃	semidirect
352. C₂×#448	C₂×C₁₃	semidirect
353. #2973	C₂×C₁₃	semidirect
363. C₂³×C₁₃	#137	semidirect
429. C₂³×Q₈	C₂²×C₁₃	semidirect
430. C₂×#137	C₂²×C₁₃	semidirect
431. C₂²×Q₁₆	C₂²×C₁₃	semidirect
432. C₂²×SD₁₆	C₂²×C₁₃	semidirect
440. D₄×Q₈	C₂²×C₁₃	semidirect
447. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
454. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
457. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
460. #497	C₂²×C₁₃	semidirect
461. #491	C₂²×C₁₃	semidirect
462. #485	C₂²×C₁₃	semidirect
463. #484	C₂²×C₁₃	semidirect
464. #484	C₂²×C₁₃	semidirect
465. #483	C₂²×C₁₃	semidirect
467. #479	C₂²×C₁₃	semidirect
468. #470	C₂²×C₁₃	semidirect
469. #468	C₂²×C₁₃	semidirect
470. #467	C₂²×C₁₃	semidirect
471. #465	C₂²×C₁₃	semidirect
472. #464	C₂²×C₁₃	semidirect
473. #462	C₂²×C₁₃	semidirect
474. #461	C₂²×C₁₃	semidirect
475. #452	C₂²×C₁₃	semidirect
476. #451	C₂²×C₁₃	semidirect
477. #451	C₂²×C₁₃	semidirect
478. #451	C₂²×C₁₃	semidirect
479. #451	C₂²×C₁₃	semidirect
480. #451	C₂²×C₁₃	semidirect
481. #451	C₂²×C₁₃	semidirect
482. #450	C₂²×C₁₃	semidirect
486. #448	C₂²×C₁₃	semidirect
487. #448	C₂²×C₁₃	semidirect
488. #441	C₂²×C₁₃	semidirect
489. #440	C₂²×C₁₃	semidirect
491. #435	C₂²×C₁₃	semidirect
492. #432	C₂²×C₁₃	semidirect
493. #419	C₂²×C₁₃	semidirect
494. C₂×#103	C₂²×C₁₃	semidirect
495. C₂×#103	C₂²×C₁₃	semidirect
496. #407	C₂²×C₁₃	semidirect
791. C₁₃	#61574	direct (N × H)
801. C₂³	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×#3505	2
C₂×D₄×Q₈×C₁₃	2
C₁₃×#3320	2
C₁₃×#3312	2
C₁₃×#3270	2
C₁₃×#3266	2
C₁₃×#3218	2
C₁₃×#3196	2
C₁₃×#3189	2
C₁₃×#3187	2
C₁₃×#3117	2
C₁₃×#3004	2
C₂×C₁₃×#451	2
C₂×C₁₃×#448	2
C₁₃×#2973	2
#61574	13

Subgroups — C13×#61574 #15747913

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61574 #15747913