Subgroups — C₁₀₉×#34202 #42152196

Order 27904.

3246 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#525×C₁₀₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#520×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#117×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₀₉×#2359	C₂	1	4	yes	maximal, complemented
5	C₁₀₉×#2358	C₂	1	4	yes	maximal, complemented
6	C₁₀₉×#2354	C₂	1	2	yes	maximal, complemented
7	C₁₀₉×#2352	C₂	1	2	yes	maximal, complemented
8	C₁₀₉×#2352	C₂	1	2	yes	maximal, complemented
9	D₄×C₄⋊C₄×C₁₀₉	C₂	1	2	yes	maximal, complemented
10	C₁₀₉×#2324	C₂	1	2	yes	maximal, complemented
11	C₁₀₉×#2323	C₂	1	2	yes	maximal, complemented
12	C₁₀₉×#2317	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₀₉×#2311	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₂²⋊Q₈×C₁₀₉	C₂	1	2	yes	maximal, complemented
15	C₄×#121×C₁₀₉	C₂	1	2	yes	maximal, complemented
16	C₂×#380×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₀₉×#2274	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#41×C₁₀₉	C₂²	1	1	yes	characteristic
19	C₂⁴×C₄×C₁₀₉	C₂²	1	1	yes	characteristic
20	#525×C₁₀₉	C₄	1	16	yes	complemented
21	C₂×#123×C₁₀₉	C₂²	1	2	yes	—
22	C₂×C₂²⋊Q₈×C₁₀₉	C₂²	1	1	yes	characteristic
23	C₂×C₂²⋊Q₈×C₁₀₉	C₂²	1	1	yes	characteristic
24	C₂×#121×C₁₀₉	C₂²	1	1	yes	characteristic
25	C₂×#121×C₁₀₉	C₂²	1	1	yes	characteristic
26	C₂×#120×C₁₀₉	C₂²	1	2	yes	—
27	#520×C₁₀₉	—	2	8	no	—
28	C₂×C₄×Q₈×C₁₀₉	C₂²	1	2	yes	complemented
29	C₂×C₄×D₄×C₁₀₉	C₂²	1	4	yes	—
30	C₂×C₄×D₄×C₁₀₉	C₂²	1	4	yes	—
31	C₂×C₄×D₄×C₁₀₉	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₁₀₉	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₁₀₉	C₂²	1	2	yes	complemented
34	C₂×#117×C₁₀₉	—	2	8	no	—
35	C₂×#117×C₁₀₉	C₂²	1	1	yes	characteristic
36	C₂×#117×C₁₀₉	C₂²	1	2	yes	—
37	C₂×#117×C₁₀₉	C₂²	1	1	yes	characteristic
38	C₂×#117×C₁₀₉	C₂²	1	1	yes	characteristic
39	C₂×#117×C₁₀₉	C₂²	1	2	yes	—
40	C₂×#117×C₁₀₉	C₂²	1	1	yes	characteristic
41	C₂×#117×C₁₀₉	C₂²	1	1	yes	characteristic
42	C₂×#117×C₁₀₉	C₂²	1	2	yes	complemented
43	C₂²×C₄⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic
44	C₂²×C₄⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic
45	C₂²×C₄⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic
46	C₂²×C₄⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic
47	C₂²×C₄⋊C₄×C₁₀₉	C₂²	1	2	yes	complemented
48	C₂²×C₂²⋊C₄×C₁₀₉	C₂²	1	2	yes	—
49	C₂²×C₂²⋊C₄×C₁₀₉	C₂²	1	2	yes	—
50	C₂²×C₄²×C₁₀₉	C₂²	1	2	yes	—
51	#391×C₁₀₉	C₂²	1	2	yes	complemented
52	#390×C₁₀₉	C₂²	1	4	yes	—
53	#390×C₁₀₉	C₂²	1	2	yes	complemented
54	#389×C₁₀₉	C₂²	1	2	yes	complemented
55	#389×C₁₀₉	C₂²	1	2	yes	complemented
56	#389×C₁₀₉	C₂²	1	4	yes	complemented
57	#388×C₁₀₉	C₂²	1	4	yes	—
58	#388×C₁₀₉	C₂²	1	4	yes	—
59	#388×C₁₀₉	C₂²	1	4	yes	complemented
60	#388×C₁₀₉	C₂²	1	4	yes	complemented
61	#387×C₁₀₉	C₂²	1	4	yes	complemented
62	#387×C₁₀₉	C₂²	1	4	yes	complemented
63	#386×C₁₀₉	C₂²	1	4	yes	—
64	#386×C₁₀₉	C₂²	1	4	yes	—
65	#386×C₁₀₉	C₂²	1	4	yes	—
66	#385×C₁₀₉	C₂²	1	4	yes	—
67	#385×C₁₀₉	C₂²	1	4	yes	—
68	#385×C₁₀₉	C₂²	1	4	yes	complemented
69	#384×C₁₀₉	C₂²	1	2	yes	complemented
70	#382×C₁₀₉	C₂²	1	2	yes	complemented
71	#380×C₁₀₉	C₂²	1	2	yes	—
72	#380×C₁₀₉	C₂²	1	2	yes	—
73	#380×C₁₀₉	C₂²	1	2	yes	—
74	#380×C₁₀₉	C₂²	1	2	yes	—
75	#380×C₁₀₉	C₂²	1	2	yes	complemented
76	#380×C₁₀₉	C₂²	1	2	yes	complemented
77	C₄×C₄⋊C₄×C₁₀₉	C₂²	1	2	yes	complemented
78	C₄×C₄⋊C₄×C₁₀₉	C₂²	1	2	yes	complemented
79	C₄×C₄⋊C₄×C₁₀₉	C₂²	1	2	yes	complemented
80	C₄×C₄⋊C₄×C₁₀₉	C₂²	1	2	yes	complemented
81	C₄×C₄⋊C₄×C₁₀₉	C₂²	1	4	yes	complemented
82	C₄×C₂²⋊C₄×C₁₀₉	C₂²	1	4	yes	—
83	C₄×C₂²⋊C₄×C₁₀₉	C₂²	1	4	yes	—
84	C₄×C₂²⋊C₄×C₁₀₉	C₂²	1	4	yes	complemented
85	C₂×#95×C₁₀₉	C₂²	1	2	yes	—
86	C₂⁵×C₁₀₉	C₂³	1	1	yes	characteristic
87	C₂×#41×C₁₀₉	—	2	4	no	—
88	C₂×#41×C₁₀₉	—	2	4	no	—
89	C₂×#41×C₁₀₉	C₂×C₄	1	8	yes	complemented
90	C₂²×Q₈×C₁₀₉	C₂³	1	1	yes	characteristic
91	C₂²×D₄×C₁₀₉	C₂³	1	2	yes	—
92	C₂²×D₄×C₁₀₉	C₂³	1	2	yes	—
93	C₂²×D₄×C₁₀₉	C₂³	1	1	yes	characteristic
94	C₂²×D₄×C₁₀₉	C₂³	1	2	yes	—
95	C₂³×C₄×C₁₀₉	—	2	4	no	—
96	C₂³×C₄×C₁₀₉	—	2	4	no	—
97	C₂³×C₄×C₁₀₉	C₂×C₄	1	8	yes	complemented
98	C₂³×C₄×C₁₀₉	C₂³	1	2	yes	—
99	C₂³×C₄×C₁₀₉	C₂³	1	2	yes	—
100	C₂³×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
101	C₂³×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
102	C₂³×C₄×C₁₀₉	C₂³	1	2	yes	—
103	C₂³×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
104	C₂³×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
105	C₂³×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
106	C₂³×C₄×C₁₀₉	C₂³	1	2	yes	—
107	C₂³×C₄×C₁₀₉	C₂³	1	2	yes	—
108	C₂³×C₄×C₁₀₉	C₂³	1	4	yes	—
109	C₂³×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
110	#123×C₁₀₉	C₂×C₄	1	16	yes	complemented
111	C₂²⋊Q₈×C₁₀₉	C₂×C₄	1	8	yes	complemented
112	C₂²⋊Q₈×C₁₀₉	C₂×C₄	1	8	yes	complemented
113	#121×C₁₀₉	C₂×C₄	1	8	yes	complemented
114	#121×C₁₀₉	C₂×C₄	1	8	yes	complemented
115	#120×C₁₀₉	C₂×C₄	1	16	yes	complemented
116	C₄×Q₈×C₁₀₉	—	2	8	no	—
117	C₄×D₄×C₁₀₉	—	2	16	no	—
118	C₄×D₄×C₁₀₉	—	2	8	no	—
119	C₄×D₄×C₁₀₉	—	4	8	no	—
120	C₄×D₄×C₁₀₉	C₂×C₄	1	16	yes	complemented
121	C₄×D₄×C₁₀₉	C₂×C₄	1	16	yes	complemented
122	#117×C₁₀₉	—	2	4	no	—
123	#117×C₁₀₉	—	2	4	no	—
124	#117×C₁₀₉	—	2	4	no	—
125	#117×C₁₀₉	—	2	8	no	—
126	#117×C₁₀₉	—	2	8	no	—
127	#117×C₁₀₉	—	2	8	no	—
128	#117×C₁₀₉	C₂×C₄	1	8	yes	complemented
129	#117×C₁₀₉	D₄	1	8	yes	complemented
130	C₂×C₄⋊C₄×C₁₀₉	—	2	4	no	—
131	C₂×C₄⋊C₄×C₁₀₉	—	2	4	no	—
132	C₂×C₄⋊C₄×C₁₀₉	—	2	4	no	—
133	C₂×C₄⋊C₄×C₁₀₉	—	2	4	no	—
134	C₂×C₄⋊C₄×C₁₀₉	—	2	8	no	—
135	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
136	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
137	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
138	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
141	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
142	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
143	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	4	yes	—
144	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	4	yes	—
145	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	4	yes	—
146	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
147	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
148	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
149	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
150	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
151	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
152	C₂×C₂²⋊C₄×C₁₀₉	—	2	8	no	—
153	C₂×C₂²⋊C₄×C₁₀₉	—	4	4	no	—
154	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
155	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
156	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
157	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	4	yes	—
158	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	4	yes	—
159	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	4	yes	—
160	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	4	yes	—
161	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	4	yes	—
162	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
163	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
164	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
165	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
166	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
167	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
168	C₂×C₄²×C₁₀₉	—	2	8	no	—
169	C₂×C₄²×C₁₀₉	C₂³	1	2	yes	—
170	C₂×C₄²×C₁₀₉	C₂³	1	2	yes	—
171	C₂×C₄²×C₁₀₉	C₂³	1	2	yes	—
172	C₂×C₄²×C₁₀₉	C₂³	1	4	yes	—
173	C₂×C₄²×C₁₀₉	C₂³	1	4	yes	—
174	C₂×C₄²×C₁₀₉	C₂³	1	4	yes	—
175	C₂×C₄²×C₁₀₉	C₂³	1	2	yes	—
176	C₂×C₄²×C₁₀₉	C₂³	1	2	yes	—
177	#95×C₁₀₉	C₂³	1	4	yes	—
178	#95×C₁₀₉	C₂³	1	4	yes	—
179	#95×C₁₀₉	C₂³	1	4	yes	—
180	#95×C₁₀₉	C₂³	1	4	yes	—
181	#95×C₁₀₉	C₂³	1	4	yes	—
182	#95×C₁₀₉	C₂³	1	4	yes	—
183	#95×C₁₀₉	C₂³	1	4	yes	—
184	#95×C₁₀₉	C₂³	1	4	yes	—
185	C₂⁴×C₁₀₉	—	2	2	no	—
186	C₂⁴×C₁₀₉	—	2	2	no	—
187	C₂⁴×C₁₀₉	—	2	2	no	—
188	C₂⁴×C₁₀₉	—	2	2	no	—
189	C₂⁴×C₁₀₉	—	4	1	no	—
190	C₂⁴×C₁₀₉	—	4	1	no	—
191	C₂⁴×C₁₀₉	C₂²×C₄	1	4	yes	—
192	C₂⁴×C₁₀₉	C₂⁴	1	1	yes	characteristic
193	C₂⁴×C₁₀₉	C₂⁴	1	2	yes	—
194	C₂⁴×C₁₀₉	C₂⁴	1	1	yes	characteristic
195	C₂⁴×C₁₀₉	C₂⁴	1	1	yes	characteristic
196	#41×C₁₀₉	—	2	32	no	—
197	C₂×Q₈×C₁₀₉	—	2	2	no	—
198	C₂×Q₈×C₁₀₉	—	2	2	no	—
199	C₂×Q₈×C₁₀₉	C₂²×C₄	1	4	yes	—
200	C₂×D₄×C₁₀₉	—	2	4	no	—
201	C₂×D₄×C₁₀₉	—	2	4	no	—
202	C₂×D₄×C₁₀₉	—	2	4	no	—
203	C₂×D₄×C₁₀₉	—	2	4	no	—
204	C₂×D₄×C₁₀₉	—	2	2	no	—
205	C₂×D₄×C₁₀₉	—	2	2	no	—
206	C₂×D₄×C₁₀₉	—	4	2	no	—
207	C₂×D₄×C₁₀₉	—	4	2	no	—
208	C₂×D₄×C₁₀₉	C₂²×C₄	1	8	yes	—
209	C₂×D₄×C₁₀₉	C₂²×C₄	1	8	yes	—
210	C₂×D₄×C₁₀₉	C₂²×C₄	1	4	yes	—
211	C₂×D₄×C₁₀₉	C₂²×C₄	1	8	yes	—
212	C₂²×C₄×C₁₀₉	—	2	2	no	—
213	C₂²×C₄×C₁₀₉	—	2	2	no	—
214	C₂²×C₄×C₁₀₉	—	2	32	no	—
215	C₂²×C₄×C₁₀₉	—	2	2	no	—
216	C₂²×C₄×C₁₀₉	—	2	2	no	—
217	C₂²×C₄×C₁₀₉	—	2	4	no	—
218	C₂²×C₄×C₁₀₉	—	2	2	no	—
219	C₂²×C₄×C₁₀₉	—	2	2	no	—
220	C₂²×C₄×C₁₀₉	—	2	2	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	4	no	—
225	C₂²×C₄×C₁₀₉	—	2	4	no	—
226	C₂²×C₄×C₁₀₉	—	2	4	no	—
227	C₂²×C₄×C₁₀₉	—	2	4	no	—
228	C₂²×C₄×C₁₀₉	—	2	4	no	—
229	C₂²×C₄×C₁₀₉	—	2	4	no	—
230	C₂²×C₄×C₁₀₉	—	2	4	no	—
231	C₂²×C₄×C₁₀₉	—	2	8	no	—
232	C₂²×C₄×C₁₀₉	—	4	2	no	—
233	C₂²×C₄×C₁₀₉	—	4	2	no	—
234	C₂²×C₄×C₁₀₉	—	4	2	no	—
235	C₂²×C₄×C₁₀₉	—	4	2	no	—
236	C₂²×C₄×C₁₀₉	—	4	4	no	—
237	C₂²×C₄×C₁₀₉	—	4	4	no	—
238	C₂²×C₄×C₁₀₉	—	4	2	no	—
239	C₂²×C₄×C₁₀₉	—	4	2	no	—
240	C₂²×C₄×C₁₀₉	C₂²×C₄	1	4	yes	—
241	C₂²×C₄×C₁₀₉	C₂²×C₄	1	4	yes	—
242	C₂²×C₄×C₁₀₉	C₂²×C₄	1	8	yes	—
243	C₂²×C₄×C₁₀₉	C₂²×C₄	1	4	yes	—
244	C₂²×C₄×C₁₀₉	C₂²×C₄	1	4	yes	—
245	C₂²×C₄×C₁₀₉	C₂²×C₄	1	4	yes	—
246	C₂²×C₄×C₁₀₉	C₂²×C₄	1	4	yes	—
247	C₂²×C₄×C₁₀₉	C₂×D₄	1	4	yes	—
248	C₂²×C₄×C₁₀₉	#41	1	4	yes	—
249	C₂²×C₄×C₁₀₉	C₂⁴	1	2	yes	—
250	C₂²×C₄×C₁₀₉	C₂⁴	1	4	yes	—
251	C₂²×C₄×C₁₀₉	C₂⁴	1	4	yes	—
252	C₂²×C₄×C₁₀₉	C₂⁴	1	2	yes	—
253	C₂²×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
254	C₂²×C₄×C₁₀₉	C₂⁴	1	2	yes	—
255	C₂²×C₄×C₁₀₉	C₂⁴	1	2	yes	—
256	C₂²×C₄×C₁₀₉	C₂⁴	1	2	yes	—
257	C₂²×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
258	C₂²×C₄×C₁₀₉	C₂⁴	1	2	yes	—
259	C₂²×C₄×C₁₀₉	C₂⁴	1	2	yes	—
260	C₂²×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
261	C₂²×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
262	C₄⋊C₄×C₁₀₉	—	2	4	no	—
263	C₄⋊C₄×C₁₀₉	—	2	4	no	—
264	C₄⋊C₄×C₁₀₉	—	2	4	no	—
265	C₄⋊C₄×C₁₀₉	—	2	2	no	—
266	C₄⋊C₄×C₁₀₉	—	2	2	no	—
267	C₄⋊C₄×C₁₀₉	—	2	8	no	—
268	C₄⋊C₄×C₁₀₉	—	2	4	no	—
269	C₄⋊C₄×C₁₀₉	—	2	4	no	—
270	C₄⋊C₄×C₁₀₉	—	2	4	no	—
271	C₄⋊C₄×C₁₀₉	—	4	4	no	—
272	C₄⋊C₄×C₁₀₉	—	4	4	no	—
273	C₄⋊C₄×C₁₀₉	C₂²×C₄	1	4	yes	—
274	C₄⋊C₄×C₁₀₉	C₂²×C₄	1	4	yes	—
275	C₄⋊C₄×C₁₀₉	C₂²×C₄	1	8	yes	—
276	C₄⋊C₄×C₁₀₉	C₂²×C₄	1	8	yes	—
277	C₄⋊C₄×C₁₀₉	C₂×D₄	1	4	yes	—
278	C₄⋊C₄×C₁₀₉	C₂×D₄	1	4	yes	—
279	C₂²⋊C₄×C₁₀₉	—	2	4	no	—
280	C₂²⋊C₄×C₁₀₉	—	2	8	no	—
281	C₂²⋊C₄×C₁₀₉	—	2	4	no	—
282	C₂²⋊C₄×C₁₀₉	—	2	4	no	—
283	C₂²⋊C₄×C₁₀₉	—	2	8	no	—
284	C₂²⋊C₄×C₁₀₉	—	4	4	no	—
285	C₂²⋊C₄×C₁₀₉	—	4	4	no	—
286	C₂²⋊C₄×C₁₀₉	—	4	4	no	—
287	C₂²⋊C₄×C₁₀₉	C₂²×C₄	1	8	yes	—
288	C₂²⋊C₄×C₁₀₉	C₂²×C₄	1	8	yes	—
289	C₂²⋊C₄×C₁₀₉	C₂²×C₄	1	8	yes	—
290	C₂²⋊C₄×C₁₀₉	C₂²×C₄	1	8	yes	—
291	C₂²⋊C₄×C₁₀₉	C₂²×C₄	1	8	yes	—
292	C₂²⋊C₄×C₁₀₉	C₂×D₄	1	8	yes	—
293	C₄²×C₁₀₉	—	2	4	no	—
294	C₄²×C₁₀₉	—	2	4	no	—
295	C₄²×C₁₀₉	—	2	4	no	—
296	C₄²×C₁₀₉	—	2	8	no	—
297	C₄²×C₁₀₉	—	4	4	no	—
298	C₄²×C₁₀₉	—	4	4	no	—
299	C₄²×C₁₀₉	C₂²×C₄	1	8	yes	—
300	C₄²×C₁₀₉	C₂×D₄	1	8	yes	—
301	C₂³×C₁₀₉	—	2	1	no	—
302	C₂³×C₁₀₉	—	2	1	no	—
303	C₂³×C₁₀₉	—	2	1	no	—
304	C₂³×C₁₀₉	—	2	1	no	—
305	C₂³×C₁₀₉	—	2	1	no	—
306	C₂³×C₁₀₉	—	2	1	no	—
307	C₂³×C₁₀₉	—	2	1	no	—
308	C₂³×C₁₀₉	—	2	1	no	—
309	C₂³×C₁₀₉	—	2	8	no	—
310	C₂³×C₁₀₉	—	2	8	no	—
311	C₂³×C₁₀₉	—	2	1	no	—
312	C₂³×C₁₀₉	—	2	2	no	—
313	C₂³×C₁₀₉	—	2	1	no	—
314	C₂³×C₁₀₉	—	2	2	no	—
315	C₂³×C₁₀₉	—	2	1	no	—
316	C₂³×C₁₀₉	—	2	2	no	—
317	C₂³×C₁₀₉	—	2	2	no	—
318	C₂³×C₁₀₉	—	2	1	no	—
319	C₂³×C₁₀₉	—	2	2	no	—
320	C₂³×C₁₀₉	—	2	2	no	—
321	C₂³×C₁₀₉	—	2	1	no	—
322	C₂³×C₁₀₉	—	2	1	no	—
323	C₂³×C₁₀₉	—	4	4	no	—
324	C₂³×C₁₀₉	—	4	4	no	—
325	C₂³×C₁₀₉	—	4	4	no	—
326	C₂³×C₁₀₉	—	4	4	no	—
327	C₂³×C₁₀₉	—	4	4	no	—
328	C₂³×C₁₀₉	C₂³×C₄	1	2	yes	—
329	C₂³×C₁₀₉	C₂³×C₄	1	4	yes	—
330	C₂³×C₁₀₉	C₂³×C₄	1	2	yes	—
331	C₂³×C₁₀₉	C₂³×C₄	1	2	yes	—
332	C₂³×C₁₀₉	C₂²×D₄	1	2	yes	—
333	C₂³×C₁₀₉	C₂×#41	1	2	yes	—
334	C₂³×C₁₀₉	H(5,𝔽₂)	1	2	yes	—
335	C₂³×C₁₀₉	2₋¹⁺⁴	1	2	yes	—
336	C₂³×C₁₀₉	C₂⁵	1	1	yes	characteristic
337	Q₈×C₁₀₉	—	2	8	no	—
338	D₄×C₁₀₉	—	2	16	no	—
339	D₄×C₁₀₉	—	2	16	no	—
340	D₄×C₁₀₉	—	2	8	no	—
341	D₄×C₁₀₉	—	4	8	no	—
342	C₂×C₄×C₁₀₉	—	2	8	no	—
343	C₂×C₄×C₁₀₉	—	2	1	no	—
344	C₂×C₄×C₁₀₉	—	2	2	no	—
345	C₂×C₄×C₁₀₉	—	2	1	no	—
346	C₂×C₄×C₁₀₉	—	2	1	no	—
347	C₂×C₄×C₁₀₉	—	2	1	no	—
348	C₂×C₄×C₁₀₉	—	2	2	no	—
349	C₂×C₄×C₁₀₉	—	2	2	no	—
350	C₂×C₄×C₁₀₉	—	2	2	no	—
351	C₂×C₄×C₁₀₉	—	2	2	no	—
352	C₂×C₄×C₁₀₉	—	2	2	no	—
353	C₂×C₄×C₁₀₉	—	2	2	no	—
354	C₂×C₄×C₁₀₉	—	2	2	no	—
355	C₂×C₄×C₁₀₉	—	2	2	no	—
356	C₂×C₄×C₁₀₉	—	2	2	no	—
357	C₂×C₄×C₁₀₉	—	2	8	no	—
358	C₂×C₄×C₁₀₉	—	2	8	no	—
359	C₂×C₄×C₁₀₉	—	2	8	no	—
360	C₂×C₄×C₁₀₉	—	2	8	no	—
361	C₂×C₄×C₁₀₉	—	2	16	no	—
362	C₂×C₄×C₁₀₉	—	2	2	no	—
363	C₂×C₄×C₁₀₉	—	2	2	no	—
364	C₂×C₄×C₁₀₉	—	2	4	no	—
365	C₂×C₄×C₁₀₉	—	2	4	no	—
366	C₂×C₄×C₁₀₉	—	2	4	no	—
367	C₂×C₄×C₁₀₉	—	2	4	no	—
368	C₂×C₄×C₁₀₉	—	2	2	no	—
369	C₂×C₄×C₁₀₉	—	2	2	no	—
370	C₂×C₄×C₁₀₉	—	2	4	no	—
371	C₂×C₄×C₁₀₉	—	2	2	no	—
372	C₂×C₄×C₁₀₉	—	2	2	no	—
373	C₂×C₄×C₁₀₉	—	2	4	no	—
374	C₂×C₄×C₁₀₉	—	4	8	no	—
375	C₂×C₄×C₁₀₉	—	4	8	no	—
376	C₂×C₄×C₁₀₉	—	8	8	no	—
377	C₂×C₄×C₁₀₉	—	8	4	no	—
378	C₂×C₄×C₁₀₉	—	8	4	no	—
379	C₂×C₄×C₁₀₉	C₄×D₄	1	16	yes	complemented
380	C₂×C₄×C₁₀₉	C₂³×C₄	1	4	yes	—
381	C₂×C₄×C₁₀₉	C₂³×C₄	1	4	yes	—
382	C₂×C₄×C₁₀₉	C₂³×C₄	1	2	yes	—
383	C₂×C₄×C₁₀₉	C₂³×C₄	1	2	yes	—
384	C₂×C₄×C₁₀₉	C₂³×C₄	1	4	yes	—
385	C₂×C₄×C₁₀₉	C₂³×C₄	1	2	yes	—
386	C₂×C₄×C₁₀₉	C₂³×C₄	1	2	yes	—
387	C₂×C₄×C₁₀₉	C₂²×D₄	1	4	yes	—
388	C₂×C₄×C₁₀₉	C₂²×D₄	1	4	yes	—
389	C₂×C₄×C₁₀₉	C₂²×D₄	1	2	yes	—
390	C₂×C₄×C₁₀₉	C₂²×D₄	1	2	yes	—
391	C₂×C₄×C₁₀₉	C₂×#41	1	2	yes	—
392	C₂×C₄×C₁₀₉	C₂×#41	1	2	yes	—
393	C₂²×C₁₀₉	—	2	2	no	—
394	C₂²×C₁₀₉	—	2	2	no	—
395	C₂²×C₁₀₉	—	2	2	no	—
396	C₂²×C₁₀₉	—	2	2	no	—
397	C₂²×C₁₀₉	—	2	2	no	—
398	C₂²×C₁₀₉	—	2	2	no	—
399	C₂²×C₁₀₉	—	2	2	no	—
400	C₂²×C₁₀₉	—	2	2	no	—
401	C₂²×C₁₀₉	—	2	2	no	—
402	C₂²×C₁₀₉	—	2	2	no	—
403	C₂²×C₁₀₉	—	2	2	no	—
404	C₂²×C₁₀₉	—	2	2	no	—
405	C₂²×C₁₀₉	—	2	2	no	—
406	C₂²×C₁₀₉	—	2	4	no	—
407	C₂²×C₁₀₉	—	2	4	no	—
408	C₂²×C₁₀₉	—	2	2	no	—
409	C₂²×C₁₀₉	—	2	2	no	—
410	C₂²×C₁₀₉	—	2	4	no	—
411	C₂²×C₁₀₉	—	4	16	no	—
412	C₂²×C₁₀₉	—	4	2	no	—
413	C₂²×C₁₀₉	—	4	1	no	—
414	C₂²×C₁₀₉	—	4	2	no	—
415	C₂²×C₁₀₉	—	4	1	no	—
416	C₂²×C₁₀₉	—	4	2	no	—
417	C₂²×C₁₀₉	—	4	1	no	—
418	C₂²×C₁₀₉	—	4	2	no	—
419	C₂²×C₁₀₉	—	4	1	no	—
420	C₂²×C₁₀₉	C₂×C₄×D₄	1	4	yes	—
421	C₂²×C₁₀₉	#520	1	4	yes	complemented
422	C₂²×C₁₀₉	C₂⁴×C₄	1	1	yes	characteristic
423	C₂²×C₁₀₉	C₂³×D₄	1	1	yes	characteristic
424	C₂²×C₁₀₉	C₂²×#41	1	1	yes	characteristic
425	C₂²×C₁₀₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
426	C₂²×C₁₀₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
427	C₂²×C₁₀₉	#585	1	1	yes	characteristic
428	C₂²×C₁₀₉	#585	1	1	yes	characteristic
429	C₄×C₁₀₉	—	2	2	no	—
430	C₄×C₁₀₉	—	2	2	no	—
431	C₄×C₁₀₉	—	2	4	no	—
432	C₄×C₁₀₉	—	2	4	no	—
433	C₄×C₁₀₉	—	2	4	no	—
434	C₄×C₁₀₉	—	2	4	no	—
435	C₄×C₁₀₉	—	2	4	no	—
436	C₄×C₁₀₉	—	4	2	no	—
437	C₄×C₁₀₉	—	4	4	no	—
438	C₄×C₁₀₉	—	4	2	no	—
439	C₄×C₁₀₉	—	4	4	no	—
440	C₄×C₁₀₉	C₂×C₄×D₄	1	4	yes	—
441	C₄×C₁₀₉	C₂×C₄×D₄	1	4	yes	—
442	#34202	C₁₀₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
443	C₂×C₁₀₉	—	2	4	no	—
444	C₂×C₁₀₉	—	2	4	no	—
445	C₂×C₁₀₉	—	4	4	no	—
446	C₂×C₁₀₉	—	4	2	no	—
447	C₂×C₁₀₉	C₂²×C₄×D₄	1	1	yes	characteristic
448	C₂×C₁₀₉	C₂×#520	1	1	yes	characteristic
449	C₂×C₁₀₉	#3428	1	1	yes	characteristic
450	C₂×C₁₀₉	#3488	1	1	yes	characteristic
451	C₂×C₁₀₉	#3489	1	1	yes	characteristic
452	C₂×C₁₀₉	#3494	1	1	yes	characteristic
453	C₂×C₁₀₉	#3495	1	1	yes	characteristic
454	C₂×#525	C₂×C₁₀₉	1	1	yes	characteristic
455	C₂×#520	C₂×C₁₀₉	1	1	yes	characteristic, complemented
456	C₂²×#117	C₂×C₁₀₉	1	1	yes	characteristic, complemented
457	#2359	C₂×C₁₀₉	1	4	yes	complemented
458	#2358	C₂×C₁₀₉	1	4	yes	complemented
459	#2354	C₂×C₁₀₉	1	2	yes	complemented
460	#2352	C₂×C₁₀₉	1	2	yes	complemented
461	#2352	C₂×C₁₀₉	1	2	yes	complemented
462	D₄×C₄⋊C₄	C₂×C₁₀₉	1	2	yes	complemented
463	#2324	C₂×C₁₀₉	1	2	yes	complemented
464	#2323	C₂×C₁₀₉	1	2	yes	complemented
465	#2317	C₂×C₁₀₉	1	1	yes	characteristic, complemented
466	#2311	C₂×C₁₀₉	1	1	yes	characteristic, complemented
467	C₄×C₂²⋊Q₈	C₂×C₁₀₉	1	2	yes	complemented
468	C₄×#121	C₂×C₁₀₉	1	2	yes	complemented
469	C₂×#380	C₂×C₁₀₉	1	1	yes	characteristic, complemented
470	#2274	C₂×C₁₀₉	1	1	yes	characteristic, complemented
471	C₁₀₉	#34202	1	1	yes	characteristic, direct product factor, Sylow
472	C₂²×#41	C₂²×C₁₀₉	1	1	yes	characteristic
473	C₂⁴×C₄	C₂²×C₁₀₉	1	1	yes	characteristic
474	#525	C₄×C₁₀₉	1	16	yes	complemented
475	C₂×#123	C₂²×C₁₀₉	1	2	yes	—
476	C₂×C₂²⋊Q₈	C₂²×C₁₀₉	1	1	yes	characteristic
477	C₂×C₂²⋊Q₈	C₂²×C₁₀₉	1	1	yes	characteristic
478	C₂×#121	C₂²×C₁₀₉	1	1	yes	characteristic
479	C₂×#121	C₂²×C₁₀₉	1	1	yes	characteristic
480	C₂×#120	C₂²×C₁₀₉	1	2	yes	—
481	#520	—	2	8	no	—
482	C₂×C₄×Q₈	C₂²×C₁₀₉	1	2	yes	complemented
483	C₂×C₄×D₄	C₂²×C₁₀₉	1	4	yes	—
484	C₂×C₄×D₄	C₂²×C₁₀₉	1	4	yes	—
485	C₂×C₄×D₄	C₂²×C₁₀₉	1	2	yes	—
486	C₂×C₄×D₄	C₂²×C₁₀₉	1	2	yes	—
487	C₂×C₄×D₄	C₂²×C₁₀₉	1	2	yes	complemented
488	C₂×#117	—	2	8	no	—
489	C₂×#117	C₂²×C₁₀₉	1	1	yes	characteristic
490	C₂×#117	C₂²×C₁₀₉	1	2	yes	—
491	C₂×#117	C₂²×C₁₀₉	1	1	yes	characteristic
492	C₂×#117	C₂²×C₁₀₉	1	1	yes	characteristic
493	C₂×#117	C₂²×C₁₀₉	1	2	yes	—
494	C₂×#117	C₂²×C₁₀₉	1	1	yes	characteristic
495	C₂×#117	C₂²×C₁₀₉	1	1	yes	characteristic
496	C₂×#117	C₂²×C₁₀₉	1	2	yes	complemented
497	C₂²×C₄⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic
498	C₂²×C₄⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic
499	C₂²×C₄⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic
500	C₂²×C₄⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic
501	C₂²×C₄⋊C₄	C₂²×C₁₀₉	1	2	yes	complemented
502	C₂²×C₂²⋊C₄	C₂²×C₁₀₉	1	2	yes	—
503	C₂²×C₂²⋊C₄	C₂²×C₁₀₉	1	2	yes	—
504	C₂²×C₄²	C₂²×C₁₀₉	1	2	yes	—
505	#391	C₂²×C₁₀₉	1	2	yes	complemented
506	#390	C₂²×C₁₀₉	1	4	yes	—
507	#390	C₂²×C₁₀₉	1	2	yes	complemented
508	#389	C₂²×C₁₀₉	1	2	yes	complemented
509	#389	C₂²×C₁₀₉	1	2	yes	complemented
510	#389	C₂²×C₁₀₉	1	4	yes	complemented
511	#388	C₂²×C₁₀₉	1	4	yes	—
512	#388	C₂²×C₁₀₉	1	4	yes	—
513	#388	C₂²×C₁₀₉	1	4	yes	complemented
514	#388	C₂²×C₁₀₉	1	4	yes	complemented
515	#387	C₂²×C₁₀₉	1	4	yes	complemented
516	#387	C₂²×C₁₀₉	1	4	yes	complemented
517	#386	C₂²×C₁₀₉	1	4	yes	—
518	#386	C₂²×C₁₀₉	1	4	yes	—
519	#386	C₂²×C₁₀₉	1	4	yes	—
520	#385	C₂²×C₁₀₉	1	4	yes	—
521	#385	C₂²×C₁₀₉	1	4	yes	—
522	#385	C₂²×C₁₀₉	1	4	yes	complemented
523	#384	C₂²×C₁₀₉	1	2	yes	complemented
524	#382	C₂²×C₁₀₉	1	2	yes	complemented
525	#380	C₂²×C₁₀₉	1	2	yes	—
526	#380	C₂²×C₁₀₉	1	2	yes	—
527	#380	C₂²×C₁₀₉	1	2	yes	—
528	#380	C₂²×C₁₀₉	1	2	yes	—
529	#380	C₂²×C₁₀₉	1	2	yes	complemented
530	#380	C₂²×C₁₀₉	1	2	yes	complemented
531	C₄×C₄⋊C₄	C₂²×C₁₀₉	1	2	yes	complemented
532	C₄×C₄⋊C₄	C₂²×C₁₀₉	1	2	yes	complemented
533	C₄×C₄⋊C₄	C₂²×C₁₀₉	1	2	yes	complemented
534	C₄×C₄⋊C₄	C₂²×C₁₀₉	1	2	yes	complemented
535	C₄×C₄⋊C₄	C₂²×C₁₀₉	1	4	yes	complemented
536	C₄×C₂²⋊C₄	C₂²×C₁₀₉	1	4	yes	—
537	C₄×C₂²⋊C₄	C₂²×C₁₀₉	1	4	yes	—
538	C₄×C₂²⋊C₄	C₂²×C₁₀₉	1	4	yes	complemented
539	C₂×#95	C₂²×C₁₀₉	1	2	yes	—
540	C₂⁵	C₂³×C₁₀₉	1	1	yes	characteristic
541	C₂×#41	—	2	4	no	—
542	C₂×#41	—	2	4	no	—
543	C₂×#41	C₂×C₄×C₁₀₉	1	8	yes	complemented
544	C₂²×Q₈	C₂³×C₁₀₉	1	1	yes	characteristic
545	C₂²×D₄	C₂³×C₁₀₉	1	2	yes	—
546	C₂²×D₄	C₂³×C₁₀₉	1	2	yes	—
547	C₂²×D₄	C₂³×C₁₀₉	1	1	yes	characteristic
548	C₂²×D₄	C₂³×C₁₀₉	1	2	yes	—
549	C₂³×C₄	—	2	4	no	—
550	C₂³×C₄	—	2	4	no	—
551	C₂³×C₄	C₂×C₄×C₁₀₉	1	8	yes	complemented
552	C₂³×C₄	C₂³×C₁₀₉	1	2	yes	—
553	C₂³×C₄	C₂³×C₁₀₉	1	2	yes	—
554	C₂³×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
555	C₂³×C₄	C₂³×C₁₀₉	1	2	yes	—
556	C₂³×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
557	C₂³×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
558	C₂³×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
559	C₂³×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
560	C₂³×C₄	C₂³×C₁₀₉	1	2	yes	—
561	C₂³×C₄	C₂³×C₁₀₉	1	2	yes	—
562	C₂³×C₄	C₂³×C₁₀₉	1	4	yes	—
563	C₂³×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
564	#123	C₂×C₄×C₁₀₉	1	16	yes	complemented
565	C₂²⋊Q₈	C₂×C₄×C₁₀₉	1	8	yes	complemented
566	C₂²⋊Q₈	C₂×C₄×C₁₀₉	1	8	yes	complemented
567	#121	C₂×C₄×C₁₀₉	1	8	yes	complemented
568	#121	C₂×C₄×C₁₀₉	1	8	yes	complemented
569	#120	C₂×C₄×C₁₀₉	1	16	yes	complemented
570	C₄×Q₈	—	2	8	no	—
571	C₄×D₄	—	2	16	no	—
572	C₄×D₄	—	2	8	no	—
573	C₄×D₄	—	4	8	no	—
574	C₄×D₄	C₂×C₄×C₁₀₉	1	16	yes	complemented
575	C₄×D₄	C₂×C₄×C₁₀₉	1	16	yes	complemented
576	#117	—	2	4	no	—
577	#117	—	2	4	no	—
578	#117	—	2	4	no	—
579	#117	—	2	8	no	—
580	#117	—	2	8	no	—
581	#117	—	2	8	no	—
582	#117	C₂×C₄×C₁₀₉	1	8	yes	complemented
583	#117	D₄×C₁₀₉	1	8	yes	complemented
584	C₂×C₄⋊C₄	—	2	4	no	—
585	C₂×C₄⋊C₄	—	2	4	no	—
586	C₂×C₄⋊C₄	—	2	4	no	—
587	C₂×C₄⋊C₄	—	2	4	no	—
588	C₂×C₄⋊C₄	—	2	8	no	—
589	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	2	yes	—
590	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
591	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
592	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	2	yes	—
593	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	2	yes	—
594	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	2	yes	—
595	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	2	yes	—
596	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	2	yes	—
597	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	4	yes	—
598	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	4	yes	—
599	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	4	yes	—
600	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
601	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
602	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	2	yes	—
603	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	2	yes	—
604	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
605	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
606	C₂×C₂²⋊C₄	—	2	8	no	—
607	C₂×C₂²⋊C₄	—	4	4	no	—
608	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
609	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
610	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
611	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	4	yes	—
612	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	4	yes	—
613	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	4	yes	—
614	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	4	yes	—
615	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	4	yes	—
616	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
617	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
618	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
619	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
620	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
621	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
622	C₂×C₄²	—	2	8	no	—
623	C₂×C₄²	C₂³×C₁₀₉	1	2	yes	—
624	C₂×C₄²	C₂³×C₁₀₉	1	2	yes	—
625	C₂×C₄²	C₂³×C₁₀₉	1	2	yes	—
626	C₂×C₄²	C₂³×C₁₀₉	1	4	yes	—
627	C₂×C₄²	C₂³×C₁₀₉	1	4	yes	—
628	C₂×C₄²	C₂³×C₁₀₉	1	4	yes	—
629	C₂×C₄²	C₂³×C₁₀₉	1	2	yes	—
630	C₂×C₄²	C₂³×C₁₀₉	1	2	yes	—
631	#95	C₂³×C₁₀₉	1	4	yes	—
632	#95	C₂³×C₁₀₉	1	4	yes	—
633	#95	C₂³×C₁₀₉	1	4	yes	—
634	#95	C₂³×C₁₀₉	1	4	yes	—
635	#95	C₂³×C₁₀₉	1	4	yes	—
636	#95	C₂³×C₁₀₉	1	4	yes	—
637	#95	C₂³×C₁₀₉	1	4	yes	—
638	#95	C₂³×C₁₀₉	1	4	yes	—
639	C₂⁴	—	2	2	no	—
640	C₂⁴	—	2	2	no	—
641	C₂⁴	—	2	2	no	—
642	C₂⁴	—	2	2	no	—
643	C₂⁴	—	4	1	no	—
644	C₂⁴	—	4	1	no	—
645	C₂⁴	C₂²×C₄×C₁₀₉	1	4	yes	—
646	C₂⁴	C₂⁴×C₁₀₉	1	1	yes	characteristic
647	C₂⁴	C₂⁴×C₁₀₉	1	2	yes	—
648	C₂⁴	C₂⁴×C₁₀₉	1	1	yes	characteristic
649	C₂⁴	C₂⁴×C₁₀₉	1	1	yes	characteristic
650	#41	—	2	32	no	—
651	C₂×Q₈	—	2	2	no	—
652	C₂×Q₈	—	2	2	no	—
653	C₂×Q₈	C₂²×C₄×C₁₀₉	1	4	yes	—
654	C₂×D₄	—	2	4	no	—
655	C₂×D₄	—	2	4	no	—
656	C₂×D₄	—	2	4	no	—
657	C₂×D₄	—	2	4	no	—
658	C₂×D₄	—	2	2	no	—
659	C₂×D₄	—	2	2	no	—
660	C₂×D₄	—	4	2	no	—
661	C₂×D₄	—	4	2	no	—
662	C₂×D₄	C₂²×C₄×C₁₀₉	1	8	yes	—
663	C₂×D₄	C₂²×C₄×C₁₀₉	1	8	yes	—
664	C₂×D₄	C₂²×C₄×C₁₀₉	1	4	yes	—
665	C₂×D₄	C₂²×C₄×C₁₀₉	1	8	yes	—
666	C₂²×C₄	—	2	2	no	—
667	C₂²×C₄	—	2	2	no	—
668	C₂²×C₄	—	2	32	no	—
669	C₂²×C₄	—	2	2	no	—
670	C₂²×C₄	—	2	2	no	—
671	C₂²×C₄	—	2	4	no	—
672	C₂²×C₄	—	2	2	no	—
673	C₂²×C₄	—	2	2	no	—
674	C₂²×C₄	—	2	2	no	—
675	C₂²×C₄	—	2	2	no	—
676	C₂²×C₄	—	2	2	no	—
677	C₂²×C₄	—	2	2	no	—
678	C₂²×C₄	—	2	4	no	—
679	C₂²×C₄	—	2	4	no	—
680	C₂²×C₄	—	2	4	no	—
681	C₂²×C₄	—	2	4	no	—
682	C₂²×C₄	—	2	4	no	—
683	C₂²×C₄	—	2	4	no	—
684	C₂²×C₄	—	2	4	no	—
685	C₂²×C₄	—	2	8	no	—
686	C₂²×C₄	—	4	2	no	—
687	C₂²×C₄	—	4	2	no	—
688	C₂²×C₄	—	4	2	no	—
689	C₂²×C₄	—	4	2	no	—
690	C₂²×C₄	—	4	4	no	—
691	C₂²×C₄	—	4	4	no	—
692	C₂²×C₄	—	4	2	no	—
693	C₂²×C₄	—	4	2	no	—
694	C₂²×C₄	C₂²×C₄×C₁₀₉	1	4	yes	—
695	C₂²×C₄	C₂²×C₄×C₁₀₉	1	4	yes	—
696	C₂²×C₄	C₂²×C₄×C₁₀₉	1	8	yes	—
697	C₂²×C₄	C₂²×C₄×C₁₀₉	1	4	yes	—
698	C₂²×C₄	C₂²×C₄×C₁₀₉	1	4	yes	—
699	C₂²×C₄	C₂²×C₄×C₁₀₉	1	4	yes	—
700	C₂²×C₄	C₂²×C₄×C₁₀₉	1	4	yes	—
701	C₂²×C₄	C₂×D₄×C₁₀₉	1	4	yes	—
702	C₂²×C₄	#41×C₁₀₉	1	4	yes	—
703	C₂²×C₄	C₂⁴×C₁₀₉	1	2	yes	—
704	C₂²×C₄	C₂⁴×C₁₀₉	1	4	yes	—
705	C₂²×C₄	C₂⁴×C₁₀₉	1	4	yes	—
706	C₂²×C₄	C₂⁴×C₁₀₉	1	2	yes	—
707	C₂²×C₄	C₂⁴×C₁₀₉	1	1	yes	characteristic
708	C₂²×C₄	C₂⁴×C₁₀₉	1	2	yes	—
709	C₂²×C₄	C₂⁴×C₁₀₉	1	2	yes	—
710	C₂²×C₄	C₂⁴×C₁₀₉	1	2	yes	—
711	C₂²×C₄	C₂⁴×C₁₀₉	1	1	yes	characteristic
712	C₂²×C₄	C₂⁴×C₁₀₉	1	2	yes	—
713	C₂²×C₄	C₂⁴×C₁₀₉	1	2	yes	—
714	C₂²×C₄	C₂⁴×C₁₀₉	1	1	yes	characteristic
715	C₂²×C₄	C₂⁴×C₁₀₉	1	1	yes	characteristic
716	C₄⋊C₄	—	2	4	no	—
717	C₄⋊C₄	—	2	4	no	—
718	C₄⋊C₄	—	2	4	no	—
719	C₄⋊C₄	—	2	2	no	—
720	C₄⋊C₄	—	2	2	no	—
721	C₄⋊C₄	—	2	8	no	—
722	C₄⋊C₄	—	2	4	no	—
723	C₄⋊C₄	—	2	4	no	—
724	C₄⋊C₄	—	2	4	no	—
725	C₄⋊C₄	—	4	4	no	—
726	C₄⋊C₄	—	4	4	no	—
727	C₄⋊C₄	C₂²×C₄×C₁₀₉	1	4	yes	—
728	C₄⋊C₄	C₂²×C₄×C₁₀₉	1	4	yes	—
729	C₄⋊C₄	C₂²×C₄×C₁₀₉	1	8	yes	—
730	C₄⋊C₄	C₂²×C₄×C₁₀₉	1	8	yes	—
731	C₄⋊C₄	C₂×D₄×C₁₀₉	1	4	yes	—
732	C₄⋊C₄	C₂×D₄×C₁₀₉	1	4	yes	—
733	C₂²⋊C₄	—	2	4	no	—
734	C₂²⋊C₄	—	2	8	no	—
735	C₂²⋊C₄	—	2	4	no	—
736	C₂²⋊C₄	—	2	4	no	—
737	C₂²⋊C₄	—	2	8	no	—
738	C₂²⋊C₄	—	4	4	no	—
739	C₂²⋊C₄	—	4	4	no	—
740	C₂²⋊C₄	—	4	4	no	—
741	C₂²⋊C₄	C₂²×C₄×C₁₀₉	1	8	yes	—
742	C₂²⋊C₄	C₂²×C₄×C₁₀₉	1	8	yes	—
743	C₂²⋊C₄	C₂²×C₄×C₁₀₉	1	8	yes	—
744	C₂²⋊C₄	C₂²×C₄×C₁₀₉	1	8	yes	—
745	C₂²⋊C₄	C₂²×C₄×C₁₀₉	1	8	yes	—
746	C₂²⋊C₄	C₂×D₄×C₁₀₉	1	8	yes	—
747	C₄²	—	2	4	no	—
748	C₄²	—	2	4	no	—
749	C₄²	—	2	4	no	—
750	C₄²	—	2	8	no	—
751	C₄²	—	4	4	no	—
752	C₄²	—	4	4	no	—
753	C₄²	C₂²×C₄×C₁₀₉	1	8	yes	—
754	C₄²	C₂×D₄×C₁₀₉	1	8	yes	—
755	C₂³	—	2	1	no	—
756	C₂³	—	2	1	no	—
757	C₂³	—	2	1	no	—
758	C₂³	—	2	1	no	—
759	C₂³	—	2	1	no	—
760	C₂³	—	2	1	no	—
761	C₂³	—	2	1	no	—
762	C₂³	—	2	1	no	—
763	C₂³	—	2	8	no	—
764	C₂³	—	2	8	no	—
765	C₂³	—	2	1	no	—
766	C₂³	—	2	2	no	—
767	C₂³	—	2	1	no	—
768	C₂³	—	2	2	no	—
769	C₂³	—	2	1	no	—
770	C₂³	—	2	2	no	—
771	C₂³	—	2	2	no	—
772	C₂³	—	2	1	no	—
773	C₂³	—	2	2	no	—
774	C₂³	—	2	2	no	—
775	C₂³	—	2	1	no	—
776	C₂³	—	2	1	no	—
777	C₂³	—	4	4	no	—
778	C₂³	—	4	4	no	—
779	C₂³	—	4	4	no	—
780	C₂³	—	4	4	no	—
781	C₂³	—	4	4	no	—
782	C₂³	C₂³×C₄×C₁₀₉	1	2	yes	—
783	C₂³	C₂³×C₄×C₁₀₉	1	4	yes	—
784	C₂³	C₂³×C₄×C₁₀₉	1	2	yes	—
785	C₂³	C₂³×C₄×C₁₀₉	1	2	yes	—
786	C₂³	C₂²×D₄×C₁₀₉	1	2	yes	—
787	C₂³	C₂×#41×C₁₀₉	1	2	yes	—
788	C₂³	H(5,𝔽₂)×C₁₀₉	1	2	yes	—
789	C₂³	2₋¹⁺⁴×C₁₀₉	1	2	yes	—
790	C₂³	C₂⁵×C₁₀₉	1	1	yes	characteristic
791	Q₈	—	2	8	no	—
792	D₄	—	2	16	no	—
793	D₄	—	2	16	no	—
794	D₄	—	2	8	no	—
795	D₄	—	4	8	no	—
796	C₂×C₄	—	2	8	no	—
797	C₂×C₄	—	2	1	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	1	no	—
800	C₂×C₄	—	2	1	no	—
801	C₂×C₄	—	2	1	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	8	no	—
812	C₂×C₄	—	2	8	no	—
813	C₂×C₄	—	2	8	no	—
814	C₂×C₄	—	2	8	no	—
815	C₂×C₄	—	2	16	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	4	no	—
819	C₂×C₄	—	2	4	no	—
820	C₂×C₄	—	2	4	no	—
821	C₂×C₄	—	2	4	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	4	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	2	4	no	—
828	C₂×C₄	—	4	8	no	—
829	C₂×C₄	—	4	8	no	—
830	C₂×C₄	—	8	8	no	—
831	C₂×C₄	—	8	4	no	—
832	C₂×C₄	—	8	4	no	—
833	C₂×C₄	C₄×D₄×C₁₀₉	1	16	yes	complemented
834	C₂×C₄	C₂³×C₄×C₁₀₉	1	4	yes	—
835	C₂×C₄	C₂³×C₄×C₁₀₉	1	4	yes	—
836	C₂×C₄	C₂³×C₄×C₁₀₉	1	2	yes	—
837	C₂×C₄	C₂³×C₄×C₁₀₉	1	2	yes	—
838	C₂×C₄	C₂³×C₄×C₁₀₉	1	4	yes	—
839	C₂×C₄	C₂³×C₄×C₁₀₉	1	2	yes	—
840	C₂×C₄	C₂³×C₄×C₁₀₉	1	2	yes	—
841	C₂×C₄	C₂²×D₄×C₁₀₉	1	4	yes	—
842	C₂×C₄	C₂²×D₄×C₁₀₉	1	4	yes	—
843	C₂×C₄	C₂²×D₄×C₁₀₉	1	2	yes	—
844	C₂×C₄	C₂²×D₄×C₁₀₉	1	2	yes	—
845	C₂×C₄	C₂×#41×C₁₀₉	1	2	yes	—
846	C₂×C₄	C₂×#41×C₁₀₉	1	2	yes	—
847	C₂²	—	2	2	no	—
848	C₂²	—	2	2	no	—
849	C₂²	—	2	2	no	—
850	C₂²	—	2	2	no	—
851	C₂²	—	2	2	no	—
852	C₂²	—	2	2	no	—
853	C₂²	—	2	2	no	—
854	C₂²	—	2	2	no	—
855	C₂²	—	2	2	no	—
856	C₂²	—	2	2	no	—
857	C₂²	—	2	2	no	—
858	C₂²	—	2	2	no	—
859	C₂²	—	2	2	no	—
860	C₂²	—	2	4	no	—
861	C₂²	—	2	4	no	—
862	C₂²	—	2	2	no	—
863	C₂²	—	2	2	no	—
864	C₂²	—	2	4	no	—
865	C₂²	—	4	16	no	—
866	C₂²	—	4	2	no	—
867	C₂²	—	4	1	no	—
868	C₂²	—	4	1	no	—
869	C₂²	—	4	2	no	—
870	C₂²	—	4	1	no	—
871	C₂²	—	4	2	no	—
872	C₂²	—	4	1	no	—
873	C₂²	—	4	2	no	—
874	C₂²	C₂×C₄×D₄×C₁₀₉	1	4	yes	—
875	C₂²	#520×C₁₀₉	1	4	yes	complemented
876	C₂²	C₂⁴×C₄×C₁₀₉	1	1	yes	characteristic
877	C₂²	C₂³×D₄×C₁₀₉	1	1	yes	characteristic
878	C₂²	C₂²×#41×C₁₀₉	1	1	yes	characteristic
879	C₂²	C₂×H(5,𝔽₂)×C₁₀₉	1	1	yes	characteristic
880	C₂²	C₂×2₋¹⁺⁴×C₁₀₉	1	1	yes	characteristic
881	C₂²	#585×C₁₀₉	1	1	yes	characteristic
882	C₂²	#585×C₁₀₉	1	1	yes	characteristic
883	C₄	—	2	4	no	—
884	C₄	—	2	4	no	—
885	C₄	—	2	2	no	—
886	C₄	—	2	2	no	—
887	C₄	—	2	4	no	—
888	C₄	—	2	4	no	—
889	C₄	—	2	4	no	—
890	C₄	—	4	2	no	—
891	C₄	—	4	4	no	—
892	C₄	—	4	2	no	—
893	C₄	—	4	4	no	—
894	C₄	C₂×C₄×D₄×C₁₀₉	1	4	yes	—
895	C₄	C₂×C₄×D₄×C₁₀₉	1	4	yes	—
896	C₂	—	2	4	no	—
897	C₂	—	2	4	no	—
898	C₂	—	4	2	no	—
899	C₂	—	4	4	no	—
900	C₂	C₂²×C₄×D₄×C₁₀₉	1	1	yes	characteristic
901	C₂	C₂×#520×C₁₀₉	1	1	yes	characteristic
902	C₂	C₁₀₉×#3428	1	1	yes	characteristic
903	C₂	C₁₀₉×#3488	1	1	yes	characteristic
904	C₂	C₁₀₉×#3489	1	1	yes	characteristic
905	C₂	C₁₀₉×#3494	1	1	yes	characteristic
906	C₂	C₁₀₉×#3495	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₀₉	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₀₉
Frattini, cosocle	C₂³	C₂⁵×C₁₀₉
prime radical	C₂×#525×C₁₀₉	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₀₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#520×C₁₀₉	C₂	semidirect
3. C₂²×#117×C₁₀₉	C₂	semidirect
4. C₁₀₉×#2359	C₂	semidirect
5. C₁₀₉×#2358	C₂	semidirect
6. C₁₀₉×#2354	C₂	semidirect
7. C₁₀₉×#2352	C₂	semidirect
8. C₁₀₉×#2352	C₂	semidirect
9. D₄×C₄⋊C₄×C₁₀₉	C₂	semidirect
10. C₁₀₉×#2324	C₂	semidirect
11. C₁₀₉×#2323	C₂	semidirect
12. C₁₀₉×#2317	C₂	semidirect
13. C₁₀₉×#2311	C₂	semidirect
14. C₄×C₂²⋊Q₈×C₁₀₉	C₂	semidirect
15. C₄×#121×C₁₀₉	C₂	semidirect
16. C₂×#380×C₁₀₉	C₂	semidirect
17. C₁₀₉×#2274	C₂	semidirect
20. #525×C₁₀₉	C₄	semidirect
28. C₂×C₄×Q₈×C₁₀₉	C₂²	semidirect
33. C₂×C₄×D₄×C₁₀₉	C₂²	semidirect
42. C₂×#117×C₁₀₉	C₂²	semidirect
47. C₂²×C₄⋊C₄×C₁₀₉	C₂²	semidirect
51. #391×C₁₀₉	C₂²	semidirect
53. #390×C₁₀₉	C₂²	semidirect
54. #389×C₁₀₉	C₂²	semidirect
55. #389×C₁₀₉	C₂²	semidirect
56. #389×C₁₀₉	C₂²	semidirect
59. #388×C₁₀₉	C₂²	semidirect
60. #388×C₁₀₉	C₂²	semidirect
61. #387×C₁₀₉	C₂²	semidirect
62. #387×C₁₀₉	C₂²	semidirect
68. #385×C₁₀₉	C₂²	semidirect
69. #384×C₁₀₉	C₂²	semidirect
70. #382×C₁₀₉	C₂²	semidirect
75. #380×C₁₀₉	C₂²	semidirect
76. #380×C₁₀₉	C₂²	semidirect
77. C₄×C₄⋊C₄×C₁₀₉	C₂²	semidirect
78. C₄×C₄⋊C₄×C₁₀₉	C₂²	semidirect
79. C₄×C₄⋊C₄×C₁₀₉	C₂²	semidirect
80. C₄×C₄⋊C₄×C₁₀₉	C₂²	semidirect
81. C₄×C₄⋊C₄×C₁₀₉	C₂²	semidirect
84. C₄×C₂²⋊C₄×C₁₀₉	C₂²	semidirect
89. C₂×#41×C₁₀₉	C₂×C₄	semidirect
97. C₂³×C₄×C₁₀₉	C₂×C₄	semidirect
110. #123×C₁₀₉	C₂×C₄	semidirect
111. C₂²⋊Q₈×C₁₀₉	C₂×C₄	semidirect
112. C₂²⋊Q₈×C₁₀₉	C₂×C₄	semidirect
113. #121×C₁₀₉	C₂×C₄	semidirect
114. #121×C₁₀₉	C₂×C₄	semidirect
115. #120×C₁₀₉	C₂×C₄	semidirect
120. C₄×D₄×C₁₀₉	C₂×C₄	semidirect
121. C₄×D₄×C₁₀₉	C₂×C₄	semidirect
128. #117×C₁₀₉	C₂×C₄	semidirect
129. #117×C₁₀₉	D₄	semidirect
379. C₂×C₄×C₁₀₉	C₄×D₄	semidirect
421. C₂²×C₁₀₉	#520	semidirect
442. #34202	C₁₀₉	direct (N × H)
455. C₂×#520	C₂×C₁₀₉	semidirect
456. C₂²×#117	C₂×C₁₀₉	semidirect
457. #2359	C₂×C₁₀₉	semidirect
458. #2358	C₂×C₁₀₉	semidirect
459. #2354	C₂×C₁₀₉	semidirect
460. #2352	C₂×C₁₀₉	semidirect
461. #2352	C₂×C₁₀₉	semidirect
462. D₄×C₄⋊C₄	C₂×C₁₀₉	semidirect
463. #2324	C₂×C₁₀₉	semidirect
464. #2323	C₂×C₁₀₉	semidirect
465. #2317	C₂×C₁₀₉	semidirect
466. #2311	C₂×C₁₀₉	semidirect
467. C₄×C₂²⋊Q₈	C₂×C₁₀₉	semidirect
468. C₄×#121	C₂×C₁₀₉	semidirect
469. C₂×#380	C₂×C₁₀₉	semidirect
470. #2274	C₂×C₁₀₉	semidirect
471. C₁₀₉	#34202	direct (N × H)
474. #525	C₄×C₁₀₉	semidirect
482. C₂×C₄×Q₈	C₂²×C₁₀₉	semidirect
487. C₂×C₄×D₄	C₂²×C₁₀₉	semidirect
496. C₂×#117	C₂²×C₁₀₉	semidirect
501. C₂²×C₄⋊C₄	C₂²×C₁₀₉	semidirect
505. #391	C₂²×C₁₀₉	semidirect
507. #390	C₂²×C₁₀₉	semidirect
508. #389	C₂²×C₁₀₉	semidirect
509. #389	C₂²×C₁₀₉	semidirect
510. #389	C₂²×C₁₀₉	semidirect
513. #388	C₂²×C₁₀₉	semidirect
514. #388	C₂²×C₁₀₉	semidirect
515. #387	C₂²×C₁₀₉	semidirect
516. #387	C₂²×C₁₀₉	semidirect
522. #385	C₂²×C₁₀₉	semidirect
523. #384	C₂²×C₁₀₉	semidirect
524. #382	C₂²×C₁₀₉	semidirect
529. #380	C₂²×C₁₀₉	semidirect
530. #380	C₂²×C₁₀₉	semidirect
531. C₄×C₄⋊C₄	C₂²×C₁₀₉	semidirect
532. C₄×C₄⋊C₄	C₂²×C₁₀₉	semidirect
533. C₄×C₄⋊C₄	C₂²×C₁₀₉	semidirect
534. C₄×C₄⋊C₄	C₂²×C₁₀₉	semidirect
535. C₄×C₄⋊C₄	C₂²×C₁₀₉	semidirect
538. C₄×C₂²⋊C₄	C₂²×C₁₀₉	semidirect
543. C₂×#41	C₂×C₄×C₁₀₉	semidirect
551. C₂³×C₄	C₂×C₄×C₁₀₉	semidirect
564. #123	C₂×C₄×C₁₀₉	semidirect
565. C₂²⋊Q₈	C₂×C₄×C₁₀₉	semidirect
566. C₂²⋊Q₈	C₂×C₄×C₁₀₉	semidirect
567. #121	C₂×C₄×C₁₀₉	semidirect
568. #121	C₂×C₄×C₁₀₉	semidirect
569. #120	C₂×C₄×C₁₀₉	semidirect
574. C₄×D₄	C₂×C₄×C₁₀₉	semidirect
575. C₄×D₄	C₂×C₄×C₁₀₉	semidirect
582. #117	C₂×C₄×C₁₀₉	semidirect
583. #117	D₄×C₁₀₉	semidirect
833. C₂×C₄	C₄×D₄×C₁₀₉	semidirect
875. C₂²	#520×C₁₀₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#525×C₁₀₉	2
C₂×#520×C₁₀₉	2
C₂²×#117×C₁₀₉	2
C₁₀₉×#2359	2
C₁₀₉×#2358	2
C₁₀₉×#2354	2
C₁₀₉×#2352	2
D₄×C₄⋊C₄×C₁₀₉	2
C₁₀₉×#2324	2
C₁₀₉×#2323	2
C₁₀₉×#2317	2
C₁₀₉×#2311	2
C₄×C₂²⋊Q₈×C₁₀₉	2
C₄×#121×C₁₀₉	2
C₂×#380×C₁₀₉	2
C₁₀₉×#2274	2
#34202	109

Subgroups — C109×#34202 #42152196

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₉×#34202 #42152196