Subgroups — C₁₃×#62054 #15748393

Order 3328.

1828 conjugacy classes of subgroups.

The subgroup lattice has 1158 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3552	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3520	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3398	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3393	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#3367	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#3359	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#3330	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#3316	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3299	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3298	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3283	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3282	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3276	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3266	C₂	1	2	yes	maximal, complemented
15	C₁₃×#3258	C₂	1	2	yes	maximal, complemented
16	C₁₃×#3248	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#3225	C₂	1	2	yes	maximal, complemented
18	C₁₃×#3209	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₃×#3120	C₂	1	2	yes	maximal, complemented
20	C₁₃×#3105	C₂	1	1	yes	maximal, characteristic, complemented
21	C₁₃×#3046	C₂	1	2	yes	maximal, complemented
22	C₂×C₁₃×#461	C₂	1	1	yes	maximal, characteristic, complemented
23	C₁₃×#2994	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₁₃×#137	C₂²	1	2	yes	—
25	C₂×C₁₃×#135	C₂²	1	2	yes	—
26	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
27	C₁₃×#563	—	2	2	no	—
28	C₁₃×#557	C₂²	1	1	yes	characteristic, complemented
29	C₁₃×#556	C₂²	1	1	yes	characteristic
30	C₁₃×#556	C₂²	1	1	yes	characteristic, complemented
31	C₁₃×#554	—	2	1	no	—
32	C₁₃×#554	C₂²	1	2	yes	—
33	C₁₃×#553	—	2	1	no	—
34	C₁₃×#552	—	2	1	no	—
35	C₁₃×#551	—	2	2	no	—
36	D₄×Q₈×C₁₃	C₂²	1	2	yes	—
37	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
38	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
39	C₁₃×#548	—	2	1	no	—
40	C₁₃×#548	C₂²	1	2	yes	—
41	C₁₃×#547	C₂²	1	1	yes	characteristic
42	C₁₃×#547	C₂²	1	1	yes	characteristic
43	C₁₃×#547	C₂²	1	1	yes	characteristic, complemented
44	C₁₃×#546	C₂²	1	2	yes	—
45	C₁₃×#544	—	2	1	no	—
46	C₁₃×#542	—	2	1	no	—
47	C₁₃×#542	C₂²	1	2	yes	—
48	C₁₃×#541	C₂²	1	2	yes	complemented
49	C₁₃×#539	—	2	2	no	—
50	C₁₃×#539	—	2	2	no	—
51	C₁₃×#536	C₂²	1	2	yes	complemented
52	C₁₃×#533	C₂²	1	1	yes	characteristic
53	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
54	C₁₃×#529	C₂²	1	1	yes	characteristic
55	C₁₃×#529	C₂²	1	1	yes	characteristic
56	C₁₃×#525	—	2	1	no	—
57	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
58	C₁₃×#520	C₂²	1	2	yes	—
59	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
60	C₁₃×#497	C₂²	1	2	yes	—
61	C₁₃×#495	C₂²	1	2	yes	—
62	C₁₃×#494	C₂²	1	1	yes	characteristic, complemented
63	C₁₃×#494	C₂²	1	1	yes	characteristic, complemented
64	C₁₃×#489	C₂²	1	2	yes	complemented
65	C₁₃×#487	C₂²	1	1	yes	characteristic, complemented
66	C₁₃×#487	C₂²	1	2	yes	complemented
67	C₁₃×#487	C₂²	1	1	yes	characteristic, complemented
68	C₁₃×#484	C₂²	1	1	yes	characteristic
69	C₁₃×#484	C₂²	1	2	yes	complemented
70	C₁₃×#483	C₂²	1	2	yes	complemented
71	C₁₃×#481	C₂²	1	1	yes	characteristic
72	C₁₃×#479	C₂²	1	2	yes	complemented
73	C₁₃×#478	C₂²	1	1	yes	characteristic
74	C₁₃×#478	C₂²	1	1	yes	characteristic
75	C₁₃×#477	C₂²	1	2	yes	complemented
76	C₁₃×#475	C₂²	1	1	yes	characteristic, complemented
77	C₁₃×#475	C₂²	1	2	yes	complemented
78	C₁₃×#474	C₂²	1	1	yes	characteristic, complemented
79	C₁₃×#470	C₂²	1	2	yes	complemented
80	C₁₃×#468	C₂²	1	2	yes	—
81	C₁₃×#467	C₂²	1	2	yes	—
82	C₁₃×#467	C₂²	1	2	yes	complemented
83	C₁₃×#465	C₂²	1	2	yes	—
84	C₁₃×#465	C₂²	1	2	yes	—
85	C₁₃×#464	C₂²	1	2	yes	—
86	C₁₃×#464	C₂²	1	2	yes	—
87	C₁₃×#464	C₂²	1	2	yes	complemented
88	C₁₃×#464	C₂²	1	2	yes	complemented
89	C₁₃×#463	C₂²	1	2	yes	—
90	C₁₃×#463	C₂²	1	1	yes	characteristic
91	C₁₃×#463	C₂²	1	1	yes	characteristic
92	C₁₃×#462	C₂²	1	1	yes	characteristic, complemented
93	C₁₃×#462	C₂²	1	2	yes	complemented
94	C₁₃×#462	C₂²	1	2	yes	complemented
95	C₁₃×#462	C₂²	1	2	yes	complemented
96	C₁₃×#461	C₂²	1	2	yes	—
97	C₁₃×#461	C₂²	1	1	yes	characteristic
98	C₁₃×#461	C₂²	1	1	yes	characteristic
99	C₁₃×#461	C₂²	1	1	yes	characteristic
100	C₁₃×#461	C₂²	1	2	yes	—
101	C₁₃×#461	C₂²	1	1	yes	characteristic
102	C₁₃×#461	C₂²	1	2	yes	—
103	C₁₃×#461	C₂²	1	1	yes	characteristic, complemented
104	C₁₃×#452	C₂²	1	2	yes	—
105	C₁₃×#452	C₂²	1	2	yes	—
106	C₁₃×#452	C₂²	1	2	yes	complemented
107	C₁₃×#451	C₂²	1	2	yes	—
108	C₁₃×#451	C₂²	1	2	yes	—
109	C₁₃×#451	C₂²	1	2	yes	complemented
110	C₁₃×#450	C₂²	1	1	yes	characteristic
111	C₁₃×#449	C₂²	1	2	yes	—
112	C₁₃×#448	C₂²	1	2	yes	—
113	C₁₃×#447	C₂²	1	1	yes	characteristic
114	C₁₃×#446	C₂²	1	1	yes	characteristic, complemented
115	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
116	C₁₃×#441	C₂²	1	2	yes	complemented
117	C₁₃×#440	C₂²	1	2	yes	—
118	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
119	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
120	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
121	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
122	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
123	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
124	C₁₃×#436	C₂²	1	1	yes	characteristic, complemented
125	C₁₃×#435	C₂²	1	2	yes	—
126	C₈×D₄×C₁₃	C₂²	1	2	yes	—
127	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
128	C₁₃×#433	C₂²	1	2	yes	complemented
129	C₁₃×#431	C₂²	1	1	yes	characteristic
130	C₁₃×#424	C₂²	1	2	yes	complemented
131	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
132	C₁₃×#417	C₂²	1	2	yes	complemented
133	C₂×C₁₃×#103	C₂²	1	2	yes	—
134	C₂×C₁₃×#103	C₂²	1	2	yes	complemented
135	C₂×C₁₃×#41	—	2	1	no	—
136	C₂×C₁₃×#41	C₂³	1	2	yes	—
137	C₂×C₁₃×#41	C₂³	1	2	yes	—
138	C₂²×Q₈×C₁₃	—	2	1	no	—
139	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
140	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
141	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
142	C₂³×C₄×C₁₃	—	2	1	no	—
143	C₁₃×#137	—	4	4	no	—
144	C₁₃×#135	—	4	4	no	—
145	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
146	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
147	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
148	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
149	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
150	C₂×C₁₃×SD₁₆	—	4	4	no	—
151	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
152	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
153	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
154	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
155	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
156	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
157	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
158	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
159	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
160	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
161	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
162	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
163	C₁₃×C₄⋊Q₈	—	2	2	no	—
164	C₁₃×C₄⋊Q₈	—	2	1	no	—
165	C₁₃×C₄⋊Q₈	—	2	1	no	—
166	C₁₃×C₄⋊Q₈	—	2	1	no	—
167	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
168	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
169	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
170	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
171	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
172	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
173	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
174	C₁₃×#126	—	2	2	no	—
175	C₁₃×#126	—	2	2	no	—
176	C₁₃×#126	—	2	2	no	—
177	C₁₃×#126	—	2	2	no	—
178	C₁₃×#126	—	2	2	no	—
179	C₁₃×#126	—	2	1	no	—
180	C₁₃×#126	D₄	1	2	yes	—
181	C₁₃×#125	—	2	2	no	—
182	C₁₃×#125	—	2	2	no	—
183	C₁₃×#125	—	2	2	no	—
184	C₁₃×#125	—	2	2	no	—
185	C₁₃×#125	—	2	1	no	—
186	C₁₃×#125	—	2	1	no	—
187	C₁₃×#125	D₄	1	1	yes	characteristic
188	C₁₃×#125	C₂³	1	1	yes	characteristic
189	C₁₃×#124	—	2	2	no	—
190	C₁₃×#124	—	2	2	no	—
191	C₁₃×#124	D₄	1	1	yes	characteristic
192	C₁₃×#124	C₂³	1	1	yes	characteristic
193	C₁₃×#124	C₂³	1	2	yes	—
194	C₁₃×#124	C₂³	1	2	yes	—
195	C₁₃×#123	—	2	1	no	—
196	C₁₃×#123	—	2	2	no	—
197	C₁₃×#123	—	2	2	no	—
198	C₁₃×#123	—	2	2	no	—
199	C₁₃×#123	—	2	2	no	—
200	C₁₃×#123	—	2	2	no	—
201	C₁₃×#123	—	2	2	no	—
202	C₁₃×#123	—	2	2	no	—
203	C₁₃×#123	D₄	1	2	yes	—
204	C₁₃×C₂²⋊Q₈	—	2	1	no	—
205	C₁₃×C₂²⋊Q₈	—	2	1	no	—
206	C₁₃×C₂²⋊Q₈	—	2	1	no	—
207	C₁₃×C₂²⋊Q₈	—	2	2	no	—
208	C₁₃×C₂²⋊Q₈	—	2	1	no	—
209	C₁₃×C₂²⋊Q₈	—	2	1	no	—
210	C₁₃×C₂²⋊Q₈	—	2	2	no	—
211	C₁₃×C₂²⋊Q₈	—	2	2	no	—
212	C₁₃×C₂²⋊Q₈	—	2	2	no	—
213	C₁₃×C₂²⋊Q₈	—	2	2	no	—
214	C₁₃×C₂²⋊Q₈	—	2	2	no	—
215	C₁₃×C₂²⋊Q₈	—	2	2	no	—
216	C₁₃×C₂²⋊Q₈	—	2	2	no	—
217	C₁₃×C₂²⋊Q₈	—	2	2	no	—
218	C₁₃×C₂²⋊Q₈	—	2	2	no	—
219	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
220	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
221	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
222	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
223	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
224	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
225	C₁₃×#121	—	2	1	no	—
226	C₁₃×#121	—	2	2	no	—
227	C₁₃×#121	—	2	1	no	—
228	C₁₃×#121	—	2	2	no	—
229	C₁₃×#121	D₄	1	1	yes	characteristic
230	C₁₃×#121	C₂³	1	1	yes	characteristic
231	C₁₃×#121	C₂³	1	2	yes	—
232	C₁₃×#120	—	2	2	no	—
233	C₄×Q₈×C₁₃	—	2	1	no	—
234	C₄×Q₈×C₁₃	—	2	1	no	—
235	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
236	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
237	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
238	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
239	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
240	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
241	C₄×D₄×C₁₃	—	2	2	no	—
242	C₄×D₄×C₁₃	—	2	2	no	—
243	C₄×D₄×C₁₃	—	2	1	no	—
244	C₄×D₄×C₁₃	—	2	1	no	—
245	C₄×D₄×C₁₃	—	2	2	no	—
246	C₄×D₄×C₁₃	—	2	2	no	—
247	C₄×D₄×C₁₃	—	2	2	no	—
248	C₄×D₄×C₁₃	—	2	1	no	—
249	C₄×D₄×C₁₃	—	2	1	no	—
250	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
251	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
252	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
253	C₄×D₄×C₁₃	C₂³	1	2	yes	—
254	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
255	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
256	C₄×D₄×C₁₃	C₂³	1	2	yes	—
257	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
258	C₁₃×#117	—	2	1	no	—
259	C₁₃×#117	—	2	2	no	—
260	C₁₃×#117	—	2	1	no	—
261	C₁₃×#117	—	2	1	no	—
262	C₁₃×#117	—	2	1	no	—
263	C₁₃×#117	C₂³	1	2	yes	—
264	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
265	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
266	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
267	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
268	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
269	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
270	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
271	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
272	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
273	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
274	C₁₃×#107	C₂³	1	1	yes	characteristic
275	C₁₃×#107	C₂³	1	1	yes	characteristic
276	C₁₃×#107	C₂³	1	2	yes	—
277	C₁₃×#106	C₂³	1	1	yes	characteristic
278	C₁₃×#106	C₂³	1	2	yes	—
279	C₁₃×#106	C₂³	1	1	yes	characteristic
280	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
281	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
282	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
283	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
284	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
285	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
286	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
287	C₁₃×#103	C₂³	1	2	yes	—
288	C₁₃×#103	C₂³	1	2	yes	—
289	C₁₃×#103	C₂³	1	2	yes	—
290	C₁₃×#103	C₂³	1	2	yes	—
291	C₁₃×#103	C₂³	1	1	yes	characteristic
292	C₁₃×#103	C₂³	1	2	yes	—
293	C₁₃×#103	C₂³	1	2	yes	—
294	C₁₃×#103	C₂³	1	2	yes	—
295	C₁₃×#103	C₂³	1	2	yes	—
296	C₁₃×#103	C₂³	1	1	yes	characteristic
297	C₁₃×#103	C₂³	1	2	yes	—
298	C₁₃×#103	C₂³	1	2	yes	—
299	C₁₃×#103	C₂³	1	2	yes	—
300	C₁₃×#102	C₂³	1	1	yes	characteristic
301	C₁₃×#102	C₂³	1	2	yes	—
302	C₁₃×#102	C₂³	1	1	yes	characteristic
303	C₁₃×#102	C₂³	1	1	yes	characteristic
304	C₁₃×#102	C₂³	1	1	yes	characteristic
305	C₁₃×#102	C₂³	1	1	yes	characteristic
306	C₁₃×#102	C₂³	1	1	yes	characteristic
307	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
308	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
309	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
310	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
311	C₁₃×#97	C₂³	1	2	yes	—
312	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
314	C₄×C₈×C₁₃	C₂³	1	2	yes	—
315	#62054	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
316	C₂⁴×C₁₃	—	2	1	no	—
317	C₁₃×#41	—	2	4	no	—
318	C₁₃×#41	—	4	2	no	—
319	C₁₃×#41	—	4	2	no	—
320	C₁₃×#41	—	4	2	no	—
321	C₁₃×#41	—	8	2	no	—
322	C₂×Q₈×C₁₃	—	2	1	no	—
323	C₂×Q₈×C₁₃	—	2	2	no	—
324	C₂×Q₈×C₁₃	—	2	2	no	—
325	C₂×Q₈×C₁₃	—	2	2	no	—
326	C₂×Q₈×C₁₃	—	4	2	no	—
327	C₂×Q₈×C₁₃	—	4	2	no	—
328	C₂×Q₈×C₁₃	—	4	2	no	—
329	C₂×Q₈×C₁₃	—	4	2	no	—
330	C₂×Q₈×C₁₃	—	8	2	no	—
331	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
332	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
333	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
334	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
335	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
336	C₂×D₄×C₁₃	—	2	2	no	—
337	C₂×D₄×C₁₃	—	2	1	no	—
338	C₂×D₄×C₁₃	—	2	2	no	—
339	C₂×D₄×C₁₃	—	2	2	no	—
340	C₂×D₄×C₁₃	—	2	2	no	—
341	C₂×D₄×C₁₃	—	2	1	no	—
342	C₂×D₄×C₁₃	—	4	1	no	—
343	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
344	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
345	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
346	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
347	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
348	C₂²×C₄×C₁₃	—	2	1	no	—
349	C₂²×C₄×C₁₃	—	2	2	no	—
350	C₂²×C₄×C₁₃	—	2	2	no	—
351	C₂²×C₄×C₁₃	—	2	2	no	—
352	C₂²×C₄×C₁₃	—	2	2	no	—
353	C₂²×C₄×C₁₃	—	2	1	no	—
354	C₂²×C₄×C₁₃	—	2	1	no	—
355	C₂²×C₄×C₁₃	—	2	1	no	—
356	C₂²×C₄×C₁₃	—	2	2	no	—
357	C₂²×C₄×C₁₃	—	2	1	no	—
358	C₂²×C₄×C₁₃	—	2	2	no	—
359	C₂²×C₄×C₁₃	—	2	1	no	—
360	C₂²×C₄×C₁₃	—	8	2	no	—
361	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
362	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
363	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
364	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
365	C₁₃×Q₁₆	—	4	2	no	—
366	C₁₃×Q₁₆	—	4	2	no	—
367	C₁₃×Q₁₆	—	4	2	no	—
368	C₁₃×Q₁₆	—	4	2	no	—
369	C₁₃×Q₁₆	—	4	2	no	—
370	C₁₃×SD₁₆	—	2	4	no	—
371	C₁₃×SD₁₆	—	2	4	no	—
372	C₁₃×SD₁₆	—	2	2	no	—
373	C₁₃×SD₁₆	—	4	2	no	—
374	C₁₃×SD₁₆	—	4	2	no	—
375	C₁₃×SD₁₆	—	4	1	no	—
376	C₁₃×SD₁₆	—	4	2	no	—
377	C₁₃×D₈	—	2	2	no	—
378	C₁₃×D₈	—	4	1	no	—
379	C₁₃×M₁₆	—	4	2	no	—
380	C₂×C₈×C₁₃	—	4	2	no	—
381	C₂×C₈×C₁₃	—	4	2	no	—
382	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
383	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
384	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
385	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
386	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
387	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
388	C₁₃×C₄⋊C₄	—	2	1	no	—
389	C₁₃×C₄⋊C₄	—	2	2	no	—
390	C₁₃×C₄⋊C₄	—	2	1	no	—
391	C₁₃×C₄⋊C₄	—	2	1	no	—
392	C₁₃×C₄⋊C₄	—	2	2	no	—
393	C₁₃×C₄⋊C₄	—	2	2	no	—
394	C₁₃×C₄⋊C₄	—	2	2	no	—
395	C₁₃×C₄⋊C₄	—	2	1	no	—
396	C₁₃×C₄⋊C₄	—	2	2	no	—
397	C₁₃×C₄⋊C₄	—	2	2	no	—
398	C₁₃×C₄⋊C₄	—	2	2	no	—
399	C₁₃×C₄⋊C₄	—	2	1	no	—
400	C₁₃×C₄⋊C₄	—	2	1	no	—
401	C₁₃×C₄⋊C₄	—	2	1	no	—
402	C₁₃×C₄⋊C₄	—	2	1	no	—
403	C₁₃×C₄⋊C₄	—	2	1	no	—
404	C₁₃×C₄⋊C₄	—	2	1	no	—
405	C₁₃×C₄⋊C₄	—	2	2	no	—
406	C₁₃×C₄⋊C₄	—	2	2	no	—
407	C₁₃×C₄⋊C₄	—	2	2	no	—
408	C₁₃×C₄⋊C₄	—	2	1	no	—
409	C₁₃×C₄⋊C₄	—	2	2	no	—
410	C₁₃×C₄⋊C₄	—	2	2	no	—
411	C₁₃×C₄⋊C₄	—	2	2	no	—
412	C₁₃×C₄⋊C₄	—	2	2	no	—
413	C₁₃×C₄⋊C₄	—	2	1	no	—
414	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
415	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
416	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
417	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
418	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
419	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
420	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
421	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
422	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
423	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
424	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
425	C₁₃×C₂²⋊C₄	—	2	2	no	—
426	C₁₃×C₂²⋊C₄	—	2	1	no	—
427	C₁₃×C₂²⋊C₄	—	2	2	no	—
428	C₁₃×C₂²⋊C₄	—	2	2	no	—
429	C₁₃×C₂²⋊C₄	—	2	2	no	—
430	C₁₃×C₂²⋊C₄	—	2	1	no	—
431	C₁₃×C₂²⋊C₄	—	2	1	no	—
432	C₁₃×C₂²⋊C₄	—	2	1	no	—
433	C₁₃×C₂²⋊C₄	—	2	1	no	—
434	C₁₃×C₂²⋊C₄	—	2	2	no	—
435	C₁₃×C₂²⋊C₄	—	2	2	no	—
436	C₁₃×C₂²⋊C₄	—	2	2	no	—
437	C₁₃×C₂²⋊C₄	—	2	2	no	—
438	C₁₃×C₂²⋊C₄	—	2	2	no	—
439	C₁₃×C₂²⋊C₄	—	2	1	no	—
440	C₁₃×C₂²⋊C₄	—	2	1	no	—
441	C₁₃×C₂²⋊C₄	—	2	1	no	—
442	C₁₃×C₂²⋊C₄	—	2	2	no	—
443	C₁₃×C₂²⋊C₄	—	2	1	no	—
444	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
445	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
446	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
447	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
448	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
449	C₄²×C₁₃	—	2	2	no	—
450	C₄²×C₁₃	—	2	2	no	—
451	C₄²×C₁₃	—	2	1	no	—
452	C₄²×C₁₃	—	2	2	no	—
453	C₄²×C₁₃	—	2	2	no	—
454	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
455	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
456	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
457	C₄²×C₁₃	C₂⁴	1	2	yes	—
458	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
459	#3552	C₂×C₁₃	1	1	yes	characteristic, complemented
460	#3520	C₂×C₁₃	1	1	yes	characteristic, complemented
461	#3398	C₂×C₁₃	1	1	yes	characteristic, complemented
462	#3393	C₂×C₁₃	1	1	yes	characteristic, complemented
463	#3367	C₂×C₁₃	1	1	yes	characteristic, complemented
464	#3359	C₂×C₁₃	1	1	yes	characteristic, complemented
465	#3330	C₂×C₁₃	1	1	yes	characteristic, complemented
466	#3316	C₂×C₁₃	1	2	yes	complemented
467	#3299	C₂×C₁₃	1	2	yes	complemented
468	#3298	C₂×C₁₃	1	1	yes	characteristic, complemented
469	#3283	C₂×C₁₃	1	1	yes	characteristic, complemented
470	#3282	C₂×C₁₃	1	2	yes	complemented
471	#3276	C₂×C₁₃	1	1	yes	characteristic, complemented
472	#3266	C₂×C₁₃	1	2	yes	complemented
473	#3258	C₂×C₁₃	1	2	yes	complemented
474	#3248	C₂×C₁₃	1	1	yes	characteristic, complemented
475	#3225	C₂×C₁₃	1	2	yes	complemented
476	#3209	C₂×C₁₃	1	1	yes	characteristic, complemented
477	#3120	C₂×C₁₃	1	2	yes	complemented
478	#3105	C₂×C₁₃	1	1	yes	characteristic, complemented
479	#3046	C₂×C₁₃	1	2	yes	complemented
480	C₂×#461	C₂×C₁₃	1	1	yes	characteristic, complemented
481	#2994	C₂×C₁₃	1	1	yes	characteristic, complemented
482	C₂³×C₁₃	—	2	1	no	—
483	C₂³×C₁₃	—	2	1	no	—
484	C₂³×C₁₃	—	2	1	no	—
485	C₂³×C₁₃	—	4	2	no	—
486	C₂³×C₁₃	—	4	2	no	—
487	C₂³×C₁₃	—	8	1	no	—
488	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
489	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
490	Q₈×C₁₃	—	2	2	no	—
491	Q₈×C₁₃	—	2	2	no	—
492	Q₈×C₁₃	—	2	2	no	—
493	Q₈×C₁₃	—	2	1	no	—
494	Q₈×C₁₃	—	2	2	no	—
495	Q₈×C₁₃	—	2	1	no	—
496	Q₈×C₁₃	—	2	2	no	—
497	Q₈×C₁₃	—	2	2	no	—
498	Q₈×C₁₃	—	2	2	no	—
499	Q₈×C₁₃	—	4	2	no	—
500	Q₈×C₁₃	—	8	2	no	—
501	Q₈×C₁₃	—	8	2	no	—
502	Q₈×C₁₃	—	8	2	no	—
503	D₄×C₁₃	—	2	4	no	—
504	D₄×C₁₃	—	2	2	no	—
505	D₄×C₁₃	—	2	1	no	—
506	D₄×C₁₃	—	2	1	no	—
507	D₄×C₁₃	—	2	1	no	—
508	D₄×C₁₃	—	2	1	no	—
509	D₄×C₁₃	—	2	1	no	—
510	D₄×C₁₃	—	4	2	no	—
511	D₄×C₁₃	—	4	4	no	—
512	D₄×C₁₃	—	4	2	no	—
513	D₄×C₁₃	—	8	2	no	—
514	D₄×C₁₃	—	8	2	no	—
515	D₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
516	C₂×C₄×C₁₃	—	2	2	no	—
517	C₂×C₄×C₁₃	—	2	2	no	—
518	C₂×C₄×C₁₃	—	2	1	no	—
519	C₂×C₄×C₁₃	—	2	2	no	—
520	C₂×C₄×C₁₃	—	2	1	no	—
521	C₂×C₄×C₁₃	—	2	2	no	—
522	C₂×C₄×C₁₃	—	2	1	no	—
523	C₂×C₄×C₁₃	—	2	1	no	—
524	C₂×C₄×C₁₃	—	2	2	no	—
525	C₂×C₄×C₁₃	—	2	1	no	—
526	C₂×C₄×C₁₃	—	2	1	no	—
527	C₂×C₄×C₁₃	—	2	2	no	—
528	C₂×C₄×C₁₃	—	2	2	no	—
529	C₂×C₄×C₁₃	—	2	2	no	—
530	C₂×C₄×C₁₃	—	2	1	no	—
531	C₂×C₄×C₁₃	—	4	4	no	—
532	C₂×C₄×C₁₃	—	4	2	no	—
533	C₂×C₄×C₁₃	—	4	2	no	—
534	C₂×C₄×C₁₃	—	4	2	no	—
535	C₂×C₄×C₁₃	—	8	1	no	—
536	C₂×C₄×C₁₃	—	8	1	no	—
537	C₂×C₄×C₁₃	—	8	2	no	—
538	C₂×C₄×C₁₃	—	8	2	no	—
539	C₂×C₄×C₁₃	—	8	1	no	—
540	C₂×C₄×C₁₃	—	8	2	no	—
541	C₂×C₄×C₁₃	—	8	2	no	—
542	C₂×C₄×C₁₃	—	8	2	no	—
543	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
544	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
545	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
546	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
547	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
548	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
549	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
550	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
551	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
552	C₈×C₁₃	—	2	1	no	—
553	C₈×C₁₃	—	2	2	no	—
554	C₈×C₁₃	—	2	2	no	—
555	C₈×C₁₃	—	2	1	no	—
556	C₈×C₁₃	—	2	1	no	—
557	C₈×C₁₃	—	2	1	no	—
558	C₂×#137	C₂²×C₁₃	1	2	yes	—
559	C₂×#135	C₂²×C₁₃	1	2	yes	—
560	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
561	#563	—	2	2	no	—
562	#557	C₂²×C₁₃	1	1	yes	characteristic, complemented
563	#556	C₂²×C₁₃	1	1	yes	characteristic
564	#556	C₂²×C₁₃	1	1	yes	characteristic, complemented
565	#554	—	2	1	no	—
566	#554	C₂²×C₁₃	1	2	yes	—
567	#553	—	2	1	no	—
568	#552	—	2	1	no	—
569	#551	—	2	2	no	—
570	D₄×Q₈	C₂²×C₁₃	1	2	yes	—
571	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
572	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
573	#548	—	2	1	no	—
574	#548	C₂²×C₁₃	1	2	yes	—
575	#547	C₂²×C₁₃	1	1	yes	characteristic
576	#547	C₂²×C₁₃	1	1	yes	characteristic
577	#547	C₂²×C₁₃	1	1	yes	characteristic, complemented
578	#546	C₂²×C₁₃	1	2	yes	—
579	#544	—	2	1	no	—
580	#542	—	2	1	no	—
581	#542	C₂²×C₁₃	1	2	yes	—
582	#541	C₂²×C₁₃	1	2	yes	complemented
583	#539	—	2	2	no	—
584	#539	—	2	2	no	—
585	#536	C₂²×C₁₃	1	2	yes	complemented
586	#533	C₂²×C₁₃	1	1	yes	characteristic
587	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
588	#529	C₂²×C₁₃	1	1	yes	characteristic
589	#529	C₂²×C₁₃	1	1	yes	characteristic
590	#525	—	2	1	no	—
591	C₂×C₂²⋊Q₈	—	2	1	no	—
592	#520	C₂²×C₁₃	1	2	yes	—
593	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
594	#497	C₂²×C₁₃	1	2	yes	—
595	#495	C₂²×C₁₃	1	2	yes	—
596	#494	C₂²×C₁₃	1	1	yes	characteristic, complemented
597	#494	C₂²×C₁₃	1	1	yes	characteristic, complemented
598	#489	C₂²×C₁₃	1	2	yes	complemented
599	#487	C₂²×C₁₃	1	1	yes	characteristic, complemented
600	#487	C₂²×C₁₃	1	2	yes	complemented
601	#487	C₂²×C₁₃	1	1	yes	characteristic, complemented
602	#484	C₂²×C₁₃	1	1	yes	characteristic
603	#484	C₂²×C₁₃	1	2	yes	complemented
604	#483	C₂²×C₁₃	1	2	yes	complemented
605	#481	C₂²×C₁₃	1	1	yes	characteristic
606	#479	C₂²×C₁₃	1	2	yes	complemented
607	#478	C₂²×C₁₃	1	1	yes	characteristic
608	#478	C₂²×C₁₃	1	1	yes	characteristic
609	#477	C₂²×C₁₃	1	2	yes	complemented
610	#475	C₂²×C₁₃	1	1	yes	characteristic, complemented
611	#475	C₂²×C₁₃	1	2	yes	complemented
612	#474	C₂²×C₁₃	1	1	yes	characteristic, complemented
613	#470	C₂²×C₁₃	1	2	yes	complemented
614	#468	C₂²×C₁₃	1	2	yes	—
615	#467	C₂²×C₁₃	1	2	yes	—
616	#467	C₂²×C₁₃	1	2	yes	complemented
617	#465	C₂²×C₁₃	1	2	yes	—
618	#465	C₂²×C₁₃	1	2	yes	—
619	#464	C₂²×C₁₃	1	2	yes	—
620	#464	C₂²×C₁₃	1	2	yes	—
621	#464	C₂²×C₁₃	1	2	yes	complemented
622	#464	C₂²×C₁₃	1	2	yes	complemented
623	#463	C₂²×C₁₃	1	1	yes	characteristic
624	#463	C₂²×C₁₃	1	1	yes	characteristic
625	#463	C₂²×C₁₃	1	2	yes	—
626	#462	C₂²×C₁₃	1	2	yes	complemented
627	#462	C₂²×C₁₃	1	1	yes	characteristic, complemented
628	#462	C₂²×C₁₃	1	2	yes	complemented
629	#462	C₂²×C₁₃	1	2	yes	complemented
630	#461	C₂²×C₁₃	1	1	yes	characteristic
631	#461	C₂²×C₁₃	1	2	yes	—
632	#461	C₂²×C₁₃	1	1	yes	characteristic
633	#461	C₂²×C₁₃	1	1	yes	characteristic
634	#461	C₂²×C₁₃	1	2	yes	—
635	#461	C₂²×C₁₃	1	1	yes	characteristic
636	#461	C₂²×C₁₃	1	2	yes	—
637	#461	C₂²×C₁₃	1	1	yes	characteristic, complemented
638	#452	C₂²×C₁₃	1	2	yes	—
639	#452	C₂²×C₁₃	1	2	yes	—
640	#452	C₂²×C₁₃	1	2	yes	complemented
641	#451	C₂²×C₁₃	1	2	yes	—
642	#451	C₂²×C₁₃	1	2	yes	—
643	#451	C₂²×C₁₃	1	2	yes	complemented
644	#450	C₂²×C₁₃	1	1	yes	characteristic
645	#449	C₂²×C₁₃	1	2	yes	—
646	#448	C₂²×C₁₃	1	2	yes	—
647	#447	C₂²×C₁₃	1	1	yes	characteristic
648	#446	C₂²×C₁₃	1	1	yes	characteristic, complemented
649	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
650	#441	C₂²×C₁₃	1	2	yes	complemented
651	#440	C₂²×C₁₃	1	2	yes	—
652	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
653	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
654	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
655	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
656	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
657	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
658	#436	C₂²×C₁₃	1	1	yes	characteristic, complemented
659	#435	C₂²×C₁₃	1	2	yes	—
660	C₈×D₄	C₂²×C₁₃	1	2	yes	—
661	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
662	#433	C₂²×C₁₃	1	2	yes	complemented
663	#431	C₂²×C₁₃	1	1	yes	characteristic
664	#424	C₂²×C₁₃	1	2	yes	complemented
665	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
666	#417	C₂²×C₁₃	1	2	yes	complemented
667	C₂×#103	C₂²×C₁₃	1	2	yes	—
668	C₂×#103	C₂²×C₁₃	1	2	yes	complemented
669	C₂²×C₁₃	—	2	1	no	—
670	C₂²×C₁₃	—	2	1	no	—
671	C₂²×C₁₃	—	2	2	no	—
672	C₂²×C₁₃	—	2	2	no	—
673	C₂²×C₁₃	—	2	2	no	—
674	C₂²×C₁₃	—	2	2	no	—
675	C₂²×C₁₃	—	4	1	no	—
676	C₂²×C₁₃	—	4	1	no	—
677	C₂²×C₁₃	—	4	1	no	—
678	C₂²×C₁₃	—	4	1	no	—
679	C₂²×C₁₃	—	4	1	no	—
680	C₂²×C₁₃	—	4	1	no	—
681	C₂²×C₁₃	—	4	1	no	—
682	C₂²×C₁₃	—	4	1	no	—
683	C₂²×C₁₃	—	8	4	no	—
684	C₂²×C₁₃	#578	1	2	yes	—
685	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
686	C₄×C₁₃	—	2	2	no	—
687	C₄×C₁₃	—	2	1	no	—
688	C₄×C₁₃	—	2	1	no	—
689	C₄×C₁₃	—	2	2	no	—
690	C₄×C₁₃	—	2	1	no	—
691	C₄×C₁₃	—	2	1	no	—
692	C₄×C₁₃	—	2	2	no	—
693	C₄×C₁₃	—	4	2	no	—
694	C₄×C₁₃	—	4	2	no	—
695	C₄×C₁₃	—	4	2	no	—
696	C₄×C₁₃	—	4	1	no	—
697	C₄×C₁₃	—	4	1	no	—
698	C₄×C₁₃	—	4	1	no	—
699	C₄×C₁₃	—	4	1	no	—
700	C₄×C₁₃	—	4	2	no	—
701	C₄×C₁₃	—	4	1	no	—
702	C₄×C₁₃	#577	1	2	yes	—
703	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
704	C₄×C₁₃	#585	1	1	yes	characteristic
705	C₂×#41	—	2	1	no	—
706	C₂×#41	C₂³×C₁₃	1	2	yes	—
707	C₂×#41	C₂³×C₁₃	1	2	yes	—
708	C₂²×Q₈	—	2	1	no	—
709	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
710	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
711	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
712	C₂³×C₄	—	2	1	no	—
713	#137	—	4	4	no	—
714	#135	—	4	4	no	—
715	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
716	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
717	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
718	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
719	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
720	C₂×SD₁₆	—	4	4	no	—
721	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
722	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
723	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
724	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
725	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
726	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
727	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
728	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
729	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
730	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
731	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
732	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
733	C₄⋊Q₈	—	2	2	no	—
734	C₄⋊Q₈	—	2	1	no	—
735	C₄⋊Q₈	—	2	1	no	—
736	C₄⋊Q₈	—	2	1	no	—
737	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
738	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
739	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
740	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
741	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
742	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
743	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
744	#126	—	2	2	no	—
745	#126	—	2	2	no	—
746	#126	—	2	2	no	—
747	#126	—	2	2	no	—
748	#126	—	2	2	no	—
749	#126	—	2	1	no	—
750	#126	D₄×C₁₃	1	2	yes	—
751	#125	—	2	2	no	—
752	#125	—	2	2	no	—
753	#125	—	2	2	no	—
754	#125	—	2	2	no	—
755	#125	—	2	1	no	—
756	#125	—	2	1	no	—
757	#125	D₄×C₁₃	1	1	yes	characteristic
758	#125	C₂³×C₁₃	1	1	yes	characteristic
759	#124	—	2	2	no	—
760	#124	—	2	2	no	—
761	#124	D₄×C₁₃	1	1	yes	characteristic
762	#124	C₂³×C₁₃	1	1	yes	characteristic
763	#124	C₂³×C₁₃	1	2	yes	—
764	#124	C₂³×C₁₃	1	2	yes	—
765	#123	—	2	1	no	—
766	#123	—	2	2	no	—
767	#123	—	2	2	no	—
768	#123	—	2	2	no	—
769	#123	—	2	2	no	—
770	#123	—	2	2	no	—
771	#123	—	2	2	no	—
772	#123	—	2	2	no	—
773	#123	D₄×C₁₃	1	2	yes	—
774	C₂²⋊Q₈	—	2	1	no	—
775	C₂²⋊Q₈	—	2	1	no	—
776	C₂²⋊Q₈	—	2	1	no	—
777	C₂²⋊Q₈	—	2	2	no	—
778	C₂²⋊Q₈	—	2	1	no	—
779	C₂²⋊Q₈	—	2	1	no	—
780	C₂²⋊Q₈	—	2	2	no	—
781	C₂²⋊Q₈	—	2	2	no	—
782	C₂²⋊Q₈	—	2	2	no	—
783	C₂²⋊Q₈	—	2	2	no	—
784	C₂²⋊Q₈	—	2	2	no	—
785	C₂²⋊Q₈	—	2	2	no	—
786	C₂²⋊Q₈	—	2	2	no	—
787	C₂²⋊Q₈	—	2	2	no	—
788	C₂²⋊Q₈	—	2	2	no	—
789	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
790	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
791	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
792	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
793	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
794	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
795	#121	—	2	1	no	—
796	#121	—	2	2	no	—
797	#121	—	2	1	no	—
798	#121	—	2	2	no	—
799	#121	D₄×C₁₃	1	1	yes	characteristic
800	#121	C₂³×C₁₃	1	1	yes	characteristic
801	#121	C₂³×C₁₃	1	2	yes	—
802	#120	—	2	2	no	—
803	C₄×Q₈	—	2	1	no	—
804	C₄×Q₈	—	2	1	no	—
805	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
806	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
807	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
808	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
809	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
810	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
811	C₄×D₄	—	2	2	no	—
812	C₄×D₄	—	2	2	no	—
813	C₄×D₄	—	2	1	no	—
814	C₄×D₄	—	2	1	no	—
815	C₄×D₄	—	2	2	no	—
816	C₄×D₄	—	2	2	no	—
817	C₄×D₄	—	2	2	no	—
818	C₄×D₄	—	2	1	no	—
819	C₄×D₄	—	2	1	no	—
820	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
821	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
822	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
823	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
824	C₄×D₄	C₂³×C₁₃	1	2	yes	—
825	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
826	C₄×D₄	C₂³×C₁₃	1	2	yes	—
827	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
828	#117	—	2	1	no	—
829	#117	—	2	2	no	—
830	#117	—	2	1	no	—
831	#117	—	2	1	no	—
832	#117	—	2	1	no	—
833	#117	C₂³×C₁₃	1	2	yes	—
834	C₂×C₄⋊C₄	—	2	1	no	—
835	C₂×C₄⋊C₄	—	2	1	no	—
836	C₂×C₄⋊C₄	—	2	2	no	—
837	C₂×C₄⋊C₄	—	2	1	no	—
838	C₂×C₄⋊C₄	—	2	1	no	—
839	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
840	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
841	C₂×C₂²⋊C₄	—	2	1	no	—
842	C₂×C₂²⋊C₄	—	2	2	no	—
843	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
844	#107	C₂³×C₁₃	1	1	yes	characteristic
845	#107	C₂³×C₁₃	1	1	yes	characteristic
846	#107	C₂³×C₁₃	1	2	yes	—
847	#106	C₂³×C₁₃	1	1	yes	characteristic
848	#106	C₂³×C₁₃	1	2	yes	—
849	#106	C₂³×C₁₃	1	1	yes	characteristic
850	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
851	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
852	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
853	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
854	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
855	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
856	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
857	#103	C₂³×C₁₃	1	2	yes	—
858	#103	C₂³×C₁₃	1	2	yes	—
859	#103	C₂³×C₁₃	1	2	yes	—
860	#103	C₂³×C₁₃	1	2	yes	—
861	#103	C₂³×C₁₃	1	1	yes	characteristic
862	#103	C₂³×C₁₃	1	2	yes	—
863	#103	C₂³×C₁₃	1	2	yes	—
864	#103	C₂³×C₁₃	1	2	yes	—
865	#103	C₂³×C₁₃	1	2	yes	—
866	#103	C₂³×C₁₃	1	1	yes	characteristic
867	#103	C₂³×C₁₃	1	2	yes	—
868	#103	C₂³×C₁₃	1	2	yes	—
869	#103	C₂³×C₁₃	1	2	yes	—
870	#102	C₂³×C₁₃	1	1	yes	characteristic
871	#102	C₂³×C₁₃	1	2	yes	—
872	#102	C₂³×C₁₃	1	1	yes	characteristic
873	#102	C₂³×C₁₃	1	1	yes	characteristic
874	#102	C₂³×C₁₃	1	1	yes	characteristic
875	#102	C₂³×C₁₃	1	1	yes	characteristic
876	#102	C₂³×C₁₃	1	1	yes	characteristic
877	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
878	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
879	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
880	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
881	#97	C₂³×C₁₃	1	2	yes	—
882	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
883	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
884	C₄×C₈	C₂³×C₁₃	1	2	yes	—
885	C₂×C₁₃	—	2	2	no	—
886	C₂×C₁₃	—	4	2	no	—
887	C₂×C₁₃	—	4	2	no	—
888	C₂×C₁₃	—	8	1	no	—
889	C₂×C₁₃	—	8	1	no	—
890	C₂×C₁₃	#3488	1	1	yes	characteristic
891	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
892	C₂×C₁₃	C₂×#578	1	1	yes	characteristic
893	C₂⁴	—	2	1	no	—
894	#41	—	2	4	no	—
895	#41	—	4	2	no	—
896	#41	—	4	2	no	—
897	#41	—	4	2	no	—
898	#41	—	8	2	no	—
899	C₂×Q₈	—	2	1	no	—
900	C₂×Q₈	—	2	2	no	—
901	C₂×Q₈	—	2	2	no	—
902	C₂×Q₈	—	2	2	no	—
903	C₂×Q₈	—	4	2	no	—
904	C₂×Q₈	—	4	2	no	—
905	C₂×Q₈	—	4	2	no	—
906	C₂×Q₈	—	4	2	no	—
907	C₂×Q₈	—	8	2	no	—
908	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
909	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
910	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
911	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
912	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
913	C₂×D₄	—	2	2	no	—
914	C₂×D₄	—	2	1	no	—
915	C₂×D₄	—	2	2	no	—
916	C₂×D₄	—	2	2	no	—
917	C₂×D₄	—	2	2	no	—
918	C₂×D₄	—	2	1	no	—
919	C₂×D₄	—	4	1	no	—
920	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
921	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
922	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
923	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
924	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
925	C₂²×C₄	—	2	1	no	—
926	C₂²×C₄	—	2	2	no	—
927	C₂²×C₄	—	2	2	no	—
928	C₂²×C₄	—	2	2	no	—
929	C₂²×C₄	—	2	2	no	—
930	C₂²×C₄	—	2	1	no	—
931	C₂²×C₄	—	2	1	no	—
932	C₂²×C₄	—	2	1	no	—
933	C₂²×C₄	—	2	2	no	—
934	C₂²×C₄	—	2	1	no	—
935	C₂²×C₄	—	2	2	no	—
936	C₂²×C₄	—	2	1	no	—
937	C₂²×C₄	—	8	2	no	—
938	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
939	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
940	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
941	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
942	Q₁₆	—	4	2	no	—
943	Q₁₆	—	4	2	no	—
944	Q₁₆	—	4	2	no	—
945	Q₁₆	—	4	2	no	—
946	Q₁₆	—	4	2	no	—
947	SD₁₆	—	2	4	no	—
948	SD₁₆	—	2	4	no	—
949	SD₁₆	—	2	2	no	—
950	SD₁₆	—	4	2	no	—
951	SD₁₆	—	4	2	no	—
952	SD₁₆	—	4	2	no	—
953	SD₁₆	—	4	1	no	—
954	D₈	—	2	2	no	—
955	D₈	—	4	1	no	—
956	M₁₆	—	4	2	no	—
957	C₂×C₈	—	4	2	no	—
958	C₂×C₈	—	4	2	no	—
959	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
960	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
961	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
962	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
963	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
964	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
965	C₄⋊C₄	—	2	1	no	—
966	C₄⋊C₄	—	2	2	no	—
967	C₄⋊C₄	—	2	1	no	—
968	C₄⋊C₄	—	2	1	no	—
969	C₄⋊C₄	—	2	2	no	—
970	C₄⋊C₄	—	2	2	no	—
971	C₄⋊C₄	—	2	2	no	—
972	C₄⋊C₄	—	2	1	no	—
973	C₄⋊C₄	—	2	2	no	—
974	C₄⋊C₄	—	2	2	no	—
975	C₄⋊C₄	—	2	2	no	—
976	C₄⋊C₄	—	2	1	no	—
977	C₄⋊C₄	—	2	1	no	—
978	C₄⋊C₄	—	2	1	no	—
979	C₄⋊C₄	—	2	1	no	—
980	C₄⋊C₄	—	2	1	no	—
981	C₄⋊C₄	—	2	1	no	—
982	C₄⋊C₄	—	2	2	no	—
983	C₄⋊C₄	—	2	2	no	—
984	C₄⋊C₄	—	2	2	no	—
985	C₄⋊C₄	—	2	1	no	—
986	C₄⋊C₄	—	2	2	no	—
987	C₄⋊C₄	—	2	2	no	—
988	C₄⋊C₄	—	2	2	no	—
989	C₄⋊C₄	—	2	2	no	—
990	C₄⋊C₄	—	2	1	no	—
991	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
992	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
993	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
994	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
995	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
996	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
997	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
998	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
999	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1000	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
1001	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
1002	C₂²⋊C₄	—	2	2	no	—
1003	C₂²⋊C₄	—	2	1	no	—
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	—	2	2	no	—
1006	C₂²⋊C₄	—	2	2	no	—
1007	C₂²⋊C₄	—	2	1	no	—
1008	C₂²⋊C₄	—	2	1	no	—
1009	C₂²⋊C₄	—	2	1	no	—
1010	C₂²⋊C₄	—	2	1	no	—
1011	C₂²⋊C₄	—	2	2	no	—
1012	C₂²⋊C₄	—	2	2	no	—
1013	C₂²⋊C₄	—	2	2	no	—
1014	C₂²⋊C₄	—	2	2	no	—
1015	C₂²⋊C₄	—	2	2	no	—
1016	C₂²⋊C₄	—	2	1	no	—
1017	C₂²⋊C₄	—	2	1	no	—
1018	C₂²⋊C₄	—	2	1	no	—
1019	C₂²⋊C₄	—	2	2	no	—
1020	C₂²⋊C₄	—	2	1	no	—
1021	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1022	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1023	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1024	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1025	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1026	C₄²	—	2	2	no	—
1027	C₄²	—	2	2	no	—
1028	C₄²	—	2	1	no	—
1029	C₄²	—	2	2	no	—
1030	C₄²	—	2	2	no	—
1031	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
1032	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
1033	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
1034	C₄²	C₂⁴×C₁₃	1	2	yes	—
1035	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
1036	C₁₃	#62054	1	1	yes	characteristic, direct product factor, Sylow
1037	C₂³	—	2	1	no	—
1038	C₂³	—	2	1	no	—
1039	C₂³	—	2	1	no	—
1040	C₂³	—	4	2	no	—
1041	C₂³	—	4	2	no	—
1042	C₂³	—	8	1	no	—
1043	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
1044	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
1045	Q₈	—	2	2	no	—
1046	Q₈	—	2	2	no	—
1047	Q₈	—	2	2	no	—
1048	Q₈	—	2	1	no	—
1049	Q₈	—	2	2	no	—
1050	Q₈	—	2	1	no	—
1051	Q₈	—	2	2	no	—
1052	Q₈	—	2	2	no	—
1053	Q₈	—	2	2	no	—
1054	Q₈	—	4	2	no	—
1055	Q₈	—	8	2	no	—
1056	Q₈	—	8	2	no	—
1057	Q₈	—	8	2	no	—
1058	D₄	—	2	4	no	—
1059	D₄	—	2	2	no	—
1060	D₄	—	2	1	no	—
1061	D₄	—	2	1	no	—
1062	D₄	—	2	1	no	—
1063	D₄	—	2	1	no	—
1064	D₄	—	2	1	no	—
1065	D₄	—	4	2	no	—
1066	D₄	—	4	4	no	—
1067	D₄	—	4	2	no	—
1068	D₄	—	8	2	no	—
1069	D₄	—	8	2	no	—
1070	D₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
1071	C₂×C₄	—	2	2	no	—
1072	C₂×C₄	—	2	2	no	—
1073	C₂×C₄	—	2	1	no	—
1074	C₂×C₄	—	2	2	no	—
1075	C₂×C₄	—	2	1	no	—
1076	C₂×C₄	—	2	2	no	—
1077	C₂×C₄	—	2	1	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	2	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	1	no	—
1082	C₂×C₄	—	2	2	no	—
1083	C₂×C₄	—	2	2	no	—
1084	C₂×C₄	—	2	2	no	—
1085	C₂×C₄	—	2	1	no	—
1086	C₂×C₄	—	4	4	no	—
1087	C₂×C₄	—	4	2	no	—
1088	C₂×C₄	—	4	2	no	—
1089	C₂×C₄	—	4	2	no	—
1090	C₂×C₄	—	8	1	no	—
1091	C₂×C₄	—	8	1	no	—
1092	C₂×C₄	—	8	2	no	—
1093	C₂×C₄	—	8	2	no	—
1094	C₂×C₄	—	8	1	no	—
1095	C₂×C₄	—	8	2	no	—
1096	C₂×C₄	—	8	2	no	—
1097	C₂×C₄	—	8	2	no	—
1098	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1099	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1100	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1101	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1102	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1103	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1104	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1105	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1106	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
1107	C₈	—	2	1	no	—
1108	C₈	—	2	2	no	—
1109	C₈	—	2	2	no	—
1110	C₈	—	2	1	no	—
1111	C₈	—	2	1	no	—
1112	C₈	—	2	1	no	—
1113	C₂²	—	2	1	no	—
1114	C₂²	—	2	1	no	—
1115	C₂²	—	2	2	no	—
1116	C₂²	—	2	2	no	—
1117	C₂²	—	2	2	no	—
1118	C₂²	—	2	2	no	—
1119	C₂²	—	4	1	no	—
1120	C₂²	—	4	1	no	—
1121	C₂²	—	4	1	no	—
1122	C₂²	—	4	1	no	—
1123	C₂²	—	4	1	no	—
1124	C₂²	—	4	1	no	—
1125	C₂²	—	4	1	no	—
1126	C₂²	—	4	1	no	—
1127	C₂²	—	8	4	no	—
1128	C₂²	C₁₃×#578	1	2	yes	—
1129	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
1130	C₄	—	2	1	no	—
1131	C₄	—	2	2	no	—
1132	C₄	—	2	1	no	—
1133	C₄	—	2	1	no	—
1134	C₄	—	2	2	no	—
1135	C₄	—	2	2	no	—
1136	C₄	—	2	1	no	—
1137	C₄	—	4	1	no	—
1138	C₄	—	4	1	no	—
1139	C₄	—	4	1	no	—
1140	C₄	—	4	2	no	—
1141	C₄	—	4	1	no	—
1142	C₄	—	4	2	no	—
1143	C₄	—	4	2	no	—
1144	C₄	—	4	2	no	—
1145	C₄	—	4	1	no	—
1146	C₄	C₁₃×#577	1	2	yes	—
1147	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
1148	C₄	C₁₃×#585	1	1	yes	characteristic
1149	C₂	—	2	2	no	—
1150	C₂	—	4	2	no	—
1151	C₂	—	4	2	no	—
1152	C₂	—	8	1	no	—
1153	C₂	—	8	1	no	—
1154	C₂	C₁₃×#3488	1	1	yes	characteristic
1155	C₂	C₂×C₁₃×#577	1	1	yes	characteristic
1156	C₂	C₂×C₁₃×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₁₃×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3552	C₂	semidirect
2. C₁₃×#3520	C₂	semidirect
3. C₁₃×#3398	C₂	semidirect
4. C₁₃×#3393	C₂	semidirect
5. C₁₃×#3367	C₂	semidirect
6. C₁₃×#3359	C₂	semidirect
7. C₁₃×#3330	C₂	semidirect
8. C₁₃×#3316	C₂	semidirect
9. C₁₃×#3299	C₂	semidirect
10. C₁₃×#3298	C₂	semidirect
11. C₁₃×#3283	C₂	semidirect
12. C₁₃×#3282	C₂	semidirect
13. C₁₃×#3276	C₂	semidirect
14. C₁₃×#3266	C₂	semidirect
15. C₁₃×#3258	C₂	semidirect
16. C₁₃×#3248	C₂	semidirect
17. C₁₃×#3225	C₂	semidirect
18. C₁₃×#3209	C₂	semidirect
19. C₁₃×#3120	C₂	semidirect
20. C₁₃×#3105	C₂	semidirect
21. C₁₃×#3046	C₂	semidirect
22. C₂×C₁₃×#461	C₂	semidirect
23. C₁₃×#2994	C₂	semidirect
28. C₁₃×#557	C₂²	semidirect
30. C₁₃×#556	C₂²	semidirect
38. D₄×Q₈×C₁₃	C₂²	semidirect
43. C₁₃×#547	C₂²	semidirect
48. C₁₃×#541	C₂²	semidirect
51. C₁₃×#536	C₂²	semidirect
62. C₁₃×#494	C₂²	semidirect
63. C₁₃×#494	C₂²	semidirect
64. C₁₃×#489	C₂²	semidirect
65. C₁₃×#487	C₂²	semidirect
66. C₁₃×#487	C₂²	semidirect
67. C₁₃×#487	C₂²	semidirect
69. C₁₃×#484	C₂²	semidirect
70. C₁₃×#483	C₂²	semidirect
72. C₁₃×#479	C₂²	semidirect
75. C₁₃×#477	C₂²	semidirect
76. C₁₃×#475	C₂²	semidirect
77. C₁₃×#475	C₂²	semidirect
78. C₁₃×#474	C₂²	semidirect
79. C₁₃×#470	C₂²	semidirect
82. C₁₃×#467	C₂²	semidirect
87. C₁₃×#464	C₂²	semidirect
88. C₁₃×#464	C₂²	semidirect
92. C₁₃×#462	C₂²	semidirect
93. C₁₃×#462	C₂²	semidirect
94. C₁₃×#462	C₂²	semidirect
95. C₁₃×#462	C₂²	semidirect
103. C₁₃×#461	C₂²	semidirect
106. C₁₃×#452	C₂²	semidirect
109. C₁₃×#451	C₂²	semidirect
114. C₁₃×#446	C₂²	semidirect
115. C₈×Q₈×C₁₃	C₂²	semidirect
116. C₁₃×#441	C₂²	semidirect
118. C₄×C₁₃×Q₁₆	C₂²	semidirect
124. C₁₃×#436	C₂²	semidirect
127. C₈×D₄×C₁₃	C₂²	semidirect
128. C₁₃×#433	C₂²	semidirect
130. C₁₃×#424	C₂²	semidirect
132. C₁₃×#417	C₂²	semidirect
134. C₂×C₁₃×#103	C₂²	semidirect
315. #62054	C₁₃	direct (N × H)
459. #3552	C₂×C₁₃	semidirect
460. #3520	C₂×C₁₃	semidirect
461. #3398	C₂×C₁₃	semidirect
462. #3393	C₂×C₁₃	semidirect
463. #3367	C₂×C₁₃	semidirect
464. #3359	C₂×C₁₃	semidirect
465. #3330	C₂×C₁₃	semidirect
466. #3316	C₂×C₁₃	semidirect
467. #3299	C₂×C₁₃	semidirect
468. #3298	C₂×C₁₃	semidirect
469. #3283	C₂×C₁₃	semidirect
470. #3282	C₂×C₁₃	semidirect
471. #3276	C₂×C₁₃	semidirect
472. #3266	C₂×C₁₃	semidirect
473. #3258	C₂×C₁₃	semidirect
474. #3248	C₂×C₁₃	semidirect
475. #3225	C₂×C₁₃	semidirect
476. #3209	C₂×C₁₃	semidirect
477. #3120	C₂×C₁₃	semidirect
478. #3105	C₂×C₁₃	semidirect
479. #3046	C₂×C₁₃	semidirect
480. C₂×#461	C₂×C₁₃	semidirect
481. #2994	C₂×C₁₃	semidirect
562. #557	C₂²×C₁₃	semidirect
564. #556	C₂²×C₁₃	semidirect
572. D₄×Q₈	C₂²×C₁₃	semidirect
577. #547	C₂²×C₁₃	semidirect
582. #541	C₂²×C₁₃	semidirect
585. #536	C₂²×C₁₃	semidirect
596. #494	C₂²×C₁₃	semidirect
597. #494	C₂²×C₁₃	semidirect
598. #489	C₂²×C₁₃	semidirect
599. #487	C₂²×C₁₃	semidirect
600. #487	C₂²×C₁₃	semidirect
601. #487	C₂²×C₁₃	semidirect
603. #484	C₂²×C₁₃	semidirect
604. #483	C₂²×C₁₃	semidirect
606. #479	C₂²×C₁₃	semidirect
609. #477	C₂²×C₁₃	semidirect
610. #475	C₂²×C₁₃	semidirect
611. #475	C₂²×C₁₃	semidirect
612. #474	C₂²×C₁₃	semidirect
613. #470	C₂²×C₁₃	semidirect
616. #467	C₂²×C₁₃	semidirect
621. #464	C₂²×C₁₃	semidirect
622. #464	C₂²×C₁₃	semidirect
626. #462	C₂²×C₁₃	semidirect
627. #462	C₂²×C₁₃	semidirect
628. #462	C₂²×C₁₃	semidirect
629. #462	C₂²×C₁₃	semidirect
637. #461	C₂²×C₁₃	semidirect
640. #452	C₂²×C₁₃	semidirect
643. #451	C₂²×C₁₃	semidirect
648. #446	C₂²×C₁₃	semidirect
649. C₈×Q₈	C₂²×C₁₃	semidirect
650. #441	C₂²×C₁₃	semidirect
652. C₄×Q₁₆	C₂²×C₁₃	semidirect
658. #436	C₂²×C₁₃	semidirect
661. C₈×D₄	C₂²×C₁₃	semidirect
662. #433	C₂²×C₁₃	semidirect
664. #424	C₂²×C₁₃	semidirect
666. #417	C₂²×C₁₃	semidirect
668. C₂×#103	C₂²×C₁₃	semidirect
1036. C₁₃	#62054	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#3552	2
C₁₃×#3520	2
C₁₃×#3398	2
C₁₃×#3393	2
C₁₃×#3367	2
C₁₃×#3359	2
C₁₃×#3330	2
C₁₃×#3316	2
C₁₃×#3299	2
C₁₃×#3298	2
C₁₃×#3283	2
C₁₃×#3282	2
C₁₃×#3276	2
C₁₃×#3266	2
C₁₃×#3258	2
C₁₃×#3248	2
C₁₃×#3225	2
C₁₃×#3209	2
C₁₃×#3120	2
C₁₃×#3105	2
C₁₃×#3046	2
C₂×C₁₃×#461	2
C₁₃×#2994	2
#62054	13

Subgroups — C13×#62054 #15748393

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62054 #15748393