Subgroups — C₂×#13115508 #15865503

Order 3328.

1046 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718785	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#88077	C₂	1	1	yes	maximal, characteristic
3	C₂×#11718898	C₂	1	1	yes	maximal, characteristic
4	C₂×M₁₆×Dic₁₃	C₂	1	1	yes	maximal, characteristic, complemented
5	#13115508	C₂	1	8	yes	maximal, direct product factor
6	C₂×#11718125	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#11718124	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#421	C₂	1	1	yes	maximal, characteristic
9	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
10	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
11	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
12	C₂²×C₄×Dic₁₃	C₂²	1	1	yes	characteristic
13	C₂²×#6099	C₂²	1	1	yes	characteristic
14	C₂²×#6099	C₂²	1	1	yes	characteristic
15	C₂²×#6099	C₂²	1	1	yes	characteristic
16	C₁₃×#421	—	2	2	no	—
17	C₁₃×#421	C₂²	1	4	yes	—
18	C₂×C₁₃×#104	—	2	2	no	—
19	#11718898	C₄	1	4	yes	complemented
20	#11718898	C₂²	1	4	yes	—
21	C₂×#88077	—	2	1	no	—
22	C₂×#88077	—	2	1	no	—
23	C₂×#88077	—	2	2	no	—
24	C₂×#88077	C₂²	1	4	yes	—
25	C₂×#88076	C₄	1	2	yes	complemented
26	C₂×#88073	C₄	1	2	yes	complemented
27	#11718785	—	2	2	no	—
28	#11718785	C₂²	1	4	yes	complemented
29	C₂×#88062	—	2	2	no	—
30	M₁₆×Dic₁₃	—	2	2	no	—
31	M₁₆×Dic₁₃	C₂²	1	4	yes	complemented
32	C₂×#88055	—	2	1	no	—
33	C₂×C₈×Dic₁₃	—	2	1	no	—
34	#11718125	C₂²	1	4	yes	complemented
35	#11718124	C₂²	1	4	yes	complemented
36	C₂×C₁₃×#41	—	2	1	no	—
37	C₂×C₁₃×#41	—	2	1	no	—
38	C₂×C₁₃×#41	—	2	1	no	—
39	C₂×C₁₃×#41	—	2	1	no	—
40	C₂×C₁₃×#41	—	2	1	no	—
41	C₂×C₁₃×#41	—	2	1	no	—
42	C₂×C₁₃×#41	—	2	1	no	—
43	C₂×C₁₃×#41	—	2	1	no	—
44	C₂×C₁₃×#41	—	2	1	no	—
45	C₂×C₁₃×#41	—	2	1	no	—
46	C₂×C₁₃×#41	C₂×C₄	1	2	yes	—
47	C₂×C₁₃×#41	C₂³	1	2	yes	—
48	C₂²×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
49	C₂²×D₄×C₁₃	—	2	1	no	—
50	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
51	C₂³×C₄×C₁₃	—	2	1	no	—
52	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
53	C₂³×Dic₁₃	—	2	1	no	—
54	C₂×C₁₃×M₁₆	—	2	1	no	—
55	C₂×C₁₃×M₁₆	—	2	1	no	—
56	C₂×C₁₃×M₁₆	—	2	1	no	—
57	C₂×C₁₃×M₁₆	D₄	1	2	yes	—
58	C₂×C₁₃×M₁₆	D₄	1	2	yes	—
59	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
60	C₂²×C₈×C₁₃	—	2	1	no	—
61	C₁₃×#117	—	2	1	no	—
62	C₁₃×#117	—	2	1	no	—
63	C₁₃×#117	—	2	1	no	—
64	C₁₃×#117	C₂³	1	2	yes	—
65	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
66	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
67	C₂×C₄²×C₁₃	—	2	1	no	—
68	C₂×C₄×Dic₁₃	—	2	1	no	—
69	C₂×C₄×Dic₁₃	—	2	1	no	—
70	C₂×C₄×Dic₁₃	—	2	1	no	—
71	C₂×C₄×Dic₁₃	D₄	1	1	yes	characteristic
72	C₂×C₄×Dic₁₃	D₄	1	1	yes	characteristic
73	C₂×C₄×Dic₁₃	D₄	1	2	yes	—
74	C₂×C₄×Dic₁₃	C₂³	1	2	yes	—
75	C₂×#6099	—	2	1	no	—
76	C₂×#6099	—	2	1	no	—
77	C₂×#6099	—	2	1	no	—
78	C₂×#6099	—	2	1	no	—
79	C₂×#6099	—	2	1	no	—
80	C₂×#6099	—	2	1	no	—
81	C₂×#6099	—	2	1	no	—
82	C₂×#6099	—	2	1	no	—
83	C₂×#6099	—	2	1	no	—
84	C₂×#6099	—	2	1	no	—
85	C₂×#6099	—	2	1	no	—
86	C₂×#6099	C₂×C₄	1	2	yes	—
87	C₂×#6099	C₂×C₄	1	2	yes	—
88	C₂×#6099	C₂×C₄	1	2	yes	—
89	C₂×#6099	C₂×C₄	1	2	yes	—
90	C₂×#6099	C₂³	1	2	yes	—
91	C₂×#6099	C₂³	1	2	yes	—
92	C₂×#6099	C₂³	1	2	yes	—
93	C₂²×#1055	—	2	1	no	—
94	C₂²×#1055	—	2	1	no	—
95	C₂²×#1055	—	2	1	no	—
96	C₁₃×#104	—	2	8	no	—
97	#88077	—	2	4	no	—
98	#88077	—	2	4	no	—
99	#88076	C₂×C₄	1	8	yes	complemented
100	#88073	C₂×C₄	1	8	yes	complemented
101	#88062	—	2	8	no	—
102	#88055	—	2	4	no	—
103	C₈×Dic₁₃	—	2	4	no	—
104	C₂×#1932	—	13	1	no	maximal, Sylow
105	C₂⁴×C₁₃	—	2	1	no	—
106	C₂⁴×C₁₃	#41	1	1	yes	characteristic
107	C₁₃×#41	—	2	2	no	—
108	C₁₃×#41	—	2	2	no	—
109	C₁₃×#41	—	2	2	no	—
110	C₁₃×#41	—	2	2	no	—
111	C₁₃×#41	—	2	2	no	—
112	C₁₃×#41	—	2	2	no	—
113	C₁₃×#41	—	2	2	no	—
114	C₁₃×#41	—	2	2	no	—
115	C₁₃×#41	—	4	1	no	—
116	C₁₃×#41	—	4	1	no	—
117	C₁₃×#41	—	4	1	no	—
118	C₁₃×#41	—	4	1	no	—
119	C₁₃×#41	—	4	1	no	—
120	C₁₃×#41	—	4	1	no	—
121	C₁₃×#41	—	4	1	no	—
122	C₁₃×#41	—	4	1	no	—
123	C₂×Q₈×C₁₃	—	2	1	no	—
124	C₂×Q₈×C₁₃	—	2	1	no	—
125	C₂×Q₈×C₁₃	—	2	1	no	—
126	C₂×Q₈×C₁₃	—	2	1	no	—
127	C₂×Q₈×C₁₃	—	2	1	no	—
128	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
129	C₂×D₄×C₁₃	—	2	2	no	—
130	C₂×D₄×C₁₃	—	2	2	no	—
131	C₂×D₄×C₁₃	—	2	1	no	—
132	C₂×D₄×C₁₃	—	2	1	no	—
133	C₂×D₄×C₁₃	—	2	1	no	—
134	C₂×D₄×C₁₃	—	2	1	no	—
135	C₂×D₄×C₁₃	—	2	1	no	—
136	C₂×D₄×C₁₃	—	4	1	no	—
137	C₂×D₄×C₁₃	—	4	1	no	—
138	C₂×D₄×C₁₃	—	4	1	no	—
139	C₂×D₄×C₁₃	—	4	1	no	—
140	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
141	C₂²×C₄×C₁₃	—	2	1	no	—
142	C₂²×C₄×C₁₃	—	2	2	no	—
143	C₂²×C₄×C₁₃	—	2	2	no	—
144	C₂²×C₄×C₁₃	—	4	1	no	—
145	C₂²×C₄×C₁₃	—	4	1	no	—
146	C₂²×C₄×C₁₃	—	4	1	no	—
147	C₂²×C₄×C₁₃	—	4	1	no	—
148	C₂²×C₄×C₁₃	—	4	1	no	—
149	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
150	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
151	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
156	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
157	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
158	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
159	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
160	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
161	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
162	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
163	C₂²×Dic₁₃	—	2	1	no	—
164	C₂²×Dic₁₃	—	2	2	no	—
165	C₂²×Dic₁₃	—	2	1	no	—
166	C₂²×Dic₁₃	—	2	2	no	—
167	C₂²×Dic₁₃	—	4	4	no	—
168	C₁₃×M₁₆	—	2	2	no	—
169	C₁₃×M₁₆	—	2	2	no	—
170	C₁₃×M₁₆	—	2	2	no	—
171	C₁₃×M₁₆	C₂×D₄	1	4	yes	—
172	C₂×C₈×C₁₃	—	2	2	no	—
173	C₂×C₈×C₁₃	—	2	2	no	—
174	C₂×C₈×C₁₃	—	2	2	no	—
175	C₁₃×C₄⋊C₄	—	2	2	no	—
176	C₁₃×C₄⋊C₄	—	4	1	no	—
177	C₁₃×C₂²⋊C₄	—	2	2	no	—
178	C₁₃×C₂²⋊C₄	—	4	1	no	—
179	C₄²×C₁₃	—	2	2	no	—
180	C₄²×C₁₃	—	4	1	no	—
181	C₄×Dic₁₃	—	2	1	no	—
182	C₄×Dic₁₃	—	2	2	no	—
183	C₄×Dic₁₃	—	2	1	no	—
184	C₄×Dic₁₃	—	2	2	no	—
185	C₄×Dic₁₃	C₂×D₄	1	2	yes	—
186	C₄×Dic₁₃	C₂×D₄	1	2	yes	—
187	#6099	—	2	2	no	—
188	#6099	—	2	2	no	—
189	#6099	—	2	2	no	—
190	#6099	—	2	2	no	—
191	#6099	—	2	2	no	—
192	#6099	—	2	2	no	—
193	#6099	—	2	2	no	—
194	#6099	—	2	2	no	—
195	#6099	—	4	1	no	—
196	#6099	—	4	1	no	—
197	#6099	C₂²×C₄	1	4	yes	—
198	#6099	C₂²×C₄	1	4	yes	—
199	C₂×#1055	—	2	2	no	—
200	C₂×#1055	—	2	2	no	—
201	C₂×#1055	—	2	2	no	—
202	C₂×#1055	—	2	2	no	—
203	C₂×#1055	—	2	2	no	—
204	C₂×#1055	—	2	2	no	—
205	C₂×#1055	—	2	2	no	—
206	C₂×#1055	—	4	1	no	—
207	C₂×#1055	—	4	1	no	—
208	C₂×#430	—	13	1	no	—
209	C₂×#421	D₁₃	1	1	yes	characteristic
210	C₂²×#104	—	13	1	no	—
211	C₂×#413	—	13	1	no	—
212	C₂×C₄×M₁₆	—	13	1	no	—
213	#1932	—	13	8	no	—
214	C₂×#344	—	13	1	no	—
215	C₂×#339	—	13	1	no	—
216	C₂³×C₁₃	—	2	2	no	—
217	C₂³×C₁₃	—	4	2	no	—
218	C₂³×C₁₃	—	4	1	no	—
219	C₂³×C₁₃	—	4	1	no	—
220	C₂³×C₁₃	—	8	2	no	—
221	C₂³×C₁₃	#117	1	1	yes	characteristic
222	C₂³×C₁₃	#117	1	1	yes	characteristic
223	C₂³×C₁₃	#123	1	1	yes	characteristic
224	C₂³×C₁₃	#123	1	1	yes	characteristic
225	C₂³×C₁₃	#124	1	1	yes	characteristic
226	C₂³×C₁₃	#124	1	1	yes	characteristic
227	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
228	Q₈×C₁₃	—	2	2	no	—
229	Q₈×C₁₃	—	2	2	no	—
230	Q₈×C₁₃	—	4	1	no	—
231	Q₈×C₁₃	—	4	1	no	—
232	D₄×C₁₃	—	2	2	no	—
233	D₄×C₁₃	—	2	2	no	—
234	D₄×C₁₃	—	4	2	no	—
235	D₄×C₁₃	—	4	2	no	—
236	D₄×C₁₃	—	4	2	no	—
237	D₄×C₁₃	—	4	2	no	—
238	D₄×C₁₃	—	4	1	no	—
239	D₄×C₁₃	—	4	1	no	—
240	C₂×C₄×C₁₃	—	2	2	no	—
241	C₂×C₄×C₁₃	—	4	1	no	—
242	C₂×C₄×C₁₃	—	4	1	no	—
243	C₂×C₄×C₁₃	—	4	2	no	—
244	C₂×C₄×C₁₃	—	4	2	no	—
245	C₂×C₄×C₁₃	—	4	2	no	—
246	C₂×C₄×C₁₃	—	4	2	no	—
247	C₂×C₄×C₁₃	—	4	2	no	—
248	C₂×C₄×C₁₃	—	8	2	no	—
249	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
250	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
251	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
252	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
253	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
254	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
255	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
256	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
257	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
258	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
259	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
260	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
261	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
262	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
263	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
264	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
265	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
266	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
267	C₂×C₄×C₁₃	#126	1	1	yes	characteristic
268	C₂×C₄×C₁₃	#126	1	1	yes	characteristic
269	C₂×C₄×C₁₃	#126	1	1	yes	characteristic
270	C₂×C₄×C₁₃	#126	1	1	yes	characteristic
271	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
272	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
273	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
274	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
275	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
276	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
277	C₂×Dic₁₃	—	2	4	no	—
278	C₂×Dic₁₃	—	2	2	no	—
279	C₂×Dic₁₃	—	2	2	no	—
280	C₂×Dic₁₃	—	4	4	no	—
281	C₂×Dic₁₃	—	4	4	no	—
282	C₂×Dic₁₃	—	4	2	no	—
283	C₈×C₁₃	—	2	4	no	—
284	#1055	—	2	4	no	—
285	#1055	—	2	4	no	—
286	#1055	—	4	2	no	—
287	C₂²×#41	C₂×D₁₃	1	1	yes	characteristic
288	C₂²×M₁₆	—	13	1	no	—
289	C₂²×M₁₆	—	13	1	no	—
290	C₂²×M₁₆	—	13	1	no	—
291	C₂²×M₁₆	C₂×D₁₃	1	1	yes	characteristic
292	C₂×#117	C₂×D₁₃	1	1	yes	characteristic
293	C₂²×C₄²	—	13	1	no	—
294	#430	—	13	4	no	—
295	#430	—	26	2	no	—
296	C₂×#108	—	26	2	no	—
297	#421	—	2	2	no	—
298	#421	C₂×D₁₃	1	4	yes	—
299	C₂×#104	—	2	2	no	—
300	C₂×#104	—	13	4	no	—
301	C₂×#104	—	26	1	no	—
302	C₂×#104	—	26	1	no	—
303	C₂×#104	—	26	2	no	—
304	#413	—	13	4	no	—
305	#413	—	13	4	no	—
306	C₂×#101	—	13	2	no	—
307	C₂×#100	—	13	2	no	—
308	C₄×M₁₆	—	13	4	no	—
309	C₄×M₁₆	—	26	2	no	—
310	C₂×#97	—	26	1	no	—
311	C₂×C₄×C₈	—	26	1	no	—
312	#344	—	13	4	no	—
313	#339	—	13	4	no	—
314	C₂²×C₁₃	—	2	2	no	—
315	C₂²×C₁₃	—	2	2	no	—
316	C₂²×C₁₃	—	2	2	no	—
317	C₂²×C₁₃	—	4	1	no	—
318	C₂²×C₁₃	—	4	1	no	—
319	C₂²×C₁₃	—	4	1	no	—
320	C₂²×C₁₃	—	4	1	no	—
321	C₂²×C₁₃	—	4	2	no	—
322	C₂²×C₁₃	—	8	2	no	—
323	C₂²×C₁₃	—	8	2	no	—
324	C₂²×C₁₃	—	8	2	no	—
325	C₂²×C₁₃	#388	1	1	yes	characteristic
326	C₂²×C₁₃	#388	1	1	yes	characteristic
327	C₂²×C₁₃	#388	1	1	yes	characteristic
328	C₂²×C₁₃	#388	1	1	yes	characteristic
329	C₂²×C₁₃	C₂×#117	1	1	yes	characteristic
330	C₂²×C₁₃	C₂×#123	1	1	yes	characteristic
331	C₂²×C₁₃	C₂×#124	1	1	yes	characteristic
332	C₄×C₁₃	—	4	2	no	—
333	C₄×C₁₃	—	8	2	no	—
334	C₄×C₁₃	#388	1	1	yes	characteristic
335	C₄×C₁₃	#388	1	1	yes	characteristic
336	C₄×C₁₃	#388	1	1	yes	characteristic
337	C₄×C₁₃	#388	1	1	yes	characteristic
338	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
339	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
340	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
341	C₄×C₁₃	C₂×#126	1	1	yes	characteristic
342	Dic₁₃	—	2	4	no	—
343	Dic₁₃	—	4	2	no	—
344	C₂×#41	—	2	1	no	—
345	C₂×#41	—	2	1	no	—
346	C₂×#41	—	2	1	no	—
347	C₂×#41	—	2	1	no	—
348	C₂×#41	—	2	1	no	—
349	C₂×#41	—	2	1	no	—
350	C₂×#41	—	2	1	no	—
351	C₂×#41	—	2	1	no	—
352	C₂×#41	—	2	1	no	—
353	C₂×#41	—	2	1	no	—
354	C₂×#41	C₄×D₁₃	1	2	yes	—
355	C₂×#41	C₂²×D₁₃	1	2	yes	—
356	C₂²×Q₈	C₄×D₁₃	1	1	yes	characteristic
357	C₂²×D₄	—	2	1	no	—
358	C₂²×D₄	C₄×D₁₃	1	1	yes	characteristic
359	C₂³×C₄	—	2	1	no	—
360	C₂³×C₄	—	26	1	no	—
361	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
362	C₂×M₁₆	—	2	1	no	—
363	C₂×M₁₆	—	2	1	no	—
364	C₂×M₁₆	—	2	1	no	—
365	C₂×M₁₆	—	13	2	no	—
366	C₂×M₁₆	—	13	2	no	—
367	C₂×M₁₆	—	13	2	no	—
368	C₂×M₁₆	—	13	2	no	—
369	C₂×M₁₆	—	13	2	no	—
370	C₂×M₁₆	—	13	2	no	—
371	C₂×M₁₆	—	13	2	no	—
372	C₂×M₁₆	—	26	1	no	—
373	C₂×M₁₆	—	26	1	no	—
374	C₂×M₁₆	—	26	1	no	—
375	C₂×M₁₆	—	26	1	no	—
376	C₂×M₁₆	—	26	1	no	—
377	C₂×M₁₆	—	26	1	no	—
378	C₂×M₁₆	—	26	1	no	—
379	C₂×M₁₆	—	26	1	no	—
380	C₂×M₁₆	—	26	1	no	—
381	C₂×M₁₆	—	26	1	no	—
382	C₂×M₁₆	—	26	1	no	—
383	C₂×M₁₆	C₂²⋊D₁₃	1	2	yes	—
384	C₂×M₁₆	C₂²⋊D₁₃	1	2	yes	—
385	C₂×M₁₆	C₂²×D₁₃	1	2	yes	—
386	C₂²×C₈	—	2	1	no	—
387	C₂²×C₈	—	26	1	no	—
388	C₂²×C₈	—	26	1	no	—
389	C₂²×C₈	—	26	1	no	—
390	#117	—	2	1	no	—
391	#117	—	2	1	no	—
392	#117	—	2	1	no	—
393	#117	C₂²×D₁₃	1	2	yes	—
394	C₂×C₄⋊C₄	—	2	1	no	—
395	C₂×C₂²⋊C₄	—	2	1	no	—
396	C₂×C₄²	—	2	1	no	—
397	C₂×C₄²	—	13	1	no	—
398	C₂×C₄²	—	13	1	no	—
399	C₂×C₄²	—	13	2	no	—
400	C₂×C₄²	—	13	2	no	—
401	C₂×C₄²	—	26	1	no	—
402	C₂×C₄²	—	26	1	no	—
403	C₂×C₄²	—	26	1	no	—
404	#108	—	26	8	no	—
405	#104	—	2	8	no	—
406	#104	—	26	4	no	—
407	#104	—	26	4	no	—
408	#101	—	13	8	no	—
409	#100	—	13	8	no	—
410	#97	—	26	4	no	—
411	C₄×C₈	—	26	4	no	—
412	C₂×C₁₃	—	2	1	no	—
413	C₂×C₁₃	—	2	1	no	—
414	C₂×C₁₃	—	2	1	no	—
415	C₂×C₁₃	—	2	1	no	—
416	C₂×C₁₃	—	2	1	no	—
417	C₂×C₁₃	—	2	1	no	—
418	C₂×C₁₃	—	8	2	no	—
419	C₂×C₁₃	#1932	1	2	yes	complemented
420	C₂×C₁₃	C₂×#388	1	1	yes	characteristic
421	C₂⁴	—	2	1	no	—
422	C₂⁴	#6129	1	1	yes	characteristic
423	#41	—	2	2	no	—
424	#41	—	2	2	no	—
425	#41	—	2	2	no	—
426	#41	—	2	2	no	—
427	#41	—	2	2	no	—
428	#41	—	2	2	no	—
429	#41	—	2	2	no	—
430	#41	—	2	2	no	—
431	#41	—	4	1	no	—
432	#41	—	4	1	no	—
433	#41	—	4	1	no	—
434	#41	—	4	1	no	—
435	#41	—	4	1	no	—
436	#41	—	4	1	no	—
437	#41	—	4	1	no	—
438	#41	—	4	1	no	—
439	C₂×Q₈	—	2	1	no	—
440	C₂×Q₈	—	2	1	no	—
441	C₂×Q₈	—	2	1	no	—
442	C₂×Q₈	—	2	1	no	—
443	C₂×Q₈	—	2	1	no	—
444	C₂×Q₈	C₂×C₄×D₁₃	1	2	yes	—
445	C₂×D₄	—	2	2	no	—
446	C₂×D₄	—	2	2	no	—
447	C₂×D₄	—	2	1	no	—
448	C₂×D₄	—	2	1	no	—
449	C₂×D₄	—	2	1	no	—
450	C₂×D₄	—	2	1	no	—
451	C₂×D₄	—	2	1	no	—
452	C₂×D₄	—	4	1	no	—
453	C₂×D₄	—	4	1	no	—
454	C₂×D₄	—	4	1	no	—
455	C₂×D₄	—	4	1	no	—
456	C₂×D₄	C₂×C₄×D₁₃	1	2	yes	—
457	C₂²×C₄	—	2	1	no	—
458	C₂²×C₄	—	2	2	no	—
459	C₂²×C₄	—	2	2	no	—
460	C₂²×C₄	—	4	1	no	—
461	C₂²×C₄	—	4	1	no	—
462	C₂²×C₄	—	4	1	no	—
463	C₂²×C₄	—	4	1	no	—
464	C₂²×C₄	—	4	1	no	—
465	C₂²×C₄	—	26	1	no	—
466	C₂²×C₄	—	26	2	no	—
467	C₂²×C₄	—	26	1	no	—
468	C₂²×C₄	—	26	2	no	—
469	C₂²×C₄	—	52	4	no	—
470	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
471	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
472	C₂²×C₄	#6127	1	1	yes	characteristic
473	C₂²×C₄	#6127	1	1	yes	characteristic
474	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
475	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
476	C₂²×C₄	#6129	1	1	yes	characteristic
477	C₂²×C₄	#6129	1	1	yes	characteristic
478	C₂²×C₄	#6129	1	1	yes	characteristic
479	C₂²×C₄	#6129	1	1	yes	characteristic
480	C₂²×C₄	#6129	1	1	yes	characteristic
481	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
482	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
483	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
484	M₁₆	—	2	2	no	—
485	M₁₆	—	2	2	no	—
486	M₁₆	—	2	2	no	—
487	M₁₆	—	13	4	no	—
488	M₁₆	—	13	4	no	—
489	M₁₆	—	26	2	no	—
490	M₁₆	—	26	2	no	—
491	M₁₆	—	26	2	no	—
492	M₁₆	—	26	2	no	—
493	M₁₆	—	26	2	no	—
494	M₁₆	—	26	2	no	—
495	M₁₆	—	26	2	no	—
496	M₁₆	—	26	2	no	—
497	M₁₆	—	52	1	no	—
498	M₁₆	—	52	1	no	—
499	M₁₆	C₂×C₂²⋊D₁₃	1	4	yes	—
500	C₂×C₈	—	2	2	no	—
501	C₂×C₈	—	2	2	no	—
502	C₂×C₈	—	2	2	no	—
503	C₂×C₈	—	26	2	no	—
504	C₂×C₈	—	26	2	no	—
505	C₂×C₈	—	26	2	no	—
506	C₂×C₈	—	26	2	no	—
507	C₂×C₈	—	26	2	no	—
508	C₂×C₈	—	26	2	no	—
509	C₂×C₈	—	26	2	no	—
510	C₂×C₈	—	52	1	no	—
511	C₂×C₈	—	52	1	no	—
512	C₄⋊C₄	—	2	2	no	—
513	C₄⋊C₄	—	4	1	no	—
514	C₂²⋊C₄	—	2	2	no	—
515	C₂²⋊C₄	—	4	1	no	—
516	C₄²	—	2	2	no	—
517	C₄²	—	4	1	no	—
518	C₄²	—	13	2	no	—
519	C₄²	—	13	2	no	—
520	C₄²	—	26	1	no	—
521	C₄²	—	26	2	no	—
522	C₄²	—	26	1	no	—
523	C₄²	—	26	2	no	—
524	C₁₃	C₂×#1932	1	1	yes	characteristic, complemented, Sylow
525	C₂³	—	2	2	no	—
526	C₂³	—	4	2	no	—
527	C₂³	—	4	1	no	—
528	C₂³	—	4	1	no	—
529	C₂³	—	8	2	no	—
530	C₂³	#88131	1	1	yes	characteristic
531	C₂³	#88131	1	1	yes	characteristic
532	C₂³	#88137	1	1	yes	characteristic
533	C₂³	#88137	1	1	yes	characteristic
534	C₂³	#88190	1	1	yes	characteristic
535	C₂³	#88190	1	1	yes	characteristic
536	C₂³	C₂×#6129	1	1	yes	characteristic
537	Q₈	—	2	2	no	—
538	Q₈	—	2	2	no	—
539	Q₈	—	4	1	no	—
540	Q₈	—	4	1	no	—
541	D₄	—	2	2	no	—
542	D₄	—	2	2	no	—
543	D₄	—	4	2	no	—
544	D₄	—	4	2	no	—
545	D₄	—	4	2	no	—
546	D₄	—	4	2	no	—
547	D₄	—	4	1	no	—
548	D₄	—	4	1	no	—
549	C₂×C₄	—	2	2	no	—
550	C₂×C₄	—	4	1	no	—
551	C₂×C₄	—	4	1	no	—
552	C₂×C₄	—	4	2	no	—
553	C₂×C₄	—	4	2	no	—
554	C₂×C₄	—	4	2	no	—
555	C₂×C₄	—	4	2	no	—
556	C₂×C₄	—	4	2	no	—
557	C₂×C₄	—	8	2	no	—
558	C₂×C₄	—	26	4	no	—
559	C₂×C₄	—	26	2	no	—
560	C₂×C₄	—	26	2	no	—
561	C₂×C₄	—	52	4	no	—
562	C₂×C₄	—	52	4	no	—
563	C₂×C₄	—	52	2	no	—
564	C₂×C₄	#88131	1	1	yes	characteristic
565	C₂×C₄	#88131	1	1	yes	characteristic
566	C₂×C₄	#88133	1	1	yes	characteristic
567	C₂×C₄	#88133	1	1	yes	characteristic
568	C₂×C₄	#88133	1	1	yes	characteristic
569	C₂×C₄	#88133	1	1	yes	characteristic
570	C₂×C₄	#88135	1	1	yes	characteristic
571	C₂×C₄	#88135	1	1	yes	characteristic
572	C₂×C₄	#88135	1	1	yes	characteristic
573	C₂×C₄	#88135	1	1	yes	characteristic
574	C₂×C₄	#88137	1	1	yes	characteristic
575	C₂×C₄	#88137	1	1	yes	characteristic
576	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
577	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
578	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
579	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
580	C₂×C₄	#88190	1	1	yes	characteristic
581	C₂×C₄	#88190	1	1	yes	characteristic
582	C₂×C₄	#88193	1	1	yes	characteristic
583	C₂×C₄	#88193	1	1	yes	characteristic
584	C₂×C₄	#88193	1	1	yes	characteristic
585	C₂×C₄	#88193	1	1	yes	characteristic
586	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
587	C₂×C₄	C₂×#6127	1	1	yes	characteristic
588	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
589	C₂×C₄	C₂×#6129	1	1	yes	characteristic
590	C₂×C₄	C₂×#6129	1	1	yes	characteristic
591	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
592	C₈	—	2	4	no	—
593	C₈	—	26	4	no	—
594	C₈	—	26	4	no	—
595	C₈	—	52	2	no	—
596	C₂²	—	2	2	no	—
597	C₂²	—	2	2	no	—
598	C₂²	—	2	2	no	—
599	C₂²	—	4	1	no	—
600	C₂²	—	4	1	no	—
601	C₂²	—	4	1	no	—
602	C₂²	—	4	1	no	—
603	C₂²	—	4	2	no	—
604	C₂²	—	8	2	no	—
605	C₂²	—	8	2	no	—
606	C₂²	—	8	2	no	—
607	C₂²	#11718606	1	1	yes	characteristic
608	C₂²	#11718606	1	1	yes	characteristic
609	C₂²	#11718606	1	1	yes	characteristic
610	C₂²	#11718606	1	1	yes	characteristic
611	C₂²	C₂×#88131	1	1	yes	characteristic
612	C₂²	C₂×#88137	1	1	yes	characteristic
613	C₂²	C₂×#88190	1	1	yes	characteristic
614	C₄	—	4	2	no	—
615	C₄	—	8	2	no	—
616	C₄	—	26	4	no	—
617	C₄	—	52	2	no	—
618	C₄	#11718606	1	1	yes	characteristic
619	C₄	#11718606	1	1	yes	characteristic
620	C₄	#11718606	1	1	yes	characteristic
621	C₄	#11718606	1	1	yes	characteristic
622	C₄	C₂×#88133	1	1	yes	characteristic
623	C₄	C₂×#88135	1	1	yes	characteristic
624	C₄	C₂×C₄×C₂²⋊D₁₃	1	1	yes	characteristic
625	C₄	C₂×#88193	1	1	yes	characteristic
626	C₂	—	2	1	no	—
627	C₂	—	2	1	no	—
628	C₂	—	2	1	no	—
629	C₂	—	2	1	no	—
630	C₂	—	2	1	no	—
631	C₂	—	2	1	no	—
632	C₂	—	8	2	no	—
633	C₂	#13115508	1	2	yes	direct product factor
634	C₂	C₂×#11718606	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#88193
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₂×C₁₃×#421	C₂
socle	C₂²×C₁₃	#388
prime radical	C₂²×C₁₃×#41	C₂²
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	C₂×#421	D₁₃
hypocenter	C₁₃	C₂×#1932
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂×#421

Complements

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

N	H ≅ G/N	type
1. C₂×#11718785	C₂	semidirect
4. C₂×M₁₆×Dic₁₃	C₂	semidirect
5. #13115508	C₂	direct (N × H)
6. C₂×#11718125	C₂	semidirect
7. C₂×#11718124	C₂	semidirect
19. #11718898	C₄	semidirect
25. C₂×#88076	C₄	semidirect
26. C₂×#88073	C₄	semidirect
28. #11718785	C₂²	semidirect
31. M₁₆×Dic₁₃	C₂²	semidirect
34. #11718125	C₂²	semidirect
35. #11718124	C₂²	semidirect
99. #88076	C₂×C₄	semidirect
100. #88073	C₂×C₄	semidirect
419. C₂×C₁₃	#1932	semidirect
524. C₁₃	C₂×#1932	semidirect
633. C₂	#13115508	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×#11718785	2
C₂²×#88077	2
C₂×#11718898	2
C₂×M₁₆×Dic₁₃	2
#13115508	2
C₂×#11718125	2
C₂×#11718124	2
C₂×C₁₃×#421	2
C₂×#1932	13

Subgroups — C2×#13115508 #15865503

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13115508 #15865503