Subgroups — #28376447

Order 13952.

1140 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20295656	C₂	1	1	yes	maximal, characteristic, complemented
2	#20295647	C₂	1	1	yes	maximal, characteristic, complemented
3	#20295644	C₂	1	2	yes	maximal, complemented
4	#20295641	C₂	1	1	yes	maximal, characteristic, complemented
5	#20295627	C₂	1	1	yes	maximal, characteristic, complemented
6	#20295626	C₂	1	2	yes	maximal, complemented
7	#20295612	C₂	1	2	yes	maximal, complemented
8	#20295608	C₂	1	2	yes	maximal, complemented
9	#20295605	C₂	1	1	yes	maximal, characteristic, complemented
10	#20295592	C₂	1	1	yes	maximal, characteristic, complemented
11	#20295589	C₂	1	1	yes	maximal, characteristic, complemented
12	#20295574	C₂	1	1	yes	maximal, characteristic, complemented
13	#20295571	C₂	1	2	yes	maximal, complemented
14	#20295571	C₂	1	1	yes	maximal, characteristic, complemented
15	#20295561	C₂	1	1	yes	maximal, characteristic, complemented
16	#20295557	C₂	1	1	yes	maximal, characteristic, complemented
17	#20295553	C₂	1	2	yes	maximal, complemented
18	#20295536	C₂	1	2	yes	maximal, complemented
19	#20295534	C₂	1	2	yes	maximal, complemented
20	#20295494	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×#13182028	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×D₄×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
23	#540×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13182029	C₂²	1	1	yes	characteristic
25	C₂×#13182028	C₂²	1	1	yes	characteristic
26	C₂×#13182028	C₂²	1	2	yes	complemented
27	C₂×#13182028	C₂²	1	2	yes	complemented
28	C₂×D₄×D₁₀₉	C₂²	1	1	yes	characteristic
29	C₂²×C₄×D₁₀₉	C₂²	1	2	yes	—
30	#16812699	C₂²	1	1	yes	characteristic, complemented
31	#16812698	C₂²	1	1	yes	characteristic, complemented
32	#16812698	C₂²	1	2	yes	complemented
33	#16812695	C₂²	1	1	yes	characteristic
34	#16812695	C₂²	1	2	yes	—
35	#16812694	C₂²	1	2	yes	complemented
36	#16812694	C₂²	1	2	yes	complemented
37	#16812692	C₂²	1	2	yes	complemented
38	#16812692	C₂²	1	2	yes	complemented
39	#16812690	C₂²	1	1	yes	characteristic, complemented
40	#16812689	C₂²	1	2	yes	complemented
41	#16812687	C₂²	1	1	yes	characteristic
42	#16812686	C₂²	1	1	yes	characteristic
43	#16812686	C₂²	1	2	yes	complemented
44	#16812685	C₂²	1	2	yes	—
45	#16812685	C₂²	1	2	yes	complemented
46	#16812685	C₂²	1	2	yes	complemented
47	#16812685	C₂²	1	2	yes	complemented
48	#16812684	C₂²	1	2	yes	complemented
49	#16812682	C₂²	1	2	yes	complemented
50	#16812682	C₂²	1	2	yes	complemented
51	#16812681	C₂²	1	2	yes	complemented
52	#16812681	C₂²	1	2	yes	complemented
53	#16812680	C₂²	1	2	yes	complemented
54	#16812679	C₂²	1	2	yes	—
55	#16812679	C₂²	1	1	yes	characteristic, complemented
56	#16812678	C₂²	1	2	yes	complemented
57	#16812678	C₂²	1	1	yes	characteristic, complemented
58	#16812677	C₂²	1	2	yes	—
59	#16812677	C₂²	1	2	yes	complemented
60	#16812676	C₂²	1	2	yes	complemented
61	#16812674	C₂²	1	1	yes	characteristic
62	#16812673	C₂²	1	1	yes	characteristic
63	#16812673	C₂²	1	2	yes	complemented
64	#16812672	C₂²	1	2	yes	—
65	#16812672	C₂²	1	2	yes	complemented
66	#16812671	C₂²	1	2	yes	—
67	#16812671	C₂²	1	2	yes	—
68	#16812671	C₂²	1	2	yes	complemented
69	#16812671	C₂²	1	2	yes	complemented
70	#16812670	C₂²	1	2	yes	—
71	#16812670	C₂²	1	1	yes	characteristic
72	#16812670	C₂²	1	1	yes	characteristic, complemented
73	#16812670	C₂²	1	2	yes	complemented
74	#16812669	C₂²	1	2	yes	—
75	#16812667	C₂²	1	2	yes	—
76	#16812667	C₂²	1	2	yes	—
77	#16812667	C₂²	1	2	yes	—
78	C₄×Dic₂₁₈	C₂²	1	1	yes	characteristic, complemented
79	#16812664	C₂²	1	1	yes	characteristic, complemented
80	#16812664	C₂²	1	1	yes	characteristic, complemented
81	#16812664	C₂²	1	1	yes	characteristic, complemented
82	C₄×D₄₃₆	C₂²	1	1	yes	characteristic
83	D₄×Dic₁₀₉	C₂²	1	1	yes	characteristic
84	D₄×Dic₁₀₉	C₂²	1	1	yes	characteristic, complemented
85	D₄×Dic₁₀₉	C₂²	1	2	yes	complemented
86	D₄×Dic₁₀₉	C₂²	1	2	yes	complemented
87	#16812661	C₂²	1	1	yes	characteristic
88	#16812661	C₂²	1	1	yes	characteristic
89	#16812661	C₂²	1	1	yes	characteristic
90	#16812661	C₂²	1	2	yes	complemented
91	C₄×C₂²⋊D₁₀₉	C₂²	1	2	yes	—
92	C₄×C₂²⋊D₁₀₉	C₂²	1	2	yes	—
93	#16812659	C₂²	1	2	yes	—
94	#16812659	C₂²	1	2	yes	—
95	#16812659	C₂²	1	1	yes	characteristic
96	#16812659	C₂²	1	1	yes	characteristic
97	#16812659	C₂²	1	1	yes	characteristic, complemented
98	#16812659	C₂²	1	1	yes	characteristic, complemented
99	#16812659	C₂²	1	2	yes	complemented
100	#16812657	C₂²	1	1	yes	characteristic
101	#16812657	C₂²	1	2	yes	complemented
102	#16812656	C₂²	1	1	yes	characteristic
103	#16812656	C₂²	1	1	yes	characteristic, complemented
104	#16812655	C₂²	1	2	yes	complemented
105	#16812655	C₂²	1	2	yes	complemented
106	C₄⋊C₄×D₁₀₉	C₂²	1	1	yes	characteristic
107	C₂²⋊C₄×D₁₀₉	C₂²	1	2	yes	—
108	C₂×C₄×Dic₁₀₉	C₂²	1	2	yes	complemented
109	C₂×C₄×Dic₁₀₉	C₂²	1	1	yes	characteristic, complemented
110	C₄²×D₁₀₉	C₂²	1	1	yes	characteristic
111	C₄²×D₁₀₉	C₂²	1	1	yes	characteristic, complemented
112	#127×C₁₀₉	C₂²	1	1	yes	characteristic
113	#125×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
114	#123×C₁₀₉	C₂²	1	2	yes	complemented
115	#123×C₁₀₉	C₂²	1	2	yes	complemented
116	#121×C₁₀₉	C₂²	1	1	yes	characteristic
117	#121×C₁₀₉	C₂²	1	2	yes	complemented
118	#121×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
119	#121×C₁₀₉	C₂²	1	2	yes	complemented
120	C₄×D₄×C₁₀₉	C₂²	1	1	yes	characteristic
121	C₄×D₄×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
122	#117×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₁₀₉	C₂³	1	2	yes	—
124	#13182029	—	2	4	no	—
125	#13182028	—	2	4	no	—
126	#13182028	—	4	4	no	—
127	#13182028	—	4	4	no	—
128	C₂×Dic₂₁₈	C₂³	1	1	yes	characteristic
129	C₂×Dic₂₁₈	C₂³	1	1	yes	characteristic
130	C₂×Dic₂₁₈	C₂³	1	2	yes	—
131	C₂×Dic₂₁₈	C₂³	1	2	yes	—
132	C₂×D₄₃₆	C₂³	1	1	yes	characteristic
133	C₂×D₄₃₆	C₂³	1	1	yes	characteristic
134	C₂×D₄₃₆	C₂³	1	2	yes	—
135	C₂×C₂²⋊D₁₀₉	C₂³	1	1	yes	characteristic
136	C₂×C₂²⋊D₁₀₉	C₂³	1	2	yes	—
137	C₂×C₂²⋊D₁₀₉	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₁₀₉	C₂³	1	1	yes	characteristic
139	C₂×C₂²⋊D₁₀₉	C₂³	1	2	yes	—
140	C₂×C₂²⋊D₁₀₉	C₂³	1	2	yes	—
141	C₂×C₂²⋊D₁₀₉	C₂³	1	2	yes	—
142	C₂×C₂²⋊D₁₀₉	C₂³	1	2	yes	—
143	C₂×C₂²⋊D₁₀₉	C₂³	1	2	yes	—
144	D₄×D₁₀₉	—	2	4	no	—
145	C₂²×Dic₁₀₉	C₂³	1	2	yes	—
146	C₂²×Dic₁₀₉	C₂³	1	2	yes	—
147	C₂²×Dic₁₀₉	C₂³	1	1	yes	characteristic
148	C₂²×Dic₁₀₉	C₂³	1	2	yes	—
149	C₂²×Dic₁₀₉	C₂³	1	1	yes	characteristic
150	C₂×C₄×D₁₀₉	—	4	4	no	—
151	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
152	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
153	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
154	C₂×C₄×D₁₀₉	C₂³	1	2	yes	—
155	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
156	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
157	C₂×C₄×D₁₀₉	C₂³	1	2	yes	—
158	C₂×C₄×D₁₀₉	C₂³	1	2	yes	—
159	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
160	C₄⋊Dic₁₀₉	C₂³	1	1	yes	characteristic
161	C₄⋊Dic₁₀₉	C₂³	1	1	yes	characteristic
162	C₄⋊Dic₁₀₉	C₂³	1	2	yes	—
163	C₄⋊Dic₁₀₉	C₂³	1	2	yes	—
164	C₄⋊Dic₁₀₉	C₂³	1	2	yes	—
165	#13182008	C₂³	1	2	yes	—
166	#13182008	C₂³	1	2	yes	—
167	#13182008	C₂³	1	2	yes	—
168	#13182008	C₂³	1	2	yes	—
169	#13182008	C₂³	1	2	yes	—
170	#13182008	C₂³	1	1	yes	characteristic
171	#13182008	C₂³	1	1	yes	characteristic
172	#13182008	C₂³	1	1	yes	characteristic
173	#13182008	C₂³	1	1	yes	characteristic
174	#13182008	C₂³	1	2	yes	—
175	C₂²⋊Dic₁₀₉	C₂³	1	2	yes	—
176	C₂²⋊Dic₁₀₉	C₂³	1	2	yes	—
177	C₂²⋊Dic₁₀₉	C₂³	1	2	yes	—
178	C₂²⋊Dic₁₀₉	C₂³	1	2	yes	—
179	C₂²⋊Dic₁₀₉	C₂³	1	2	yes	—
180	C₂²⋊Dic₁₀₉	C₂³	1	2	yes	—
181	C₂²⋊Dic₁₀₉	C₂³	1	2	yes	—
182	#13182006	C₂³	1	2	yes	—
183	#13182006	C₂³	1	2	yes	—
184	#13182006	C₂³	1	1	yes	characteristic
185	#13182006	C₂³	1	1	yes	characteristic
186	#13182006	C₂³	1	1	yes	characteristic
187	#13182006	C₂³	1	1	yes	characteristic
188	#13182006	C₂³	1	2	yes	—
189	#13182006	C₂³	1	2	yes	—
190	#13182006	C₂³	1	2	yes	—
191	#13182006	C₂³	1	2	yes	—
192	#13182006	C₂³	1	2	yes	—
193	#13182006	C₂³	1	2	yes	—
194	C₄×Dic₁₀₉	C₂³	1	1	yes	characteristic
195	C₄×Dic₁₀₉	C₂³	1	1	yes	characteristic
196	C₄×Dic₁₀₉	C₂³	1	1	yes	characteristic
197	C₄×Dic₁₀₉	C₂³	1	1	yes	characteristic
198	C₄×Dic₁₀₉	C₂³	1	1	yes	characteristic
199	C₄×Dic₁₀₉	C₂³	1	1	yes	characteristic
200	C₄×Dic₁₀₉	C₂³	1	2	yes	—
201	C₄×Dic₁₀₉	C₂³	1	2	yes	—
202	C₄×Dic₁₀₉	C₂³	1	1	yes	characteristic
203	C₄×Dic₁₀₉	C₂³	1	2	yes	—
204	C₄×Dic₁₀₉	C₂³	1	1	yes	characteristic
205	C₂×D₄×C₁₀₉	C₂³	1	1	yes	characteristic
206	C₂×D₄×C₁₀₉	C₂³	1	1	yes	characteristic
207	C₂×D₄×C₁₀₉	C₂³	1	2	yes	—
208	C₂×D₄×C₁₀₉	C₂³	1	2	yes	—
209	C₂×D₄×C₁₀₉	C₂³	1	2	yes	—
210	C₂×D₄×C₁₀₉	C₂³	1	2	yes	—
211	C₂²×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
212	C₂²×C₄×C₁₀₉	C₂³	1	2	yes	—
213	C₂²×C₄×C₁₀₉	C₂³	1	2	yes	—
214	C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
215	C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
216	C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
217	C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
218	C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
219	C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
220	C₂²⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
221	C₂²⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
222	C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
223	C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
224	C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
225	C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
226	C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
227	C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
228	C₂³×C₁₀₉	C₂⁴	1	2	yes	—
229	C₂³×C₁₀₉	C₂⁴	1	2	yes	—
230	C₂³×C₁₀₉	C₂⁴	1	1	yes	characteristic
231	C₂²×D₁₀₉	—	2	4	no	—
232	C₂²×D₁₀₉	—	4	2	no	—
233	C₂²×D₁₀₉	—	4	2	no	—
234	C₂²×D₁₀₉	C₂⁴	1	2	yes	—
235	C₂²×D₁₀₉	C₂⁴	1	1	yes	characteristic
236	C₂²×D₁₀₉	C₂⁴	1	1	yes	characteristic
237	D₄×C₁₀₉	—	2	2	no	—
238	D₄×C₁₀₉	—	2	2	no	—
239	D₄×C₁₀₉	—	4	2	no	—
240	D₄×C₁₀₉	—	4	2	no	—
241	D₄×C₁₀₉	—	4	2	no	—
242	D₄×C₁₀₉	—	4	2	no	—
243	C₂×C₄×C₁₀₉	—	2	2	no	—
244	C₂×C₄×C₁₀₉	—	4	2	no	—
245	C₂×C₄×C₁₀₉	—	4	2	no	—
246	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
247	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
248	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
249	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
250	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
251	C₂×C₄×C₁₀₉	C₂⁴	1	2	yes	—
252	C₂×C₄×C₁₀₉	C₂⁴	1	2	yes	—
253	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
254	C₂²⋊D₁₀₉	—	2	4	no	—
255	C₂²⋊D₁₀₉	—	2	2	no	—
256	C₂²⋊D₁₀₉	—	2	4	no	—
257	C₂²⋊D₁₀₉	—	2	2	no	—
258	C₂²⋊D₁₀₉	—	4	2	no	—
259	C₂²⋊D₁₀₉	—	4	2	no	—
260	C₂²⋊D₁₀₉	—	4	2	no	—
261	C₂²⋊D₁₀₉	—	4	2	no	—
262	C₂²⋊D₁₀₉	—	4	2	no	—
263	C₂×Dic₁₀₉	—	2	4	no	—
264	C₂×Dic₁₀₉	—	2	4	no	—
265	C₂×Dic₁₀₉	—	2	4	no	—
266	C₂×Dic₁₀₉	—	2	2	no	—
267	C₂×Dic₁₀₉	—	4	1	no	—
268	C₂×Dic₁₀₉	C₂⁴	1	1	yes	characteristic
269	C₂×Dic₁₀₉	C₂⁴	1	2	yes	—
270	C₂×Dic₁₀₉	C₂⁴	1	1	yes	characteristic
271	C₂×Dic₁₀₉	C₂⁴	1	1	yes	characteristic
272	C₂×Dic₁₀₉	C₂⁴	1	2	yes	—
273	C₂×Dic₁₀₉	C₂⁴	1	1	yes	characteristic
274	C₂×Dic₁₀₉	C₂⁴	1	2	yes	—
275	C₂×Dic₁₀₉	C₂⁴	1	1	yes	characteristic
276	C₂×Dic₁₀₉	C₂⁴	1	1	yes	characteristic
277	D₄₃₆	—	2	2	no	—
278	D₄₃₆	—	2	2	no	—
279	D₄₃₆	—	4	2	no	—
280	C₄×D₁₀₉	—	2	2	no	—
281	C₄×D₁₀₉	—	2	2	no	—
282	C₄×D₁₀₉	—	2	4	no	—
283	C₄×D₁₀₉	—	2	2	no	—
284	C₄×D₁₀₉	—	4	2	no	—
285	C₄×D₁₀₉	—	4	2	no	—
286	C₄×D₁₀₉	—	4	1	no	—
287	C₄×D₁₀₉	—	4	1	no	—
288	C₄×D₁₀₉	#41	1	4	yes	complemented
289	Dic₂₁₈	—	2	2	no	—
290	Dic₂₁₈	—	2	2	no	—
291	Dic₂₁₈	—	4	2	no	—
292	Dic₂₁₈	—	4	2	no	—
293	C₂²×C₁₀₉	—	2	2	no	—
294	C₂²×C₁₀₉	—	2	1	no	—
295	C₂²×C₁₀₉	—	2	2	no	—
296	C₂²×C₁₀₉	—	2	2	no	—
297	C₂²×C₁₀₉	—	2	1	no	—
298	C₂²×C₁₀₉	—	2	2	no	—
299	C₂²×C₁₀₉	—	2	1	no	—
300	C₂²×C₁₀₉	—	2	2	no	—
301	C₂²×C₁₀₉	—	2	2	no	—
302	C₂²×C₁₀₉	C₂⁵	1	1	yes	characteristic
303	C₂×D₁₀₉	—	2	1	no	—
304	C₂×D₁₀₉	—	2	1	no	—
305	C₂×D₁₀₉	—	2	1	no	—
306	C₂×D₁₀₉	—	2	2	no	—
307	C₂×D₁₀₉	—	2	2	no	—
308	C₂×D₁₀₉	—	2	1	no	—
309	C₂×D₁₀₉	—	2	1	no	—
310	C₂×D₁₀₉	—	2	2	no	—
311	C₂×D₁₀₉	—	4	8	no	—
312	C₂×D₁₀₉	C₂×#41	1	2	yes	—
313	C₄×C₁₀₉	—	2	1	no	—
314	C₄×C₁₀₉	—	2	1	no	—
315	C₄×C₁₀₉	—	2	2	no	—
316	C₄×C₁₀₉	—	2	1	no	—
317	C₄×C₁₀₉	—	2	1	no	—
318	C₄×C₁₀₉	—	2	1	no	—
319	C₄×C₁₀₉	—	2	2	no	—
320	C₄×C₁₀₉	C₂×#41	1	2	yes	—
321	Dic₁₀₉	—	2	1	no	—
322	Dic₁₀₉	—	2	2	no	—
323	Dic₁₀₉	—	2	1	no	—
324	Dic₁₀₉	—	2	2	no	—
325	Dic₁₀₉	—	2	2	no	—
326	Dic₁₀₉	—	2	1	no	—
327	Dic₁₀₉	—	2	1	no	—
328	Dic₁₀₉	C₂×#41	1	2	yes	—
329	Dic₁₀₉	H(5,𝔽₂)	1	2	yes	—
330	C₂×C₁₀₉	—	4	2	no	—
331	C₂×C₁₀₉	—	4	2	no	—
332	C₂×C₁₀₉	—	4	1	no	—
333	C₂×C₁₀₉	C₂²×#41	1	1	yes	characteristic
334	C₂×C₁₀₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
335	C₂×C₁₀₉	#585	1	1	yes	characteristic
336	D₁₀₉	—	2	2	no	—
337	D₁₀₉	—	4	1	no	—
338	D₁₀₉	—	4	2	no	—
339	#3460	—	109	1	no	maximal, Sylow
340	C₁₀₉	#3460	1	1	yes	characteristic, complemented, Sylow
341	#544	—	109	1	no	—
342	#542	—	109	2	no	—
343	#542	—	109	1	no	—
344	#542	—	109	1	no	—
345	#540	—	109	2	no	—
346	#540	—	109	1	no	—
347	#540	D₁₀₉	1	1	yes	characteristic, complemented
348	#538	—	109	2	no	—
349	#538	—	109	2	no	—
350	#537	—	109	1	no	—
351	#535	—	109	1	no	—
352	#535	—	109	1	no	—
353	#532	—	109	1	no	—
354	#532	—	109	1	no	—
355	#532	—	109	2	no	—
356	#529	—	109	1	no	—
357	#529	—	109	2	no	—
358	#529	—	109	1	no	—
359	#525	—	109	2	no	—
360	#525	—	109	2	no	—
361	C₄×#41	—	109	1	no	—
362	C₄×#41	—	109	1	no	—
363	C₂×C₄×D₄	—	109	1	no	—
364	C₂×#41	—	109	2	no	—
365	C₂×#41	—	109	2	no	—
366	C₂×#41	—	109	1	no	—
367	C₂×#41	—	109	1	no	—
368	C₂²×D₄	—	109	1	no	—
369	C₂³×C₄	—	109	2	no	—
370	C₄⋊Q₈	—	109	2	no	—
371	C₄⋊Q₈	—	109	1	no	—
372	C₄⋊Q₈	—	109	1	no	—
373	#127	—	109	1	no	—
374	#127	—	109	2	no	—
375	#127	C₂×D₁₀₉	1	1	yes	characteristic
376	#126	—	109	2	no	—
377	#126	—	109	2	no	—
378	#126	—	109	2	no	—
379	#126	—	109	2	no	—
380	#125	—	109	2	no	—
381	#125	—	109	1	no	—
382	#125	C₂×D₁₀₉	1	1	yes	characteristic, complemented
383	#124	—	109	1	no	—
384	#124	—	109	2	no	—
385	#124	—	109	2	no	—
386	#124	—	109	2	no	—
387	#124	—	109	2	no	—
388	#124	—	109	2	no	—
389	#124	—	109	1	no	—
390	#123	—	109	2	no	—
391	#123	—	109	2	no	—
392	#123	—	109	2	no	—
393	#123	—	109	2	no	—
394	#123	—	109	2	no	—
395	#123	—	109	2	no	—
396	#123	C₂×D₁₀₉	1	2	yes	complemented
397	#123	C₂×D₁₀₉	1	2	yes	complemented
398	C₂²⋊Q₈	—	109	2	no	—
399	C₂²⋊Q₈	—	109	1	no	—
400	C₂²⋊Q₈	—	109	2	no	—
401	C₂²⋊Q₈	—	109	2	no	—
402	C₂²⋊Q₈	—	109	2	no	—
403	C₂²⋊Q₈	—	109	1	no	—
404	C₂²⋊Q₈	—	109	2	no	—
405	#121	—	109	2	no	—
406	#121	—	109	2	no	—
407	#121	—	109	1	no	—
408	#121	—	109	2	no	—
409	#121	—	109	1	no	—
410	#121	—	109	2	no	—
411	#121	—	109	2	no	—
412	#121	—	109	2	no	—
413	#121	—	109	1	no	—
414	#121	—	109	2	no	—
415	#121	—	109	1	no	—
416	#121	—	109	2	no	—
417	#121	—	109	2	no	—
418	#121	C₂×D₁₀₉	1	1	yes	characteristic
419	#121	C₂×D₁₀₉	1	2	yes	complemented
420	#121	C₂×D₁₀₉	1	1	yes	characteristic, complemented
421	#121	C₂×D₁₀₉	1	2	yes	complemented
422	#120	—	109	2	no	—
423	#120	—	109	2	no	—
424	#120	—	109	2	no	—
425	#120	—	109	2	no	—
426	C₄×Q₈	—	109	1	no	—
427	C₄×Q₈	—	109	1	no	—
428	C₄×Q₈	—	109	1	no	—
429	C₄×Q₈	—	109	1	no	—
430	C₄×D₄	—	109	1	no	—
431	C₄×D₄	—	109	1	no	—
432	C₄×D₄	—	109	2	no	—
433	C₄×D₄	—	109	2	no	—
434	C₄×D₄	—	109	2	no	—
435	C₄×D₄	—	109	2	no	—
436	C₄×D₄	—	109	1	no	—
437	C₄×D₄	—	109	1	no	—
438	C₄×D₄	—	109	1	no	—
439	C₄×D₄	—	109	2	no	—
440	C₄×D₄	—	109	2	no	—
441	C₄×D₄	—	109	2	no	—
442	C₄×D₄	—	109	1	no	—
443	C₄×D₄	—	109	1	no	—
444	C₄×D₄	—	109	1	no	—
445	C₄×D₄	—	109	1	no	—
446	C₄×D₄	—	109	2	no	—
447	C₄×D₄	—	109	1	no	—
448	C₄×D₄	C₂×D₁₀₉	1	1	yes	characteristic
449	C₄×D₄	C₂×D₁₀₉	1	1	yes	characteristic, complemented
450	#117	—	109	1	no	—
451	#117	—	109	2	no	—
452	#117	—	109	2	no	—
453	#117	—	109	2	no	—
454	#117	—	109	1	no	—
455	#117	—	109	1	no	—
456	#117	C₂×D₁₀₉	1	1	yes	characteristic, complemented
457	C₂×C₄⋊C₄	—	109	1	no	—
458	C₂×C₂²⋊C₄	—	109	2	no	—
459	C₂×C₄²	—	109	1	no	—
460	C₂×C₄²	—	109	2	no	—
461	C₂×C₄²	—	109	1	no	—
462	C₂×C₄²	—	109	1	no	—
463	C₂⁴	—	109	2	no	—
464	#41	—	436	4	no	—
465	#41	—	436	4	no	—
466	#41	—	218	4	no	—
467	#41	—	218	4	no	—
468	C₂×Q₈	—	109	2	no	—
469	C₂×Q₈	—	109	2	no	—
470	C₂×Q₈	—	109	1	no	—
471	C₂×Q₈	—	109	1	no	—
472	C₂×D₄	—	109	2	no	—
473	C₂×D₄	—	109	2	no	—
474	C₂×D₄	—	109	2	no	—
475	C₂×D₄	—	109	2	no	—
476	C₂×D₄	—	109	2	no	—
477	C₂×D₄	—	109	1	no	—
478	C₂×D₄	—	109	2	no	—
479	C₂×D₄	—	109	2	no	—
480	C₂×D₄	—	109	1	no	—
481	C₂×D₄	—	109	2	no	—
482	C₂×D₄	—	109	1	no	—
483	C₂×D₄	—	109	1	no	—
484	C₂×D₄	—	218	4	no	—
485	C₂×D₄	C₂²×D₁₀₉	1	1	yes	characteristic
486	C₂×D₄	C₂²×D₁₀₉	1	1	yes	characteristic
487	C₂×D₄	C₂²×D₁₀₉	1	2	yes	—
488	C₂×D₄	C₂²×D₁₀₉	1	2	yes	—
489	C₂×D₄	C₂²×D₁₀₉	1	2	yes	—
490	C₂×D₄	C₂²×D₁₀₉	1	2	yes	—
491	C₂²×C₄	—	109	1	no	—
492	C₂²×C₄	—	109	1	no	—
493	C₂²×C₄	—	109	2	no	—
494	C₂²×C₄	—	109	2	no	—
495	C₂²×C₄	—	109	1	no	—
496	C₂²×C₄	—	109	2	no	—
497	C₂²×C₄	—	109	1	no	—
498	C₂²×C₄	—	109	1	no	—
499	C₂²×C₄	—	109	2	no	—
500	C₂²×C₄	—	109	2	no	—
501	C₂²×C₄	—	109	1	no	—
502	C₂²×C₄	—	109	1	no	—
503	C₂²×C₄	—	109	1	no	—
504	C₂²×C₄	—	109	2	no	—
505	C₂²×C₄	—	436	4	no	—
506	C₂²×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
507	C₂²×C₄	C₂²×D₁₀₉	1	2	yes	—
508	C₂²×C₄	C₂²×D₁₀₉	1	2	yes	—
509	C₄⋊C₄	—	109	2	no	—
510	C₄⋊C₄	—	109	1	no	—
511	C₄⋊C₄	—	109	1	no	—
512	C₄⋊C₄	—	109	2	no	—
513	C₄⋊C₄	—	109	1	no	—
514	C₄⋊C₄	—	109	2	no	—
515	C₄⋊C₄	—	109	1	no	—
516	C₄⋊C₄	—	109	2	no	—
517	C₄⋊C₄	—	109	2	no	—
518	C₄⋊C₄	—	109	2	no	—
519	C₄⋊C₄	—	109	1	no	—
520	C₄⋊C₄	—	109	1	no	—
521	C₄⋊C₄	—	109	2	no	—
522	C₄⋊C₄	—	109	2	no	—
523	C₄⋊C₄	—	109	2	no	—
524	C₄⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic
525	C₄⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic
526	C₄⋊C₄	C₂²×D₁₀₉	1	2	yes	—
527	C₄⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic
528	C₄⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic
529	C₄⋊C₄	C₂²×D₁₀₉	1	2	yes	—
530	C₂²⋊C₄	—	109	2	no	—
531	C₂²⋊C₄	—	109	2	no	—
532	C₂²⋊C₄	—	109	2	no	—
533	C₂²⋊C₄	—	109	2	no	—
534	C₂²⋊C₄	—	109	2	no	—
535	C₂²⋊C₄	—	109	2	no	—
536	C₂²⋊C₄	—	109	2	no	—
537	C₂²⋊C₄	—	109	2	no	—
538	C₂²⋊C₄	—	109	2	no	—
539	C₂²⋊C₄	—	109	1	no	—
540	C₂²⋊C₄	—	109	2	no	—
541	C₂²⋊C₄	—	109	1	no	—
542	C₂²⋊C₄	—	109	1	no	—
543	C₂²⋊C₄	—	109	1	no	—
544	C₂²⋊C₄	—	109	2	no	—
545	C₂²⋊C₄	—	109	2	no	—
546	C₂²⋊C₄	—	109	2	no	—
547	C₂²⋊C₄	—	109	2	no	—
548	C₂²⋊C₄	—	109	2	no	—
549	C₂²⋊C₄	C₂²×D₁₀₉	1	2	yes	—
550	C₂²⋊C₄	C₂²×D₁₀₉	1	2	yes	—
551	C₂²⋊C₄	C₂²×D₁₀₉	1	2	yes	—
552	C₂²⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic
553	C₂²⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic
554	C₂²⋊C₄	C₂²×D₁₀₉	1	2	yes	—
555	C₄²	—	109	1	no	—
556	C₄²	—	109	1	no	—
557	C₄²	—	109	2	no	—
558	C₄²	—	109	1	no	—
559	C₄²	—	109	1	no	—
560	C₄²	—	109	1	no	—
561	C₄²	—	109	2	no	—
562	C₄²	—	109	1	no	—
563	C₄²	—	109	1	no	—
564	C₄²	—	109	1	no	—
565	C₄²	—	109	2	no	—
566	C₄²	C₂²×D₁₀₉	1	1	yes	characteristic
567	C₄²	C₂²×D₁₀₉	1	1	yes	characteristic
568	C₂³	—	109	1	no	—
569	C₂³	—	109	2	no	—
570	C₂³	—	109	1	no	—
571	C₂³	—	436	2	no	—
572	C₂³	—	436	2	no	—
573	C₂³	—	218	4	no	—
574	C₂³	C₂³×D₁₀₉	1	2	yes	—
575	C₂³	C₂³×D₁₀₉	1	1	yes	characteristic
576	C₂³	C₂³×D₁₀₉	1	2	yes	—
577	Q₈	—	436	2	no	—
578	Q₈	—	436	2	no	—
579	Q₈	—	218	2	no	—
580	Q₈	—	218	2	no	—
581	D₄	—	2	2	no	—
582	D₄	—	2	2	no	—
583	D₄	—	4	2	no	—
584	D₄	—	4	2	no	—
585	D₄	—	4	2	no	—
586	D₄	—	4	2	no	—
587	D₄	—	436	2	no	—
588	D₄	—	436	2	no	—
589	D₄	—	436	2	no	—
590	D₄	—	436	2	no	—
591	D₄	—	436	2	no	—
592	D₄	—	436	2	no	—
593	D₄	—	218	2	no	—
594	D₄	—	218	4	no	—
595	D₄	—	218	2	no	—
596	D₄	—	218	2	no	—
597	D₄	—	218	4	no	—
598	D₄	—	218	2	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	4	2	no	—
601	C₂×C₄	—	4	2	no	—
602	C₂×C₄	—	109	1	no	—
603	C₂×C₄	—	109	1	no	—
604	C₂×C₄	—	109	4	no	—
605	C₂×C₄	—	109	1	no	—
606	C₂×C₄	—	109	2	no	—
607	C₂×C₄	—	109	1	no	—
608	C₂×C₄	—	109	1	no	—
609	C₂×C₄	—	109	2	no	—
610	C₂×C₄	—	109	1	no	—
611	C₂×C₄	—	109	2	no	—
612	C₂×C₄	—	436	2	no	—
613	C₂×C₄	—	436	2	no	—
614	C₂×C₄	—	436	1	no	—
615	C₂×C₄	—	436	1	no	—
616	C₂×C₄	—	436	1	no	—
617	C₂×C₄	—	218	2	no	—
618	C₂×C₄	—	218	4	no	—
619	C₂×C₄	—	218	2	no	—
620	C₂×C₄	—	218	4	no	—
621	C₂×C₄	—	218	4	no	—
622	C₂×C₄	—	218	2	no	—
623	C₂×C₄	—	218	4	no	—
624	C₂×C₄	—	218	2	no	—
625	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
626	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
627	C₂×C₄	C₂³×D₁₀₉	1	2	yes	—
628	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
629	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
630	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
631	C₂×C₄	C₂³×D₁₀₉	1	2	yes	—
632	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
633	C₂²	—	2	1	no	—
634	C₂²	—	2	2	no	—
635	C₂²	—	2	2	no	—
636	C₂²	—	2	2	no	—
637	C₂²	—	2	1	no	—
638	C₂²	—	2	2	no	—
639	C₂²	—	2	2	no	—
640	C₂²	—	2	1	no	—
641	C₂²	—	2	2	no	—
642	C₂²	—	109	2	no	—
643	C₂²	—	436	8	no	—
644	C₂²	—	218	1	no	—
645	C₂²	—	218	2	no	—
646	C₂²	—	218	2	no	—
647	C₂²	—	218	1	no	—
648	C₂²	—	218	1	no	—
649	C₂²	—	218	2	no	—
650	C₂²	—	218	1	no	—
651	C₂²	—	218	1	no	—
652	C₂²	C₂⁴×D₁₀₉	1	1	yes	characteristic
653	C₄	—	2	1	no	—
654	C₄	—	2	1	no	—
655	C₄	—	2	2	no	—
656	C₄	—	2	1	no	—
657	C₄	—	2	1	no	—
658	C₄	—	2	2	no	—
659	C₄	—	2	1	no	—
660	C₄	—	109	2	no	—
661	C₄	—	109	2	no	—
662	C₄	—	218	2	no	—
663	C₄	—	218	1	no	—
664	C₄	—	218	2	no	—
665	C₄	—	218	2	no	—
666	C₄	—	218	1	no	—
667	C₄	—	218	1	no	—
668	C₄	—	218	1	no	—
669	C₄	#41×D₁₀₉	1	2	yes	—
670	C₂	—	4	2	no	—
671	C₂	—	4	1	no	—
672	C₂	—	4	2	no	—
673	C₂	—	436	2	no	—
674	C₂	—	436	1	no	—
675	C₂	—	218	2	no	—
676	C₂	C₂×#41×D₁₀₉	1	1	yes	characteristic
677	C₂	H(5,𝔽₂)×D₁₀₉	1	1	yes	characteristic
678	C₂	#20295861	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₀₉
commutator, socle, cosocle	C₂²×C₁₀₉	C₂⁵
Fitting	#540×C₁₀₉	C₂
hypercenter	#540	D₁₀₉
hypocenter	C₁₀₉	#3460
LCS	G ▷ C₂²×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂² ◁ #540

Complements

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

N	H ≅ G/N	type
1. #20295656	C₂	semidirect
2. #20295647	C₂	semidirect
3. #20295644	C₂	semidirect
4. #20295641	C₂	semidirect
5. #20295627	C₂	semidirect
6. #20295626	C₂	semidirect
7. #20295612	C₂	semidirect
8. #20295608	C₂	semidirect
9. #20295605	C₂	semidirect
10. #20295592	C₂	semidirect
11. #20295589	C₂	semidirect
12. #20295574	C₂	semidirect
13. #20295571	C₂	semidirect
14. #20295571	C₂	semidirect
15. #20295561	C₂	semidirect
16. #20295557	C₂	semidirect
17. #20295553	C₂	semidirect
18. #20295536	C₂	semidirect
19. #20295534	C₂	semidirect
20. #20295494	C₂	semidirect
21. C₄×#13182028	C₂	semidirect
22. C₄×D₄×D₁₀₉	C₂	semidirect
23. #540×C₁₀₉	C₂	semidirect
26. C₂×#13182028	C₂²	semidirect
27. C₂×#13182028	C₂²	semidirect
30. #16812699	C₂²	semidirect
31. #16812698	C₂²	semidirect
32. #16812698	C₂²	semidirect
35. #16812694	C₂²	semidirect
36. #16812694	C₂²	semidirect
37. #16812692	C₂²	semidirect
38. #16812692	C₂²	semidirect
39. #16812690	C₂²	semidirect
40. #16812689	C₂²	semidirect
43. #16812686	C₂²	semidirect
45. #16812685	C₂²	semidirect
46. #16812685	C₂²	semidirect
47. #16812685	C₂²	semidirect
48. #16812684	C₂²	semidirect
49. #16812682	C₂²	semidirect
50. #16812682	C₂²	semidirect
51. #16812681	C₂²	semidirect
52. #16812681	C₂²	semidirect
53. #16812680	C₂²	semidirect
55. #16812679	C₂²	semidirect
56. #16812678	C₂²	semidirect
57. #16812678	C₂²	semidirect
59. #16812677	C₂²	semidirect
60. #16812676	C₂²	semidirect
63. #16812673	C₂²	semidirect
65. #16812672	C₂²	semidirect
68. #16812671	C₂²	semidirect
69. #16812671	C₂²	semidirect
72. #16812670	C₂²	semidirect
73. #16812670	C₂²	semidirect
78. C₄×Dic₂₁₈	C₂²	semidirect
79. #16812664	C₂²	semidirect
80. #16812664	C₂²	semidirect
81. #16812664	C₂²	semidirect
84. D₄×Dic₁₀₉	C₂²	semidirect
85. D₄×Dic₁₀₉	C₂²	semidirect
86. D₄×Dic₁₀₉	C₂²	semidirect
90. #16812661	C₂²	semidirect
97. #16812659	C₂²	semidirect
98. #16812659	C₂²	semidirect
99. #16812659	C₂²	semidirect
101. #16812657	C₂²	semidirect
103. #16812656	C₂²	semidirect
104. #16812655	C₂²	semidirect
105. #16812655	C₂²	semidirect
108. C₂×C₄×Dic₁₀₉	C₂²	semidirect
109. C₂×C₄×Dic₁₀₉	C₂²	semidirect
111. C₄²×D₁₀₉	C₂²	semidirect
113. #125×C₁₀₉	C₂²	semidirect
114. #123×C₁₀₉	C₂²	semidirect
115. #123×C₁₀₉	C₂²	semidirect
117. #121×C₁₀₉	C₂²	semidirect
118. #121×C₁₀₉	C₂²	semidirect
119. #121×C₁₀₉	C₂²	semidirect
121. C₄×D₄×C₁₀₉	C₂²	semidirect
122. #117×C₁₀₉	C₂²	semidirect
288. C₄×D₁₀₉	#41	semidirect
340. C₁₀₉	#3460	semidirect
347. #540	D₁₀₉	semidirect
382. #125	C₂×D₁₀₉	semidirect
396. #123	C₂×D₁₀₉	semidirect
397. #123	C₂×D₁₀₉	semidirect
419. #121	C₂×D₁₀₉	semidirect
420. #121	C₂×D₁₀₉	semidirect
421. #121	C₂×D₁₀₉	semidirect
449. C₄×D₄	C₂×D₁₀₉	semidirect
456. #117	C₂×D₁₀₉	semidirect

Maximal subgroups

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

subgroup	index
#20295656	2
#20295647	2
#20295644	2
#20295641	2
#20295627	2
#20295626	2
#20295612	2
#20295608	2
#20295605	2
#20295592	2
#20295589	2
#20295574	2
#20295571	2
#20295561	2
#20295557	2
#20295553	2
#20295536	2
#20295534	2
#20295494	2
C₄×#13182028	2
C₄×D₄×D₁₀₉	2
#540×C₁₀₉	2
#3460	109