Subgroups — #28376662

Order 13952.

1900 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16812745	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×D₄×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#20295669	C₂	1	1	yes	maximal, characteristic, complemented
4	#20295668	C₂	1	2	yes	maximal, complemented
5	#20295667	C₂	1	1	yes	maximal, characteristic, complemented
6	#20295666	C₂	1	2	yes	maximal, complemented
7	#20295664	C₂	1	1	yes	maximal, characteristic, complemented
8	D₄×D₄₃₆	C₂	1	1	yes	maximal, characteristic, complemented
9	D₄×D₄₃₆	C₂	1	1	yes	maximal, characteristic, complemented
10	#20295660	C₂	1	2	yes	maximal, complemented
11	#20295660	C₂	1	1	yes	maximal, characteristic, complemented
12	D₄×C₂²⋊D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
13	#20295658	C₂	1	2	yes	maximal, complemented
14	#20295594	C₂	1	1	yes	maximal, characteristic, complemented
15	#20295592	C₂	1	1	yes	maximal, characteristic, complemented
16	#20295587	C₂	1	2	yes	maximal, complemented
17	#20295584	C₂	1	2	yes	maximal, complemented
18	#20295539	C₂	1	1	yes	maximal, characteristic, complemented
19	#20295535	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#16812669	C₂	1	2	yes	maximal, complemented
21	#120×D₁₀₉	C₂	1	2	yes	maximal, complemented
22	#20295498	C₂	1	1	yes	maximal, characteristic, complemented
23	#546×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂⁴×D₁₀₉	C₂²	1	2	yes	complemented
25	#16812745	—	2	8	no	—
26	C₂×#13182030	C₂²	1	1	yes	characteristic, complemented
27	C₂×#13182030	C₂²	1	1	yes	characteristic, complemented
28	C₂×#13182029	C₂²	1	1	yes	characteristic, complemented
29	C₂×#13182029	C₂²	1	2	yes	complemented
30	C₂²×D₄₃₆	C₂²	1	1	yes	characteristic, complemented
31	C₂²×D₄₃₆	C₂²	1	2	yes	complemented
32	C₂²×D₄₃₆	C₂²	1	1	yes	characteristic, complemented
33	C₂²×D₄₃₆	C₂²	1	2	yes	complemented
34	C₂²×C₂²⋊D₁₀₉	C₂²	1	2	yes	complemented
35	C₂²×C₂²⋊D₁₀₉	C₂²	1	2	yes	complemented
36	C₂×D₄×D₁₀₉	—	2	8	no	—
37	C₂×D₄×D₁₀₉	C₂²	1	1	yes	characteristic
38	C₂×D₄×D₁₀₉	C₂²	1	2	yes	complemented
39	C₂×D₄×D₁₀₉	C₂²	1	1	yes	characteristic, complemented
40	C₂×D₄×D₁₀₉	C₂²	1	2	yes	complemented
41	C₂×D₄×D₁₀₉	C₂²	1	1	yes	characteristic, complemented
42	C₂×D₄×D₁₀₉	C₂²	1	1	yes	characteristic, complemented
43	C₂×D₄×D₁₀₉	C₂²	1	1	yes	characteristic, complemented
44	C₂×D₄×D₁₀₉	C₂²	1	2	yes	complemented
45	C₂×D₄×D₁₀₉	C₂²	1	2	yes	complemented
46	C₂×D₄×D₁₀₉	C₂²	1	2	yes	complemented
47	C₂×D₄×D₁₀₉	C₂²	1	2	yes	complemented
48	C₂²×C₄×D₁₀₉	C₂²	1	1	yes	characteristic, complemented
49	#16812696	C₂²	1	1	yes	characteristic, complemented
50	#16812695	C₂²	1	1	yes	characteristic, complemented
51	#16812695	C₂²	1	2	yes	complemented
52	#16812688	C₂²	1	1	yes	characteristic, complemented
53	#16812685	C₂²	1	2	yes	complemented
54	#16812684	C₂²	1	1	yes	characteristic, complemented
55	#16812684	C₂²	1	2	yes	complemented
56	#16812684	C₂²	1	2	yes	complemented
57	#16812682	C₂²	1	2	yes	complemented
58	#16812681	C₂²	1	1	yes	characteristic, complemented
59	#16812681	C₂²	1	2	yes	complemented
60	#16812677	C₂²	1	1	yes	characteristic, complemented
61	#16812676	C₂²	1	1	yes	characteristic, complemented
62	#16812675	C₂²	1	1	yes	characteristic, complemented
63	#16812674	C₂²	1	1	yes	characteristic, complemented
64	#16812674	C₂²	1	2	yes	complemented
65	#16812674	C₂²	1	2	yes	complemented
66	#16812674	C₂²	1	1	yes	characteristic, complemented
67	#16812673	C₂²	1	1	yes	characteristic, complemented
68	#16812673	C₂²	1	2	yes	complemented
69	#16812673	C₂²	1	1	yes	characteristic, complemented
70	#16812672	C₂²	1	1	yes	characteristic, complemented
71	#16812672	C₂²	1	2	yes	complemented
72	#16812672	C₂²	1	2	yes	complemented
73	#16812672	C₂²	1	2	yes	complemented
74	#16812672	C₂²	1	2	yes	complemented
75	#16812671	C₂²	1	1	yes	characteristic, complemented
76	#16812671	C₂²	1	2	yes	complemented
77	#16812671	C₂²	1	2	yes	complemented
78	#16812670	C₂²	1	1	yes	characteristic, complemented
79	#16812669	C₂²	1	2	yes	complemented
80	#16812669	C₂²	1	1	yes	characteristic, complemented
81	#16812669	C₂²	1	2	yes	complemented
82	#16812669	C₂²	1	2	yes	complemented
83	#16812669	C₂²	1	2	yes	complemented
84	#16812669	C₂²	1	2	yes	complemented
85	#16812669	C₂²	1	2	yes	complemented
86	#16812669	C₂²	1	2	yes	complemented
87	#16812669	C₂²	1	2	yes	complemented
88	#16812669	C₂²	1	2	yes	complemented
89	#16812669	C₂²	1	2	yes	complemented
90	#16812669	C₂²	1	2	yes	complemented
91	#16812668	C₂²	1	2	yes	complemented
92	#16812667	C₂²	1	1	yes	characteristic, complemented
93	#16812667	C₂²	1	2	yes	complemented
94	#16812667	C₂²	1	2	yes	complemented
95	#16812667	C₂²	1	2	yes	complemented
96	#16812667	C₂²	1	2	yes	complemented
97	C₄×D₄₃₆	C₂²	1	1	yes	characteristic, complemented
98	C₄×D₄₃₆	C₂²	1	1	yes	characteristic, complemented
99	D₄×Dic₁₀₉	C₂²	1	1	yes	characteristic, complemented
100	#16812661	C₂²	1	2	yes	complemented
101	#16812661	C₂²	1	1	yes	characteristic, complemented
102	C₄×C₂²⋊D₁₀₉	C₂²	1	1	yes	characteristic, complemented
103	C₄×C₂²⋊D₁₀₉	C₂²	1	1	yes	characteristic, complemented
104	C₄×C₂²⋊D₁₀₉	C₂²	1	2	yes	complemented
105	#16812659	C₂²	1	2	yes	complemented
106	#16812659	C₂²	1	2	yes	complemented
107	#16812657	C₂²	1	1	yes	characteristic, complemented
108	#16812656	C₂²	1	1	yes	characteristic, complemented
109	C₂×#13182006	C₂²	1	2	yes	complemented
110	C₂×#13182006	C₂²	1	2	yes	complemented
111	C₂²⋊C₄×D₁₀₉	C₂²	1	2	yes	complemented
112	C₂²⋊C₄×D₁₀₉	C₂²	1	2	yes	complemented
113	C₂²⋊C₄×D₁₀₉	C₂²	1	2	yes	complemented
114	C₂×#41×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
115	C₂²×D₄×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
116	#124×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
117	#123×C₁₀₉	C₂²	1	2	yes	complemented
118	C₂²⋊Q₈×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
119	#121×C₁₀₉	C₂²	1	2	yes	complemented
120	#121×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
121	#120×C₁₀₉	C₂²	1	2	yes	complemented
122	C₄×D₄×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
123	C₄×D₄×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
124	C₂×C₂²⋊C₄×C₁₀₉	C₂²	1	2	yes	complemented
125	C₂³×D₁₀₉	—	2	8	no	—
126	C₂³×D₁₀₉	—	4	4	no	—
127	C₂³×D₁₀₉	—	4	4	no	—
128	C₂³×D₁₀₉	C₂³	1	1	yes	characteristic
129	C₂³×D₁₀₉	C₂³	1	2	yes	—
130	C₂³×D₁₀₉	C₂³	1	2	yes	—
131	C₂³×D₁₀₉	C₂³	1	2	yes	—
132	C₂³×D₁₀₉	C₂³	1	2	yes	—
133	C₂³×D₁₀₉	C₂³	1	2	yes	—
134	C₂³×D₁₀₉	C₂³	1	2	yes	complemented
135	C₂³×D₁₀₉	C₂³	1	2	yes	complemented
136	#13182030	—	2	4	no	—
137	#13182030	—	2	4	no	—
138	#13182029	—	2	8	no	—
139	#13182029	—	2	4	no	—
140	C₂×Dic₂₁₈	C₂³	1	1	yes	characteristic, complemented
141	C₂×D₄₃₆	—	2	8	no	—
142	C₂×D₄₃₆	—	2	4	no	—
143	C₂×D₄₃₆	—	2	4	no	—
144	C₂×D₄₃₆	—	4	4	no	—
145	C₂×D₄₃₆	C₂³	1	2	yes	—
146	C₂×D₄₃₆	C₂³	1	1	yes	characteristic
147	C₂×D₄₃₆	C₂³	1	2	yes	—
148	C₂×D₄₃₆	C₂³	1	1	yes	characteristic
149	C₂×D₄₃₆	C₂³	1	2	yes	—
150	C₂×D₄₃₆	C₂³	1	1	yes	characteristic
151	C₂×D₄₃₆	C₂³	1	1	yes	characteristic
152	C₂×D₄₃₆	C₂³	1	2	yes	complemented
153	C₂×D₄₃₆	C₂³	1	2	yes	complemented
154	C₂×D₄₃₆	C₂³	1	1	yes	characteristic, complemented
155	C₂×D₄₃₆	C₂³	1	2	yes	complemented
156	C₂×D₄₃₆	C₂³	1	2	yes	complemented
157	C₂×D₄₃₆	C₂³	1	2	yes	complemented
158	C₂×C₂²⋊D₁₀₉	—	2	8	no	—
159	C₂×C₂²⋊D₁₀₉	—	4	4	no	—
160	C₂×C₂²⋊D₁₀₉	C₂³	1	2	yes	—
161	C₂×C₂²⋊D₁₀₉	C₂³	1	1	yes	characteristic
162	C₂×C₂²⋊D₁₀₉	C₂³	1	1	yes	characteristic
163	C₂×C₂²⋊D₁₀₉	C₂³	1	1	yes	characteristic
164	C₂×C₂²⋊D₁₀₉	C₂³	1	2	yes	—
165	C₂×C₂²⋊D₁₀₉	C₂³	1	2	yes	—
166	C₂×C₂²⋊D₁₀₉	C₂³	1	2	yes	—
167	C₂×C₂²⋊D₁₀₉	C₂³	1	2	yes	—
168	C₂×C₂²⋊D₁₀₉	C₂³	1	2	yes	complemented
169	C₂×C₂²⋊D₁₀₉	C₂³	1	1	yes	characteristic, complemented
170	C₂×C₂²⋊D₁₀₉	C₂³	1	2	yes	complemented
171	C₂×C₂²⋊D₁₀₉	C₂³	1	2	yes	complemented
172	C₂×C₂²⋊D₁₀₉	C₂³	1	2	yes	complemented
173	C₂×C₂²⋊D₁₀₉	C₂³	1	2	yes	complemented
174	D₄×D₁₀₉	—	2	8	no	—
175	D₄×D₁₀₉	—	2	8	no	—
176	D₄×D₁₀₉	—	2	4	no	—
177	D₄×D₁₀₉	—	2	4	no	—
178	D₄×D₁₀₉	—	2	8	no	—
179	D₄×D₁₀₉	—	2	8	no	—
180	D₄×D₁₀₉	—	2	4	no	—
181	D₄×D₁₀₉	—	2	4	no	—
182	D₄×D₁₀₉	—	4	4	no	—
183	D₄×D₁₀₉	—	4	4	no	—
184	D₄×D₁₀₉	D₄	1	8	yes	complemented
185	C₂²×Dic₁₀₉	C₂³	1	1	yes	characteristic
186	C₂²×Dic₁₀₉	C₂³	1	2	yes	complemented
187	C₂×C₄×D₁₀₉	—	2	4	no	—
188	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
189	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
190	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
191	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
192	C₂×C₄×D₁₀₉	C₂³	1	2	yes	complemented
193	C₂×C₄×D₁₀₉	C₂³	1	2	yes	complemented
194	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic, complemented
195	C₂×C₄×D₁₀₉	C₂³	1	2	yes	complemented
196	C₂×C₄×D₁₀₉	C₂³	1	2	yes	complemented
197	C₄⋊Dic₁₀₉	C₂³	1	1	yes	characteristic, complemented
198	C₄⋊Dic₁₀₉	C₂³	1	1	yes	characteristic, complemented
199	#13182008	C₂³	1	1	yes	characteristic, complemented
200	#13182008	C₂³	1	1	yes	characteristic, complemented
201	#13182008	C₂³	1	2	yes	complemented
202	#13182008	C₂³	1	1	yes	characteristic, complemented
203	#13182008	C₂³	1	1	yes	characteristic, complemented
204	C₂²⋊Dic₁₀₉	C₂³	1	1	yes	characteristic
205	C₂²⋊Dic₁₀₉	C₂³	1	2	yes	complemented
206	C₂²⋊Dic₁₀₉	C₂³	1	2	yes	complemented
207	C₂²⋊Dic₁₀₉	C₂³	1	1	yes	characteristic, complemented
208	#13182006	C₂³	1	1	yes	characteristic
209	#13182006	C₂³	1	1	yes	characteristic
210	#13182006	C₂³	1	2	yes	—
211	#13182006	C₂³	1	2	yes	—
212	#13182006	C₂³	1	1	yes	characteristic
213	#13182006	C₂³	1	1	yes	characteristic
214	#13182006	C₂³	1	2	yes	complemented
215	#13182006	C₂³	1	2	yes	complemented
216	#13182006	C₂³	1	2	yes	complemented
217	#13182006	C₂³	1	2	yes	complemented
218	#13182006	C₂³	1	2	yes	complemented
219	#13182006	C₂³	1	2	yes	complemented
220	#13182006	C₂³	1	2	yes	complemented
221	#13182006	C₂³	1	1	yes	characteristic, complemented
222	#13182006	C₂³	1	2	yes	complemented
223	#13182006	C₂³	1	1	yes	characteristic, complemented
224	C₄×Dic₁₀₉	C₂³	1	1	yes	characteristic, complemented
225	C₄×Dic₁₀₉	C₂³	1	2	yes	complemented
226	C₂⁴×C₁₀₉	C₂³	1	2	yes	—
227	#41×C₁₀₉	—	2	4	no	—
228	C₂×Q₈×C₁₀₉	C₂³	1	1	yes	characteristic, complemented
229	C₂×D₄×C₁₀₉	—	2	4	no	—
230	C₂×D₄×C₁₀₉	C₂³	1	1	yes	characteristic
231	C₂×D₄×C₁₀₉	C₂³	1	2	yes	—
232	C₂×D₄×C₁₀₉	C₂³	1	1	yes	characteristic
233	C₂×D₄×C₁₀₉	C₂³	1	1	yes	characteristic
234	C₂×D₄×C₁₀₉	C₂³	1	2	yes	complemented
235	C₂×D₄×C₁₀₉	C₂³	1	2	yes	complemented
236	C₂²×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
237	C₂²×C₄×C₁₀₉	C₂³	1	2	yes	complemented
238	C₂²×C₄×C₁₀₉	C₂³	1	1	yes	characteristic, complemented
239	C₂²×C₄×C₁₀₉	C₂³	1	2	yes	complemented
240	C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic, complemented
241	C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic, complemented
242	C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	complemented
243	C₂²⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
244	C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
245	C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	complemented
246	C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	complemented
247	C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	complemented
248	C₂²⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic, complemented
249	C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	complemented
250	C₄²×C₁₀₉	C₂³	1	1	yes	characteristic, complemented
251	C₂³×C₁₀₉	—	2	4	no	—
252	C₂³×C₁₀₉	—	2	4	no	—
253	C₂³×C₁₀₉	—	4	2	no	—
254	C₂³×C₁₀₉	C₂⁴	1	2	yes	—
255	C₂³×C₁₀₉	C₂⁴	1	1	yes	characteristic
256	C₂³×C₁₀₉	C₂⁴	1	2	yes	—
257	C₂³×C₁₀₉	C₂⁴	1	1	yes	characteristic
258	C₂²×D₁₀₉	—	2	2	no	—
259	C₂²×D₁₀₉	—	2	2	no	—
260	C₂²×D₁₀₉	—	2	2	no	—
261	C₂²×D₁₀₉	—	2	4	no	—
262	C₂²×D₁₀₉	—	2	4	no	—
263	C₂²×D₁₀₉	—	2	4	no	—
264	C₂²×D₁₀₉	—	2	4	no	—
265	C₂²×D₁₀₉	—	2	4	no	—
266	C₂²×D₁₀₉	—	2	4	no	—
267	C₂²×D₁₀₉	—	2	4	no	—
268	C₂²×D₁₀₉	—	2	4	no	—
269	C₂²×D₁₀₉	—	2	4	no	—
270	C₂²×D₁₀₉	—	4	2	no	—
271	C₂²×D₁₀₉	—	4	2	no	—
272	C₂²×D₁₀₉	—	4	2	no	—
273	C₂²×D₁₀₉	—	4	2	no	—
274	C₂²×D₁₀₉	—	4	2	no	—
275	C₂²×D₁₀₉	—	4	2	no	—
276	C₂²×D₁₀₉	—	4	2	no	—
277	C₂²×D₁₀₉	—	4	2	no	—
278	C₂²×D₁₀₉	—	4	2	no	—
279	C₂²×D₁₀₉	—	4	2	no	—
280	C₂²×D₁₀₉	—	4	2	no	—
281	C₂²×D₁₀₉	—	4	32	no	—
282	C₂²×D₁₀₉	C₂×D₄	1	8	yes	complemented
283	C₂²×D₁₀₉	C₂⁴	1	2	yes	—
284	C₂²×D₁₀₉	C₂⁴	1	1	yes	characteristic
285	C₂²×D₁₀₉	C₂⁴	1	2	yes	—
286	C₂²×D₁₀₉	C₂⁴	1	1	yes	characteristic
287	C₂²×D₁₀₉	C₂⁴	1	2	yes	—
288	C₂²×D₁₀₉	C₂⁴	1	1	yes	characteristic
289	Q₈×C₁₀₉	—	2	2	no	—
290	D₄×C₁₀₉	—	2	4	no	—
291	D₄×C₁₀₉	—	2	4	no	—
292	D₄×C₁₀₉	—	2	2	no	—
293	D₄×C₁₀₉	—	2	2	no	—
294	D₄×C₁₀₉	—	4	2	no	—
295	D₄×C₁₀₉	C₂×D₄	1	4	yes	complemented
296	C₂×C₄×C₁₀₉	—	2	4	no	—
297	C₂×C₄×C₁₀₉	—	2	2	no	—
298	C₂×C₄×C₁₀₉	—	2	2	no	—
299	C₂×C₄×C₁₀₉	—	4	2	no	—
300	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
301	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
302	C₂×C₄×C₁₀₉	C₂⁴	1	2	yes	—
303	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
304	C₂×C₄×C₁₀₉	C₂⁴	1	2	yes	—
305	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
306	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
307	C₂²⋊D₁₀₉	—	2	4	no	—
308	C₂²⋊D₁₀₉	—	2	4	no	—
309	C₂²⋊D₁₀₉	—	2	4	no	—
310	C₂²⋊D₁₀₉	—	2	2	no	—
311	C₂²⋊D₁₀₉	—	2	4	no	—
312	C₂²⋊D₁₀₉	—	2	2	no	—
313	C₂²⋊D₁₀₉	—	2	2	no	—
314	C₂²⋊D₁₀₉	—	2	4	no	—
315	C₂²⋊D₁₀₉	—	2	2	no	—
316	C₂²⋊D₁₀₉	—	4	2	no	—
317	C₂²⋊D₁₀₉	—	4	2	no	—
318	C₂²⋊D₁₀₉	—	4	2	no	—
319	C₂²⋊D₁₀₉	—	4	2	no	—
320	C₂²⋊D₁₀₉	C₂×D₄	1	8	yes	complemented
321	C₂×Dic₁₀₉	—	2	2	no	—
322	C₂×Dic₁₀₉	—	4	2	no	—
323	C₂×Dic₁₀₉	C₂⁴	1	1	yes	characteristic
324	C₂×Dic₁₀₉	C₂⁴	1	2	yes	—
325	C₂×Dic₁₀₉	C₂⁴	1	1	yes	characteristic
326	C₂×Dic₁₀₉	C₂⁴	1	1	yes	characteristic
327	C₂×Dic₁₀₉	C₂⁴	1	1	yes	characteristic
328	C₂×Dic₁₀₉	C₂⁴	1	1	yes	characteristic
329	D₄₃₆	—	2	4	no	—
330	D₄₃₆	—	2	4	no	—
331	D₄₃₆	—	2	4	no	—
332	D₄₃₆	—	2	2	no	—
333	D₄₃₆	—	2	4	no	—
334	D₄₃₆	—	2	4	no	—
335	D₄₃₆	—	2	2	no	—
336	D₄₃₆	—	2	2	no	—
337	D₄₃₆	—	2	2	no	—
338	D₄₃₆	—	4	2	no	—
339	D₄₃₆	—	4	2	no	—
340	D₄₃₆	—	4	2	no	—
341	D₄₃₆	C₂×D₄	1	4	yes	complemented
342	C₄×D₁₀₉	—	2	2	no	—
343	C₄×D₁₀₉	—	2	4	no	—
344	C₄×D₁₀₉	—	2	2	no	—
345	C₄×D₁₀₉	—	2	2	no	—
346	C₄×D₁₀₉	—	2	2	no	—
347	C₄×D₁₀₉	—	2	4	no	—
348	C₄×D₁₀₉	—	4	2	no	—
349	C₄×D₁₀₉	—	4	2	no	—
350	C₄×D₁₀₉	C₂×D₄	1	4	yes	complemented
351	Dic₂₁₈	—	2	2	no	—
352	C₂²×C₁₀₉	—	2	1	no	—
353	C₂²×C₁₀₉	—	2	2	no	—
354	C₂²×C₁₀₉	—	2	2	no	—
355	C₂²×C₁₀₉	—	2	1	no	—
356	C₂²×C₁₀₉	—	2	1	no	—
357	C₂²×C₁₀₉	—	2	2	no	—
358	C₂²×C₁₀₉	—	2	1	no	—
359	C₂²×C₁₀₉	—	2	1	no	—
360	C₂²×C₁₀₉	—	2	2	no	—
361	C₂²×C₁₀₉	—	2	2	no	—
362	C₂²×C₁₀₉	—	4	8	no	—
363	C₂²×C₁₀₉	C₂²×D₄	1	4	yes	—
364	C₂²×C₁₀₉	H(5,𝔽₂)	1	2	yes	complemented
365	C₂²×C₁₀₉	C₂⁵	1	1	yes	characteristic
366	C₂×D₁₀₉	—	2	8	no	—
367	C₂×D₁₀₉	—	2	1	no	—
368	C₂×D₁₀₉	—	2	2	no	—
369	C₂×D₁₀₉	—	2	2	no	—
370	C₂×D₁₀₉	—	2	1	no	—
371	C₂×D₁₀₉	—	2	1	no	—
372	C₂×D₁₀₉	—	2	1	no	—
373	C₂×D₁₀₉	—	2	1	no	—
374	C₂×D₁₀₉	—	2	2	no	—
375	C₂×D₁₀₉	—	2	2	no	—
376	C₂×D₁₀₉	—	2	1	no	—
377	C₂×D₁₀₉	—	2	2	no	—
378	C₂×D₁₀₉	—	2	2	no	—
379	C₂×D₁₀₉	—	2	2	no	—
380	C₂×D₁₀₉	—	2	2	no	—
381	C₂×D₁₀₉	—	2	1	no	—
382	C₂×D₁₀₉	—	4	8	no	—
383	C₂×D₁₀₉	—	4	8	no	—
384	C₂×D₁₀₉	—	4	8	no	—
385	C₂×D₁₀₉	—	4	8	no	—
386	C₂×D₁₀₉	—	4	8	no	—
387	C₂×D₁₀₉	—	8	4	no	—
388	C₂×D₁₀₉	—	8	4	no	—
389	C₂×D₁₀₉	C₂²×D₄	1	2	yes	—
390	C₂×D₁₀₉	C₂²×D₄	1	4	yes	—
391	C₂×D₁₀₉	H(5,𝔽₂)	1	2	yes	complemented
392	C₄×C₁₀₉	—	2	1	no	—
393	C₄×C₁₀₉	—	2	1	no	—
394	C₄×C₁₀₉	—	2	2	no	—
395	C₄×C₁₀₉	—	2	1	no	—
396	C₄×C₁₀₉	—	2	2	no	—
397	C₄×C₁₀₉	—	2	1	no	—
398	C₄×C₁₀₉	C₂²×D₄	1	2	yes	—
399	Dic₁₀₉	—	2	1	no	—
400	Dic₁₀₉	—	2	1	no	—
401	Dic₁₀₉	—	2	1	no	—
402	Dic₁₀₉	—	2	2	no	—
403	Dic₁₀₉	—	2	1	no	—
404	Dic₁₀₉	C₂²×D₄	1	2	yes	—
405	C₂×C₁₀₉	—	2	2	no	—
406	C₂×C₁₀₉	—	2	4	no	—
407	C₂×C₁₀₉	—	4	2	no	—
408	C₂×C₁₀₉	—	4	1	no	—
409	C₂×C₁₀₉	C₂³×D₄	1	1	yes	characteristic
410	C₂×C₁₀₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
411	C₂×C₁₀₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
412	D₁₀₉	—	2	2	no	—
413	D₁₀₉	—	2	2	no	—
414	D₁₀₉	—	2	4	no	—
415	D₁₀₉	—	4	2	no	—
416	D₁₀₉	—	4	1	no	—
417	D₁₀₉	—	4	2	no	—
418	#3484	—	109	1	no	maximal, Sylow
419	C₁₀₉	#3484	1	1	yes	characteristic, complemented, Sylow
420	C₂×H(5,𝔽₂)	—	109	1	no	—
421	C₂³×D₄	—	109	1	no	—
422	#546	—	109	1	no	—
423	#546	—	109	1	no	—
424	#546	—	109	2	no	—
425	#546	—	109	1	no	—
426	#546	—	109	2	no	—
427	#546	D₁₀₉	1	1	yes	characteristic, complemented
428	D₄²	—	109	1	no	—
429	D₄²	—	109	2	no	—
430	D₄²	—	109	1	no	—
431	D₄²	—	109	2	no	—
432	D₄²	—	109	1	no	—
433	D₄²	—	109	1	no	—
434	#535	—	109	1	no	—
435	#535	—	109	1	no	—
436	#534	—	109	2	no	—
437	#534	—	109	2	no	—
438	#525	—	109	1	no	—
439	#525	—	109	1	no	—
440	C₂×#120	—	109	2	no	—
441	C₂×#120	—	109	2	no	—
442	#518	—	109	1	no	—
443	C₂⁵	—	109	2	no	—
444	H(5,𝔽₂)	—	218	8	no	—
445	C₂×#41	—	109	1	no	—
446	C₂×#41	—	109	1	no	—
447	C₂×#41	—	109	1	no	—
448	C₂×#41	—	109	2	no	—
449	C₂×#41	C₂×D₁₀₉	1	1	yes	characteristic, complemented
450	C₂²×D₄	—	109	1	no	—
451	C₂²×D₄	—	109	2	no	—
452	C₂²×D₄	—	109	2	no	—
453	C₂²×D₄	—	109	2	no	—
454	C₂²×D₄	—	109	2	no	—
455	C₂²×D₄	—	109	2	no	—
456	C₂²×D₄	—	109	1	no	—
457	C₂²×D₄	—	109	1	no	—
458	C₂²×D₄	—	109	2	no	—
459	C₂²×D₄	—	109	1	no	—
460	C₂²×D₄	—	109	1	no	—
461	C₂²×D₄	—	109	2	no	—
462	C₂²×D₄	—	109	2	no	—
463	C₂²×D₄	—	109	1	no	—
464	C₂²×D₄	—	109	2	no	—
465	C₂²×D₄	—	109	2	no	—
466	C₂²×D₄	—	109	1	no	—
467	C₂²×D₄	—	218	8	no	—
468	C₂²×D₄	C₂×D₁₀₉	1	1	yes	characteristic, complemented
469	C₂³×C₄	—	109	1	no	—
470	#127	—	109	1	no	—
471	#127	—	109	2	no	—
472	#127	—	109	1	no	—
473	#124	—	109	1	no	—
474	#124	—	109	2	no	—
475	#124	C₂×D₁₀₉	1	1	yes	characteristic, complemented
476	#123	—	109	2	no	—
477	#123	—	109	2	no	—
478	#123	—	109	1	no	—
479	#123	—	109	2	no	—
480	#123	—	109	1	no	—
481	#123	—	109	2	no	—
482	#123	C₂×D₁₀₉	1	2	yes	complemented
483	C₂²⋊Q₈	—	109	1	no	—
484	C₂²⋊Q₈	—	109	1	no	—
485	C₂²⋊Q₈	—	109	1	no	—
486	C₂²⋊Q₈	C₂×D₁₀₉	1	1	yes	characteristic, complemented
487	#121	—	109	1	no	—
488	#121	—	109	2	no	—
489	#121	—	109	1	no	—
490	#121	—	109	2	no	—
491	#121	—	109	1	no	—
492	#121	—	109	2	no	—
493	#121	—	109	1	no	—
494	#121	—	109	1	no	—
495	#121	—	109	2	no	—
496	#121	—	109	2	no	—
497	#121	—	109	1	no	—
498	#121	—	109	1	no	—
499	#121	—	109	2	no	—
500	#121	—	109	2	no	—
501	#121	—	109	2	no	—
502	#121	—	109	2	no	—
503	#121	C₂×D₁₀₉	1	2	yes	complemented
504	#121	C₂×D₁₀₉	1	1	yes	characteristic, complemented
505	#120	—	109	2	no	—
506	#120	—	109	1	no	—
507	#120	—	109	2	no	—
508	#120	—	109	2	no	—
509	#120	—	109	2	no	—
510	#120	—	109	2	no	—
511	#120	—	109	2	no	—
512	#120	—	109	1	no	—
513	#120	—	109	2	no	—
514	#120	—	109	2	no	—
515	#120	—	109	2	no	—
516	#120	—	109	2	no	—
517	#120	—	109	2	no	—
518	#120	—	109	2	no	—
519	#120	—	109	2	no	—
520	#120	—	109	2	no	—
521	#120	—	109	2	no	—
522	#120	—	109	2	no	—
523	#120	C₂×D₁₀₉	1	2	yes	complemented
524	C₄×D₄	—	109	1	no	—
525	C₄×D₄	—	109	1	no	—
526	C₄×D₄	—	109	2	no	—
527	C₄×D₄	—	109	1	no	—
528	C₄×D₄	—	109	1	no	—
529	C₄×D₄	—	109	2	no	—
530	C₄×D₄	—	109	2	no	—
531	C₄×D₄	—	109	2	no	—
532	C₄×D₄	—	109	1	no	—
533	C₄×D₄	—	109	1	no	—
534	C₄×D₄	C₂×D₁₀₉	1	1	yes	characteristic, complemented
535	C₄×D₄	C₂×D₁₀₉	1	1	yes	characteristic, complemented
536	#117	—	109	1	no	—
537	#117	—	109	1	no	—
538	C₂×C₂²⋊C₄	—	109	2	no	—
539	C₂×C₂²⋊C₄	—	109	2	no	—
540	C₂×C₂²⋊C₄	—	109	2	no	—
541	C₂×C₂²⋊C₄	—	109	2	no	—
542	C₂×C₂²⋊C₄	—	109	2	no	—
543	C₂×C₂²⋊C₄	C₂×D₁₀₉	1	2	yes	complemented
544	C₂⁴	—	109	2	no	—
545	C₂⁴	—	109	2	no	—
546	C₂⁴	—	109	2	no	—
547	C₂⁴	—	109	2	no	—
548	C₂⁴	—	109	2	no	—
549	C₂⁴	—	109	2	no	—
550	C₂⁴	—	109	2	no	—
551	C₂⁴	—	109	1	no	—
552	C₂⁴	—	436	4	no	—
553	C₂⁴	—	436	4	no	—
554	C₂⁴	—	218	8	no	—
555	C₂⁴	C₂²×D₁₀₉	1	2	yes	—
556	#41	—	2	4	no	—
557	#41	—	218	4	no	—
558	#41	—	218	8	no	—
559	#41	—	218	4	no	—
560	#41	—	218	4	no	—
561	C₂×Q₈	—	109	1	no	—
562	C₂×Q₈	C₂²×D₁₀₉	1	1	yes	characteristic, complemented
563	C₂×D₄	—	2	4	no	—
564	C₂×D₄	—	109	2	no	—
565	C₂×D₄	—	109	8	no	—
566	C₂×D₄	—	109	2	no	—
567	C₂×D₄	—	109	2	no	—
568	C₂×D₄	—	109	2	no	—
569	C₂×D₄	—	109	2	no	—
570	C₂×D₄	—	109	1	no	—
571	C₂×D₄	—	109	2	no	—
572	C₂×D₄	—	109	1	no	—
573	C₂×D₄	—	109	1	no	—
574	C₂×D₄	—	109	2	no	—
575	C₂×D₄	—	109	2	no	—
576	C₂×D₄	—	109	2	no	—
577	C₂×D₄	—	109	2	no	—
578	C₂×D₄	—	109	1	no	—
579	C₂×D₄	—	109	1	no	—
580	C₂×D₄	—	109	2	no	—
581	C₂×D₄	—	109	2	no	—
582	C₂×D₄	—	109	2	no	—
583	C₂×D₄	—	109	2	no	—
584	C₂×D₄	—	109	1	no	—
585	C₂×D₄	—	109	2	no	—
586	C₂×D₄	—	109	1	no	—
587	C₂×D₄	—	109	2	no	—
588	C₂×D₄	—	109	1	no	—
589	C₂×D₄	—	109	2	no	—
590	C₂×D₄	—	109	2	no	—
591	C₂×D₄	—	109	1	no	—
592	C₂×D₄	—	436	4	no	—
593	C₂×D₄	—	436	4	no	—
594	C₂×D₄	—	436	4	no	—
595	C₂×D₄	—	436	4	no	—
596	C₂×D₄	—	218	4	no	—
597	C₂×D₄	—	218	4	no	—
598	C₂×D₄	—	218	8	no	—
599	C₂×D₄	—	218	4	no	—
600	C₂×D₄	—	218	8	no	—
601	C₂×D₄	—	218	4	no	—
602	C₂×D₄	—	218	8	no	—
603	C₂×D₄	—	218	8	no	—
604	C₂×D₄	—	218	8	no	—
605	C₂×D₄	—	218	8	no	—
606	C₂×D₄	—	218	4	no	—
607	C₂×D₄	—	218	4	no	—
608	C₂×D₄	C₂²×D₁₀₉	1	1	yes	characteristic
609	C₂×D₄	C₂²×D₁₀₉	1	2	yes	—
610	C₂×D₄	C₂²×D₁₀₉	1	1	yes	characteristic
611	C₂×D₄	C₂²×D₁₀₉	1	1	yes	characteristic
612	C₂×D₄	C₂²×D₁₀₉	1	2	yes	complemented
613	C₂×D₄	C₂²×D₁₀₉	1	2	yes	complemented
614	C₂²×C₄	—	109	1	no	—
615	C₂²×C₄	—	109	2	no	—
616	C₂²×C₄	—	109	1	no	—
617	C₂²×C₄	—	109	2	no	—
618	C₂²×C₄	—	109	2	no	—
619	C₂²×C₄	—	109	1	no	—
620	C₂²×C₄	—	109	1	no	—
621	C₂²×C₄	—	109	1	no	—
622	C₂²×C₄	—	109	2	no	—
623	C₂²×C₄	—	109	2	no	—
624	C₂²×C₄	—	109	1	no	—
625	C₂²×C₄	—	218	4	no	—
626	C₂²×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
627	C₂²×C₄	C₂²×D₁₀₉	1	2	yes	complemented
628	C₂²×C₄	C₂²×D₁₀₉	1	1	yes	characteristic, complemented
629	C₂²×C₄	C₂²×D₁₀₉	1	2	yes	complemented
630	C₄⋊C₄	—	109	1	no	—
631	C₄⋊C₄	—	109	1	no	—
632	C₄⋊C₄	—	109	1	no	—
633	C₄⋊C₄	—	109	2	no	—
634	C₄⋊C₄	—	109	1	no	—
635	C₄⋊C₄	—	109	1	no	—
636	C₄⋊C₄	—	109	1	no	—
637	C₄⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic, complemented
638	C₄⋊C₄	C₂²×D₁₀₉	1	2	yes	complemented
639	C₄⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic, complemented
640	C₂²⋊C₄	—	109	1	no	—
641	C₂²⋊C₄	—	109	2	no	—
642	C₂²⋊C₄	—	109	2	no	—
643	C₂²⋊C₄	—	109	1	no	—
644	C₂²⋊C₄	—	109	2	no	—
645	C₂²⋊C₄	—	109	1	no	—
646	C₂²⋊C₄	—	109	1	no	—
647	C₂²⋊C₄	—	109	2	no	—
648	C₂²⋊C₄	—	109	1	no	—
649	C₂²⋊C₄	—	109	1	no	—
650	C₂²⋊C₄	—	109	2	no	—
651	C₂²⋊C₄	—	109	2	no	—
652	C₂²⋊C₄	—	109	2	no	—
653	C₂²⋊C₄	—	109	2	no	—
654	C₂²⋊C₄	—	109	2	no	—
655	C₂²⋊C₄	—	109	2	no	—
656	C₂²⋊C₄	—	109	1	no	—
657	C₂²⋊C₄	—	109	2	no	—
658	C₂²⋊C₄	—	109	2	no	—
659	C₂²⋊C₄	—	109	1	no	—
660	C₂²⋊C₄	C₂²×D₁₀₉	1	2	yes	—
661	C₂²⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic
662	C₂²⋊C₄	C₂²×D₁₀₉	1	2	yes	complemented
663	C₂²⋊C₄	C₂²×D₁₀₉	1	2	yes	complemented
664	C₂²⋊C₄	C₂²×D₁₀₉	1	2	yes	complemented
665	C₂²⋊C₄	C₂²×D₁₀₉	1	2	yes	complemented
666	C₂²⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic, complemented
667	C₄²	—	109	2	no	—
668	C₄²	—	109	1	no	—
669	C₄²	C₂²×D₁₀₉	1	1	yes	characteristic, complemented
670	C₂³	—	2	4	no	—
671	C₂³	—	2	4	no	—
672	C₂³	—	4	2	no	—
673	C₂³	—	109	8	no	—
674	C₂³	—	109	1	no	—
675	C₂³	—	109	1	no	—
676	C₂³	—	109	2	no	—
677	C₂³	—	109	2	no	—
678	C₂³	—	109	2	no	—
679	C₂³	—	109	1	no	—
680	C₂³	—	436	2	no	—
681	C₂³	—	436	2	no	—
682	C₂³	—	436	2	no	—
683	C₂³	—	436	2	no	—
684	C₂³	—	436	2	no	—
685	C₂³	—	436	2	no	—
686	C₂³	—	436	2	no	—
687	C₂³	—	436	2	no	—
688	C₂³	—	436	2	no	—
689	C₂³	—	436	2	no	—
690	C₂³	—	436	2	no	—
691	C₂³	—	436	32	no	—
692	C₂³	—	218	4	no	—
693	C₂³	—	218	4	no	—
694	C₂³	—	218	4	no	—
695	C₂³	—	218	4	no	—
696	C₂³	—	218	4	no	—
697	C₂³	—	218	4	no	—
698	C₂³	—	218	2	no	—
699	C₂³	—	218	2	no	—
700	C₂³	—	218	4	no	—
701	C₂³	—	218	4	no	—
702	C₂³	—	218	4	no	—
703	C₂³	—	218	2	no	—
704	C₂³	C₂³×D₁₀₉	1	2	yes	—
705	C₂³	C₂³×D₁₀₉	1	1	yes	characteristic
706	C₂³	C₂³×D₁₀₉	1	2	yes	—
707	C₂³	C₂³×D₁₀₉	1	1	yes	characteristic
708	Q₈	—	2	2	no	—
709	Q₈	—	218	2	no	—
710	D₄	—	2	4	no	—
711	D₄	—	2	4	no	—
712	D₄	—	2	2	no	—
713	D₄	—	2	2	no	—
714	D₄	—	4	2	no	—
715	D₄	—	109	8	no	—
716	D₄	—	109	4	no	—
717	D₄	—	436	2	no	—
718	D₄	—	436	2	no	—
719	D₄	—	436	2	no	—
720	D₄	—	436	2	no	—
721	D₄	—	436	2	no	—
722	D₄	—	436	2	no	—
723	D₄	—	436	2	no	—
724	D₄	—	218	2	no	—
725	D₄	—	218	4	no	—
726	D₄	—	218	4	no	—
727	D₄	—	218	2	no	—
728	D₄	—	218	4	no	—
729	D₄	—	218	4	no	—
730	D₄	—	218	4	no	—
731	D₄	—	218	4	no	—
732	D₄	—	218	2	no	—
733	D₄	—	218	2	no	—
734	D₄	—	218	4	no	—
735	D₄	—	218	2	no	—
736	D₄	—	218	4	no	—
737	D₄	—	218	4	no	—
738	D₄	—	218	4	no	—
739	D₄	—	218	2	no	—
740	D₄	—	218	2	no	—
741	D₄	—	218	2	no	—
742	D₄	D₄×D₁₀₉	1	4	yes	complemented
743	C₂×C₄	—	2	4	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	4	2	no	—
747	C₂×C₄	—	109	1	no	—
748	C₂×C₄	—	109	4	no	—
749	C₂×C₄	—	109	1	no	—
750	C₂×C₄	—	109	2	no	—
751	C₂×C₄	—	109	1	no	—
752	C₂×C₄	—	109	1	no	—
753	C₂×C₄	—	109	1	no	—
754	C₂×C₄	—	436	2	no	—
755	C₂×C₄	—	436	2	no	—
756	C₂×C₄	—	436	2	no	—
757	C₂×C₄	—	218	2	no	—
758	C₂×C₄	—	218	4	no	—
759	C₂×C₄	—	218	2	no	—
760	C₂×C₄	—	218	4	no	—
761	C₂×C₄	—	218	2	no	—
762	C₂×C₄	—	218	2	no	—
763	C₂×C₄	—	218	2	no	—
764	C₂×C₄	C₂³×D₁₀₉	1	2	yes	—
765	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
766	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
767	C₂×C₄	C₂³×D₁₀₉	1	2	yes	—
768	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
769	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
770	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
771	C₂²	—	2	1	no	—
772	C₂²	—	2	2	no	—
773	C₂²	—	2	1	no	—
774	C₂²	—	2	2	no	—
775	C₂²	—	2	1	no	—
776	C₂²	—	2	2	no	—
777	C₂²	—	2	1	no	—
778	C₂²	—	2	2	no	—
779	C₂²	—	2	1	no	—
780	C₂²	—	2	2	no	—
781	C₂²	—	4	8	no	—
782	C₂²	—	872	4	no	—
783	C₂²	—	872	4	no	—
784	C₂²	—	109	2	no	—
785	C₂²	—	109	4	no	—
786	C₂²	—	109	2	no	—
787	C₂²	—	436	8	no	—
788	C₂²	—	436	8	no	—
789	C₂²	—	436	8	no	—
790	C₂²	—	436	8	no	—
791	C₂²	—	436	8	no	—
792	C₂²	—	218	8	no	—
793	C₂²	—	218	2	no	—
794	C₂²	—	218	1	no	—
795	C₂²	—	218	2	no	—
796	C₂²	—	218	1	no	—
797	C₂²	—	218	2	no	—
798	C₂²	—	218	2	no	—
799	C₂²	—	218	2	no	—
800	C₂²	—	218	1	no	—
801	C₂²	—	218	2	no	—
802	C₂²	—	218	1	no	—
803	C₂²	—	218	2	no	—
804	C₂²	—	218	1	no	—
805	C₂²	—	218	2	no	—
806	C₂²	—	218	1	no	—
807	C₂²	—	218	1	no	—
808	C₂²	C₂×D₄×D₁₀₉	1	4	yes	—
809	C₂²	#16812745	1	2	yes	complemented
810	C₂²	C₂⁴×D₁₀₉	1	1	yes	characteristic
811	C₄	—	2	1	no	—
812	C₄	—	2	1	no	—
813	C₄	—	2	2	no	—
814	C₄	—	2	1	no	—
815	C₄	—	2	2	no	—
816	C₄	—	2	1	no	—
817	C₄	—	109	2	no	—
818	C₄	—	218	1	no	—
819	C₄	—	218	1	no	—
820	C₄	—	218	1	no	—
821	C₄	—	218	2	no	—
822	C₄	—	218	1	no	—
823	C₄	C₂×D₄×D₁₀₉	1	2	yes	—
824	C₂	—	2	2	no	—
825	C₂	—	2	4	no	—
826	C₂	—	4	2	no	—
827	C₂	—	4	1	no	—
828	C₂	—	436	1	no	—
829	C₂	—	436	2	no	—
830	C₂	—	436	2	no	—
831	C₂	—	218	4	no	—
832	C₂	—	218	2	no	—
833	C₂	—	218	2	no	—
834	C₂	C₂²×D₄×D₁₀₉	1	1	yes	characteristic
835	C₂	H(5,𝔽₂)×D₁₀₉	1	1	yes	characteristic
836	C₂	C₂×#16812745	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₀₉
commutator, socle, cosocle	C₂²×C₁₀₉	C₂⁵
Fitting	#546×C₁₀₉	C₂
hypercenter	#546	D₁₀₉
hypocenter	C₁₀₉	#3484
LCS	G ▷ C₂²×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂² ◁ #546

Complements

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

N	H ≅ G/N	type
1. C₂×#16812745	C₂	semidirect
2. C₂²×D₄×D₁₀₉	C₂	semidirect
3. #20295669	C₂	semidirect
4. #20295668	C₂	semidirect
5. #20295667	C₂	semidirect
6. #20295666	C₂	semidirect
7. #20295664	C₂	semidirect
8. D₄×D₄₃₆	C₂	semidirect
9. D₄×D₄₃₆	C₂	semidirect
10. #20295660	C₂	semidirect
11. #20295660	C₂	semidirect
12. D₄×C₂²⋊D₁₀₉	C₂	semidirect
13. #20295658	C₂	semidirect
14. #20295594	C₂	semidirect
15. #20295592	C₂	semidirect
16. #20295587	C₂	semidirect
17. #20295584	C₂	semidirect
18. #20295539	C₂	semidirect
19. #20295535	C₂	semidirect
20. C₂×#16812669	C₂	semidirect
21. #120×D₁₀₉	C₂	semidirect
22. #20295498	C₂	semidirect
23. #546×C₁₀₉	C₂	semidirect
24. C₂⁴×D₁₀₉	C₂²	semidirect
26. C₂×#13182030	C₂²	semidirect
27. C₂×#13182030	C₂²	semidirect
28. C₂×#13182029	C₂²	semidirect
29. C₂×#13182029	C₂²	semidirect
30. C₂²×D₄₃₆	C₂²	semidirect
31. C₂²×D₄₃₆	C₂²	semidirect
32. C₂²×D₄₃₆	C₂²	semidirect
33. C₂²×D₄₃₆	C₂²	semidirect
34. C₂²×C₂²⋊D₁₀₉	C₂²	semidirect
35. C₂²×C₂²⋊D₁₀₉	C₂²	semidirect
38. C₂×D₄×D₁₀₉	C₂²	semidirect
39. C₂×D₄×D₁₀₉	C₂²	semidirect
40. C₂×D₄×D₁₀₉	C₂²	semidirect
41. C₂×D₄×D₁₀₉	C₂²	semidirect
42. C₂×D₄×D₁₀₉	C₂²	semidirect
43. C₂×D₄×D₁₀₉	C₂²	semidirect
44. C₂×D₄×D₁₀₉	C₂²	semidirect
45. C₂×D₄×D₁₀₉	C₂²	semidirect
46. C₂×D₄×D₁₀₉	C₂²	semidirect
47. C₂×D₄×D₁₀₉	C₂²	semidirect
48. C₂²×C₄×D₁₀₉	C₂²	semidirect
49. #16812696	C₂²	semidirect
50. #16812695	C₂²	semidirect
51. #16812695	C₂²	semidirect
52. #16812688	C₂²	semidirect
53. #16812685	C₂²	semidirect
54. #16812684	C₂²	semidirect
55. #16812684	C₂²	semidirect
56. #16812684	C₂²	semidirect
57. #16812682	C₂²	semidirect
58. #16812681	C₂²	semidirect
59. #16812681	C₂²	semidirect
60. #16812677	C₂²	semidirect
61. #16812676	C₂²	semidirect
62. #16812675	C₂²	semidirect
63. #16812674	C₂²	semidirect
64. #16812674	C₂²	semidirect
65. #16812674	C₂²	semidirect
66. #16812674	C₂²	semidirect
67. #16812673	C₂²	semidirect
68. #16812673	C₂²	semidirect
69. #16812673	C₂²	semidirect
70. #16812672	C₂²	semidirect
71. #16812672	C₂²	semidirect
72. #16812672	C₂²	semidirect
73. #16812672	C₂²	semidirect
74. #16812672	C₂²	semidirect
75. #16812671	C₂²	semidirect
76. #16812671	C₂²	semidirect
77. #16812671	C₂²	semidirect
78. #16812670	C₂²	semidirect
79. #16812669	C₂²	semidirect
80. #16812669	C₂²	semidirect
81. #16812669	C₂²	semidirect
82. #16812669	C₂²	semidirect
83. #16812669	C₂²	semidirect
84. #16812669	C₂²	semidirect
85. #16812669	C₂²	semidirect
86. #16812669	C₂²	semidirect
87. #16812669	C₂²	semidirect
88. #16812669	C₂²	semidirect
89. #16812669	C₂²	semidirect
90. #16812669	C₂²	semidirect
91. #16812668	C₂²	semidirect
92. #16812667	C₂²	semidirect
93. #16812667	C₂²	semidirect
94. #16812667	C₂²	semidirect
95. #16812667	C₂²	semidirect
96. #16812667	C₂²	semidirect
97. C₄×D₄₃₆	C₂²	semidirect
98. C₄×D₄₃₆	C₂²	semidirect
99. D₄×Dic₁₀₉	C₂²	semidirect
100. #16812661	C₂²	semidirect
101. #16812661	C₂²	semidirect
102. C₄×C₂²⋊D₁₀₉	C₂²	semidirect
103. C₄×C₂²⋊D₁₀₉	C₂²	semidirect
104. C₄×C₂²⋊D₁₀₉	C₂²	semidirect
105. #16812659	C₂²	semidirect
106. #16812659	C₂²	semidirect
107. #16812657	C₂²	semidirect
108. #16812656	C₂²	semidirect
109. C₂×#13182006	C₂²	semidirect
110. C₂×#13182006	C₂²	semidirect
111. C₂²⋊C₄×D₁₀₉	C₂²	semidirect
112. C₂²⋊C₄×D₁₀₉	C₂²	semidirect
113. C₂²⋊C₄×D₁₀₉	C₂²	semidirect
114. C₂×#41×C₁₀₉	C₂²	semidirect
115. C₂²×D₄×C₁₀₉	C₂²	semidirect
116. #124×C₁₀₉	C₂²	semidirect
117. #123×C₁₀₉	C₂²	semidirect
118. C₂²⋊Q₈×C₁₀₉	C₂²	semidirect
119. #121×C₁₀₉	C₂²	semidirect
120. #121×C₁₀₉	C₂²	semidirect
121. #120×C₁₀₉	C₂²	semidirect
122. C₄×D₄×C₁₀₉	C₂²	semidirect
123. C₄×D₄×C₁₀₉	C₂²	semidirect
124. C₂×C₂²⋊C₄×C₁₀₉	C₂²	semidirect
134. C₂³×D₁₀₉	C₂³	semidirect
135. C₂³×D₁₀₉	C₂³	semidirect
140. C₂×Dic₂₁₈	C₂³	semidirect
152. C₂×D₄₃₆	C₂³	semidirect
153. C₂×D₄₃₆	C₂³	semidirect
154. C₂×D₄₃₆	C₂³	semidirect
155. C₂×D₄₃₆	C₂³	semidirect
156. C₂×D₄₃₆	C₂³	semidirect
157. C₂×D₄₃₆	C₂³	semidirect
168. C₂×C₂²⋊D₁₀₉	C₂³	semidirect
169. C₂×C₂²⋊D₁₀₉	C₂³	semidirect
170. C₂×C₂²⋊D₁₀₉	C₂³	semidirect
171. C₂×C₂²⋊D₁₀₉	C₂³	semidirect
172. C₂×C₂²⋊D₁₀₉	C₂³	semidirect
173. C₂×C₂²⋊D₁₀₉	C₂³	semidirect
184. D₄×D₁₀₉	D₄	semidirect
186. C₂²×Dic₁₀₉	C₂³	semidirect
192. C₂×C₄×D₁₀₉	C₂³	semidirect
193. C₂×C₄×D₁₀₉	C₂³	semidirect
194. C₂×C₄×D₁₀₉	C₂³	semidirect
195. C₂×C₄×D₁₀₉	C₂³	semidirect
196. C₂×C₄×D₁₀₉	C₂³	semidirect
197. C₄⋊Dic₁₀₉	C₂³	semidirect
198. C₄⋊Dic₁₀₉	C₂³	semidirect
199. #13182008	C₂³	semidirect
200. #13182008	C₂³	semidirect
201. #13182008	C₂³	semidirect
202. #13182008	C₂³	semidirect
203. #13182008	C₂³	semidirect
205. C₂²⋊Dic₁₀₉	C₂³	semidirect
206. C₂²⋊Dic₁₀₉	C₂³	semidirect
207. C₂²⋊Dic₁₀₉	C₂³	semidirect
214. #13182006	C₂³	semidirect
215. #13182006	C₂³	semidirect
216. #13182006	C₂³	semidirect
217. #13182006	C₂³	semidirect
218. #13182006	C₂³	semidirect
219. #13182006	C₂³	semidirect
220. #13182006	C₂³	semidirect
221. #13182006	C₂³	semidirect
222. #13182006	C₂³	semidirect
223. #13182006	C₂³	semidirect
224. C₄×Dic₁₀₉	C₂³	semidirect
225. C₄×Dic₁₀₉	C₂³	semidirect
228. C₂×Q₈×C₁₀₉	C₂³	semidirect
234. C₂×D₄×C₁₀₉	C₂³	semidirect
235. C₂×D₄×C₁₀₉	C₂³	semidirect
237. C₂²×C₄×C₁₀₉	C₂³	semidirect
238. C₂²×C₄×C₁₀₉	C₂³	semidirect
239. C₂²×C₄×C₁₀₉	C₂³	semidirect
240. C₄⋊C₄×C₁₀₉	C₂³	semidirect
241. C₄⋊C₄×C₁₀₉	C₂³	semidirect
242. C₄⋊C₄×C₁₀₉	C₂³	semidirect
245. C₂²⋊C₄×C₁₀₉	C₂³	semidirect
246. C₂²⋊C₄×C₁₀₉	C₂³	semidirect
247. C₂²⋊C₄×C₁₀₉	C₂³	semidirect
248. C₂²⋊C₄×C₁₀₉	C₂³	semidirect
249. C₂²⋊C₄×C₁₀₉	C₂³	semidirect
250. C₄²×C₁₀₉	C₂³	semidirect
282. C₂²×D₁₀₉	C₂×D₄	semidirect
295. D₄×C₁₀₉	C₂×D₄	semidirect
320. C₂²⋊D₁₀₉	C₂×D₄	semidirect
341. D₄₃₆	C₂×D₄	semidirect
350. C₄×D₁₀₉	C₂×D₄	semidirect
364. C₂²×C₁₀₉	H(5,𝔽₂)	semidirect
391. C₂×D₁₀₉	H(5,𝔽₂)	semidirect
419. C₁₀₉	#3484	semidirect
427. #546	D₁₀₉	semidirect
449. C₂×#41	C₂×D₁₀₉	semidirect
468. C₂²×D₄	C₂×D₁₀₉	semidirect
475. #124	C₂×D₁₀₉	semidirect
482. #123	C₂×D₁₀₉	semidirect
486. C₂²⋊Q₈	C₂×D₁₀₉	semidirect
503. #121	C₂×D₁₀₉	semidirect
504. #121	C₂×D₁₀₉	semidirect
523. #120	C₂×D₁₀₉	semidirect
534. C₄×D₄	C₂×D₁₀₉	semidirect
535. C₄×D₄	C₂×D₁₀₉	semidirect
543. C₂×C₂²⋊C₄	C₂×D₁₀₉	semidirect
562. C₂×Q₈	C₂²×D₁₀₉	semidirect
612. C₂×D₄	C₂²×D₁₀₉	semidirect
613. C₂×D₄	C₂²×D₁₀₉	semidirect
627. C₂²×C₄	C₂²×D₁₀₉	semidirect
628. C₂²×C₄	C₂²×D₁₀₉	semidirect
629. C₂²×C₄	C₂²×D₁₀₉	semidirect
637. C₄⋊C₄	C₂²×D₁₀₉	semidirect
638. C₄⋊C₄	C₂²×D₁₀₉	semidirect
639. C₄⋊C₄	C₂²×D₁₀₉	semidirect
662. C₂²⋊C₄	C₂²×D₁₀₉	semidirect
663. C₂²⋊C₄	C₂²×D₁₀₉	semidirect
664. C₂²⋊C₄	C₂²×D₁₀₉	semidirect
665. C₂²⋊C₄	C₂²×D₁₀₉	semidirect
666. C₂²⋊C₄	C₂²×D₁₀₉	semidirect
669. C₄²	C₂²×D₁₀₉	semidirect
742. D₄	D₄×D₁₀₉	semidirect
809. C₂²	#16812745	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16812745	2
C₂²×D₄×D₁₀₉	2
#20295669	2
#20295668	2
#20295667	2
#20295666	2
#20295664	2
D₄×D₄₃₆	2
#20295660	2
D₄×C₂²⋊D₁₀₉	2
#20295658	2
#20295594	2
#20295592	2
#20295587	2
#20295584	2
#20295539	2
#20295535	2
C₂×#16812669	2
#120×D₁₀₉	2
#20295498	2
#546×C₁₀₉	2
#3484	109