Subgroups — C₂×#13115734 #15866893

Order 3328.

1474 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	C₂²×#88158	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718767	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#11718800	C₂	1	2	yes	maximal, complemented
4	C₂×#11718667	C₂	1	2	yes	maximal, complemented
5	#13115734	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₁₃×#405	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#6127	C₂²	1	2	yes	—
8	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
9	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
10	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
11	C₂×#88180	C₂²	1	2	yes	—
12	C₂²×Dic₅₂	C₄	1	1	yes	characteristic, complemented
13	C₂×#88158	—	2	1	no	—
14	C₂×#88158	—	2	1	no	—
15	C₂×#88158	—	2	2	no	—
16	C₂×#88158	—	2	1	no	—
17	C₂×#88158	—	2	1	no	—
18	C₂×#88158	—	2	2	no	—
19	C₂×#88158	C₄	1	4	yes	complemented
20	C₂×#88158	C₂²	1	4	yes	—
21	C₂²×D₁₀₄	C₄	1	1	yes	characteristic, complemented
22	C₂²×#6095	C₄	1	2	yes	complemented
23	C₁₃×#405	—	2	2	no	—
24	C₁₃×#405	C₂²	1	4	yes	complemented
25	C₂×C₁₃×#97	—	2	1	no	—
26	C₂×C₄×C₈×C₁₃	—	2	1	no	—
27	#11718800	—	2	4	no	—
28	#11718800	C₂²	1	8	yes	complemented
29	C₂×#88065	—	2	4	no	—
30	#11718767	—	2	2	no	—
31	#11718767	C₂²	1	4	yes	complemented
32	C₂×#88058	—	2	1	no	—
33	C₂×#88057	—	2	1	no	—
34	#11718667	—	2	4	no	—
35	#11718667	C₂²	1	8	yes	complemented
36	C₂×#88046	—	2	4	no	—
37	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
38	C₂²×C₂²⋊D₁₃	—	2	2	no	—
39	C₂×#6127	—	2	2	no	—
40	C₂×#6127	—	2	2	no	—
41	C₂×#6127	—	2	2	no	—
42	C₂×#6127	—	2	2	no	—
43	C₂×#6127	—	2	2	no	—
44	C₂×#6127	—	2	2	no	—
45	C₂×#6127	—	2	2	no	—
46	C₂×#6127	—	2	2	no	—
47	C₂×#6127	—	2	2	no	—
48	C₂×#6127	—	2	2	no	—
49	C₂×#6127	C₂×C₄	1	4	yes	—
50	C₂×#6127	C₂³	1	4	yes	—
51	C₂²×D₅₂	C₂×C₄	1	2	yes	—
52	C₂²×C₄×D₁₃	—	2	2	no	—
53	C₂²×Dic₂₆	C₂×C₄	1	2	yes	—
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	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
62	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
63	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
64	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
65	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
66	C₂²×C₈×C₁₃	D₄	1	2	yes	—
67	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
68	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
69	C₂²×C₈×C₁₃	D₄	1	2	yes	—
70	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
71	C₁₃×#117	—	2	1	no	—
72	C₁₃×#117	—	2	1	no	—
73	C₁₃×#117	D₄	1	2	yes	—
74	C₁₃×#117	C₂³	1	2	yes	—
75	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
76	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
77	C₂×C₄²×C₁₃	—	2	1	no	—
78	C₂×C₂²⋊Dic₁₃	—	2	2	no	—
79	#88180	—	2	2	no	—
80	#88180	—	2	2	no	—
81	#88180	—	2	2	no	—
82	#88180	C₂³	1	4	yes	—
83	C₂×C₄⋊Dic₁₃	—	2	2	no	—
84	C₂×C₄×Dic₁₃	—	2	2	no	—
85	C₂×Dic₅₂	—	2	1	no	—
86	C₂×Dic₅₂	—	2	1	no	—
87	C₂×Dic₅₂	—	2	2	no	—
88	C₂×Dic₅₂	C₂×C₄	1	4	yes	complemented
89	#88158	—	2	4	no	—
90	#88158	—	2	4	no	—
91	#88158	—	2	4	no	—
92	#88158	—	2	4	no	—
93	#88158	—	2	4	no	—
94	#88158	—	2	4	no	—
95	#88158	—	2	4	no	—
96	#88158	—	2	4	no	—
97	C₂×D₁₀₄	—	2	1	no	—
98	C₂×D₁₀₄	—	2	1	no	—
99	C₂×D₁₀₄	—	2	2	no	—
100	C₂×D₁₀₄	C₂×C₄	1	4	yes	complemented
101	C₂×#6095	—	2	2	no	—
102	C₂×#6095	—	2	2	no	—
103	C₂×#6095	—	2	4	no	—
104	C₂×#6095	C₂×C₄	1	8	yes	complemented
105	C₁₃×#97	—	2	4	no	—
106	C₄×C₈×C₁₃	—	2	4	no	—
107	#88065	—	2	16	no	—
108	#88058	—	2	4	no	—
109	#88057	—	2	4	no	—
110	#88046	—	2	16	no	—
111	C₂×#1976	—	13	1	no	maximal, Sylow
112	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
113	C₂³×D₁₃	—	2	2	no	—
114	C₂²×C₄×C₁₃	—	2	2	no	—
115	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
125	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
126	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
127	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
128	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
129	C₂×C₂²⋊D₁₃	—	2	4	no	—
130	C₂×C₂²⋊D₁₃	—	2	4	no	—
131	C₂×C₂²⋊D₁₃	—	4	2	no	—
132	C₂×C₂²⋊D₁₃	—	4	2	no	—
133	C₂×C₂²⋊D₁₃	—	4	2	no	—
134	C₂×C₂²⋊D₁₃	—	4	2	no	—
135	C₂²×Dic₁₃	—	2	2	no	—
136	C₂²×Dic₁₃	—	4	2	no	—
137	#6127	—	2	4	no	—
138	#6127	—	2	4	no	—
139	#6127	—	2	4	no	—
140	#6127	—	2	4	no	—
141	#6127	—	2	4	no	—
142	#6127	—	2	4	no	—
143	#6127	—	2	4	no	—
144	#6127	—	2	4	no	—
145	#6127	—	4	2	no	—
146	#6127	—	4	2	no	—
147	#6127	—	4	2	no	—
148	#6127	—	4	2	no	—
149	#6127	—	4	2	no	—
150	#6127	—	4	2	no	—
151	#6127	—	4	2	no	—
152	#6127	—	4	2	no	—
153	C₂×D₅₂	—	2	2	no	—
154	C₂×D₅₂	—	2	2	no	—
155	C₂×D₅₂	—	2	2	no	—
156	C₂×D₅₂	—	2	2	no	—
157	C₂×D₅₂	—	2	2	no	—
158	C₂×D₅₂	C₂²×C₄	1	4	yes	—
159	C₂×C₄×D₁₃	—	2	4	no	—
160	C₂×C₄×D₁₃	—	2	4	no	—
161	C₂×C₄×D₁₃	—	4	2	no	—
162	C₂×C₄×D₁₃	—	4	2	no	—
163	C₂×C₄×D₁₃	—	4	2	no	—
164	C₂×C₄×D₁₃	—	4	2	no	—
165	C₂×Dic₂₆	—	2	2	no	—
166	C₂×Dic₂₆	—	2	2	no	—
167	C₂×Dic₂₆	—	2	2	no	—
168	C₂×Dic₂₆	—	2	2	no	—
169	C₂×Dic₂₆	—	2	2	no	—
170	C₂×Dic₂₆	C₂²×C₄	1	4	yes	—
171	C₁₃×M₁₆	—	2	2	no	—
172	C₁₃×M₁₆	—	2	2	no	—
173	C₁₃×M₁₆	—	2	2	no	—
174	C₁₃×M₁₆	C₂×D₄	1	4	yes	—
175	C₂×C₈×C₁₃	—	2	2	no	—
176	C₂×C₈×C₁₃	—	2	2	no	—
177	C₂×C₈×C₁₃	—	2	2	no	—
178	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
179	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
180	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
181	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
182	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
183	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
184	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
185	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
186	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
187	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
188	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
189	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
190	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
191	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
192	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
193	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
194	C₁₃×C₄⋊C₄	—	2	2	no	—
195	C₁₃×C₄⋊C₄	—	2	2	no	—
196	C₁₃×C₂²⋊C₄	—	2	2	no	—
197	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
198	C₄²×C₁₃	—	2	2	no	—
199	C₄²×C₁₃	—	2	2	no	—
200	C₂²⋊Dic₁₃	—	2	4	no	—
201	C₂²⋊Dic₁₃	—	4	2	no	—
202	C₄⋊Dic₁₃	—	2	4	no	—
203	C₄⋊Dic₁₃	—	4	2	no	—
204	C₄×Dic₁₃	—	2	4	no	—
205	C₄×Dic₁₃	—	4	2	no	—
206	Dic₅₂	—	2	4	no	—
207	Dic₅₂	—	2	4	no	—
208	D₁₀₄	—	2	4	no	—
209	D₁₀₄	—	2	4	no	—
210	#6095	—	2	8	no	—
211	#6095	—	2	8	no	—
212	C₂²×#135	—	13	1	no	—
213	C₂×#427	—	13	1	no	—
214	C₂×#421	—	13	2	no	—
215	C₂×#410	—	13	2	no	—
216	C₂×#405	D₁₃	1	1	yes	characteristic, complemented
217	#1976	—	13	8	no	—
218	C₂³×C₁₃	—	4	2	no	—
219	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
220	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
221	C₂³×C₁₃	#121	1	1	yes	characteristic
222	C₂³×C₁₃	#121	1	1	yes	characteristic
223	C₂³×C₁₃	#127	1	1	yes	characteristic
224	C₂³×C₁₃	#127	1	1	yes	characteristic
225	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
226	C₂²×D₁₃	—	2	4	no	—
227	C₂²×D₁₃	—	4	2	no	—
228	C₂²×D₁₃	—	4	2	no	—
229	C₂²×D₁₃	—	8	4	no	—
230	C₂×C₄×C₁₃	—	2	4	no	—
231	C₂×C₄×C₁₃	—	4	4	no	—
232	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
233	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
234	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
235	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
236	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
237	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
238	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
239	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
240	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
241	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
242	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
243	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
244	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
245	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
246	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
247	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
248	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
249	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
250	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
251	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
252	C₂×C₄×C₁₃	#127	1	1	yes	characteristic
253	C₂×C₄×C₁₃	#127	1	1	yes	characteristic
254	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
255	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
256	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
257	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
258	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
259	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
260	C₂²⋊D₁₃	—	4	4	no	—
261	C₂²⋊D₁₃	—	4	4	no	—
262	C₂²⋊D₁₃	—	4	4	no	—
263	C₂²⋊D₁₃	—	4	4	no	—
264	C₂×Dic₁₃	—	2	4	no	—
265	C₂×Dic₁₃	—	4	2	no	—
266	C₂×Dic₁₃	—	4	2	no	—
267	C₂×Dic₁₃	—	4	4	no	—
268	C₂×Dic₁₃	—	8	4	no	—
269	D₅₂	—	2	4	no	—
270	D₅₂	—	2	4	no	—
271	D₅₂	—	4	2	no	—
272	D₅₂	—	4	2	no	—
273	C₄×D₁₃	—	4	4	no	—
274	C₄×D₁₃	—	4	4	no	—
275	C₄×D₁₃	—	4	4	no	—
276	C₄×D₁₃	—	4	4	no	—
277	Dic₂₆	—	2	4	no	—
278	Dic₂₆	—	2	4	no	—
279	Dic₂₆	—	4	2	no	—
280	Dic₂₆	—	4	2	no	—
281	C₈×C₁₃	—	2	4	no	—
282	C₈×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
283	C₈×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
284	C₈×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
285	C₈×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
286	C₂²×#41	—	13	2	no	—
287	C₂×#135	—	13	4	no	—
288	C₂×#135	—	13	4	no	—
289	C₂×#135	—	26	1	no	—
290	C₂×#135	—	26	1	no	—
291	C₂×#135	—	26	2	no	—
292	C₂×#135	—	26	1	no	—
293	C₂×#135	—	26	1	no	—
294	C₂×#135	—	26	2	no	—
295	C₂²×Q₁₆	—	13	1	no	—
296	C₂²×SD₁₆	—	13	2	no	—
297	C₂²×D₈	—	13	1	no	—
298	C₂²×M₁₆	C₂×D₁₃	1	1	yes	characteristic
299	C₂³×C₈	C₂×D₁₃	1	1	yes	characteristic
300	C₂×#117	—	13	2	no	—
301	C₂×#117	C₂×D₁₃	1	1	yes	characteristic
302	#427	—	13	4	no	—
303	#427	—	26	2	no	—
304	C₂×#107	—	26	1	no	—
305	C₂×#106	—	26	1	no	—
306	#421	—	13	8	no	—
307	#421	—	26	4	no	—
308	C₂×#104	—	26	4	no	—
309	#410	—	13	8	no	—
310	#410	—	26	4	no	—
311	C₂×#99	—	26	4	no	—
312	#405	—	2	2	no	—
313	#405	C₂×D₁₃	1	4	yes	complemented
314	C₂×#97	—	2	1	no	—
315	C₂×C₄×C₈	—	2	1	no	—
316	C₂²×C₁₃	—	2	2	no	—
317	C₂²×C₁₃	—	2	2	no	—
318	C₂²×C₁₃	—	2	2	no	—
319	C₂²×C₁₃	—	4	1	no	—
320	C₂²×C₁₃	—	4	1	no	—
321	C₂²×C₁₃	—	4	1	no	—
322	C₂²×C₁₃	—	4	1	no	—
323	C₂²×C₁₃	#390	1	1	yes	characteristic
324	C₂²×C₁₃	#390	1	1	yes	characteristic
325	C₂²×C₁₃	#390	1	1	yes	characteristic
326	C₂²×C₁₃	#390	1	1	yes	characteristic
327	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
328	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
329	C₂²×C₁₃	C₂×#127	1	1	yes	characteristic
330	C₂×D₁₃	—	4	4	no	—
331	C₂×D₁₃	—	8	4	no	—
332	C₂×D₁₃	—	8	4	no	—
333	C₂×D₁₃	—	8	4	no	—
334	C₄×C₁₃	—	4	4	no	—
335	C₄×C₁₃	#390	1	1	yes	characteristic
336	C₄×C₁₃	#390	1	1	yes	characteristic
337	C₄×C₁₃	#390	1	1	yes	characteristic
338	C₄×C₁₃	#390	1	1	yes	characteristic
339	C₄×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
340	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
341	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
342	C₄×C₁₃	C₂×#124	1	1	yes	characteristic
343	Dic₁₃	—	4	4	no	—
344	Dic₁₃	—	8	4	no	—
345	C₂×#41	—	13	4	no	—
346	C₂×#41	—	13	4	no	—
347	C₂×#41	—	26	2	no	—
348	C₂×#41	—	26	2	no	—
349	C₂×#41	—	26	2	no	—
350	C₂×#41	—	26	2	no	—
351	C₂×#41	—	26	2	no	—
352	C₂×#41	—	26	2	no	—
353	C₂×#41	—	26	2	no	—
354	C₂×#41	—	26	2	no	—
355	C₂×#41	—	26	2	no	—
356	C₂×#41	—	26	2	no	—
357	C₂²×Q₈	—	13	2	no	—
358	C₂²×D₄	—	13	2	no	—
359	C₂²×D₄	—	26	2	no	—
360	C₂³×C₄	—	26	2	no	—
361	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
362	#135	—	26	4	no	—
363	#135	—	26	4	no	—
364	#135	—	26	4	no	—
365	#135	—	26	4	no	—
366	#135	—	26	4	no	—
367	#135	—	26	4	no	—
368	#135	—	26	4	no	—
369	#135	—	26	4	no	—
370	C₂×Q₁₆	—	13	4	no	—
371	C₂×Q₁₆	—	26	1	no	—
372	C₂×Q₁₆	—	26	1	no	—
373	C₂×Q₁₆	—	26	2	no	—
374	C₂×SD₁₆	—	13	8	no	—
375	C₂×SD₁₆	—	26	2	no	—
376	C₂×SD₁₆	—	26	2	no	—
377	C₂×SD₁₆	—	26	4	no	—
378	C₂×D₈	—	13	4	no	—
379	C₂×D₈	—	26	1	no	—
380	C₂×D₈	—	26	1	no	—
381	C₂×D₈	—	26	2	no	—
382	C₂×M₁₆	—	2	1	no	—
383	C₂×M₁₆	—	2	1	no	—
384	C₂×M₁₆	—	2	1	no	—
385	C₂×M₁₆	D₅₂	1	2	yes	—
386	C₂×M₁₆	D₅₂	1	2	yes	—
387	C₂×M₁₆	C₂²×D₁₃	1	2	yes	—
388	C₂²×C₈	—	2	1	no	—
389	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
390	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
391	C₂²×C₈	C₄×D₁₃	1	2	yes	—
392	C₂²×C₈	D₅₂	1	1	yes	characteristic
393	C₂²×C₈	D₅₂	1	1	yes	characteristic
394	C₂²×C₈	D₅₂	1	2	yes	—
395	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
396	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
397	C₂²×C₈	C₂²⋊D₁₃	1	2	yes	—
398	C₂²×C₈	C₂²×D₁₃	1	2	yes	—
399	#117	—	2	1	no	—
400	#117	—	2	1	no	—
401	#117	—	13	4	no	—
402	#117	—	26	2	no	—
403	#117	—	26	2	no	—
404	#117	—	26	2	no	—
405	#117	D₅₂	1	2	yes	—
406	#117	C₂²×D₁₃	1	2	yes	—
407	C₂×C₄⋊C₄	—	2	1	no	—
408	C₂×C₄⋊C₄	—	26	2	no	—
409	C₂×C₂²⋊C₄	—	26	2	no	—
410	C₂×C₂²⋊C₄	D₅₂	1	2	yes	—
411	C₂×C₄²	—	2	1	no	—
412	C₂×C₄²	—	26	2	no	—
413	#107	—	26	4	no	—
414	#106	—	26	4	no	—
415	#104	—	26	16	no	—
416	#99	—	26	16	no	—
417	#97	—	2	4	no	—
418	C₄×C₈	—	2	4	no	—
419	C₂×C₁₃	—	2	1	no	—
420	C₂×C₁₃	—	2	1	no	—
421	C₂×C₁₃	—	2	1	no	—
422	C₂×C₁₃	—	2	1	no	—
423	C₂×C₁₃	—	2	1	no	—
424	C₂×C₁₃	—	2	1	no	—
425	C₂×C₁₃	#1976	1	2	yes	complemented
426	C₂×C₁₃	C₂×#390	1	1	yes	characteristic
427	D₁₃	—	8	4	no	—
428	C₂⁴	—	26	2	no	—
429	C₂⁴	C₂×D₅₂	1	1	yes	characteristic
430	#41	—	26	4	no	—
431	#41	—	26	4	no	—
432	#41	—	26	4	no	—
433	#41	—	26	4	no	—
434	#41	—	26	4	no	—
435	#41	—	26	4	no	—
436	#41	—	26	4	no	—
437	#41	—	26	4	no	—
438	#41	—	52	2	no	—
439	#41	—	52	2	no	—
440	#41	—	52	2	no	—
441	#41	—	52	2	no	—
442	#41	—	52	2	no	—
443	#41	—	52	2	no	—
444	#41	—	52	2	no	—
445	#41	—	52	2	no	—
446	C₂×Q₈	—	13	4	no	—
447	C₂×Q₈	—	26	2	no	—
448	C₂×Q₈	—	26	2	no	—
449	C₂×Q₈	—	26	2	no	—
450	C₂×Q₈	—	26	2	no	—
451	C₂×Q₈	—	26	2	no	—
452	C₂×D₄	—	13	4	no	—
453	C₂×D₄	—	26	4	no	—
454	C₂×D₄	—	26	4	no	—
455	C₂×D₄	—	26	2	no	—
456	C₂×D₄	—	26	2	no	—
457	C₂×D₄	—	26	2	no	—
458	C₂×D₄	—	26	2	no	—
459	C₂×D₄	—	26	2	no	—
460	C₂×D₄	—	52	2	no	—
461	C₂×D₄	—	52	2	no	—
462	C₂×D₄	—	52	2	no	—
463	C₂×D₄	—	52	2	no	—
464	C₂²×C₄	—	2	2	no	—
465	C₂²×C₄	—	26	2	no	—
466	C₂²×C₄	—	26	4	no	—
467	C₂²×C₄	—	26	4	no	—
468	C₂²×C₄	—	52	2	no	—
469	C₂²×C₄	—	52	2	no	—
470	C₂²×C₄	—	52	2	no	—
471	C₂²×C₄	—	52	2	no	—
472	C₂²×C₄	—	52	2	no	—
473	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
474	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
475	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
476	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
477	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
478	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
479	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
480	C₂²×C₄	#6127	1	1	yes	characteristic
481	C₂²×C₄	#6127	1	1	yes	characteristic
482	C₂²×C₄	#6127	1	1	yes	characteristic
483	C₂²×C₄	#6127	1	1	yes	characteristic
484	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
485	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
486	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
487	Q₁₆	—	26	4	no	—
488	Q₁₆	—	26	4	no	—
489	SD₁₆	—	26	8	no	—
490	SD₁₆	—	26	8	no	—
491	D₈	—	26	4	no	—
492	D₈	—	26	4	no	—
493	M₁₆	—	2	2	no	—
494	M₁₆	—	2	2	no	—
495	M₁₆	—	2	2	no	—
496	M₁₆	C₂×D₅₂	1	4	yes	—
497	C₂×C₈	—	2	2	no	—
498	C₂×C₈	—	2	2	no	—
499	C₂×C₈	—	2	2	no	—
500	C₂×C₈	#6103	1	1	yes	characteristic
501	C₂×C₈	#6103	1	1	yes	characteristic
502	C₂×C₈	#6103	1	2	yes	—
503	C₂×C₈	#6103	1	1	yes	characteristic
504	C₂×C₈	#6103	1	1	yes	characteristic
505	C₂×C₈	#6103	1	2	yes	—
506	C₂×C₈	#6103	1	2	yes	—
507	C₂×C₈	#6103	1	2	yes	—
508	C₂×C₈	#6103	1	2	yes	—
509	C₂×C₈	#6103	1	2	yes	—
510	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
511	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
512	C₂×C₈	C₂×D₅₂	1	2	yes	—
513	C₂×C₈	C₂×D₅₂	1	2	yes	—
514	C₂×C₈	C₂×C₂²⋊D₁₃	1	2	yes	—
515	C₂×C₈	C₂×C₂²⋊D₁₃	1	2	yes	—
516	C₄⋊C₄	—	2	2	no	—
517	C₄⋊C₄	—	2	2	no	—
518	C₄⋊C₄	—	26	4	no	—
519	C₄⋊C₄	—	52	2	no	—
520	C₂²⋊C₄	—	2	2	no	—
521	C₂²⋊C₄	—	26	4	no	—
522	C₂²⋊C₄	—	52	2	no	—
523	C₂²⋊C₄	C₂×D₅₂	1	4	yes	—
524	C₄²	—	2	2	no	—
525	C₄²	—	2	2	no	—
526	C₄²	—	26	4	no	—
527	C₄²	—	52	2	no	—
528	C₁₃	C₂×#1976	1	1	yes	characteristic, complemented, Sylow
529	C₂³	—	4	2	no	—
530	C₂³	—	26	4	no	—
531	C₂³	—	52	2	no	—
532	C₂³	—	52	2	no	—
533	C₂³	—	104	4	no	—
534	C₂³	C₄×D₅₂	1	1	yes	characteristic
535	C₂³	C₄×D₅₂	1	1	yes	characteristic
536	C₂³	#88128	1	1	yes	characteristic
537	C₂³	#88128	1	1	yes	characteristic
538	C₂³	#88184	1	1	yes	characteristic
539	C₂³	#88184	1	1	yes	characteristic
540	C₂³	C₂²×D₅₂	1	1	yes	characteristic
541	Q₈	—	26	4	no	—
542	Q₈	—	26	4	no	—
543	Q₈	—	52	2	no	—
544	Q₈	—	52	2	no	—
545	D₄	—	26	4	no	—
546	D₄	—	26	4	no	—
547	D₄	—	52	4	no	—
548	D₄	—	52	4	no	—
549	D₄	—	52	4	no	—
550	D₄	—	52	4	no	—
551	D₄	—	52	2	no	—
552	D₄	—	52	2	no	—
553	C₂×C₄	—	2	4	no	—
554	C₂×C₄	—	4	4	no	—
555	C₂×C₄	—	26	4	no	—
556	C₂×C₄	—	52	2	no	—
557	C₂×C₄	—	52	2	no	—
558	C₂×C₄	—	52	4	no	—
559	C₂×C₄	—	52	4	no	—
560	C₂×C₄	—	52	4	no	—
561	C₂×C₄	—	52	4	no	—
562	C₂×C₄	—	52	4	no	—
563	C₂×C₄	—	104	4	no	—
564	C₂×C₄	C₄×D₅₂	1	1	yes	characteristic
565	C₂×C₄	C₄×D₅₂	1	1	yes	characteristic
566	C₂×C₄	C₄×D₅₂	1	1	yes	characteristic
567	C₂×C₄	C₄×D₅₂	1	1	yes	characteristic
568	C₂×C₄	C₄×D₅₂	1	1	yes	characteristic
569	C₂×C₄	C₄×D₅₂	1	1	yes	characteristic
570	C₂×C₄	#88128	1	1	yes	characteristic
571	C₂×C₄	#88128	1	1	yes	characteristic
572	C₂×C₄	#88129	1	1	yes	characteristic
573	C₂×C₄	#88129	1	1	yes	characteristic
574	C₂×C₄	#88129	1	1	yes	characteristic
575	C₂×C₄	#88129	1	1	yes	characteristic
576	C₂×C₄	C₂×#6103	1	1	yes	characteristic
577	C₂×C₄	C₂×#6103	1	1	yes	characteristic
578	C₂×C₄	C₂×#6103	1	1	yes	characteristic
579	C₂×C₄	C₂×#6103	1	1	yes	characteristic
580	C₂×C₄	#88184	1	1	yes	characteristic
581	C₂×C₄	#88184	1	1	yes	characteristic
582	C₂×C₄	#88184	1	1	yes	characteristic
583	C₂×C₄	#88184	1	1	yes	characteristic
584	C₂×C₄	#88184	1	1	yes	characteristic
585	C₂×C₄	#88184	1	1	yes	characteristic
586	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
587	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
588	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
589	C₂×C₄	C₂×#6127	1	1	yes	characteristic
590	C₂×C₄	C₂×#6127	1	1	yes	characteristic
591	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
592	C₈	—	2	4	no	—
593	C₈	C₂×#6103	1	2	yes	—
594	C₈	C₂×#6103	1	2	yes	—
595	C₈	C₂×#6103	1	2	yes	—
596	C₈	C₂×#6103	1	2	yes	—
597	C₂²	—	2	2	no	—
598	C₂²	—	2	2	no	—
599	C₂²	—	2	2	no	—
600	C₂²	—	4	1	no	—
601	C₂²	—	4	1	no	—
602	C₂²	—	4	1	no	—
603	C₂²	—	4	1	no	—
604	C₂²	—	52	4	no	—
605	C₂²	—	104	4	no	—
606	C₂²	—	104	4	no	—
607	C₂²	—	104	4	no	—
608	C₂²	#11718600	1	1	yes	characteristic
609	C₂²	#11718600	1	1	yes	characteristic
610	C₂²	#11718600	1	1	yes	characteristic
611	C₂²	#11718600	1	1	yes	characteristic
612	C₂²	C₂×C₄×D₅₂	1	1	yes	characteristic
613	C₂²	C₂×#88128	1	1	yes	characteristic
614	C₂²	C₂×#88184	1	1	yes	characteristic
615	C₄	—	4	4	no	—
616	C₄	—	52	4	no	—
617	C₄	—	104	4	no	—
618	C₄	#11718600	1	1	yes	characteristic
619	C₄	#11718600	1	1	yes	characteristic
620	C₄	#11718600	1	1	yes	characteristic
621	C₄	#11718600	1	1	yes	characteristic
622	C₄	C₂×C₄×D₅₂	1	1	yes	characteristic
623	C₄	C₂×#88129	1	1	yes	characteristic
624	C₄	C₂²×#6103	1	1	yes	characteristic
625	C₄	C₂×#88184	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	—	104	4	no	—
633	C₂	#13115734	1	2	yes	direct product factor
634	C₂	C₂×#11718600	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#88184
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₂×C₁₃×#405	C₂
socle	C₂²×C₁₃	#390
prime radical	C₂²×#88158	C₂
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	C₂×#405	D₁₃
hypocenter	C₁₃	C₂×#1976
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂×#405

Complements

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

N	H ≅ G/N	type
2. C₂×#11718767	C₂	semidirect
3. C₂×#11718800	C₂	semidirect
4. C₂×#11718667	C₂	semidirect
5. #13115734	C₂	direct (N × H)
6. C₂×C₁₃×#405	C₂	semidirect
12. C₂²×Dic₅₂	C₄	semidirect
19. C₂×#88158	C₄	semidirect
21. C₂²×D₁₀₄	C₄	semidirect
22. C₂²×#6095	C₄	semidirect
24. C₁₃×#405	C₂²	semidirect
28. #11718800	C₂²	semidirect
31. #11718767	C₂²	semidirect
35. #11718667	C₂²	semidirect
88. C₂×Dic₅₂	C₂×C₄	semidirect
100. C₂×D₁₀₄	C₂×C₄	semidirect
104. C₂×#6095	C₂×C₄	semidirect
216. C₂×#405	D₁₃	semidirect
313. #405	C₂×D₁₃	semidirect
425. C₂×C₁₃	#1976	semidirect
528. C₁₃	C₂×#1976	semidirect
633. C₂	#13115734	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#88158	2
C₂×#11718767	2
C₂×#11718800	2
C₂×#11718667	2
#13115734	2
C₂×C₁₃×#405	2
C₂×#1976	13

Subgroups — C2×#13115734 #15866893

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13115734 #15866893