Subgroups — C₁₀₉×#34813 #42152807

Order 27904.

2646 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#533×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#525×C₁₀₉	C₂	1	1	yes	maximal, characteristic
3	C₁₀₉×#2492	C₂	1	2	yes	maximal, complemented
4	C₁₀₉×#2491	C₂	1	2	yes	maximal, complemented
5	C₁₀₉×#2490	C₂	1	2	yes	maximal, complemented
6	C₁₀₉×#2489	C₂	1	2	yes	maximal, complemented
7	C₁₀₉×#2488	C₂	1	4	yes	maximal, complemented
8	C₁₀₉×#2472	C₂	1	4	yes	maximal, complemented
9	C₁₀₉×#2398	C₂	1	4	yes	maximal, complemented
10	C₄×#124×C₁₀₉	C₂	1	4	yes	maximal, complemented
11	C₁₀₉×#2297	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₀₉×#2297	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₀₉×#2280	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×#117×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₄×C₂²⋊C₄×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₁₀₉	C₂²	1	1	yes	characteristic
17	C₂⁴×C₄×C₁₀₉	C₂²	1	1	yes	characteristic
18	#533×C₁₀₉	—	2	8	no	—
19	C₂×C₄⋊Q₈×C₁₀₉	C₂²	1	2	yes	complemented
20	C₂×#125×C₁₀₉	C₂²	1	2	yes	complemented
21	C₂×#124×C₁₀₉	C₂²	1	4	yes	—
22	#525×C₁₀₉	—	2	8	no	—
23	C₂×#123×C₁₀₉	C₂²	1	2	yes	—
24	C₂×C₂²⋊Q₈×C₁₀₉	C₂²	1	4	yes	—
25	C₂×C₂²⋊Q₈×C₁₀₉	C₂²	1	2	yes	—
26	C₂×#121×C₁₀₉	C₂²	1	2	yes	—
27	C₂×#120×C₁₀₉	C₂²	1	2	yes	—
28	C₂×C₄×Q₈×C₁₀₉	C₂²	1	4	yes	complemented
29	C₂×C₄×D₄×C₁₀₉	C₂²	1	4	yes	—
30	C₂×#117×C₁₀₉	C₂²	1	1	yes	characteristic
31	C₂×#117×C₁₀₉	C₂²	1	1	yes	characteristic
32	C₂×#117×C₁₀₉	C₂²	1	1	yes	characteristic
33	C₂²×C₂²⋊C₄×C₁₀₉	C₂²	1	2	yes	—
34	C₂²×C₄²×C₁₀₉	C₂²	1	1	yes	characteristic
35	C₂²×C₄²×C₁₀₉	C₂²	1	1	yes	characteristic
36	#400×C₁₀₉	C₂²	1	4	yes	complemented
37	#400×C₁₀₉	C₂²	1	4	yes	complemented
38	#397×C₁₀₉	C₂²	1	4	yes	—
39	#397×C₁₀₉	C₂²	1	4	yes	complemented
40	#394×C₁₀₉	C₂²	1	4	yes	—
41	#394×C₁₀₉	C₂²	1	4	yes	—
42	#393×C₁₀₉	C₂²	1	4	yes	—
43	#393×C₁₀₉	C₂²	1	4	yes	complemented
44	#391×C₁₀₉	C₂²	1	4	yes	complemented
45	#391×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
46	#391×C₁₀₉	C₂²	1	2	yes	complemented
47	#391×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
48	#390×C₁₀₉	C₂²	1	4	yes	—
49	#390×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
50	#390×C₁₀₉	C₂²	1	2	yes	complemented
51	#390×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
52	#388×C₁₀₉	C₂²	1	4	yes	—
53	#388×C₁₀₉	C₂²	1	4	yes	—
54	#388×C₁₀₉	C₂²	1	4	yes	complemented
55	#388×C₁₀₉	C₂²	1	4	yes	complemented
56	#386×C₁₀₉	C₂²	1	4	yes	—
57	#386×C₁₀₉	C₂²	1	4	yes	—
58	#382×C₁₀₉	C₂²	1	4	yes	complemented
59	#381×C₁₀₉	C₂²	1	2	yes	—
60	#380×C₁₀₉	C₂²	1	2	yes	—
61	#380×C₁₀₉	C₂²	1	2	yes	—
62	#379×C₁₀₉	C₂²	1	2	yes	—
63	C₄×C₄⋊C₄×C₁₀₉	C₂²	1	2	yes	complemented
64	C₄×C₄⋊C₄×C₁₀₉	C₂²	1	2	yes	complemented
65	C₄×C₂²⋊C₄×C₁₀₉	C₂²	1	4	yes	—
66	C₄×C₂²⋊C₄×C₁₀₉	C₂²	1	2	yes	—
67	C₄×C₂²⋊C₄×C₁₀₉	C₂²	1	2	yes	—
68	C₄×C₂²⋊C₄×C₁₀₉	C₂²	1	2	yes	—
69	C₄×C₂²⋊C₄×C₁₀₉	C₂²	1	2	yes	—
70	C₄×C₂²⋊C₄×C₁₀₉	C₂²	1	4	yes	—
71	C₄×C₂²⋊C₄×C₁₀₉	C₂²	1	2	yes	complemented
72	C₄×C₂²⋊C₄×C₁₀₉	C₂²	1	4	yes	complemented
73	C₄×C₂²⋊C₄×C₁₀₉	C₂²	1	2	yes	complemented
74	#376×C₁₀₉	C₂²	1	2	yes	complemented
75	C₂×#95×C₁₀₉	C₂²	1	2	yes	—
76	C₄³×C₁₀₉	C₂²	1	2	yes	complemented
77	C₂⁵×C₁₀₉	C₂³	1	1	yes	characteristic
78	C₂×#41×C₁₀₉	—	2	4	no	—
79	C₂×#41×C₁₀₉	—	2	4	no	—
80	C₂×#41×C₁₀₉	—	2	4	no	—
81	C₂²×Q₈×C₁₀₉	C₂³	1	1	yes	characteristic
82	C₂²×Q₈×C₁₀₉	C₂³	1	4	yes	—
83	C₂²×D₄×C₁₀₉	C₂³	1	2	yes	—
84	C₂²×D₄×C₁₀₉	C₂³	1	1	yes	characteristic
85	C₂²×D₄×C₁₀₉	C₂³	1	4	yes	—
86	C₂³×C₄×C₁₀₉	—	2	4	no	—
87	C₂³×C₄×C₁₀₉	—	2	4	no	—
88	C₂³×C₄×C₁₀₉	—	2	4	no	—
89	C₂³×C₄×C₁₀₉	C₂³	1	2	yes	—
90	C₂³×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₁₀₉	C₂³	1	2	yes	—
92	C₂³×C₄×C₁₀₉	C₂³	1	2	yes	—
93	C₂³×C₄×C₁₀₉	C₂³	1	2	yes	—
94	C₂³×C₄×C₁₀₉	C₂³	1	2	yes	—
95	C₂³×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
96	C₄⋊Q₈×C₁₀₉	—	2	8	no	—
97	#125×C₁₀₉	—	2	8	no	—
98	#124×C₁₀₉	—	2	16	no	—
99	#123×C₁₀₉	—	2	8	no	—
100	C₂²⋊Q₈×C₁₀₉	—	2	8	no	—
101	C₂²⋊Q₈×C₁₀₉	—	2	16	no	—
102	#121×C₁₀₉	—	2	8	no	—
103	#120×C₁₀₉	—	2	8	no	—
104	C₄×Q₈×C₁₀₉	—	2	16	no	—
105	C₄×D₄×C₁₀₉	—	2	16	no	—
106	#117×C₁₀₉	—	2	4	no	—
107	#117×C₁₀₉	—	2	4	no	—
108	#117×C₁₀₉	D₄	1	8	yes	—
109	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
110	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
111	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
112	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	4	yes	—
113	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	4	yes	—
114	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	4	yes	—
115	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	4	yes	—
116	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
117	C₂×C₂²⋊C₄×C₁₀₉	—	2	8	no	—
118	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
119	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
120	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
121	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
122	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
123	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	4	yes	—
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	4	yes	—
128	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	4	yes	—
129	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	4	yes	—
130	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	4	yes	—
131	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
132	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
133	C₂×C₄²×C₁₀₉	—	2	4	no	—
134	C₂×C₄²×C₁₀₉	—	2	4	no	—
135	C₂×C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
136	C₂×C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
137	C₂×C₄²×C₁₀₉	C₂³	1	2	yes	—
138	C₂×C₄²×C₁₀₉	C₂³	1	4	yes	—
139	C₂×C₄²×C₁₀₉	C₂³	1	2	yes	—
140	C₂×C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
141	C₂×C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
142	C₂×C₄²×C₁₀₉	C₂³	1	2	yes	—
143	C₂×C₄²×C₁₀₉	C₂³	1	2	yes	—
144	C₂×C₄²×C₁₀₉	C₂³	1	4	yes	—
145	C₂×C₄²×C₁₀₉	C₂³	1	2	yes	—
146	#95×C₁₀₉	C₂³	1	2	yes	—
147	#95×C₁₀₉	C₂³	1	2	yes	—
148	#95×C₁₀₉	C₂³	1	2	yes	—
149	#95×C₁₀₉	C₂³	1	2	yes	—
150	#95×C₁₀₉	C₂³	1	4	yes	—
151	#95×C₁₀₉	C₂³	1	4	yes	—
152	#95×C₁₀₉	C₂³	1	4	yes	—
153	#95×C₁₀₉	C₂³	1	4	yes	—
154	#95×C₁₀₉	C₂³	1	4	yes	—
155	#95×C₁₀₉	C₂³	1	4	yes	—
156	#95×C₁₀₉	C₂³	1	4	yes	—
157	#95×C₁₀₉	C₂³	1	4	yes	—
158	C₂⁴×C₁₀₉	—	2	4	no	—
159	C₂⁴×C₁₀₉	—	2	2	no	—
160	C₂⁴×C₁₀₉	—	2	2	no	—
161	C₂⁴×C₁₀₉	—	2	2	no	—
162	C₂⁴×C₁₀₉	—	4	2	no	—
163	C₂⁴×C₁₀₉	C₂⁴	1	2	yes	—
164	C₂⁴×C₁₀₉	C₂⁴	1	2	yes	—
165	C₂⁴×C₁₀₉	C₂⁴	1	1	yes	characteristic
166	#41×C₁₀₉	—	4	16	no	—
167	C₂×Q₈×C₁₀₉	—	2	8	no	—
168	C₂×Q₈×C₁₀₉	—	2	2	no	—
169	C₂×Q₈×C₁₀₉	—	2	8	no	—
170	C₂×Q₈×C₁₀₉	—	2	2	no	—
171	C₂×Q₈×C₁₀₉	—	2	2	no	—
172	C₂×Q₈×C₁₀₉	—	4	4	no	—
173	C₂×D₄×C₁₀₉	—	2	4	no	—
174	C₂×D₄×C₁₀₉	—	2	8	no	—
175	C₂×D₄×C₁₀₉	—	2	4	no	—
176	C₂×D₄×C₁₀₉	—	2	4	no	—
177	C₂×D₄×C₁₀₉	—	2	8	no	—
178	C₂×D₄×C₁₀₉	—	2	2	no	—
179	C₂×D₄×C₁₀₉	—	2	2	no	—
180	C₂×D₄×C₁₀₉	—	2	2	no	—
181	C₂×D₄×C₁₀₉	—	4	4	no	—
182	C₂²×C₄×C₁₀₉	—	2	4	no	—
183	C₂²×C₄×C₁₀₉	—	2	2	no	—
184	C₂²×C₄×C₁₀₉	—	2	4	no	—
185	C₂²×C₄×C₁₀₉	—	2	2	no	—
186	C₂²×C₄×C₁₀₉	—	2	2	no	—
187	C₂²×C₄×C₁₀₉	—	2	4	no	—
188	C₂²×C₄×C₁₀₉	—	2	4	no	—
189	C₂²×C₄×C₁₀₉	—	2	4	no	—
190	C₂²×C₄×C₁₀₉	—	2	4	no	—
191	C₂²×C₄×C₁₀₉	—	2	4	no	—
192	C₂²×C₄×C₁₀₉	—	2	4	no	—
193	C₂²×C₄×C₁₀₉	—	2	4	no	—
194	C₂²×C₄×C₁₀₉	—	2	4	no	—
195	C₂²×C₄×C₁₀₉	—	2	4	no	—
196	C₂²×C₄×C₁₀₉	—	2	4	no	—
197	C₂²×C₄×C₁₀₉	—	2	4	no	—
198	C₂²×C₄×C₁₀₉	—	4	2	no	—
199	C₂²×C₄×C₁₀₉	—	4	2	no	—
200	C₂²×C₄×C₁₀₉	—	4	16	no	—
201	C₂²×C₄×C₁₀₉	C₂×D₄	1	4	yes	—
202	C₂²×C₄×C₁₀₉	#41	1	4	yes	—
203	C₂²×C₄×C₁₀₉	#41	1	4	yes	—
204	C₂²×C₄×C₁₀₉	C₂⁴	1	2	yes	—
205	C₂²×C₄×C₁₀₉	C₂⁴	1	2	yes	—
206	C₂²×C₄×C₁₀₉	C₂⁴	1	2	yes	—
207	C₂²×C₄×C₁₀₉	C₂⁴	1	2	yes	—
208	C₂²×C₄×C₁₀₉	C₂⁴	1	2	yes	—
209	C₂²×C₄×C₁₀₉	C₂⁴	1	2	yes	—
210	C₂²×C₄×C₁₀₉	C₂⁴	1	4	yes	—
211	C₂²×C₄×C₁₀₉	C₂⁴	1	4	yes	—
212	C₂²×C₄×C₁₀₉	C₂⁴	1	2	yes	—
213	C₂²×C₄×C₁₀₉	C₂⁴	1	2	yes	—
214	C₂²×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
215	C₂²×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
216	C₄⋊C₄×C₁₀₉	—	2	4	no	—
217	C₄⋊C₄×C₁₀₉	—	2	8	no	—
218	C₄⋊C₄×C₁₀₉	—	2	8	no	—
219	C₄⋊C₄×C₁₀₉	—	2	8	no	—
220	C₄⋊C₄×C₁₀₉	—	2	8	no	—
221	C₄⋊C₄×C₁₀₉	—	2	2	no	—
222	C₄⋊C₄×C₁₀₉	—	2	2	no	—
223	C₄⋊C₄×C₁₀₉	C₂×D₄	1	8	yes	—
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	8	no	—
228	C₂²⋊C₄×C₁₀₉	—	2	8	no	—
229	C₂²⋊C₄×C₁₀₉	—	2	8	no	—
230	C₂²⋊C₄×C₁₀₉	—	2	4	no	—
231	C₂²⋊C₄×C₁₀₉	—	2	4	no	—
232	C₂²⋊C₄×C₁₀₉	—	2	8	no	—
233	C₂²⋊C₄×C₁₀₉	—	2	8	no	—
234	C₂²⋊C₄×C₁₀₉	—	4	4	no	—
235	C₂²⋊C₄×C₁₀₉	—	4	4	no	—
236	C₂²⋊C₄×C₁₀₉	—	4	4	no	—
237	C₂²⋊C₄×C₁₀₉	C₂×D₄	1	8	yes	—
238	C₂²⋊C₄×C₁₀₉	#41	1	8	yes	complemented
239	C₄²×C₁₀₉	—	2	4	no	—
240	C₄²×C₁₀₉	—	2	2	no	—
241	C₄²×C₁₀₉	—	2	2	no	—
242	C₄²×C₁₀₉	—	2	4	no	—
243	C₄²×C₁₀₉	—	2	2	no	—
244	C₄²×C₁₀₉	—	2	4	no	—
245	C₄²×C₁₀₉	—	2	2	no	—
246	C₄²×C₁₀₉	—	2	4	no	—
247	C₄²×C₁₀₉	—	2	8	no	—
248	C₄²×C₁₀₉	—	4	4	no	—
249	C₄²×C₁₀₉	C₂×D₄	1	8	yes	—
250	C₂³×C₁₀₉	—	2	2	no	—
251	C₂³×C₁₀₉	—	2	2	no	—
252	C₂³×C₁₀₉	—	2	8	no	—
253	C₂³×C₁₀₉	—	2	2	no	—
254	C₂³×C₁₀₉	—	2	2	no	—
255	C₂³×C₁₀₉	—	2	2	no	—
256	C₂³×C₁₀₉	—	2	2	no	—
257	C₂³×C₁₀₉	—	2	2	no	—
258	C₂³×C₁₀₉	—	2	2	no	—
259	C₂³×C₁₀₉	—	2	2	no	—
260	C₂³×C₁₀₉	—	2	4	no	—
261	C₂³×C₁₀₉	—	2	2	no	—
262	C₂³×C₁₀₉	—	2	2	no	—
263	C₂³×C₁₀₉	—	2	4	no	—
264	C₂³×C₁₀₉	—	4	8	no	—
265	C₂³×C₁₀₉	—	4	8	no	—
266	C₂³×C₁₀₉	—	4	4	no	—
267	C₂³×C₁₀₉	—	4	4	no	—
268	C₂³×C₁₀₉	C₂²×D₄	1	2	yes	—
269	C₂³×C₁₀₉	C₂×#41	1	4	yes	—
270	C₂³×C₁₀₉	C₂×#41	1	2	yes	—
271	C₂³×C₁₀₉	C₂×#41	1	2	yes	—
272	C₂³×C₁₀₉	C₂⁵	1	1	yes	characteristic
273	Q₈×C₁₀₉	—	4	16	no	—
274	Q₈×C₁₀₉	—	4	4	no	—
275	D₄×C₁₀₉	—	4	16	no	—
276	D₄×C₁₀₉	—	4	8	no	—
277	D₄×C₁₀₉	—	4	4	no	—
278	C₂×C₄×C₁₀₉	—	2	2	no	—
279	C₂×C₄×C₁₀₉	—	2	2	no	—
280	C₂×C₄×C₁₀₉	—	2	4	no	—
281	C₂×C₄×C₁₀₉	—	2	2	no	—
282	C₂×C₄×C₁₀₉	—	2	4	no	—
283	C₂×C₄×C₁₀₉	—	2	2	no	—
284	C₂×C₄×C₁₀₉	—	2	2	no	—
285	C₂×C₄×C₁₀₉	—	2	4	no	—
286	C₂×C₄×C₁₀₉	—	2	2	no	—
287	C₂×C₄×C₁₀₉	—	2	2	no	—
288	C₂×C₄×C₁₀₉	—	2	2	no	—
289	C₂×C₄×C₁₀₉	—	2	4	no	—
290	C₂×C₄×C₁₀₉	—	2	2	no	—
291	C₂×C₄×C₁₀₉	—	2	2	no	—
292	C₂×C₄×C₁₀₉	—	2	2	no	—
293	C₂×C₄×C₁₀₉	—	2	2	no	—
294	C₂×C₄×C₁₀₉	—	2	4	no	—
295	C₂×C₄×C₁₀₉	—	2	2	no	—
296	C₂×C₄×C₁₀₉	—	2	2	no	—
297	C₂×C₄×C₁₀₉	—	2	2	no	—
298	C₂×C₄×C₁₀₉	—	2	2	no	—
299	C₂×C₄×C₁₀₉	—	2	4	no	—
300	C₂×C₄×C₁₀₉	—	2	2	no	—
301	C₂×C₄×C₁₀₉	—	2	2	no	—
302	C₂×C₄×C₁₀₉	—	2	4	no	—
303	C₂×C₄×C₁₀₉	—	4	8	no	—
304	C₂×C₄×C₁₀₉	—	4	8	no	—
305	C₂×C₄×C₁₀₉	—	4	4	no	—
306	C₂×C₄×C₁₀₉	—	4	8	no	—
307	C₂×C₄×C₁₀₉	—	4	8	no	—
308	C₂×C₄×C₁₀₉	—	4	8	no	—
309	C₂×C₄×C₁₀₉	#124	1	16	yes	complemented
310	C₂×C₄×C₁₀₉	C₂²×D₄	1	8	yes	—
311	C₂×C₄×C₁₀₉	C₂²×D₄	1	2	yes	—
312	C₂×C₄×C₁₀₉	C₂²×D₄	1	2	yes	—
313	C₂×C₄×C₁₀₉	C₂×#41	1	4	yes	—
314	C₂×C₄×C₁₀₉	C₂×#41	1	4	yes	—
315	C₂×C₄×C₁₀₉	C₂×#41	1	2	yes	—
316	C₂×C₄×C₁₀₉	C₂×#41	1	2	yes	—
317	C₂×C₄×C₁₀₉	C₂×#41	1	2	yes	—
318	C₂×C₄×C₁₀₉	C₂×#41	1	2	yes	—
319	C₂²×C₁₀₉	—	2	2	no	—
320	C₂²×C₁₀₉	—	2	2	no	—
321	C₂²×C₁₀₉	—	2	4	no	—
322	C₂²×C₁₀₉	—	2	4	no	—
323	C₂²×C₁₀₉	—	2	4	no	—
324	C₂²×C₁₀₉	—	2	4	no	—
325	C₂²×C₁₀₉	—	2	4	no	—
326	C₂²×C₁₀₉	—	4	16	no	—
327	C₂²×C₁₀₉	—	4	2	no	—
328	C₂²×C₁₀₉	—	4	2	no	—
329	C₂²×C₁₀₉	—	4	2	no	—
330	C₂²×C₁₀₉	—	4	2	no	—
331	C₂²×C₁₀₉	—	4	2	no	—
332	C₂²×C₁₀₉	—	4	2	no	—
333	C₂²×C₁₀₉	—	4	2	no	—
334	C₂²×C₁₀₉	—	4	4	no	—
335	C₂²×C₁₀₉	—	4	4	no	—
336	C₂²×C₁₀₉	C₂×#124	1	4	yes	—
337	C₂²×C₁₀₉	C₂³×D₄	1	1	yes	characteristic
338	C₂²×C₁₀₉	C₂²×#41	1	1	yes	characteristic
339	C₂²×C₁₀₉	C₂²×#41	1	1	yes	characteristic
340	C₂²×C₁₀₉	C₂²×#41	1	2	yes	—
341	C₂²×C₁₀₉	#585	1	2	yes	—
342	C₄×C₁₀₉	—	2	4	no	—
343	C₄×C₁₀₉	—	2	8	no	—
344	C₄×C₁₀₉	—	2	4	no	—
345	C₄×C₁₀₉	—	4	2	no	—
346	C₄×C₁₀₉	—	4	2	no	—
347	C₄×C₁₀₉	—	4	2	no	—
348	C₄×C₁₀₉	—	4	2	no	—
349	C₄×C₁₀₉	—	4	2	no	—
350	C₄×C₁₀₉	—	4	4	no	—
351	C₄×C₁₀₉	—	4	2	no	—
352	C₄×C₁₀₉	C₂×#124	1	4	yes	—
353	C₄×C₁₀₉	C₂×#124	1	4	yes	—
354	#34813	C₁₀₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
355	C₂×C₁₀₉	—	2	4	no	—
356	C₂×C₁₀₉	—	4	4	no	—
357	C₂×C₁₀₉	—	8	2	no	—
358	C₂×C₁₀₉	C₂²×#124	1	1	yes	characteristic
359	C₂×C₁₀₉	#3444	1	1	yes	characteristic
360	C₂×C₁₀₉	#3455	1	1	yes	characteristic
361	C₂×C₁₀₉	D₄×#41	1	2	yes	—
362	C₂×C₁₀₉	#3475	1	2	yes	—
363	C₂×#533	C₂×C₁₀₉	1	1	yes	characteristic, complemented
364	C₂×#525	C₂×C₁₀₉	1	1	yes	characteristic
365	#2492	C₂×C₁₀₉	1	2	yes	complemented
366	#2491	C₂×C₁₀₉	1	2	yes	complemented
367	#2490	C₂×C₁₀₉	1	2	yes	complemented
368	#2489	C₂×C₁₀₉	1	2	yes	complemented
369	#2488	C₂×C₁₀₉	1	4	yes	complemented
370	#2472	C₂×C₁₀₉	1	4	yes	complemented
371	#2398	C₂×C₁₀₉	1	4	yes	complemented
372	C₄×#124	C₂×C₁₀₉	1	4	yes	complemented
373	#2297	C₂×C₁₀₉	1	1	yes	characteristic, complemented
374	#2297	C₂×C₁₀₉	1	1	yes	characteristic, complemented
375	#2280	C₂×C₁₀₉	1	1	yes	characteristic, complemented
376	C₄×#117	C₂×C₁₀₉	1	1	yes	characteristic, complemented
377	C₂×C₄×C₂²⋊C₄	C₂×C₁₀₉	1	1	yes	characteristic, complemented
378	C₁₀₉	#34813	1	1	yes	characteristic, direct product factor, Sylow
379	C₂²×#41	C₂²×C₁₀₉	1	1	yes	characteristic
380	C₂⁴×C₄	C₂²×C₁₀₉	1	1	yes	characteristic
381	#533	—	2	8	no	—
382	C₂×C₄⋊Q₈	C₂²×C₁₀₉	1	2	yes	complemented
383	C₂×#125	C₂²×C₁₀₉	1	2	yes	complemented
384	C₂×#124	C₂²×C₁₀₉	1	4	yes	—
385	#525	—	2	8	no	—
386	C₂×#123	C₂²×C₁₀₉	1	2	yes	—
387	C₂×C₂²⋊Q₈	C₂²×C₁₀₉	1	2	yes	—
388	C₂×C₂²⋊Q₈	C₂²×C₁₀₉	1	4	yes	—
389	C₂×#121	C₂²×C₁₀₉	1	2	yes	—
390	C₂×#120	C₂²×C₁₀₉	1	2	yes	—
391	C₂×C₄×Q₈	C₂²×C₁₀₉	1	4	yes	complemented
392	C₂×C₄×D₄	C₂²×C₁₀₉	1	4	yes	—
393	C₂×#117	C₂²×C₁₀₉	1	1	yes	characteristic
394	C₂×#117	C₂²×C₁₀₉	1	1	yes	characteristic
395	C₂×#117	C₂²×C₁₀₉	1	1	yes	characteristic
396	C₂²×C₂²⋊C₄	C₂²×C₁₀₉	1	2	yes	—
397	C₂²×C₄²	C₂²×C₁₀₉	1	1	yes	characteristic
398	C₂²×C₄²	C₂²×C₁₀₉	1	1	yes	characteristic
399	#400	C₂²×C₁₀₉	1	4	yes	complemented
400	#400	C₂²×C₁₀₉	1	4	yes	complemented
401	#397	C₂²×C₁₀₉	1	4	yes	—
402	#397	C₂²×C₁₀₉	1	4	yes	complemented
403	#394	C₂²×C₁₀₉	1	4	yes	—
404	#394	C₂²×C₁₀₉	1	4	yes	—
405	#393	C₂²×C₁₀₉	1	4	yes	—
406	#393	C₂²×C₁₀₉	1	4	yes	complemented
407	#391	C₂²×C₁₀₉	1	4	yes	complemented
408	#391	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
409	#391	C₂²×C₁₀₉	1	2	yes	complemented
410	#391	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
411	#390	C₂²×C₁₀₉	1	4	yes	—
412	#390	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
413	#390	C₂²×C₁₀₉	1	2	yes	complemented
414	#390	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
415	#388	C₂²×C₁₀₉	1	4	yes	—
416	#388	C₂²×C₁₀₉	1	4	yes	—
417	#388	C₂²×C₁₀₉	1	4	yes	complemented
418	#388	C₂²×C₁₀₉	1	4	yes	complemented
419	#386	C₂²×C₁₀₉	1	4	yes	—
420	#386	C₂²×C₁₀₉	1	4	yes	—
421	#382	C₂²×C₁₀₉	1	4	yes	complemented
422	#381	C₂²×C₁₀₉	1	2	yes	—
423	#380	C₂²×C₁₀₉	1	2	yes	—
424	#380	C₂²×C₁₀₉	1	2	yes	—
425	#379	C₂²×C₁₀₉	1	2	yes	—
426	C₄×C₄⋊C₄	C₂²×C₁₀₉	1	2	yes	complemented
427	C₄×C₄⋊C₄	C₂²×C₁₀₉	1	2	yes	complemented
428	C₄×C₂²⋊C₄	C₂²×C₁₀₉	1	2	yes	—
429	C₄×C₂²⋊C₄	C₂²×C₁₀₉	1	4	yes	—
430	C₄×C₂²⋊C₄	C₂²×C₁₀₉	1	4	yes	—
431	C₄×C₂²⋊C₄	C₂²×C₁₀₉	1	2	yes	—
432	C₄×C₂²⋊C₄	C₂²×C₁₀₉	1	2	yes	—
433	C₄×C₂²⋊C₄	C₂²×C₁₀₉	1	2	yes	—
434	C₄×C₂²⋊C₄	C₂²×C₁₀₉	1	2	yes	complemented
435	C₄×C₂²⋊C₄	C₂²×C₁₀₉	1	4	yes	complemented
436	C₄×C₂²⋊C₄	C₂²×C₁₀₉	1	2	yes	complemented
437	#376	C₂²×C₁₀₉	1	2	yes	complemented
438	C₂×#95	C₂²×C₁₀₉	1	2	yes	—
439	C₄³	C₂²×C₁₀₉	1	2	yes	complemented
440	C₂⁵	C₂³×C₁₀₉	1	1	yes	characteristic
441	C₂×#41	—	2	4	no	—
442	C₂×#41	—	2	4	no	—
443	C₂×#41	—	2	4	no	—
444	C₂²×Q₈	C₂³×C₁₀₉	1	1	yes	characteristic
445	C₂²×Q₈	C₂³×C₁₀₉	1	4	yes	—
446	C₂²×D₄	C₂³×C₁₀₉	1	2	yes	—
447	C₂²×D₄	C₂³×C₁₀₉	1	1	yes	characteristic
448	C₂²×D₄	C₂³×C₁₀₉	1	4	yes	—
449	C₂³×C₄	—	2	4	no	—
450	C₂³×C₄	—	2	4	no	—
451	C₂³×C₄	—	2	4	no	—
452	C₂³×C₄	C₂³×C₁₀₉	1	2	yes	—
453	C₂³×C₄	C₂³×C₁₀₉	1	2	yes	—
454	C₂³×C₄	C₂³×C₁₀₉	1	2	yes	—
455	C₂³×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
456	C₂³×C₄	C₂³×C₁₀₉	1	2	yes	—
457	C₂³×C₄	C₂³×C₁₀₉	1	2	yes	—
458	C₂³×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
459	C₄⋊Q₈	—	2	8	no	—
460	#125	—	2	8	no	—
461	#124	—	2	16	no	—
462	#123	—	2	8	no	—
463	C₂²⋊Q₈	—	2	8	no	—
464	C₂²⋊Q₈	—	2	16	no	—
465	#121	—	2	8	no	—
466	#120	—	2	8	no	—
467	C₄×Q₈	—	2	16	no	—
468	C₄×D₄	—	2	16	no	—
469	#117	—	2	4	no	—
470	#117	—	2	4	no	—
471	#117	D₄×C₁₀₉	1	8	yes	—
472	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	2	yes	—
473	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
474	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
475	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	4	yes	—
476	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	4	yes	—
477	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	4	yes	—
478	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	4	yes	—
479	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	2	yes	—
480	C₂×C₂²⋊C₄	—	2	8	no	—
481	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
482	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
483	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
484	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
485	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
486	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	4	yes	—
487	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	4	yes	—
488	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	4	yes	—
489	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	4	yes	—
490	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	4	yes	—
491	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	4	yes	—
492	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	4	yes	—
493	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	4	yes	—
494	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
495	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
496	C₂×C₄²	—	2	4	no	—
497	C₂×C₄²	—	2	4	no	—
498	C₂×C₄²	C₂³×C₁₀₉	1	2	yes	—
499	C₂×C₄²	C₂³×C₁₀₉	1	2	yes	—
500	C₂×C₄²	C₂³×C₁₀₉	1	2	yes	—
501	C₂×C₄²	C₂³×C₁₀₉	1	4	yes	—
502	C₂×C₄²	C₂³×C₁₀₉	1	1	yes	characteristic
503	C₂×C₄²	C₂³×C₁₀₉	1	1	yes	characteristic
504	C₂×C₄²	C₂³×C₁₀₉	1	1	yes	characteristic
505	C₂×C₄²	C₂³×C₁₀₉	1	1	yes	characteristic
506	C₂×C₄²	C₂³×C₁₀₉	1	2	yes	—
507	C₂×C₄²	C₂³×C₁₀₉	1	4	yes	—
508	C₂×C₄²	C₂³×C₁₀₉	1	2	yes	—
509	#95	C₂³×C₁₀₉	1	2	yes	—
510	#95	C₂³×C₁₀₉	1	2	yes	—
511	#95	C₂³×C₁₀₉	1	2	yes	—
512	#95	C₂³×C₁₀₉	1	2	yes	—
513	#95	C₂³×C₁₀₉	1	4	yes	—
514	#95	C₂³×C₁₀₉	1	4	yes	—
515	#95	C₂³×C₁₀₉	1	4	yes	—
516	#95	C₂³×C₁₀₉	1	4	yes	—
517	#95	C₂³×C₁₀₉	1	4	yes	—
518	#95	C₂³×C₁₀₉	1	4	yes	—
519	#95	C₂³×C₁₀₉	1	4	yes	—
520	#95	C₂³×C₁₀₉	1	4	yes	—
521	C₂⁴	—	2	4	no	—
522	C₂⁴	—	2	2	no	—
523	C₂⁴	—	2	2	no	—
524	C₂⁴	—	2	2	no	—
525	C₂⁴	—	4	2	no	—
526	C₂⁴	C₂⁴×C₁₀₉	1	2	yes	—
527	C₂⁴	C₂⁴×C₁₀₉	1	2	yes	—
528	C₂⁴	C₂⁴×C₁₀₉	1	1	yes	characteristic
529	#41	—	4	16	no	—
530	C₂×Q₈	—	2	8	no	—
531	C₂×Q₈	—	2	2	no	—
532	C₂×Q₈	—	2	8	no	—
533	C₂×Q₈	—	2	2	no	—
534	C₂×Q₈	—	2	2	no	—
535	C₂×Q₈	—	4	4	no	—
536	C₂×D₄	—	2	4	no	—
537	C₂×D₄	—	2	8	no	—
538	C₂×D₄	—	2	4	no	—
539	C₂×D₄	—	2	4	no	—
540	C₂×D₄	—	2	8	no	—
541	C₂×D₄	—	2	2	no	—
542	C₂×D₄	—	2	2	no	—
543	C₂×D₄	—	2	2	no	—
544	C₂×D₄	—	4	4	no	—
545	C₂²×C₄	—	2	4	no	—
546	C₂²×C₄	—	2	2	no	—
547	C₂²×C₄	—	2	4	no	—
548	C₂²×C₄	—	2	2	no	—
549	C₂²×C₄	—	2	2	no	—
550	C₂²×C₄	—	2	4	no	—
551	C₂²×C₄	—	2	4	no	—
552	C₂²×C₄	—	2	4	no	—
553	C₂²×C₄	—	2	4	no	—
554	C₂²×C₄	—	2	4	no	—
555	C₂²×C₄	—	2	4	no	—
556	C₂²×C₄	—	2	4	no	—
557	C₂²×C₄	—	2	4	no	—
558	C₂²×C₄	—	2	4	no	—
559	C₂²×C₄	—	2	4	no	—
560	C₂²×C₄	—	2	4	no	—
561	C₂²×C₄	—	4	2	no	—
562	C₂²×C₄	—	4	2	no	—
563	C₂²×C₄	—	4	16	no	—
564	C₂²×C₄	C₂×D₄×C₁₀₉	1	4	yes	—
565	C₂²×C₄	#41×C₁₀₉	1	4	yes	—
566	C₂²×C₄	#41×C₁₀₉	1	4	yes	—
567	C₂²×C₄	C₂⁴×C₁₀₉	1	2	yes	—
568	C₂²×C₄	C₂⁴×C₁₀₉	1	2	yes	—
569	C₂²×C₄	C₂⁴×C₁₀₉	1	2	yes	—
570	C₂²×C₄	C₂⁴×C₁₀₉	1	2	yes	—
571	C₂²×C₄	C₂⁴×C₁₀₉	1	2	yes	—
572	C₂²×C₄	C₂⁴×C₁₀₉	1	2	yes	—
573	C₂²×C₄	C₂⁴×C₁₀₉	1	4	yes	—
574	C₂²×C₄	C₂⁴×C₁₀₉	1	4	yes	—
575	C₂²×C₄	C₂⁴×C₁₀₉	1	2	yes	—
576	C₂²×C₄	C₂⁴×C₁₀₉	1	2	yes	—
577	C₂²×C₄	C₂⁴×C₁₀₉	1	1	yes	characteristic
578	C₂²×C₄	C₂⁴×C₁₀₉	1	1	yes	characteristic
579	C₄⋊C₄	—	2	4	no	—
580	C₄⋊C₄	—	2	8	no	—
581	C₄⋊C₄	—	2	8	no	—
582	C₄⋊C₄	—	2	8	no	—
583	C₄⋊C₄	—	2	8	no	—
584	C₄⋊C₄	—	2	2	no	—
585	C₄⋊C₄	—	2	2	no	—
586	C₄⋊C₄	C₂×D₄×C₁₀₉	1	8	yes	—
587	C₂²⋊C₄	—	2	4	no	—
588	C₂²⋊C₄	—	2	4	no	—
589	C₂²⋊C₄	—	2	4	no	—
590	C₂²⋊C₄	—	2	8	no	—
591	C₂²⋊C₄	—	2	8	no	—
592	C₂²⋊C₄	—	2	8	no	—
593	C₂²⋊C₄	—	2	4	no	—
594	C₂²⋊C₄	—	2	4	no	—
595	C₂²⋊C₄	—	2	8	no	—
596	C₂²⋊C₄	—	2	8	no	—
597	C₂²⋊C₄	—	4	4	no	—
598	C₂²⋊C₄	—	4	4	no	—
599	C₂²⋊C₄	—	4	4	no	—
600	C₂²⋊C₄	C₂×D₄×C₁₀₉	1	8	yes	—
601	C₂²⋊C₄	#41×C₁₀₉	1	8	yes	complemented
602	C₄²	—	2	4	no	—
603	C₄²	—	2	2	no	—
604	C₄²	—	2	2	no	—
605	C₄²	—	2	4	no	—
606	C₄²	—	2	2	no	—
607	C₄²	—	2	4	no	—
608	C₄²	—	2	2	no	—
609	C₄²	—	2	4	no	—
610	C₄²	—	2	8	no	—
611	C₄²	—	4	4	no	—
612	C₄²	C₂×D₄×C₁₀₉	1	8	yes	—
613	C₂³	—	2	2	no	—
614	C₂³	—	2	2	no	—
615	C₂³	—	2	8	no	—
616	C₂³	—	2	2	no	—
617	C₂³	—	2	2	no	—
618	C₂³	—	2	2	no	—
619	C₂³	—	2	2	no	—
620	C₂³	—	2	2	no	—
621	C₂³	—	2	2	no	—
622	C₂³	—	2	2	no	—
623	C₂³	—	2	4	no	—
624	C₂³	—	2	2	no	—
625	C₂³	—	2	2	no	—
626	C₂³	—	2	4	no	—
627	C₂³	—	4	8	no	—
628	C₂³	—	4	8	no	—
629	C₂³	—	4	4	no	—
630	C₂³	—	4	4	no	—
631	C₂³	C₂²×D₄×C₁₀₉	1	2	yes	—
632	C₂³	C₂×#41×C₁₀₉	1	4	yes	—
633	C₂³	C₂×#41×C₁₀₉	1	2	yes	—
634	C₂³	C₂×#41×C₁₀₉	1	2	yes	—
635	C₂³	C₂⁵×C₁₀₉	1	1	yes	characteristic
636	Q₈	—	4	16	no	—
637	Q₈	—	4	4	no	—
638	D₄	—	4	16	no	—
639	D₄	—	4	8	no	—
640	D₄	—	4	4	no	—
641	C₂×C₄	—	2	2	no	—
642	C₂×C₄	—	2	2	no	—
643	C₂×C₄	—	2	4	no	—
644	C₂×C₄	—	2	2	no	—
645	C₂×C₄	—	2	4	no	—
646	C₂×C₄	—	2	2	no	—
647	C₂×C₄	—	2	2	no	—
648	C₂×C₄	—	2	4	no	—
649	C₂×C₄	—	2	2	no	—
650	C₂×C₄	—	2	2	no	—
651	C₂×C₄	—	2	2	no	—
652	C₂×C₄	—	2	4	no	—
653	C₂×C₄	—	2	2	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	2	no	—
656	C₂×C₄	—	2	2	no	—
657	C₂×C₄	—	2	4	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	2	2	no	—
660	C₂×C₄	—	2	2	no	—
661	C₂×C₄	—	2	2	no	—
662	C₂×C₄	—	2	4	no	—
663	C₂×C₄	—	2	2	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	4	no	—
666	C₂×C₄	—	4	8	no	—
667	C₂×C₄	—	4	8	no	—
668	C₂×C₄	—	4	4	no	—
669	C₂×C₄	—	4	8	no	—
670	C₂×C₄	—	4	8	no	—
671	C₂×C₄	—	4	8	no	—
672	C₂×C₄	#124×C₁₀₉	1	16	yes	complemented
673	C₂×C₄	C₂²×D₄×C₁₀₉	1	8	yes	—
674	C₂×C₄	C₂²×D₄×C₁₀₉	1	2	yes	—
675	C₂×C₄	C₂²×D₄×C₁₀₉	1	2	yes	—
676	C₂×C₄	C₂×#41×C₁₀₉	1	4	yes	—
677	C₂×C₄	C₂×#41×C₁₀₉	1	4	yes	—
678	C₂×C₄	C₂×#41×C₁₀₉	1	2	yes	—
679	C₂×C₄	C₂×#41×C₁₀₉	1	2	yes	—
680	C₂×C₄	C₂×#41×C₁₀₉	1	2	yes	—
681	C₂×C₄	C₂×#41×C₁₀₉	1	2	yes	—
682	C₂²	—	2	2	no	—
683	C₂²	—	2	4	no	—
684	C₂²	—	2	4	no	—
685	C₂²	—	2	2	no	—
686	C₂²	—	2	4	no	—
687	C₂²	—	2	4	no	—
688	C₂²	—	2	4	no	—
689	C₂²	—	4	16	no	—
690	C₂²	—	4	2	no	—
691	C₂²	—	4	2	no	—
692	C₂²	—	4	2	no	—
693	C₂²	—	4	2	no	—
694	C₂²	—	4	2	no	—
695	C₂²	—	4	4	no	—
696	C₂²	—	4	4	no	—
697	C₂²	—	4	2	no	—
698	C₂²	—	4	2	no	—
699	C₂²	C₂×#124×C₁₀₉	1	4	yes	—
700	C₂²	C₂³×D₄×C₁₀₉	1	1	yes	characteristic
701	C₂²	C₂²×#41×C₁₀₉	1	1	yes	characteristic
702	C₂²	C₂²×#41×C₁₀₉	1	2	yes	—
703	C₂²	C₂²×#41×C₁₀₉	1	1	yes	characteristic
704	C₂²	#585×C₁₀₉	1	2	yes	—
705	C₄	—	2	4	no	—
706	C₄	—	2	8	no	—
707	C₄	—	2	4	no	—
708	C₄	—	4	2	no	—
709	C₄	—	4	2	no	—
710	C₄	—	4	4	no	—
711	C₄	—	4	2	no	—
712	C₄	—	4	2	no	—
713	C₄	—	4	2	no	—
714	C₄	—	4	2	no	—
715	C₄	C₂×#124×C₁₀₉	1	4	yes	—
716	C₄	C₂×#124×C₁₀₉	1	4	yes	—
717	C₂	—	2	4	no	—
718	C₂	—	4	4	no	—
719	C₂	—	8	2	no	—
720	C₂	C₂²×#124×C₁₀₉	1	1	yes	characteristic
721	C₂	C₁₀₉×#3444	1	1	yes	characteristic
722	C₂	C₁₀₉×#3455	1	1	yes	characteristic
723	C₂	D₄×#41×C₁₀₉	1	2	yes	—
724	C₂	C₁₀₉×#3475	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₂×#533×C₁₀₉	C₂	semidirect
3. C₁₀₉×#2492	C₂	semidirect
4. C₁₀₉×#2491	C₂	semidirect
5. C₁₀₉×#2490	C₂	semidirect
6. C₁₀₉×#2489	C₂	semidirect
7. C₁₀₉×#2488	C₂	semidirect
8. C₁₀₉×#2472	C₂	semidirect
9. C₁₀₉×#2398	C₂	semidirect
10. C₄×#124×C₁₀₉	C₂	semidirect
11. C₁₀₉×#2297	C₂	semidirect
12. C₁₀₉×#2297	C₂	semidirect
13. C₁₀₉×#2280	C₂	semidirect
14. C₄×#117×C₁₀₉	C₂	semidirect
15. C₂×C₄×C₂²⋊C₄×C₁₀₉	C₂	semidirect
19. C₂×C₄⋊Q₈×C₁₀₉	C₂²	semidirect
20. C₂×#125×C₁₀₉	C₂²	semidirect
28. C₂×C₄×Q₈×C₁₀₉	C₂²	semidirect
36. #400×C₁₀₉	C₂²	semidirect
37. #400×C₁₀₉	C₂²	semidirect
39. #397×C₁₀₉	C₂²	semidirect
43. #393×C₁₀₉	C₂²	semidirect
44. #391×C₁₀₉	C₂²	semidirect
45. #391×C₁₀₉	C₂²	semidirect
46. #391×C₁₀₉	C₂²	semidirect
47. #391×C₁₀₉	C₂²	semidirect
49. #390×C₁₀₉	C₂²	semidirect
50. #390×C₁₀₉	C₂²	semidirect
51. #390×C₁₀₉	C₂²	semidirect
54. #388×C₁₀₉	C₂²	semidirect
55. #388×C₁₀₉	C₂²	semidirect
58. #382×C₁₀₉	C₂²	semidirect
63. C₄×C₄⋊C₄×C₁₀₉	C₂²	semidirect
64. C₄×C₄⋊C₄×C₁₀₉	C₂²	semidirect
71. C₄×C₂²⋊C₄×C₁₀₉	C₂²	semidirect
72. C₄×C₂²⋊C₄×C₁₀₉	C₂²	semidirect
73. C₄×C₂²⋊C₄×C₁₀₉	C₂²	semidirect
74. #376×C₁₀₉	C₂²	semidirect
76. C₄³×C₁₀₉	C₂²	semidirect
238. C₂²⋊C₄×C₁₀₉	#41	semidirect
309. C₂×C₄×C₁₀₉	#124	semidirect
354. #34813	C₁₀₉	direct (N × H)
363. C₂×#533	C₂×C₁₀₉	semidirect
365. #2492	C₂×C₁₀₉	semidirect
366. #2491	C₂×C₁₀₉	semidirect
367. #2490	C₂×C₁₀₉	semidirect
368. #2489	C₂×C₁₀₉	semidirect
369. #2488	C₂×C₁₀₉	semidirect
370. #2472	C₂×C₁₀₉	semidirect
371. #2398	C₂×C₁₀₉	semidirect
372. C₄×#124	C₂×C₁₀₉	semidirect
373. #2297	C₂×C₁₀₉	semidirect
374. #2297	C₂×C₁₀₉	semidirect
375. #2280	C₂×C₁₀₉	semidirect
376. C₄×#117	C₂×C₁₀₉	semidirect
377. C₂×C₄×C₂²⋊C₄	C₂×C₁₀₉	semidirect
378. C₁₀₉	#34813	direct (N × H)
382. C₂×C₄⋊Q₈	C₂²×C₁₀₉	semidirect
383. C₂×#125	C₂²×C₁₀₉	semidirect
391. C₂×C₄×Q₈	C₂²×C₁₀₉	semidirect
399. #400	C₂²×C₁₀₉	semidirect
400. #400	C₂²×C₁₀₉	semidirect
402. #397	C₂²×C₁₀₉	semidirect
406. #393	C₂²×C₁₀₉	semidirect
407. #391	C₂²×C₁₀₉	semidirect
408. #391	C₂²×C₁₀₉	semidirect
409. #391	C₂²×C₁₀₉	semidirect
410. #391	C₂²×C₁₀₉	semidirect
412. #390	C₂²×C₁₀₉	semidirect
413. #390	C₂²×C₁₀₉	semidirect
414. #390	C₂²×C₁₀₉	semidirect
417. #388	C₂²×C₁₀₉	semidirect
418. #388	C₂²×C₁₀₉	semidirect
421. #382	C₂²×C₁₀₉	semidirect
426. C₄×C₄⋊C₄	C₂²×C₁₀₉	semidirect
427. C₄×C₄⋊C₄	C₂²×C₁₀₉	semidirect
434. C₄×C₂²⋊C₄	C₂²×C₁₀₉	semidirect
435. C₄×C₂²⋊C₄	C₂²×C₁₀₉	semidirect
436. C₄×C₂²⋊C₄	C₂²×C₁₀₉	semidirect
437. #376	C₂²×C₁₀₉	semidirect
439. C₄³	C₂²×C₁₀₉	semidirect
601. C₂²⋊C₄	#41×C₁₀₉	semidirect
672. C₂×C₄	#124×C₁₀₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#533×C₁₀₉	2
C₂×#525×C₁₀₉	2
C₁₀₉×#2492	2
C₁₀₉×#2491	2
C₁₀₉×#2490	2
C₁₀₉×#2489	2
C₁₀₉×#2488	2
C₁₀₉×#2472	2
C₁₀₉×#2398	2
C₄×#124×C₁₀₉	2
C₁₀₉×#2297	2
C₁₀₉×#2280	2
C₄×#117×C₁₀₉	2
C₂×C₄×C₂²⋊C₄×C₁₀₉	2
#34813	109

Subgroups — C109×#34813 #42152807

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₉×#34813 #42152807