Subgroups — #15829928

Order 3328.

1010 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13123961	C₂	1	1	yes	maximal, characteristic, complemented
2	#13123480	C₂	1	1	yes	maximal, characteristic, complemented
3	#13113305	C₂	1	1	yes	maximal, characteristic, complemented
4	#13113301	C₂	1	1	yes	maximal, characteristic, complemented
5	#13113296	C₂	1	1	yes	maximal, characteristic, complemented
6	#13113279	C₂	1	1	yes	maximal, characteristic, complemented
7	#13113270	C₂	1	1	yes	maximal, characteristic, complemented
8	#13113261	C₂	1	1	yes	maximal, characteristic, complemented
9	#13113249	C₂	1	1	yes	maximal, characteristic, complemented
10	#13113244	C₂	1	1	yes	maximal, characteristic, complemented
11	#13113235	C₂	1	1	yes	maximal, characteristic, complemented
12	#13113227	C₂	1	1	yes	maximal, characteristic, complemented
13	#13113223	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×D₄⋊#1055	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3481	C₂	1	1	yes	maximal, characteristic
16	C₁₃×#559	C₄	1	1	yes	characteristic
17	C₁₃×#554	C₄	1	1	yes	characteristic
18	C₁₃×#554	C₄	1	1	yes	characteristic
19	C₁₃×#553	—	2	1	no	—
20	C₁₃×#553	C₄	1	1	yes	characteristic
21	C₁₃×#553	C₄	1	1	yes	characteristic
22	C₁₃×#551	—	2	1	no	—
23	C₁₃×#551	—	2	1	no	—
24	C₁₃×#546	—	2	1	no	—
25	C₁₃×#546	C₄	1	1	yes	characteristic
26	C₁₃×#546	C₄	1	1	yes	characteristic
27	D₄²×C₁₃	C₄	1	1	yes	characteristic
28	C₁₃×#532	C₂²	1	1	yes	characteristic
29	C₁₃×#529	—	2	1	no	—
30	C₁₃×#529	C₂²	1	1	yes	characteristic
31	C₁₃×#529	C₂²	1	1	yes	characteristic
32	C₁₃×#525	—	2	1	no	—
33	C₁₃×#525	—	2	1	no	—
34	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
35	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
36	C₂×C₄×D₄×C₁₃	—	2	1	no	—
37	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
39	#11718895	—	2	1	no	—
40	#11718685	—	2	1	no	—
41	#11718672	—	2	1	no	—
42	#11718672	—	2	1	no	—
43	D₄×#1055	—	2	1	no	—
44	#11718661	—	2	1	no	—
45	#11718661	—	2	1	no	—
46	#11718660	—	2	1	no	—
47	#11718587	C₂²	1	1	yes	characteristic, complemented
48	#11718587	C₂²	1	1	yes	characteristic, complemented
49	#11718586	C₂²	1	1	yes	characteristic, complemented
50	#11718586	C₂²	1	1	yes	characteristic, complemented
51	#11718586	C₂²	1	1	yes	characteristic, complemented
52	#11718586	C₂²	1	1	yes	characteristic, complemented
53	#11718586	C₂²	1	1	yes	characteristic, complemented
54	#11718585	C₂²	1	1	yes	characteristic, complemented
55	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic, complemented
56	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic, complemented
57	C₄×#6099	C₂²	1	1	yes	characteristic, complemented
58	C₂×C₄×#1055	C₂²	1	1	yes	characteristic, complemented
59	Q₈⋊#1055	C₂²	1	1	yes	characteristic, complemented
60	Q₈⋊#1055	C₂²	1	1	yes	characteristic, complemented
61	Q₈⋊#1055	C₂²	1	1	yes	characteristic, complemented
62	Q₈⋊#1055	C₂²	1	1	yes	characteristic, complemented
63	D₄⋊#1055	C₂²	1	1	yes	characteristic
64	D₄⋊#1055	C₂²	1	1	yes	characteristic
65	D₄⋊#1055	C₂²	1	1	yes	characteristic
66	D₄⋊#1055	C₂²	1	1	yes	characteristic
67	D₄⋊#1055	C₂²	1	1	yes	characteristic, complemented
68	D₄⋊#1055	C₂²	1	1	yes	characteristic, complemented
69	D₄⋊#1055	C₂²	1	1	yes	characteristic, complemented
70	D₄⋊#1055	C₂²	1	1	yes	characteristic, complemented
71	D₄⋊#1055	C₂²	1	1	yes	characteristic, complemented
72	D₄⋊#1055	C₂²	1	1	yes	characteristic, complemented
73	D₄⋊#1055	C₂²	1	1	yes	characteristic, complemented
74	D₄⋊#1055	C₂²	1	1	yes	characteristic, complemented
75	C₂×C₁₃×#41	—	2	1	no	—
76	C₂×C₁₃×#41	C₂×C₄	1	1	yes	characteristic
77	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
78	C₂²×D₄×C₁₃	—	2	1	no	—
79	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
80	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
81	C₂³×C₄×C₁₃	—	2	1	no	—
82	C₂³×C₄×C₁₃	—	2	1	no	—
83	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
84	C₁₃×#127	C₂×C₄	1	1	yes	characteristic
85	C₁₃×#126	—	2	1	no	—
86	C₁₃×#126	—	2	1	no	—
87	C₁₃×#126	—	2	1	no	—
88	C₁₃×#126	—	2	1	no	—
89	C₁₃×#125	—	2	1	no	—
90	C₁₃×#125	C₂×C₄	1	1	yes	characteristic
91	C₁₃×#125	C₂×C₄	1	1	yes	characteristic
92	C₁₃×#124	—	2	1	no	—
93	C₁₃×#124	—	2	1	no	—
94	C₁₃×#124	C₂×C₄	1	1	yes	characteristic
95	C₁₃×#124	C₂×C₄	1	1	yes	characteristic
96	C₁₃×#123	—	2	1	no	—
97	C₁₃×#123	—	2	1	no	—
98	C₁₃×#123	—	2	1	no	—
99	C₁₃×#123	—	2	1	no	—
100	C₁₃×#123	—	2	1	no	—
101	C₁₃×#123	—	2	1	no	—
102	C₁₃×#123	—	2	1	no	—
103	C₁₃×#123	—	2	1	no	—
104	C₁₃×C₂²⋊Q₈	—	2	1	no	—
105	C₁₃×C₂²⋊Q₈	—	2	1	no	—
106	C₁₃×C₂²⋊Q₈	—	2	1	no	—
107	C₁₃×C₂²⋊Q₈	—	2	1	no	—
108	C₁₃×C₂²⋊Q₈	—	2	1	no	—
109	C₁₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
110	C₁₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
111	C₁₃×#121	—	2	1	no	—
112	C₁₃×#121	—	2	1	no	—
113	C₁₃×#121	—	2	1	no	—
114	C₁₃×#121	—	2	1	no	—
115	C₁₃×#121	—	2	1	no	—
116	C₁₃×#121	—	2	1	no	—
117	C₁₃×#121	C₂×C₄	1	1	yes	characteristic
118	C₁₃×#121	C₂×C₄	1	1	yes	characteristic
119	C₁₃×#121	C₂×C₄	1	1	yes	characteristic
120	C₁₃×#121	C₂×C₄	1	1	yes	characteristic
121	C₁₃×#120	—	2	1	no	—
122	C₁₃×#120	—	2	1	no	—
123	C₁₃×#120	—	2	1	no	—
124	C₁₃×#120	—	2	1	no	—
125	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
126	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
127	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
128	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
129	C₄×D₄×C₁₃	—	2	1	no	—
130	C₄×D₄×C₁₃	—	2	1	no	—
131	C₄×D₄×C₁₃	—	2	1	no	—
132	C₄×D₄×C₁₃	—	2	1	no	—
133	C₄×D₄×C₁₃	—	2	1	no	—
134	C₄×D₄×C₁₃	—	2	1	no	—
135	C₄×D₄×C₁₃	—	2	1	no	—
136	C₄×D₄×C₁₃	—	2	1	no	—
137	C₄×D₄×C₁₃	—	2	1	no	—
138	C₄×D₄×C₁₃	—	2	1	no	—
139	C₄×D₄×C₁₃	—	2	1	no	—
140	C₄×D₄×C₁₃	—	2	1	no	—
141	C₄×D₄×C₁₃	—	2	1	no	—
142	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
143	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
144	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
145	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
146	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
147	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
148	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
149	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
150	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
151	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
152	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
153	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
154	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
155	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
156	C₁₃×#117	—	2	1	no	—
157	C₁₃×#117	—	2	1	no	—
158	C₁₃×#117	—	2	1	no	—
159	C₁₃×#117	C₂×C₄	1	1	yes	characteristic
160	C₁₃×#117	D₄	1	1	yes	characteristic
161	C₁₃×#117	D₄	1	1	yes	characteristic
162	C₁₃×#117	D₄	1	1	yes	characteristic
163	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
164	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
165	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
166	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
167	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
168	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
169	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
170	C₂×C₄²×C₁₃	—	2	1	no	—
171	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
172	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
173	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
174	C₂×#6099	—	2	1	no	—
175	C₂×#6099	—	2	1	no	—
176	C₂²×#1055	—	2	1	no	—
177	C₂²×#1055	—	2	1	no	—
178	C₂²×#1055	—	2	1	no	—
179	C₂²⋊#1055	—	2	1	no	—
180	C₂²⋊#1055	—	2	1	no	—
181	C₂²⋊#1055	—	2	1	no	—
182	C₂²⋊#1055	—	2	1	no	—
183	C₂²⋊#1055	—	2	1	no	—
184	C₂²⋊#1055	—	2	1	no	—
185	C₂²⋊#1055	—	2	1	no	—
186	C₄⋊#1055	—	2	1	no	—
187	C₄⋊#1055	—	2	1	no	—
188	C₄⋊#1055	—	2	1	no	—
189	C₄⋊#1055	—	2	1	no	—
190	C₄⋊#1055	—	2	1	no	—
191	C₄⋊#1055	—	2	1	no	—
192	C₄⋊#1055	—	2	1	no	—
193	C₄⋊#1055	C₂³	1	1	yes	characteristic
194	C₄⋊#1055	C₂³	1	1	yes	characteristic
195	C₄⋊#1055	C₂³	1	1	yes	characteristic
196	C₄⋊#1055	C₂³	1	1	yes	characteristic
197	#88043	—	2	1	no	—
198	#88043	—	2	1	no	—
199	#88043	—	2	1	no	—
200	C₄×#1055	—	2	1	no	—
201	C₄×#1055	—	2	1	no	—
202	C₄×#1055	C₂³	1	1	yes	characteristic
203	C₄×#1055	C₂³	1	1	yes	characteristic
204	C₄×#1055	C₂³	1	1	yes	characteristic
205	C₄×#1055	C₂³	1	1	yes	characteristic
206	#17521	—	13	1	no	maximal, Sylow
207	C₂⁴×C₁₃	—	2	1	no	—
208	C₂⁴×C₁₃	—	2	1	no	—
209	C₁₃×#41	—	2	2	no	—
210	C₁₃×#41	—	4	2	no	—
211	C₁₃×#41	—	4	1	no	—
212	C₁₃×#41	—	8	1	no	—
213	C₁₃×#41	—	8	1	no	—
214	C₂×Q₈×C₁₃	—	2	1	no	—
215	C₂×Q₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
216	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
217	C₂×D₄×C₁₃	—	2	2	no	—
218	C₂×D₄×C₁₃	—	2	2	no	—
219	C₂×D₄×C₁₃	—	2	1	no	—
220	C₂×D₄×C₁₃	—	2	1	no	—
221	C₂×D₄×C₁₃	—	2	1	no	—
222	C₂×D₄×C₁₃	—	2	1	no	—
223	C₂×D₄×C₁₃	—	2	1	no	—
224	C₂×D₄×C₁₃	—	2	1	no	—
225	C₂×D₄×C₁₃	—	2	1	no	—
226	C₂×D₄×C₁₃	—	2	1	no	—
227	C₂×D₄×C₁₃	—	2	1	no	—
228	C₂×D₄×C₁₃	—	4	1	no	—
229	C₂×D₄×C₁₃	—	4	1	no	—
230	C₂×D₄×C₁₃	—	4	4	no	—
231	C₂×D₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
232	C₂×D₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
233	C₂×D₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
234	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
235	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
236	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
237	C₂²×C₄×C₁₃	—	2	1	no	—
238	C₂²×C₄×C₁₃	—	2	1	no	—
239	C₂²×C₄×C₁₃	—	2	1	no	—
240	C₂²×C₄×C₁₃	—	2	1	no	—
241	C₂²×C₄×C₁₃	—	2	1	no	—
242	C₂²×C₄×C₁₃	—	2	1	no	—
243	C₂²×C₄×C₁₃	—	2	1	no	—
244	C₂²×C₄×C₁₃	—	2	1	no	—
245	C₂²×C₄×C₁₃	—	2	1	no	—
246	C₂²×C₄×C₁₃	—	2	1	no	—
247	C₂²×C₄×C₁₃	—	2	1	no	—
248	C₂²×C₄×C₁₃	—	8	1	no	—
249	C₂²×C₄×C₁₃	—	8	1	no	—
250	C₂²×C₄×C₁₃	—	8	1	no	—
251	C₂²×C₄×C₁₃	—	8	1	no	—
252	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
253	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
254	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
255	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
256	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
257	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
258	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
259	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
260	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
261	C₁₃×C₄⋊C₄	—	2	1	no	—
262	C₁₃×C₄⋊C₄	—	2	1	no	—
263	C₁₃×C₄⋊C₄	—	2	1	no	—
264	C₁₃×C₄⋊C₄	—	2	1	no	—
265	C₁₃×C₄⋊C₄	—	2	1	no	—
266	C₁₃×C₄⋊C₄	—	2	1	no	—
267	C₁₃×C₄⋊C₄	—	2	1	no	—
268	C₁₃×C₄⋊C₄	—	2	1	no	—
269	C₁₃×C₄⋊C₄	—	2	1	no	—
270	C₁₃×C₄⋊C₄	—	2	1	no	—
271	C₁₃×C₄⋊C₄	—	2	1	no	—
272	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
273	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
274	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
275	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
276	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
277	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
278	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
279	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
280	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
281	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
282	C₁₃×C₂²⋊C₄	—	2	1	no	—
283	C₁₃×C₂²⋊C₄	—	2	1	no	—
284	C₁₃×C₂²⋊C₄	—	2	1	no	—
285	C₁₃×C₂²⋊C₄	—	2	1	no	—
286	C₁₃×C₂²⋊C₄	—	2	1	no	—
287	C₁₃×C₂²⋊C₄	—	2	1	no	—
288	C₁₃×C₂²⋊C₄	—	2	1	no	—
289	C₁₃×C₂²⋊C₄	—	2	1	no	—
290	C₁₃×C₂²⋊C₄	—	2	1	no	—
291	C₁₃×C₂²⋊C₄	—	2	1	no	—
292	C₁₃×C₂²⋊C₄	—	2	1	no	—
293	C₁₃×C₂²⋊C₄	—	2	1	no	—
294	C₁₃×C₂²⋊C₄	—	2	1	no	—
295	C₁₃×C₂²⋊C₄	—	2	1	no	—
296	C₁₃×C₂²⋊C₄	—	2	1	no	—
297	C₁₃×C₂²⋊C₄	—	2	1	no	—
298	C₁₃×C₂²⋊C₄	—	2	1	no	—
299	C₁₃×C₂²⋊C₄	—	2	1	no	—
300	C₁₃×C₂²⋊C₄	—	2	1	no	—
301	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
302	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
303	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
304	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
305	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
306	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
307	C₄²×C₁₃	—	2	1	no	—
308	C₄²×C₁₃	—	2	1	no	—
309	C₄²×C₁₃	—	2	1	no	—
310	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
311	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
312	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
313	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
314	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
315	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
316	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
317	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
318	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
319	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
320	#6099	—	4	2	no	—
321	#6099	—	8	1	no	—
322	C₂×#1055	—	2	1	no	—
323	C₂×#1055	—	2	1	no	—
324	C₂×#1055	—	2	1	no	—
325	C₂×#1055	—	2	1	no	—
326	C₂×#1055	—	2	1	no	—
327	C₂×#1055	—	2	1	no	—
328	C₂×#1055	—	2	1	no	—
329	C₂×#1055	—	2	1	no	—
330	C₂×#1055	—	4	2	no	—
331	C₂×#1055	—	8	1	no	—
332	C₂×#1055	—	8	1	no	—
333	#3481	D₁₃	1	1	yes	characteristic
334	#2990	—	13	1	no	—
335	#2922	—	13	1	no	—
336	#1496	—	13	1	no	—
337	#1495	—	13	1	no	—
338	#1494	—	13	1	no	—
339	#1490	—	13	1	no	—
340	#1488	—	13	1	no	—
341	#1486	—	13	1	no	—
342	#1483	—	13	1	no	—
343	#1482	—	13	1	no	—
344	#1480	—	13	1	no	—
345	#1478	—	13	1	no	—
346	#1477	—	13	1	no	—
347	C₂×D₄⋊C₈	—	13	1	no	—
348	C₂³×C₁₃	—	2	1	no	—
349	C₂³×C₁₃	—	2	1	no	—
350	C₂³×C₁₃	—	2	1	no	—
351	C₂³×C₁₃	—	4	2	no	—
352	C₂³×C₁₃	—	4	2	no	—
353	C₂³×C₁₃	—	4	2	no	—
354	C₂³×C₁₃	—	4	2	no	—
355	C₂³×C₁₃	—	8	1	no	—
356	C₂³×C₁₃	—	8	1	no	—
357	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
358	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
359	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
360	Q₈×C₁₃	—	2	1	no	—
361	Q₈×C₁₃	—	2	1	no	—
362	Q₈×C₁₃	—	4	1	no	—
363	Q₈×C₁₃	—	8	1	no	—
364	D₄×C₁₃	—	2	2	no	—
365	D₄×C₁₃	—	2	2	no	—
366	D₄×C₁₃	—	2	1	no	—
367	D₄×C₁₃	—	2	1	no	—
368	D₄×C₁₃	—	2	1	no	—
369	D₄×C₁₃	—	2	1	no	—
370	D₄×C₁₃	—	2	1	no	—
371	D₄×C₁₃	—	4	1	no	—
372	D₄×C₁₃	—	4	2	no	—
373	D₄×C₁₃	—	4	2	no	—
374	D₄×C₁₃	—	4	2	no	—
375	D₄×C₁₃	—	4	2	no	—
376	D₄×C₁₃	—	4	2	no	—
377	D₄×C₁₃	—	4	2	no	—
378	D₄×C₁₃	—	8	1	no	—
379	D₄×C₁₃	—	8	1	no	—
380	D₄×C₁₃	—	8	1	no	—
381	D₄×C₁₃	#131	1	2	yes	—
382	C₂×C₄×C₁₃	—	2	2	no	—
383	C₂×C₄×C₁₃	—	2	1	no	—
384	C₂×C₄×C₁₃	—	2	1	no	—
385	C₂×C₄×C₁₃	—	2	1	no	—
386	C₂×C₄×C₁₃	—	2	1	no	—
387	C₂×C₄×C₁₃	—	2	1	no	—
388	C₂×C₄×C₁₃	—	2	1	no	—
389	C₂×C₄×C₁₃	—	2	1	no	—
390	C₂×C₄×C₁₃	—	2	1	no	—
391	C₂×C₄×C₁₃	—	2	1	no	—
392	C₂×C₄×C₁₃	—	2	1	no	—
393	C₂×C₄×C₁₃	—	2	1	no	—
394	C₂×C₄×C₁₃	—	2	1	no	—
395	C₂×C₄×C₁₃	—	2	1	no	—
396	C₂×C₄×C₁₃	—	2	1	no	—
397	C₂×C₄×C₁₃	—	2	1	no	—
398	C₂×C₄×C₁₃	—	2	1	no	—
399	C₂×C₄×C₁₃	—	2	1	no	—
400	C₂×C₄×C₁₃	—	4	1	no	—
401	C₂×C₄×C₁₃	—	4	1	no	—
402	C₂×C₄×C₁₃	—	4	2	no	—
403	C₂×C₄×C₁₃	—	4	2	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	1	no	—
409	C₂×C₄×C₁₃	—	4	1	no	—
410	C₂×C₄×C₁₃	—	8	1	no	—
411	C₂×C₄×C₁₃	—	8	1	no	—
412	C₂×C₄×C₁₃	—	8	1	no	—
413	C₂×C₄×C₁₃	—	8	1	no	—
414	C₂×C₄×C₁₃	—	8	1	no	—
415	C₂×C₄×C₁₃	—	8	1	no	—
416	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
417	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
418	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
419	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
420	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
421	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
422	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
423	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
424	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
425	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
426	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
427	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
428	#1055	—	4	1	no	—
429	#1055	—	4	1	no	—
430	#1055	—	4	1	no	—
431	#1055	—	4	1	no	—
432	#1055	—	4	1	no	—
433	#1055	—	4	1	no	—
434	#1055	—	4	1	no	—
435	#1055	—	4	1	no	—
436	#559	Dic₁₃	1	1	yes	characteristic
437	#554	Dic₁₃	1	1	yes	characteristic
438	#554	Dic₁₃	1	1	yes	characteristic
439	#553	—	2	1	no	—
440	#553	Dic₁₃	1	1	yes	characteristic
441	#553	Dic₁₃	1	1	yes	characteristic
442	#551	—	2	1	no	—
443	#551	—	2	1	no	—
444	#546	—	2	1	no	—
445	#546	Dic₁₃	1	1	yes	characteristic
446	#546	Dic₁₃	1	1	yes	characteristic
447	D₄²	Dic₁₃	1	1	yes	characteristic
448	#532	C₂×D₁₃	1	1	yes	characteristic
449	#529	—	2	1	no	—
450	#529	C₂×D₁₃	1	1	yes	characteristic
451	#529	C₂×D₁₃	1	1	yes	characteristic
452	#525	—	2	1	no	—
453	#525	—	2	1	no	—
454	C₄×#41	C₂×D₁₃	1	1	yes	characteristic
455	C₄×#41	C₂×D₁₃	1	1	yes	characteristic
456	C₂×C₄×D₄	—	2	1	no	—
457	C₂×C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
458	C₂×C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
459	#446	—	26	1	no	—
460	#435	—	26	1	no	—
461	#435	—	26	1	no	—
462	C₈×D₄	—	26	1	no	—
463	#433	—	26	1	no	—
464	#433	—	26	1	no	—
465	#432	—	13	1	no	—
466	#432	—	13	1	no	—
467	#431	—	13	1	no	—
468	#431	—	13	1	no	—
469	#431	—	13	1	no	—
470	#431	—	13	1	no	—
471	#431	—	13	1	no	—
472	#424	—	26	1	no	—
473	#423	—	13	1	no	—
474	C₂×C₄⋊C₈	—	13	1	no	—
475	C₂×C₄⋊C₈	—	13	1	no	—
476	#408	—	26	1	no	—
477	C₄×M₁₆	—	13	1	no	—
478	C₂×C₄×C₈	—	13	1	no	—
479	Q₈⋊C₈	—	13	1	no	—
480	Q₈⋊C₈	—	13	1	no	—
481	Q₈⋊C₈	—	13	1	no	—
482	Q₈⋊C₈	—	13	1	no	—
483	D₄⋊C₈	—	13	1	no	—
484	D₄⋊C₈	—	13	1	no	—
485	D₄⋊C₈	—	13	1	no	—
486	D₄⋊C₈	—	13	1	no	—
487	D₄⋊C₈	—	13	1	no	—
488	D₄⋊C₈	—	13	1	no	—
489	D₄⋊C₈	—	13	1	no	—
490	D₄⋊C₈	—	13	1	no	—
491	D₄⋊C₈	—	13	1	no	—
492	D₄⋊C₈	—	13	1	no	—
493	D₄⋊C₈	—	13	1	no	—
494	D₄⋊C₈	—	13	1	no	—
495	C₂²×C₁₃	—	2	1	no	—
496	C₂²×C₁₃	—	2	1	no	—
497	C₂²×C₁₃	—	2	1	no	—
498	C₂²×C₁₃	—	2	1	no	—
499	C₂²×C₁₃	—	2	2	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	—	4	1	no	—
505	C₂²×C₁₃	—	4	1	no	—
506	C₂²×C₁₃	—	4	1	no	—
507	C₂²×C₁₃	—	4	1	no	—
508	C₂²×C₁₃	—	4	1	no	—
509	C₂²×C₁₃	—	4	1	no	—
510	C₂²×C₁₃	—	4	1	no	—
511	C₂²×C₁₃	—	4	1	no	—
512	C₂²×C₁₃	—	8	4	no	—
513	C₂²×C₁₃	—	8	4	no	—
514	C₂²×C₁₃	#421	1	2	yes	—
515	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
516	C₄×C₁₃	—	2	1	no	—
517	C₄×C₁₃	—	2	1	no	—
518	C₄×C₁₃	—	2	1	no	—
519	C₄×C₁₃	—	2	1	no	—
520	C₄×C₁₃	—	2	1	no	—
521	C₄×C₁₃	—	2	1	no	—
522	C₄×C₁₃	—	2	1	no	—
523	C₄×C₁₃	—	2	1	no	—
524	C₄×C₁₃	—	2	1	no	—
525	C₄×C₁₃	—	2	1	no	—
526	C₄×C₁₃	—	4	1	no	—
527	C₄×C₁₃	—	4	1	no	—
528	C₄×C₁₃	—	4	1	no	—
529	C₄×C₁₃	—	4	1	no	—
530	C₄×C₁₃	—	4	1	no	—
531	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
532	C₄×C₁₃	#568	1	1	yes	characteristic
533	C₄×C₁₃	#576	1	1	yes	characteristic
534	C₄×C₁₃	#577	1	1	yes	characteristic
535	C₂×#41	—	2	1	no	—
536	C₂×#41	C₂×Dic₁₃	1	1	yes	characteristic
537	C₂×#41	C₂²⋊D₁₃	1	1	yes	characteristic
538	C₂²×D₄	—	2	1	no	—
539	C₂²×D₄	C₂×Dic₁₃	1	1	yes	characteristic
540	C₂²×D₄	C₂×Dic₁₃	1	1	yes	characteristic
541	C₂³×C₄	—	2	1	no	—
542	C₂³×C₄	—	2	1	no	—
543	C₂×M₁₆	—	26	1	no	—
544	C₂×M₁₆	—	26	1	no	—
545	C₂²×C₈	—	26	1	no	—
546	C₂²×C₈	—	26	1	no	—
547	C₂²×C₈	—	26	1	no	—
548	C₄⋊Q₈	C₂×Dic₁₃	1	1	yes	characteristic
549	#127	C₂×Dic₁₃	1	1	yes	characteristic
550	#126	—	2	1	no	—
551	#126	—	2	1	no	—
552	#126	—	2	1	no	—
553	#126	—	2	1	no	—
554	#125	—	2	1	no	—
555	#125	C₂×Dic₁₃	1	1	yes	characteristic
556	#125	C₂×Dic₁₃	1	1	yes	characteristic
557	#124	—	2	1	no	—
558	#124	—	2	1	no	—
559	#124	C₂×Dic₁₃	1	1	yes	characteristic
560	#124	C₂×Dic₁₃	1	1	yes	characteristic
561	#123	—	2	1	no	—
562	#123	—	2	1	no	—
563	#123	—	2	1	no	—
564	#123	—	2	1	no	—
565	#123	—	2	1	no	—
566	#123	—	2	1	no	—
567	#123	—	2	1	no	—
568	#123	—	2	1	no	—
569	C₂²⋊Q₈	—	2	1	no	—
570	C₂²⋊Q₈	—	2	1	no	—
571	C₂²⋊Q₈	—	2	1	no	—
572	C₂²⋊Q₈	—	2	1	no	—
573	C₂²⋊Q₈	—	2	1	no	—
574	C₂²⋊Q₈	C₂×Dic₁₃	1	1	yes	characteristic
575	C₂²⋊Q₈	C₂×Dic₁₃	1	1	yes	characteristic
576	#121	—	2	1	no	—
577	#121	—	2	1	no	—
578	#121	—	2	1	no	—
579	#121	—	2	1	no	—
580	#121	—	2	1	no	—
581	#121	—	2	1	no	—
582	#121	C₂×Dic₁₃	1	1	yes	characteristic
583	#121	C₂×Dic₁₃	1	1	yes	characteristic
584	#121	C₂×Dic₁₃	1	1	yes	characteristic
585	#121	C₂×Dic₁₃	1	1	yes	characteristic
586	#120	—	2	1	no	—
587	#120	—	2	1	no	—
588	#120	—	2	1	no	—
589	#120	—	2	1	no	—
590	C₄×Q₈	C₂×Dic₁₃	1	1	yes	characteristic
591	C₄×Q₈	C₂×Dic₁₃	1	1	yes	characteristic
592	C₄×Q₈	C₂²⋊D₁₃	1	1	yes	characteristic
593	C₄×Q₈	C₂²×D₁₃	1	1	yes	characteristic
594	C₄×D₄	—	2	1	no	—
595	C₄×D₄	—	2	1	no	—
596	C₄×D₄	—	2	1	no	—
597	C₄×D₄	—	2	1	no	—
598	C₄×D₄	—	2	1	no	—
599	C₄×D₄	—	2	1	no	—
600	C₄×D₄	—	2	1	no	—
601	C₄×D₄	—	2	1	no	—
602	C₄×D₄	—	2	1	no	—
603	C₄×D₄	—	2	1	no	—
604	C₄×D₄	—	2	1	no	—
605	C₄×D₄	—	2	1	no	—
606	C₄×D₄	—	2	1	no	—
607	C₄×D₄	C₂×Dic₁₃	1	1	yes	characteristic
608	C₄×D₄	C₂×Dic₁₃	1	1	yes	characteristic
609	C₄×D₄	C₂×Dic₁₃	1	1	yes	characteristic
610	C₄×D₄	C₂×Dic₁₃	1	1	yes	characteristic
611	C₄×D₄	C₂×Dic₁₃	1	1	yes	characteristic
612	C₄×D₄	C₂×Dic₁₃	1	1	yes	characteristic
613	C₄×D₄	C₂×Dic₁₃	1	1	yes	characteristic
614	C₄×D₄	C₂×Dic₁₃	1	1	yes	characteristic
615	C₄×D₄	C₂²⋊D₁₃	1	1	yes	characteristic
616	C₄×D₄	C₂²⋊D₁₃	1	1	yes	characteristic
617	C₄×D₄	C₂²⋊D₁₃	1	1	yes	characteristic
618	C₄×D₄	C₂²×D₁₃	1	1	yes	characteristic
619	C₄×D₄	C₂²×D₁₃	1	1	yes	characteristic
620	C₄×D₄	C₂²×D₁₃	1	1	yes	characteristic
621	#117	—	2	1	no	—
622	#117	—	2	1	no	—
623	#117	—	2	1	no	—
624	#117	C₂×Dic₁₃	1	1	yes	characteristic
625	#117	C₂²⋊D₁₃	1	1	yes	characteristic
626	#117	C₂²⋊D₁₃	1	1	yes	characteristic
627	#117	C₂²⋊D₁₃	1	1	yes	characteristic
628	C₂×C₄⋊C₄	—	2	1	no	—
629	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
630	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
631	C₂×C₂²⋊C₄	—	2	1	no	—
632	C₂×C₂²⋊C₄	—	2	1	no	—
633	C₂×C₂²⋊C₄	—	2	1	no	—
634	C₂×C₂²⋊C₄	—	2	1	no	—
635	C₂×C₄²	—	2	1	no	—
636	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
637	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
638	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
639	C₄⋊C₈	—	13	1	no	—
640	C₄⋊C₈	—	13	1	no	—
641	C₄⋊C₈	—	13	1	no	—
642	C₄⋊C₈	—	13	1	no	—
643	C₄⋊C₈	—	26	1	no	—
644	C₄⋊C₈	—	26	1	no	—
645	C₄⋊C₈	—	26	1	no	—
646	C₄⋊C₈	—	26	1	no	—
647	C₄⋊C₈	—	26	1	no	—
648	C₄⋊C₈	—	26	1	no	—
649	C₄⋊C₈	—	26	1	no	—
650	C₂²⋊C₈	—	26	1	no	—
651	C₂²⋊C₈	—	26	1	no	—
652	C₂²⋊C₈	—	26	1	no	—
653	C₂²⋊C₈	—	26	1	no	—
654	C₂²⋊C₈	—	26	1	no	—
655	C₂²⋊C₈	—	26	1	no	—
656	C₂²⋊C₈	—	26	1	no	—
657	#97	—	26	1	no	—
658	#97	—	26	1	no	—
659	#97	—	26	1	no	—
660	C₄×C₈	—	13	1	no	—
661	C₄×C₈	—	13	1	no	—
662	C₄×C₈	—	13	1	no	—
663	C₄×C₈	—	13	1	no	—
664	C₄×C₈	—	26	1	no	—
665	C₄×C₈	—	26	1	no	—
666	C₂×C₁₃	—	2	2	no	—
667	C₂×C₁₃	—	4	1	no	—
668	C₂×C₁₃	—	4	1	no	—
669	C₂×C₁₃	—	4	2	no	—
670	C₂×C₁₃	—	8	1	no	—
671	C₂×C₁₃	—	8	1	no	—
672	C₂×C₁₃	#2880	1	1	yes	characteristic
673	C₂×C₁₃	#2897	1	1	yes	characteristic
674	C₂×C₁₃	C₂×#421	1	1	yes	characteristic
675	C₂⁴	—	2	1	no	—
676	C₂⁴	—	2	1	no	—
677	#41	—	2	2	no	—
678	#41	—	4	2	no	—
679	#41	—	4	1	no	—
680	#41	—	8	1	no	—
681	#41	—	8	1	no	—
682	C₂×Q₈	—	2	1	no	—
683	C₂×Q₈	C₂²⋊Dic₁₃	1	1	yes	characteristic
684	C₂×Q₈	C₂²×Dic₁₃	1	1	yes	characteristic
685	C₂×D₄	—	2	2	no	—
686	C₂×D₄	—	2	2	no	—
687	C₂×D₄	—	2	1	no	—
688	C₂×D₄	—	2	1	no	—
689	C₂×D₄	—	2	1	no	—
690	C₂×D₄	—	2	1	no	—
691	C₂×D₄	—	2	1	no	—
692	C₂×D₄	—	2	1	no	—
693	C₂×D₄	—	2	1	no	—
694	C₂×D₄	—	2	1	no	—
695	C₂×D₄	—	2	1	no	—
696	C₂×D₄	—	4	1	no	—
697	C₂×D₄	—	4	1	no	—
698	C₂×D₄	—	4	4	no	—
699	C₂×D₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
700	C₂×D₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
701	C₂×D₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
702	C₂×D₄	C₂²×Dic₁₃	1	1	yes	characteristic
703	C₂×D₄	C₂²×Dic₁₃	1	1	yes	characteristic
704	C₂×D₄	C₂²×Dic₁₃	1	1	yes	characteristic
705	C₂²×C₄	—	2	1	no	—
706	C₂²×C₄	—	2	1	no	—
707	C₂²×C₄	—	2	1	no	—
708	C₂²×C₄	—	2	1	no	—
709	C₂²×C₄	—	2	1	no	—
710	C₂²×C₄	—	2	1	no	—
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	—	8	1	no	—
717	C₂²×C₄	—	8	1	no	—
718	C₂²×C₄	—	8	1	no	—
719	C₂²×C₄	—	8	1	no	—
720	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
721	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
722	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
723	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
724	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
725	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
726	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
727	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
728	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
729	M₁₆	—	52	2	no	—
730	M₁₆	—	104	1	no	—
731	C₂×C₈	—	26	1	no	—
732	C₂×C₈	—	26	1	no	—
733	C₂×C₈	—	26	1	no	—
734	C₂×C₈	—	26	1	no	—
735	C₂×C₈	—	26	1	no	—
736	C₂×C₈	—	26	1	no	—
737	C₂×C₈	—	26	1	no	—
738	C₂×C₈	—	26	1	no	—
739	C₂×C₈	—	52	2	no	—
740	C₂×C₈	—	104	1	no	—
741	C₂×C₈	—	104	1	no	—
742	C₄⋊C₄	—	2	1	no	—
743	C₄⋊C₄	—	2	1	no	—
744	C₄⋊C₄	—	2	1	no	—
745	C₄⋊C₄	—	2	1	no	—
746	C₄⋊C₄	—	2	1	no	—
747	C₄⋊C₄	—	2	1	no	—
748	C₄⋊C₄	—	2	1	no	—
749	C₄⋊C₄	—	2	1	no	—
750	C₄⋊C₄	—	2	1	no	—
751	C₄⋊C₄	—	2	1	no	—
752	C₄⋊C₄	—	2	1	no	—
753	C₄⋊C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
754	C₄⋊C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
755	C₄⋊C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
756	C₄⋊C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
757	C₄⋊C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
758	C₄⋊C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
759	C₄⋊C₄	C₂²×Dic₁₃	1	1	yes	characteristic
760	C₄⋊C₄	C₂²×Dic₁₃	1	1	yes	characteristic
761	C₄⋊C₄	C₂²×Dic₁₃	1	1	yes	characteristic
762	C₄⋊C₄	C₂²×Dic₁₃	1	1	yes	characteristic
763	C₂²⋊C₄	—	2	1	no	—
764	C₂²⋊C₄	—	2	1	no	—
765	C₂²⋊C₄	—	2	1	no	—
766	C₂²⋊C₄	—	2	1	no	—
767	C₂²⋊C₄	—	2	1	no	—
768	C₂²⋊C₄	—	2	1	no	—
769	C₂²⋊C₄	—	2	1	no	—
770	C₂²⋊C₄	—	2	1	no	—
771	C₂²⋊C₄	—	2	1	no	—
772	C₂²⋊C₄	—	2	1	no	—
773	C₂²⋊C₄	—	2	1	no	—
774	C₂²⋊C₄	—	2	1	no	—
775	C₂²⋊C₄	—	2	1	no	—
776	C₂²⋊C₄	—	2	1	no	—
777	C₂²⋊C₄	—	2	1	no	—
778	C₂²⋊C₄	—	2	1	no	—
779	C₂²⋊C₄	—	2	1	no	—
780	C₂²⋊C₄	—	2	1	no	—
781	C₂²⋊C₄	—	2	1	no	—
782	C₂²⋊C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
783	C₂²⋊C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
784	C₂²⋊C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
785	C₂²⋊C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
786	C₂²⋊C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
787	C₂²⋊C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
788	C₄²	—	2	1	no	—
789	C₄²	—	2	1	no	—
790	C₄²	—	2	1	no	—
791	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
792	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
793	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
794	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
795	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
796	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
797	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
798	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
799	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
800	C₄²	C₂³×D₁₃	1	1	yes	characteristic
801	C₁₃	#17521	1	1	yes	characteristic, complemented, Sylow
802	C₂³	—	2	1	no	—
803	C₂³	—	2	1	no	—
804	C₂³	—	2	1	no	—
805	C₂³	—	4	2	no	—
806	C₂³	—	4	2	no	—
807	C₂³	—	4	2	no	—
808	C₂³	—	4	2	no	—
809	C₂³	—	8	1	no	—
810	C₂³	—	8	1	no	—
811	C₂³	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
812	C₂³	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
813	C₂³	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
814	Q₈	—	2	1	no	—
815	Q₈	—	2	1	no	—
816	Q₈	—	4	1	no	—
817	Q₈	—	8	1	no	—
818	D₄	—	2	2	no	—
819	D₄	—	2	2	no	—
820	D₄	—	2	1	no	—
821	D₄	—	2	1	no	—
822	D₄	—	2	1	no	—
823	D₄	—	2	1	no	—
824	D₄	—	2	1	no	—
825	D₄	—	4	1	no	—
826	D₄	—	4	2	no	—
827	D₄	—	4	2	no	—
828	D₄	—	4	2	no	—
829	D₄	—	4	2	no	—
830	D₄	—	4	2	no	—
831	D₄	—	4	2	no	—
832	D₄	—	8	1	no	—
833	D₄	—	8	1	no	—
834	D₄	—	8	1	no	—
835	D₄	#88202	1	2	yes	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	1	no	—
838	C₂×C₄	—	2	1	no	—
839	C₂×C₄	—	2	1	no	—
840	C₂×C₄	—	2	1	no	—
841	C₂×C₄	—	2	1	no	—
842	C₂×C₄	—	2	1	no	—
843	C₂×C₄	—	2	1	no	—
844	C₂×C₄	—	2	1	no	—
845	C₂×C₄	—	2	1	no	—
846	C₂×C₄	—	2	1	no	—
847	C₂×C₄	—	2	1	no	—
848	C₂×C₄	—	2	1	no	—
849	C₂×C₄	—	2	1	no	—
850	C₂×C₄	—	2	1	no	—
851	C₂×C₄	—	2	1	no	—
852	C₂×C₄	—	2	1	no	—
853	C₂×C₄	—	2	1	no	—
854	C₂×C₄	—	4	1	no	—
855	C₂×C₄	—	4	1	no	—
856	C₂×C₄	—	4	2	no	—
857	C₂×C₄	—	4	2	no	—
858	C₂×C₄	—	4	1	no	—
859	C₂×C₄	—	4	1	no	—
860	C₂×C₄	—	4	1	no	—
861	C₂×C₄	—	4	1	no	—
862	C₂×C₄	—	4	1	no	—
863	C₂×C₄	—	4	1	no	—
864	C₂×C₄	—	8	1	no	—
865	C₂×C₄	—	8	1	no	—
866	C₂×C₄	—	8	1	no	—
867	C₂×C₄	—	8	1	no	—
868	C₂×C₄	—	8	1	no	—
869	C₂×C₄	—	8	1	no	—
870	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
871	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
872	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
873	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
874	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
875	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
876	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
877	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
878	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
879	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
880	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
881	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
882	C₈	—	52	1	no	—
883	C₈	—	52	1	no	—
884	C₈	—	52	1	no	—
885	C₈	—	52	1	no	—
886	C₈	—	52	1	no	—
887	C₈	—	52	1	no	—
888	C₈	—	52	1	no	—
889	C₈	—	52	1	no	—
890	C₂²	—	2	1	no	—
891	C₂²	—	2	1	no	—
892	C₂²	—	2	1	no	—
893	C₂²	—	2	1	no	—
894	C₂²	—	2	1	no	—
895	C₂²	—	2	1	no	—
896	C₂²	—	2	1	no	—
897	C₂²	—	2	1	no	—
898	C₂²	—	2	2	no	—
899	C₂²	—	4	1	no	—
900	C₂²	—	4	1	no	—
901	C₂²	—	4	1	no	—
902	C₂²	—	4	1	no	—
903	C₂²	—	4	1	no	—
904	C₂²	—	4	1	no	—
905	C₂²	—	4	1	no	—
906	C₂²	—	4	1	no	—
907	C₂²	—	8	4	no	—
908	C₂²	—	8	4	no	—
909	C₂²	#11718897	1	2	yes	—
910	C₂²	C₂²×C₂²⋊Dic₁₃	1	1	yes	characteristic
911	C₄	—	2	1	no	—
912	C₄	—	2	1	no	—
913	C₄	—	2	1	no	—
914	C₄	—	2	1	no	—
915	C₄	—	2	1	no	—
916	C₄	—	2	1	no	—
917	C₄	—	2	1	no	—
918	C₄	—	2	1	no	—
919	C₄	—	2	1	no	—
920	C₄	—	2	1	no	—
921	C₄	—	4	1	no	—
922	C₄	—	4	1	no	—
923	C₄	—	4	1	no	—
924	C₄	—	4	1	no	—
925	C₄	—	4	1	no	—
926	C₄	C₂×#88202	1	1	yes	characteristic
927	C₄	#11719524	1	1	yes	characteristic
928	C₄	#11719540	1	1	yes	characteristic
929	C₄	#11719541	1	1	yes	characteristic
930	C₂	—	2	2	no	—
931	C₂	—	4	1	no	—
932	C₂	—	4	1	no	—
933	C₂	—	4	2	no	—
934	C₂	—	8	1	no	—
935	C₂	—	8	1	no	—
936	C₂	#13123285	1	1	yes	characteristic
937	C₂	#13123362	1	1	yes	characteristic
938	C₂	C₂×#11718897	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₁₃
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₄²	C₂³×D₁₃
Fitting, prime radical	C₁₃×#3481	C₂
socle	C₂²×C₁₃	C₂²×C₂²⋊C₄
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	#3481	D₁₃
hypocenter	C₁₃	#17521
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×#41 ◁ #3481

Complements

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

N	H ≅ G/N	type
1. #13123961	C₂	semidirect
2. #13123480	C₂	semidirect
3. #13113305	C₂	semidirect
4. #13113301	C₂	semidirect
5. #13113296	C₂	semidirect
6. #13113279	C₂	semidirect
7. #13113270	C₂	semidirect
8. #13113261	C₂	semidirect
9. #13113249	C₂	semidirect
10. #13113244	C₂	semidirect
11. #13113235	C₂	semidirect
12. #13113227	C₂	semidirect
13. #13113223	C₂	semidirect
14. C₂×D₄⋊#1055	C₂	semidirect
47. #11718587	C₂²	semidirect
48. #11718587	C₂²	semidirect
49. #11718586	C₂²	semidirect
50. #11718586	C₂²	semidirect
51. #11718586	C₂²	semidirect
52. #11718586	C₂²	semidirect
53. #11718586	C₂²	semidirect
54. #11718585	C₂²	semidirect
55. C₂×C₄⋊#1055	C₂²	semidirect
56. C₂×C₄⋊#1055	C₂²	semidirect
57. C₄×#6099	C₂²	semidirect
58. C₂×C₄×#1055	C₂²	semidirect
59. Q₈⋊#1055	C₂²	semidirect
60. Q₈⋊#1055	C₂²	semidirect
61. Q₈⋊#1055	C₂²	semidirect
62. Q₈⋊#1055	C₂²	semidirect
67. D₄⋊#1055	C₂²	semidirect
68. D₄⋊#1055	C₂²	semidirect
69. D₄⋊#1055	C₂²	semidirect
70. D₄⋊#1055	C₂²	semidirect
71. D₄⋊#1055	C₂²	semidirect
72. D₄⋊#1055	C₂²	semidirect
73. D₄⋊#1055	C₂²	semidirect
74. D₄⋊#1055	C₂²	semidirect
801. C₁₃	#17521	semidirect

Maximal subgroups

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

subgroup	index
#13123961	2
#13123480	2
#13113305	2
#13113301	2
#13113296	2
#13113279	2
#13113270	2
#13113261	2
#13113249	2
#13113244	2
#13113235	2
#13113227	2
#13113223	2
C₂×D₄⋊#1055	2
C₁₃×#3481	2
#17521	13