Subgroups — #542×D₁₀₉ #28376402

Order 13952.

1132 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20295650	C₂	1	1	yes	maximal, characteristic, complemented
2	#20295649	C₂	1	1	yes	maximal, characteristic, complemented
3	#20295648	C₂	1	1	yes	maximal, characteristic, complemented
4	#20295647	C₂	1	1	yes	maximal, characteristic, complemented
5	#20295646	C₂	1	2	yes	maximal, complemented
6	#20295645	C₂	1	1	yes	maximal, characteristic, complemented
7	#20295644	C₂	1	2	yes	maximal, complemented
8	#20295643	C₂	1	1	yes	maximal, characteristic, complemented
9	#20295642	C₂	1	2	yes	maximal, complemented
10	#20295641	C₂	1	1	yes	maximal, characteristic, complemented
11	#20295640	C₂	1	2	yes	maximal, complemented
12	C₄⋊Q₈×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
13	#126×D₁₀₉	C₂	1	2	yes	maximal, complemented
14	#124×D₁₀₉	C₂	1	2	yes	maximal, complemented
15	#124×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
16	#123×D₁₀₉	C₂	1	2	yes	maximal, complemented
17	C₂²⋊Q₈×D₁₀₉	C₂	1	2	yes	maximal, complemented
18	C₂²⋊Q₈×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
19	#121×D₁₀₉	C₂	1	1	yes	maximal, characteristic
20	C₄×Q₈×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×D₄×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
22	#117×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
23	#542×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×Q₈×D₁₀₉	C₂²	1	1	yes	characteristic
25	C₂×Q₈×D₁₀₉	C₂²	1	2	yes	—
26	C₂×D₄×D₁₀₉	C₂²	1	1	yes	characteristic
27	C₂×D₄×D₁₀₉	C₂²	1	2	yes	—
28	C₂²×C₄×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	#16812698	C₂²	1	1	yes	characteristic, complemented
34	#16812697	C₂²	1	2	yes	complemented
35	#16812694	C₂²	1	2	yes	complemented
36	#16812694	C₂²	1	2	yes	complemented
37	#16812694	C₂²	1	2	yes	complemented
38	#16812693	C₂²	1	2	yes	complemented
39	#16812692	C₂²	1	2	yes	complemented
40	#16812692	C₂²	1	2	yes	complemented
41	#16812692	C₂²	1	2	yes	complemented
42	#16812688	C₂²	1	2	yes	complemented
43	#16812688	C₂²	1	1	yes	characteristic, complemented
44	#16812687	C₂²	1	2	yes	complemented
45	#16812687	C₂²	1	1	yes	characteristic, complemented
46	#16812686	C₂²	1	1	yes	characteristic, complemented
47	#16812686	C₂²	1	2	yes	complemented
48	#16812685	C₂²	1	2	yes	complemented
49	#16812685	C₂²	1	2	yes	complemented
50	#16812685	C₂²	1	2	yes	complemented
51	#16812685	C₂²	1	2	yes	complemented
52	#16812685	C₂²	1	2	yes	complemented
53	#16812685	C₂²	1	2	yes	complemented
54	#16812684	C₂²	1	2	yes	complemented
55	#16812684	C₂²	1	2	yes	complemented
56	#16812683	C₂²	1	2	yes	complemented
57	#16812682	C₂²	1	2	yes	complemented
58	#16812681	C₂²	1	2	yes	complemented
59	#16812681	C₂²	1	2	yes	complemented
60	#16812680	C₂²	1	2	yes	complemented
61	#16812679	C₂²	1	1	yes	characteristic, complemented
62	#16812679	C₂²	1	2	yes	complemented
63	#16812678	C₂²	1	2	yes	complemented
64	#16812678	C₂²	1	1	yes	characteristic, complemented
65	#16812677	C₂²	1	2	yes	complemented
66	#16812677	C₂²	1	2	yes	complemented
67	#16812677	C₂²	1	2	yes	complemented
68	#16812676	C₂²	1	2	yes	complemented
69	#16812676	C₂²	1	2	yes	complemented
70	#16812676	C₂²	1	2	yes	complemented
71	#16812675	C₂²	1	2	yes	complemented
72	#16812675	C₂²	1	1	yes	characteristic, complemented
73	#16812674	C₂²	1	1	yes	characteristic
74	#16812673	C₂²	1	1	yes	characteristic
75	#16812672	C₂²	1	2	yes	—
76	#16812671	C₂²	1	2	yes	—
77	#16812670	C₂²	1	1	yes	characteristic
78	Q₈×Dic₁₀₉	C₂²	1	1	yes	characteristic, complemented
79	C₄×Dic₂₁₈	C₂²	1	2	yes	complemented
80	C₄×Dic₂₁₈	C₂²	1	1	yes	characteristic, complemented
81	#16812664	C₂²	1	1	yes	characteristic, complemented
82	#16812664	C₂²	1	2	yes	complemented
83	C₄×D₄₃₆	C₂²	1	1	yes	characteristic, complemented
84	D₄×Dic₁₀₉	C₂²	1	1	yes	characteristic, complemented
85	#16812661	C₂²	1	1	yes	characteristic, complemented
86	C₄×C₂²⋊D₁₀₉	C₂²	1	2	yes	complemented
87	#16812659	C₂²	1	2	yes	complemented
88	#16812658	C₂²	1	1	yes	characteristic, complemented
89	#16812657	C₂²	1	1	yes	characteristic, complemented
90	#16812657	C₂²	1	1	yes	characteristic, complemented
91	#16812656	C₂²	1	1	yes	characteristic, complemented
92	#16812656	C₂²	1	1	yes	characteristic, complemented
93	#16812655	C₂²	1	1	yes	characteristic, complemented
94	#16812655	C₂²	1	1	yes	characteristic, complemented
95	C₄⋊C₄×D₁₀₉	C₂²	1	1	yes	characteristic
96	C₄⋊C₄×D₁₀₉	C₂²	1	1	yes	characteristic
97	C₄⋊C₄×D₁₀₉	C₂²	1	1	yes	characteristic
98	C₄⋊C₄×D₁₀₉	C₂²	1	1	yes	characteristic
99	C₄⋊C₄×D₁₀₉	C₂²	1	2	yes	—
100	C₄⋊C₄×D₁₀₉	C₂²	1	2	yes	—
101	C₄⋊C₄×D₁₀₉	C₂²	1	2	yes	—
102	C₂²⋊C₄×D₁₀₉	C₂²	1	1	yes	characteristic
103	C₂²⋊C₄×D₁₀₉	C₂²	1	1	yes	characteristic
104	C₂²⋊C₄×D₁₀₉	C₂²	1	2	yes	—
105	C₂²⋊C₄×D₁₀₉	C₂²	1	2	yes	—
106	C₂²⋊C₄×D₁₀₉	C₂²	1	2	yes	—
107	C₂²⋊C₄×D₁₀₉	C₂²	1	2	yes	—
108	C₂²⋊C₄×D₁₀₉	C₂²	1	2	yes	—
109	C₄²×D₁₀₉	C₂²	1	1	yes	characteristic
110	C₄²×D₁₀₉	C₂²	1	1	yes	characteristic
111	C₄²×D₁₀₉	C₂²	1	2	yes	—
112	C₄⋊Q₈×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
113	#126×C₁₀₉	C₂²	1	2	yes	complemented
114	#124×C₁₀₉	C₂²	1	2	yes	complemented
115	#124×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
116	#123×C₁₀₉	C₂²	1	2	yes	complemented
117	C₂²⋊Q₈×C₁₀₉	C₂²	1	2	yes	complemented
118	C₂²⋊Q₈×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
119	#121×C₁₀₉	C₂²	1	1	yes	characteristic
120	C₄×Q₈×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
121	C₄×D₄×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
122	#117×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₁₀₉	C₂³	1	1	yes	characteristic
124	C₂³×D₁₀₉	C₂³	1	2	yes	—
125	C₂×Dic₂₁₈	C₂³	1	2	yes	—
126	C₂×Dic₂₁₈	C₂³	1	1	yes	characteristic
127	C₂×Dic₂₁₈	C₂³	1	2	yes	—
128	C₂×Dic₂₁₈	C₂³	1	2	yes	—
129	C₂×Dic₂₁₈	C₂³	1	2	yes	—
130	Q₈×D₁₀₉	—	2	4	no	—
131	Q₈×D₁₀₉	—	4	4	no	—
132	C₂×D₄₃₆	C₂³	1	1	yes	characteristic
133	C₂×D₄₃₆	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₁₀₉	C₂³	1	2	yes	—
135	C₂×C₂²⋊D₁₀₉	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₁₀₉	C₂³	1	2	yes	—
137	D₄×D₁₀₉	—	2	4	no	—
138	D₄×D₁₀₉	—	4	4	no	—
139	C₂²×Dic₁₀₉	C₂³	1	1	yes	characteristic
140	C₂²×Dic₁₀₉	C₂³	1	2	yes	—
141	C₂×C₄×D₁₀₉	—	2	4	no	—
142	C₂×C₄×D₁₀₉	—	4	4	no	—
143	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
144	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
145	C₂×C₄×D₁₀₉	C₂³	1	2	yes	—
146	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
147	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
148	C₂×C₄×D₁₀₉	C₂³	1	2	yes	—
149	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
150	C₂×C₄×D₁₀₉	C₂³	1	2	yes	—
151	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
152	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
153	C₂×C₄×D₁₀₉	C₂³	1	2	yes	—
154	C₂×C₄×D₁₀₉	C₂³	1	2	yes	—
155	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
156	C₄⋊Dic₁₀₉	C₂³	1	1	yes	characteristic
157	C₄⋊Dic₁₀₉	C₂³	1	1	yes	characteristic
158	C₄⋊Dic₁₀₉	C₂³	1	1	yes	characteristic
159	C₄⋊Dic₁₀₉	C₂³	1	1	yes	characteristic
160	C₄⋊Dic₁₀₉	C₂³	1	2	yes	—
161	C₄⋊Dic₁₀₉	C₂³	1	2	yes	—
162	C₄⋊Dic₁₀₉	C₂³	1	2	yes	—
163	#13182008	C₂³	1	1	yes	characteristic
164	#13182008	C₂³	1	1	yes	characteristic
165	#13182008	C₂³	1	1	yes	characteristic
166	#13182008	C₂³	1	1	yes	characteristic
167	#13182008	C₂³	1	2	yes	—
168	#13182008	C₂³	1	2	yes	—
169	#13182008	C₂³	1	2	yes	—
170	#13182008	C₂³	1	2	yes	—
171	#13182008	C₂³	1	2	yes	—
172	#13182008	C₂³	1	2	yes	—
173	#13182008	C₂³	1	2	yes	—
174	#13182008	C₂³	1	2	yes	—
175	C₂²⋊Dic₁₀₉	C₂³	1	1	yes	characteristic
176	C₂²⋊Dic₁₀₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
183	#13182006	C₂³	1	1	yes	characteristic
184	#13182006	C₂³	1	1	yes	characteristic
185	#13182006	C₂³	1	1	yes	characteristic
186	#13182006	C₂³	1	2	yes	—
187	#13182006	C₂³	1	2	yes	—
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	#13182006	C₂³	1	2	yes	—
195	#13182006	C₂³	1	2	yes	—
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	1	yes	characteristic
201	C₄×Dic₁₀₉	C₂³	1	1	yes	characteristic
202	C₄×Dic₁₀₉	C₂³	1	2	yes	—
203	C₄×Dic₁₀₉	C₂³	1	2	yes	—
204	C₄×Dic₁₀₉	C₂³	1	2	yes	—
205	C₂×Q₈×C₁₀₉	C₂³	1	1	yes	characteristic
206	C₂×Q₈×C₁₀₉	C₂³	1	2	yes	—
207	C₂×D₄×C₁₀₉	C₂³	1	1	yes	characteristic
208	C₂×D₄×C₁₀₉	C₂³	1	2	yes	—
209	C₂²×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
210	C₂²×C₄×C₁₀₉	C₂³	1	2	yes	—
211	C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
212	C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
213	C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
214	C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
215	C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
216	C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
217	C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
218	C₂²⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
219	C₂²⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
220	C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
221	C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
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	C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
226	C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
227	C₄²×C₁₀₉	C₂³	1	2	yes	—
228	C₂³×C₁₀₉	C₂⁴	1	1	yes	characteristic
229	C₂³×C₁₀₉	C₂⁴	1	2	yes	—
230	C₂²×D₁₀₉	—	2	2	no	—
231	C₂²×D₁₀₉	—	2	4	no	—
232	C₂²×D₁₀₉	—	2	4	no	—
233	C₂²×D₁₀₉	—	2	2	no	—
234	C₂²×D₁₀₉	—	2	2	no	—
235	C₂²×D₁₀₉	—	2	4	no	—
236	C₂²×D₁₀₉	C₂⁴	1	1	yes	characteristic
237	C₂²×D₁₀₉	C₂⁴	1	2	yes	—
238	C₂²×D₁₀₉	C₂⁴	1	1	yes	characteristic
239	Q₈×C₁₀₉	—	2	2	no	—
240	Q₈×C₁₀₉	—	4	2	no	—
241	D₄×C₁₀₉	—	2	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	C₂⁴	1	1	yes	characteristic
246	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
247	C₂×C₄×C₁₀₉	C₂⁴	1	2	yes	—
248	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
249	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
250	C₂×C₄×C₁₀₉	C₂⁴	1	2	yes	—
251	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
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	—	4	2	no	—
256	C₂²⋊D₁₀₉	—	4	2	no	—
257	C₂×Dic₁₀₉	—	2	2	no	—
258	C₂×Dic₁₀₉	—	4	2	no	—
259	C₂×Dic₁₀₉	C₂⁴	1	1	yes	characteristic
260	C₂×Dic₁₀₉	C₂⁴	1	1	yes	characteristic
261	C₂×Dic₁₀₉	C₂⁴	1	2	yes	—
262	C₂×Dic₁₀₉	C₂⁴	1	1	yes	characteristic
263	C₂×Dic₁₀₉	C₂⁴	1	1	yes	characteristic
264	C₂×Dic₁₀₉	C₂⁴	1	2	yes	—
265	C₂×Dic₁₀₉	C₂⁴	1	1	yes	characteristic
266	C₂×Dic₁₀₉	C₂⁴	1	2	yes	—
267	C₂×Dic₁₀₉	C₂⁴	1	1	yes	characteristic
268	D₄₃₆	—	2	2	no	—
269	D₄₃₆	—	4	2	no	—
270	C₄×D₁₀₉	—	2	2	no	—
271	C₄×D₁₀₉	—	2	4	no	—
272	C₄×D₁₀₉	—	2	2	no	—
273	C₄×D₁₀₉	—	2	4	no	—
274	C₄×D₁₀₉	—	2	4	no	—
275	C₄×D₁₀₉	—	2	2	no	—
276	C₄×D₁₀₉	—	2	2	no	—
277	C₄×D₁₀₉	—	2	2	no	—
278	C₄×D₁₀₉	—	2	2	no	—
279	C₄×D₁₀₉	—	2	2	no	—
280	C₄×D₁₀₉	—	4	2	no	—
281	C₄×D₁₀₉	—	4	2	no	—
282	C₄×D₁₀₉	#41	1	4	yes	—
283	Dic₂₁₈	—	2	2	no	—
284	Dic₂₁₈	—	2	4	no	—
285	Dic₂₁₈	—	4	2	no	—
286	Dic₂₁₈	—	4	2	no	—
287	Dic₂₁₈	—	4	2	no	—
288	C₂²×C₁₀₉	—	2	1	no	—
289	C₂²×C₁₀₉	—	2	2	no	—
290	C₂²×C₁₀₉	—	2	2	no	—
291	C₂²×C₁₀₉	—	2	1	no	—
292	C₂²×C₁₀₉	—	2	1	no	—
293	C₂²×C₁₀₉	—	2	2	no	—
294	C₂²×C₁₀₉	C₂⁵	1	1	yes	characteristic
295	C₂×D₁₀₉	—	2	1	no	—
296	C₂×D₁₀₉	—	2	2	no	—
297	C₂×D₁₀₉	—	2	2	no	—
298	C₂×D₁₀₉	—	2	1	no	—
299	C₂×D₁₀₉	—	2	1	no	—
300	C₂×D₁₀₉	—	2	2	no	—
301	C₂×D₁₀₉	—	4	4	no	—
302	C₂×D₁₀₉	—	4	8	no	—
303	C₂×D₁₀₉	C₂×#41	1	2	yes	—
304	C₂×D₁₀₉	H(5,𝔽₂)	1	2	yes	—
305	C₂×D₁₀₉	2₋¹⁺⁴	1	2	yes	—
306	C₄×C₁₀₉	—	2	2	no	—
307	C₄×C₁₀₉	—	2	1	no	—
308	C₄×C₁₀₉	—	2	1	no	—
309	C₄×C₁₀₉	—	2	2	no	—
310	C₄×C₁₀₉	—	2	2	no	—
311	C₄×C₁₀₉	—	2	1	no	—
312	C₄×C₁₀₉	—	2	1	no	—
313	C₄×C₁₀₉	—	2	1	no	—
314	C₄×C₁₀₉	C₂×#41	1	2	yes	—
315	Dic₁₀₉	—	2	2	no	—
316	Dic₁₀₉	—	2	1	no	—
317	Dic₁₀₉	—	2	1	no	—
318	Dic₁₀₉	—	2	2	no	—
319	Dic₁₀₉	—	2	2	no	—
320	Dic₁₀₉	—	2	1	no	—
321	Dic₁₀₉	—	2	1	no	—
322	Dic₁₀₉	—	2	1	no	—
323	Dic₁₀₉	C₂×#41	1	2	yes	—
324	C₂×C₁₀₉	—	4	1	no	—
325	C₂×C₁₀₉	—	4	2	no	—
326	C₂×C₁₀₉	C₂²×#41	1	1	yes	characteristic
327	C₂×C₁₀₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
328	C₂×C₁₀₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
329	D₁₀₉	—	4	1	no	—
330	D₁₀₉	—	4	2	no	—
331	D₁₀₉	#542	1	4	yes	direct product factor
332	C₂×#542	—	109	1	no	maximal, Sylow
333	C₁₀₉	C₂×#542	1	1	yes	characteristic, complemented, Sylow
334	#542	—	109	1	no	—
335	#542	—	109	2	no	—
336	#542	—	109	2	no	—
337	#542	—	109	1	no	—
338	#542	—	109	2	no	—
339	#542	—	109	2	no	—
340	#542	—	109	1	no	—
341	#542	—	109	1	no	—
342	#542	—	109	1	no	—
343	#542	—	109	1	no	—
344	#542	—	109	1	no	—
345	#542	D₁₀₉	1	1	yes	characteristic, direct product factor
346	C₂×C₄⋊Q₈	—	109	1	no	—
347	C₂×#126	—	109	2	no	—
348	C₂×#124	—	109	1	no	—
349	C₂×#124	—	109	2	no	—
350	C₂×#123	—	109	2	no	—
351	C₂×C₂²⋊Q₈	—	109	2	no	—
352	C₂×C₂²⋊Q₈	—	109	1	no	—
353	C₂×#121	—	109	1	no	—
354	C₂×C₄×Q₈	—	109	1	no	—
355	C₂×C₄×D₄	—	109	1	no	—
356	C₂×#117	—	109	1	no	—
357	C₂²×Q₈	—	109	2	no	—
358	C₂²×Q₈	—	109	1	no	—
359	C₂²×D₄	—	109	2	no	—
360	C₂²×D₄	—	109	1	no	—
361	C₂³×C₄	—	109	2	no	—
362	C₂³×C₄	—	109	1	no	—
363	C₄⋊Q₈	—	109	2	no	—
364	C₄⋊Q₈	—	109	2	no	—
365	C₄⋊Q₈	—	109	1	no	—
366	C₄⋊Q₈	—	109	1	no	—
367	C₄⋊Q₈	—	109	1	no	—
368	C₄⋊Q₈	C₂×D₁₀₉	1	1	yes	characteristic, complemented
369	#126	—	109	2	no	—
370	#126	—	109	2	no	—
371	#126	—	109	2	no	—
372	#126	—	109	2	no	—
373	#126	—	109	2	no	—
374	#126	—	109	2	no	—
375	#126	—	109	2	no	—
376	#126	C₂×D₁₀₉	1	2	yes	complemented
377	#124	—	109	1	no	—
378	#124	—	109	2	no	—
379	#124	—	109	1	no	—
380	#124	—	109	2	no	—
381	#124	—	109	2	no	—
382	#124	—	109	2	no	—
383	#124	—	109	2	no	—
384	#124	—	109	2	no	—
385	#124	—	109	2	no	—
386	#124	—	109	2	no	—
387	#124	—	109	1	no	—
388	#124	—	109	2	no	—
389	#124	C₂×D₁₀₉	1	1	yes	characteristic, complemented
390	#124	C₂×D₁₀₉	1	2	yes	complemented
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	—	109	2	no	—
397	#123	—	109	2	no	—
398	#123	C₂×D₁₀₉	1	2	yes	complemented
399	C₂²⋊Q₈	—	109	2	no	—
400	C₂²⋊Q₈	—	109	1	no	—
401	C₂²⋊Q₈	—	109	2	no	—
402	C₂²⋊Q₈	—	109	1	no	—
403	C₂²⋊Q₈	—	109	2	no	—
404	C₂²⋊Q₈	—	109	2	no	—
405	C₂²⋊Q₈	—	109	2	no	—
406	C₂²⋊Q₈	—	109	2	no	—
407	C₂²⋊Q₈	—	109	1	no	—
408	C₂²⋊Q₈	—	109	2	no	—
409	C₂²⋊Q₈	—	109	2	no	—
410	C₂²⋊Q₈	—	109	2	no	—
411	C₂²⋊Q₈	C₂×D₁₀₉	1	2	yes	complemented
412	C₂²⋊Q₈	C₂×D₁₀₉	1	1	yes	characteristic, complemented
413	#121	—	109	1	no	—
414	#121	—	109	2	no	—
415	#121	—	109	1	no	—
416	#121	—	109	1	no	—
417	#121	—	109	2	no	—
418	#121	C₂×D₁₀₉	1	1	yes	characteristic
419	C₄×Q₈	—	109	1	no	—
420	C₄×Q₈	—	109	2	no	—
421	C₄×Q₈	—	109	1	no	—
422	C₄×Q₈	—	109	2	no	—
423	C₄×Q₈	—	109	1	no	—
424	C₄×Q₈	C₂×D₁₀₉	1	1	yes	characteristic, complemented
425	C₄×D₄	—	109	1	no	—
426	C₄×D₄	—	109	2	no	—
427	C₄×D₄	—	109	1	no	—
428	C₄×D₄	—	109	2	no	—
429	C₄×D₄	—	109	1	no	—
430	C₄×D₄	C₂×D₁₀₉	1	1	yes	characteristic, complemented
431	#117	—	109	1	no	—
432	#117	—	109	1	no	—
433	#117	—	109	1	no	—
434	#117	—	109	1	no	—
435	#117	—	109	1	no	—
436	#117	—	109	1	no	—
437	#117	—	109	1	no	—
438	#117	C₂×D₁₀₉	1	1	yes	characteristic, complemented
439	C₂×C₄⋊C₄	—	109	1	no	—
440	C₂×C₄⋊C₄	—	109	1	no	—
441	C₂×C₄⋊C₄	—	109	1	no	—
442	C₂×C₄⋊C₄	—	109	1	no	—
443	C₂×C₄⋊C₄	—	109	2	no	—
444	C₂×C₄⋊C₄	—	109	2	no	—
445	C₂×C₄⋊C₄	—	109	2	no	—
446	C₂×C₂²⋊C₄	—	109	1	no	—
447	C₂×C₂²⋊C₄	—	109	1	no	—
448	C₂×C₂²⋊C₄	—	109	2	no	—
449	C₂×C₂²⋊C₄	—	109	2	no	—
450	C₂×C₂²⋊C₄	—	109	2	no	—
451	C₂×C₂²⋊C₄	—	109	2	no	—
452	C₂×C₂²⋊C₄	—	109	2	no	—
453	C₂×C₄²	—	109	1	no	—
454	C₂×C₄²	—	109	1	no	—
455	C₂×C₄²	—	109	2	no	—
456	C₂⁴	—	109	2	no	—
457	C₂⁴	—	109	1	no	—
458	C₂×Q₈	—	109	2	no	—
459	C₂×Q₈	—	109	2	no	—
460	C₂×Q₈	—	109	2	no	—
461	C₂×Q₈	—	109	2	no	—
462	C₂×Q₈	—	109	1	no	—
463	C₂×Q₈	—	436	4	no	—
464	C₂×Q₈	—	218	4	no	—
465	C₂×Q₈	C₂²×D₁₀₉	1	1	yes	characteristic
466	C₂×Q₈	C₂²×D₁₀₉	1	2	yes	—
467	C₂×D₄	—	109	2	no	—
468	C₂×D₄	—	109	2	no	—
469	C₂×D₄	—	109	2	no	—
470	C₂×D₄	—	109	2	no	—
471	C₂×D₄	—	109	1	no	—
472	C₂×D₄	—	436	4	no	—
473	C₂×D₄	—	218	4	no	—
474	C₂×D₄	C₂²×D₁₀₉	1	1	yes	characteristic
475	C₂×D₄	C₂²×D₁₀₉	1	2	yes	—
476	C₂²×C₄	—	109	1	no	—
477	C₂²×C₄	—	109	2	no	—
478	C₂²×C₄	—	109	1	no	—
479	C₂²×C₄	—	109	2	no	—
480	C₂²×C₄	—	109	2	no	—
481	C₂²×C₄	—	109	1	no	—
482	C₂²×C₄	—	109	1	no	—
483	C₂²×C₄	—	109	2	no	—
484	C₂²×C₄	—	109	1	no	—
485	C₂²×C₄	—	109	1	no	—
486	C₂²×C₄	—	109	2	no	—
487	C₂²×C₄	—	109	1	no	—
488	C₂²×C₄	—	109	2	no	—
489	C₂²×C₄	—	109	1	no	—
490	C₂²×C₄	—	109	1	no	—
491	C₂²×C₄	—	436	4	no	—
492	C₂²×C₄	—	218	4	no	—
493	C₂²×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
494	C₂²×C₄	C₂²×D₁₀₉	1	2	yes	—
495	C₄⋊C₄	—	109	1	no	—
496	C₄⋊C₄	—	109	1	no	—
497	C₄⋊C₄	—	109	1	no	—
498	C₄⋊C₄	—	109	1	no	—
499	C₄⋊C₄	—	109	2	no	—
500	C₄⋊C₄	—	109	2	no	—
501	C₄⋊C₄	—	109	2	no	—
502	C₄⋊C₄	—	109	2	no	—
503	C₄⋊C₄	—	109	2	no	—
504	C₄⋊C₄	—	109	2	no	—
505	C₄⋊C₄	—	109	2	no	—
506	C₄⋊C₄	—	109	2	no	—
507	C₄⋊C₄	—	109	1	no	—
508	C₄⋊C₄	—	109	1	no	—
509	C₄⋊C₄	—	109	1	no	—
510	C₄⋊C₄	—	109	1	no	—
511	C₄⋊C₄	—	109	2	no	—
512	C₄⋊C₄	—	109	2	no	—
513	C₄⋊C₄	—	109	2	no	—
514	C₄⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic
515	C₄⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic
516	C₄⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic
517	C₄⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic
518	C₄⋊C₄	C₂²×D₁₀₉	1	2	yes	—
519	C₄⋊C₄	C₂²×D₁₀₉	1	2	yes	—
520	C₄⋊C₄	C₂²×D₁₀₉	1	2	yes	—
521	C₂²⋊C₄	—	109	1	no	—
522	C₂²⋊C₄	—	109	1	no	—
523	C₂²⋊C₄	—	109	2	no	—
524	C₂²⋊C₄	—	109	2	no	—
525	C₂²⋊C₄	—	109	2	no	—
526	C₂²⋊C₄	—	109	2	no	—
527	C₂²⋊C₄	—	109	2	no	—
528	C₂²⋊C₄	—	109	1	no	—
529	C₂²⋊C₄	—	109	1	no	—
530	C₂²⋊C₄	—	109	1	no	—
531	C₂²⋊C₄	—	109	1	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	2	no	—
540	C₂²⋊C₄	—	109	2	no	—
541	C₂²⋊C₄	—	109	2	no	—
542	C₂²⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic
543	C₂²⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic
544	C₂²⋊C₄	C₂²×D₁₀₉	1	2	yes	—
545	C₂²⋊C₄	C₂²×D₁₀₉	1	2	yes	—
546	C₂²⋊C₄	C₂²×D₁₀₉	1	2	yes	—
547	C₂²⋊C₄	C₂²×D₁₀₉	1	2	yes	—
548	C₂²⋊C₄	C₂²×D₁₀₉	1	2	yes	—
549	C₄²	—	109	1	no	—
550	C₄²	—	109	1	no	—
551	C₄²	—	109	1	no	—
552	C₄²	—	109	1	no	—
553	C₄²	—	109	1	no	—
554	C₄²	—	109	1	no	—
555	C₄²	—	109	2	no	—
556	C₄²	—	109	2	no	—
557	C₄²	—	109	2	no	—
558	C₄²	C₂²×D₁₀₉	1	1	yes	characteristic
559	C₄²	C₂²×D₁₀₉	1	1	yes	characteristic
560	C₄²	C₂²×D₁₀₉	1	2	yes	—
561	C₂³	—	109	1	no	—
562	C₂³	—	109	1	no	—
563	C₂³	—	109	2	no	—
564	C₂³	—	218	4	no	—
565	C₂³	—	218	2	no	—
566	C₂³	—	218	2	no	—
567	C₂³	—	218	4	no	—
568	C₂³	—	218	4	no	—
569	C₂³	—	218	2	no	—
570	C₂³	C₂³×D₁₀₉	1	1	yes	characteristic
571	C₂³	C₂³×D₁₀₉	1	2	yes	—
572	Q₈	—	2	2	no	—
573	Q₈	—	4	2	no	—
574	Q₈	—	436	2	no	—
575	Q₈	—	436	2	no	—
576	Q₈	—	436	2	no	—
577	Q₈	—	218	4	no	—
578	Q₈	—	218	2	no	—
579	D₄	—	2	2	no	—
580	D₄	—	4	2	no	—
581	D₄	—	436	2	no	—
582	D₄	—	436	2	no	—
583	D₄	—	436	2	no	—
584	D₄	—	218	4	no	—
585	D₄	—	218	2	no	—
586	C₂×C₄	—	2	2	no	—
587	C₂×C₄	—	4	2	no	—
588	C₂×C₄	—	109	1	no	—
589	C₂×C₄	—	109	4	no	—
590	C₂×C₄	—	109	1	no	—
591	C₂×C₄	—	109	1	no	—
592	C₂×C₄	—	109	2	no	—
593	C₂×C₄	—	109	1	no	—
594	C₂×C₄	—	109	1	no	—
595	C₂×C₄	—	109	2	no	—
596	C₂×C₄	—	109	1	no	—
597	C₂×C₄	—	109	2	no	—
598	C₂×C₄	—	436	2	no	—
599	C₂×C₄	—	436	2	no	—
600	C₂×C₄	—	436	2	no	—
601	C₂×C₄	—	218	2	no	—
602	C₂×C₄	—	218	2	no	—
603	C₂×C₄	—	218	4	no	—
604	C₂×C₄	—	218	2	no	—
605	C₂×C₄	—	218	4	no	—
606	C₂×C₄	—	218	2	no	—
607	C₂×C₄	—	218	4	no	—
608	C₂×C₄	—	218	2	no	—
609	C₂×C₄	—	218	2	no	—
610	C₂×C₄	—	218	2	no	—
611	C₂×C₄	—	218	2	no	—
612	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
613	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
614	C₂×C₄	C₂³×D₁₀₉	1	2	yes	—
615	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
616	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
617	C₂×C₄	C₂³×D₁₀₉	1	2	yes	—
618	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
619	C₂×C₄	C₂³×D₁₀₉	1	2	yes	—
620	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
621	C₂²	—	2	1	no	—
622	C₂²	—	2	2	no	—
623	C₂²	—	2	2	no	—
624	C₂²	—	2	1	no	—
625	C₂²	—	2	1	no	—
626	C₂²	—	2	2	no	—
627	C₂²	—	109	2	no	—
628	C₂²	—	109	2	no	—
629	C₂²	—	109	2	no	—
630	C₂²	—	436	8	no	—
631	C₂²	—	436	4	no	—
632	C₂²	—	218	1	no	—
633	C₂²	—	218	2	no	—
634	C₂²	—	218	2	no	—
635	C₂²	—	218	1	no	—
636	C₂²	—	218	1	no	—
637	C₂²	—	218	2	no	—
638	C₂²	C₂⁴×D₁₀₉	1	1	yes	characteristic
639	C₄	—	2	1	no	—
640	C₄	—	2	2	no	—
641	C₄	—	2	1	no	—
642	C₄	—	2	2	no	—
643	C₄	—	2	2	no	—
644	C₄	—	2	1	no	—
645	C₄	—	2	1	no	—
646	C₄	—	2	1	no	—
647	C₄	—	109	2	no	—
648	C₄	—	218	1	no	—
649	C₄	—	218	2	no	—
650	C₄	—	218	1	no	—
651	C₄	—	218	2	no	—
652	C₄	—	218	2	no	—
653	C₄	—	218	1	no	—
654	C₄	—	218	1	no	—
655	C₄	—	218	1	no	—
656	C₄	#41×D₁₀₉	1	2	yes	—
657	C₂	—	4	1	no	—
658	C₂	—	4	2	no	—
659	C₂	—	109	4	no	—
660	C₂	—	436	1	no	—
661	C₂	—	436	2	no	—
662	C₂	C₂×#41×D₁₀₉	1	1	yes	characteristic
663	C₂	H(5,𝔽₂)×D₁₀₉	1	1	yes	characteristic
664	C₂	2₋¹⁺⁴×D₁₀₉	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₀₉
commutator, socle, cosocle	C₂²×C₁₀₉	C₂⁵
Fitting	#542×C₁₀₉	C₂
prime radical	#121×D₁₀₉	C₂
hypercenter	#542	D₁₀₉
hypocenter	C₁₀₉	C₂×#542
LCS	G ▷ C₂²×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂² ◁ #542

Complements

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

N	H ≅ G/N	type
1. #20295650	C₂	semidirect
2. #20295649	C₂	semidirect
3. #20295648	C₂	semidirect
4. #20295647	C₂	semidirect
5. #20295646	C₂	semidirect
6. #20295645	C₂	semidirect
7. #20295644	C₂	semidirect
8. #20295643	C₂	semidirect
9. #20295642	C₂	semidirect
10. #20295641	C₂	semidirect
11. #20295640	C₂	semidirect
12. C₄⋊Q₈×D₁₀₉	C₂	semidirect
13. #126×D₁₀₉	C₂	semidirect
14. #124×D₁₀₉	C₂	semidirect
15. #124×D₁₀₉	C₂	semidirect
16. #123×D₁₀₉	C₂	semidirect
17. C₂²⋊Q₈×D₁₀₉	C₂	semidirect
18. C₂²⋊Q₈×D₁₀₉	C₂	semidirect
20. C₄×Q₈×D₁₀₉	C₂	semidirect
21. C₄×D₄×D₁₀₉	C₂	semidirect
22. #117×D₁₀₉	C₂	semidirect
23. #542×C₁₀₉	C₂	semidirect
30. #16812699	C₂²	semidirect
31. #16812698	C₂²	semidirect
32. #16812698	C₂²	semidirect
33. #16812698	C₂²	semidirect
34. #16812697	C₂²	semidirect
35. #16812694	C₂²	semidirect
36. #16812694	C₂²	semidirect
37. #16812694	C₂²	semidirect
38. #16812693	C₂²	semidirect
39. #16812692	C₂²	semidirect
40. #16812692	C₂²	semidirect
41. #16812692	C₂²	semidirect
42. #16812688	C₂²	semidirect
43. #16812688	C₂²	semidirect
44. #16812687	C₂²	semidirect
45. #16812687	C₂²	semidirect
46. #16812686	C₂²	semidirect
47. #16812686	C₂²	semidirect
48. #16812685	C₂²	semidirect
49. #16812685	C₂²	semidirect
50. #16812685	C₂²	semidirect
51. #16812685	C₂²	semidirect
52. #16812685	C₂²	semidirect
53. #16812685	C₂²	semidirect
54. #16812684	C₂²	semidirect
55. #16812684	C₂²	semidirect
56. #16812683	C₂²	semidirect
57. #16812682	C₂²	semidirect
58. #16812681	C₂²	semidirect
59. #16812681	C₂²	semidirect
60. #16812680	C₂²	semidirect
61. #16812679	C₂²	semidirect
62. #16812679	C₂²	semidirect
63. #16812678	C₂²	semidirect
64. #16812678	C₂²	semidirect
65. #16812677	C₂²	semidirect
66. #16812677	C₂²	semidirect
67. #16812677	C₂²	semidirect
68. #16812676	C₂²	semidirect
69. #16812676	C₂²	semidirect
70. #16812676	C₂²	semidirect
71. #16812675	C₂²	semidirect
72. #16812675	C₂²	semidirect
78. Q₈×Dic₁₀₉	C₂²	semidirect
79. C₄×Dic₂₁₈	C₂²	semidirect
80. C₄×Dic₂₁₈	C₂²	semidirect
81. #16812664	C₂²	semidirect
82. #16812664	C₂²	semidirect
83. C₄×D₄₃₆	C₂²	semidirect
84. D₄×Dic₁₀₉	C₂²	semidirect
85. #16812661	C₂²	semidirect
86. C₄×C₂²⋊D₁₀₉	C₂²	semidirect
87. #16812659	C₂²	semidirect
88. #16812658	C₂²	semidirect
89. #16812657	C₂²	semidirect
90. #16812657	C₂²	semidirect
91. #16812656	C₂²	semidirect
92. #16812656	C₂²	semidirect
93. #16812655	C₂²	semidirect
94. #16812655	C₂²	semidirect
112. C₄⋊Q₈×C₁₀₉	C₂²	semidirect
113. #126×C₁₀₉	C₂²	semidirect
114. #124×C₁₀₉	C₂²	semidirect
115. #124×C₁₀₉	C₂²	semidirect
116. #123×C₁₀₉	C₂²	semidirect
117. C₂²⋊Q₈×C₁₀₉	C₂²	semidirect
118. C₂²⋊Q₈×C₁₀₉	C₂²	semidirect
120. C₄×Q₈×C₁₀₉	C₂²	semidirect
121. C₄×D₄×C₁₀₉	C₂²	semidirect
122. #117×C₁₀₉	C₂²	semidirect
331. D₁₀₉	#542	direct (N × H)
333. C₁₀₉	C₂×#542	semidirect
345. #542	D₁₀₉	direct (N × H)
368. C₄⋊Q₈	C₂×D₁₀₉	semidirect
376. #126	C₂×D₁₀₉	semidirect
389. #124	C₂×D₁₀₉	semidirect
390. #124	C₂×D₁₀₉	semidirect
398. #123	C₂×D₁₀₉	semidirect
411. C₂²⋊Q₈	C₂×D₁₀₉	semidirect
412. C₂²⋊Q₈	C₂×D₁₀₉	semidirect
424. C₄×Q₈	C₂×D₁₀₉	semidirect
430. C₄×D₄	C₂×D₁₀₉	semidirect
438. #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
#20295650	2
#20295649	2
#20295648	2
#20295647	2
#20295646	2
#20295645	2
#20295644	2
#20295643	2
#20295642	2
#20295641	2
#20295640	2
C₄⋊Q₈×D₁₀₉	2
#126×D₁₀₉	2
#124×D₁₀₉	2
#123×D₁₀₉	2
C₂²⋊Q₈×D₁₀₉	2
#121×D₁₀₉	2
C₄×Q₈×D₁₀₉	2
C₄×D₄×D₁₀₉	2
#117×D₁₀₉	2
#542×C₁₀₉	2
C₂×#542	109

Subgroups — #542×D109 #28376402

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #542×D₁₀₉ #28376402