Subgroups — C₂×#20295825 #28377778

Order 13952.

1484 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13182030	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#41×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#20295825	C₂	1	16	yes	maximal, direct product factor
4	C₂×#16812731	C₂	1	2	yes	maximal, complemented
5	C₂×#16812730	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#16812727	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#16812726	C₂	1	2	yes	maximal, complemented
8	C₂×#16812724	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#16812722	C₂	1	2	yes	maximal, complemented
10	C₂×#16812720	C₂	1	2	yes	maximal, complemented
11	C₂×M₁₆×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#137×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#13182030	—	2	1	no	—
14	C₂×#13182030	—	2	1	no	—
15	C₂×#13182030	—	2	4	no	—
16	C₂×#13182030	C₂²	1	2	yes	—
17	C₂×#13182030	C₂²	1	2	yes	complemented
18	C₂×#13182030	C₂²	1	1	yes	characteristic, complemented
19	C₂×#13182030	C₂²	1	8	yes	complemented
20	C₂×#13182029	—	2	1	no	—
21	C₂×#13182029	C₂²	1	1	yes	characteristic
22	C₂×#13182028	—	2	1	no	—
23	C₂×#13182028	C₂²	1	1	yes	characteristic, complemented
24	#41×D₁₀₉	—	2	4	no	—
25	#41×D₁₀₉	C₂²	1	8	yes	complemented
26	C₂×Q₈×D₁₀₉	C₂²	1	1	yes	characteristic, complemented
27	C₂²×D₄₃₆	—	2	1	no	—
28	C₂²×D₄₃₆	C₂²	1	1	yes	characteristic, complemented
29	C₂×D₄×D₁₀₉	—	2	1	no	—
30	C₂×D₄×D₁₀₉	C₂²	1	1	yes	characteristic, complemented
31	C₂²×C₄×D₁₀₉	—	2	1	no	—
32	C₂²×C₄×D₁₀₉	—	2	1	no	—
33	C₂²×C₄×D₁₀₉	C₂²	1	1	yes	characteristic
34	#16812731	C₂²	1	16	yes	complemented
35	#16812730	C₂²	1	8	yes	complemented
36	#16812727	C₂²	1	8	yes	complemented
37	#16812726	C₂²	1	16	yes	complemented
38	#16812724	C₂²	1	8	yes	complemented
39	#16812722	C₂²	1	16	yes	complemented
40	#16812720	C₂²	1	16	yes	complemented
41	C₂×#13182019	C₂²	1	2	yes	complemented
42	C₂×#13182018	C₂²	1	2	yes	complemented
43	C₂×#13182016	C₂²	1	2	yes	complemented
44	C₂×#13182016	C₂²	1	2	yes	complemented
45	C₂×D₈₇₂	C₂²	1	2	yes	complemented
46	C₂×#13182014	C₂²	1	2	yes	complemented
47	C₂×#13182013	C₂²	1	1	yes	characteristic, complemented
48	C₂×#13182012	C₂²	1	2	yes	complemented
49	M₁₆×D₁₀₉	C₂²	1	8	yes	complemented
50	C₂×C₈×D₁₀₉	C₂²	1	2	yes	complemented
51	C₂×#41×C₁₀₉	C₂²	1	1	yes	characteristic
52	C₂²×Q₈×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
53	#137×C₁₀₉	C₂²	1	8	yes	complemented
54	C₂×Q₁₆×C₁₀₉	C₂²	1	2	yes	complemented
55	C₂×SD₁₆×C₁₀₉	C₂²	1	2	yes	complemented
56	C₂×M₁₆×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
57	C₂³×D₁₀₉	—	2	1	no	—
58	C₂³×D₁₀₉	—	2	1	no	—
59	C₂³×D₁₀₉	D₄	1	1	yes	characteristic
60	#13182030	—	2	2	no	—
61	#13182030	—	2	4	no	—
62	#13182030	—	2	8	no	—
63	#13182030	—	2	8	no	—
64	#13182030	—	2	4	no	—
65	#13182030	C₂³	1	8	yes	—
66	#13182030	C₂³	1	8	yes	complemented
67	#13182030	C₂³	1	4	yes	complemented
68	#13182029	—	2	2	no	—
69	#13182029	—	2	8	no	—
70	#13182029	C₂³	1	4	yes	—
71	#13182028	—	2	8	no	—
72	#13182028	—	2	2	no	—
73	#13182028	C₂³	1	4	yes	complemented
74	C₂×Dic₂₁₈	—	2	1	no	—
75	C₂×Dic₂₁₈	C₂³	1	1	yes	characteristic
76	Q₈×D₁₀₉	—	2	2	no	—
77	Q₈×D₁₀₉	C₂³	1	4	yes	complemented
78	C₂×D₄₃₆	—	2	1	no	—
79	C₂×D₄₃₆	—	2	2	no	—
80	C₂×D₄₃₆	—	2	8	no	—
81	C₂×D₄₃₆	—	2	2	no	—
82	C₂×D₄₃₆	—	2	2	no	—
83	C₂×D₄₃₆	—	2	1	no	—
84	C₂×D₄₃₆	C₂³	1	2	yes	—
85	C₂×D₄₃₆	C₂³	1	1	yes	characteristic
86	C₂×D₄₃₆	C₂³	1	4	yes	complemented
87	C₂×C₂²⋊D₁₀₉	—	2	1	no	—
88	C₂×C₂²⋊D₁₀₉	—	2	1	no	—
89	C₂×C₂²⋊D₁₀₉	—	2	1	no	—
90	D₄×D₁₀₉	—	2	8	no	—
91	D₄×D₁₀₉	—	2	2	no	—
92	D₄×D₁₀₉	C₂³	1	4	yes	complemented
93	C₂²×Dic₁₀₉	—	2	1	no	—
94	C₂²×Dic₁₀₉	D₄	1	1	yes	characteristic
95	C₂×C₄×D₁₀₉	—	2	1	no	—
96	C₂×C₄×D₁₀₉	—	2	1	no	—
97	C₂×C₄×D₁₀₉	—	2	1	no	—
98	C₂×C₄×D₁₀₉	—	2	2	no	—
99	C₂×C₄×D₁₀₉	—	2	8	no	—
100	C₂×C₄×D₁₀₉	—	2	2	no	—
101	C₂×C₄×D₁₀₉	—	2	8	no	—
102	C₂×C₄×D₁₀₉	D₄	1	1	yes	characteristic
103	C₂×C₄×D₁₀₉	D₄	1	4	yes	—
104	C₂×C₄×D₁₀₉	D₄	1	1	yes	characteristic
105	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
106	C₂×C₄×D₁₀₉	C₂³	1	4	yes	—
107	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
108	#13182019	C₂³	1	8	yes	complemented
109	#13182018	C₂³	1	8	yes	complemented
110	#13182016	C₂³	1	8	yes	complemented
111	#13182016	C₂³	1	8	yes	complemented
112	D₈₇₂	C₂³	1	8	yes	complemented
113	#13182014	C₂³	1	8	yes	complemented
114	#13182013	C₂³	1	4	yes	complemented
115	#13182012	C₂³	1	8	yes	complemented
116	C₂×#11724784	C₂³	1	2	yes	—
117	C₈×D₁₀₉	C₂³	1	8	yes	complemented
118	#41×C₁₀₉	—	2	2	no	—
119	#41×C₁₀₉	C₂³	1	4	yes	—
120	C₂×Q₈×C₁₀₉	—	2	1	no	—
121	C₂×Q₈×C₁₀₉	—	2	2	no	—
122	C₂×Q₈×C₁₀₉	C₂³	1	2	yes	—
123	C₂×Q₈×C₁₀₉	C₂³	1	1	yes	characteristic
124	C₂×Q₈×C₁₀₉	C₂³	1	4	yes	complemented
125	C₂×D₄×C₁₀₉	—	2	1	no	—
126	C₂×D₄×C₁₀₉	C₂³	1	1	yes	characteristic
127	C₂²×C₄×C₁₀₉	—	2	1	no	—
128	C₂²×C₄×C₁₀₉	—	2	1	no	—
129	C₂²×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
130	Q₁₆×C₁₀₉	C₂³	1	8	yes	complemented
131	SD₁₆×C₁₀₉	C₂³	1	8	yes	complemented
132	M₁₆×C₁₀₉	C₂³	1	4	yes	complemented
133	C₂×C₈×C₁₀₉	C₂³	1	2	yes	—
134	C₂³×C₁₀₉	—	2	1	no	—
135	C₂³×C₁₀₉	C₂×D₄	1	1	yes	characteristic
136	C₂²×D₁₀₉	—	2	1	no	—
137	C₂²×D₁₀₉	—	2	2	no	—
138	C₂²×D₁₀₉	—	2	4	no	—
139	C₂²×D₁₀₉	—	2	4	no	—
140	C₂²×D₁₀₉	—	4	2	no	—
141	C₂²×D₁₀₉	—	4	4	no	—
142	C₂²×D₁₀₉	—	4	4	no	—
143	C₂²×D₁₀₉	C₂×D₄	1	1	yes	characteristic
144	C₂²×D₁₀₉	C₂×D₄	1	1	yes	characteristic
145	C₂²×D₁₀₉	C₂×D₄	1	4	yes	—
146	Q₈×C₁₀₉	—	2	2	no	—
147	Q₈×C₁₀₉	—	2	4	no	—
148	Q₈×C₁₀₉	—	2	1	no	—
149	Q₈×C₁₀₉	C₂⁴	1	4	yes	—
150	Q₈×C₁₀₉	C₂⁴	1	2	yes	—
151	D₄×C₁₀₉	—	2	4	no	—
152	D₄×C₁₀₉	—	2	1	no	—
153	D₄×C₁₀₉	C₂⁴	1	2	yes	—
154	C₂×C₄×C₁₀₉	—	2	1	no	—
155	C₂×C₄×C₁₀₉	—	2	2	no	—
156	C₂×C₄×C₁₀₉	—	2	4	no	—
157	C₂×C₄×C₁₀₉	—	2	4	no	—
158	C₂×C₄×C₁₀₉	C₂×D₄	1	1	yes	characteristic
159	C₂×C₄×C₁₀₉	C₂×D₄	1	2	yes	—
160	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
161	C₂×C₄×C₁₀₉	C₂⁴	1	2	yes	—
162	C₂²⋊D₁₀₉	—	2	4	no	—
163	C₂²⋊D₁₀₉	—	2	4	no	—
164	C₂²⋊D₁₀₉	—	2	4	no	—
165	C₂×Dic₁₀₉	—	2	1	no	—
166	C₂×Dic₁₀₉	—	2	4	no	—
167	C₂×Dic₁₀₉	C₂×D₄	1	1	yes	characteristic
168	C₂×Dic₁₀₉	C₂×D₄	1	1	yes	characteristic
169	C₂×Dic₁₀₉	C₂×D₄	1	4	yes	—
170	D₄₃₆	—	2	4	no	—
171	D₄₃₆	—	2	8	no	—
172	D₄₃₆	—	2	8	no	—
173	D₄₃₆	—	2	1	no	—
174	D₄₃₆	—	2	2	no	—
175	D₄₃₆	—	2	4	no	—
176	D₄₃₆	C₂⁴	1	4	yes	—
177	D₄₃₆	C₂⁴	1	2	yes	—
178	C₄×D₁₀₉	—	2	4	no	—
179	C₄×D₁₀₉	—	2	4	no	—
180	C₄×D₁₀₉	—	2	4	no	—
181	C₄×D₁₀₉	—	2	8	no	—
182	C₄×D₁₀₉	—	2	8	no	—
183	C₄×D₁₀₉	C₂×D₄	1	4	yes	—
184	C₄×D₁₀₉	C₂×D₄	1	2	yes	—
185	C₄×D₁₀₉	C₂×D₄	1	2	yes	—
186	C₄×D₁₀₉	C₂×D₄	1	4	yes	—
187	C₄×D₁₀₉	C₂⁴	1	2	yes	—
188	C₄×D₁₀₉	C₂⁴	1	2	yes	—
189	Dic₂₁₈	—	2	1	no	—
190	Dic₂₁₈	—	2	4	no	—
191	Dic₂₁₈	C₂⁴	1	2	yes	—
192	C₈×C₁₀₉	C₂⁴	1	4	yes	—
193	#11724784	C₂⁴	1	4	yes	—
194	C₂²×C₁₀₉	—	2	2	no	—
195	C₂²×C₁₀₉	—	2	2	no	—
196	C₂²×C₁₀₉	—	4	2	no	—
197	C₂²×C₁₀₉	C₂²×D₄	1	2	yes	—
198	C₂²×C₁₀₉	C₂²×D₄	1	1	yes	characteristic
199	C₂×D₁₀₉	—	2	2	no	—
200	C₂×D₁₀₉	—	2	2	no	—
201	C₂×D₁₀₉	—	2	4	no	—
202	C₂×D₁₀₉	—	2	2	no	—
203	C₂×D₁₀₉	—	4	4	no	—
204	C₂×D₁₀₉	—	4	8	no	—
205	C₂×D₁₀₉	—	4	8	no	—
206	C₂×D₁₀₉	—	4	2	no	—
207	C₂×D₁₀₉	—	4	4	no	—
208	C₂×D₁₀₉	C₂²×D₄	1	2	yes	—
209	C₂×D₁₀₉	C₂²×D₄	1	2	yes	—
210	C₄×C₁₀₉	—	2	2	no	—
211	C₄×C₁₀₉	—	2	4	no	—
212	C₄×C₁₀₉	C₂²×D₄	1	1	yes	characteristic
213	C₄×C₁₀₉	C₂²×D₄	1	2	yes	—
214	C₄×C₁₀₉	C₂⁵	1	1	yes	characteristic
215	Dic₁₀₉	—	2	2	no	—
216	Dic₁₀₉	C₂²×D₄	1	2	yes	—
217	Dic₁₀₉	C₂²×D₄	1	2	yes	—
218	C₂×C₁₀₉	—	2	2	no	—
219	C₂×C₁₀₉	—	4	2	no	—
220	C₂×C₁₀₉	#575	1	2	yes	complemented
221	C₂×C₁₀₉	C₂³×D₄	1	1	yes	characteristic
222	D₁₀₉	—	2	2	no	—
223	D₁₀₉	—	2	2	no	—
224	D₁₀₉	—	4	4	no	—
225	D₁₀₉	—	4	2	no	—
226	C₂×#575	—	109	1	no	maximal, Sylow
227	C₁₀₉	C₂×#575	1	1	yes	characteristic, complemented, Sylow
228	C₂²×#41	—	109	1	no	—
229	C₂²×#41	—	109	1	no	—
230	#575	—	109	16	no	—
231	C₂×#137	—	109	1	no	—
232	C₂×#137	—	109	2	no	—
233	C₂×#137	D₁₀₉	1	1	yes	characteristic, complemented
234	C₂×AGL(1,ℤ/8)	—	109	1	no	—
235	C₂×AGL(1,ℤ/8)	—	109	2	no	—
236	C₂×AGL(1,ℤ/8)	—	109	1	no	—
237	C₂×#135	—	109	2	no	—
238	C₂×#135	—	109	2	no	—
239	C₂²×M₁₆	—	109	1	no	—
240	C₂×#41	—	109	8	no	—
241	C₂×#41	—	109	1	no	—
242	C₂×#41	—	109	2	no	—
243	C₂×#41	—	109	2	no	—
244	C₂×#41	—	109	8	no	—
245	C₂×#41	—	109	1	no	—
246	C₂×#41	—	109	1	no	—
247	C₂×#41	—	218	1	no	—
248	C₂×#41	—	218	1	no	—
249	C₂×#41	—	218	1	no	—
250	C₂×#41	—	218	4	no	—
251	C₂×#41	—	218	1	no	—
252	C₂×#41	—	218	4	no	—
253	C₂×#41	C₂×D₁₀₉	1	1	yes	characteristic
254	C₂²×Q₈	—	109	1	no	—
255	C₂²×Q₈	C₂×D₁₀₉	1	1	yes	characteristic, complemented
256	C₂²×D₄	—	109	1	no	—
257	C₂²×D₄	—	109	1	no	—
258	C₂²×D₄	—	218	1	no	—
259	C₂²×D₄	—	218	1	no	—
260	C₂³×C₄	—	109	1	no	—
261	C₂³×C₄	—	218	1	no	—
262	C₂³×C₄	—	218	1	no	—
263	#137	—	109	8	no	—
264	#137	—	109	16	no	—
265	#137	C₂×D₁₀₉	1	8	yes	complemented
266	AGL(1,ℤ/8)	—	109	8	no	—
267	AGL(1,ℤ/8)	—	109	16	no	—
268	AGL(1,ℤ/8)	—	109	8	no	—
269	#135	—	109	16	no	—
270	#135	—	109	16	no	—
271	C₂×Q₁₆	—	109	2	no	—
272	C₂×Q₁₆	C₂×D₁₀₉	1	2	yes	complemented
273	C₂×SD₁₆	—	109	2	no	—
274	C₂×SD₁₆	—	109	2	no	—
275	C₂×SD₁₆	—	109	2	no	—
276	C₂×SD₁₆	C₂×D₁₀₉	1	2	yes	complemented
277	C₂×D₈	—	109	2	no	—
278	C₂×D₈	—	109	2	no	—
279	C₂×M₁₆	—	109	1	no	—
280	C₂×M₁₆	—	109	8	no	—
281	C₂×M₁₆	—	109	2	no	—
282	C₂×M₁₆	C₂×D₁₀₉	1	1	yes	characteristic, complemented
283	C₂²×C₈	—	109	2	no	—
284	C₂⁴	—	109	1	no	—
285	C₂⁴	—	218	1	no	—
286	C₂⁴	—	218	1	no	—
287	#41	—	2	2	no	—
288	#41	—	109	8	no	—
289	#41	—	109	4	no	—
290	#41	—	109	8	no	—
291	#41	—	109	4	no	—
292	#41	—	109	4	no	—
293	#41	—	218	8	no	—
294	#41	—	218	8	no	—
295	#41	—	218	2	no	—
296	#41	—	218	8	no	—
297	#41	—	218	4	no	—
298	#41	—	218	4	no	—
299	#41	—	218	8	no	—
300	#41	—	218	2	no	—
301	#41	—	218	2	no	—
302	#41	C₂²×D₁₀₉	1	4	yes	—
303	C₂×Q₈	—	2	2	no	—
304	C₂×Q₈	—	2	1	no	—
305	C₂×Q₈	—	109	4	no	—
306	C₂×Q₈	—	109	1	no	—
307	C₂×Q₈	—	218	1	no	—
308	C₂×Q₈	—	218	2	no	—
309	C₂×Q₈	C₂²×D₁₀₉	1	1	yes	characteristic
310	C₂×Q₈	C₂²×D₁₀₉	1	2	yes	—
311	C₂×Q₈	C₂²×D₁₀₉	1	4	yes	complemented
312	C₂×D₄	—	2	1	no	—
313	C₂×D₄	—	109	4	no	—
314	C₂×D₄	—	109	2	no	—
315	C₂×D₄	—	109	1	no	—
316	C₂×D₄	—	109	4	no	—
317	C₂×D₄	—	218	8	no	—
318	C₂×D₄	—	218	1	no	—
319	C₂×D₄	—	218	2	no	—
320	C₂×D₄	—	218	2	no	—
321	C₂×D₄	—	218	2	no	—
322	C₂×D₄	—	218	1	no	—
323	C₂×D₄	—	218	8	no	—
324	C₂×D₄	—	218	1	no	—
325	C₂×D₄	—	218	1	no	—
326	C₂×D₄	—	218	2	no	—
327	C₂×D₄	—	218	1	no	—
328	C₂×D₄	C₂²×D₁₀₉	1	1	yes	characteristic
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	109	1	no	—
332	C₂²×C₄	—	109	1	no	—
333	C₂²×C₄	—	109	4	no	—
334	C₂²×C₄	—	109	1	no	—
335	C₂²×C₄	—	109	1	no	—
336	C₂²×C₄	—	109	1	no	—
337	C₂²×C₄	—	109	4	no	—
338	C₂²×C₄	—	218	8	no	—
339	C₂²×C₄	—	218	1	no	—
340	C₂²×C₄	—	218	2	no	—
341	C₂²×C₄	—	218	2	no	—
342	C₂²×C₄	—	218	8	no	—
343	C₂²×C₄	—	218	1	no	—
344	C₂²×C₄	—	218	1	no	—
345	C₂²×C₄	—	218	1	no	—
346	C₂²×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
347	Q₁₆	—	109	8	no	—
348	Q₁₆	C₂²×D₁₀₉	1	8	yes	complemented
349	SD₁₆	—	109	8	no	—
350	SD₁₆	—	109	8	no	—
351	SD₁₆	—	109	8	no	—
352	SD₁₆	C₂²×D₁₀₉	1	8	yes	complemented
353	D₈	—	109	8	no	—
354	D₈	—	109	8	no	—
355	M₁₆	—	109	4	no	—
356	M₁₆	—	109	8	no	—
357	M₁₆	C₂²×D₁₀₉	1	4	yes	complemented
358	C₂×C₈	—	109	2	no	—
359	C₂×C₈	—	109	8	no	—
360	C₂×C₈	C₂²×D₁₀₉	1	2	yes	—
361	C₂³	—	2	1	no	—
362	C₂³	—	109	4	no	—
363	C₂³	—	109	1	no	—
364	C₂³	—	109	1	no	—
365	C₂³	—	436	4	no	—
366	C₂³	—	436	2	no	—
367	C₂³	—	436	4	no	—
368	C₂³	—	218	4	no	—
369	C₂³	—	218	4	no	—
370	C₂³	—	218	2	no	—
371	C₂³	—	218	1	no	—
372	C₂³	D₄×D₁₀₉	1	1	yes	characteristic
373	Q₈	—	2	2	no	—
374	Q₈	—	2	4	no	—
375	Q₈	—	2	1	no	—
376	Q₈	—	109	2	no	—
377	Q₈	—	218	4	no	—
378	Q₈	—	218	1	no	—
379	Q₈	C₂³×D₁₀₉	1	2	yes	—
380	Q₈	C₂³×D₁₀₉	1	4	yes	—
381	D₄	—	2	4	no	—
382	D₄	—	2	1	no	—
383	D₄	—	109	4	no	—
384	D₄	—	109	2	no	—
385	D₄	—	218	4	no	—
386	D₄	—	218	8	no	—
387	D₄	—	218	8	no	—
388	D₄	—	218	4	no	—
389	D₄	—	218	4	no	—
390	D₄	—	218	4	no	—
391	D₄	—	218	4	no	—
392	D₄	—	218	1	no	—
393	D₄	—	218	2	no	—
394	D₄	C₂³×D₁₀₉	1	2	yes	—
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	109	4	no	—
400	C₂×C₄	—	109	1	no	—
401	C₂×C₄	—	109	1	no	—
402	C₂×C₄	—	109	4	no	—
403	C₂×C₄	—	109	2	no	—
404	C₂×C₄	—	109	2	no	—
405	C₂×C₄	—	109	4	no	—
406	C₂×C₄	—	109	2	no	—
407	C₂×C₄	—	109	2	no	—
408	C₂×C₄	—	218	4	no	—
409	C₂×C₄	—	218	8	no	—
410	C₂×C₄	—	218	8	no	—
411	C₂×C₄	—	218	4	no	—
412	C₂×C₄	—	218	4	no	—
413	C₂×C₄	—	218	1	no	—
414	C₂×C₄	—	218	4	no	—
415	C₂×C₄	D₄×D₁₀₉	1	2	yes	—
416	C₂×C₄	D₄×D₁₀₉	1	1	yes	characteristic
417	C₂×C₄	C₂³×D₁₀₉	1	2	yes	—
418	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
419	C₈	—	109	4	no	—
420	C₈	C₂³×D₁₀₉	1	4	yes	—
421	C₂²	—	2	2	no	—
422	C₂²	—	2	2	no	—
423	C₂²	—	4	2	no	—
424	C₂²	—	109	2	no	—
425	C₂²	—	109	2	no	—
426	C₂²	—	436	8	no	—
427	C₂²	—	436	4	no	—
428	C₂²	—	436	8	no	—
429	C₂²	—	436	4	no	—
430	C₂²	—	436	2	no	—
431	C₂²	—	218	4	no	—
432	C₂²	—	218	2	no	—
433	C₂²	—	218	2	no	—
434	C₂²	—	218	2	no	—
435	C₂²	C₂×D₄×D₁₀₉	1	2	yes	—
436	C₂²	C₂×D₄×D₁₀₉	1	1	yes	characteristic
437	C₄	—	2	2	no	—
438	C₄	—	2	4	no	—
439	C₄	—	109	2	no	—
440	C₄	—	109	2	no	—
441	C₄	—	218	2	no	—
442	C₄	C₂×D₄×D₁₀₉	1	2	yes	—
443	C₄	C₂×D₄×D₁₀₉	1	1	yes	characteristic
444	C₄	C₂⁴×D₁₀₉	1	1	yes	characteristic
445	C₂	—	2	2	no	—
446	C₂	—	4	2	no	—
447	C₂	—	436	4	no	—
448	C₂	—	436	2	no	—
449	C₂	—	218	2	no	—
450	C₂	—	218	2	no	—
451	C₂	#20295825	1	2	yes	direct product factor
452	C₂	C₂²×D₄×D₁₀₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₁₀₉
commutator, cosocle	C₄×C₁₀₉	C₂⁵
Frattini	C₄	C₂⁴×D₁₀₉
Fitting	C₂×#137×C₁₀₉	C₂
socle	C₂²×C₁₀₉	C₂²×D₄
hypercenter	C₂×#137	D₁₀₉
hypocenter	C₁₀₉	C₂×#575
LCS	G ▷ C₄×C₁₀₉ ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#137

Complements

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

N	H ≅ G/N	type
1. C₂²×#13182030	C₂	semidirect
2. C₂×#41×D₁₀₉	C₂	semidirect
3. #20295825	C₂	direct (N × H)
4. C₂×#16812731	C₂	semidirect
5. C₂×#16812730	C₂	semidirect
6. C₂×#16812727	C₂	semidirect
7. C₂×#16812726	C₂	semidirect
8. C₂×#16812724	C₂	semidirect
9. C₂×#16812722	C₂	semidirect
10. C₂×#16812720	C₂	semidirect
11. C₂×M₁₆×D₁₀₉	C₂	semidirect
12. C₂×#137×C₁₀₉	C₂	semidirect
17. C₂×#13182030	C₂²	semidirect
18. C₂×#13182030	C₂²	semidirect
19. C₂×#13182030	C₂²	semidirect
23. C₂×#13182028	C₂²	semidirect
25. #41×D₁₀₉	C₂²	semidirect
26. C₂×Q₈×D₁₀₉	C₂²	semidirect
28. C₂²×D₄₃₆	C₂²	semidirect
30. C₂×D₄×D₁₀₉	C₂²	semidirect
34. #16812731	C₂²	semidirect
35. #16812730	C₂²	semidirect
36. #16812727	C₂²	semidirect
37. #16812726	C₂²	semidirect
38. #16812724	C₂²	semidirect
39. #16812722	C₂²	semidirect
40. #16812720	C₂²	semidirect
41. C₂×#13182019	C₂²	semidirect
42. C₂×#13182018	C₂²	semidirect
43. C₂×#13182016	C₂²	semidirect
44. C₂×#13182016	C₂²	semidirect
45. C₂×D₈₇₂	C₂²	semidirect
46. C₂×#13182014	C₂²	semidirect
47. C₂×#13182013	C₂²	semidirect
48. C₂×#13182012	C₂²	semidirect
49. M₁₆×D₁₀₉	C₂²	semidirect
50. C₂×C₈×D₁₀₉	C₂²	semidirect
52. C₂²×Q₈×C₁₀₉	C₂²	semidirect
53. #137×C₁₀₉	C₂²	semidirect
54. C₂×Q₁₆×C₁₀₉	C₂²	semidirect
55. C₂×SD₁₆×C₁₀₉	C₂²	semidirect
56. C₂×M₁₆×C₁₀₉	C₂²	semidirect
66. #13182030	C₂³	semidirect
67. #13182030	C₂³	semidirect
73. #13182028	C₂³	semidirect
77. Q₈×D₁₀₉	C₂³	semidirect
86. C₂×D₄₃₆	C₂³	semidirect
92. D₄×D₁₀₉	C₂³	semidirect
108. #13182019	C₂³	semidirect
109. #13182018	C₂³	semidirect
110. #13182016	C₂³	semidirect
111. #13182016	C₂³	semidirect
112. D₈₇₂	C₂³	semidirect
113. #13182014	C₂³	semidirect
114. #13182013	C₂³	semidirect
115. #13182012	C₂³	semidirect
117. C₈×D₁₀₉	C₂³	semidirect
124. C₂×Q₈×C₁₀₉	C₂³	semidirect
130. Q₁₆×C₁₀₉	C₂³	semidirect
131. SD₁₆×C₁₀₉	C₂³	semidirect
132. M₁₆×C₁₀₉	C₂³	semidirect
220. C₂×C₁₀₉	#575	semidirect
227. C₁₀₉	C₂×#575	semidirect
233. C₂×#137	D₁₀₉	semidirect
255. C₂²×Q₈	C₂×D₁₀₉	semidirect
265. #137	C₂×D₁₀₉	semidirect
272. C₂×Q₁₆	C₂×D₁₀₉	semidirect
276. C₂×SD₁₆	C₂×D₁₀₉	semidirect
282. C₂×M₁₆	C₂×D₁₀₉	semidirect
311. C₂×Q₈	C₂²×D₁₀₉	semidirect
348. Q₁₆	C₂²×D₁₀₉	semidirect
352. SD₁₆	C₂²×D₁₀₉	semidirect
357. M₁₆	C₂²×D₁₀₉	semidirect
451. C₂	#20295825	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#13182030	2
C₂×#41×D₁₀₉	2
#20295825	2
C₂×#16812731	2
C₂×#16812730	2
C₂×#16812727	2
C₂×#16812726	2
C₂×#16812724	2
C₂×#16812722	2
C₂×#16812720	2
C₂×M₁₆×D₁₀₉	2
C₂×#137×C₁₀₉	2
C₂×#575	109

Subgroups — C2×#20295825 #28377778

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20295825 #28377778