Subgroups — D₄×C₁₃×#104 #15708772

Order 3328.

1608 conjugacy classes of subgroups.

The subgroup lattice has 824 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	C₂²×C₁₃×#104	C₂	1	2	yes	maximal, complemented
4	C₄²×D₄×C₁₃	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×#1896	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	—	2	1	no	—
30	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
31	C₂²×C₄²×C₁₃	C₂²	1	2	yes	complemented
32	C₁₃×#436	—	2	1	no	—
33	C₁₃×#435	—	2	2	no	—
34	C₈×D₄×C₁₃	—	2	1	no	—
35	C₁₃×#423	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₁₃×#104	—	2	8	no	—
37	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×#104	C₂²	1	2	yes	—
39	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic
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	C₂×C₁₃×#104	C₂²	1	2	yes	complemented
44	C₁₃×#407	C₂²	1	2	yes	complemented
45	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic, complemented
46	C₄×C₁₃×C₄⋊C₄	—	2	1	no	—
47	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
48	C₄×C₁₃×C₂²⋊C₄	—	2	2	no	—
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	complemented
61	C₂×C₁₃×#41	C₂×C₄	1	2	yes	complemented
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	complemented
65	C₂²×D₄×C₁₃	—	2	2	no	—
66	C₂²×D₄×C₁₃	—	2	1	no	—
67	C₂²×D₄×C₁₃	C₂×C₄	1	2	yes	complemented
68	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
69	C₂³×C₄×C₁₃	—	2	2	no	—
70	C₂³×C₄×C₁₃	—	2	2	no	—
71	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
72	C₂×C₁₃×M₁₆	—	2	2	no	—
73	C₂×C₁₃×M₁₆	—	2	4	no	—
74	C₂×C₁₃×M₁₆	—	4	2	no	—
75	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
76	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
77	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
78	C₂²×C₈×C₁₃	—	2	2	no	—
79	C₁₃×C₄⋊Q₈	—	2	1	no	—
80	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic, complemented
81	C₁₃×#127	—	2	1	no	—
82	C₁₃×#127	C₂×C₄	1	1	yes	characteristic, complemented
83	C₁₃×#124	—	2	2	no	—
84	C₁₃×#124	C₂×C₄	1	2	yes	complemented
85	C₁₃×#123	—	2	2	no	—
86	C₁₃×#123	—	2	2	no	—
87	C₁₃×#123	—	2	2	no	—
88	C₁₃×C₂²⋊Q₈	—	2	2	no	—
89	C₁₃×C₂²⋊Q₈	—	2	2	no	—
90	C₁₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	complemented
91	C₁₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	complemented
92	C₁₃×#121	—	2	2	no	—
93	C₁₃×#121	—	2	1	no	—
94	C₁₃×#121	—	2	1	no	—
95	C₁₃×#121	—	2	1	no	—
96	C₁₃×#121	—	2	1	no	—
97	C₁₃×#121	—	2	2	no	—
98	C₁₃×#121	—	2	2	no	—
99	C₁₃×#121	C₂×C₄	1	2	yes	complemented
100	C₁₃×#121	C₂×C₄	1	2	yes	complemented
101	C₁₃×#120	—	2	2	no	—
102	C₁₃×#120	—	2	2	no	—
103	C₁₃×#120	—	2	2	no	—
104	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic, complemented
105	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic, complemented
106	C₄×D₄×C₁₃	—	2	8	no	—
107	C₄×D₄×C₁₃	—	2	1	no	—
108	C₄×D₄×C₁₃	—	2	2	no	—
109	C₄×D₄×C₁₃	—	2	1	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	2	no	—
114	C₄×D₄×C₁₃	—	2	1	no	—
115	C₄×D₄×C₁₃	—	2	1	no	—
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	C₂×C₄	1	1	yes	characteristic, complemented
120	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic, complemented
121	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
122	C₄×D₄×C₁₃	D₄	1	2	yes	—
123	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
124	C₁₃×#117	—	2	1	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	D₄	1	1	yes	characteristic
129	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
130	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
131	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
132	C₂×C₄²×C₁₃	—	2	1	no	—
133	C₂×C₄²×C₁₃	—	2	1	no	—
134	C₂×C₄²×C₁₃	—	2	4	no	—
135	C₂×C₄²×C₁₃	—	2	1	no	—
136	C₂×C₄²×C₁₃	—	2	2	no	—
137	C₂×C₄²×C₁₃	—	4	2	no	—
138	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
139	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
140	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
141	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
142	C₁₃×C₄⋊C₈	—	2	1	no	—
143	C₁₃×C₄⋊C₈	—	2	1	no	—
144	C₁₃×#104	—	2	4	no	—
145	C₁₃×#104	—	2	2	no	—
146	C₁₃×#104	—	2	4	no	—
147	C₁₃×#104	—	2	4	no	—
148	C₁₃×#104	—	4	2	no	—
149	C₁₃×#104	—	4	2	no	—
150	C₁₃×#104	D₄	1	4	yes	direct product factor
151	C₁₃×C₂²⋊C₈	—	2	2	no	—
152	C₁₃×C₂²⋊C₈	—	2	2	no	—
153	C₁₃×#97	—	2	1	no	—
154	C₄×C₈×C₁₃	—	2	1	no	—
155	C₁₃×#95	—	2	1	no	—
156	C₁₃×#95	—	2	2	no	—
157	D₄×#104	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
158	C₂⁴×C₁₃	—	2	2	no	—
159	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
160	C₁₃×#41	—	2	1	no	—
161	C₁₃×#41	—	2	1	no	—
162	C₁₃×#41	—	2	4	no	—
163	C₁₃×#41	—	2	4	no	—
164	C₁₃×#41	—	2	2	no	—
165	C₁₃×#41	—	2	2	no	—
166	C₁₃×#41	—	2	2	no	—
167	C₁₃×#41	—	2	2	no	—
168	C₁₃×#41	—	4	4	no	—
169	C₁₃×#41	—	4	4	no	—
170	C₁₃×#41	—	4	2	no	—
171	C₁₃×#41	—	4	2	no	—
172	C₁₃×#41	—	4	4	no	—
173	C₁₃×#41	—	4	4	no	—
174	C₁₃×#41	C₂×D₄	1	2	yes	—
175	C₁₃×#41	#41	1	2	yes	—
176	C₂×Q₈×C₁₃	—	2	2	no	—
177	C₂×Q₈×C₁₃	—	2	4	no	—
178	C₂×Q₈×C₁₃	—	4	2	no	—
179	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
180	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
181	C₂×D₄×C₁₃	—	2	1	no	—
182	C₂×D₄×C₁₃	—	2	4	no	—
183	C₂×D₄×C₁₃	—	2	4	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	2	no	—
188	C₂×D₄×C₁₃	—	2	2	no	—
189	C₂×D₄×C₁₃	—	2	1	no	—
190	C₂×D₄×C₁₃	—	2	2	no	—
191	C₂×D₄×C₁₃	—	2	1	no	—
192	C₂×D₄×C₁₃	—	4	2	no	—
193	C₂×D₄×C₁₃	—	4	4	no	—
194	C₂×D₄×C₁₃	—	4	4	no	—
195	C₂×D₄×C₁₃	—	4	4	no	—
196	C₂×D₄×C₁₃	C₂²⋊C₄	1	2	yes	—
197	C₂×D₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
198	C₂×D₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
199	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
200	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
201	C₂²×C₄×C₁₃	—	2	1	no	—
202	C₂²×C₄×C₁₃	—	2	2	no	—
203	C₂²×C₄×C₁₃	—	2	1	no	—
204	C₂²×C₄×C₁₃	—	2	2	no	—
205	C₂²×C₄×C₁₃	—	2	2	no	—
206	C₂²×C₄×C₁₃	—	2	2	no	—
207	C₂²×C₄×C₁₃	—	2	8	no	—
208	C₂²×C₄×C₁₃	—	2	2	no	—
209	C₂²×C₄×C₁₃	—	2	1	no	—
210	C₂²×C₄×C₁₃	—	2	2	no	—
211	C₂²×C₄×C₁₃	—	2	1	no	—
212	C₂²×C₄×C₁₃	—	2	2	no	—
213	C₂²×C₄×C₁₃	—	2	2	no	—
214	C₂²×C₄×C₁₃	—	2	2	no	—
215	C₂²×C₄×C₁₃	—	2	1	no	—
216	C₂²×C₄×C₁₃	—	4	4	no	—
217	C₂²×C₄×C₁₃	—	4	4	no	—
218	C₂²×C₄×C₁₃	—	4	4	no	—
219	C₂²×C₄×C₁₃	—	4	4	no	—
220	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
221	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
222	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
223	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
224	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
225	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
226	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
227	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
228	C₁₃×M₁₆	—	2	1	no	—
229	C₁₃×M₁₆	—	2	2	no	—
230	C₁₃×M₁₆	—	2	1	no	—
231	C₁₃×M₁₆	—	2	1	no	—
232	C₁₃×M₁₆	—	2	2	no	—
233	C₁₃×M₁₆	—	4	4	no	—
234	C₁₃×M₁₆	C₂×D₄	1	2	yes	complemented
235	C₂×C₈×C₁₃	—	2	1	no	—
236	C₂×C₈×C₁₃	—	2	1	no	—
237	C₂×C₈×C₁₃	—	2	2	no	—
238	C₂×C₈×C₁₃	—	4	4	no	—
239	C₁₃×C₄⋊C₄	—	2	4	no	—
240	C₁₃×C₄⋊C₄	—	2	1	no	—
241	C₁₃×C₄⋊C₄	—	2	2	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	2	no	—
246	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
247	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
248	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	2	yes	—
249	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
250	C₁₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
251	C₁₃×C₂²⋊C₄	—	2	8	no	—
252	C₁₃×C₂²⋊C₄	—	2	2	no	—
253	C₁₃×C₂²⋊C₄	—	2	2	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	—	2	1	no	—
258	C₁₃×C₂²⋊C₄	—	2	1	no	—
259	C₁₃×C₂²⋊C₄	—	2	2	no	—
260	C₁₃×C₂²⋊C₄	—	2	2	no	—
261	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	—
262	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	—
263	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	—
264	C₁₃×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	—
265	C₄²×C₁₃	—	2	4	no	—
266	C₄²×C₁₃	—	2	1	no	—
267	C₄²×C₁₃	—	2	1	no	—
268	C₄²×C₁₃	—	2	1	no	—
269	C₄²×C₁₃	—	2	1	no	—
270	C₄²×C₁₃	—	2	2	no	—
271	C₄²×C₁₃	—	2	1	no	—
272	C₄²×C₁₃	—	2	1	no	—
273	C₄²×C₁₃	—	2	2	no	—
274	C₄²×C₁₃	—	4	4	no	—
275	C₄²×C₁₃	—	4	2	no	—
276	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
277	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
278	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
279	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
280	C₄²×C₁₃	C₂×D₄	1	2	yes	complemented
281	D₄×#41	C₂×C₁₃	1	1	yes	characteristic
282	D₄×M₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
283	C₂²×#104	C₂×C₁₃	1	2	yes	complemented
284	C₄²×D₄	C₂×C₁₃	1	1	yes	characteristic, complemented
285	#1980	C₂×C₁₃	1	1	yes	characteristic, complemented
286	#1962	C₂×C₁₃	1	1	yes	characteristic, complemented
287	#1896	C₂×C₁₃	1	2	yes	complemented
288	#1871	C₂×C₁₃	1	2	yes	complemented
289	#1806	C₂×C₁₃	1	1	yes	characteristic, complemented
290	#1789	C₂×C₁₃	1	2	yes	complemented
291	C₄×#104	C₂×C₁₃	1	1	yes	characteristic, complemented
292	C₂³×C₁₃	—	2	1	no	—
293	C₂³×C₁₃	—	2	2	no	—
294	C₂³×C₁₃	—	2	2	no	—
295	C₂³×C₁₃	—	2	4	no	—
296	C₂³×C₁₃	—	2	2	no	—
297	C₂³×C₁₃	—	4	2	no	—
298	C₂³×C₁₃	—	4	4	no	—
299	C₂³×C₁₃	—	4	4	no	—
300	C₂³×C₁₃	—	8	2	no	—
301	C₂³×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
302	C₂³×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
303	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
304	Q₈×C₁₃	—	2	1	no	—
305	Q₈×C₁₃	—	2	2	no	—
306	Q₈×C₁₃	—	2	2	no	—
307	Q₈×C₁₃	—	4	4	no	—
308	Q₈×C₁₃	C₄×D₄	1	2	yes	complemented
309	D₄×C₁₃	—	2	2	no	—
310	D₄×C₁₃	—	2	2	no	—
311	D₄×C₁₃	—	2	4	no	—
312	D₄×C₁₃	—	2	2	no	—
313	D₄×C₁₃	—	2	1	no	—
314	D₄×C₁₃	—	2	2	no	—
315	D₄×C₁₃	—	2	2	no	—
316	D₄×C₁₃	—	4	4	no	—
317	D₄×C₁₃	—	4	4	no	—
318	D₄×C₁₃	—	4	4	no	—
319	D₄×C₁₃	—	4	2	no	—
320	D₄×C₁₃	—	4	2	no	—
321	D₄×C₁₃	—	4	4	no	—
322	D₄×C₁₃	—	4	2	no	—
323	D₄×C₁₃	—	8	1	no	—
324	D₄×C₁₃	—	8	2	no	—
325	D₄×C₁₃	#104	1	4	yes	direct product factor
326	D₄×C₁₃	C₄×D₄	1	2	yes	complemented
327	C₂×C₄×C₁₃	—	2	2	no	—
328	C₂×C₄×C₁₃	—	2	2	no	—
329	C₂×C₄×C₁₃	—	2	1	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	2	no	—
340	C₂×C₄×C₁₃	—	2	2	no	—
341	C₂×C₄×C₁₃	—	2	2	no	—
342	C₂×C₄×C₁₃	—	2	2	no	—
343	C₂×C₄×C₁₃	—	2	2	no	—
344	C₂×C₄×C₁₃	—	2	2	no	—
345	C₂×C₄×C₁₃	—	2	4	no	—
346	C₂×C₄×C₁₃	—	2	1	no	—
347	C₂×C₄×C₁₃	—	2	1	no	—
348	C₂×C₄×C₁₃	—	2	2	no	—
349	C₂×C₄×C₁₃	—	4	1	no	—
350	C₂×C₄×C₁₃	—	4	4	no	—
351	C₂×C₄×C₁₃	—	4	4	no	—
352	C₂×C₄×C₁₃	—	4	4	no	—
353	C₂×C₄×C₁₃	—	4	16	no	—
354	C₂×C₄×C₁₃	—	4	1	no	—
355	C₂×C₄×C₁₃	—	4	2	no	—
356	C₂×C₄×C₁₃	—	4	2	no	—
357	C₂×C₄×C₁₃	—	4	1	no	—
358	C₂×C₄×C₁₃	—	4	2	no	—
359	C₂×C₄×C₁₃	—	4	2	no	—
360	C₂×C₄×C₁₃	—	4	2	no	—
361	C₂×C₄×C₁₃	—	8	1	no	—
362	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
363	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
364	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
365	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
366	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
367	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
368	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
369	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
370	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
371	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
372	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
373	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
374	C₈×C₁₃	—	2	2	no	—
375	C₈×C₁₃	—	4	2	no	—
376	C₈×C₁₃	—	4	1	no	—
377	C₂²×#41	C₂²×C₁₃	1	2	yes	—
378	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	complemented
379	#550	C₄×C₁₃	1	1	yes	characteristic, complemented
380	D₄×Q₈	C₄×C₁₃	1	1	yes	characteristic, complemented
381	#548	C₄×C₁₃	1	2	yes	complemented
382	#547	—	2	1	no	—
383	#547	C₄×C₁₃	1	1	yes	characteristic, complemented
384	#546	—	2	2	no	—
385	#546	C₄×C₁₃	1	2	yes	complemented
386	D₄²	—	2	1	no	—
387	D₄²	C₄×C₁₃	1	1	yes	characteristic, complemented
388	#532	—	2	1	no	—
389	#532	C₂²×C₁₃	1	1	yes	characteristic
390	#525	—	2	2	no	—
391	#525	C₂²×C₁₃	1	2	yes	—
392	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
393	C₂×C₄×D₄	—	2	1	no	—
394	C₂×C₄×D₄	—	2	1	no	—
395	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
396	C₂²×C₄²	C₂²×C₁₃	1	2	yes	complemented
397	#436	—	2	1	no	—
398	#435	—	2	2	no	—
399	C₈×D₄	—	2	1	no	—
400	#423	C₂²×C₁₃	1	1	yes	characteristic, complemented
401	C₂×#104	—	2	8	no	—
402	C₂×#104	C₂²×C₁₃	1	2	yes	—
403	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic
404	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic
405	C₂×#104	C₂²×C₁₃	1	2	yes	complemented
406	C₂×#104	C₂²×C₁₃	1	2	yes	complemented
407	C₂×#104	C₂²×C₁₃	1	2	yes	complemented
408	C₂×#104	C₂²×C₁₃	1	2	yes	complemented
409	#407	C₂²×C₁₃	1	2	yes	complemented
410	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
411	C₄×C₄⋊C₄	—	2	1	no	—
412	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
413	C₄×C₂²⋊C₄	—	2	2	no	—
414	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
415	C₄³	C₂²×C₁₃	1	1	yes	characteristic, complemented
416	#339	C₂²×C₁₃	1	2	yes	complemented
417	#339	C₂²×C₁₃	1	1	yes	characteristic, complemented
418	#339	C₂²×C₁₃	1	1	yes	characteristic, complemented
419	C₂²×C₁₃	—	2	2	no	—
420	C₂²×C₁₃	—	2	1	no	—
421	C₂²×C₁₃	—	2	1	no	—
422	C₂²×C₁₃	—	2	2	no	—
423	C₂²×C₁₃	—	2	2	no	—
424	C₂²×C₁₃	—	2	2	no	—
425	C₂²×C₁₃	—	2	2	no	—
426	C₂²×C₁₃	—	2	2	no	—
427	C₂²×C₁₃	—	4	4	no	—
428	C₂²×C₁₃	—	4	4	no	—
429	C₂²×C₁₃	—	4	1	no	—
430	C₂²×C₁₃	—	4	1	no	—
431	C₂²×C₁₃	—	4	2	no	—
432	C₂²×C₁₃	—	4	2	no	—
433	C₂²×C₁₃	—	4	2	no	—
434	C₂²×C₁₃	—	8	8	no	—
435	C₂²×C₁₃	C₂×#104	1	4	yes	complemented
436	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
437	C₂²×C₁₃	D₄²	1	1	yes	characteristic
438	C₂²×C₁₃	#546	1	1	yes	characteristic
439	C₄×C₁₃	—	2	4	no	—
440	C₄×C₁₃	—	2	2	no	—
441	C₄×C₁₃	—	2	2	no	—
442	C₄×C₁₃	—	2	2	no	—
443	C₄×C₁₃	—	2	1	no	—
444	C₄×C₁₃	—	2	1	no	—
445	C₄×C₁₃	—	2	1	no	—
446	C₄×C₁₃	—	4	2	no	—
447	C₄×C₁₃	—	4	4	no	—
448	C₄×C₁₃	—	4	2	no	—
449	C₄×C₁₃	—	4	1	no	—
450	C₄×C₁₃	—	4	1	no	—
451	C₄×C₁₃	C₂×#104	1	2	yes	complemented
452	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
453	C₄×C₁₃	#518	1	1	yes	characteristic
454	C₄×C₁₃	D₄²	1	1	yes	characteristic
455	C₄×C₁₃	#546	1	1	yes	characteristic
456	C₂×#41	—	2	2	no	—
457	C₂×#41	—	2	2	no	—
458	C₂×#41	—	2	4	no	—
459	C₂×#41	—	2	4	no	—
460	C₂×#41	—	4	2	no	—
461	C₂×#41	—	4	2	no	—
462	C₂×#41	C₂×C₄×C₁₃	1	2	yes	complemented
463	C₂×#41	C₂×C₄×C₁₃	1	2	yes	complemented
464	C₂×#41	C₂³×C₁₃	1	2	yes	—
465	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
466	C₂²×Q₈	C₂×C₄×C₁₃	1	2	yes	complemented
467	C₂²×D₄	—	2	2	no	—
468	C₂²×D₄	—	2	1	no	—
469	C₂²×D₄	C₂×C₄×C₁₃	1	2	yes	complemented
470	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
471	C₂³×C₄	—	2	2	no	—
472	C₂³×C₄	—	2	2	no	—
473	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
474	C₂×M₁₆	—	2	2	no	—
475	C₂×M₁₆	—	2	4	no	—
476	C₂×M₁₆	—	4	2	no	—
477	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
478	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
479	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
480	C₂²×C₈	—	2	2	no	—
481	C₄⋊Q₈	—	2	1	no	—
482	C₄⋊Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic, complemented
483	#127	—	2	1	no	—
484	#127	C₂×C₄×C₁₃	1	1	yes	characteristic, complemented
485	#124	—	2	2	no	—
486	#124	C₂×C₄×C₁₃	1	2	yes	complemented
487	#123	—	2	2	no	—
488	#123	—	2	2	no	—
489	#123	—	2	2	no	—
490	C₂²⋊Q₈	—	2	2	no	—
491	C₂²⋊Q₈	—	2	2	no	—
492	C₂²⋊Q₈	C₂×C₄×C₁₃	1	2	yes	complemented
493	C₂²⋊Q₈	C₂×C₄×C₁₃	1	2	yes	complemented
494	#121	—	2	2	no	—
495	#121	—	2	1	no	—
496	#121	—	2	1	no	—
497	#121	—	2	1	no	—
498	#121	—	2	1	no	—
499	#121	—	2	2	no	—
500	#121	—	2	2	no	—
501	#121	C₂×C₄×C₁₃	1	2	yes	complemented
502	#121	C₂×C₄×C₁₃	1	2	yes	complemented
503	#120	—	2	2	no	—
504	#120	—	2	2	no	—
505	#120	—	2	2	no	—
506	C₄×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic, complemented
507	C₄×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic, complemented
508	C₄×D₄	—	2	8	no	—
509	C₄×D₄	—	2	1	no	—
510	C₄×D₄	—	2	2	no	—
511	C₄×D₄	—	2	1	no	—
512	C₄×D₄	—	2	1	no	—
513	C₄×D₄	—	2	2	no	—
514	C₄×D₄	—	2	1	no	—
515	C₄×D₄	—	2	2	no	—
516	C₄×D₄	—	2	1	no	—
517	C₄×D₄	—	2	1	no	—
518	C₄×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
519	C₄×D₄	C₂×C₄×C₁₃	1	2	yes	—
520	C₄×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
521	C₄×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic, complemented
522	C₄×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic, complemented
523	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
524	C₄×D₄	D₄×C₁₃	1	2	yes	—
525	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
526	#117	—	2	1	no	—
527	#117	C₂³×C₁₃	1	1	yes	characteristic
528	C₂×C₄⋊C₄	—	2	1	no	—
529	C₂×C₄⋊C₄	—	2	1	no	—
530	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
531	C₂×C₂²⋊C₄	—	2	2	no	—
532	C₂×C₂²⋊C₄	—	2	2	no	—
533	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
534	C₂×C₄²	—	2	1	no	—
535	C₂×C₄²	—	2	1	no	—
536	C₂×C₄²	—	2	4	no	—
537	C₂×C₄²	—	2	1	no	—
538	C₂×C₄²	—	2	2	no	—
539	C₂×C₄²	—	4	2	no	—
540	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
541	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
542	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
543	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
544	C₄⋊C₈	—	2	1	no	—
545	C₄⋊C₈	—	2	1	no	—
546	#104	—	2	4	no	—
547	#104	—	2	2	no	—
548	#104	—	2	4	no	—
549	#104	—	2	4	no	—
550	#104	—	4	2	no	—
551	#104	—	4	2	no	—
552	#104	D₄×C₁₃	1	4	yes	direct product factor
553	C₂²⋊C₈	—	2	2	no	—
554	C₂²⋊C₈	—	2	2	no	—
555	#97	—	2	1	no	—
556	C₄×C₈	—	2	1	no	—
557	#95	—	2	1	no	—
558	#95	—	2	2	no	—
559	C₂×C₁₃	—	2	1	no	—
560	C₂×C₁₃	—	2	1	no	—
561	C₂×C₁₃	—	2	4	no	—
562	C₂×C₁₃	—	4	2	no	—
563	C₂×C₁₃	—	4	2	no	—
564	C₂×C₁₃	—	8	2	no	—
565	C₂×C₁₃	D₄×C₂²⋊C₄	1	1	yes	characteristic
566	C₂×C₁₃	C₂²×#104	1	1	yes	characteristic
567	C₂×C₁₃	#2901	1	1	yes	characteristic
568	C₂⁴	—	2	2	no	—
569	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
570	#41	—	2	1	no	—
571	#41	—	2	1	no	—
572	#41	—	2	4	no	—
573	#41	—	2	4	no	—
574	#41	—	2	2	no	—
575	#41	—	2	2	no	—
576	#41	—	2	2	no	—
577	#41	—	2	2	no	—
578	#41	—	4	4	no	—
579	#41	—	4	4	no	—
580	#41	—	4	2	no	—
581	#41	—	4	2	no	—
582	#41	—	4	4	no	—
583	#41	—	4	4	no	—
584	#41	C₂×D₄×C₁₃	1	2	yes	—
585	#41	C₁₃×#41	1	2	yes	—
586	C₂×Q₈	—	2	2	no	—
587	C₂×Q₈	—	2	4	no	—
588	C₂×Q₈	—	4	2	no	—
589	C₂×Q₈	C₂²×C₄×C₁₃	1	2	yes	—
590	C₂×Q₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
591	C₂×D₄	—	2	1	no	—
592	C₂×D₄	—	2	4	no	—
593	C₂×D₄	—	2	4	no	—
594	C₂×D₄	—	2	2	no	—
595	C₂×D₄	—	2	2	no	—
596	C₂×D₄	—	2	2	no	—
597	C₂×D₄	—	2	2	no	—
598	C₂×D₄	—	2	2	no	—
599	C₂×D₄	—	2	1	no	—
600	C₂×D₄	—	2	2	no	—
601	C₂×D₄	—	2	1	no	—
602	C₂×D₄	—	4	2	no	—
603	C₂×D₄	—	4	4	no	—
604	C₂×D₄	—	4	4	no	—
605	C₂×D₄	—	4	4	no	—
606	C₂×D₄	C₁₃×C₂²⋊C₄	1	2	yes	—
607	C₂×D₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
608	C₂×D₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
609	C₂×D₄	C₂²×C₄×C₁₃	1	2	yes	—
610	C₂×D₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
611	C₂²×C₄	—	2	1	no	—
612	C₂²×C₄	—	2	2	no	—
613	C₂²×C₄	—	2	1	no	—
614	C₂²×C₄	—	2	2	no	—
615	C₂²×C₄	—	2	2	no	—
616	C₂²×C₄	—	2	2	no	—
617	C₂²×C₄	—	2	8	no	—
618	C₂²×C₄	—	2	2	no	—
619	C₂²×C₄	—	2	1	no	—
620	C₂²×C₄	—	2	2	no	—
621	C₂²×C₄	—	2	1	no	—
622	C₂²×C₄	—	2	2	no	—
623	C₂²×C₄	—	2	2	no	—
624	C₂²×C₄	—	2	2	no	—
625	C₂²×C₄	—	2	1	no	—
626	C₂²×C₄	—	4	4	no	—
627	C₂²×C₄	—	4	4	no	—
628	C₂²×C₄	—	4	4	no	—
629	C₂²×C₄	—	4	4	no	—
630	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
631	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
632	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
633	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
634	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
635	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
636	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
637	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
638	M₁₆	—	2	1	no	—
639	M₁₆	—	2	2	no	—
640	M₁₆	—	2	1	no	—
641	M₁₆	—	2	1	no	—
642	M₁₆	—	2	2	no	—
643	M₁₆	—	4	4	no	—
644	M₁₆	C₂×D₄×C₁₃	1	2	yes	complemented
645	C₂×C₈	—	2	1	no	—
646	C₂×C₈	—	2	1	no	—
647	C₂×C₈	—	2	2	no	—
648	C₂×C₈	—	4	4	no	—
649	C₄⋊C₄	—	2	4	no	—
650	C₄⋊C₄	—	2	1	no	—
651	C₄⋊C₄	—	2	2	no	—
652	C₄⋊C₄	—	2	1	no	—
653	C₄⋊C₄	—	2	1	no	—
654	C₄⋊C₄	—	2	1	no	—
655	C₄⋊C₄	—	2	2	no	—
656	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
657	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
658	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
659	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
660	C₄⋊C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
661	C₂²⋊C₄	—	2	8	no	—
662	C₂²⋊C₄	—	2	2	no	—
663	C₂²⋊C₄	—	2	2	no	—
664	C₂²⋊C₄	—	2	1	no	—
665	C₂²⋊C₄	—	2	2	no	—
666	C₂²⋊C₄	—	2	2	no	—
667	C₂²⋊C₄	—	2	1	no	—
668	C₂²⋊C₄	—	2	1	no	—
669	C₂²⋊C₄	—	2	2	no	—
670	C₂²⋊C₄	—	2	2	no	—
671	C₂²⋊C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
672	C₂²⋊C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
673	C₂²⋊C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
674	C₂²⋊C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
675	C₄²	—	2	4	no	—
676	C₄²	—	2	1	no	—
677	C₄²	—	2	1	no	—
678	C₄²	—	2	1	no	—
679	C₄²	—	2	1	no	—
680	C₄²	—	2	2	no	—
681	C₄²	—	2	1	no	—
682	C₄²	—	2	1	no	—
683	C₄²	—	2	2	no	—
684	C₄²	—	4	4	no	—
685	C₄²	—	4	2	no	—
686	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
687	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
688	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
689	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
690	C₄²	C₂×D₄×C₁₃	1	2	yes	complemented
691	C₁₃	D₄×#104	1	1	yes	characteristic, direct product factor, Sylow
692	C₂³	—	2	4	no	—
693	C₂³	—	2	1	no	—
694	C₂³	—	2	2	no	—
695	C₂³	—	2	2	no	—
696	C₂³	—	2	2	no	—
697	C₂³	—	4	2	no	—
698	C₂³	—	4	4	no	—
699	C₂³	—	4	4	no	—
700	C₂³	—	8	2	no	—
701	C₂³	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
702	C₂³	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
703	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
704	Q₈	—	2	1	no	—
705	Q₈	—	2	2	no	—
706	Q₈	—	2	2	no	—
707	Q₈	—	4	4	no	—
708	Q₈	C₄×D₄×C₁₃	1	2	yes	complemented
709	D₄	—	2	4	no	—
710	D₄	—	2	2	no	—
711	D₄	—	2	2	no	—
712	D₄	—	2	2	no	—
713	D₄	—	2	2	no	—
714	D₄	—	2	1	no	—
715	D₄	—	2	2	no	—
716	D₄	—	4	4	no	—
717	D₄	—	4	4	no	—
718	D₄	—	4	4	no	—
719	D₄	—	4	4	no	—
720	D₄	—	4	2	no	—
721	D₄	—	4	2	no	—
722	D₄	—	4	2	no	—
723	D₄	—	8	1	no	—
724	D₄	—	8	2	no	—
725	D₄	C₁₃×#104	1	4	yes	direct product factor
726	D₄	C₄×D₄×C₁₃	1	2	yes	complemented
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	1	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	2	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	4	no	—
746	C₂×C₄	—	2	1	no	—
747	C₂×C₄	—	2	1	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	4	1	no	—
750	C₂×C₄	—	4	4	no	—
751	C₂×C₄	—	4	4	no	—
752	C₂×C₄	—	4	4	no	—
753	C₂×C₄	—	4	16	no	—
754	C₂×C₄	—	4	1	no	—
755	C₂×C₄	—	4	2	no	—
756	C₂×C₄	—	4	2	no	—
757	C₂×C₄	—	4	1	no	—
758	C₂×C₄	—	4	2	no	—
759	C₂×C₄	—	4	2	no	—
760	C₂×C₄	—	4	2	no	—
761	C₂×C₄	—	8	1	no	—
762	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
763	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
764	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
765	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
766	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
767	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
768	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
769	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
770	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
771	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
772	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
773	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
774	C₈	—	2	2	no	—
775	C₈	—	4	2	no	—
776	C₈	—	4	1	no	—
777	C₂²	—	2	2	no	—
778	C₂²	—	2	1	no	—
779	C₂²	—	2	1	no	—
780	C₂²	—	2	2	no	—
781	C₂²	—	2	2	no	—
782	C₂²	—	2	2	no	—
783	C₂²	—	2	2	no	—
784	C₂²	—	2	2	no	—
785	C₂²	—	4	4	no	—
786	C₂²	—	4	4	no	—
787	C₂²	—	4	1	no	—
788	C₂²	—	4	1	no	—
789	C₂²	—	4	2	no	—
790	C₂²	—	4	2	no	—
791	C₂²	—	4	2	no	—
792	C₂²	—	8	8	no	—
793	C₂²	C₂×C₁₃×#104	1	4	yes	complemented
794	C₂²	C₂²×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
795	C₂²	D₄²×C₁₃	1	1	yes	characteristic
796	C₂²	C₁₃×#546	1	1	yes	characteristic
797	C₄	—	2	4	no	—
798	C₄	—	2	2	no	—
799	C₄	—	2	2	no	—
800	C₄	—	2	2	no	—
801	C₄	—	2	1	no	—
802	C₄	—	2	1	no	—
803	C₄	—	2	1	no	—
804	C₄	—	4	2	no	—
805	C₄	—	4	4	no	—
806	C₄	—	4	2	no	—
807	C₄	—	4	1	no	—
808	C₄	—	4	1	no	—
809	C₄	C₂×C₁₃×#104	1	2	yes	complemented
810	C₄	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
811	C₄	C₁₃×#518	1	1	yes	characteristic
812	C₄	D₄²×C₁₃	1	1	yes	characteristic
813	C₄	C₁₃×#546	1	1	yes	characteristic
814	C₂	—	2	1	no	—
815	C₂	—	2	1	no	—
816	C₂	—	2	4	no	—
817	C₂	—	4	2	no	—
818	C₂	—	4	2	no	—
819	C₂	—	8	2	no	—
820	C₂	D₄×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
821	C₂	C₂²×C₁₃×#104	1	1	yes	characteristic
822	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. C₂²×C₁₃×#104	C₂	semidirect
4. C₄²×D₄×C₁₃	C₂	semidirect
5. C₁₃×#1980	C₂	semidirect
6. C₁₃×#1962	C₂	semidirect
7. C₁₃×#1896	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
31. C₂²×C₄²×C₁₃	C₂²	semidirect
35. C₁₃×#423	C₂²	semidirect
40. C₂×C₁₃×#104	C₂²	semidirect
41. C₂×C₁₃×#104	C₂²	semidirect
42. C₂×C₁₃×#104	C₂²	semidirect
43. C₂×C₁₃×#104	C₂²	semidirect
44. C₁₃×#407	C₂²	semidirect
45. C₄×C₁₃×M₁₆	C₂²	semidirect
47. 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
60. C₂×C₁₃×#41	C₂×C₄	semidirect
61. C₂×C₁₃×#41	C₂×C₄	semidirect
64. C₂²×Q₈×C₁₃	C₂×C₄	semidirect
67. C₂²×D₄×C₁₃	C₂×C₄	semidirect
80. C₁₃×C₄⋊Q₈	C₂×C₄	semidirect
82. C₁₃×#127	C₂×C₄	semidirect
84. C₁₃×#124	C₂×C₄	semidirect
90. C₁₃×C₂²⋊Q₈	C₂×C₄	semidirect
91. C₁₃×C₂²⋊Q₈	C₂×C₄	semidirect
99. C₁₃×#121	C₂×C₄	semidirect
100. C₁₃×#121	C₂×C₄	semidirect
104. C₄×Q₈×C₁₃	C₂×C₄	semidirect
105. C₄×Q₈×C₁₃	C₂×C₄	semidirect
119. C₄×D₄×C₁₃	C₂×C₄	semidirect
120. C₄×D₄×C₁₃	C₂×C₄	semidirect
150. C₁₃×#104	D₄	direct (N × H)
157. D₄×#104	C₁₃	direct (N × H)
234. C₁₃×M₁₆	C₂×D₄	semidirect
280. C₄²×C₁₃	C₂×D₄	semidirect
282. D₄×M₁₆	C₂×C₁₃	semidirect
283. C₂²×#104	C₂×C₁₃	semidirect
284. C₄²×D₄	C₂×C₁₃	semidirect
285. #1980	C₂×C₁₃	semidirect
286. #1962	C₂×C₁₃	semidirect
287. #1896	C₂×C₁₃	semidirect
288. #1871	C₂×C₁₃	semidirect
289. #1806	C₂×C₁₃	semidirect
290. #1789	C₂×C₁₃	semidirect
291. C₄×#104	C₂×C₁₃	semidirect
308. Q₈×C₁₃	C₄×D₄	semidirect
325. D₄×C₁₃	#104	direct (N × H)
326. D₄×C₁₃	C₄×D₄	semidirect
378. C₂²×M₁₆	C₂²×C₁₃	semidirect
379. #550	C₄×C₁₃	semidirect
380. D₄×Q₈	C₄×C₁₃	semidirect
381. #548	C₄×C₁₃	semidirect
383. #547	C₄×C₁₃	semidirect
385. #546	C₄×C₁₃	semidirect
387. D₄²	C₄×C₁₃	semidirect
396. C₂²×C₄²	C₂²×C₁₃	semidirect
400. #423	C₂²×C₁₃	semidirect
405. C₂×#104	C₂²×C₁₃	semidirect
406. C₂×#104	C₂²×C₁₃	semidirect
407. C₂×#104	C₂²×C₁₃	semidirect
408. C₂×#104	C₂²×C₁₃	semidirect
409. #407	C₂²×C₁₃	semidirect
410. C₄×M₁₆	C₂²×C₁₃	semidirect
412. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
414. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
415. C₄³	C₂²×C₁₃	semidirect
416. #339	C₂²×C₁₃	semidirect
417. #339	C₂²×C₁₃	semidirect
418. #339	C₂²×C₁₃	semidirect
435. C₂²×C₁₃	C₂×#104	semidirect
451. C₄×C₁₃	C₂×#104	semidirect
462. C₂×#41	C₂×C₄×C₁₃	semidirect
463. C₂×#41	C₂×C₄×C₁₃	semidirect
466. C₂²×Q₈	C₂×C₄×C₁₃	semidirect
469. C₂²×D₄	C₂×C₄×C₁₃	semidirect
482. C₄⋊Q₈	C₂×C₄×C₁₃	semidirect
484. #127	C₂×C₄×C₁₃	semidirect
486. #124	C₂×C₄×C₁₃	semidirect
492. C₂²⋊Q₈	C₂×C₄×C₁₃	semidirect
493. C₂²⋊Q₈	C₂×C₄×C₁₃	semidirect
501. #121	C₂×C₄×C₁₃	semidirect
502. #121	C₂×C₄×C₁₃	semidirect
506. C₄×Q₈	C₂×C₄×C₁₃	semidirect
507. C₄×Q₈	C₂×C₄×C₁₃	semidirect
521. C₄×D₄	C₂×C₄×C₁₃	semidirect
522. C₄×D₄	C₂×C₄×C₁₃	semidirect
552. #104	D₄×C₁₃	direct (N × H)
644. M₁₆	C₂×D₄×C₁₃	semidirect
690. C₄²	C₂×D₄×C₁₃	semidirect
691. C₁₃	D₄×#104	direct (N × H)
708. Q₈	C₄×D₄×C₁₃	semidirect
725. D₄	C₁₃×#104	direct (N × H)
726. D₄	C₄×D₄×C₁₃	semidirect
793. C₂²	C₂×C₁₃×#104	semidirect
809. C₄	C₂×C₁₃×#104	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
C₂²×C₁₃×#104	2
C₄²×D₄×C₁₃	2
C₁₃×#1980	2
C₁₃×#1962	2
C₁₃×#1896	2
C₁₃×#1871	2
C₁₃×#1806	2
C₁₃×#1789	2
C₄×C₁₃×#104	2
D₄×#104	13

Subgroups — D4×C13×#104 #15708772

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄×C₁₃×#104 #15708772