Subgroups — C₂×#20295660 #28376470

Order 13952.

2536 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×D₄₃₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×D₄×D₁₀₉	C₂	1	2	yes	maximal, complemented
3	C₂²×D₄×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#20295660	C₂	1	16	yes	maximal, direct product factor
5	C₂×#16812695	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#16812674	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#16812672	C₂	1	2	yes	maximal, complemented
8	C₂×#16812669	C₂	1	2	yes	maximal, complemented
9	C₂×#16812667	C₂	1	2	yes	maximal, complemented
10	C₂×#16812661	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄×C₂²⋊D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#121×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂⁴×D₁₀₉	C₂²	1	2	yes	complemented
14	C₂⁴×D₁₀₉	C₂²	1	2	yes	complemented
15	C₂²×D₄₃₆	—	2	8	no	—
16	C₂²×D₄₃₆	C₂²	1	1	yes	characteristic
17	C₂²×D₄₃₆	C₂²	1	2	yes	complemented
18	C₂²×D₄₃₆	C₂²	1	2	yes	complemented
19	C₂²×D₄₃₆	C₂²	1	1	yes	characteristic, complemented
20	C₂²×D₄₃₆	C₂²	1	8	yes	complemented
21	C₂²×C₂²⋊D₁₀₉	C₂²	1	1	yes	characteristic
22	C₂²×C₂²⋊D₁₀₉	C₂²	1	2	yes	complemented
23	C₂²×C₂²⋊D₁₀₉	C₂²	1	2	yes	complemented
24	C₂²×C₂²⋊D₁₀₉	C₂²	1	2	yes	complemented
25	C₂×D₄×D₁₀₉	—	2	8	no	—
26	C₂×D₄×D₁₀₉	—	2	16	no	—
27	C₂×D₄×D₁₀₉	C₂²	1	16	yes	complemented
28	C₂×D₄×D₁₀₉	C₂²	1	8	yes	complemented
29	C₂²×C₄×D₁₀₉	C₂²	1	1	yes	characteristic, complemented
30	C₂²×C₄×D₁₀₉	C₂²	1	2	yes	complemented
31	#16812695	C₂²	1	8	yes	complemented
32	#16812674	C₂²	1	8	yes	complemented
33	#16812672	C₂²	1	16	yes	complemented
34	#16812669	C₂²	1	16	yes	complemented
35	#16812667	C₂²	1	16	yes	complemented
36	#16812661	C₂²	1	8	yes	complemented
37	C₄×C₂²⋊D₁₀₉	C₂²	1	8	yes	complemented
38	C₂×#13182008	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₂²⋊Dic₁₀₉	C₂²	1	1	yes	characteristic, complemented
40	C₂×#13182006	C₂²	1	1	yes	characteristic, complemented
41	C₂×#13182006	C₂²	1	2	yes	complemented
42	C₂×#13182006	C₂²	1	2	yes	complemented
43	C₂×C₄×Dic₁₀₉	C₂²	1	1	yes	characteristic, complemented
44	C₂²×D₄×C₁₀₉	C₂²	1	2	yes	complemented
45	C₂²×D₄×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
46	C₂³×C₄×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
47	#121×C₁₀₉	C₂²	1	8	yes	complemented
48	C₂×C₄⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
49	C₂×C₂²⋊C₄×C₁₀₉	C₂²	1	2	yes	complemented
50	C₂³×D₁₀₉	—	2	8	no	—
51	C₂³×D₁₀₉	—	2	8	no	—
52	C₂³×D₁₀₉	—	2	8	no	—
53	C₂³×D₁₀₉	—	2	8	no	—
54	C₂³×D₁₀₉	—	4	4	no	—
55	C₂³×D₁₀₉	—	4	4	no	—
56	C₂³×D₁₀₉	C₂³	1	2	yes	—
57	C₂³×D₁₀₉	C₂³	1	1	yes	characteristic
58	C₂³×D₁₀₉	C₂³	1	2	yes	—
59	C₂³×D₁₀₉	C₂³	1	8	yes	complemented
60	C₂³×D₁₀₉	C₂³	1	8	yes	complemented
61	C₂×D₄₃₆	—	2	8	no	—
62	C₂×D₄₃₆	—	2	8	no	—
63	C₂×D₄₃₆	—	2	4	no	—
64	C₂×D₄₃₆	—	2	32	no	—
65	C₂×D₄₃₆	D₄	1	8	yes	complemented
66	C₂×D₄₃₆	C₂³	1	4	yes	—
67	C₂×D₄₃₆	C₂³	1	8	yes	complemented
68	C₂×D₄₃₆	C₂³	1	8	yes	complemented
69	C₂×D₄₃₆	C₂³	1	4	yes	complemented
70	C₂×C₂²⋊D₁₀₉	—	2	8	no	—
71	C₂×C₂²⋊D₁₀₉	—	2	8	no	—
72	C₂×C₂²⋊D₁₀₉	—	4	4	no	—
73	C₂×C₂²⋊D₁₀₉	D₄	1	8	yes	complemented
74	C₂×C₂²⋊D₁₀₉	C₂³	1	4	yes	—
75	C₂×C₂²⋊D₁₀₉	C₂³	1	8	yes	complemented
76	C₂×C₂²⋊D₁₀₉	C₂³	1	8	yes	complemented
77	C₂×C₂²⋊D₁₀₉	C₂³	1	8	yes	complemented
78	D₄×D₁₀₉	—	2	64	no	—
79	D₄×D₁₀₉	—	2	32	no	—
80	C₂²×Dic₁₀₉	C₂³	1	1	yes	characteristic
81	C₂²×Dic₁₀₉	C₂³	1	1	yes	characteristic
82	C₂²×Dic₁₀₉	C₂³	1	1	yes	characteristic
83	C₂×C₄×D₁₀₉	—	2	4	no	—
84	C₂×C₄×D₁₀₉	—	2	8	no	—
85	C₂×C₄×D₁₀₉	C₂³	1	4	yes	complemented
86	C₂×C₄×D₁₀₉	C₂³	1	8	yes	complemented
87	#13182008	C₂³	1	4	yes	complemented
88	C₂²⋊Dic₁₀₉	C₂³	1	4	yes	complemented
89	#13182006	C₂³	1	4	yes	complemented
90	#13182006	C₂³	1	8	yes	complemented
91	#13182006	C₂³	1	8	yes	complemented
92	C₄×Dic₁₀₉	C₂³	1	4	yes	complemented
93	C₂⁴×C₁₀₉	C₂³	1	2	yes	—
94	C₂⁴×C₁₀₉	C₂³	1	1	yes	characteristic
95	C₂×D₄×C₁₀₉	—	2	8	no	—
96	C₂×D₄×C₁₀₉	—	2	4	no	—
97	C₂×D₄×C₁₀₉	C₂³	1	8	yes	complemented
98	C₂×D₄×C₁₀₉	C₂³	1	4	yes	complemented
99	C₂²×C₄×C₁₀₉	—	2	4	no	—
100	C₂²×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
101	C₂²×C₄×C₁₀₉	C₂³	1	2	yes	—
102	C₂²×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
103	C₂²×C₄×C₁₀₉	C₂³	1	4	yes	complemented
104	C₄⋊C₄×C₁₀₉	C₂³	1	4	yes	complemented
105	C₂²⋊C₄×C₁₀₉	C₂³	1	8	yes	complemented
106	C₂³×C₁₀₉	—	2	2	no	—
107	C₂³×C₁₀₉	—	2	2	no	—
108	C₂³×C₁₀₉	—	2	4	no	—
109	C₂³×C₁₀₉	—	2	4	no	—
110	C₂³×C₁₀₉	—	2	4	no	—
111	C₂³×C₁₀₉	C₂×D₄	1	4	yes	complemented
112	C₂³×C₁₀₉	C₂⁴	1	4	yes	—
113	C₂³×C₁₀₉	C₂⁴	1	2	yes	—
114	C₂³×C₁₀₉	C₂⁴	1	1	yes	characteristic
115	C₂²×D₁₀₉	—	2	2	no	—
116	C₂²×D₁₀₉	—	2	4	no	—
117	C₂²×D₁₀₉	—	2	2	no	—
118	C₂²×D₁₀₉	—	2	4	no	—
119	C₂²×D₁₀₉	—	2	4	no	—
120	C₂²×D₁₀₉	—	2	4	no	—
121	C₂²×D₁₀₉	—	2	16	no	—
122	C₂²×D₁₀₉	—	2	4	no	—
123	C₂²×D₁₀₉	—	2	16	no	—
124	C₂²×D₁₀₉	—	2	16	no	—
125	C₂²×D₁₀₉	—	2	16	no	—
126	C₂²×D₁₀₉	—	4	8	no	—
127	C₂²×D₁₀₉	—	4	8	no	—
128	C₂²×D₁₀₉	—	4	32	no	—
129	C₂²×D₁₀₉	—	4	32	no	—
130	C₂²×D₁₀₉	C₂×D₄	1	8	yes	complemented
131	C₂²×D₁₀₉	C₂×D₄	1	4	yes	complemented
132	C₂²×D₁₀₉	C₂⁴	1	4	yes	—
133	C₂²×D₁₀₉	C₂⁴	1	2	yes	—
134	C₂²×D₁₀₉	C₂⁴	1	4	yes	—
135	D₄×C₁₀₉	—	2	16	no	—
136	D₄×C₁₀₉	—	2	8	no	—
137	C₂×C₄×C₁₀₉	—	2	2	no	—
138	C₂×C₄×C₁₀₉	—	2	4	no	—
139	C₂×C₄×C₁₀₉	—	2	8	no	—
140	C₂×C₄×C₁₀₉	C₂×D₄	1	4	yes	complemented
141	C₂×C₄×C₁₀₉	C₂⁴	1	2	yes	—
142	C₂×C₄×C₁₀₉	C₂⁴	1	4	yes	—
143	C₂×C₄×C₁₀₉	C₂⁴	1	2	yes	—
144	C₂²⋊D₁₀₉	—	2	16	no	—
145	C₂²⋊D₁₀₉	—	2	16	no	—
146	C₂²⋊D₁₀₉	—	4	8	no	—
147	C₂²⋊D₁₀₉	C₂×D₄	1	16	yes	complemented
148	C₂×Dic₁₀₉	—	2	2	no	—
149	C₂×Dic₁₀₉	—	2	2	no	—
150	C₂×Dic₁₀₉	C₂×D₄	1	4	yes	complemented
151	C₂×Dic₁₀₉	C₂⁴	1	2	yes	—
152	C₂×Dic₁₀₉	C₂⁴	1	2	yes	—
153	C₂×Dic₁₀₉	C₂⁴	1	2	yes	—
154	D₄₃₆	—	2	16	no	—
155	D₄₃₆	—	2	16	no	—
156	D₄₃₆	—	2	8	no	—
157	D₄₃₆	C₂×D₄	1	16	yes	complemented
158	C₄×D₁₀₉	—	2	8	no	—
159	C₄×D₁₀₉	—	2	16	no	—
160	C₂²×C₁₀₉	—	2	8	no	—
161	C₂²×C₁₀₉	—	2	2	no	—
162	C₂²×C₁₀₉	—	2	2	no	—
163	C₂²×C₁₀₉	—	2	4	no	—
164	C₂²×C₁₀₉	—	2	4	no	—
165	C₂²×C₁₀₉	—	2	4	no	—
166	C₂²×C₁₀₉	—	4	8	no	—
167	C₂²×C₁₀₉	C₂²×D₄	1	2	yes	—
168	C₂²×C₁₀₉	C₂²×D₄	1	2	yes	—
169	C₂²×C₁₀₉	C₂²×D₄	1	4	yes	complemented
170	C₂²×C₁₀₉	H(5,𝔽₂)	1	2	yes	—
171	C₂²×C₁₀₉	C₂⁵	1	1	yes	characteristic
172	C₂×D₁₀₉	—	2	8	no	—
173	C₂×D₁₀₉	—	2	16	no	—
174	C₂×D₁₀₉	—	2	2	no	—
175	C₂×D₁₀₉	—	2	4	no	—
176	C₂×D₁₀₉	—	2	2	no	—
177	C₂×D₁₀₉	—	2	4	no	—
178	C₂×D₁₀₉	—	2	4	no	—
179	C₂×D₁₀₉	—	2	4	no	—
180	C₂×D₁₀₉	—	2	4	no	—
181	C₂×D₁₀₉	—	4	32	no	—
182	C₂×D₁₀₉	—	4	32	no	—
183	C₂×D₁₀₉	—	4	8	no	—
184	C₂×D₁₀₉	C₂²×D₄	1	4	yes	complemented
185	C₂×D₁₀₉	C₂²×D₄	1	8	yes	complemented
186	C₄×C₁₀₉	—	2	4	no	—
187	C₄×C₁₀₉	—	2	2	no	—
188	C₄×C₁₀₉	C₂²×D₄	1	4	yes	complemented
189	Dic₁₀₉	—	2	2	no	—
190	Dic₁₀₉	—	2	2	no	—
191	Dic₁₀₉	C₂²×D₄	1	4	yes	complemented
192	C₂×C₁₀₉	—	2	4	no	—
193	C₂×C₁₀₉	—	4	4	no	—
194	C₂×C₁₀₉	D₄²	1	4	yes	complemented
195	C₂×C₁₀₉	C₂³×D₄	1	1	yes	characteristic
196	C₂×C₁₀₉	C₂³×D₄	1	1	yes	characteristic
197	C₂×C₁₀₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
198	D₁₀₉	—	2	4	no	—
199	D₁₀₉	—	2	8	no	—
200	D₁₀₉	—	4	4	no	—
201	C₂×D₄²	—	109	1	no	maximal, Sylow
202	C₁₀₉	C₂×D₄²	1	1	yes	characteristic, complemented, Sylow
203	C₂³×D₄	—	109	2	no	—
204	C₂³×D₄	—	109	1	no	—
205	C₂³×D₄	—	109	1	no	—
206	D₄²	—	109	16	no	—
207	C₂×#127	—	109	1	no	—
208	C₂×#121	—	109	1	no	—
209	C₂×#121	—	109	2	no	—
210	C₂×#121	D₁₀₉	1	1	yes	characteristic, complemented
211	C₂×#120	—	109	2	no	—
212	C₂×#120	—	109	2	no	—
213	C₂×C₄×D₄	—	109	1	no	—
214	C₂×C₄×D₄	—	109	1	no	—
215	C₂⁵	—	109	2	no	—
216	C₂⁵	—	109	2	no	—
217	C₂²×D₄	—	109	1	no	—
218	C₂²×D₄	—	109	2	no	—
219	C₂²×D₄	—	109	2	no	—
220	C₂²×D₄	—	109	2	no	—
221	C₂²×D₄	—	109	16	no	—
222	C₂²×D₄	—	109	8	no	—
223	C₂²×D₄	—	109	1	no	—
224	C₂²×D₄	—	109	2	no	—
225	C₂²×D₄	—	109	2	no	—
226	C₂²×D₄	—	109	1	no	—
227	C₂²×D₄	—	109	8	no	—
228	C₂²×D₄	—	218	8	no	—
229	C₂²×D₄	—	218	16	no	—
230	C₂²×D₄	—	218	8	no	—
231	C₂²×D₄	C₂×D₁₀₉	1	2	yes	complemented
232	C₂²×D₄	C₂×D₁₀₉	1	1	yes	characteristic, complemented
233	C₂³×C₄	—	109	2	no	—
234	C₂³×C₄	—	109	1	no	—
235	C₂³×C₄	C₂×D₁₀₉	1	1	yes	characteristic, complemented
236	#127	—	109	8	no	—
237	#121	—	109	8	no	—
238	#121	—	109	16	no	—
239	#121	C₂×D₁₀₉	1	8	yes	complemented
240	#120	—	109	16	no	—
241	#120	—	109	16	no	—
242	C₄×D₄	—	109	8	no	—
243	C₄×D₄	—	109	8	no	—
244	C₂×C₄⋊C₄	—	109	1	no	—
245	C₂×C₄⋊C₄	C₂×D₁₀₉	1	1	yes	characteristic, complemented
246	C₂×C₂²⋊C₄	—	109	1	no	—
247	C₂×C₂²⋊C₄	—	109	2	no	—
248	C₂×C₂²⋊C₄	—	109	1	no	—
249	C₂×C₂²⋊C₄	—	109	2	no	—
250	C₂×C₂²⋊C₄	C₂×D₁₀₉	1	2	yes	complemented
251	C₂×C₄²	—	109	1	no	—
252	C₂⁴	—	109	1	no	—
253	C₂⁴	—	109	2	no	—
254	C₂⁴	—	109	8	no	—
255	C₂⁴	—	109	8	no	—
256	C₂⁴	—	109	2	no	—
257	C₂⁴	—	436	4	no	—
258	C₂⁴	—	436	4	no	—
259	C₂⁴	—	218	8	no	—
260	C₂⁴	—	218	8	no	—
261	C₂⁴	—	218	8	no	—
262	C₂⁴	—	218	8	no	—
263	C₂⁴	C₂²×D₁₀₉	1	2	yes	—
264	C₂⁴	C₂²×D₁₀₉	1	1	yes	characteristic
265	C₂×D₄	—	2	8	no	—
266	C₂×D₄	—	2	4	no	—
267	C₂×D₄	—	109	8	no	—
268	C₂×D₄	—	109	4	no	—
269	C₂×D₄	—	109	8	no	—
270	C₂×D₄	—	109	8	no	—
271	C₂×D₄	—	109	8	no	—
272	C₂×D₄	—	109	8	no	—
273	C₂×D₄	—	109	4	no	—
274	C₂×D₄	—	109	8	no	—
275	C₂×D₄	—	109	8	no	—
276	C₂×D₄	—	109	4	no	—
277	C₂×D₄	—	436	4	no	—
278	C₂×D₄	—	218	32	no	—
279	C₂×D₄	—	218	8	no	—
280	C₂×D₄	—	218	8	no	—
281	C₂×D₄	—	218	8	no	—
282	C₂×D₄	—	218	64	no	—
283	C₂×D₄	—	218	32	no	—
284	C₂×D₄	—	218	8	no	—
285	C₂×D₄	—	218	4	no	—
286	C₂×D₄	C₂²×D₁₀₉	1	8	yes	complemented
287	C₂×D₄	C₂²×D₁₀₉	1	4	yes	complemented
288	C₂²×C₄	—	2	4	no	—
289	C₂²×C₄	—	109	1	no	—
290	C₂²×C₄	—	109	1	no	—
291	C₂²×C₄	—	109	1	no	—
292	C₂²×C₄	—	109	8	no	—
293	C₂²×C₄	—	109	4	no	—
294	C₂²×C₄	—	218	8	no	—
295	C₂²×C₄	—	218	4	no	—
296	C₂²×C₄	C₂²×D₁₀₉	1	2	yes	—
297	C₂²×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
298	C₂²×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
299	C₂²×C₄	C₂²×D₁₀₉	1	4	yes	complemented
300	C₄⋊C₄	—	109	4	no	—
301	C₄⋊C₄	C₂²×D₁₀₉	1	4	yes	complemented
302	C₂²⋊C₄	—	109	4	no	—
303	C₂²⋊C₄	—	109	8	no	—
304	C₂²⋊C₄	—	109	4	no	—
305	C₂²⋊C₄	—	109	8	no	—
306	C₂²⋊C₄	C₂²×D₁₀₉	1	8	yes	complemented
307	C₄²	—	109	4	no	—
308	C₂³	—	2	2	no	—
309	C₂³	—	2	2	no	—
310	C₂³	—	2	4	no	—
311	C₂³	—	2	4	no	—
312	C₂³	—	2	4	no	—
313	C₂³	—	109	4	no	—
314	C₂³	—	109	8	no	—
315	C₂³	—	109	2	no	—
316	C₂³	—	109	4	no	—
317	C₂³	—	109	4	no	—
318	C₂³	—	436	32	no	—
319	C₂³	—	436	8	no	—
320	C₂³	—	436	8	no	—
321	C₂³	—	436	32	no	—
322	C₂³	—	218	16	no	—
323	C₂³	—	218	16	no	—
324	C₂³	—	218	16	no	—
325	C₂³	—	218	4	no	—
326	C₂³	—	218	4	no	—
327	C₂³	—	218	16	no	—
328	C₂³	—	218	4	no	—
329	C₂³	—	218	4	no	—
330	C₂³	—	218	2	no	—
331	C₂³	—	218	4	no	—
332	C₂³	—	218	2	no	—
333	C₂³	D₄×D₁₀₉	1	4	yes	complemented
334	C₂³	C₂³×D₁₀₉	1	4	yes	—
335	C₂³	C₂³×D₁₀₉	1	2	yes	—
336	C₂³	C₂³×D₁₀₉	1	1	yes	characteristic
337	D₄	—	2	16	no	—
338	D₄	—	2	8	no	—
339	D₄	—	109	16	no	—
340	D₄	—	109	16	no	—
341	D₄	—	436	8	no	—
342	D₄	—	218	16	no	—
343	D₄	—	218	16	no	—
344	D₄	—	218	16	no	—
345	D₄	—	218	16	no	—
346	D₄	—	218	8	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	4	no	—
349	C₂×C₄	—	2	8	no	—
350	C₂×C₄	—	109	4	no	—
351	C₂×C₄	—	109	2	no	—
352	C₂×C₄	—	109	2	no	—
353	C₂×C₄	—	109	2	no	—
354	C₂×C₄	—	218	16	no	—
355	C₂×C₄	—	218	2	no	—
356	C₂×C₄	—	218	2	no	—
357	C₂×C₄	—	218	8	no	—
358	C₂×C₄	D₄×D₁₀₉	1	4	yes	complemented
359	C₂×C₄	C₂³×D₁₀₉	1	4	yes	—
360	C₂×C₄	C₂³×D₁₀₉	1	2	yes	—
361	C₂×C₄	C₂³×D₁₀₉	1	2	yes	—
362	C₂²	—	2	2	no	—
363	C₂²	—	2	2	no	—
364	C₂²	—	2	8	no	—
365	C₂²	—	2	4	no	—
366	C₂²	—	2	4	no	—
367	C₂²	—	2	4	no	—
368	C₂²	—	4	8	no	—
369	C₂²	—	109	4	no	—
370	C₂²	—	109	8	no	—
371	C₂²	—	436	32	no	—
372	C₂²	—	436	32	no	—
373	C₂²	—	436	8	no	—
374	C₂²	—	218	4	no	—
375	C₂²	—	218	4	no	—
376	C₂²	—	218	4	no	—
377	C₂²	—	218	4	no	—
378	C₂²	—	218	2	no	—
379	C₂²	—	218	4	no	—
380	C₂²	—	218	2	no	—
381	C₂²	—	218	16	no	—
382	C₂²	—	218	8	no	—
383	C₂²	C₂×D₄×D₁₀₉	1	2	yes	—
384	C₂²	C₂×D₄×D₁₀₉	1	2	yes	—
385	C₂²	C₂×D₄×D₁₀₉	1	4	yes	complemented
386	C₂²	#16812745	1	2	yes	—
387	C₂²	C₂⁴×D₁₀₉	1	1	yes	characteristic
388	C₄	—	2	2	no	—
389	C₄	—	2	4	no	—
390	C₄	—	109	4	no	—
391	C₄	—	218	2	no	—
392	C₄	—	218	2	no	—
393	C₄	C₂×D₄×D₁₀₉	1	4	yes	complemented
394	C₂	—	2	4	no	—
395	C₂	—	4	4	no	—
396	C₂	—	436	4	no	—
397	C₂	—	218	8	no	—
398	C₂	—	218	4	no	—
399	C₂	#20295660	1	4	yes	direct product factor
400	C₂	C₂²×D₄×D₁₀₉	1	1	yes	characteristic
401	C₂	C₂²×D₄×D₁₀₉	1	1	yes	characteristic
402	C₂	C₂×#16812745	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂³×D₁₀₉
commutator, cosocle	C₂²×C₁₀₉	C₂⁵
Frattini	C₂²	C₂⁴×D₁₀₉
Fitting	C₂×#121×C₁₀₉	C₂
socle	C₂³×C₁₀₉	C₂⁴
hypercenter	C₂×#121	D₁₀₉
hypocenter	C₁₀₉	C₂×D₄²
LCS	G ▷ C₂²×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂³ ◁ C₂×#121

Complements

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

N	H ≅ G/N	type
1. C₂³×D₄₃₆	C₂	semidirect
2. C₂²×D₄×D₁₀₉	C₂	semidirect
3. C₂²×D₄×D₁₀₉	C₂	semidirect
4. #20295660	C₂	direct (N × H)
5. C₂×#16812695	C₂	semidirect
6. C₂×#16812674	C₂	semidirect
7. C₂×#16812672	C₂	semidirect
8. C₂×#16812669	C₂	semidirect
9. C₂×#16812667	C₂	semidirect
10. C₂×#16812661	C₂	semidirect
11. C₂×C₄×C₂²⋊D₁₀₉	C₂	semidirect
12. C₂×#121×C₁₀₉	C₂	semidirect
13. C₂⁴×D₁₀₉	C₂²	semidirect
14. C₂⁴×D₁₀₉	C₂²	semidirect
17. C₂²×D₄₃₆	C₂²	semidirect
18. C₂²×D₄₃₆	C₂²	semidirect
19. C₂²×D₄₃₆	C₂²	semidirect
20. C₂²×D₄₃₆	C₂²	semidirect
22. C₂²×C₂²⋊D₁₀₉	C₂²	semidirect
23. C₂²×C₂²⋊D₁₀₉	C₂²	semidirect
24. C₂²×C₂²⋊D₁₀₉	C₂²	semidirect
27. C₂×D₄×D₁₀₉	C₂²	semidirect
28. C₂×D₄×D₁₀₉	C₂²	semidirect
29. C₂²×C₄×D₁₀₉	C₂²	semidirect
30. C₂²×C₄×D₁₀₉	C₂²	semidirect
31. #16812695	C₂²	semidirect
32. #16812674	C₂²	semidirect
33. #16812672	C₂²	semidirect
34. #16812669	C₂²	semidirect
35. #16812667	C₂²	semidirect
36. #16812661	C₂²	semidirect
37. C₄×C₂²⋊D₁₀₉	C₂²	semidirect
38. C₂×#13182008	C₂²	semidirect
39. C₂×C₂²⋊Dic₁₀₉	C₂²	semidirect
40. C₂×#13182006	C₂²	semidirect
41. C₂×#13182006	C₂²	semidirect
42. C₂×#13182006	C₂²	semidirect
43. C₂×C₄×Dic₁₀₉	C₂²	semidirect
44. C₂²×D₄×C₁₀₉	C₂²	semidirect
45. C₂²×D₄×C₁₀₉	C₂²	semidirect
46. C₂³×C₄×C₁₀₉	C₂²	semidirect
47. #121×C₁₀₉	C₂²	semidirect
48. C₂×C₄⋊C₄×C₁₀₉	C₂²	semidirect
49. C₂×C₂²⋊C₄×C₁₀₉	C₂²	semidirect
59. C₂³×D₁₀₉	C₂³	semidirect
60. C₂³×D₁₀₉	C₂³	semidirect
65. C₂×D₄₃₆	D₄	semidirect
67. C₂×D₄₃₆	C₂³	semidirect
68. C₂×D₄₃₆	C₂³	semidirect
69. C₂×D₄₃₆	C₂³	semidirect
73. C₂×C₂²⋊D₁₀₉	D₄	semidirect
75. C₂×C₂²⋊D₁₀₉	C₂³	semidirect
76. C₂×C₂²⋊D₁₀₉	C₂³	semidirect
77. C₂×C₂²⋊D₁₀₉	C₂³	semidirect
85. C₂×C₄×D₁₀₉	C₂³	semidirect
86. C₂×C₄×D₁₀₉	C₂³	semidirect
87. #13182008	C₂³	semidirect
88. C₂²⋊Dic₁₀₉	C₂³	semidirect
89. #13182006	C₂³	semidirect
90. #13182006	C₂³	semidirect
91. #13182006	C₂³	semidirect
92. C₄×Dic₁₀₉	C₂³	semidirect
97. C₂×D₄×C₁₀₉	C₂³	semidirect
98. C₂×D₄×C₁₀₉	C₂³	semidirect
103. C₂²×C₄×C₁₀₉	C₂³	semidirect
104. C₄⋊C₄×C₁₀₉	C₂³	semidirect
105. C₂²⋊C₄×C₁₀₉	C₂³	semidirect
111. C₂³×C₁₀₉	C₂×D₄	semidirect
130. C₂²×D₁₀₉	C₂×D₄	semidirect
131. C₂²×D₁₀₉	C₂×D₄	semidirect
140. C₂×C₄×C₁₀₉	C₂×D₄	semidirect
147. C₂²⋊D₁₀₉	C₂×D₄	semidirect
150. C₂×Dic₁₀₉	C₂×D₄	semidirect
157. D₄₃₆	C₂×D₄	semidirect
169. C₂²×C₁₀₉	C₂²×D₄	semidirect
184. C₂×D₁₀₉	C₂²×D₄	semidirect
185. C₂×D₁₀₉	C₂²×D₄	semidirect
188. C₄×C₁₀₉	C₂²×D₄	semidirect
191. Dic₁₀₉	C₂²×D₄	semidirect
194. C₂×C₁₀₉	D₄²	semidirect
202. C₁₀₉	C₂×D₄²	semidirect
210. C₂×#121	D₁₀₉	semidirect
231. C₂²×D₄	C₂×D₁₀₉	semidirect
232. C₂²×D₄	C₂×D₁₀₉	semidirect
235. C₂³×C₄	C₂×D₁₀₉	semidirect
239. #121	C₂×D₁₀₉	semidirect
245. C₂×C₄⋊C₄	C₂×D₁₀₉	semidirect
250. C₂×C₂²⋊C₄	C₂×D₁₀₉	semidirect
286. C₂×D₄	C₂²×D₁₀₉	semidirect
287. C₂×D₄	C₂²×D₁₀₉	semidirect
299. C₂²×C₄	C₂²×D₁₀₉	semidirect
301. C₄⋊C₄	C₂²×D₁₀₉	semidirect
306. C₂²⋊C₄	C₂²×D₁₀₉	semidirect
333. C₂³	D₄×D₁₀₉	semidirect
358. C₂×C₄	D₄×D₁₀₉	semidirect
385. C₂²	C₂×D₄×D₁₀₉	semidirect
393. C₄	C₂×D₄×D₁₀₉	semidirect
399. C₂	#20295660	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×D₄₃₆	2
C₂²×D₄×D₁₀₉	2
#20295660	2
C₂×#16812695	2
C₂×#16812674	2
C₂×#16812672	2
C₂×#16812669	2
C₂×#16812667	2
C₂×#16812661	2
C₂×C₄×C₂²⋊D₁₀₉	2
C₂×#121×C₁₀₉	2
C₂×D₄²	109

Subgroups — C2×#20295660 #28376470

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20295660 #28376470