Subgroups — C₂×C₁₃×#3224 #15747132

Order 3328.

2278 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#542	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#535	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3224	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#496	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#495	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃×#489	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#486	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#464	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#460	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×#463	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×#459	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#452	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₁₃×#449	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₁₃×#450	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₁₃×#447	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#433	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
18	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
19	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
20	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
21	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
22	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic, complemented
23	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic, complemented
24	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
25	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
26	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic, complemented
27	C₁₃×#542	—	2	4	no	—
28	C₁₃×#542	C₂²	1	8	yes	complemented
29	C₁₃×#535	—	2	4	no	—
30	C₁₃×#535	C₂²	1	8	yes	complemented
31	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×#126	—	2	1	no	—
35	C₂×C₁₃×#124	—	2	1	no	—
36	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₁₃×#123	—	2	1	no	—
40	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
41	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
42	C₂×C₁₃×#121	—	2	1	no	—
43	C₂×C₁₃×#121	—	2	1	no	—
44	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
45	C₂×C₁₃×#120	—	2	1	no	—
46	C₂×C₁₃×#120	—	2	1	no	—
47	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
48	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
49	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
50	C₁₃×#496	C₂²	1	8	yes	complemented
51	C₁₃×#495	C₂²	1	8	yes	complemented
52	C₁₃×#489	C₂²	1	8	yes	complemented
53	C₁₃×#486	C₂²	1	8	yes	complemented
54	C₁₃×#464	C₂²	1	8	yes	complemented
55	C₁₃×#463	C₂²	1	8	yes	complemented
56	C₁₃×#460	C₂²	1	8	yes	complemented
57	C₁₃×#459	C₂²	1	8	yes	complemented
58	C₁₃×#452	C₂²	1	8	yes	complemented
59	C₁₃×#450	C₂²	1	8	yes	complemented
60	C₁₃×#449	C₂²	1	8	yes	complemented
61	C₁₃×#447	C₂²	1	8	yes	complemented
62	C₁₃×#433	C₂²	1	8	yes	complemented
63	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
64	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
65	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic, complemented
66	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic, complemented
67	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
68	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
69	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
70	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
71	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic, complemented
72	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic, complemented
73	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
74	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
75	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic, complemented
76	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
77	C₂⁵×C₁₃	—	2	1	no	—
78	C₂×C₁₃×#41	—	2	2	no	—
79	C₂×C₁₃×#41	—	4	2	no	—
80	C₂×C₁₃×#41	—	4	2	no	—
81	C₂×C₁₃×#41	C₂³	1	4	yes	—
82	C₂²×Q₈×C₁₃	—	2	1	no	—
83	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
84	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
85	C₂²×D₄×C₁₃	—	2	1	no	—
86	C₂²×D₄×C₁₃	—	2	1	no	—
87	C₂²×D₄×C₁₃	—	2	1	no	—
88	C₂²×D₄×C₁₃	—	2	2	no	—
89	C₂²×D₄×C₁₃	—	2	1	no	—
90	C₂²×D₄×C₁₃	—	2	1	no	—
91	C₂²×D₄×C₁₃	—	2	1	no	—
92	C₂²×D₄×C₁₃	—	2	1	no	—
93	C₂²×D₄×C₁₃	—	4	2	no	—
94	C₂²×D₄×C₁₃	—	4	2	no	—
95	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
96	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
97	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
98	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
99	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
100	C₂³×C₄×C₁₃	—	2	1	no	—
101	C₂³×C₄×C₁₃	—	2	1	no	—
102	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
103	C₂×C₁₃×Q₁₆	—	4	2	no	—
104	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	complemented
105	C₂×C₁₃×SD₁₆	—	4	2	no	—
106	C₂×C₁₃×SD₁₆	—	4	2	no	—
107	C₂×C₁₃×SD₁₆	—	4	2	no	—
108	C₂×C₁₃×SD₁₆	—	4	2	no	—
109	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
110	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
111	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	complemented
112	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	complemented
113	C₂×C₁₃×D₈	—	4	2	no	—
114	C₂×C₁₃×D₈	—	4	2	no	—
115	C₂×C₁₃×D₈	—	4	2	no	—
116	C₂×C₁₃×D₈	C₂³	1	4	yes	—
117	C₂×C₁₃×D₈	C₂³	1	4	yes	—
118	C₂×C₁₃×D₈	C₂³	1	4	yes	complemented
119	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
120	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
121	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
122	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
123	C₁₃×C₄⋊Q₈	—	2	2	no	—
124	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	complemented
125	C₁₃×#127	—	2	2	no	—
126	C₁₃×#127	—	2	2	no	—
127	C₁₃×#127	C₂³	1	4	yes	—
128	C₁₃×#127	C₂³	1	4	yes	—
129	C₁₃×#126	—	2	8	no	—
130	C₁₃×#124	—	2	8	no	—
131	C₁₃×#124	—	2	2	no	—
132	C₁₃×#124	—	2	2	no	—
133	C₁₃×#124	—	2	2	no	—
134	C₁₃×#124	C₂³	1	4	yes	—
135	C₁₃×#124	C₂³	1	4	yes	—
136	C₁₃×#124	C₂³	1	4	yes	complemented
137	C₁₃×#123	—	2	8	no	—
138	C₁₃×C₂²⋊Q₈	—	2	2	no	—
139	C₁₃×C₂²⋊Q₈	—	2	8	no	—
140	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
141	C₁₃×#121	—	2	2	no	—
142	C₁₃×#121	—	2	8	no	—
143	C₁₃×#121	—	2	8	no	—
144	C₁₃×#121	C₂³	1	4	yes	—
145	C₁₃×#120	—	2	8	no	—
146	C₁₃×#120	—	2	8	no	—
147	C₄×Q₈×C₁₃	—	2	2	no	—
148	C₄×Q₈×C₁₃	C₂³	1	4	yes	complemented
149	C₄×D₄×C₁₃	—	2	2	no	—
150	C₄×D₄×C₁₃	C₂³	1	4	yes	complemented
151	C₁₃×#117	D₄	1	4	yes	—
152	C₁₃×#117	C₂³	1	4	yes	—
153	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
154	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
155	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
156	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
157	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
158	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
159	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
160	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
161	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
162	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
163	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
164	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
165	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
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	D₄	1	1	yes	characteristic
170	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
171	C₂×C₄²×C₁₃	—	2	1	no	—
172	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
173	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
174	C₁₃×C₄⋊C₈	C₂³	1	4	yes	complemented
175	C₁₃×C₄⋊C₈	C₂³	1	4	yes	complemented
176	C₁₃×#103	C₂³	1	4	yes	complemented
177	C₁₃×#103	C₂³	1	4	yes	complemented
178	C₁₃×#102	C₂³	1	4	yes	—
179	C₁₃×#102	C₂³	1	4	yes	—
180	C₁₃×#102	C₂³	1	4	yes	—
181	C₁₃×#102	C₂³	1	4	yes	—
182	C₁₃×#102	C₂³	1	4	yes	complemented
183	C₁₃×#102	C₂³	1	4	yes	complemented
184	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
185	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
186	C₁₃×#97	C₂³	1	4	yes	complemented
187	C₄×C₈×C₁₃	C₂³	1	4	yes	complemented
188	C₂×#3224	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
189	C₂⁴×C₁₃	—	2	1	no	—
190	C₂⁴×C₁₃	—	2	1	no	—
191	C₂⁴×C₁₃	—	2	1	no	—
192	C₂⁴×C₁₃	—	2	1	no	—
193	C₂⁴×C₁₃	—	2	4	no	—
194	C₂⁴×C₁₃	—	4	4	no	—
195	C₂⁴×C₁₃	—	8	2	no	—
196	C₂⁴×C₁₃	—	8	2	no	—
197	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
198	C₁₃×#41	—	4	4	no	—
199	C₁₃×#41	—	4	4	no	—
200	C₁₃×#41	—	4	8	no	—
201	C₂×Q₈×C₁₃	—	2	1	no	—
202	C₂×Q₈×C₁₃	—	2	1	no	—
203	C₂×Q₈×C₁₃	—	2	4	no	—
204	C₂×Q₈×C₁₃	—	2	2	no	—
205	C₂×Q₈×C₁₃	—	2	2	no	—
206	C₂×Q₈×C₁₃	—	2	2	no	—
207	C₂×Q₈×C₁₃	—	2	2	no	—
208	C₂×Q₈×C₁₃	—	8	2	no	—
209	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
210	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
211	C₂×D₄×C₁₃	—	2	4	no	—
212	C₂×D₄×C₁₃	—	2	4	no	—
213	C₂×D₄×C₁₃	—	2	1	no	—
214	C₂×D₄×C₁₃	—	2	4	no	—
215	C₂×D₄×C₁₃	—	2	1	no	—
216	C₂×D₄×C₁₃	—	2	1	no	—
217	C₂×D₄×C₁₃	—	2	1	no	—
218	C₂×D₄×C₁₃	—	2	4	no	—
219	C₂×D₄×C₁₃	—	2	4	no	—
220	C₂×D₄×C₁₃	—	2	4	no	—
221	C₂×D₄×C₁₃	—	2	4	no	—
222	C₂×D₄×C₁₃	—	2	2	no	—
223	C₂×D₄×C₁₃	—	2	2	no	—
224	C₂×D₄×C₁₃	—	2	2	no	—
225	C₂×D₄×C₁₃	—	2	2	no	—
226	C₂×D₄×C₁₃	—	2	2	no	—
227	C₂×D₄×C₁₃	—	2	2	no	—
228	C₂×D₄×C₁₃	—	2	2	no	—
229	C₂×D₄×C₁₃	—	2	2	no	—
230	C₂×D₄×C₁₃	—	4	4	no	—
231	C₂×D₄×C₁₃	—	4	4	no	—
232	C₂×D₄×C₁₃	—	4	4	no	—
233	C₂×D₄×C₁₃	—	4	8	no	—
234	C₂×D₄×C₁₃	—	4	4	no	—
235	C₂×D₄×C₁₃	—	8	2	no	—
236	C₂×D₄×C₁₃	—	8	2	no	—
237	C₂×D₄×C₁₃	—	8	2	no	—
238	C₂×D₄×C₁₃	—	8	2	no	—
239	C₂×D₄×C₁₃	—	8	2	no	—
240	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
241	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
242	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
243	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
244	C₂²×C₄×C₁₃	—	2	2	no	—
245	C₂²×C₄×C₁₃	—	2	2	no	—
246	C₂²×C₄×C₁₃	—	2	1	no	—
247	C₂²×C₄×C₁₃	—	2	1	no	—
248	C₂²×C₄×C₁₃	—	2	1	no	—
249	C₂²×C₄×C₁₃	—	2	1	no	—
250	C₂²×C₄×C₁₃	—	2	4	no	—
251	C₂²×C₄×C₁₃	—	2	4	no	—
252	C₂²×C₄×C₁₃	—	4	4	no	—
253	C₂²×C₄×C₁₃	—	8	2	no	—
254	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
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	C₂⁴	1	2	yes	—
261	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
262	C₁₃×Q₁₆	—	4	4	no	—
263	C₁₃×SD₁₆	—	4	4	no	—
264	C₁₃×SD₁₆	—	4	4	no	—
265	C₁₃×SD₁₆	—	4	4	no	—
266	C₁₃×SD₁₆	—	4	4	no	—
267	C₁₃×D₈	—	4	4	no	—
268	C₁₃×D₈	—	4	4	no	—
269	C₁₃×D₈	—	4	4	no	—
270	C₂×C₈×C₁₃	—	2	2	no	—
271	C₂×C₈×C₁₃	—	2	2	no	—
272	C₂×C₈×C₁₃	—	2	2	no	—
273	C₂×C₈×C₁₃	—	2	2	no	—
274	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
275	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
276	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
277	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
278	C₁₃×C₄⋊C₄	—	2	4	no	—
279	C₁₃×C₄⋊C₄	—	2	4	no	—
280	C₁₃×C₄⋊C₄	—	2	4	no	—
281	C₁₃×C₄⋊C₄	—	2	1	no	—
282	C₁₃×C₄⋊C₄	—	2	1	no	—
283	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
284	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
285	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
286	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
287	C₁₃×C₂²⋊C₄	—	2	4	no	—
288	C₁₃×C₂²⋊C₄	—	2	4	no	—
289	C₁₃×C₂²⋊C₄	—	2	4	no	—
290	C₁₃×C₂²⋊C₄	—	2	4	no	—
291	C₁₃×C₂²⋊C₄	—	2	4	no	—
292	C₁₃×C₂²⋊C₄	—	2	4	no	—
293	C₁₃×C₂²⋊C₄	—	2	4	no	—
294	C₁₃×C₂²⋊C₄	—	2	4	no	—
295	C₁₃×C₂²⋊C₄	—	2	4	no	—
296	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
297	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
298	C₄²×C₁₃	—	2	4	no	—
299	C₄²×C₁₃	C₂×D₄	1	2	yes	—
300	C₄²×C₁₃	C₂×D₄	1	2	yes	—
301	C₄²×C₁₃	C₂⁴	1	2	yes	—
302	C₄²×C₁₃	C₂⁴	1	2	yes	—
303	C₂×#542	C₂×C₁₃	1	1	yes	characteristic, complemented
304	C₂×#535	C₂×C₁₃	1	1	yes	characteristic, complemented
305	#3224	C₂×C₁₃	1	16	yes	direct product factor
306	C₂×#496	C₂×C₁₃	1	1	yes	characteristic, complemented
307	C₂×#495	C₂×C₁₃	1	1	yes	characteristic, complemented
308	C₂×#489	C₂×C₁₃	1	1	yes	characteristic, complemented
309	C₂×#486	C₂×C₁₃	1	1	yes	characteristic, complemented
310	C₂×#464	C₂×C₁₃	1	1	yes	characteristic, complemented
311	C₂×#460	C₂×C₁₃	1	1	yes	characteristic, complemented
312	C₂×#463	C₂×C₁₃	1	1	yes	characteristic, complemented
313	C₂×#459	C₂×C₁₃	1	1	yes	characteristic, complemented
314	C₂×#452	C₂×C₁₃	1	1	yes	characteristic, complemented
315	C₂×#449	C₂×C₁₃	1	1	yes	characteristic, complemented
316	C₂×#450	C₂×C₁₃	1	1	yes	characteristic, complemented
317	C₂×#447	C₂×C₁₃	1	1	yes	characteristic, complemented
318	C₂×#433	C₂×C₁₃	1	1	yes	characteristic, complemented
319	C₂³×C₁₃	—	2	2	no	—
320	C₂³×C₁₃	—	2	2	no	—
321	C₂³×C₁₃	—	2	2	no	—
322	C₂³×C₁₃	—	2	2	no	—
323	C₂³×C₁₃	—	2	2	no	—
324	C₂³×C₁₃	—	2	2	no	—
325	C₂³×C₁₃	—	2	2	no	—
326	C₂³×C₁₃	—	4	8	no	—
327	C₂³×C₁₃	—	4	2	no	—
328	C₂³×C₁₃	—	4	2	no	—
329	C₂³×C₁₃	—	4	2	no	—
330	C₂³×C₁₃	—	4	2	no	—
331	C₂³×C₁₃	—	4	2	no	—
332	C₂³×C₁₃	—	4	2	no	—
333	C₂³×C₁₃	—	4	2	no	—
334	C₂³×C₁₃	—	4	2	no	—
335	C₂³×C₁₃	—	4	2	no	—
336	C₂³×C₁₃	—	4	2	no	—
337	C₂³×C₁₃	—	4	2	no	—
338	C₂³×C₁₃	—	4	2	no	—
339	C₂³×C₁₃	—	8	4	no	—
340	C₂³×C₁₃	—	8	4	no	—
341	C₂³×C₁₃	—	8	16	no	—
342	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
343	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
344	Q₈×C₁₃	—	2	2	no	—
345	Q₈×C₁₃	—	2	2	no	—
346	Q₈×C₁₃	—	2	2	no	—
347	Q₈×C₁₃	—	2	2	no	—
348	Q₈×C₁₃	—	4	2	no	—
349	Q₈×C₁₃	—	4	2	no	—
350	Q₈×C₁₃	—	8	4	no	—
351	D₄×C₁₃	—	2	2	no	—
352	D₄×C₁₃	—	2	2	no	—
353	D₄×C₁₃	—	2	2	no	—
354	D₄×C₁₃	—	2	2	no	—
355	D₄×C₁₃	—	2	2	no	—
356	D₄×C₁₃	—	2	2	no	—
357	D₄×C₁₃	—	2	2	no	—
358	D₄×C₁₃	—	2	2	no	—
359	D₄×C₁₃	—	4	8	no	—
360	D₄×C₁₃	—	4	8	no	—
361	D₄×C₁₃	—	4	2	no	—
362	D₄×C₁₃	—	4	2	no	—
363	D₄×C₁₃	—	4	2	no	—
364	D₄×C₁₃	—	4	2	no	—
365	D₄×C₁₃	—	8	4	no	—
366	D₄×C₁₃	—	8	4	no	—
367	D₄×C₁₃	—	8	4	no	—
368	D₄×C₁₃	—	8	4	no	—
369	D₄×C₁₃	—	8	4	no	—
370	C₂×C₄×C₁₃	—	2	2	no	—
371	C₂×C₄×C₁₃	—	2	2	no	—
372	C₂×C₄×C₁₃	—	2	2	no	—
373	C₂×C₄×C₁₃	—	2	2	no	—
374	C₂×C₄×C₁₃	—	2	2	no	—
375	C₂×C₄×C₁₃	—	2	4	no	—
376	C₂×C₄×C₁₃	—	2	2	no	—
377	C₂×C₄×C₁₃	—	2	2	no	—
378	C₂×C₄×C₁₃	—	2	2	no	—
379	C₂×C₄×C₁₃	—	2	2	no	—
380	C₂×C₄×C₁₃	—	2	2	no	—
381	C₂×C₄×C₁₃	—	2	2	no	—
382	C₂×C₄×C₁₃	—	4	8	no	—
383	C₂×C₄×C₁₃	—	4	2	no	—
384	C₂×C₄×C₁₃	—	4	2	no	—
385	C₂×C₄×C₁₃	—	4	2	no	—
386	C₂×C₄×C₁₃	—	4	2	no	—
387	C₂×C₄×C₁₃	—	8	4	no	—
388	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
389	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
390	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
391	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
392	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
393	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
394	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
395	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
396	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
397	C₈×C₁₃	—	2	2	no	—
398	C₈×C₁₃	—	2	2	no	—
399	C₈×C₁₃	—	2	2	no	—
400	C₈×C₁₃	—	2	2	no	—
401	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
402	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
403	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
404	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
405	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
406	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
407	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
408	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
409	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
410	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
411	#542	—	2	4	no	—
412	#542	C₂²×C₁₃	1	8	yes	complemented
413	#535	—	2	4	no	—
414	#535	C₂²×C₁₃	1	8	yes	complemented
415	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
416	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
417	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
418	C₂×#126	—	2	1	no	—
419	C₂×#124	—	2	1	no	—
420	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
421	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
422	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic, complemented
423	C₂×#123	—	2	1	no	—
424	C₂×C₂²⋊Q₈	—	2	1	no	—
425	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
426	C₂×#121	—	2	1	no	—
427	C₂×#121	—	2	1	no	—
428	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
429	C₂×#120	—	2	1	no	—
430	C₂×#120	—	2	1	no	—
431	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
432	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
433	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
434	#496	C₂²×C₁₃	1	8	yes	complemented
435	#495	C₂²×C₁₃	1	8	yes	complemented
436	#489	C₂²×C₁₃	1	8	yes	complemented
437	#486	C₂²×C₁₃	1	8	yes	complemented
438	#464	C₂²×C₁₃	1	8	yes	complemented
439	#463	C₂²×C₁₃	1	8	yes	complemented
440	#460	C₂²×C₁₃	1	8	yes	complemented
441	#459	C₂²×C₁₃	1	8	yes	complemented
442	#452	C₂²×C₁₃	1	8	yes	complemented
443	#450	C₂²×C₁₃	1	8	yes	complemented
444	#449	C₂²×C₁₃	1	8	yes	complemented
445	#447	C₂²×C₁₃	1	8	yes	complemented
446	#433	C₂²×C₁₃	1	8	yes	complemented
447	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
448	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
449	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
450	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
451	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
452	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
453	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
454	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
455	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic, complemented
456	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic, complemented
457	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
458	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
459	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic, complemented
460	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
461	C₂²×C₁₃	—	2	2	no	—
462	C₂²×C₁₃	—	2	2	no	—
463	C₂²×C₁₃	—	2	2	no	—
464	C₂²×C₁₃	—	4	4	no	—
465	C₂²×C₁₃	—	4	2	no	—
466	C₂²×C₁₃	—	4	2	no	—
467	C₂²×C₁₃	—	4	2	no	—
468	C₂²×C₁₃	—	4	2	no	—
469	C₂²×C₁₃	—	4	2	no	—
470	C₂²×C₁₃	—	4	2	no	—
471	C₂²×C₁₃	—	4	2	no	—
472	C₂²×C₁₃	—	4	2	no	—
473	C₂²×C₁₃	—	4	2	no	—
474	C₂²×C₁₃	—	4	2	no	—
475	C₂²×C₁₃	—	4	2	no	—
476	C₂²×C₁₃	—	4	2	no	—
477	C₂²×C₁₃	—	8	16	no	—
478	C₂²×C₁₃	—	8	4	no	—
479	C₂²×C₁₃	—	8	4	no	—
480	C₂²×C₁₃	—	8	4	no	—
481	C₂²×C₁₃	—	8	4	no	—
482	C₂²×C₁₃	#535	1	2	yes	—
483	C₂²×C₁₃	#576	1	2	yes	—
484	C₂²×C₁₃	#577	1	2	yes	—
485	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
486	C₄×C₁₃	—	2	2	no	—
487	C₄×C₁₃	—	2	2	no	—
488	C₄×C₁₃	—	2	2	no	—
489	C₄×C₁₃	—	2	2	no	—
490	C₄×C₁₃	—	2	2	no	—
491	C₄×C₁₃	—	4	2	no	—
492	C₄×C₁₃	—	4	2	no	—
493	C₄×C₁₃	—	4	2	no	—
494	C₄×C₁₃	—	4	2	no	—
495	C₄×C₁₃	#535	1	2	yes	—
496	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
497	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
498	C₂⁵	—	2	1	no	—
499	C₂×#41	—	2	2	no	—
500	C₂×#41	—	4	2	no	—
501	C₂×#41	—	4	2	no	—
502	C₂×#41	C₂³×C₁₃	1	4	yes	—
503	C₂²×Q₈	—	2	1	no	—
504	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
505	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
506	C₂²×D₄	—	2	1	no	—
507	C₂²×D₄	—	2	1	no	—
508	C₂²×D₄	—	2	1	no	—
509	C₂²×D₄	—	2	2	no	—
510	C₂²×D₄	—	2	1	no	—
511	C₂²×D₄	—	2	1	no	—
512	C₂²×D₄	—	2	1	no	—
513	C₂²×D₄	—	2	1	no	—
514	C₂²×D₄	—	4	2	no	—
515	C₂²×D₄	—	4	2	no	—
516	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
517	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
518	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
519	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
520	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
521	C₂³×C₄	—	2	1	no	—
522	C₂³×C₄	—	2	1	no	—
523	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
524	C₂×Q₁₆	—	4	2	no	—
525	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	complemented
526	C₂×SD₁₆	—	4	2	no	—
527	C₂×SD₁₆	—	4	2	no	—
528	C₂×SD₁₆	—	4	2	no	—
529	C₂×SD₁₆	—	4	2	no	—
530	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
531	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
532	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	complemented
533	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	complemented
534	C₂×D₈	—	4	2	no	—
535	C₂×D₈	—	4	2	no	—
536	C₂×D₈	—	4	2	no	—
537	C₂×D₈	C₂³×C₁₃	1	4	yes	—
538	C₂×D₈	C₂³×C₁₃	1	4	yes	—
539	C₂×D₈	C₂³×C₁₃	1	4	yes	complemented
540	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
541	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
542	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
543	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
544	C₄⋊Q₈	—	2	2	no	—
545	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	complemented
546	#127	—	2	2	no	—
547	#127	—	2	2	no	—
548	#127	C₂³×C₁₃	1	4	yes	—
549	#127	C₂³×C₁₃	1	4	yes	—
550	#126	—	2	8	no	—
551	#124	—	2	8	no	—
552	#124	—	2	2	no	—
553	#124	—	2	2	no	—
554	#124	—	2	2	no	—
555	#124	C₂³×C₁₃	1	4	yes	—
556	#124	C₂³×C₁₃	1	4	yes	—
557	#124	C₂³×C₁₃	1	4	yes	complemented
558	#123	—	2	8	no	—
559	C₂²⋊Q₈	—	2	2	no	—
560	C₂²⋊Q₈	—	2	8	no	—
561	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
562	#121	—	2	2	no	—
563	#121	—	2	8	no	—
564	#121	—	2	8	no	—
565	#121	C₂³×C₁₃	1	4	yes	—
566	#120	—	2	8	no	—
567	#120	—	2	8	no	—
568	C₄×Q₈	—	2	2	no	—
569	C₄×Q₈	C₂³×C₁₃	1	4	yes	complemented
570	C₄×D₄	—	2	2	no	—
571	C₄×D₄	C₂³×C₁₃	1	4	yes	complemented
572	#117	D₄×C₁₃	1	4	yes	—
573	#117	C₂³×C₁₃	1	4	yes	—
574	C₂×C₄⋊C₄	—	2	1	no	—
575	C₂×C₄⋊C₄	—	2	1	no	—
576	C₂×C₄⋊C₄	—	2	1	no	—
577	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
578	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
579	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
580	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
581	C₂×C₂²⋊C₄	—	2	1	no	—
582	C₂×C₂²⋊C₄	—	2	1	no	—
583	C₂×C₂²⋊C₄	—	2	1	no	—
584	C₂×C₂²⋊C₄	—	2	1	no	—
585	C₂×C₂²⋊C₄	—	2	1	no	—
586	C₂×C₂²⋊C₄	—	2	1	no	—
587	C₂×C₂²⋊C₄	—	2	1	no	—
588	C₂×C₂²⋊C₄	—	2	1	no	—
589	C₂×C₂²⋊C₄	—	2	1	no	—
590	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
591	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
592	C₂×C₄²	—	2	1	no	—
593	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
594	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
595	C₄⋊C₈	C₂³×C₁₃	1	4	yes	complemented
596	C₄⋊C₈	C₂³×C₁₃	1	4	yes	complemented
597	#103	C₂³×C₁₃	1	4	yes	complemented
598	#103	C₂³×C₁₃	1	4	yes	complemented
599	#102	C₂³×C₁₃	1	4	yes	—
600	#102	C₂³×C₁₃	1	4	yes	—
601	#102	C₂³×C₁₃	1	4	yes	—
602	#102	C₂³×C₁₃	1	4	yes	—
603	#102	C₂³×C₁₃	1	4	yes	complemented
604	#102	C₂³×C₁₃	1	4	yes	complemented
605	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
606	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
607	#97	C₂³×C₁₃	1	4	yes	complemented
608	C₄×C₈	C₂³×C₁₃	1	4	yes	complemented
609	C₂×C₁₃	—	4	2	no	—
610	C₂×C₁₃	—	8	2	no	—
611	C₂×C₁₃	—	8	2	no	—
612	C₂×C₁₃	—	8	2	no	—
613	C₂×C₁₃	—	8	2	no	—
614	C₂×C₁₃	#3224	1	4	yes	direct product factor
615	C₂×C₁₃	C₂×#535	1	1	yes	characteristic
616	C₂×C₁₃	C₂×#576	1	1	yes	characteristic
617	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
618	C₂⁴	—	2	1	no	—
619	C₂⁴	—	2	1	no	—
620	C₂⁴	—	2	1	no	—
621	C₂⁴	—	2	1	no	—
622	C₂⁴	—	2	4	no	—
623	C₂⁴	—	4	4	no	—
624	C₂⁴	—	8	2	no	—
625	C₂⁴	—	8	2	no	—
626	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
627	#41	—	4	4	no	—
628	#41	—	4	4	no	—
629	#41	—	4	8	no	—
630	C₂×Q₈	—	2	1	no	—
631	C₂×Q₈	—	2	1	no	—
632	C₂×Q₈	—	2	4	no	—
633	C₂×Q₈	—	2	2	no	—
634	C₂×Q₈	—	2	2	no	—
635	C₂×Q₈	—	2	2	no	—
636	C₂×Q₈	—	2	2	no	—
637	C₂×Q₈	—	8	2	no	—
638	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
639	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
640	C₂×D₄	—	2	4	no	—
641	C₂×D₄	—	2	4	no	—
642	C₂×D₄	—	2	1	no	—
643	C₂×D₄	—	2	4	no	—
644	C₂×D₄	—	2	1	no	—
645	C₂×D₄	—	2	1	no	—
646	C₂×D₄	—	2	1	no	—
647	C₂×D₄	—	2	4	no	—
648	C₂×D₄	—	2	4	no	—
649	C₂×D₄	—	2	4	no	—
650	C₂×D₄	—	2	4	no	—
651	C₂×D₄	—	2	2	no	—
652	C₂×D₄	—	2	2	no	—
653	C₂×D₄	—	2	2	no	—
654	C₂×D₄	—	2	2	no	—
655	C₂×D₄	—	2	2	no	—
656	C₂×D₄	—	2	2	no	—
657	C₂×D₄	—	2	2	no	—
658	C₂×D₄	—	2	2	no	—
659	C₂×D₄	—	4	4	no	—
660	C₂×D₄	—	4	4	no	—
661	C₂×D₄	—	4	4	no	—
662	C₂×D₄	—	4	8	no	—
663	C₂×D₄	—	4	4	no	—
664	C₂×D₄	—	8	2	no	—
665	C₂×D₄	—	8	2	no	—
666	C₂×D₄	—	8	2	no	—
667	C₂×D₄	—	8	2	no	—
668	C₂×D₄	—	8	2	no	—
669	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
670	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
671	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
672	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
673	C₂²×C₄	—	2	2	no	—
674	C₂²×C₄	—	2	2	no	—
675	C₂²×C₄	—	2	1	no	—
676	C₂²×C₄	—	2	1	no	—
677	C₂²×C₄	—	2	1	no	—
678	C₂²×C₄	—	2	1	no	—
679	C₂²×C₄	—	2	4	no	—
680	C₂²×C₄	—	2	4	no	—
681	C₂²×C₄	—	4	4	no	—
682	C₂²×C₄	—	8	2	no	—
683	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
684	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
685	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
686	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
687	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
688	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
689	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
690	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
691	Q₁₆	—	4	4	no	—
692	SD₁₆	—	4	4	no	—
693	SD₁₆	—	4	4	no	—
694	SD₁₆	—	4	4	no	—
695	SD₁₆	—	4	4	no	—
696	D₈	—	4	4	no	—
697	D₈	—	4	4	no	—
698	D₈	—	4	4	no	—
699	C₂×C₈	—	2	2	no	—
700	C₂×C₈	—	2	2	no	—
701	C₂×C₈	—	2	2	no	—
702	C₂×C₈	—	2	2	no	—
703	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
704	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
705	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
706	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
707	C₄⋊C₄	—	2	4	no	—
708	C₄⋊C₄	—	2	4	no	—
709	C₄⋊C₄	—	2	4	no	—
710	C₄⋊C₄	—	2	1	no	—
711	C₄⋊C₄	—	2	1	no	—
712	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
713	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
714	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
715	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
716	C₂²⋊C₄	—	2	4	no	—
717	C₂²⋊C₄	—	2	4	no	—
718	C₂²⋊C₄	—	2	4	no	—
719	C₂²⋊C₄	—	2	4	no	—
720	C₂²⋊C₄	—	2	4	no	—
721	C₂²⋊C₄	—	2	4	no	—
722	C₂²⋊C₄	—	2	4	no	—
723	C₂²⋊C₄	—	2	4	no	—
724	C₂²⋊C₄	—	2	4	no	—
725	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
726	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
727	C₄²	—	2	4	no	—
728	C₄²	C₂×D₄×C₁₃	1	2	yes	—
729	C₄²	C₂×D₄×C₁₃	1	2	yes	—
730	C₄²	C₂⁴×C₁₃	1	2	yes	—
731	C₄²	C₂⁴×C₁₃	1	2	yes	—
732	C₁₃	C₂×#3224	1	1	yes	characteristic, direct product factor, Sylow
733	C₂³	—	2	2	no	—
734	C₂³	—	2	2	no	—
735	C₂³	—	2	2	no	—
736	C₂³	—	2	2	no	—
737	C₂³	—	2	2	no	—
738	C₂³	—	2	2	no	—
739	C₂³	—	2	2	no	—
740	C₂³	—	4	8	no	—
741	C₂³	—	4	2	no	—
742	C₂³	—	4	2	no	—
743	C₂³	—	4	2	no	—
744	C₂³	—	4	2	no	—
745	C₂³	—	4	2	no	—
746	C₂³	—	4	2	no	—
747	C₂³	—	4	2	no	—
748	C₂³	—	4	2	no	—
749	C₂³	—	4	2	no	—
750	C₂³	—	4	2	no	—
751	C₂³	—	4	2	no	—
752	C₂³	—	4	2	no	—
753	C₂³	—	8	4	no	—
754	C₂³	—	8	4	no	—
755	C₂³	—	8	16	no	—
756	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
757	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
758	Q₈	—	2	2	no	—
759	Q₈	—	2	2	no	—
760	Q₈	—	2	2	no	—
761	Q₈	—	2	2	no	—
762	Q₈	—	4	2	no	—
763	Q₈	—	4	2	no	—
764	Q₈	—	8	4	no	—
765	D₄	—	2	2	no	—
766	D₄	—	2	2	no	—
767	D₄	—	2	2	no	—
768	D₄	—	2	2	no	—
769	D₄	—	2	2	no	—
770	D₄	—	2	2	no	—
771	D₄	—	2	2	no	—
772	D₄	—	2	2	no	—
773	D₄	—	4	8	no	—
774	D₄	—	4	8	no	—
775	D₄	—	4	2	no	—
776	D₄	—	4	2	no	—
777	D₄	—	4	2	no	—
778	D₄	—	4	2	no	—
779	D₄	—	8	4	no	—
780	D₄	—	8	4	no	—
781	D₄	—	8	4	no	—
782	D₄	—	8	4	no	—
783	D₄	—	8	4	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	4	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	4	8	no	—
797	C₂×C₄	—	4	2	no	—
798	C₂×C₄	—	4	2	no	—
799	C₂×C₄	—	4	2	no	—
800	C₂×C₄	—	4	2	no	—
801	C₂×C₄	—	8	4	no	—
802	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
803	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
804	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
805	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
806	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
807	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
808	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
809	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
810	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
811	C₈	—	2	2	no	—
812	C₈	—	2	2	no	—
813	C₈	—	2	2	no	—
814	C₈	—	2	2	no	—
815	C₂²	—	2	2	no	—
816	C₂²	—	2	2	no	—
817	C₂²	—	2	2	no	—
818	C₂²	—	4	4	no	—
819	C₂²	—	4	2	no	—
820	C₂²	—	4	2	no	—
821	C₂²	—	4	2	no	—
822	C₂²	—	4	2	no	—
823	C₂²	—	4	2	no	—
824	C₂²	—	4	2	no	—
825	C₂²	—	4	2	no	—
826	C₂²	—	4	2	no	—
827	C₂²	—	4	2	no	—
828	C₂²	—	4	2	no	—
829	C₂²	—	4	2	no	—
830	C₂²	—	4	2	no	—
831	C₂²	—	8	16	no	—
832	C₂²	—	8	4	no	—
833	C₂²	—	8	4	no	—
834	C₂²	—	8	4	no	—
835	C₂²	—	8	4	no	—
836	C₂²	C₁₃×#535	1	2	yes	—
837	C₂²	C₁₃×#576	1	2	yes	—
838	C₂²	C₁₃×#577	1	2	yes	—
839	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
840	C₄	—	2	2	no	—
841	C₄	—	2	2	no	—
842	C₄	—	2	2	no	—
843	C₄	—	2	2	no	—
844	C₄	—	2	2	no	—
845	C₄	—	4	2	no	—
846	C₄	—	4	2	no	—
847	C₄	—	4	2	no	—
848	C₄	—	4	2	no	—
849	C₄	C₁₃×#535	1	2	yes	—
850	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
851	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
852	C₂	—	4	2	no	—
853	C₂	—	8	2	no	—
854	C₂	—	8	2	no	—
855	C₂	—	8	2	no	—
856	C₂	—	8	2	no	—
857	C₂	C₁₃×#3224	1	4	yes	direct product factor
858	C₂	C₂×C₁₃×#535	1	1	yes	characteristic
859	C₂	C₂×C₁₃×#576	1	1	yes	characteristic
860	C₂	C₂×C₁₃×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₁₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#542	C₂	semidirect
2. C₂×C₁₃×#535	C₂	semidirect
3. C₁₃×#3224	C₂	direct (N × H)
4. C₂×C₁₃×#496	C₂	semidirect
5. C₂×C₁₃×#495	C₂	semidirect
6. C₂×C₁₃×#489	C₂	semidirect
7. C₂×C₁₃×#486	C₂	semidirect
8. C₂×C₁₃×#464	C₂	semidirect
9. C₂×C₁₃×#460	C₂	semidirect
10. C₂×C₁₃×#463	C₂	semidirect
11. C₂×C₁₃×#459	C₂	semidirect
12. C₂×C₁₃×#452	C₂	semidirect
13. C₂×C₁₃×#449	C₂	semidirect
14. C₂×C₁₃×#450	C₂	semidirect
15. C₂×C₁₃×#447	C₂	semidirect
16. C₂×C₁₃×#433	C₂	semidirect
19. C₂²×C₁₃×Q₁₆	C₂²	semidirect
22. C₂²×C₁₃×SD₁₆	C₂²	semidirect
23. C₂²×C₁₃×SD₁₆	C₂²	semidirect
26. C₂²×C₁₃×D₈	C₂²	semidirect
28. C₁₃×#542	C₂²	semidirect
30. C₁₃×#535	C₂²	semidirect
31. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
38. C₂×C₁₃×#124	C₂²	semidirect
47. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
48. C₂×C₄×D₄×C₁₃	C₂²	semidirect
50. C₁₃×#496	C₂²	semidirect
51. C₁₃×#495	C₂²	semidirect
52. C₁₃×#489	C₂²	semidirect
53. C₁₃×#486	C₂²	semidirect
54. C₁₃×#464	C₂²	semidirect
55. C₁₃×#463	C₂²	semidirect
56. C₁₃×#460	C₂²	semidirect
57. C₁₃×#459	C₂²	semidirect
58. C₁₃×#452	C₂²	semidirect
59. C₁₃×#450	C₂²	semidirect
60. C₁₃×#449	C₂²	semidirect
61. C₁₃×#447	C₂²	semidirect
62. C₁₃×#433	C₂²	semidirect
63. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
64. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
65. C₂×C₁₃×#103	C₂²	semidirect
66. C₂×C₁₃×#103	C₂²	semidirect
71. C₂×C₁₃×#102	C₂²	semidirect
72. C₂×C₁₃×#102	C₂²	semidirect
75. C₂×C₁₃×#97	C₂²	semidirect
76. C₂×C₄×C₈×C₁₃	C₂²	semidirect
104. C₂×C₁₃×Q₁₆	C₂³	semidirect
111. C₂×C₁₃×SD₁₆	C₂³	semidirect
112. C₂×C₁₃×SD₁₆	C₂³	semidirect
118. C₂×C₁₃×D₈	C₂³	semidirect
124. C₁₃×C₄⋊Q₈	C₂³	semidirect
136. C₁₃×#124	C₂³	semidirect
148. C₄×Q₈×C₁₃	C₂³	semidirect
150. C₄×D₄×C₁₃	C₂³	semidirect
174. C₁₃×C₄⋊C₈	C₂³	semidirect
175. C₁₃×C₄⋊C₈	C₂³	semidirect
176. C₁₃×#103	C₂³	semidirect
177. C₁₃×#103	C₂³	semidirect
182. C₁₃×#102	C₂³	semidirect
183. C₁₃×#102	C₂³	semidirect
186. C₁₃×#97	C₂³	semidirect
187. C₄×C₈×C₁₃	C₂³	semidirect
188. C₂×#3224	C₁₃	direct (N × H)
303. C₂×#542	C₂×C₁₃	semidirect
304. C₂×#535	C₂×C₁₃	semidirect
305. #3224	C₂×C₁₃	direct (N × H)
306. C₂×#496	C₂×C₁₃	semidirect
307. C₂×#495	C₂×C₁₃	semidirect
308. C₂×#489	C₂×C₁₃	semidirect
309. C₂×#486	C₂×C₁₃	semidirect
310. C₂×#464	C₂×C₁₃	semidirect
311. C₂×#460	C₂×C₁₃	semidirect
312. C₂×#463	C₂×C₁₃	semidirect
313. C₂×#459	C₂×C₁₃	semidirect
314. C₂×#452	C₂×C₁₃	semidirect
315. C₂×#449	C₂×C₁₃	semidirect
316. C₂×#450	C₂×C₁₃	semidirect
317. C₂×#447	C₂×C₁₃	semidirect
318. C₂×#433	C₂×C₁₃	semidirect
403. C₂²×Q₁₆	C₂²×C₁₃	semidirect
406. C₂²×SD₁₆	C₂²×C₁₃	semidirect
407. C₂²×SD₁₆	C₂²×C₁₃	semidirect
410. C₂²×D₈	C₂²×C₁₃	semidirect
412. #542	C₂²×C₁₃	semidirect
414. #535	C₂²×C₁₃	semidirect
415. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
422. C₂×#124	C₂²×C₁₃	semidirect
431. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
432. C₂×C₄×D₄	C₂²×C₁₃	semidirect
434. #496	C₂²×C₁₃	semidirect
435. #495	C₂²×C₁₃	semidirect
436. #489	C₂²×C₁₃	semidirect
437. #486	C₂²×C₁₃	semidirect
438. #464	C₂²×C₁₃	semidirect
439. #463	C₂²×C₁₃	semidirect
440. #460	C₂²×C₁₃	semidirect
441. #459	C₂²×C₁₃	semidirect
442. #452	C₂²×C₁₃	semidirect
443. #450	C₂²×C₁₃	semidirect
444. #449	C₂²×C₁₃	semidirect
445. #447	C₂²×C₁₃	semidirect
446. #433	C₂²×C₁₃	semidirect
447. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
448. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
449. C₂×#103	C₂²×C₁₃	semidirect
450. C₂×#103	C₂²×C₁₃	semidirect
455. C₂×#102	C₂²×C₁₃	semidirect
456. C₂×#102	C₂²×C₁₃	semidirect
459. C₂×#97	C₂²×C₁₃	semidirect
460. C₂×C₄×C₈	C₂²×C₁₃	semidirect
525. C₂×Q₁₆	C₂³×C₁₃	semidirect
532. C₂×SD₁₆	C₂³×C₁₃	semidirect
533. C₂×SD₁₆	C₂³×C₁₃	semidirect
539. C₂×D₈	C₂³×C₁₃	semidirect
545. C₄⋊Q₈	C₂³×C₁₃	semidirect
557. #124	C₂³×C₁₃	semidirect
569. C₄×Q₈	C₂³×C₁₃	semidirect
571. C₄×D₄	C₂³×C₁₃	semidirect
595. C₄⋊C₈	C₂³×C₁₃	semidirect
596. C₄⋊C₈	C₂³×C₁₃	semidirect
597. #103	C₂³×C₁₃	semidirect
598. #103	C₂³×C₁₃	semidirect
603. #102	C₂³×C₁₃	semidirect
604. #102	C₂³×C₁₃	semidirect
607. #97	C₂³×C₁₃	semidirect
608. C₄×C₈	C₂³×C₁₃	semidirect
614. C₂×C₁₃	#3224	direct (N × H)
732. C₁₃	C₂×#3224	direct (N × H)
857. C₂	C₁₃×#3224	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#542	2
C₂×C₁₃×#535	2
C₁₃×#3224	2
C₂×C₁₃×#496	2
C₂×C₁₃×#495	2
C₂×C₁₃×#489	2
C₂×C₁₃×#486	2
C₂×C₁₃×#464	2
C₂×C₁₃×#460	2
C₂×C₁₃×#463	2
C₂×C₁₃×#459	2
C₂×C₁₃×#452	2
C₂×C₁₃×#449	2
C₂×C₁₃×#450	2
C₂×C₁₃×#447	2
C₂×C₁₃×#433	2
C₂×#3224	13

Subgroups — C2×C13×#3224 #15747132

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3224 #15747132