Subgroups — D₄×#13110105 #27208632

Order 13184.

1648 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13110105	C₂	1	2	yes	maximal, complemented
2	#20268462	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×Dic₂₀₆	C₂	1	1	yes	maximal, characteristic, complemented
4	#20268450	C₂	1	2	yes	maximal, complemented
5	#20268446	C₂	1	1	yes	maximal, characteristic, complemented
6	#20268442	C₂	1	2	yes	maximal, complemented
7	#20268437	C₂	1	2	yes	maximal, complemented
8	#20268431	C₂	1	4	yes	maximal, complemented
9	D₄×D₄₁₂	C₂	1	1	yes	maximal, characteristic, complemented
10	D₄×C₂²⋊D₁₀₃	C₂	1	2	yes	maximal, complemented
11	#20268341	C₂	1	1	yes	maximal, characteristic, complemented
12	#20268338	C₂	1	2	yes	maximal, complemented
13	#20268302	C₂	1	2	yes	maximal, complemented
14	#20268300	C₂	1	4	yes	maximal, complemented
15	C₄×#13110105	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×D₄×D₁₀₃	C₂	1	2	yes	maximal, complemented
17	C₂×C₄×D₄×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#13110105	—	2	16	no	—
19	C₂×#13110105	C₂²	1	1	yes	characteristic
20	C₂×#13110105	C₂²	1	4	yes	complemented
21	C₂×#13110105	C₂²	1	2	yes	complemented
22	C₂×#13110105	C₂²	1	4	yes	complemented
23	C₂×#13110105	C₂²	1	2	yes	complemented
24	C₂×#13110105	C₂²	1	2	yes	complemented
25	C₂²×Dic₂₀₆	C₂²	1	2	yes	complemented
26	C₂²×D₄₁₂	C₂²	1	2	yes	complemented
27	C₂²×C₂²⋊D₁₀₃	C₂²	1	4	yes	complemented
28	C₂×D₄×D₁₀₃	C₂²	1	2	yes	—
29	C₂²×C₄×D₁₀₃	C₂²	1	4	yes	complemented
30	#15693021	C₂²	1	1	yes	characteristic, complemented
31	#15693020	C₂²	1	2	yes	complemented
32	#15693018	C₂²	1	1	yes	characteristic, complemented
33	#15693017	C₂²	1	2	yes	complemented
34	#15693009	C₂²	1	2	yes	complemented
35	#15693007	C₂²	1	4	yes	complemented
36	#15693006	C₂²	1	4	yes	complemented
37	#15693004	C₂²	1	4	yes	complemented
38	#15693003	C₂²	1	4	yes	complemented
39	#15693000	C₂²	1	2	yes	complemented
40	#15693000	C₂²	1	2	yes	complemented
41	#15692999	C₂²	1	4	yes	complemented
42	#15692998	C₂²	1	4	yes	complemented
43	#15692996	C₂²	1	2	yes	complemented
44	#15692995	C₂²	1	2	yes	complemented
45	#15692995	C₂²	1	2	yes	complemented
46	#15692995	C₂²	1	2	yes	complemented
47	#15692995	C₂²	1	2	yes	complemented
48	#15692994	C₂²	1	4	yes	complemented
49	#15692994	C₂²	1	4	yes	complemented
50	#15692993	C₂²	1	4	yes	complemented
51	#15692992	C₂²	1	2	yes	complemented
52	#15692991	C₂²	1	4	yes	complemented
53	#15692990	C₂²	1	4	yes	complemented
54	#15692989	C₂²	1	4	yes	complemented
55	C₄×Dic₂₀₆	C₂²	1	1	yes	characteristic, complemented
56	C₄×Dic₂₀₆	C₂²	1	1	yes	characteristic, complemented
57	C₄×D₄₁₂	C₂²	1	2	yes	complemented
58	C₄×D₄₁₂	C₂²	1	2	yes	complemented
59	C₄×D₄₁₂	C₂²	1	1	yes	characteristic, complemented
60	C₄×D₄₁₂	C₂²	1	1	yes	characteristic, complemented
61	D₄×Dic₁₀₃	C₂²	1	2	yes	—
62	#15692983	C₂²	1	2	yes	complemented
63	C₄×C₂²⋊D₁₀₃	C₂²	1	4	yes	complemented
64	C₄×C₂²⋊D₁₀₃	C₂²	1	4	yes	complemented
65	C₄×C₂²⋊D₁₀₃	C₂²	1	2	yes	complemented
66	C₄×C₂²⋊D₁₀₃	C₂²	1	2	yes	complemented
67	(C₂²⋊D₁₀₃)⋊C₄	C₂²	1	4	yes	complemented
68	#15692980	C₂²	1	1	yes	characteristic, complemented
69	#15692978	C₂²	1	2	yes	complemented
70	C₄⋊C₄×D₁₀₃	C₂²	1	2	yes	complemented
71	C₂²⋊C₄×D₁₀₃	C₂²	1	4	yes	complemented
72	C₄²×D₁₀₃	C₂²	1	2	yes	complemented
73	C₂²×D₄×C₁₀₃	C₂²	1	1	yes	characteristic
74	C₂³×C₄×C₁₀₃	C₂²	1	2	yes	complemented
75	C₄×D₄×C₁₀₃	C₂²	1	1	yes	characteristic
76	C₄×D₄×C₁₀₃	C₂²	1	1	yes	characteristic
77	C₄×D₄×C₁₀₃	C₂²	1	2	yes	complemented
78	C₄×D₄×C₁₀₃	C₂²	1	1	yes	characteristic, complemented
79	C₄×D₄×C₁₀₃	C₂²	1	2	yes	complemented
80	C₄×D₄×C₁₀₃	C₂²	1	1	yes	characteristic, complemented
81	C₂×C₄⋊C₄×C₁₀₃	C₂²	1	1	yes	characteristic, complemented
82	C₂×C₂²⋊C₄×C₁₀₃	C₂²	1	2	yes	complemented
83	C₂×C₄²×C₁₀₃	C₂²	1	1	yes	characteristic, complemented
84	C₂³×D₁₀₃	C₂³	1	4	yes	—
85	#13110105	—	2	8	no	—
86	#13110105	—	2	16	no	—
87	#13110105	—	2	8	no	—
88	#13110105	—	2	16	no	—
89	#13110105	—	2	8	no	—
90	#13110105	D₄	1	8	yes	direct product factor
91	C₂×Dic₂₀₆	—	2	8	no	—
92	C₂×Dic₂₀₆	C₂³	1	4	yes	—
93	C₂×Dic₂₀₆	C₂³	1	2	yes	—
94	C₂×Dic₂₀₆	C₂³	1	1	yes	characteristic
95	C₂×D₄₁₂	—	2	8	no	—
96	C₂×D₄₁₂	C₂³	1	2	yes	—
97	C₂×D₄₁₂	C₂³	1	4	yes	—
98	C₂×D₄₁₂	C₂³	1	2	yes	—
99	C₂×D₄₁₂	C₂³	1	2	yes	—
100	C₂×D₄₁₂	C₂³	1	1	yes	characteristic
101	C₂×C₂²⋊D₁₀₃	—	2	16	no	—
102	C₂×C₂²⋊D₁₀₃	C₂³	1	4	yes	—
103	C₂×C₂²⋊D₁₀₃	C₂³	1	4	yes	—
104	C₂×C₂²⋊D₁₀₃	C₂³	1	4	yes	—
105	C₂×C₂²⋊D₁₀₃	C₂³	1	4	yes	—
106	C₂×C₂²⋊D₁₀₃	C₂³	1	4	yes	—
107	C₂×C₂²⋊D₁₀₃	C₂³	1	2	yes	—
108	D₄×D₁₀₃	—	2	8	no	—
109	C₂²×Dic₁₀₃	C₂³	1	4	yes	—
110	C₂×C₄×D₁₀₃	—	2	16	no	—
111	C₂×C₄×D₁₀₃	C₂³	1	2	yes	—
112	C₂×C₄×D₁₀₃	C₂³	1	4	yes	—
113	C₂×C₄×D₁₀₃	C₂³	1	4	yes	—
114	C₂×C₄×D₁₀₃	C₂³	1	4	yes	—
115	C₂×C₄×D₁₀₃	C₂³	1	2	yes	—
116	C₂×C₄×D₁₀₃	C₂³	1	2	yes	—
117	C₄⋊Dic₁₀₃	C₂³	1	2	yes	—
118	C₄⋊Dic₁₀₃	C₂³	1	1	yes	characteristic
119	C₄⋊Dic₁₀₃	C₂³	1	1	yes	characteristic
120	C₄⋊Dic₁₀₃	C₂³	1	2	yes	—
121	Dic₁₀₃⋊C₄	C₂³	1	4	yes	—
122	Dic₁₀₃⋊C₄	C₂³	1	2	yes	—
123	Dic₁₀₃⋊C₄	C₂³	1	2	yes	—
124	Dic₁₀₃⋊C₄	C₂³	1	4	yes	—
125	C₂²⋊Dic₁₀₃	C₂³	1	4	yes	—
126	C₂²⋊Dic₁₀₃	C₂³	1	2	yes	—
127	C₂²⋊Dic₁₀₃	C₂³	1	4	yes	—
128	(C₂×D₁₀₃)⋊C₄	C₂³	1	4	yes	—
129	(C₂×D₁₀₃)⋊C₄	C₂³	1	4	yes	—
130	(C₂×D₁₀₃)⋊C₄	C₂³	1	2	yes	—
131	(C₂×D₁₀₃)⋊C₄	C₂³	1	2	yes	—
132	(C₂×D₁₀₃)⋊C₄	C₂³	1	4	yes	—
133	(C₂×D₁₀₃)⋊C₄	C₂³	1	4	yes	—
134	C₄×Dic₁₀₃	C₂³	1	2	yes	—
135	C₄×Dic₁₀₃	C₂³	1	2	yes	—
136	C₄×Dic₁₀₃	C₂³	1	2	yes	—
137	C₂⁴×C₁₀₃	C₂³	1	2	yes	—
138	C₂×D₄×C₁₀₃	—	2	4	no	—
139	C₂×D₄×C₁₀₃	C₂³	1	2	yes	—
140	C₂×D₄×C₁₀₃	C₂³	1	1	yes	characteristic
141	C₂×D₄×C₁₀₃	C₂³	1	1	yes	characteristic
142	C₂²×C₄×C₁₀₃	—	2	8	no	—
143	C₂²×C₄×C₁₀₃	C₂³	1	2	yes	—
144	C₂²×C₄×C₁₀₃	C₂³	1	2	yes	—
145	C₂²×C₄×C₁₀₃	C₂³	1	2	yes	—
146	C₂²×C₄×C₁₀₃	C₂³	1	2	yes	—
147	C₂²×C₄×C₁₀₃	C₂³	1	1	yes	characteristic
148	C₂²×C₄×C₁₀₃	C₂³	1	2	yes	—
149	C₂²×C₄×C₁₀₃	C₂³	1	1	yes	characteristic
150	C₂²×C₄×C₁₀₃	C₂³	1	1	yes	characteristic
151	C₄⋊C₄×C₁₀₃	C₂³	1	1	yes	characteristic
152	C₄⋊C₄×C₁₀₃	C₂³	1	1	yes	characteristic
153	C₄⋊C₄×C₁₀₃	C₂³	1	2	yes	—
154	C₂²⋊C₄×C₁₀₃	C₂³	1	2	yes	—
155	C₂²⋊C₄×C₁₀₃	C₂³	1	2	yes	—
156	C₂²⋊C₄×C₁₀₃	C₂³	1	2	yes	—
157	C₂²⋊C₄×C₁₀₃	C₂³	1	2	yes	—
158	C₄²×C₁₀₃	C₂³	1	1	yes	characteristic
159	C₄²×C₁₀₃	C₂³	1	1	yes	characteristic
160	C₄²×C₁₀₃	C₂³	1	1	yes	characteristic
161	C₄²×C₁₀₃	C₂³	1	1	yes	characteristic
162	C₂³×C₁₀₃	—	2	4	no	—
163	C₂³×C₁₀₃	—	2	4	no	—
164	C₂³×C₁₀₃	—	4	2	no	—
165	C₂³×C₁₀₃	C₂⁴	1	2	yes	—
166	C₂³×C₁₀₃	C₂⁴	1	1	yes	characteristic
167	C₂³×C₁₀₃	C₂⁴	1	2	yes	—
168	C₂²×D₁₀₃	—	2	8	no	—
169	C₂²×D₁₀₃	—	2	8	no	—
170	C₂²×D₁₀₃	—	4	4	no	—
171	C₂²×D₁₀₃	C₂⁴	1	4	yes	—
172	C₂²×D₁₀₃	C₂⁴	1	2	yes	—
173	D₄×C₁₀₃	—	2	4	no	—
174	D₄×C₁₀₃	—	2	2	no	—
175	D₄×C₁₀₃	#41	1	4	yes	complemented
176	C₂×C₄×C₁₀₃	—	2	4	no	—
177	C₂×C₄×C₁₀₃	—	2	4	no	—
178	C₂×C₄×C₁₀₃	—	2	4	no	—
179	C₂×C₄×C₁₀₃	—	2	4	no	—
180	C₂×C₄×C₁₀₃	—	2	4	no	—
181	C₂×C₄×C₁₀₃	—	2	2	no	—
182	C₂×C₄×C₁₀₃	—	4	1	no	—
183	C₂×C₄×C₁₀₃	C₂×D₄	1	4	yes	complemented
184	C₂×C₄×C₁₀₃	C₂⁴	1	1	yes	characteristic
185	C₂×C₄×C₁₀₃	C₂⁴	1	1	yes	characteristic
186	C₂×C₄×C₁₀₃	C₂⁴	1	1	yes	characteristic
187	C₂×C₄×C₁₀₃	C₂⁴	1	2	yes	—
188	C₂×C₄×C₁₀₃	C₂⁴	1	2	yes	—
189	C₂×C₄×C₁₀₃	C₂⁴	1	1	yes	characteristic
190	C₂×C₄×C₁₀₃	C₂⁴	1	1	yes	characteristic
191	C₂×C₄×C₁₀₃	C₂⁴	1	1	yes	characteristic
192	C₂²⋊D₁₀₃	—	2	8	no	—
193	C₂²⋊D₁₀₃	—	2	8	no	—
194	C₂²⋊D₁₀₃	—	2	8	no	—
195	C₂²⋊D₁₀₃	—	2	8	no	—
196	C₂²⋊D₁₀₃	—	4	4	no	—
197	C₂²⋊D₁₀₃	C₂×D₄	1	8	yes	complemented
198	C₂×Dic₁₀₃	—	2	8	no	—
199	C₂×Dic₁₀₃	C₂⁴	1	2	yes	—
200	C₂×Dic₁₀₃	C₂⁴	1	2	yes	—
201	C₂×Dic₁₀₃	C₂⁴	1	4	yes	—
202	C₂×Dic₁₀₃	C₂⁴	1	2	yes	—
203	D₄₁₂	—	2	8	no	—
204	D₄₁₂	—	2	4	no	—
205	D₄₁₂	—	2	4	no	—
206	D₄₁₂	—	4	2	no	—
207	D₄₁₂	C₂×D₄	1	4	yes	complemented
208	C₄×D₁₀₃	—	2	8	no	—
209	C₄×D₁₀₃	—	2	8	no	—
210	C₄×D₁₀₃	—	2	4	no	—
211	C₄×D₁₀₃	—	2	8	no	—
212	C₄×D₁₀₃	—	4	2	no	—
213	C₄×D₁₀₃	C₂×D₄	1	8	yes	complemented
214	Dic₂₀₆	—	2	4	no	—
215	Dic₂₀₆	—	2	8	no	—
216	Dic₂₀₆	C₂×D₄	1	4	yes	complemented
217	C₂²×C₁₀₃	—	2	2	no	—
218	C₂²×C₁₀₃	—	2	1	no	—
219	C₂²×C₁₀₃	—	2	1	no	—
220	C₂²×C₁₀₃	—	2	2	no	—
221	C₂²×C₁₀₃	—	2	2	no	—
222	C₂²×C₁₀₃	—	2	2	no	—
223	C₂²×C₁₀₃	—	2	2	no	—
224	C₂²×C₁₀₃	—	4	8	no	—
225	C₂²×C₁₀₃	C₂²×D₄	1	2	yes	—
226	C₂²×C₁₀₃	C₂×#41	1	4	yes	complemented
227	C₂²×C₁₀₃	C₂⁵	1	1	yes	characteristic
228	C₂×D₁₀₃	—	2	2	no	—
229	C₂×D₁₀₃	—	2	2	no	—
230	C₂×D₁₀₃	—	2	4	no	—
231	C₂×D₁₀₃	—	2	4	no	—
232	C₂×D₁₀₃	—	2	4	no	—
233	C₂×D₁₀₃	—	4	16	no	—
234	C₂×D₁₀₃	C₂²×D₄	1	4	yes	—
235	C₄×C₁₀₃	—	2	2	no	—
236	C₄×C₁₀₃	—	2	2	no	—
237	C₄×C₁₀₃	—	2	1	no	—
238	C₄×C₁₀₃	—	2	1	no	—
239	C₄×C₁₀₃	—	2	1	no	—
240	C₄×C₁₀₃	C₂²×D₄	1	2	yes	—
241	C₄×C₁₀₃	C₂²×D₄	1	2	yes	—
242	C₄×C₁₀₃	C₂×#41	1	2	yes	complemented
243	Dic₁₀₃	—	2	4	no	—
244	Dic₁₀₃	—	2	2	no	—
245	Dic₁₀₃	—	2	2	no	—
246	Dic₁₀₃	C₂²×D₄	1	4	yes	—
247	C₂×C₁₀₃	—	2	4	no	—
248	C₂×C₁₀₃	—	2	2	no	—
249	C₂×C₁₀₃	—	4	2	no	—
250	C₂×C₁₀₃	C₂³×D₄	1	1	yes	characteristic
251	C₂×C₁₀₃	C₂²×#41	1	1	yes	characteristic
252	C₂×C₁₀₃	#585	1	1	yes	characteristic
253	D₁₀₃	—	2	4	no	—
254	D₁₀₃	—	4	4	no	—
255	D₄×#41	—	103	1	no	maximal, Sylow
256	C₁₀₃	D₄×#41	1	1	yes	characteristic, complemented, Sylow
257	C₂²×#41	—	103	2	no	—
258	#550	—	103	1	no	—
259	D₄×Q₈	—	103	1	no	—
260	#548	—	103	2	no	—
261	#547	—	103	1	no	—
262	#547	—	103	2	no	—
263	#546	—	103	2	no	—
264	#546	—	103	4	no	—
265	D₄²	—	103	2	no	—
266	D₄²	—	103	1	no	—
267	#532	—	103	2	no	—
268	#532	—	103	1	no	—
269	#525	—	103	2	no	—
270	#525	—	103	4	no	—
271	C₄×#41	—	103	1	no	—
272	C₂×C₄×D₄	—	103	2	no	—
273	C₂×C₄×D₄	D₁₀₃	1	1	yes	characteristic, complemented
274	C₂×#41	—	103	1	no	—
275	C₂×#41	—	103	4	no	—
276	C₂×#41	—	103	2	no	—
277	C₂×#41	—	103	2	no	—
278	C₂×#41	—	103	4	no	—
279	C₂×#41	—	103	2	no	—
280	C₂×#41	—	206	16	no	—
281	C₂²×Q₈	—	103	2	no	—
282	C₂²×D₄	—	103	4	no	—
283	C₂²×D₄	—	103	2	no	—
284	C₂²×D₄	—	103	2	no	—
285	C₂²×D₄	C₂×D₁₀₃	1	1	yes	characteristic
286	C₂³×C₄	—	103	4	no	—
287	C₂³×C₄	C₂×D₁₀₃	1	2	yes	complemented
288	C₄⋊Q₈	—	103	2	no	—
289	C₄⋊Q₈	—	103	1	no	—
290	#127	—	103	2	no	—
291	#127	—	103	1	no	—
292	#124	—	103	4	no	—
293	#124	—	103	2	no	—
294	#123	—	103	4	no	—
295	#123	—	103	4	no	—
296	#123	—	103	4	no	—
297	C₂²⋊Q₈	—	103	2	no	—
298	C₂²⋊Q₈	—	103	2	no	—
299	C₂²⋊Q₈	—	103	4	no	—
300	C₂²⋊Q₈	—	103	4	no	—
301	#121	—	103	4	no	—
302	#121	—	103	2	no	—
303	#121	—	103	2	no	—
304	#121	—	103	2	no	—
305	#121	—	103	2	no	—
306	#121	—	103	2	no	—
307	#121	—	103	2	no	—
308	#121	—	103	4	no	—
309	#121	—	103	4	no	—
310	#120	—	103	4	no	—
311	#120	—	103	4	no	—
312	#120	—	103	4	no	—
313	C₄×Q₈	—	103	1	no	—
314	C₄×Q₈	—	103	1	no	—
315	C₄×D₄	—	103	2	no	—
316	C₄×D₄	—	103	4	no	—
317	C₄×D₄	—	103	2	no	—
318	C₄×D₄	—	103	2	no	—
319	C₄×D₄	—	103	4	no	—
320	C₄×D₄	—	103	2	no	—
321	C₄×D₄	—	103	4	no	—
322	C₄×D₄	—	103	2	no	—
323	C₄×D₄	—	103	1	no	—
324	C₄×D₄	—	103	1	no	—
325	C₄×D₄	—	103	2	no	—
326	C₄×D₄	C₂×D₁₀₃	1	1	yes	characteristic
327	C₄×D₄	C₂×D₁₀₃	1	1	yes	characteristic
328	C₄×D₄	C₂×D₁₀₃	1	2	yes	complemented
329	C₄×D₄	C₂×D₁₀₃	1	1	yes	characteristic, complemented
330	C₄×D₄	C₂×D₁₀₃	1	2	yes	complemented
331	C₄×D₄	C₂×D₁₀₃	1	1	yes	characteristic, complemented
332	#117	—	103	1	no	—
333	#117	—	103	2	no	—
334	C₂×C₄⋊C₄	—	103	2	no	—
335	C₂×C₄⋊C₄	C₂×D₁₀₃	1	1	yes	characteristic, complemented
336	C₂×C₂²⋊C₄	—	103	4	no	—
337	C₂×C₂²⋊C₄	C₂×D₁₀₃	1	2	yes	complemented
338	C₂×C₄²	—	103	2	no	—
339	C₂×C₄²	C₂×D₁₀₃	1	1	yes	characteristic, complemented
340	C₂⁴	—	103	4	no	—
341	C₂⁴	C₂²×D₁₀₃	1	2	yes	—
342	#41	—	103	8	no	—
343	#41	—	206	16	no	—
344	#41	—	206	16	no	—
345	#41	—	206	8	no	—
346	#41	—	206	8	no	—
347	#41	—	206	8	no	—
348	C₂×Q₈	—	103	1	no	—
349	C₂×Q₈	—	103	4	no	—
350	C₂×Q₈	—	103	2	no	—
351	C₂×Q₈	—	206	8	no	—
352	C₂×D₄	—	2	4	no	—
353	C₂×D₄	—	103	2	no	—
354	C₂×D₄	—	103	4	no	—
355	C₂×D₄	—	103	4	no	—
356	C₂×D₄	—	103	4	no	—
357	C₂×D₄	—	103	4	no	—
358	C₂×D₄	—	103	4	no	—
359	C₂×D₄	—	103	1	no	—
360	C₂×D₄	—	103	2	no	—
361	C₂×D₄	—	103	2	no	—
362	C₂×D₄	—	103	4	no	—
363	C₂×D₄	—	103	2	no	—
364	C₂×D₄	—	206	8	no	—
365	C₂×D₄	—	206	16	no	—
366	C₂×D₄	—	206	8	no	—
367	C₂×D₄	C₂²×D₁₀₃	1	2	yes	—
368	C₂×D₄	C₂²×D₁₀₃	1	1	yes	characteristic
369	C₂×D₄	C₂²×D₁₀₃	1	1	yes	characteristic
370	C₂²×C₄	—	2	8	no	—
371	C₂²×C₄	—	103	2	no	—
372	C₂²×C₄	—	103	4	no	—
373	C₂²×C₄	—	103	2	no	—
374	C₂²×C₄	—	103	2	no	—
375	C₂²×C₄	—	103	4	no	—
376	C₂²×C₄	—	103	4	no	—
377	C₂²×C₄	—	103	4	no	—
378	C₂²×C₄	—	206	16	no	—
379	C₂²×C₄	C₂²×D₁₀₃	1	1	yes	characteristic
380	C₂²×C₄	C₂²×D₁₀₃	1	2	yes	—
381	C₂²×C₄	C₂²×D₁₀₃	1	2	yes	—
382	C₂²×C₄	C₂²×D₁₀₃	1	2	yes	—
383	C₂²×C₄	C₂²×D₁₀₃	1	2	yes	—
384	C₂²×C₄	C₂²×D₁₀₃	1	2	yes	—
385	C₂²×C₄	C₂²×D₁₀₃	1	1	yes	characteristic
386	C₂²×C₄	C₂²×D₁₀₃	1	1	yes	characteristic
387	C₄⋊C₄	—	103	4	no	—
388	C₄⋊C₄	—	103	2	no	—
389	C₄⋊C₄	—	103	2	no	—
390	C₄⋊C₄	—	103	4	no	—
391	C₄⋊C₄	—	103	2	no	—
392	C₄⋊C₄	—	103	1	no	—
393	C₄⋊C₄	—	103	1	no	—
394	C₄⋊C₄	—	103	2	no	—
395	C₄⋊C₄	C₂²×D₁₀₃	1	1	yes	characteristic
396	C₄⋊C₄	C₂²×D₁₀₃	1	1	yes	characteristic
397	C₄⋊C₄	C₂²×D₁₀₃	1	2	yes	—
398	C₂²⋊C₄	—	103	4	no	—
399	C₂²⋊C₄	—	103	2	no	—
400	C₂²⋊C₄	—	103	4	no	—
401	C₂²⋊C₄	—	103	4	no	—
402	C₂²⋊C₄	—	103	4	no	—
403	C₂²⋊C₄	—	103	2	no	—
404	C₂²⋊C₄	—	103	2	no	—
405	C₂²⋊C₄	—	103	4	no	—
406	C₂²⋊C₄	—	103	4	no	—
407	C₂²⋊C₄	C₂²×D₁₀₃	1	2	yes	—
408	C₂²⋊C₄	C₂²×D₁₀₃	1	2	yes	—
409	C₂²⋊C₄	C₂²×D₁₀₃	1	2	yes	—
410	C₂²⋊C₄	C₂²×D₁₀₃	1	2	yes	—
411	C₄²	—	103	2	no	—
412	C₄²	—	103	2	no	—
413	C₄²	—	103	2	no	—
414	C₄²	C₂²×D₁₀₃	1	1	yes	characteristic
415	C₄²	C₂²×D₁₀₃	1	1	yes	characteristic
416	C₄²	C₂²×D₁₀₃	1	1	yes	characteristic
417	C₄²	C₂²×D₁₀₃	1	1	yes	characteristic
418	C₂³	—	2	4	no	—
419	C₂³	—	2	4	no	—
420	C₂³	—	4	2	no	—
421	C₂³	—	103	2	no	—
422	C₂³	—	103	4	no	—
423	C₂³	—	412	4	no	—
424	C₂³	—	206	8	no	—
425	C₂³	—	206	8	no	—
426	C₂³	C₂³×D₁₀₃	1	2	yes	—
427	C₂³	C₂³×D₁₀₃	1	1	yes	characteristic
428	C₂³	C₂³×D₁₀₃	1	2	yes	—
429	Q₈	—	103	4	no	—
430	Q₈	—	206	8	no	—
431	Q₈	—	206	4	no	—
432	D₄	—	2	4	no	—
433	D₄	—	2	2	no	—
434	D₄	—	103	8	no	—
435	D₄	—	103	4	no	—
436	D₄	—	412	2	no	—
437	D₄	—	412	4	no	—
438	D₄	—	206	8	no	—
439	D₄	—	206	8	no	—
440	D₄	—	206	8	no	—
441	D₄	—	206	8	no	—
442	D₄	—	206	8	no	—
443	D₄	—	206	4	no	—
444	D₄	—	206	4	no	—
445	D₄	#13110105	1	4	yes	direct product factor
446	C₂×C₄	—	2	4	no	—
447	C₂×C₄	—	2	4	no	—
448	C₂×C₄	—	2	4	no	—
449	C₂×C₄	—	2	4	no	—
450	C₂×C₄	—	2	4	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	4	1	no	—
453	C₂×C₄	—	103	2	no	—
454	C₂×C₄	—	103	8	no	—
455	C₂×C₄	—	103	2	no	—
456	C₂×C₄	—	103	2	no	—
457	C₂×C₄	—	103	4	no	—
458	C₂×C₄	—	412	2	no	—
459	C₂×C₄	—	206	8	no	—
460	C₂×C₄	—	206	8	no	—
461	C₂×C₄	—	206	8	no	—
462	C₂×C₄	—	206	8	no	—
463	C₂×C₄	—	206	4	no	—
464	C₂×C₄	D₄×D₁₀₃	1	4	yes	complemented
465	C₂×C₄	C₂³×D₁₀₃	1	1	yes	characteristic
466	C₂×C₄	C₂³×D₁₀₃	1	1	yes	characteristic
467	C₂×C₄	C₂³×D₁₀₃	1	1	yes	characteristic
468	C₂×C₄	C₂³×D₁₀₃	1	2	yes	—
469	C₂×C₄	C₂³×D₁₀₃	1	2	yes	—
470	C₂×C₄	C₂³×D₁₀₃	1	1	yes	characteristic
471	C₂×C₄	C₂³×D₁₀₃	1	1	yes	characteristic
472	C₂×C₄	C₂³×D₁₀₃	1	1	yes	characteristic
473	C₂²	—	2	2	no	—
474	C₂²	—	2	1	no	—
475	C₂²	—	2	1	no	—
476	C₂²	—	2	2	no	—
477	C₂²	—	2	2	no	—
478	C₂²	—	2	2	no	—
479	C₂²	—	2	2	no	—
480	C₂²	—	4	8	no	—
481	C₂²	—	103	4	no	—
482	C₂²	—	412	16	no	—
483	C₂²	—	206	4	no	—
484	C₂²	—	206	4	no	—
485	C₂²	—	206	4	no	—
486	C₂²	—	206	2	no	—
487	C₂²	—	206	2	no	—
488	C₂²	C₂×D₄×D₁₀₃	1	2	yes	—
489	C₂²	C₂×#13110105	1	4	yes	complemented
490	C₂²	C₂⁴×D₁₀₃	1	1	yes	characteristic
491	C₄	—	2	2	no	—
492	C₄	—	2	2	no	—
493	C₄	—	2	1	no	—
494	C₄	—	2	1	no	—
495	C₄	—	2	1	no	—
496	C₄	—	103	4	no	—
497	C₄	—	206	4	no	—
498	C₄	—	206	2	no	—
499	C₄	—	206	2	no	—
500	C₄	C₂×D₄×D₁₀₃	1	2	yes	—
501	C₄	C₂×D₄×D₁₀₃	1	2	yes	—
502	C₄	C₂×#13110105	1	2	yes	complemented
503	C₂	—	2	2	no	—
504	C₂	—	2	4	no	—
505	C₂	—	4	2	no	—
506	C₂	—	412	4	no	—
507	C₂	—	206	4	no	—
508	C₂	C₂²×D₄×D₁₀₃	1	1	yes	characteristic
509	C₂	C₂²×#13110105	1	1	yes	characteristic
510	C₂	#20268627	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₁₀₃
commutator, socle, cosocle	C₂²×C₁₀₃	C₂⁵
Frattini	C₂²	C₂⁴×D₁₀₃
Fitting	C₂×C₄×D₄×C₁₀₃	C₂
hypercenter	C₂×C₄×D₄	D₁₀₃
hypocenter	C₁₀₃	D₄×#41
LCS	G ▷ C₂²×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×D₄

Complements

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

N	H ≅ G/N	type
1. C₂²×#13110105	C₂	semidirect
2. #20268462	C₂	semidirect
3. D₄×Dic₂₀₆	C₂	semidirect
4. #20268450	C₂	semidirect
5. #20268446	C₂	semidirect
6. #20268442	C₂	semidirect
7. #20268437	C₂	semidirect
8. #20268431	C₂	semidirect
9. D₄×D₄₁₂	C₂	semidirect
10. D₄×C₂²⋊D₁₀₃	C₂	semidirect
11. #20268341	C₂	semidirect
12. #20268338	C₂	semidirect
13. #20268302	C₂	semidirect
14. #20268300	C₂	semidirect
15. C₄×#13110105	C₂	semidirect
16. C₄×D₄×D₁₀₃	C₂	semidirect
17. C₂×C₄×D₄×C₁₀₃	C₂	semidirect
20. C₂×#13110105	C₂²	semidirect
21. C₂×#13110105	C₂²	semidirect
22. C₂×#13110105	C₂²	semidirect
23. C₂×#13110105	C₂²	semidirect
24. C₂×#13110105	C₂²	semidirect
25. C₂²×Dic₂₀₆	C₂²	semidirect
26. C₂²×D₄₁₂	C₂²	semidirect
27. C₂²×C₂²⋊D₁₀₃	C₂²	semidirect
29. C₂²×C₄×D₁₀₃	C₂²	semidirect
30. #15693021	C₂²	semidirect
31. #15693020	C₂²	semidirect
32. #15693018	C₂²	semidirect
33. #15693017	C₂²	semidirect
34. #15693009	C₂²	semidirect
35. #15693007	C₂²	semidirect
36. #15693006	C₂²	semidirect
37. #15693004	C₂²	semidirect
38. #15693003	C₂²	semidirect
39. #15693000	C₂²	semidirect
40. #15693000	C₂²	semidirect
41. #15692999	C₂²	semidirect
42. #15692998	C₂²	semidirect
43. #15692996	C₂²	semidirect
44. #15692995	C₂²	semidirect
45. #15692995	C₂²	semidirect
46. #15692995	C₂²	semidirect
47. #15692995	C₂²	semidirect
48. #15692994	C₂²	semidirect
49. #15692994	C₂²	semidirect
50. #15692993	C₂²	semidirect
51. #15692992	C₂²	semidirect
52. #15692991	C₂²	semidirect
53. #15692990	C₂²	semidirect
54. #15692989	C₂²	semidirect
55. C₄×Dic₂₀₆	C₂²	semidirect
56. C₄×Dic₂₀₆	C₂²	semidirect
57. C₄×D₄₁₂	C₂²	semidirect
58. C₄×D₄₁₂	C₂²	semidirect
59. C₄×D₄₁₂	C₂²	semidirect
60. C₄×D₄₁₂	C₂²	semidirect
62. #15692983	C₂²	semidirect
63. C₄×C₂²⋊D₁₀₃	C₂²	semidirect
64. C₄×C₂²⋊D₁₀₃	C₂²	semidirect
65. C₄×C₂²⋊D₁₀₃	C₂²	semidirect
66. C₄×C₂²⋊D₁₀₃	C₂²	semidirect
67. (C₂²⋊D₁₀₃)⋊C₄	C₂²	semidirect
68. #15692980	C₂²	semidirect
69. #15692978	C₂²	semidirect
70. C₄⋊C₄×D₁₀₃	C₂²	semidirect
71. C₂²⋊C₄×D₁₀₃	C₂²	semidirect
72. C₄²×D₁₀₃	C₂²	semidirect
74. C₂³×C₄×C₁₀₃	C₂²	semidirect
77. C₄×D₄×C₁₀₃	C₂²	semidirect
78. C₄×D₄×C₁₀₃	C₂²	semidirect
79. C₄×D₄×C₁₀₃	C₂²	semidirect
80. C₄×D₄×C₁₀₃	C₂²	semidirect
81. C₂×C₄⋊C₄×C₁₀₃	C₂²	semidirect
82. C₂×C₂²⋊C₄×C₁₀₃	C₂²	semidirect
83. C₂×C₄²×C₁₀₃	C₂²	semidirect
90. #13110105	D₄	direct (N × H)
175. D₄×C₁₀₃	#41	semidirect
183. C₂×C₄×C₁₀₃	C₂×D₄	semidirect
197. C₂²⋊D₁₀₃	C₂×D₄	semidirect
207. D₄₁₂	C₂×D₄	semidirect
213. C₄×D₁₀₃	C₂×D₄	semidirect
216. Dic₂₀₆	C₂×D₄	semidirect
226. C₂²×C₁₀₃	C₂×#41	semidirect
242. C₄×C₁₀₃	C₂×#41	semidirect
256. C₁₀₃	D₄×#41	semidirect
273. C₂×C₄×D₄	D₁₀₃	semidirect
287. C₂³×C₄	C₂×D₁₀₃	semidirect
328. C₄×D₄	C₂×D₁₀₃	semidirect
329. C₄×D₄	C₂×D₁₀₃	semidirect
330. C₄×D₄	C₂×D₁₀₃	semidirect
331. C₄×D₄	C₂×D₁₀₃	semidirect
335. C₂×C₄⋊C₄	C₂×D₁₀₃	semidirect
337. C₂×C₂²⋊C₄	C₂×D₁₀₃	semidirect
339. C₂×C₄²	C₂×D₁₀₃	semidirect
445. D₄	#13110105	direct (N × H)
464. C₂×C₄	D₄×D₁₀₃	semidirect
489. C₂²	C₂×#13110105	semidirect
502. C₄	C₂×#13110105	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#13110105	2
#20268462	2
D₄×Dic₂₀₆	2
#20268450	2
#20268446	2
#20268442	2
#20268437	2
#20268431	2
D₄×D₄₁₂	2
D₄×C₂²⋊D₁₀₃	2
#20268341	2
#20268338	2
#20268302	2
#20268300	2
C₄×#13110105	2
C₄×D₄×D₁₀₃	2
C₂×C₄×D₄×C₁₀₃	2
D₄×#41	103

Subgroups — D4×#13110105 #27208632

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄×#13110105 #27208632