Subgroups — C₂×C₁₀₉×#2410 #42152640

Order 27904.

8730 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×D₄×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#121×C₁₀₉	C₂	1	2	yes	maximal, complemented
3	C₂²×#120×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×#120×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂³×C₂²⋊C₄×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₀₉×#2410	C₂	1	16	yes	maximal, direct product factor
7	C₂×#394×C₁₀₉	C₂	1	2	yes	maximal, complemented
8	C₂×#392×C₁₀₉	C₂	1	2	yes	maximal, complemented
9	C₂×#386×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#386×C₁₀₉	C₂	1	2	yes	maximal, complemented
11	C₂×#385×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#379×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂⁶×C₁₀₉	C₂²	1	1	yes	characteristic
14	C₂⁶×C₁₀₉	C₂²	1	1	yes	characteristic
15	C₂³×D₄×C₁₀₉	—	2	8	no	—
16	C₂³×D₄×C₁₀₉	—	2	16	no	—
17	C₂³×D₄×C₁₀₉	C₂²	1	1	yes	characteristic
18	C₂³×D₄×C₁₀₉	C₂²	1	2	yes	—
19	C₂³×D₄×C₁₀₉	C₂²	1	2	yes	—
20	C₂³×D₄×C₁₀₉	C₂²	1	8	yes	complemented
21	C₂³×D₄×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
22	C₂³×D₄×C₁₀₉	C₂²	1	2	yes	complemented
23	C₂³×D₄×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
24	C₂⁴×C₄×C₁₀₉	C₂²	1	1	yes	characteristic
25	C₂⁴×C₄×C₁₀₉	C₂²	1	2	yes	complemented
26	C₂×#121×C₁₀₉	—	2	16	no	—
27	C₂×#121×C₁₀₉	C₂²	1	16	yes	complemented
28	C₂×#120×C₁₀₉	—	2	8	no	—
29	C₂×#120×C₁₀₉	—	2	8	no	—
30	C₂×#120×C₁₀₉	C₂²	1	8	yes	complemented
31	C₂×#120×C₁₀₉	C₂²	1	8	yes	complemented
32	C₂²×C₄⋊C₄×C₁₀₉	C₂²	1	2	yes	complemented
33	C₂²×C₂²⋊C₄×C₁₀₉	—	2	8	no	—
34	C₂²×C₂²⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic
35	C₂²×C₂²⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic
36	C₂²×C₂²⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic
37	C₂²×C₂²⋊C₄×C₁₀₉	C₂²	1	8	yes	complemented
38	C₂²×C₂²⋊C₄×C₁₀₉	C₂²	1	2	yes	complemented
39	C₂²×C₂²⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
40	C₂²×C₂²⋊C₄×C₁₀₉	C₂²	1	2	yes	complemented
41	C₂²×C₂²⋊C₄×C₁₀₉	C₂²	1	2	yes	complemented
42	C₂²×C₂²⋊C₄×C₁₀₉	C₂²	1	2	yes	complemented
43	C₂²×C₂²⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
44	C₂²×C₂²⋊C₄×C₁₀₉	C₂²	1	2	yes	complemented
45	#394×C₁₀₉	C₂²	1	16	yes	complemented
46	#392×C₁₀₉	C₂²	1	16	yes	complemented
47	#386×C₁₀₉	C₂²	1	8	yes	complemented
48	#386×C₁₀₉	C₂²	1	16	yes	complemented
49	#385×C₁₀₉	C₂²	1	8	yes	complemented
50	#379×C₁₀₉	C₂²	1	8	yes	complemented
51	C₂×#95×C₁₀₉	C₂²	1	2	yes	complemented
52	C₂×#95×C₁₀₉	C₂²	1	2	yes	complemented
53	C₂⁵×C₁₀₉	—	2	4	no	—
54	C₂⁵×C₁₀₉	—	2	8	no	—
55	C₂⁵×C₁₀₉	—	2	8	no	—
56	C₂⁵×C₁₀₉	—	2	4	no	—
57	C₂⁵×C₁₀₉	—	2	4	no	—
58	C₂⁵×C₁₀₉	—	2	4	no	—
59	C₂⁵×C₁₀₉	—	2	4	no	—
60	C₂⁵×C₁₀₉	—	4	4	no	—
61	C₂⁵×C₁₀₉	—	4	4	no	—
62	C₂⁵×C₁₀₉	D₄	1	8	yes	complemented
63	C₂⁵×C₁₀₉	C₂³	1	1	yes	characteristic
64	C₂⁵×C₁₀₉	C₂³	1	1	yes	characteristic
65	C₂⁵×C₁₀₉	C₂³	1	2	yes	—
66	C₂⁵×C₁₀₉	C₂³	1	4	yes	—
67	C₂⁵×C₁₀₉	C₂³	1	4	yes	—
68	C₂⁵×C₁₀₉	C₂³	1	1	yes	characteristic
69	C₂⁵×C₁₀₉	C₂³	1	1	yes	characteristic
70	C₂²×D₄×C₁₀₉	—	2	128	no	—
71	C₂²×D₄×C₁₀₉	—	2	8	no	—
72	C₂²×D₄×C₁₀₉	—	2	8	no	—
73	C₂²×D₄×C₁₀₉	—	2	8	no	—
74	C₂²×D₄×C₁₀₉	—	2	8	no	—
75	C₂²×D₄×C₁₀₉	—	2	32	no	—
76	C₂²×D₄×C₁₀₉	—	2	64	no	—
77	C₂²×D₄×C₁₀₉	—	2	4	no	—
78	C₂²×D₄×C₁₀₉	—	2	4	no	—
79	C₂²×D₄×C₁₀₉	—	2	4	no	—
80	C₂²×D₄×C₁₀₉	—	2	4	no	—
81	C₂²×D₄×C₁₀₉	—	2	8	no	—
82	C₂²×D₄×C₁₀₉	—	2	8	no	—
83	C₂²×D₄×C₁₀₉	—	2	4	no	—
84	C₂²×D₄×C₁₀₉	—	2	8	no	—
85	C₂²×D₄×C₁₀₉	—	2	8	no	—
86	C₂²×D₄×C₁₀₉	—	4	4	no	—
87	C₂²×D₄×C₁₀₉	—	4	4	no	—
88	C₂²×D₄×C₁₀₉	D₄	1	16	yes	complemented
89	C₂²×D₄×C₁₀₉	C₂³	1	4	yes	—
90	C₂²×D₄×C₁₀₉	C₂³	1	8	yes	—
91	C₂²×D₄×C₁₀₉	C₂³	1	8	yes	—
92	C₂²×D₄×C₁₀₉	C₂³	1	4	yes	complemented
93	C₂²×D₄×C₁₀₉	C₂³	1	8	yes	complemented
94	C₂²×D₄×C₁₀₉	C₂³	1	4	yes	complemented
95	C₂³×C₄×C₁₀₉	—	2	4	no	—
96	C₂³×C₄×C₁₀₉	—	2	8	no	—
97	C₂³×C₄×C₁₀₉	—	2	8	no	—
98	C₂³×C₄×C₁₀₉	—	2	8	no	—
99	C₂³×C₄×C₁₀₉	—	4	4	no	—
100	C₂³×C₄×C₁₀₉	C₂³	1	4	yes	—
101	C₂³×C₄×C₁₀₉	C₂³	1	2	yes	—
102	C₂³×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
103	C₂³×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
104	C₂³×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
105	C₂³×C₄×C₁₀₉	C₂³	1	2	yes	—
106	C₂³×C₄×C₁₀₉	C₂³	1	2	yes	—
107	C₂³×C₄×C₁₀₉	C₂³	1	8	yes	complemented
108	#121×C₁₀₉	—	2	64	no	—
109	#120×C₁₀₉	—	2	32	no	—
110	#120×C₁₀₉	—	2	32	no	—
111	C₂×C₄⋊C₄×C₁₀₉	—	2	8	no	—
112	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	8	yes	complemented
113	C₂×C₂²⋊C₄×C₁₀₉	—	2	4	no	—
114	C₂×C₂²⋊C₄×C₁₀₉	—	2	4	no	—
115	C₂×C₂²⋊C₄×C₁₀₉	—	2	4	no	—
116	C₂×C₂²⋊C₄×C₁₀₉	—	2	4	no	—
117	C₂×C₂²⋊C₄×C₁₀₉	—	2	8	no	—
118	C₂×C₂²⋊C₄×C₁₀₉	—	2	8	no	—
119	C₂×C₂²⋊C₄×C₁₀₉	—	2	8	no	—
120	C₂×C₂²⋊C₄×C₁₀₉	—	2	8	no	—
121	C₂×C₂²⋊C₄×C₁₀₉	—	2	32	no	—
122	C₂×C₂²⋊C₄×C₁₀₉	—	4	4	no	—
123	C₂×C₂²⋊C₄×C₁₀₉	D₄	1	8	yes	complemented
124	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	4	yes	—
125	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	4	yes	—
126	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	4	yes	—
127	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	8	yes	complemented
128	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	4	yes	complemented
129	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	8	yes	complemented
130	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	4	yes	complemented
131	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	8	yes	complemented
132	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	8	yes	complemented
133	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	8	yes	complemented
134	#95×C₁₀₉	C₂³	1	8	yes	complemented
135	#95×C₁₀₉	C₂³	1	8	yes	complemented
136	C₂⁴×C₁₀₉	—	2	2	no	—
137	C₂⁴×C₁₀₉	—	2	4	no	—
138	C₂⁴×C₁₀₉	—	2	2	no	—
139	C₂⁴×C₁₀₉	—	2	4	no	—
140	C₂⁴×C₁₀₉	—	2	4	no	—
141	C₂⁴×C₁₀₉	—	2	32	no	—
142	C₂⁴×C₁₀₉	—	2	32	no	—
143	C₂⁴×C₁₀₉	—	2	32	no	—
144	C₂⁴×C₁₀₉	—	2	8	no	—
145	C₂⁴×C₁₀₉	—	2	2	no	—
146	C₂⁴×C₁₀₉	—	2	4	no	—
147	C₂⁴×C₁₀₉	—	2	16	no	—
148	C₂⁴×C₁₀₉	—	2	16	no	—
149	C₂⁴×C₁₀₉	—	2	8	no	—
150	C₂⁴×C₁₀₉	—	2	4	no	—
151	C₂⁴×C₁₀₉	—	2	4	no	—
152	C₂⁴×C₁₀₉	—	2	4	no	—
153	C₂⁴×C₁₀₉	—	2	8	no	—
154	C₂⁴×C₁₀₉	—	2	2	no	—
155	C₂⁴×C₁₀₉	—	2	4	no	—
156	C₂⁴×C₁₀₉	—	2	4	no	—
157	C₂⁴×C₁₀₉	—	2	4	no	—
158	C₂⁴×C₁₀₉	—	2	4	no	—
159	C₂⁴×C₁₀₉	—	2	4	no	—
160	C₂⁴×C₁₀₉	—	2	8	no	—
161	C₂⁴×C₁₀₉	—	2	2	no	—
162	C₂⁴×C₁₀₉	—	2	2	no	—
163	C₂⁴×C₁₀₉	—	2	2	no	—
164	C₂⁴×C₁₀₉	—	2	8	no	—
165	C₂⁴×C₁₀₉	—	2	4	no	—
166	C₂⁴×C₁₀₉	—	4	16	no	—
167	C₂⁴×C₁₀₉	—	4	8	no	—
168	C₂⁴×C₁₀₉	—	4	8	no	—
169	C₂⁴×C₁₀₉	—	4	32	no	—
170	C₂⁴×C₁₀₉	—	4	32	no	—
171	C₂⁴×C₁₀₉	—	4	32	no	—
172	C₂⁴×C₁₀₉	—	4	32	no	—
173	C₂⁴×C₁₀₉	—	4	16	no	—
174	C₂⁴×C₁₀₉	—	4	16	no	—
175	C₂⁴×C₁₀₉	C₂×D₄	1	4	yes	—
176	C₂⁴×C₁₀₉	C₂×D₄	1	8	yes	—
177	C₂⁴×C₁₀₉	C₂×D₄	1	4	yes	—
178	C₂⁴×C₁₀₉	C₂×D₄	1	8	yes	—
179	C₂⁴×C₁₀₉	C₂×D₄	1	4	yes	—
180	C₂⁴×C₁₀₉	C₂×D₄	1	4	yes	—
181	C₂⁴×C₁₀₉	C₂×D₄	1	16	yes	complemented
182	C₂⁴×C₁₀₉	#41	1	4	yes	—
183	C₂⁴×C₁₀₉	C₂⁴	1	2	yes	—
184	C₂⁴×C₁₀₉	C₂⁴	1	2	yes	—
185	C₂⁴×C₁₀₉	C₂⁴	1	4	yes	—
186	C₂⁴×C₁₀₉	C₂⁴	1	2	yes	—
187	C₂⁴×C₁₀₉	C₂⁴	1	2	yes	—
188	C₂⁴×C₁₀₉	C₂⁴	1	1	yes	characteristic
189	C₂×D₄×C₁₀₉	—	2	256	no	—
190	C₂×D₄×C₁₀₉	—	2	64	no	—
191	C₂×D₄×C₁₀₉	—	2	64	no	—
192	C₂×D₄×C₁₀₉	—	2	16	no	—
193	C₂×D₄×C₁₀₉	—	2	16	no	—
194	C₂×D₄×C₁₀₉	—	2	16	no	—
195	C₂×D₄×C₁₀₉	—	2	16	no	—
196	C₂×D₄×C₁₀₉	—	2	8	no	—
197	C₂×D₄×C₁₀₉	—	2	8	no	—
198	C₂×D₄×C₁₀₉	—	2	8	no	—
199	C₂×D₄×C₁₀₉	—	2	8	no	—
200	C₂×D₄×C₁₀₉	—	2	16	no	—
201	C₂×D₄×C₁₀₉	—	2	16	no	—
202	C₂×D₄×C₁₀₉	—	2	8	no	—
203	C₂×D₄×C₁₀₉	—	2	16	no	—
204	C₂×D₄×C₁₀₉	—	2	16	no	—
205	C₂×D₄×C₁₀₉	—	4	8	no	—
206	C₂×D₄×C₁₀₉	—	4	8	no	—
207	C₂×D₄×C₁₀₉	—	4	32	no	—
208	C₂×D₄×C₁₀₉	—	4	16	no	—
209	C₂×D₄×C₁₀₉	—	4	16	no	—
210	C₂×D₄×C₁₀₉	—	4	16	no	—
211	C₂×D₄×C₁₀₉	C₂×D₄	1	32	yes	complemented
212	C₂²×C₄×C₁₀₉	—	2	32	no	—
213	C₂²×C₄×C₁₀₉	—	2	4	no	—
214	C₂²×C₄×C₁₀₉	—	2	8	no	—
215	C₂²×C₄×C₁₀₉	—	2	4	no	—
216	C₂²×C₄×C₁₀₉	—	2	4	no	—
217	C₂²×C₄×C₁₀₉	—	2	4	no	—
218	C₂²×C₄×C₁₀₉	—	2	16	no	—
219	C₂²×C₄×C₁₀₉	—	2	4	no	—
220	C₂²×C₄×C₁₀₉	—	2	4	no	—
221	C₂²×C₄×C₁₀₉	—	2	2	no	—
222	C₂²×C₄×C₁₀₉	—	2	2	no	—
223	C₂²×C₄×C₁₀₉	—	2	2	no	—
224	C₂²×C₄×C₁₀₉	—	2	2	no	—
225	C₂²×C₄×C₁₀₉	—	2	4	no	—
226	C₂²×C₄×C₁₀₉	—	2	16	no	—
227	C₂²×C₄×C₁₀₉	—	2	2	no	—
228	C₂²×C₄×C₁₀₉	—	2	4	no	—
229	C₂²×C₄×C₁₀₉	—	2	4	no	—
230	C₂²×C₄×C₁₀₉	—	2	16	no	—
231	C₂²×C₄×C₁₀₉	—	4	8	no	—
232	C₂²×C₄×C₁₀₉	—	4	32	no	—
233	C₂²×C₄×C₁₀₉	C₂×D₄	1	8	yes	—
234	C₂²×C₄×C₁₀₉	C₂×D₄	1	8	yes	complemented
235	C₂²×C₄×C₁₀₉	C₂⁴	1	2	yes	—
236	C₂²×C₄×C₁₀₉	C₂⁴	1	2	yes	—
237	C₂²×C₄×C₁₀₉	C₂⁴	1	4	yes	—
238	C₂²×C₄×C₁₀₉	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₁₀₉	C₂⁴	1	4	yes	—
240	C₂²×C₄×C₁₀₉	C₂⁴	1	4	yes	—
241	C₄⋊C₄×C₁₀₉	—	2	16	no	—
242	C₂²⋊C₄×C₁₀₉	—	2	8	no	—
243	C₂²⋊C₄×C₁₀₉	—	2	8	no	—
244	C₂²⋊C₄×C₁₀₉	—	2	8	no	—
245	C₂²⋊C₄×C₁₀₉	—	2	8	no	—
246	C₂²⋊C₄×C₁₀₉	—	2	16	no	—
247	C₂²⋊C₄×C₁₀₉	—	2	16	no	—
248	C₂²⋊C₄×C₁₀₉	—	2	16	no	—
249	C₂²⋊C₄×C₁₀₉	—	2	16	no	—
250	C₂²⋊C₄×C₁₀₉	—	4	8	no	—
251	C₂²⋊C₄×C₁₀₉	C₂×D₄	1	16	yes	complemented
252	C₂³×C₁₀₉	—	2	8	no	—
253	C₂³×C₁₀₉	—	2	8	no	—
254	C₂³×C₁₀₉	—	2	8	no	—
255	C₂³×C₁₀₉	—	2	8	no	—
256	C₂³×C₁₀₉	—	2	16	no	—
257	C₂³×C₁₀₉	—	2	16	no	—
258	C₂³×C₁₀₉	—	2	16	no	—
259	C₂³×C₁₀₉	—	2	16	no	—
260	C₂³×C₁₀₉	—	2	2	no	—
261	C₂³×C₁₀₉	—	2	4	no	—
262	C₂³×C₁₀₉	—	2	2	no	—
263	C₂³×C₁₀₉	—	2	4	no	—
264	C₂³×C₁₀₉	—	2	4	no	—
265	C₂³×C₁₀₉	—	2	32	no	—
266	C₂³×C₁₀₉	—	2	8	no	—
267	C₂³×C₁₀₉	—	2	16	no	—
268	C₂³×C₁₀₉	—	2	32	no	—
269	C₂³×C₁₀₉	—	2	8	no	—
270	C₂³×C₁₀₉	—	2	32	no	—
271	C₂³×C₁₀₉	—	2	8	no	—
272	C₂³×C₁₀₉	—	2	16	no	—
273	C₂³×C₁₀₉	—	2	16	no	—
274	C₂³×C₁₀₉	—	2	2	no	—
275	C₂³×C₁₀₉	—	2	4	no	—
276	C₂³×C₁₀₉	—	2	4	no	—
277	C₂³×C₁₀₉	—	2	4	no	—
278	C₂³×C₁₀₉	—	2	4	no	—
279	C₂³×C₁₀₉	—	2	2	no	—
280	C₂³×C₁₀₉	—	2	4	no	—
281	C₂³×C₁₀₉	—	2	4	no	—
282	C₂³×C₁₀₉	—	2	4	no	—
283	C₂³×C₁₀₉	—	2	4	no	—
284	C₂³×C₁₀₉	—	2	4	no	—
285	C₂³×C₁₀₉	—	2	2	no	—
286	C₂³×C₁₀₉	—	2	2	no	—
287	C₂³×C₁₀₉	—	2	2	no	—
288	C₂³×C₁₀₉	—	2	4	no	—
289	C₂³×C₁₀₉	—	4	16	no	—
290	C₂³×C₁₀₉	—	4	128	no	—
291	C₂³×C₁₀₉	—	4	32	no	—
292	C₂³×C₁₀₉	—	4	32	no	—
293	C₂³×C₁₀₉	—	4	32	no	—
294	C₂³×C₁₀₉	—	4	32	no	—
295	C₂³×C₁₀₉	—	4	128	no	—
296	C₂³×C₁₀₉	—	4	16	no	—
297	C₂³×C₁₀₉	—	4	8	no	—
298	C₂³×C₁₀₉	—	4	16	no	—
299	C₂³×C₁₀₉	—	4	8	no	—
300	C₂³×C₁₀₉	—	4	8	no	—
301	C₂³×C₁₀₉	—	4	8	no	—
302	C₂³×C₁₀₉	—	4	8	no	—
303	C₂³×C₁₀₉	—	4	8	no	—
304	C₂³×C₁₀₉	—	4	4	no	—
305	C₂³×C₁₀₉	—	4	4	no	—
306	C₂³×C₁₀₉	—	4	4	no	—
307	C₂³×C₁₀₉	—	4	8	no	—
308	C₂³×C₁₀₉	—	4	8	no	—
309	C₂³×C₁₀₉	#120	1	16	yes	complemented
310	C₂³×C₁₀₉	#121	1	16	yes	complemented
311	C₂³×C₁₀₉	C₂²×D₄	1	4	yes	—
312	C₂³×C₁₀₉	C₂²×D₄	1	8	yes	—
313	C₂³×C₁₀₉	C₂²×D₄	1	4	yes	—
314	C₂³×C₁₀₉	C₂²×D₄	1	8	yes	—
315	C₂³×C₁₀₉	C₂²×D₄	1	4	yes	—
316	C₂³×C₁₀₉	C₂²×D₄	1	4	yes	—
317	C₂³×C₁₀₉	C₂²×D₄	1	2	yes	—
318	C₂³×C₁₀₉	C₂²×D₄	1	4	yes	—
319	C₂³×C₁₀₉	C₂²×D₄	1	2	yes	—
320	C₂³×C₁₀₉	C₂×#41	1	4	yes	—
321	C₂³×C₁₀₉	C₂×#41	1	2	yes	—
322	C₂³×C₁₀₉	H(5,𝔽₂)	1	4	yes	—
323	C₂³×C₁₀₉	C₂⁵	1	1	yes	characteristic
324	D₄×C₁₀₉	—	2	64	no	—
325	D₄×C₁₀₉	—	2	64	no	—
326	D₄×C₁₀₉	—	4	32	no	—
327	D₄×C₁₀₉	—	4	16	no	—
328	D₄×C₁₀₉	—	4	16	no	—
329	D₄×C₁₀₉	—	4	16	no	—
330	C₂×C₄×C₁₀₉	—	2	32	no	—
331	C₂×C₄×C₁₀₉	—	2	16	no	—
332	C₂×C₄×C₁₀₉	—	2	16	no	—
333	C₂×C₄×C₁₀₉	—	2	4	no	—
334	C₂×C₄×C₁₀₉	—	2	4	no	—
335	C₂×C₄×C₁₀₉	—	2	4	no	—
336	C₂×C₄×C₁₀₉	—	2	4	no	—
337	C₂×C₄×C₁₀₉	—	2	4	no	—
338	C₂×C₄×C₁₀₉	—	2	4	no	—
339	C₂×C₄×C₁₀₉	—	2	2	no	—
340	C₂×C₄×C₁₀₉	—	2	2	no	—
341	C₂×C₄×C₁₀₉	—	2	2	no	—
342	C₂×C₄×C₁₀₉	—	2	2	no	—
343	C₂×C₄×C₁₀₉	—	2	4	no	—
344	C₂×C₄×C₁₀₉	—	2	2	no	—
345	C₂×C₄×C₁₀₉	—	2	4	no	—
346	C₂×C₄×C₁₀₉	—	2	4	no	—
347	C₂×C₄×C₁₀₉	—	4	32	no	—
348	C₂×C₄×C₁₀₉	—	4	4	no	—
349	C₂×C₄×C₁₀₉	—	4	4	no	—
350	C₂×C₄×C₁₀₉	—	4	4	no	—
351	C₂×C₄×C₁₀₉	—	4	8	no	—
352	C₂×C₄×C₁₀₉	C₂²×D₄	1	8	yes	—
353	C₂×C₄×C₁₀₉	C₂²×D₄	1	8	yes	complemented
354	C₂²×C₁₀₉	—	2	4	no	—
355	C₂²×C₁₀₉	—	2	4	no	—
356	C₂²×C₁₀₉	—	2	32	no	—
357	C₂²×C₁₀₉	—	2	32	no	—
358	C₂²×C₁₀₉	—	2	4	no	—
359	C₂²×C₁₀₉	—	2	4	no	—
360	C₂²×C₁₀₉	—	2	8	no	—
361	C₂²×C₁₀₉	—	2	8	no	—
362	C₂²×C₁₀₉	—	2	8	no	—
363	C₂²×C₁₀₉	—	2	8	no	—
364	C₂²×C₁₀₉	—	2	4	no	—
365	C₂²×C₁₀₉	—	2	8	no	—
366	C₂²×C₁₀₉	—	2	4	no	—
367	C₂²×C₁₀₉	—	2	4	no	—
368	C₂²×C₁₀₉	—	2	8	no	—
369	C₂²×C₁₀₉	—	2	8	no	—
370	C₂²×C₁₀₉	—	4	64	no	—
371	C₂²×C₁₀₉	—	4	64	no	—
372	C₂²×C₁₀₉	—	4	4	no	—
373	C₂²×C₁₀₉	—	4	16	no	—
374	C₂²×C₁₀₉	—	4	32	no	—
375	C₂²×C₁₀₉	—	4	4	no	—
376	C₂²×C₁₀₉	—	4	4	no	—
377	C₂²×C₁₀₉	—	4	4	no	—
378	C₂²×C₁₀₉	—	4	4	no	—
379	C₂²×C₁₀₉	—	4	4	no	—
380	C₂²×C₁₀₉	—	4	2	no	—
381	C₂²×C₁₀₉	—	4	2	no	—
382	C₂²×C₁₀₉	—	4	2	no	—
383	C₂²×C₁₀₉	—	4	4	no	—
384	C₂²×C₁₀₉	—	4	4	no	—
385	C₂²×C₁₀₉	—	8	8	no	—
386	C₂²×C₁₀₉	C₂×#120	1	4	yes	—
387	C₂²×C₁₀₉	C₂×#120	1	8	yes	complemented
388	C₂²×C₁₀₉	C₂×#121	1	4	yes	—
389	C₂²×C₁₀₉	C₂×#121	1	8	yes	complemented
390	C₂²×C₁₀₉	#534	1	4	yes	—
391	C₂²×C₁₀₉	D₄²	1	8	yes	—
392	C₂²×C₁₀₉	#546	1	8	yes	—
393	C₂²×C₁₀₉	C₂³×D₄	1	1	yes	characteristic
394	C₂²×C₁₀₉	C₂³×D₄	1	2	yes	—
395	C₂²×C₁₀₉	C₂³×D₄	1	1	yes	characteristic
396	C₂²×C₁₀₉	C₂²×#41	1	1	yes	characteristic
397	C₂²×C₁₀₉	C₂×H(5,𝔽₂)	1	2	yes	—
398	C₄×C₁₀₉	—	2	8	no	—
399	C₄×C₁₀₉	—	2	8	no	—
400	C₄×C₁₀₉	—	4	2	no	—
401	C₄×C₁₀₉	—	4	2	no	—
402	C₄×C₁₀₉	—	4	2	no	—
403	C₄×C₁₀₉	—	4	4	no	—
404	C₂×#2410	C₁₀₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
405	C₂×C₁₀₉	—	2	8	no	—
406	C₂×C₁₀₉	—	2	8	no	—
407	C₂×C₁₀₉	—	4	4	no	—
408	C₂×C₁₀₉	—	4	8	no	—
409	C₂×C₁₀₉	—	8	2	no	—
410	C₂×C₁₀₉	#2410	1	8	yes	direct product factor
411	C₂×C₁₀₉	C₂²×#120	1	1	yes	characteristic
412	C₂×C₁₀₉	C₂²×#121	1	1	yes	characteristic
413	C₂×C₁₀₉	C₂×#534	1	1	yes	characteristic
414	C₂×C₁₀₉	C₂×D₄²	1	2	yes	—
415	C₂×C₁₀₉	C₂×#546	1	2	yes	—
416	C₂⁴×D₄	C₂×C₁₀₉	1	1	yes	characteristic, complemented
417	C₂²×#121	C₂×C₁₀₉	1	2	yes	complemented
418	C₂²×#120	C₂×C₁₀₉	1	1	yes	characteristic, complemented
419	C₂²×#120	C₂×C₁₀₉	1	1	yes	characteristic, complemented
420	C₂³×C₂²⋊C₄	C₂×C₁₀₉	1	1	yes	characteristic, complemented
421	#2410	C₂×C₁₀₉	1	16	yes	direct product factor
422	C₂×#394	C₂×C₁₀₉	1	2	yes	complemented
423	C₂×#392	C₂×C₁₀₉	1	2	yes	complemented
424	C₂×#386	C₂×C₁₀₉	1	1	yes	characteristic, complemented
425	C₂×#386	C₂×C₁₀₉	1	2	yes	complemented
426	C₂×#385	C₂×C₁₀₉	1	1	yes	characteristic, complemented
427	C₂×#379	C₂×C₁₀₉	1	1	yes	characteristic, complemented
428	C₁₀₉	C₂×#2410	1	1	yes	characteristic, direct product factor, Sylow
429	C₂⁶	C₂²×C₁₀₉	1	1	yes	characteristic
430	C₂⁶	C₂²×C₁₀₉	1	1	yes	characteristic
431	C₂³×D₄	—	2	8	no	—
432	C₂³×D₄	—	2	16	no	—
433	C₂³×D₄	C₂²×C₁₀₉	1	2	yes	—
434	C₂³×D₄	C₂²×C₁₀₉	1	1	yes	characteristic
435	C₂³×D₄	C₂²×C₁₀₉	1	2	yes	—
436	C₂³×D₄	C₂²×C₁₀₉	1	8	yes	complemented
437	C₂³×D₄	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
438	C₂³×D₄	C₂²×C₁₀₉	1	2	yes	complemented
439	C₂³×D₄	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
440	C₂⁴×C₄	C₂²×C₁₀₉	1	1	yes	characteristic
441	C₂⁴×C₄	C₂²×C₁₀₉	1	2	yes	complemented
442	C₂×#121	—	2	16	no	—
443	C₂×#121	C₂²×C₁₀₉	1	16	yes	complemented
444	C₂×#120	—	2	8	no	—
445	C₂×#120	—	2	8	no	—
446	C₂×#120	C₂²×C₁₀₉	1	8	yes	complemented
447	C₂×#120	C₂²×C₁₀₉	1	8	yes	complemented
448	C₂²×C₄⋊C₄	C₂²×C₁₀₉	1	2	yes	complemented
449	C₂²×C₂²⋊C₄	—	2	8	no	—
450	C₂²×C₂²⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic
451	C₂²×C₂²⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic
452	C₂²×C₂²⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic
453	C₂²×C₂²⋊C₄	C₂²×C₁₀₉	1	8	yes	complemented
454	C₂²×C₂²⋊C₄	C₂²×C₁₀₉	1	2	yes	complemented
455	C₂²×C₂²⋊C₄	C₂²×C₁₀₉	1	2	yes	complemented
456	C₂²×C₂²⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
457	C₂²×C₂²⋊C₄	C₂²×C₁₀₉	1	2	yes	complemented
458	C₂²×C₂²⋊C₄	C₂²×C₁₀₉	1	2	yes	complemented
459	C₂²×C₂²⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
460	C₂²×C₂²⋊C₄	C₂²×C₁₀₉	1	2	yes	complemented
461	#394	C₂²×C₁₀₉	1	16	yes	complemented
462	#392	C₂²×C₁₀₉	1	16	yes	complemented
463	#386	C₂²×C₁₀₉	1	8	yes	complemented
464	#386	C₂²×C₁₀₉	1	16	yes	complemented
465	#385	C₂²×C₁₀₉	1	8	yes	complemented
466	#379	C₂²×C₁₀₉	1	8	yes	complemented
467	C₂×#95	C₂²×C₁₀₉	1	2	yes	complemented
468	C₂×#95	C₂²×C₁₀₉	1	2	yes	complemented
469	C₂⁵	—	2	4	no	—
470	C₂⁵	—	2	8	no	—
471	C₂⁵	—	2	8	no	—
472	C₂⁵	—	2	4	no	—
473	C₂⁵	—	2	4	no	—
474	C₂⁵	—	2	4	no	—
475	C₂⁵	—	2	4	no	—
476	C₂⁵	—	4	4	no	—
477	C₂⁵	—	4	4	no	—
478	C₂⁵	D₄×C₁₀₉	1	8	yes	complemented
479	C₂⁵	C₂³×C₁₀₉	1	1	yes	characteristic
480	C₂⁵	C₂³×C₁₀₉	1	1	yes	characteristic
481	C₂⁵	C₂³×C₁₀₉	1	2	yes	—
482	C₂⁵	C₂³×C₁₀₉	1	4	yes	—
483	C₂⁵	C₂³×C₁₀₉	1	4	yes	—
484	C₂⁵	C₂³×C₁₀₉	1	1	yes	characteristic
485	C₂⁵	C₂³×C₁₀₉	1	1	yes	characteristic
486	C₂²×D₄	—	2	128	no	—
487	C₂²×D₄	—	2	8	no	—
488	C₂²×D₄	—	2	8	no	—
489	C₂²×D₄	—	2	8	no	—
490	C₂²×D₄	—	2	8	no	—
491	C₂²×D₄	—	2	32	no	—
492	C₂²×D₄	—	2	64	no	—
493	C₂²×D₄	—	2	4	no	—
494	C₂²×D₄	—	2	4	no	—
495	C₂²×D₄	—	2	4	no	—
496	C₂²×D₄	—	2	4	no	—
497	C₂²×D₄	—	2	8	no	—
498	C₂²×D₄	—	2	8	no	—
499	C₂²×D₄	—	2	4	no	—
500	C₂²×D₄	—	2	8	no	—
501	C₂²×D₄	—	2	8	no	—
502	C₂²×D₄	—	4	4	no	—
503	C₂²×D₄	—	4	4	no	—
504	C₂²×D₄	D₄×C₁₀₉	1	16	yes	complemented
505	C₂²×D₄	C₂³×C₁₀₉	1	4	yes	—
506	C₂²×D₄	C₂³×C₁₀₉	1	8	yes	—
507	C₂²×D₄	C₂³×C₁₀₉	1	8	yes	—
508	C₂²×D₄	C₂³×C₁₀₉	1	4	yes	complemented
509	C₂²×D₄	C₂³×C₁₀₉	1	8	yes	complemented
510	C₂²×D₄	C₂³×C₁₀₉	1	4	yes	complemented
511	C₂³×C₄	—	2	4	no	—
512	C₂³×C₄	—	2	8	no	—
513	C₂³×C₄	—	2	8	no	—
514	C₂³×C₄	—	2	8	no	—
515	C₂³×C₄	—	4	4	no	—
516	C₂³×C₄	C₂³×C₁₀₉	1	2	yes	—
517	C₂³×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
518	C₂³×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
519	C₂³×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
520	C₂³×C₄	C₂³×C₁₀₉	1	4	yes	—
521	C₂³×C₄	C₂³×C₁₀₉	1	2	yes	—
522	C₂³×C₄	C₂³×C₁₀₉	1	2	yes	—
523	C₂³×C₄	C₂³×C₁₀₉	1	8	yes	complemented
524	#121	—	2	64	no	—
525	#120	—	2	32	no	—
526	#120	—	2	32	no	—
527	C₂×C₄⋊C₄	—	2	8	no	—
528	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	8	yes	complemented
529	C₂×C₂²⋊C₄	—	2	4	no	—
530	C₂×C₂²⋊C₄	—	2	4	no	—
531	C₂×C₂²⋊C₄	—	2	4	no	—
532	C₂×C₂²⋊C₄	—	2	4	no	—
533	C₂×C₂²⋊C₄	—	2	8	no	—
534	C₂×C₂²⋊C₄	—	2	8	no	—
535	C₂×C₂²⋊C₄	—	2	8	no	—
536	C₂×C₂²⋊C₄	—	2	8	no	—
537	C₂×C₂²⋊C₄	—	2	32	no	—
538	C₂×C₂²⋊C₄	—	4	4	no	—
539	C₂×C₂²⋊C₄	D₄×C₁₀₉	1	8	yes	complemented
540	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	4	yes	—
541	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	4	yes	—
542	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	4	yes	—
543	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	8	yes	complemented
544	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	4	yes	complemented
545	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	8	yes	complemented
546	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	4	yes	complemented
547	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	8	yes	complemented
548	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	8	yes	complemented
549	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	8	yes	complemented
550	#95	C₂³×C₁₀₉	1	8	yes	complemented
551	#95	C₂³×C₁₀₉	1	8	yes	complemented
552	C₂⁴	—	2	2	no	—
553	C₂⁴	—	2	4	no	—
554	C₂⁴	—	2	2	no	—
555	C₂⁴	—	2	4	no	—
556	C₂⁴	—	2	4	no	—
557	C₂⁴	—	2	32	no	—
558	C₂⁴	—	2	32	no	—
559	C₂⁴	—	2	32	no	—
560	C₂⁴	—	2	8	no	—
561	C₂⁴	—	2	2	no	—
562	C₂⁴	—	2	4	no	—
563	C₂⁴	—	2	16	no	—
564	C₂⁴	—	2	16	no	—
565	C₂⁴	—	2	8	no	—
566	C₂⁴	—	2	4	no	—
567	C₂⁴	—	2	4	no	—
568	C₂⁴	—	2	4	no	—
569	C₂⁴	—	2	8	no	—
570	C₂⁴	—	2	2	no	—
571	C₂⁴	—	2	4	no	—
572	C₂⁴	—	2	4	no	—
573	C₂⁴	—	2	4	no	—
574	C₂⁴	—	2	4	no	—
575	C₂⁴	—	2	4	no	—
576	C₂⁴	—	2	8	no	—
577	C₂⁴	—	2	2	no	—
578	C₂⁴	—	2	2	no	—
579	C₂⁴	—	2	2	no	—
580	C₂⁴	—	2	8	no	—
581	C₂⁴	—	2	4	no	—
582	C₂⁴	—	4	16	no	—
583	C₂⁴	—	4	8	no	—
584	C₂⁴	—	4	8	no	—
585	C₂⁴	—	4	32	no	—
586	C₂⁴	—	4	32	no	—
587	C₂⁴	—	4	32	no	—
588	C₂⁴	—	4	32	no	—
589	C₂⁴	—	4	16	no	—
590	C₂⁴	—	4	16	no	—
591	C₂⁴	C₂×D₄×C₁₀₉	1	4	yes	—
592	C₂⁴	C₂×D₄×C₁₀₉	1	8	yes	—
593	C₂⁴	C₂×D₄×C₁₀₉	1	4	yes	—
594	C₂⁴	C₂×D₄×C₁₀₉	1	8	yes	—
595	C₂⁴	C₂×D₄×C₁₀₉	1	4	yes	—
596	C₂⁴	C₂×D₄×C₁₀₉	1	4	yes	—
597	C₂⁴	C₂×D₄×C₁₀₉	1	16	yes	complemented
598	C₂⁴	#41×C₁₀₉	1	4	yes	—
599	C₂⁴	C₂⁴×C₁₀₉	1	2	yes	—
600	C₂⁴	C₂⁴×C₁₀₉	1	2	yes	—
601	C₂⁴	C₂⁴×C₁₀₉	1	4	yes	—
602	C₂⁴	C₂⁴×C₁₀₉	1	2	yes	—
603	C₂⁴	C₂⁴×C₁₀₉	1	2	yes	—
604	C₂⁴	C₂⁴×C₁₀₉	1	1	yes	characteristic
605	C₂×D₄	—	2	256	no	—
606	C₂×D₄	—	2	64	no	—
607	C₂×D₄	—	2	64	no	—
608	C₂×D₄	—	2	16	no	—
609	C₂×D₄	—	2	16	no	—
610	C₂×D₄	—	2	16	no	—
611	C₂×D₄	—	2	16	no	—
612	C₂×D₄	—	2	8	no	—
613	C₂×D₄	—	2	8	no	—
614	C₂×D₄	—	2	8	no	—
615	C₂×D₄	—	2	8	no	—
616	C₂×D₄	—	2	16	no	—
617	C₂×D₄	—	2	16	no	—
618	C₂×D₄	—	2	8	no	—
619	C₂×D₄	—	2	16	no	—
620	C₂×D₄	—	2	16	no	—
621	C₂×D₄	—	4	8	no	—
622	C₂×D₄	—	4	8	no	—
623	C₂×D₄	—	4	32	no	—
624	C₂×D₄	—	4	16	no	—
625	C₂×D₄	—	4	16	no	—
626	C₂×D₄	—	4	16	no	—
627	C₂×D₄	C₂×D₄×C₁₀₉	1	32	yes	complemented
628	C₂²×C₄	—	2	32	no	—
629	C₂²×C₄	—	2	4	no	—
630	C₂²×C₄	—	2	8	no	—
631	C₂²×C₄	—	2	4	no	—
632	C₂²×C₄	—	2	4	no	—
633	C₂²×C₄	—	2	4	no	—
634	C₂²×C₄	—	2	16	no	—
635	C₂²×C₄	—	2	4	no	—
636	C₂²×C₄	—	2	4	no	—
637	C₂²×C₄	—	2	2	no	—
638	C₂²×C₄	—	2	2	no	—
639	C₂²×C₄	—	2	2	no	—
640	C₂²×C₄	—	2	2	no	—
641	C₂²×C₄	—	2	4	no	—
642	C₂²×C₄	—	2	16	no	—
643	C₂²×C₄	—	2	2	no	—
644	C₂²×C₄	—	2	4	no	—
645	C₂²×C₄	—	2	4	no	—
646	C₂²×C₄	—	2	16	no	—
647	C₂²×C₄	—	4	8	no	—
648	C₂²×C₄	—	4	32	no	—
649	C₂²×C₄	C₂×D₄×C₁₀₉	1	8	yes	—
650	C₂²×C₄	C₂×D₄×C₁₀₉	1	8	yes	complemented
651	C₂²×C₄	C₂⁴×C₁₀₉	1	2	yes	—
652	C₂²×C₄	C₂⁴×C₁₀₉	1	2	yes	—
653	C₂²×C₄	C₂⁴×C₁₀₉	1	4	yes	—
654	C₂²×C₄	C₂⁴×C₁₀₉	1	2	yes	—
655	C₂²×C₄	C₂⁴×C₁₀₉	1	4	yes	—
656	C₂²×C₄	C₂⁴×C₁₀₉	1	4	yes	—
657	C₄⋊C₄	—	2	16	no	—
658	C₂²⋊C₄	—	2	8	no	—
659	C₂²⋊C₄	—	2	8	no	—
660	C₂²⋊C₄	—	2	8	no	—
661	C₂²⋊C₄	—	2	8	no	—
662	C₂²⋊C₄	—	2	16	no	—
663	C₂²⋊C₄	—	2	16	no	—
664	C₂²⋊C₄	—	2	16	no	—
665	C₂²⋊C₄	—	2	16	no	—
666	C₂²⋊C₄	—	4	8	no	—
667	C₂²⋊C₄	C₂×D₄×C₁₀₉	1	16	yes	complemented
668	C₂³	—	2	8	no	—
669	C₂³	—	2	8	no	—
670	C₂³	—	2	8	no	—
671	C₂³	—	2	8	no	—
672	C₂³	—	2	16	no	—
673	C₂³	—	2	16	no	—
674	C₂³	—	2	16	no	—
675	C₂³	—	2	16	no	—
676	C₂³	—	2	2	no	—
677	C₂³	—	2	4	no	—
678	C₂³	—	2	2	no	—
679	C₂³	—	2	4	no	—
680	C₂³	—	2	4	no	—
681	C₂³	—	2	32	no	—
682	C₂³	—	2	8	no	—
683	C₂³	—	2	16	no	—
684	C₂³	—	2	32	no	—
685	C₂³	—	2	8	no	—
686	C₂³	—	2	32	no	—
687	C₂³	—	2	8	no	—
688	C₂³	—	2	16	no	—
689	C₂³	—	2	16	no	—
690	C₂³	—	2	2	no	—
691	C₂³	—	2	4	no	—
692	C₂³	—	2	4	no	—
693	C₂³	—	2	4	no	—
694	C₂³	—	2	4	no	—
695	C₂³	—	2	4	no	—
696	C₂³	—	2	2	no	—
697	C₂³	—	2	4	no	—
698	C₂³	—	2	4	no	—
699	C₂³	—	2	4	no	—
700	C₂³	—	2	4	no	—
701	C₂³	—	2	2	no	—
702	C₂³	—	2	2	no	—
703	C₂³	—	2	2	no	—
704	C₂³	—	2	4	no	—
705	C₂³	—	4	16	no	—
706	C₂³	—	4	32	no	—
707	C₂³	—	4	32	no	—
708	C₂³	—	4	32	no	—
709	C₂³	—	4	32	no	—
710	C₂³	—	4	128	no	—
711	C₂³	—	4	128	no	—
712	C₂³	—	4	16	no	—
713	C₂³	—	4	8	no	—
714	C₂³	—	4	16	no	—
715	C₂³	—	4	8	no	—
716	C₂³	—	4	8	no	—
717	C₂³	—	4	8	no	—
718	C₂³	—	4	8	no	—
719	C₂³	—	4	8	no	—
720	C₂³	—	4	4	no	—
721	C₂³	—	4	4	no	—
722	C₂³	—	4	4	no	—
723	C₂³	—	4	8	no	—
724	C₂³	—	4	8	no	—
725	C₂³	#120×C₁₀₉	1	16	yes	complemented
726	C₂³	#121×C₁₀₉	1	16	yes	complemented
727	C₂³	C₂²×D₄×C₁₀₉	1	4	yes	—
728	C₂³	C₂²×D₄×C₁₀₉	1	8	yes	—
729	C₂³	C₂²×D₄×C₁₀₉	1	4	yes	—
730	C₂³	C₂²×D₄×C₁₀₉	1	8	yes	—
731	C₂³	C₂²×D₄×C₁₀₉	1	4	yes	—
732	C₂³	C₂²×D₄×C₁₀₉	1	4	yes	—
733	C₂³	C₂²×D₄×C₁₀₉	1	2	yes	—
734	C₂³	C₂²×D₄×C₁₀₉	1	4	yes	—
735	C₂³	C₂²×D₄×C₁₀₉	1	2	yes	—
736	C₂³	C₂×#41×C₁₀₉	1	4	yes	—
737	C₂³	C₂×#41×C₁₀₉	1	2	yes	—
738	C₂³	H(5,𝔽₂)×C₁₀₉	1	4	yes	—
739	C₂³	C₂⁵×C₁₀₉	1	1	yes	characteristic
740	D₄	—	2	64	no	—
741	D₄	—	2	64	no	—
742	D₄	—	4	32	no	—
743	D₄	—	4	16	no	—
744	D₄	—	4	16	no	—
745	D₄	—	4	16	no	—
746	C₂×C₄	—	2	32	no	—
747	C₂×C₄	—	2	16	no	—
748	C₂×C₄	—	2	16	no	—
749	C₂×C₄	—	2	4	no	—
750	C₂×C₄	—	2	4	no	—
751	C₂×C₄	—	2	4	no	—
752	C₂×C₄	—	2	4	no	—
753	C₂×C₄	—	2	4	no	—
754	C₂×C₄	—	2	4	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	4	no	—
760	C₂×C₄	—	2	2	no	—
761	C₂×C₄	—	2	4	no	—
762	C₂×C₄	—	2	4	no	—
763	C₂×C₄	—	4	32	no	—
764	C₂×C₄	—	4	4	no	—
765	C₂×C₄	—	4	4	no	—
766	C₂×C₄	—	4	4	no	—
767	C₂×C₄	—	4	8	no	—
768	C₂×C₄	C₂²×D₄×C₁₀₉	1	8	yes	—
769	C₂×C₄	C₂²×D₄×C₁₀₉	1	8	yes	complemented
770	C₂²	—	2	8	no	—
771	C₂²	—	2	8	no	—
772	C₂²	—	2	8	no	—
773	C₂²	—	2	8	no	—
774	C₂²	—	2	4	no	—
775	C₂²	—	2	4	no	—
776	C₂²	—	2	32	no	—
777	C₂²	—	2	32	no	—
778	C₂²	—	2	4	no	—
779	C₂²	—	2	4	no	—
780	C₂²	—	2	8	no	—
781	C₂²	—	2	8	no	—
782	C₂²	—	2	4	no	—
783	C₂²	—	2	8	no	—
784	C₂²	—	2	4	no	—
785	C₂²	—	2	4	no	—
786	C₂²	—	4	64	no	—
787	C₂²	—	4	64	no	—
788	C₂²	—	4	4	no	—
789	C₂²	—	4	4	no	—
790	C₂²	—	4	4	no	—
791	C₂²	—	4	4	no	—
792	C₂²	—	4	4	no	—
793	C₂²	—	4	16	no	—
794	C₂²	—	4	32	no	—
795	C₂²	—	4	4	no	—
796	C₂²	—	4	4	no	—
797	C₂²	—	4	4	no	—
798	C₂²	—	4	2	no	—
799	C₂²	—	4	2	no	—
800	C₂²	—	4	2	no	—
801	C₂²	—	8	8	no	—
802	C₂²	C₂×#120×C₁₀₉	1	4	yes	—
803	C₂²	C₂×#120×C₁₀₉	1	8	yes	complemented
804	C₂²	C₂×#121×C₁₀₉	1	4	yes	—
805	C₂²	C₂×#121×C₁₀₉	1	8	yes	complemented
806	C₂²	#534×C₁₀₉	1	4	yes	—
807	C₂²	D₄²×C₁₀₉	1	8	yes	—
808	C₂²	#546×C₁₀₉	1	8	yes	—
809	C₂²	C₂³×D₄×C₁₀₉	1	1	yes	characteristic
810	C₂²	C₂³×D₄×C₁₀₉	1	2	yes	—
811	C₂²	C₂³×D₄×C₁₀₉	1	1	yes	characteristic
812	C₂²	C₂²×#41×C₁₀₉	1	1	yes	characteristic
813	C₂²	C₂×H(5,𝔽₂)×C₁₀₉	1	2	yes	—
814	C₄	—	2	8	no	—
815	C₄	—	2	8	no	—
816	C₄	—	4	4	no	—
817	C₄	—	4	2	no	—
818	C₄	—	4	2	no	—
819	C₄	—	4	2	no	—
820	C₂	—	2	8	no	—
821	C₂	—	2	8	no	—
822	C₂	—	4	8	no	—
823	C₂	—	4	4	no	—
824	C₂	—	8	2	no	—
825	C₂	C₁₀₉×#2410	1	8	yes	direct product factor
826	C₂	C₂²×#120×C₁₀₉	1	1	yes	characteristic
827	C₂	C₂²×#121×C₁₀₉	1	1	yes	characteristic
828	C₂	C₂×#534×C₁₀₉	1	1	yes	characteristic
829	C₂	C₂×D₄²×C₁₀₉	1	2	yes	—
830	C₂	C₂×#546×C₁₀₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₁₀₉	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₀₉
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₀₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂⁴×D₄×C₁₀₉	C₂	semidirect
2. C₂²×#121×C₁₀₉	C₂	semidirect
3. C₂²×#120×C₁₀₉	C₂	semidirect
4. C₂²×#120×C₁₀₉	C₂	semidirect
5. C₂³×C₂²⋊C₄×C₁₀₉	C₂	semidirect
6. C₁₀₉×#2410	C₂	direct (N × H)
7. C₂×#394×C₁₀₉	C₂	semidirect
8. C₂×#392×C₁₀₉	C₂	semidirect
9. C₂×#386×C₁₀₉	C₂	semidirect
10. C₂×#386×C₁₀₉	C₂	semidirect
11. C₂×#385×C₁₀₉	C₂	semidirect
12. C₂×#379×C₁₀₉	C₂	semidirect
20. C₂³×D₄×C₁₀₉	C₂²	semidirect
21. C₂³×D₄×C₁₀₉	C₂²	semidirect
22. C₂³×D₄×C₁₀₉	C₂²	semidirect
23. C₂³×D₄×C₁₀₉	C₂²	semidirect
25. C₂⁴×C₄×C₁₀₉	C₂²	semidirect
27. C₂×#121×C₁₀₉	C₂²	semidirect
30. C₂×#120×C₁₀₉	C₂²	semidirect
31. C₂×#120×C₁₀₉	C₂²	semidirect
32. C₂²×C₄⋊C₄×C₁₀₉	C₂²	semidirect
37. C₂²×C₂²⋊C₄×C₁₀₉	C₂²	semidirect
38. C₂²×C₂²⋊C₄×C₁₀₉	C₂²	semidirect
39. C₂²×C₂²⋊C₄×C₁₀₉	C₂²	semidirect
40. C₂²×C₂²⋊C₄×C₁₀₉	C₂²	semidirect
41. C₂²×C₂²⋊C₄×C₁₀₉	C₂²	semidirect
42. C₂²×C₂²⋊C₄×C₁₀₉	C₂²	semidirect
43. C₂²×C₂²⋊C₄×C₁₀₉	C₂²	semidirect
44. C₂²×C₂²⋊C₄×C₁₀₉	C₂²	semidirect
45. #394×C₁₀₉	C₂²	semidirect
46. #392×C₁₀₉	C₂²	semidirect
47. #386×C₁₀₉	C₂²	semidirect
48. #386×C₁₀₉	C₂²	semidirect
49. #385×C₁₀₉	C₂²	semidirect
50. #379×C₁₀₉	C₂²	semidirect
51. C₂×#95×C₁₀₉	C₂²	semidirect
52. C₂×#95×C₁₀₉	C₂²	semidirect
62. C₂⁵×C₁₀₉	D₄	semidirect
88. C₂²×D₄×C₁₀₉	D₄	semidirect
92. C₂²×D₄×C₁₀₉	C₂³	semidirect
93. C₂²×D₄×C₁₀₉	C₂³	semidirect
94. C₂²×D₄×C₁₀₉	C₂³	semidirect
107. C₂³×C₄×C₁₀₉	C₂³	semidirect
112. C₂×C₄⋊C₄×C₁₀₉	C₂³	semidirect
123. C₂×C₂²⋊C₄×C₁₀₉	D₄	semidirect
127. C₂×C₂²⋊C₄×C₁₀₉	C₂³	semidirect
128. C₂×C₂²⋊C₄×C₁₀₉	C₂³	semidirect
129. C₂×C₂²⋊C₄×C₁₀₉	C₂³	semidirect
130. C₂×C₂²⋊C₄×C₁₀₉	C₂³	semidirect
131. C₂×C₂²⋊C₄×C₁₀₉	C₂³	semidirect
132. C₂×C₂²⋊C₄×C₁₀₉	C₂³	semidirect
133. C₂×C₂²⋊C₄×C₁₀₉	C₂³	semidirect
134. #95×C₁₀₉	C₂³	semidirect
135. #95×C₁₀₉	C₂³	semidirect
181. C₂⁴×C₁₀₉	C₂×D₄	semidirect
211. C₂×D₄×C₁₀₉	C₂×D₄	semidirect
234. C₂²×C₄×C₁₀₉	C₂×D₄	semidirect
251. C₂²⋊C₄×C₁₀₉	C₂×D₄	semidirect
309. C₂³×C₁₀₉	#120	semidirect
310. C₂³×C₁₀₉	#121	semidirect
353. C₂×C₄×C₁₀₉	C₂²×D₄	semidirect
387. C₂²×C₁₀₉	C₂×#120	semidirect
389. C₂²×C₁₀₉	C₂×#121	semidirect
404. C₂×#2410	C₁₀₉	direct (N × H)
410. C₂×C₁₀₉	#2410	direct (N × H)
416. C₂⁴×D₄	C₂×C₁₀₉	semidirect
417. C₂²×#121	C₂×C₁₀₉	semidirect
418. C₂²×#120	C₂×C₁₀₉	semidirect
419. C₂²×#120	C₂×C₁₀₉	semidirect
420. C₂³×C₂²⋊C₄	C₂×C₁₀₉	semidirect
421. #2410	C₂×C₁₀₉	direct (N × H)
422. C₂×#394	C₂×C₁₀₉	semidirect
423. C₂×#392	C₂×C₁₀₉	semidirect
424. C₂×#386	C₂×C₁₀₉	semidirect
425. C₂×#386	C₂×C₁₀₉	semidirect
426. C₂×#385	C₂×C₁₀₉	semidirect
427. C₂×#379	C₂×C₁₀₉	semidirect
428. C₁₀₉	C₂×#2410	direct (N × H)
436. C₂³×D₄	C₂²×C₁₀₉	semidirect
437. C₂³×D₄	C₂²×C₁₀₉	semidirect
438. C₂³×D₄	C₂²×C₁₀₉	semidirect
439. C₂³×D₄	C₂²×C₁₀₉	semidirect
441. C₂⁴×C₄	C₂²×C₁₀₉	semidirect
443. C₂×#121	C₂²×C₁₀₉	semidirect
446. C₂×#120	C₂²×C₁₀₉	semidirect
447. C₂×#120	C₂²×C₁₀₉	semidirect
448. C₂²×C₄⋊C₄	C₂²×C₁₀₉	semidirect
453. C₂²×C₂²⋊C₄	C₂²×C₁₀₉	semidirect
454. C₂²×C₂²⋊C₄	C₂²×C₁₀₉	semidirect
455. C₂²×C₂²⋊C₄	C₂²×C₁₀₉	semidirect
456. C₂²×C₂²⋊C₄	C₂²×C₁₀₉	semidirect
457. C₂²×C₂²⋊C₄	C₂²×C₁₀₉	semidirect
458. C₂²×C₂²⋊C₄	C₂²×C₁₀₉	semidirect
459. C₂²×C₂²⋊C₄	C₂²×C₁₀₉	semidirect
460. C₂²×C₂²⋊C₄	C₂²×C₁₀₉	semidirect
461. #394	C₂²×C₁₀₉	semidirect
462. #392	C₂²×C₁₀₉	semidirect
463. #386	C₂²×C₁₀₉	semidirect
464. #386	C₂²×C₁₀₉	semidirect
465. #385	C₂²×C₁₀₉	semidirect
466. #379	C₂²×C₁₀₉	semidirect
467. C₂×#95	C₂²×C₁₀₉	semidirect
468. C₂×#95	C₂²×C₁₀₉	semidirect
478. C₂⁵	D₄×C₁₀₉	semidirect
504. C₂²×D₄	D₄×C₁₀₉	semidirect
508. C₂²×D₄	C₂³×C₁₀₉	semidirect
509. C₂²×D₄	C₂³×C₁₀₉	semidirect
510. C₂²×D₄	C₂³×C₁₀₉	semidirect
523. C₂³×C₄	C₂³×C₁₀₉	semidirect
528. C₂×C₄⋊C₄	C₂³×C₁₀₉	semidirect
539. C₂×C₂²⋊C₄	D₄×C₁₀₉	semidirect
543. C₂×C₂²⋊C₄	C₂³×C₁₀₉	semidirect
544. C₂×C₂²⋊C₄	C₂³×C₁₀₉	semidirect
545. C₂×C₂²⋊C₄	C₂³×C₁₀₉	semidirect
546. C₂×C₂²⋊C₄	C₂³×C₁₀₉	semidirect
547. C₂×C₂²⋊C₄	C₂³×C₁₀₉	semidirect
548. C₂×C₂²⋊C₄	C₂³×C₁₀₉	semidirect
549. C₂×C₂²⋊C₄	C₂³×C₁₀₉	semidirect
550. #95	C₂³×C₁₀₉	semidirect
551. #95	C₂³×C₁₀₉	semidirect
597. C₂⁴	C₂×D₄×C₁₀₉	semidirect
627. C₂×D₄	C₂×D₄×C₁₀₉	semidirect
650. C₂²×C₄	C₂×D₄×C₁₀₉	semidirect
667. C₂²⋊C₄	C₂×D₄×C₁₀₉	semidirect
725. C₂³	#120×C₁₀₉	semidirect
726. C₂³	#121×C₁₀₉	semidirect
769. C₂×C₄	C₂²×D₄×C₁₀₉	semidirect
803. C₂²	C₂×#120×C₁₀₉	semidirect
805. C₂²	C₂×#121×C₁₀₉	semidirect
825. C₂	C₁₀₉×#2410	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×D₄×C₁₀₉	2
C₂²×#121×C₁₀₉	2
C₂²×#120×C₁₀₉	2
C₂³×C₂²⋊C₄×C₁₀₉	2
C₁₀₉×#2410	2
C₂×#394×C₁₀₉	2
C₂×#392×C₁₀₉	2
C₂×#386×C₁₀₉	2
C₂×#385×C₁₀₉	2
C₂×#379×C₁₀₉	2
C₂×#2410	109

Subgroups — C2×C109×#2410 #42152640

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₀₉×#2410 #42152640