Subgroups — #15831079

Order 3328.

878 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13123850	C₂	1	1	yes	maximal, characteristic, complemented
2	#13123487	C₂	1	1	yes	maximal, characteristic, complemented
3	#13113474	C₂	1	1	yes	maximal, characteristic, complemented
4	#13113467	C₂	1	1	yes	maximal, characteristic, complemented
5	#13113467	C₂	1	1	yes	maximal, characteristic, complemented
6	#13113463	C₂	1	1	yes	maximal, characteristic, complemented
7	#13113456	C₂	1	1	yes	maximal, characteristic, complemented
8	#13113456	C₂	1	1	yes	maximal, characteristic, complemented
9	#13113451	C₂	1	1	yes	maximal, characteristic, complemented
10	#13113443	C₂	1	1	yes	maximal, characteristic, complemented
11	#13113438	C₂	1	1	yes	maximal, characteristic, complemented
12	#13113438	C₂	1	1	yes	maximal, characteristic, complemented
13	#13113424	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#11718135	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3515	C₂	1	1	yes	maximal, characteristic
16	C₁₃×#557	C₄	1	1	yes	characteristic
17	C₁₃×#554	C₄	1	1	yes	characteristic
18	C₁₃×#554	C₄	1	1	yes	characteristic
19	C₁₃×#553	C₄	1	1	yes	characteristic
20	C₁₃×#553	C₄	1	1	yes	characteristic
21	C₁₃×#552	—	2	1	no	—
22	C₁₃×#552	—	2	1	no	—
23	C₁₃×#552	—	2	1	no	—
24	C₁₃×#552	C₄	1	1	yes	characteristic
25	C₁₃×#552	C₄	1	1	yes	characteristic
26	C₁₃×#547	—	2	1	no	—
27	C₁₃×#547	C₄	1	1	yes	characteristic
28	C₁₃×#541	—	2	1	no	—
29	C₁₃×#539	—	2	1	no	—
30	C₁₃×#539	—	2	1	no	—
31	C₁₃×#533	C₂²	1	1	yes	characteristic
32	C₁₃×#529	C₂²	1	1	yes	characteristic
33	C₁₃×#529	C₂²	1	1	yes	characteristic
34	C₁₃×#529	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
37	C₁₃×#520	—	2	1	no	—
38	C₄×C₁₃×#41	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
48	#11718587	C₂²	1	1	yes	characteristic
49	#11718587	C₂²	1	1	yes	characteristic
50	#11718587	C₂²	1	1	yes	characteristic
51	#11718587	C₂²	1	1	yes	characteristic
52	#11718587	C₂²	1	1	yes	characteristic
53	#11718587	C₂²	1	1	yes	characteristic
54	C₄×#6099	C₂²	1	1	yes	characteristic
55	C₄×#6099	C₂²	1	1	yes	characteristic
56	C₂×#88043	C₂²	1	1	yes	characteristic
57	C₂×#88043	C₂²	1	1	yes	characteristic
58	C₂×#88043	C₂²	1	1	yes	characteristic
59	#11718135	C₂²	1	1	yes	characteristic
60	#11718135	C₂²	1	1	yes	characteristic
61	#11718135	C₂²	1	1	yes	characteristic
62	#11718135	C₂²	1	1	yes	characteristic
63	#11718135	C₂²	1	1	yes	characteristic
64	#11718135	C₂²	1	1	yes	characteristic
65	#11718135	C₂²	1	1	yes	characteristic
66	#11718135	C₂²	1	1	yes	characteristic
67	#11718135	C₂²	1	1	yes	characteristic
68	#11718135	C₂²	1	1	yes	characteristic
69	#11718135	C₂²	1	1	yes	characteristic
70	#11718135	C₂²	1	1	yes	characteristic
71	#11718132	C₂²	1	1	yes	characteristic
72	#11718132	C₂²	1	1	yes	characteristic
73	#11718132	C₂²	1	1	yes	characteristic
74	#11718132	C₂²	1	1	yes	characteristic
75	C₂×C₁₃×#41	—	2	1	no	—
76	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
77	C₁₃×C₄⋊Q₈	—	2	1	no	—
78	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
79	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
80	C₁₃×#126	—	2	1	no	—
81	C₁₃×#126	—	2	1	no	—
82	C₁₃×#126	—	2	1	no	—
83	C₁₃×#126	—	2	1	no	—
84	C₁₃×#126	—	2	1	no	—
85	C₁₃×#126	—	2	1	no	—
86	C₁₃×#126	—	2	1	no	—
87	C₁₃×#125	—	2	1	no	—
88	C₁₃×#125	—	2	1	no	—
89	C₁₃×#125	—	2	1	no	—
90	C₁₃×#125	—	2	1	no	—
91	C₁₃×#125	—	2	1	no	—
92	C₁₃×#125	—	2	1	no	—
93	C₁₃×#125	—	2	1	no	—
94	C₁₃×#125	—	2	1	no	—
95	C₁₃×#125	—	2	1	no	—
96	C₁₃×#125	C₂×C₄	1	1	yes	characteristic
97	C₁₃×#125	C₂×C₄	1	1	yes	characteristic
98	C₁₃×#125	C₂×C₄	1	1	yes	characteristic
99	C₁₃×#125	C₂×C₄	1	1	yes	characteristic
100	C₁₃×#125	C₂³	1	1	yes	characteristic
101	C₁₃×#125	C₂³	1	1	yes	characteristic
102	C₁₃×#125	C₂³	1	1	yes	characteristic
103	C₁₃×#124	C₂³	1	1	yes	characteristic
104	C₁₃×#123	—	2	1	no	—
105	C₁₃×#123	—	2	1	no	—
106	C₁₃×#123	—	2	1	no	—
107	C₁₃×#123	—	2	1	no	—
108	C₁₃×#123	—	2	1	no	—
109	C₁₃×#123	—	2	1	no	—
110	C₁₃×#123	—	2	1	no	—
111	C₁₃×#123	—	2	1	no	—
112	C₁₃×#123	—	2	1	no	—
113	C₁₃×C₂²⋊Q₈	—	2	1	no	—
114	C₁₃×C₂²⋊Q₈	—	2	1	no	—
115	C₁₃×C₂²⋊Q₈	—	2	1	no	—
116	C₁₃×C₂²⋊Q₈	—	2	1	no	—
117	C₁₃×C₂²⋊Q₈	—	2	1	no	—
118	C₁₃×C₂²⋊Q₈	—	2	1	no	—
119	C₁₃×C₂²⋊Q₈	—	2	1	no	—
120	C₁₃×C₂²⋊Q₈	—	2	1	no	—
121	C₁₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
122	C₁₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
123	C₁₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
124	C₁₃×#121	—	2	1	no	—
125	C₁₃×#121	—	2	1	no	—
126	C₁₃×#121	C₂×C₄	1	1	yes	characteristic
127	C₁₃×#121	C₂×C₄	1	1	yes	characteristic
128	C₁₃×#121	C₂×C₄	1	1	yes	characteristic
129	C₄×Q₈×C₁₃	—	2	1	no	—
130	C₄×Q₈×C₁₃	—	2	1	no	—
131	C₄×Q₈×C₁₃	—	2	1	no	—
132	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
133	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
134	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
135	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
136	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
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	—	2	1	no	—
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	D₄	1	1	yes	characteristic
150	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
151	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
152	C₁₃×#117	—	2	1	no	—
153	C₁₃×#117	—	2	1	no	—
154	C₁₃×#117	—	2	1	no	—
155	C₁₃×#117	—	2	1	no	—
156	C₁₃×#117	—	2	1	no	—
157	C₁₃×#117	C₂×C₄	1	1	yes	characteristic
158	C₁₃×#117	C₂×C₄	1	1	yes	characteristic
159	C₁₃×#117	D₄	1	1	yes	characteristic
160	C₁₃×#117	D₄	1	1	yes	characteristic
161	C₁₃×#117	D₄	1	1	yes	characteristic
162	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
163	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
164	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
165	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
166	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
167	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
168	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
169	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
170	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
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	#88043	—	2	1	no	—
194	#88043	—	2	1	no	—
195	#88043	—	2	1	no	—
196	#88043	C₂³	1	1	yes	characteristic
197	#88043	C₂³	1	1	yes	characteristic
198	#88043	C₂³	1	1	yes	characteristic
199	#88043	C₂³	1	1	yes	characteristic
200	#88043	C₂³	1	1	yes	characteristic
201	#88043	C₂³	1	1	yes	characteristic
202	#88043	C₂³	1	1	yes	characteristic
203	#88043	C₂³	1	1	yes	characteristic
204	C₄×#1055	—	2	1	no	—
205	C₄×#1055	—	2	1	no	—
206	#17680	—	13	1	no	maximal, Sylow
207	C₁₃×#41	—	4	2	no	—
208	C₁₃×#41	—	4	4	no	—
209	C₂×Q₈×C₁₃	—	2	1	no	—
210	C₂×Q₈×C₁₃	—	2	1	no	—
211	C₂×Q₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
212	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
213	C₂×D₄×C₁₃	—	2	1	no	—
214	C₂×D₄×C₁₃	—	2	1	no	—
215	C₂×D₄×C₁₃	—	2	1	no	—
216	C₂×D₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
217	C₂×D₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
218	C₂×D₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
219	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
220	C₂²×C₄×C₁₃	—	2	1	no	—
221	C₂²×C₄×C₁₃	—	2	1	no	—
222	C₂²×C₄×C₁₃	—	2	1	no	—
223	C₂²×C₄×C₁₃	—	2	1	no	—
224	C₂²×C₄×C₁₃	—	2	1	no	—
225	C₂²×C₄×C₁₃	—	2	1	no	—
226	C₂²×C₄×C₁₃	—	2	1	no	—
227	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
228	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
229	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
230	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
231	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
232	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
233	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
234	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
235	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
236	C₁₃×C₄⋊C₄	—	2	1	no	—
237	C₁₃×C₄⋊C₄	—	2	1	no	—
238	C₁₃×C₄⋊C₄	—	2	1	no	—
239	C₁₃×C₄⋊C₄	—	2	1	no	—
240	C₁₃×C₄⋊C₄	—	2	1	no	—
241	C₁₃×C₄⋊C₄	—	2	1	no	—
242	C₁₃×C₄⋊C₄	—	2	1	no	—
243	C₁₃×C₄⋊C₄	—	2	1	no	—
244	C₁₃×C₄⋊C₄	—	2	1	no	—
245	C₁₃×C₄⋊C₄	—	2	1	no	—
246	C₁₃×C₄⋊C₄	—	2	1	no	—
247	C₁₃×C₄⋊C₄	—	2	1	no	—
248	C₁₃×C₄⋊C₄	—	2	1	no	—
249	C₁₃×C₄⋊C₄	—	2	1	no	—
250	C₁₃×C₄⋊C₄	—	2	1	no	—
251	C₁₃×C₄⋊C₄	—	2	1	no	—
252	C₁₃×C₄⋊C₄	—	2	1	no	—
253	C₁₃×C₄⋊C₄	—	2	1	no	—
254	C₁₃×C₄⋊C₄	—	2	1	no	—
255	C₁₃×C₄⋊C₄	—	2	1	no	—
256	C₁₃×C₄⋊C₄	—	2	1	no	—
257	C₁₃×C₄⋊C₄	—	2	1	no	—
258	C₁₃×C₄⋊C₄	—	2	1	no	—
259	C₁₃×C₄⋊C₄	—	2	1	no	—
260	C₁₃×C₄⋊C₄	—	2	1	no	—
261	C₁₃×C₄⋊C₄	—	2	1	no	—
262	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
263	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
264	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
265	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
266	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
267	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
268	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
269	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
270	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
271	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
272	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
273	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
274	C₁₃×C₂²⋊C₄	—	2	1	no	—
275	C₁₃×C₂²⋊C₄	—	2	1	no	—
276	C₁₃×C₂²⋊C₄	—	2	1	no	—
277	C₁₃×C₂²⋊C₄	—	2	1	no	—
278	C₁₃×C₂²⋊C₄	—	2	1	no	—
279	C₁₃×C₂²⋊C₄	—	2	1	no	—
280	C₁₃×C₂²⋊C₄	—	2	1	no	—
281	C₁₃×C₂²⋊C₄	—	2	1	no	—
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	C₂²⋊C₄	1	1	yes	characteristic
288	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
289	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
290	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
291	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
292	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
293	C₄²×C₁₃	—	2	1	no	—
294	C₄²×C₁₃	—	2	1	no	—
295	C₄²×C₁₃	—	2	1	no	—
296	C₄²×C₁₃	—	2	1	no	—
297	C₄²×C₁₃	—	2	1	no	—
298	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
299	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
300	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
301	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
302	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
303	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
304	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
305	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
306	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
307	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
308	#6099	—	4	2	no	—
309	#6099	—	4	2	no	—
310	C₂×#1055	—	2	1	no	—
311	C₂×#1055	—	2	1	no	—
312	C₂×#1055	—	2	1	no	—
313	C₂×#1055	—	2	1	no	—
314	C₂×#1055	—	2	1	no	—
315	C₂×#1055	—	2	1	no	—
316	C₂×#1055	—	2	1	no	—
317	C₂×#1055	—	2	1	no	—
318	C₂×#1055	—	4	2	no	—
319	C₂×#1055	—	4	2	no	—
320	C₂×#1055	—	4	2	no	—
321	#3515	D₁₃	1	1	yes	characteristic
322	#2970	—	13	1	no	—
323	#2923	—	13	1	no	—
324	#1537	—	13	1	no	—
325	#1535	—	13	1	no	—
326	#1535	—	13	1	no	—
327	#1534	—	13	1	no	—
328	#1532	—	13	1	no	—
329	#1532	—	13	1	no	—
330	#1531	—	13	1	no	—
331	#1529	—	13	1	no	—
332	#1528	—	13	1	no	—
333	#1528	—	13	1	no	—
334	#1524	—	13	1	no	—
335	C₂×#330	—	13	1	no	—
336	C₂³×C₁₃	—	2	1	no	—
337	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
338	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
339	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
340	Q₈×C₁₃	—	4	1	no	—
341	Q₈×C₁₃	—	4	2	no	—
342	Q₈×C₁₃	—	4	1	no	—
343	Q₈×C₁₃	—	8	1	no	—
344	D₄×C₁₃	—	2	2	no	—
345	D₄×C₁₃	—	2	2	no	—
346	D₄×C₁₃	—	4	1	no	—
347	D₄×C₁₃	—	4	1	no	—
348	D₄×C₁₃	—	4	2	no	—
349	D₄×C₁₃	—	4	2	no	—
350	D₄×C₁₃	—	8	1	no	—
351	C₂×C₄×C₁₃	—	2	2	no	—
352	C₂×C₄×C₁₃	—	2	1	no	—
353	C₂×C₄×C₁₃	—	2	1	no	—
354	C₂×C₄×C₁₃	—	2	1	no	—
355	C₂×C₄×C₁₃	—	2	1	no	—
356	C₂×C₄×C₁₃	—	2	1	no	—
357	C₂×C₄×C₁₃	—	2	1	no	—
358	C₂×C₄×C₁₃	—	2	1	no	—
359	C₂×C₄×C₁₃	—	4	1	no	—
360	C₂×C₄×C₁₃	—	4	1	no	—
361	C₂×C₄×C₁₃	—	4	1	no	—
362	C₂×C₄×C₁₃	—	4	1	no	—
363	C₂×C₄×C₁₃	—	4	1	no	—
364	C₂×C₄×C₁₃	—	4	1	no	—
365	C₂×C₄×C₁₃	—	4	1	no	—
366	C₂×C₄×C₁₃	—	4	1	no	—
367	C₂×C₄×C₁₃	—	4	2	no	—
368	C₂×C₄×C₁₃	—	4	2	no	—
369	C₂×C₄×C₁₃	—	4	2	no	—
370	C₂×C₄×C₁₃	—	8	1	no	—
371	C₂×C₄×C₁₃	—	8	1	no	—
372	C₂×C₄×C₁₃	—	8	1	no	—
373	C₂×C₄×C₁₃	—	8	1	no	—
374	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
375	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
376	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
377	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
378	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
379	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
380	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
381	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
382	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
383	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
384	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
385	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
386	#1055	—	2	2	no	—
387	#1055	—	4	1	no	—
388	#1055	—	4	1	no	—
389	#1055	—	4	1	no	—
390	#1055	—	4	1	no	—
391	#1055	—	4	1	no	—
392	#1055	—	4	1	no	—
393	#1055	—	4	1	no	—
394	#557	Dic₁₃	1	1	yes	characteristic
395	#554	Dic₁₃	1	1	yes	characteristic
396	#554	Dic₁₃	1	1	yes	characteristic
397	#553	Dic₁₃	1	1	yes	characteristic
398	#553	Dic₁₃	1	1	yes	characteristic
399	#552	—	2	1	no	—
400	#552	—	2	1	no	—
401	#552	—	2	1	no	—
402	#552	Dic₁₃	1	1	yes	characteristic
403	#552	Dic₁₃	1	1	yes	characteristic
404	#547	—	2	1	no	—
405	#547	Dic₁₃	1	1	yes	characteristic
406	#541	—	2	1	no	—
407	#539	—	2	1	no	—
408	#539	—	2	1	no	—
409	#533	C₂×D₁₃	1	1	yes	characteristic
410	#529	C₂×D₁₃	1	1	yes	characteristic
411	#529	C₂×D₁₃	1	1	yes	characteristic
412	#529	C₂×D₁₃	1	1	yes	characteristic
413	C₂×#125	C₂×D₁₃	1	1	yes	characteristic
414	C₂×#125	C₂×D₁₃	1	1	yes	characteristic
415	#520	—	2	1	no	—
416	C₄×#41	C₂×D₁₃	1	1	yes	characteristic
417	#446	—	26	1	no	—
418	#435	—	26	1	no	—
419	#435	—	26	1	no	—
420	C₈×D₄	—	26	1	no	—
421	#433	—	26	1	no	—
422	#433	—	26	1	no	—
423	#432	—	13	1	no	—
424	#432	—	13	1	no	—
425	#432	—	13	1	no	—
426	#432	—	13	1	no	—
427	#432	—	13	1	no	—
428	#432	—	13	1	no	—
429	#432	—	13	1	no	—
430	#424	—	26	1	no	—
431	#408	—	26	1	no	—
432	C₄×M₁₆	—	13	1	no	—
433	C₄×M₁₆	—	13	1	no	—
434	C₂×#97	—	13	1	no	—
435	C₂×#97	—	13	1	no	—
436	C₂×#97	—	13	1	no	—
437	#330	—	13	1	no	—
438	#330	—	13	1	no	—
439	#330	—	13	1	no	—
440	#330	—	13	1	no	—
441	#330	—	13	1	no	—
442	#330	—	13	1	no	—
443	#330	—	13	1	no	—
444	#330	—	13	1	no	—
445	#330	—	13	1	no	—
446	#330	—	13	1	no	—
447	#330	—	13	1	no	—
448	#330	—	13	1	no	—
449	#329	—	13	1	no	—
450	#329	—	13	1	no	—
451	#329	—	13	1	no	—
452	#329	—	13	1	no	—
453	C₂²×C₁₃	—	2	1	no	—
454	C₂²×C₁₃	—	2	1	no	—
455	C₂²×C₁₃	—	2	1	no	—
456	C₂²×C₁₃	—	2	1	no	—
457	C₂²×C₁₃	—	2	1	no	—
458	C₂²×C₁₃	—	2	1	no	—
459	C₂²×C₁₃	—	2	1	no	—
460	C₂²×C₁₃	—	2	1	no	—
461	C₂²×C₁₃	—	4	1	no	—
462	C₂²×C₁₃	—	4	1	no	—
463	C₂²×C₁₃	—	4	1	no	—
464	C₂²×C₁₃	#421	1	2	yes	—
465	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
466	C₄×C₁₃	—	2	1	no	—
467	C₄×C₁₃	—	2	1	no	—
468	C₄×C₁₃	—	2	1	no	—
469	C₄×C₁₃	—	2	1	no	—
470	C₄×C₁₃	—	2	1	no	—
471	C₄×C₁₃	—	2	1	no	—
472	C₄×C₁₃	—	2	1	no	—
473	C₄×C₁₃	—	2	1	no	—
474	C₄×C₁₃	—	2	1	no	—
475	C₄×C₁₃	—	2	1	no	—
476	C₄×C₁₃	—	2	1	no	—
477	C₄×C₁₃	—	2	1	no	—
478	C₄×C₁₃	—	4	1	no	—
479	C₄×C₁₃	—	4	1	no	—
480	C₄×C₁₃	—	4	1	no	—
481	C₄×C₁₃	—	4	1	no	—
482	C₄×C₁₃	—	4	1	no	—
483	C₄×C₁₃	—	4	1	no	—
484	C₄×C₁₃	—	4	1	no	—
485	C₂×#41	—	2	1	no	—
486	C₂×#41	C₂²⋊D₁₃	1	1	yes	characteristic
487	C₂×M₁₆	—	26	1	no	—
488	C₂×M₁₆	—	26	1	no	—
489	C₂²×C₈	—	26	1	no	—
490	C₂²×C₈	—	26	1	no	—
491	C₂²×C₈	—	26	1	no	—
492	C₄⋊Q₈	—	2	1	no	—
493	C₄⋊Q₈	C₂×Dic₁₃	1	1	yes	characteristic
494	C₄⋊Q₈	C₂×Dic₁₃	1	1	yes	characteristic
495	#126	—	2	1	no	—
496	#126	—	2	1	no	—
497	#126	—	2	1	no	—
498	#126	—	2	1	no	—
499	#126	—	2	1	no	—
500	#126	—	2	1	no	—
501	#126	—	2	1	no	—
502	#125	—	2	1	no	—
503	#125	—	2	1	no	—
504	#125	—	2	1	no	—
505	#125	—	2	1	no	—
506	#125	—	2	1	no	—
507	#125	—	2	1	no	—
508	#125	—	2	1	no	—
509	#125	—	2	1	no	—
510	#125	—	2	1	no	—
511	#125	C₂×Dic₁₃	1	1	yes	characteristic
512	#125	C₂×Dic₁₃	1	1	yes	characteristic
513	#125	C₂×Dic₁₃	1	1	yes	characteristic
514	#125	C₂×Dic₁₃	1	1	yes	characteristic
515	#125	C₂²×D₁₃	1	1	yes	characteristic
516	#125	C₂²×D₁₃	1	1	yes	characteristic
517	#125	C₂²×D₁₃	1	1	yes	characteristic
518	#124	C₂²×D₁₃	1	1	yes	characteristic
519	#123	—	2	1	no	—
520	#123	—	2	1	no	—
521	#123	—	2	1	no	—
522	#123	—	2	1	no	—
523	#123	—	2	1	no	—
524	#123	—	2	1	no	—
525	#123	—	2	1	no	—
526	#123	—	2	1	no	—
527	#123	—	2	1	no	—
528	C₂²⋊Q₈	—	2	1	no	—
529	C₂²⋊Q₈	—	2	1	no	—
530	C₂²⋊Q₈	—	2	1	no	—
531	C₂²⋊Q₈	—	2	1	no	—
532	C₂²⋊Q₈	—	2	1	no	—
533	C₂²⋊Q₈	—	2	1	no	—
534	C₂²⋊Q₈	—	2	1	no	—
535	C₂²⋊Q₈	—	2	1	no	—
536	C₂²⋊Q₈	C₂×Dic₁₃	1	1	yes	characteristic
537	C₂²⋊Q₈	C₂×Dic₁₃	1	1	yes	characteristic
538	C₂²⋊Q₈	C₂×Dic₁₃	1	1	yes	characteristic
539	#121	—	2	1	no	—
540	#121	—	2	1	no	—
541	#121	C₂×Dic₁₃	1	1	yes	characteristic
542	#121	C₂×Dic₁₃	1	1	yes	characteristic
543	#121	C₂×Dic₁₃	1	1	yes	characteristic
544	C₄×Q₈	—	2	1	no	—
545	C₄×Q₈	—	2	1	no	—
546	C₄×Q₈	—	2	1	no	—
547	C₄×Q₈	C₂×Dic₁₃	1	1	yes	characteristic
548	C₄×Q₈	C₂×Dic₁₃	1	1	yes	characteristic
549	C₄×Q₈	C₂×Dic₁₃	1	1	yes	characteristic
550	C₄×Q₈	C₂×Dic₁₃	1	1	yes	characteristic
551	C₄×Q₈	C₂²⋊D₁₃	1	1	yes	characteristic
552	C₄×D₄	—	2	1	no	—
553	C₄×D₄	—	2	1	no	—
554	C₄×D₄	—	2	1	no	—
555	C₄×D₄	—	2	1	no	—
556	C₄×D₄	—	2	1	no	—
557	C₄×D₄	—	2	1	no	—
558	C₄×D₄	C₂×Dic₁₃	1	1	yes	characteristic
559	C₄×D₄	C₂×Dic₁₃	1	1	yes	characteristic
560	C₄×D₄	C₂×Dic₁₃	1	1	yes	characteristic
561	C₄×D₄	C₂×Dic₁₃	1	1	yes	characteristic
562	C₄×D₄	C₂×Dic₁₃	1	1	yes	characteristic
563	C₄×D₄	C₂×Dic₁₃	1	1	yes	characteristic
564	C₄×D₄	C₂²⋊D₁₃	1	1	yes	characteristic
565	C₄×D₄	C₂²⋊D₁₃	1	1	yes	characteristic
566	C₄×D₄	C₂²⋊D₁₃	1	1	yes	characteristic
567	#117	—	2	1	no	—
568	#117	—	2	1	no	—
569	#117	—	2	1	no	—
570	#117	—	2	1	no	—
571	#117	—	2	1	no	—
572	#117	C₂×Dic₁₃	1	1	yes	characteristic
573	#117	C₂×Dic₁₃	1	1	yes	characteristic
574	#117	C₂²⋊D₁₃	1	1	yes	characteristic
575	#117	C₂²⋊D₁₃	1	1	yes	characteristic
576	#117	C₂²⋊D₁₃	1	1	yes	characteristic
577	C₂×C₄⋊C₄	—	2	1	no	—
578	C₂×C₄⋊C₄	—	2	1	no	—
579	C₂×C₄⋊C₄	—	2	1	no	—
580	C₂×C₄⋊C₄	—	2	1	no	—
581	C₂×C₄⋊C₄	—	2	1	no	—
582	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
583	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
584	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
585	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
586	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
587	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
588	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
589	C₄⋊C₈	—	26	1	no	—
590	C₄⋊C₈	—	26	1	no	—
591	C₄⋊C₈	—	26	1	no	—
592	C₄⋊C₈	—	26	1	no	—
593	C₄⋊C₈	—	26	1	no	—
594	C₄⋊C₈	—	26	1	no	—
595	C₄⋊C₈	—	26	1	no	—
596	C₂²⋊C₈	—	26	1	no	—
597	C₂²⋊C₈	—	26	1	no	—
598	C₂²⋊C₈	—	26	1	no	—
599	C₂²⋊C₈	—	26	1	no	—
600	C₂²⋊C₈	—	26	1	no	—
601	C₂²⋊C₈	—	26	1	no	—
602	C₂²⋊C₈	—	26	1	no	—
603	#97	—	13	1	no	—
604	#97	—	13	1	no	—
605	#97	—	13	1	no	—
606	#97	—	13	1	no	—
607	#97	—	13	1	no	—
608	#97	—	13	1	no	—
609	#97	—	13	1	no	—
610	#97	—	13	1	no	—
611	#97	—	26	1	no	—
612	#97	—	26	1	no	—
613	#97	—	26	1	no	—
614	C₄×C₈	—	26	1	no	—
615	C₄×C₈	—	26	1	no	—
616	C₂×C₁₃	—	2	2	no	—
617	C₂×C₁₃	—	4	1	no	—
618	C₂×C₁₃	—	4	1	no	—
619	C₂×C₁₃	—	8	1	no	—
620	C₂×C₁₃	#2889	1	1	yes	characteristic
621	C₂×C₁₃	C₂×#421	1	1	yes	characteristic
622	C₂×C₁₃	#2901	1	1	yes	characteristic
623	#41	—	4	2	no	—
624	#41	—	4	4	no	—
625	C₂×Q₈	—	2	1	no	—
626	C₂×Q₈	—	2	1	no	—
627	C₂×Q₈	C₂²⋊Dic₁₃	1	1	yes	characteristic
628	C₂×Q₈	C₂²×Dic₁₃	1	1	yes	characteristic
629	C₂×D₄	—	2	1	no	—
630	C₂×D₄	—	2	1	no	—
631	C₂×D₄	—	2	1	no	—
632	C₂×D₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
633	C₂×D₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
634	C₂×D₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
635	C₂×D₄	C₂²×Dic₁₃	1	1	yes	characteristic
636	C₂²×C₄	—	2	1	no	—
637	C₂²×C₄	—	2	1	no	—
638	C₂²×C₄	—	2	1	no	—
639	C₂²×C₄	—	2	1	no	—
640	C₂²×C₄	—	2	1	no	—
641	C₂²×C₄	—	2	1	no	—
642	C₂²×C₄	—	2	1	no	—
643	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
644	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
645	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
646	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
647	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
648	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
649	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
650	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
651	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
652	M₁₆	—	52	2	no	—
653	M₁₆	—	52	2	no	—
654	C₂×C₈	—	26	1	no	—
655	C₂×C₈	—	26	1	no	—
656	C₂×C₈	—	26	1	no	—
657	C₂×C₈	—	26	1	no	—
658	C₂×C₈	—	26	1	no	—
659	C₂×C₈	—	26	1	no	—
660	C₂×C₈	—	26	1	no	—
661	C₂×C₈	—	26	1	no	—
662	C₂×C₈	—	52	2	no	—
663	C₂×C₈	—	52	2	no	—
664	C₂×C₈	—	52	2	no	—
665	C₄⋊C₄	—	2	1	no	—
666	C₄⋊C₄	—	2	1	no	—
667	C₄⋊C₄	—	2	1	no	—
668	C₄⋊C₄	—	2	1	no	—
669	C₄⋊C₄	—	2	1	no	—
670	C₄⋊C₄	—	2	1	no	—
671	C₄⋊C₄	—	2	1	no	—
672	C₄⋊C₄	—	2	1	no	—
673	C₄⋊C₄	—	2	1	no	—
674	C₄⋊C₄	—	2	1	no	—
675	C₄⋊C₄	—	2	1	no	—
676	C₄⋊C₄	—	2	1	no	—
677	C₄⋊C₄	—	2	1	no	—
678	C₄⋊C₄	—	2	1	no	—
679	C₄⋊C₄	—	2	1	no	—
680	C₄⋊C₄	—	2	1	no	—
681	C₄⋊C₄	—	2	1	no	—
682	C₄⋊C₄	—	2	1	no	—
683	C₄⋊C₄	—	2	1	no	—
684	C₄⋊C₄	—	2	1	no	—
685	C₄⋊C₄	—	2	1	no	—
686	C₄⋊C₄	—	2	1	no	—
687	C₄⋊C₄	—	2	1	no	—
688	C₄⋊C₄	—	2	1	no	—
689	C₄⋊C₄	—	2	1	no	—
690	C₄⋊C₄	—	2	1	no	—
691	C₄⋊C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
692	C₄⋊C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
693	C₄⋊C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
694	C₄⋊C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
695	C₄⋊C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
696	C₄⋊C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
697	C₄⋊C₄	C₂²×Dic₁₃	1	1	yes	characteristic
698	C₄⋊C₄	C₂²×Dic₁₃	1	1	yes	characteristic
699	C₄⋊C₄	C₂²×Dic₁₃	1	1	yes	characteristic
700	C₄⋊C₄	C₂²×Dic₁₃	1	1	yes	characteristic
701	C₄⋊C₄	C₂²×Dic₁₃	1	1	yes	characteristic
702	C₄⋊C₄	C₂²×Dic₁₃	1	1	yes	characteristic
703	C₂²⋊C₄	—	2	1	no	—
704	C₂²⋊C₄	—	2	1	no	—
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	C₂²⋊Dic₁₃	1	1	yes	characteristic
717	C₂²⋊C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
718	C₂²⋊C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
719	C₂²⋊C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
720	C₂²⋊C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
721	C₂²⋊C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
722	C₄²	—	2	1	no	—
723	C₄²	—	2	1	no	—
724	C₄²	—	2	1	no	—
725	C₄²	—	2	1	no	—
726	C₄²	—	2	1	no	—
727	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
728	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
729	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
730	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
731	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
732	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
733	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
734	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
735	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
736	C₄²	C₂³×D₁₃	1	1	yes	characteristic
737	C₁₃	#17680	1	1	yes	characteristic, complemented, Sylow
738	C₂³	—	2	1	no	—
739	C₂³	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
740	C₂³	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
741	C₂³	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
742	Q₈	—	4	1	no	—
743	Q₈	—	4	1	no	—
744	Q₈	—	4	2	no	—
745	Q₈	—	8	1	no	—
746	D₄	—	2	2	no	—
747	D₄	—	2	2	no	—
748	D₄	—	4	1	no	—
749	D₄	—	4	1	no	—
750	D₄	—	4	2	no	—
751	D₄	—	4	2	no	—
752	D₄	—	8	1	no	—
753	C₂×C₄	—	2	2	no	—
754	C₂×C₄	—	2	1	no	—
755	C₂×C₄	—	2	1	no	—
756	C₂×C₄	—	2	1	no	—
757	C₂×C₄	—	2	1	no	—
758	C₂×C₄	—	2	1	no	—
759	C₂×C₄	—	2	1	no	—
760	C₂×C₄	—	2	1	no	—
761	C₂×C₄	—	4	1	no	—
762	C₂×C₄	—	4	1	no	—
763	C₂×C₄	—	4	1	no	—
764	C₂×C₄	—	4	1	no	—
765	C₂×C₄	—	4	1	no	—
766	C₂×C₄	—	4	1	no	—
767	C₂×C₄	—	4	1	no	—
768	C₂×C₄	—	4	1	no	—
769	C₂×C₄	—	4	2	no	—
770	C₂×C₄	—	4	2	no	—
771	C₂×C₄	—	4	2	no	—
772	C₂×C₄	—	8	1	no	—
773	C₂×C₄	—	8	1	no	—
774	C₂×C₄	—	8	1	no	—
775	C₂×C₄	—	8	1	no	—
776	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
777	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
778	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
779	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
780	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
781	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
782	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
783	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
784	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
785	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
786	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
787	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
788	C₈	—	26	2	no	—
789	C₈	—	52	1	no	—
790	C₈	—	52	1	no	—
791	C₈	—	52	1	no	—
792	C₈	—	52	1	no	—
793	C₈	—	52	1	no	—
794	C₈	—	52	1	no	—
795	C₈	—	52	1	no	—
796	C₂²	—	2	1	no	—
797	C₂²	—	2	1	no	—
798	C₂²	—	2	1	no	—
799	C₂²	—	2	1	no	—
800	C₂²	—	2	1	no	—
801	C₂²	—	2	1	no	—
802	C₂²	—	2	1	no	—
803	C₂²	—	2	1	no	—
804	C₂²	—	4	1	no	—
805	C₂²	—	4	1	no	—
806	C₂²	—	4	1	no	—
807	C₂²	#11718897	1	2	yes	—
808	C₂²	C₂²×C₂²⋊Dic₁₃	1	1	yes	characteristic
809	C₄	—	2	1	no	—
810	C₄	—	2	1	no	—
811	C₄	—	2	1	no	—
812	C₄	—	2	1	no	—
813	C₄	—	2	1	no	—
814	C₄	—	2	1	no	—
815	C₄	—	2	1	no	—
816	C₄	—	2	1	no	—
817	C₄	—	2	1	no	—
818	C₄	—	2	1	no	—
819	C₄	—	2	1	no	—
820	C₄	—	2	1	no	—
821	C₄	—	4	1	no	—
822	C₄	—	4	1	no	—
823	C₄	—	4	1	no	—
824	C₄	—	4	1	no	—
825	C₄	—	4	1	no	—
826	C₄	—	4	1	no	—
827	C₄	—	4	1	no	—
828	C₂	—	2	2	no	—
829	C₂	—	4	1	no	—
830	C₂	—	4	1	no	—
831	C₂	—	8	1	no	—
832	C₂	#13123319	1	1	yes	characteristic
833	C₂	C₂×#11718897	1	1	yes	characteristic
834	C₂	#13123383	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×C₂²⋊Dic₁₃
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₄²	C₂³×D₁₃
Fitting, prime radical	C₁₃×#3515	C₂
socle	C₂²×C₁₃	C₂²×C₂²⋊C₄
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	#3515	D₁₃
hypocenter	C₁₃	#17680
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₄×#41 ◁ #3515

Complements

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

N	H ≅ G/N	type
1. #13123850	C₂	semidirect
2. #13123487	C₂	semidirect
3. #13113474	C₂	semidirect
4. #13113467	C₂	semidirect
5. #13113467	C₂	semidirect
6. #13113463	C₂	semidirect
7. #13113456	C₂	semidirect
8. #13113456	C₂	semidirect
9. #13113451	C₂	semidirect
10. #13113443	C₂	semidirect
11. #13113438	C₂	semidirect
12. #13113438	C₂	semidirect
13. #13113424	C₂	semidirect
14. C₂×#11718135	C₂	semidirect
737. C₁₃	#17680	semidirect

Maximal subgroups

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

subgroup	index
#13123850	2
#13123487	2
#13113474	2
#13113467	2
#13113463	2
#13113456	2
#13113451	2
#13113443	2
#13113438	2
#13113424	2
C₂×#11718135	2
C₁₃×#3515	2
#17680	13