Subgroups — C₁₃×#22435 #15708774

Order 3328.

1472 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×C₁₃×#41	C₂	1	1	yes	maximal, characteristic
2	D₄×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#421	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2293	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1980	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1962	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1897	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1871	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1806	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1789	C₂	1	2	yes	maximal, complemented
11	C₄×C₁₃×#104	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×#41	C₂²	1	2	yes	—
13	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	complemented
14	C₁₃×#550	C₄	1	1	yes	characteristic, complemented
15	D₄×Q₈×C₁₃	C₄	1	1	yes	characteristic, complemented
16	C₁₃×#548	C₄	1	2	yes	complemented
17	C₁₃×#547	—	2	1	no	—
18	C₁₃×#547	C₄	1	1	yes	characteristic, complemented
19	C₁₃×#546	—	2	2	no	—
20	C₁₃×#546	C₄	1	2	yes	complemented
21	D₄²×C₁₃	—	2	1	no	—
22	D₄²×C₁₃	C₄	1	1	yes	characteristic, complemented
23	C₁₃×#532	—	2	1	no	—
24	C₁₃×#532	C₂²	1	1	yes	characteristic
25	C₁₃×#525	—	2	2	no	—
26	C₁₃×#525	C₂²	1	2	yes	—
27	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₁₃	—	2	1	no	—
29	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#117	C₂²	1	2	yes	complemented
31	C₁₃×#436	—	2	1	no	—
32	C₁₃×#435	—	2	2	no	—
33	C₈×D₄×C₁₃	—	2	1	no	—
34	C₁₃×#423	C₂²	1	1	yes	characteristic, complemented
35	C₁₃×#421	—	2	8	no	—
36	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×#104	C₂²	1	2	yes	—
38	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×#104	C₂²	1	2	yes	complemented
40	C₂×C₁₃×#104	C₂²	1	2	yes	complemented
41	C₂×C₁₃×#104	C₂²	1	2	yes	complemented
42	C₂×C₁₃×#104	C₂²	1	2	yes	complemented
43	C₁₃×#407	C₂²	1	2	yes	complemented
44	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic, complemented
45	C₁₃×#390	—	2	1	no	—
46	C₁₃×#389	—	2	1	no	—
47	C₁₃×#388	—	2	2	no	—
48	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
49	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
50	C₄³×C₁₃	C₂²	1	1	yes	characteristic, complemented
51	C₁₃×#339	C₂²	1	1	yes	characteristic, complemented
52	C₁₃×#339	C₂²	1	1	yes	characteristic, complemented
53	C₁₃×#339	C₂²	1	2	yes	complemented
54	C₂×C₁₃×#41	—	2	2	no	—
55	C₂×C₁₃×#41	—	2	2	no	—
56	C₂×C₁₃×#41	—	2	4	no	—
57	C₂×C₁₃×#41	—	2	4	no	—
58	C₂×C₁₃×#41	—	4	2	no	—
59	C₂×C₁₃×#41	—	4	2	no	—
60	C₂×C₁₃×#41	C₂×C₄	1	2	yes	—
61	C₂×C₁₃×#41	C₂×C₄	1	2	yes	—
62	C₂×C₁₃×#41	C₂³	1	2	yes	—
63	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
64	C₂²×Q₈×C₁₃	C₂×C₄	1	2	yes	—
65	C₂²×D₄×C₁₃	—	2	2	no	—
66	C₂²×D₄×C₁₃	—	2	1	no	—
67	C₂²×D₄×C₁₃	C₂×C₄	1	2	yes	—
68	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
69	C₂³×C₄×C₁₃	—	2	2	no	—
70	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
71	C₂×C₁₃×M₁₆	—	2	2	no	—
72	C₂×C₁₃×M₁₆	—	2	4	no	—
73	C₂×C₁₃×M₁₆	—	4	2	no	—
74	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
75	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
76	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
77	C₂²×C₈×C₁₃	—	2	2	no	—
78	C₁₃×C₄⋊Q₈	—	2	1	no	—
79	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
80	C₁₃×#127	—	2	1	no	—
81	C₁₃×#127	C₂×C₄	1	1	yes	characteristic
82	C₁₃×#124	—	2	2	no	—
83	C₁₃×#124	C₂×C₄	1	2	yes	—
84	C₁₃×#123	—	2	2	no	—
85	C₁₃×#123	—	2	2	no	—
86	C₁₃×#123	—	2	2	no	—
87	C₁₃×C₂²⋊Q₈	—	2	2	no	—
88	C₁₃×C₂²⋊Q₈	—	2	2	no	—
89	C₁₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
90	C₁₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
91	C₁₃×#121	—	2	2	no	—
92	C₁₃×#121	—	2	1	no	—
93	C₁₃×#121	—	2	1	no	—
94	C₁₃×#121	—	2	1	no	—
95	C₁₃×#121	—	2	1	no	—
96	C₁₃×#121	—	2	2	no	—
97	C₁₃×#121	—	2	2	no	—
98	C₁₃×#121	C₂×C₄	1	2	yes	—
99	C₁₃×#121	C₂×C₄	1	2	yes	—
100	C₁₃×#120	—	2	2	no	—
101	C₁₃×#120	—	2	2	no	—
102	C₁₃×#120	—	2	2	no	—
103	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
104	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
105	C₄×D₄×C₁₃	—	2	1	no	—
106	C₄×D₄×C₁₃	—	2	2	no	—
107	C₄×D₄×C₁₃	—	2	1	no	—
108	C₄×D₄×C₁₃	—	2	1	no	—
109	C₄×D₄×C₁₃	—	2	2	no	—
110	C₄×D₄×C₁₃	—	2	1	no	—
111	C₄×D₄×C₁₃	—	2	2	no	—
112	C₄×D₄×C₁₃	—	2	1	no	—
113	C₄×D₄×C₁₃	—	2	1	no	—
114	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
115	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
116	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
117	C₄×D₄×C₁₃	C₂×C₄	1	2	yes	—
118	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
119	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
120	C₄×D₄×C₁₃	D₄	1	2	yes	—
121	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
122	C₁₃×#117	—	2	1	no	—
123	C₁₃×#117	—	2	4	no	—
124	C₁₃×#117	—	4	2	no	—
125	C₁₃×#117	C₂³	1	1	yes	characteristic
126	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
127	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
128	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
129	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
130	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
131	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
132	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
133	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
134	C₂×C₄²×C₁₃	—	2	1	no	—
135	C₂×C₄²×C₁₃	—	2	1	no	—
136	C₂×C₄²×C₁₃	—	2	1	no	—
137	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
138	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
139	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
140	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
141	C₁₃×C₄⋊C₈	—	2	1	no	—
142	C₁₃×C₄⋊C₈	—	2	1	no	—
143	C₁₃×#104	—	2	4	no	—
144	C₁₃×#104	—	2	2	no	—
145	C₁₃×#104	—	2	4	no	—
146	C₁₃×#104	—	2	4	no	—
147	C₁₃×#104	—	4	2	no	—
148	C₁₃×#104	—	4	2	no	—
149	C₁₃×#104	D₄	1	4	yes	complemented
150	C₁₃×C₂²⋊C₈	—	2	2	no	—
151	C₁₃×C₂²⋊C₈	—	2	2	no	—
152	C₁₃×#97	—	2	1	no	—
153	C₄×C₈×C₁₃	—	2	1	no	—
154	C₁₃×#95	—	2	2	no	—
155	C₁₃×#95	—	2	1	no	—
156	#22435	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
157	C₂⁴×C₁₃	—	2	2	no	—
158	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
159	C₁₃×#41	—	2	1	no	—
160	C₁₃×#41	—	2	1	no	—
161	C₁₃×#41	—	2	4	no	—
162	C₁₃×#41	—	2	4	no	—
163	C₁₃×#41	—	2	2	no	—
164	C₁₃×#41	—	2	2	no	—
165	C₁₃×#41	—	2	2	no	—
166	C₁₃×#41	—	2	2	no	—
167	C₁₃×#41	—	4	4	no	—
168	C₁₃×#41	—	4	4	no	—
169	C₁₃×#41	—	4	2	no	—
170	C₁₃×#41	—	4	2	no	—
171	C₁₃×#41	—	4	4	no	—
172	C₁₃×#41	—	4	4	no	—
173	C₁₃×#41	C₂×D₄	1	2	yes	—
174	C₁₃×#41	#41	1	2	yes	—
175	C₂×Q₈×C₁₃	—	2	2	no	—
176	C₂×Q₈×C₁₃	—	2	4	no	—
177	C₂×Q₈×C₁₃	—	4	2	no	—
178	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
179	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
180	C₂×D₄×C₁₃	—	2	1	no	—
181	C₂×D₄×C₁₃	—	2	4	no	—
182	C₂×D₄×C₁₃	—	2	2	no	—
183	C₂×D₄×C₁₃	—	2	2	no	—
184	C₂×D₄×C₁₃	—	2	2	no	—
185	C₂×D₄×C₁₃	—	2	2	no	—
186	C₂×D₄×C₁₃	—	2	2	no	—
187	C₂×D₄×C₁₃	—	2	1	no	—
188	C₂×D₄×C₁₃	—	2	2	no	—
189	C₂×D₄×C₁₃	—	2	1	no	—
190	C₂×D₄×C₁₃	—	4	2	no	—
191	C₂×D₄×C₁₃	—	4	2	no	—
192	C₂×D₄×C₁₃	—	4	4	no	—
193	C₂×D₄×C₁₃	—	4	4	no	—
194	C₂×D₄×C₁₃	—	4	4	no	—
195	C₂×D₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
196	C₂×D₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
197	C₂×D₄×C₁₃	C₂²⋊C₄	1	2	yes	—
198	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
199	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
200	C₂²×C₄×C₁₃	—	2	2	no	—
201	C₂²×C₄×C₁₃	—	2	1	no	—
202	C₂²×C₄×C₁₃	—	2	2	no	—
203	C₂²×C₄×C₁₃	—	2	2	no	—
204	C₂²×C₄×C₁₃	—	2	2	no	—
205	C₂²×C₄×C₁₃	—	2	2	no	—
206	C₂²×C₄×C₁₃	—	2	1	no	—
207	C₂²×C₄×C₁₃	—	2	1	no	—
208	C₂²×C₄×C₁₃	—	2	1	no	—
209	C₂²×C₄×C₁₃	—	2	2	no	—
210	C₂²×C₄×C₁₃	—	2	2	no	—
211	C₂²×C₄×C₁₃	—	2	2	no	—
212	C₂²×C₄×C₁₃	—	2	1	no	—
213	C₂²×C₄×C₁₃	—	2	2	no	—
214	C₂²×C₄×C₁₃	—	4	4	no	—
215	C₂²×C₄×C₁₃	—	4	4	no	—
216	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
217	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
218	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
219	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
220	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
221	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
222	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
223	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
224	C₁₃×M₁₆	—	2	1	no	—
225	C₁₃×M₁₆	—	2	2	no	—
226	C₁₃×M₁₆	—	2	1	no	—
227	C₁₃×M₁₆	—	2	1	no	—
228	C₁₃×M₁₆	—	2	2	no	—
229	C₁₃×M₁₆	—	4	4	no	—
230	C₁₃×M₁₆	C₂×D₄	1	2	yes	complemented
231	C₂×C₈×C₁₃	—	2	1	no	—
232	C₂×C₈×C₁₃	—	2	1	no	—
233	C₂×C₈×C₁₃	—	2	2	no	—
234	C₂×C₈×C₁₃	—	4	4	no	—
235	C₁₃×C₄⋊C₄	—	2	1	no	—
236	C₁₃×C₄⋊C₄	—	2	2	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	2	no	—
241	C₁₃×C₄⋊C₄	—	4	4	no	—
242	C₁₃×C₄⋊C₄	—	4	2	no	—
243	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
244	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
245	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	2	yes	—
246	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
247	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
248	C₁₃×C₂²⋊C₄	—	2	2	no	—
249	C₁₃×C₂²⋊C₄	—	2	2	no	—
250	C₁₃×C₂²⋊C₄	—	2	1	no	—
251	C₁₃×C₂²⋊C₄	—	2	2	no	—
252	C₁₃×C₂²⋊C₄	—	2	2	no	—
253	C₁₃×C₂²⋊C₄	—	2	1	no	—
254	C₁₃×C₂²⋊C₄	—	2	1	no	—
255	C₁₃×C₂²⋊C₄	—	2	2	no	—
256	C₁₃×C₂²⋊C₄	—	2	2	no	—
257	C₁₃×C₂²⋊C₄	—	4	4	no	—
258	C₁₃×C₂²⋊C₄	—	4	4	no	—
259	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	—
260	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	—
261	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	—
262	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	—
263	C₄²×C₁₃	—	2	1	no	—
264	C₄²×C₁₃	—	2	1	no	—
265	C₄²×C₁₃	—	2	1	no	—
266	C₄²×C₁₃	—	2	1	no	—
267	C₄²×C₁₃	—	2	2	no	—
268	C₄²×C₁₃	—	2	1	no	—
269	C₄²×C₁₃	—	2	1	no	—
270	C₄²×C₁₃	—	2	2	no	—
271	C₄²×C₁₃	—	4	2	no	—
272	C₄²×C₁₃	—	4	2	no	—
273	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
274	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
275	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
276	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
277	C₄²×C₁₃	C₂×D₄	1	2	yes	complemented
278	D₄×#41	C₂×C₁₃	1	1	yes	characteristic
279	D₄×M₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
280	C₂×#421	C₂×C₁₃	1	2	yes	complemented
281	#2293	C₂×C₁₃	1	1	yes	characteristic, complemented
282	#1980	C₂×C₁₃	1	1	yes	characteristic, complemented
283	#1962	C₂×C₁₃	1	1	yes	characteristic, complemented
284	#1897	C₂×C₁₃	1	2	yes	complemented
285	#1871	C₂×C₁₃	1	2	yes	complemented
286	#1806	C₂×C₁₃	1	1	yes	characteristic, complemented
287	#1789	C₂×C₁₃	1	2	yes	complemented
288	C₄×#104	C₂×C₁₃	1	1	yes	characteristic, complemented
289	C₂³×C₁₃	—	2	1	no	—
290	C₂³×C₁₃	—	2	2	no	—
291	C₂³×C₁₃	—	2	2	no	—
292	C₂³×C₁₃	—	2	2	no	—
293	C₂³×C₁₃	—	4	2	no	—
294	C₂³×C₁₃	—	4	2	no	—
295	C₂³×C₁₃	—	4	4	no	—
296	C₂³×C₁₃	—	4	4	no	—
297	C₂³×C₁₃	—	8	2	no	—
298	C₂³×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
299	C₂³×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
300	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
301	Q₈×C₁₃	—	2	1	no	—
302	Q₈×C₁₃	—	2	2	no	—
303	Q₈×C₁₃	—	2	2	no	—
304	Q₈×C₁₃	—	4	4	no	—
305	Q₈×C₁₃	C₄×D₄	1	2	yes	—
306	D₄×C₁₃	—	2	2	no	—
307	D₄×C₁₃	—	2	2	no	—
308	D₄×C₁₃	—	2	2	no	—
309	D₄×C₁₃	—	2	1	no	—
310	D₄×C₁₃	—	2	2	no	—
311	D₄×C₁₃	—	2	2	no	—
312	D₄×C₁₃	—	2	2	no	—
313	D₄×C₁₃	—	4	2	no	—
314	D₄×C₁₃	—	4	4	no	—
315	D₄×C₁₃	—	4	4	no	—
316	D₄×C₁₃	—	4	4	no	—
317	D₄×C₁₃	—	4	4	no	—
318	D₄×C₁₃	—	4	2	no	—
319	D₄×C₁₃	—	4	2	no	—
320	D₄×C₁₃	—	4	2	no	—
321	D₄×C₁₃	—	8	1	no	—
322	D₄×C₁₃	—	8	2	no	—
323	D₄×C₁₃	C₄×D₄	1	2	yes	—
324	C₂×C₄×C₁₃	—	2	1	no	—
325	C₂×C₄×C₁₃	—	2	2	no	—
326	C₂×C₄×C₁₃	—	2	2	no	—
327	C₂×C₄×C₁₃	—	2	2	no	—
328	C₂×C₄×C₁₃	—	2	2	no	—
329	C₂×C₄×C₁₃	—	2	2	no	—
330	C₂×C₄×C₁₃	—	2	2	no	—
331	C₂×C₄×C₁₃	—	2	2	no	—
332	C₂×C₄×C₁₃	—	2	2	no	—
333	C₂×C₄×C₁₃	—	2	2	no	—
334	C₂×C₄×C₁₃	—	2	2	no	—
335	C₂×C₄×C₁₃	—	2	2	no	—
336	C₂×C₄×C₁₃	—	2	2	no	—
337	C₂×C₄×C₁₃	—	2	2	no	—
338	C₂×C₄×C₁₃	—	2	2	no	—
339	C₂×C₄×C₁₃	—	2	1	no	—
340	C₂×C₄×C₁₃	—	2	1	no	—
341	C₂×C₄×C₁₃	—	2	2	no	—
342	C₂×C₄×C₁₃	—	2	2	no	—
343	C₂×C₄×C₁₃	—	4	1	no	—
344	C₂×C₄×C₁₃	—	4	4	no	—
345	C₂×C₄×C₁₃	—	4	4	no	—
346	C₂×C₄×C₁₃	—	4	4	no	—
347	C₂×C₄×C₁₃	—	4	1	no	—
348	C₂×C₄×C₁₃	—	4	1	no	—
349	C₂×C₄×C₁₃	—	4	1	no	—
350	C₂×C₄×C₁₃	—	4	1	no	—
351	C₂×C₄×C₁₃	—	4	2	no	—
352	C₂×C₄×C₁₃	—	4	2	no	—
353	C₂×C₄×C₁₃	—	4	2	no	—
354	C₂×C₄×C₁₃	—	4	2	no	—
355	C₂×C₄×C₁₃	—	4	2	no	—
356	C₂×C₄×C₁₃	—	4	2	no	—
357	C₂×C₄×C₁₃	—	8	1	no	—
358	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
359	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
360	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
361	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
362	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
363	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
364	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
365	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
366	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
367	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
368	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
369	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
370	C₈×C₁₃	—	2	2	no	—
371	C₈×C₁₃	—	4	2	no	—
372	C₈×C₁₃	—	4	1	no	—
373	C₂²×#41	C₂²×C₁₃	1	2	yes	—
374	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	complemented
375	#550	C₄×C₁₃	1	1	yes	characteristic, complemented
376	D₄×Q₈	C₄×C₁₃	1	1	yes	characteristic, complemented
377	#548	C₄×C₁₃	1	2	yes	complemented
378	#547	—	2	1	no	—
379	#547	C₄×C₁₃	1	1	yes	characteristic, complemented
380	#546	—	2	2	no	—
381	#546	C₄×C₁₃	1	2	yes	complemented
382	D₄²	—	2	1	no	—
383	D₄²	C₄×C₁₃	1	1	yes	characteristic, complemented
384	#532	—	2	1	no	—
385	#532	C₂²×C₁₃	1	1	yes	characteristic
386	#525	—	2	2	no	—
387	#525	C₂²×C₁₃	1	2	yes	—
388	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
389	C₂×C₄×D₄	—	2	1	no	—
390	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
391	C₂×#117	C₂²×C₁₃	1	2	yes	complemented
392	#436	—	2	1	no	—
393	#435	—	2	2	no	—
394	C₈×D₄	—	2	1	no	—
395	#423	C₂²×C₁₃	1	1	yes	characteristic, complemented
396	#421	—	2	8	no	—
397	C₂×#104	C₂²×C₁₃	1	2	yes	—
398	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic
399	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic
400	C₂×#104	C₂²×C₁₃	1	2	yes	complemented
401	C₂×#104	C₂²×C₁₃	1	2	yes	complemented
402	C₂×#104	C₂²×C₁₃	1	2	yes	complemented
403	C₂×#104	C₂²×C₁₃	1	2	yes	complemented
404	#407	C₂²×C₁₃	1	2	yes	complemented
405	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
406	#390	—	2	1	no	—
407	#389	—	2	1	no	—
408	#388	—	2	2	no	—
409	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
410	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
411	C₄³	C₂²×C₁₃	1	1	yes	characteristic, complemented
412	#339	C₂²×C₁₃	1	2	yes	complemented
413	#339	C₂²×C₁₃	1	1	yes	characteristic, complemented
414	#339	C₂²×C₁₃	1	1	yes	characteristic, complemented
415	C₂²×C₁₃	—	2	1	no	—
416	C₂²×C₁₃	—	2	1	no	—
417	C₂²×C₁₃	—	2	2	no	—
418	C₂²×C₁₃	—	2	2	no	—
419	C₂²×C₁₃	—	2	2	no	—
420	C₂²×C₁₃	—	2	2	no	—
421	C₂²×C₁₃	—	2	2	no	—
422	C₂²×C₁₃	—	2	2	no	—
423	C₂²×C₁₃	—	2	2	no	—
424	C₂²×C₁₃	—	4	1	no	—
425	C₂²×C₁₃	—	4	1	no	—
426	C₂²×C₁₃	—	4	2	no	—
427	C₂²×C₁₃	—	4	2	no	—
428	C₂²×C₁₃	—	4	2	no	—
429	C₂²×C₁₃	—	8	2	no	—
430	C₂²×C₁₃	—	8	2	no	—
431	C₂²×C₁₃	—	8	8	no	—
432	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
433	C₂²×C₁₃	D₄²	1	1	yes	characteristic
434	C₂²×C₁₃	#546	1	1	yes	characteristic
435	C₄×C₁₃	—	2	2	no	—
436	C₄×C₁₃	—	2	2	no	—
437	C₄×C₁₃	—	2	2	no	—
438	C₄×C₁₃	—	2	1	no	—
439	C₄×C₁₃	—	2	1	no	—
440	C₄×C₁₃	—	2	1	no	—
441	C₄×C₁₃	—	4	2	no	—
442	C₄×C₁₃	—	4	2	no	—
443	C₄×C₁₃	—	4	2	no	—
444	C₄×C₁₃	—	4	1	no	—
445	C₄×C₁₃	—	4	1	no	—
446	C₄×C₁₃	—	8	2	no	—
447	C₄×C₁₃	#421	1	2	yes	complemented
448	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
449	C₄×C₁₃	#518	1	1	yes	characteristic
450	C₄×C₁₃	D₄²	1	1	yes	characteristic
451	C₄×C₁₃	#546	1	1	yes	characteristic
452	C₂×#41	—	2	2	no	—
453	C₂×#41	—	2	2	no	—
454	C₂×#41	—	2	4	no	—
455	C₂×#41	—	2	4	no	—
456	C₂×#41	—	4	2	no	—
457	C₂×#41	—	4	2	no	—
458	C₂×#41	C₂×C₄×C₁₃	1	2	yes	—
459	C₂×#41	C₂×C₄×C₁₃	1	2	yes	—
460	C₂×#41	C₂³×C₁₃	1	2	yes	—
461	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
462	C₂²×Q₈	C₂×C₄×C₁₃	1	2	yes	—
463	C₂²×D₄	—	2	2	no	—
464	C₂²×D₄	—	2	1	no	—
465	C₂²×D₄	C₂×C₄×C₁₃	1	2	yes	—
466	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
467	C₂³×C₄	—	2	2	no	—
468	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
469	C₂×M₁₆	—	2	2	no	—
470	C₂×M₁₆	—	2	4	no	—
471	C₂×M₁₆	—	4	2	no	—
472	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
473	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
474	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
475	C₂²×C₈	—	2	2	no	—
476	C₄⋊Q₈	—	2	1	no	—
477	C₄⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
478	#127	—	2	1	no	—
479	#127	C₂×C₄×C₁₃	1	1	yes	characteristic
480	#124	—	2	2	no	—
481	#124	C₂×C₄×C₁₃	1	2	yes	—
482	#123	—	2	2	no	—
483	#123	—	2	2	no	—
484	#123	—	2	2	no	—
485	C₂²⋊Q₈	—	2	2	no	—
486	C₂²⋊Q₈	—	2	2	no	—
487	C₂²⋊Q₈	C₂×C₄×C₁₃	1	2	yes	—
488	C₂²⋊Q₈	C₂×C₄×C₁₃	1	2	yes	—
489	#121	—	2	2	no	—
490	#121	—	2	1	no	—
491	#121	—	2	1	no	—
492	#121	—	2	1	no	—
493	#121	—	2	1	no	—
494	#121	—	2	2	no	—
495	#121	—	2	2	no	—
496	#121	C₂×C₄×C₁₃	1	2	yes	—
497	#121	C₂×C₄×C₁₃	1	2	yes	—
498	#120	—	2	2	no	—
499	#120	—	2	2	no	—
500	#120	—	2	2	no	—
501	C₄×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
502	C₄×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
503	C₄×D₄	—	2	1	no	—
504	C₄×D₄	—	2	2	no	—
505	C₄×D₄	—	2	1	no	—
506	C₄×D₄	—	2	1	no	—
507	C₄×D₄	—	2	2	no	—
508	C₄×D₄	—	2	1	no	—
509	C₄×D₄	—	2	2	no	—
510	C₄×D₄	—	2	1	no	—
511	C₄×D₄	—	2	1	no	—
512	C₄×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
513	C₄×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
514	C₄×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
515	C₄×D₄	C₂×C₄×C₁₃	1	2	yes	—
516	C₄×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
517	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
518	C₄×D₄	D₄×C₁₃	1	2	yes	—
519	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
520	#117	—	2	1	no	—
521	#117	—	2	4	no	—
522	#117	—	4	2	no	—
523	#117	C₂³×C₁₃	1	1	yes	characteristic
524	C₂×C₄⋊C₄	—	2	1	no	—
525	C₂×C₄⋊C₄	—	2	2	no	—
526	C₂×C₄⋊C₄	—	2	1	no	—
527	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
528	C₂×C₂²⋊C₄	—	2	2	no	—
529	C₂×C₂²⋊C₄	—	2	2	no	—
530	C₂×C₂²⋊C₄	—	2	2	no	—
531	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
532	C₂×C₄²	—	2	1	no	—
533	C₂×C₄²	—	2	1	no	—
534	C₂×C₄²	—	2	1	no	—
535	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
536	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
537	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
538	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
539	C₄⋊C₈	—	2	1	no	—
540	C₄⋊C₈	—	2	1	no	—
541	#104	—	2	4	no	—
542	#104	—	2	2	no	—
543	#104	—	2	4	no	—
544	#104	—	2	4	no	—
545	#104	—	4	2	no	—
546	#104	—	4	2	no	—
547	#104	D₄×C₁₃	1	4	yes	complemented
548	C₂²⋊C₈	—	2	2	no	—
549	C₂²⋊C₈	—	2	2	no	—
550	#97	—	2	1	no	—
551	C₄×C₈	—	2	1	no	—
552	#95	—	2	2	no	—
553	#95	—	2	1	no	—
554	C₂×C₁₃	—	2	1	no	—
555	C₂×C₁₃	—	2	1	no	—
556	C₂×C₁₃	—	4	2	no	—
557	C₂×C₁₃	—	4	2	no	—
558	C₂×C₁₃	—	4	2	no	—
559	C₂×C₁₃	—	8	2	no	—
560	C₂×C₁₃	D₄×C₂²⋊C₄	1	1	yes	characteristic
561	C₂×C₁₃	C₂×#421	1	1	yes	characteristic
562	C₂×C₁₃	#2901	1	1	yes	characteristic
563	C₂⁴	—	2	2	no	—
564	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
565	#41	—	2	1	no	—
566	#41	—	2	1	no	—
567	#41	—	2	4	no	—
568	#41	—	2	4	no	—
569	#41	—	2	2	no	—
570	#41	—	2	2	no	—
571	#41	—	2	2	no	—
572	#41	—	2	2	no	—
573	#41	—	4	4	no	—
574	#41	—	4	4	no	—
575	#41	—	4	2	no	—
576	#41	—	4	2	no	—
577	#41	—	4	4	no	—
578	#41	—	4	4	no	—
579	#41	C₂×D₄×C₁₃	1	2	yes	—
580	#41	C₁₃×#41	1	2	yes	—
581	C₂×Q₈	—	2	2	no	—
582	C₂×Q₈	—	2	4	no	—
583	C₂×Q₈	—	4	2	no	—
584	C₂×Q₈	C₂²×C₄×C₁₃	1	2	yes	—
585	C₂×Q₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
586	C₂×D₄	—	2	1	no	—
587	C₂×D₄	—	2	4	no	—
588	C₂×D₄	—	2	2	no	—
589	C₂×D₄	—	2	2	no	—
590	C₂×D₄	—	2	2	no	—
591	C₂×D₄	—	2	2	no	—
592	C₂×D₄	—	2	2	no	—
593	C₂×D₄	—	2	1	no	—
594	C₂×D₄	—	2	2	no	—
595	C₂×D₄	—	2	1	no	—
596	C₂×D₄	—	4	2	no	—
597	C₂×D₄	—	4	2	no	—
598	C₂×D₄	—	4	4	no	—
599	C₂×D₄	—	4	4	no	—
600	C₂×D₄	—	4	4	no	—
601	C₂×D₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
602	C₂×D₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
603	C₂×D₄	C₁₃×C₂²⋊C₄	1	2	yes	—
604	C₂×D₄	C₂²×C₄×C₁₃	1	2	yes	—
605	C₂×D₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
606	C₂²×C₄	—	2	1	no	—
607	C₂²×C₄	—	2	2	no	—
608	C₂²×C₄	—	2	2	no	—
609	C₂²×C₄	—	2	2	no	—
610	C₂²×C₄	—	2	2	no	—
611	C₂²×C₄	—	2	2	no	—
612	C₂²×C₄	—	2	1	no	—
613	C₂²×C₄	—	2	1	no	—
614	C₂²×C₄	—	2	1	no	—
615	C₂²×C₄	—	2	2	no	—
616	C₂²×C₄	—	2	2	no	—
617	C₂²×C₄	—	2	2	no	—
618	C₂²×C₄	—	2	1	no	—
619	C₂²×C₄	—	2	2	no	—
620	C₂²×C₄	—	4	4	no	—
621	C₂²×C₄	—	4	4	no	—
622	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
623	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
624	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
625	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
626	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
627	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
628	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
629	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
630	M₁₆	—	2	1	no	—
631	M₁₆	—	2	2	no	—
632	M₁₆	—	2	1	no	—
633	M₁₆	—	2	1	no	—
634	M₁₆	—	2	2	no	—
635	M₁₆	—	4	4	no	—
636	M₁₆	C₂×D₄×C₁₃	1	2	yes	complemented
637	C₂×C₈	—	2	1	no	—
638	C₂×C₈	—	2	1	no	—
639	C₂×C₈	—	2	2	no	—
640	C₂×C₈	—	4	4	no	—
641	C₄⋊C₄	—	2	1	no	—
642	C₄⋊C₄	—	2	2	no	—
643	C₄⋊C₄	—	2	1	no	—
644	C₄⋊C₄	—	2	1	no	—
645	C₄⋊C₄	—	2	1	no	—
646	C₄⋊C₄	—	2	2	no	—
647	C₄⋊C₄	—	4	4	no	—
648	C₄⋊C₄	—	4	2	no	—
649	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
650	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
651	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
652	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
653	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
654	C₂²⋊C₄	—	2	2	no	—
655	C₂²⋊C₄	—	2	2	no	—
656	C₂²⋊C₄	—	2	1	no	—
657	C₂²⋊C₄	—	2	2	no	—
658	C₂²⋊C₄	—	2	2	no	—
659	C₂²⋊C₄	—	2	1	no	—
660	C₂²⋊C₄	—	2	1	no	—
661	C₂²⋊C₄	—	2	2	no	—
662	C₂²⋊C₄	—	2	2	no	—
663	C₂²⋊C₄	—	4	4	no	—
664	C₂²⋊C₄	—	4	4	no	—
665	C₂²⋊C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
666	C₂²⋊C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
667	C₂²⋊C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
668	C₂²⋊C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
669	C₄²	—	2	1	no	—
670	C₄²	—	2	1	no	—
671	C₄²	—	2	1	no	—
672	C₄²	—	2	1	no	—
673	C₄²	—	2	2	no	—
674	C₄²	—	2	1	no	—
675	C₄²	—	2	1	no	—
676	C₄²	—	2	2	no	—
677	C₄²	—	4	2	no	—
678	C₄²	—	4	2	no	—
679	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
680	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
681	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
682	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
683	C₄²	C₂×D₄×C₁₃	1	2	yes	complemented
684	C₁₃	#22435	1	1	yes	characteristic, direct product factor, Sylow
685	C₂³	—	2	1	no	—
686	C₂³	—	2	2	no	—
687	C₂³	—	2	2	no	—
688	C₂³	—	2	2	no	—
689	C₂³	—	4	2	no	—
690	C₂³	—	4	2	no	—
691	C₂³	—	4	4	no	—
692	C₂³	—	4	4	no	—
693	C₂³	—	8	2	no	—
694	C₂³	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
695	C₂³	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
696	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
697	Q₈	—	2	1	no	—
698	Q₈	—	2	2	no	—
699	Q₈	—	2	2	no	—
700	Q₈	—	4	4	no	—
701	Q₈	C₄×D₄×C₁₃	1	2	yes	—
702	D₄	—	2	2	no	—
703	D₄	—	2	2	no	—
704	D₄	—	2	2	no	—
705	D₄	—	2	2	no	—
706	D₄	—	2	2	no	—
707	D₄	—	2	1	no	—
708	D₄	—	2	2	no	—
709	D₄	—	4	2	no	—
710	D₄	—	4	4	no	—
711	D₄	—	4	4	no	—
712	D₄	—	4	4	no	—
713	D₄	—	4	4	no	—
714	D₄	—	4	2	no	—
715	D₄	—	4	2	no	—
716	D₄	—	4	2	no	—
717	D₄	—	8	1	no	—
718	D₄	—	8	2	no	—
719	D₄	C₄×D₄×C₁₃	1	2	yes	—
720	C₂×C₄	—	2	1	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	2	1	no	—
736	C₂×C₄	—	2	1	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	4	1	no	—
740	C₂×C₄	—	4	4	no	—
741	C₂×C₄	—	4	4	no	—
742	C₂×C₄	—	4	4	no	—
743	C₂×C₄	—	4	1	no	—
744	C₂×C₄	—	4	1	no	—
745	C₂×C₄	—	4	1	no	—
746	C₂×C₄	—	4	1	no	—
747	C₂×C₄	—	4	2	no	—
748	C₂×C₄	—	4	2	no	—
749	C₂×C₄	—	4	2	no	—
750	C₂×C₄	—	4	2	no	—
751	C₂×C₄	—	4	2	no	—
752	C₂×C₄	—	4	2	no	—
753	C₂×C₄	—	8	1	no	—
754	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
755	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
756	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
757	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
758	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
759	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
760	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
761	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
762	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
763	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
764	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
765	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
766	C₈	—	2	2	no	—
767	C₈	—	4	2	no	—
768	C₈	—	4	1	no	—
769	C₂²	—	2	1	no	—
770	C₂²	—	2	1	no	—
771	C₂²	—	2	2	no	—
772	C₂²	—	2	2	no	—
773	C₂²	—	2	2	no	—
774	C₂²	—	2	2	no	—
775	C₂²	—	2	2	no	—
776	C₂²	—	2	2	no	—
777	C₂²	—	2	2	no	—
778	C₂²	—	4	1	no	—
779	C₂²	—	4	1	no	—
780	C₂²	—	4	2	no	—
781	C₂²	—	4	2	no	—
782	C₂²	—	4	2	no	—
783	C₂²	—	8	2	no	—
784	C₂²	—	8	2	no	—
785	C₂²	—	8	8	no	—
786	C₂²	C₂²×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
787	C₂²	D₄²×C₁₃	1	1	yes	characteristic
788	C₂²	C₁₃×#546	1	1	yes	characteristic
789	C₄	—	2	2	no	—
790	C₄	—	2	2	no	—
791	C₄	—	2	2	no	—
792	C₄	—	2	1	no	—
793	C₄	—	2	1	no	—
794	C₄	—	2	1	no	—
795	C₄	—	4	2	no	—
796	C₄	—	4	2	no	—
797	C₄	—	4	2	no	—
798	C₄	—	4	1	no	—
799	C₄	—	4	1	no	—
800	C₄	—	8	2	no	—
801	C₄	C₁₃×#421	1	2	yes	complemented
802	C₄	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
803	C₄	C₁₃×#518	1	1	yes	characteristic
804	C₄	D₄²×C₁₃	1	1	yes	characteristic
805	C₄	C₁₃×#546	1	1	yes	characteristic
806	C₂	—	2	1	no	—
807	C₂	—	2	1	no	—
808	C₂	—	4	2	no	—
809	C₂	—	4	2	no	—
810	C₂	—	4	2	no	—
811	C₂	—	8	2	no	—
812	C₂	D₄×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
813	C₂	C₂×C₁₃×#421	1	1	yes	characteristic
814	C₂	C₁₃×#2901	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
socle	C₂²×C₁₃	C₂²×C₂²⋊C₄
prime radical	D₄×C₁₃×#41	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₂×C₄×D₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. D₄×C₁₃×M₁₆	C₂	semidirect
3. C₂×C₁₃×#421	C₂	semidirect
4. C₁₃×#2293	C₂	semidirect
5. C₁₃×#1980	C₂	semidirect
6. C₁₃×#1962	C₂	semidirect
7. C₁₃×#1897	C₂	semidirect
8. C₁₃×#1871	C₂	semidirect
9. C₁₃×#1806	C₂	semidirect
10. C₁₃×#1789	C₂	semidirect
11. C₄×C₁₃×#104	C₂	semidirect
13. C₂²×C₁₃×M₁₆	C₂²	semidirect
14. C₁₃×#550	C₄	semidirect
15. D₄×Q₈×C₁₃	C₄	semidirect
16. C₁₃×#548	C₄	semidirect
18. C₁₃×#547	C₄	semidirect
20. C₁₃×#546	C₄	semidirect
22. D₄²×C₁₃	C₄	semidirect
30. C₂×C₁₃×#117	C₂²	semidirect
34. C₁₃×#423	C₂²	semidirect
39. C₂×C₁₃×#104	C₂²	semidirect
40. C₂×C₁₃×#104	C₂²	semidirect
41. C₂×C₁₃×#104	C₂²	semidirect
42. C₂×C₁₃×#104	C₂²	semidirect
43. C₁₃×#407	C₂²	semidirect
44. C₄×C₁₃×M₁₆	C₂²	semidirect
48. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
49. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
50. C₄³×C₁₃	C₂²	semidirect
51. C₁₃×#339	C₂²	semidirect
52. C₁₃×#339	C₂²	semidirect
53. C₁₃×#339	C₂²	semidirect
149. C₁₃×#104	D₄	semidirect
156. #22435	C₁₃	direct (N × H)
230. C₁₃×M₁₆	C₂×D₄	semidirect
277. C₄²×C₁₃	C₂×D₄	semidirect
279. D₄×M₁₆	C₂×C₁₃	semidirect
280. C₂×#421	C₂×C₁₃	semidirect
281. #2293	C₂×C₁₃	semidirect
282. #1980	C₂×C₁₃	semidirect
283. #1962	C₂×C₁₃	semidirect
284. #1897	C₂×C₁₃	semidirect
285. #1871	C₂×C₁₃	semidirect
286. #1806	C₂×C₁₃	semidirect
287. #1789	C₂×C₁₃	semidirect
288. C₄×#104	C₂×C₁₃	semidirect
374. C₂²×M₁₆	C₂²×C₁₃	semidirect
375. #550	C₄×C₁₃	semidirect
376. D₄×Q₈	C₄×C₁₃	semidirect
377. #548	C₄×C₁₃	semidirect
379. #547	C₄×C₁₃	semidirect
381. #546	C₄×C₁₃	semidirect
383. D₄²	C₄×C₁₃	semidirect
391. C₂×#117	C₂²×C₁₃	semidirect
395. #423	C₂²×C₁₃	semidirect
400. C₂×#104	C₂²×C₁₃	semidirect
401. C₂×#104	C₂²×C₁₃	semidirect
402. C₂×#104	C₂²×C₁₃	semidirect
403. C₂×#104	C₂²×C₁₃	semidirect
404. #407	C₂²×C₁₃	semidirect
405. C₄×M₁₆	C₂²×C₁₃	semidirect
409. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
410. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
411. C₄³	C₂²×C₁₃	semidirect
412. #339	C₂²×C₁₃	semidirect
413. #339	C₂²×C₁₃	semidirect
414. #339	C₂²×C₁₃	semidirect
447. C₄×C₁₃	#421	semidirect
547. #104	D₄×C₁₃	semidirect
636. M₁₆	C₂×D₄×C₁₃	semidirect
683. C₄²	C₂×D₄×C₁₃	semidirect
684. C₁₃	#22435	direct (N × H)
801. C₄	C₁₃×#421	semidirect

Maximal subgroups

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

subgroup	index
D₄×C₁₃×#41	2
D₄×C₁₃×M₁₆	2
C₂×C₁₃×#421	2
C₁₃×#2293	2
C₁₃×#1980	2
C₁₃×#1962	2
C₁₃×#1897	2
C₁₃×#1871	2
C₁₃×#1806	2
C₁₃×#1789	2
C₄×C₁₃×#104	2
#22435	13

Subgroups — C13×#22435 #15708774

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#22435 #15708774