Subgroups — C₂×C₄×#123×C₁₀₃ #39939304

Order 26368.

4070 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#123×C₁₀₃	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×D₄×C₁₀₃	C₂	1	1	yes	maximal, characteristic
3	C₂³×C₄²×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×#123×C₁₀₃	C₂	1	16	yes	maximal, direct product factor
5	C₂×#388×C₁₀₃	C₂	1	2	yes	maximal, complemented
6	C₂×#387×C₁₀₃	C₂	1	2	yes	maximal, complemented
7	C₂×#386×C₁₀₃	C₂	1	1	yes	maximal, characteristic
8	C₂×#385×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#381×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₄×C₄⋊C₄×C₁₀₃	C₂	1	2	yes	maximal, complemented
11	C₂×C₄×C₂²⋊C₄×C₁₀₃	C₂	1	2	yes	maximal, complemented
12	C₂×C₄×C₂²⋊C₄×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂³×D₄×C₁₀₃	C₂²	1	1	yes	characteristic
14	C₂⁴×C₄×C₁₀₃	C₂²	1	1	yes	characteristic
15	C₂⁴×C₄×C₁₀₃	C₂²	1	1	yes	characteristic
16	C₂⁴×C₄×C₁₀₃	C₂²	1	1	yes	characteristic
17	C₂⁴×C₄×C₁₀₃	C₂²	1	1	yes	characteristic
18	C₂×#123×C₁₀₃	C₄	1	16	yes	direct product factor
19	C₂×#123×C₁₀₃	C₂²	1	8	yes	—
20	C₂×C₄×D₄×C₁₀₃	—	2	8	no	—
21	C₂×C₄×D₄×C₁₀₃	C₂²	1	8	yes	—
22	C₂²×C₄⋊C₄×C₁₀₃	C₂²	1	2	yes	—
23	C₂²×C₄⋊C₄×C₁₀₃	C₂²	1	1	yes	characteristic
24	C₂²×C₄⋊C₄×C₁₀₃	C₂²	1	2	yes	—
25	C₂²×C₂²⋊C₄×C₁₀₃	C₂²	1	1	yes	characteristic
26	C₂²×C₂²⋊C₄×C₁₀₃	C₂²	1	2	yes	—
27	C₂²×C₂²⋊C₄×C₁₀₃	C₂²	1	1	yes	characteristic
28	C₂²×C₂²⋊C₄×C₁₀₃	C₂²	1	1	yes	characteristic
29	C₂²×C₂²⋊C₄×C₁₀₃	C₂²	1	1	yes	characteristic
30	C₂²×C₂²⋊C₄×C₁₀₃	C₂²	1	2	yes	—
31	C₂²×C₄²×C₁₀₃	—	2	8	no	—
32	C₂²×C₄²×C₁₀₃	C₂²	1	2	yes	—
33	C₂²×C₄²×C₁₀₃	C₂²	1	2	yes	—
34	C₂²×C₄²×C₁₀₃	C₂²	1	2	yes	—
35	C₂²×C₄²×C₁₀₃	C₂²	1	1	yes	characteristic
36	C₂²×C₄²×C₁₀₃	C₂²	1	8	yes	complemented
37	#388×C₁₀₃	C₂²	1	16	yes	complemented
38	#387×C₁₀₃	C₂²	1	16	yes	complemented
39	#386×C₁₀₃	C₂²	1	8	yes	—
40	#385×C₁₀₃	C₂²	1	8	yes	complemented
41	#381×C₁₀₃	C₂²	1	8	yes	complemented
42	C₄×C₄⋊C₄×C₁₀₃	C₂²	1	16	yes	complemented
43	C₄×C₂²⋊C₄×C₁₀₃	C₂²	1	16	yes	complemented
44	C₄×C₂²⋊C₄×C₁₀₃	C₂²	1	8	yes	complemented
45	C₂×#95×C₁₀₃	C₂²	1	2	yes	—
46	C₂×#95×C₁₀₃	C₂²	1	2	yes	—
47	C₂×#95×C₁₀₃	C₂²	1	2	yes	—
48	C₂×#95×C₁₀₃	C₂²	1	2	yes	—
49	C₂×#95×C₁₀₃	C₂²	1	2	yes	—
50	C₂⁵×C₁₀₃	C₂³	1	1	yes	characteristic
51	C₂⁵×C₁₀₃	C₂³	1	1	yes	characteristic
52	C₂²×D₄×C₁₀₃	—	2	4	no	—
53	C₂²×D₄×C₁₀₃	—	2	4	no	—
54	C₂²×D₄×C₁₀₃	C₂×C₄	1	8	yes	—
55	C₂²×D₄×C₁₀₃	C₂³	1	4	yes	—
56	C₂³×C₄×C₁₀₃	—	2	4	no	—
57	C₂³×C₄×C₁₀₃	—	2	4	no	—
58	C₂³×C₄×C₁₀₃	—	2	4	no	—
59	C₂³×C₄×C₁₀₃	—	2	8	no	—
60	C₂³×C₄×C₁₀₃	—	2	8	no	—
61	C₂³×C₄×C₁₀₃	—	2	4	no	—
62	C₂³×C₄×C₁₀₃	—	2	8	no	—
63	C₂³×C₄×C₁₀₃	C₂×C₄	1	8	yes	complemented
64	C₂³×C₄×C₁₀₃	D₄	1	8	yes	—
65	C₂³×C₄×C₁₀₃	C₂³	1	2	yes	—
66	C₂³×C₄×C₁₀₃	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₁₀₃	C₂³	1	1	yes	characteristic
68	C₂³×C₄×C₁₀₃	C₂³	1	4	yes	—
69	C₂³×C₄×C₁₀₃	C₂³	1	4	yes	—
70	C₂³×C₄×C₁₀₃	C₂³	1	2	yes	—
71	C₂³×C₄×C₁₀₃	C₂³	1	2	yes	—
72	C₂³×C₄×C₁₀₃	C₂³	1	1	yes	characteristic
73	C₂³×C₄×C₁₀₃	C₂³	1	4	yes	—
74	C₂³×C₄×C₁₀₃	C₂³	1	1	yes	characteristic
75	C₂³×C₄×C₁₀₃	C₂³	1	4	yes	—
76	C₂³×C₄×C₁₀₃	C₂³	1	2	yes	—
77	C₂³×C₄×C₁₀₃	C₂³	1	1	yes	characteristic
78	#123×C₁₀₃	C₂×C₄	1	64	yes	direct product factor
79	C₄×D₄×C₁₀₃	—	2	32	no	—
80	C₂×C₄⋊C₄×C₁₀₃	—	2	4	no	—
81	C₂×C₄⋊C₄×C₁₀₃	—	2	8	no	—
82	C₂×C₄⋊C₄×C₁₀₃	C₂×C₄	1	16	yes	complemented
83	C₂×C₄⋊C₄×C₁₀₃	C₂³	1	8	yes	—
84	C₂×C₄⋊C₄×C₁₀₃	C₂³	1	4	yes	—
85	C₂×C₄⋊C₄×C₁₀₃	C₂³	1	8	yes	—
86	C₂×C₂²⋊C₄×C₁₀₃	—	2	4	no	—
87	C₂×C₂²⋊C₄×C₁₀₃	—	2	4	no	—
88	C₂×C₂²⋊C₄×C₁₀₃	—	2	4	no	—
89	C₂×C₂²⋊C₄×C₁₀₃	—	2	8	no	—
90	C₂×C₂²⋊C₄×C₁₀₃	C₂×C₄	1	8	yes	complemented
91	C₂×C₂²⋊C₄×C₁₀₃	C₂×C₄	1	16	yes	complemented
92	C₂×C₂²⋊C₄×C₁₀₃	C₂³	1	4	yes	—
93	C₂×C₂²⋊C₄×C₁₀₃	C₂³	1	8	yes	—
94	C₂×C₂²⋊C₄×C₁₀₃	C₂³	1	4	yes	—
95	C₂×C₂²⋊C₄×C₁₀₃	C₂³	1	4	yes	—
96	C₂×C₂²⋊C₄×C₁₀₃	C₂³	1	4	yes	—
97	C₂×C₂²⋊C₄×C₁₀₃	C₂³	1	8	yes	—
98	C₂×C₄²×C₁₀₃	—	2	8	no	—
99	C₂×C₄²×C₁₀₃	—	2	8	no	—
100	C₂×C₄²×C₁₀₃	—	2	32	no	—
101	C₂×C₄²×C₁₀₃	—	2	4	no	—
102	C₂×C₄²×C₁₀₃	—	2	8	no	—
103	C₂×C₄²×C₁₀₃	C₂³	1	8	yes	—
104	C₂×C₄²×C₁₀₃	C₂³	1	8	yes	—
105	C₂×C₄²×C₁₀₃	C₂³	1	4	yes	—
106	C₂×C₄²×C₁₀₃	C₂³	1	8	yes	—
107	#95×C₁₀₃	C₂³	1	8	yes	—
108	#95×C₁₀₃	C₂³	1	8	yes	—
109	#95×C₁₀₃	C₂³	1	8	yes	—
110	#95×C₁₀₃	C₂³	1	8	yes	—
111	#95×C₁₀₃	C₂³	1	8	yes	—
112	C₂⁴×C₁₀₃	—	2	4	no	—
113	C₂⁴×C₁₀₃	—	2	4	no	—
114	C₂⁴×C₁₀₃	—	2	2	no	—
115	C₂⁴×C₁₀₃	—	2	4	no	—
116	C₂⁴×C₁₀₃	—	2	4	no	—
117	C₂⁴×C₁₀₃	—	2	2	no	—
118	C₂⁴×C₁₀₃	C₂²×C₄	1	4	yes	—
119	C₂⁴×C₁₀₃	C₂²×C₄	1	4	yes	—
120	C₂⁴×C₁₀₃	C₂×D₄	1	4	yes	—
121	C₂⁴×C₁₀₃	#41	1	4	yes	—
122	C₂⁴×C₁₀₃	C₂⁴	1	2	yes	—
123	C₂⁴×C₁₀₃	C₂⁴	1	2	yes	—
124	C₂⁴×C₁₀₃	C₂⁴	1	1	yes	characteristic
125	C₂×D₄×C₁₀₃	—	2	32	no	—
126	C₂×D₄×C₁₀₃	—	2	8	no	—
127	C₂×D₄×C₁₀₃	—	2	8	no	—
128	C₂×D₄×C₁₀₃	C₂²×C₄	1	16	yes	—
129	C₂²×C₄×C₁₀₃	—	2	32	no	—
130	C₂²×C₄×C₁₀₃	—	2	32	no	—
131	C₂²×C₄×C₁₀₃	—	2	8	no	—
132	C₂²×C₄×C₁₀₃	—	2	4	no	—
133	C₂²×C₄×C₁₀₃	—	2	8	no	—
134	C₂²×C₄×C₁₀₃	—	2	4	no	—
135	C₂²×C₄×C₁₀₃	—	2	2	no	—
136	C₂²×C₄×C₁₀₃	—	2	4	no	—
137	C₂²×C₄×C₁₀₃	—	2	4	no	—
138	C₂²×C₄×C₁₀₃	—	2	4	no	—
139	C₂²×C₄×C₁₀₃	—	2	8	no	—
140	C₂²×C₄×C₁₀₃	—	2	4	no	—
141	C₂²×C₄×C₁₀₃	—	2	4	no	—
142	C₂²×C₄×C₁₀₃	—	2	2	no	—
143	C₂²×C₄×C₁₀₃	—	2	32	no	—
144	C₂²×C₄×C₁₀₃	—	2	16	no	—
145	C₂²×C₄×C₁₀₃	—	2	16	no	—
146	C₂²×C₄×C₁₀₃	—	2	2	no	—
147	C₂²×C₄×C₁₀₃	—	2	2	no	—
148	C₂²×C₄×C₁₀₃	—	2	4	no	—
149	C₂²×C₄×C₁₀₃	—	2	4	no	—
150	C₂²×C₄×C₁₀₃	—	2	4	no	—
151	C₂²×C₄×C₁₀₃	—	2	4	no	—
152	C₂²×C₄×C₁₀₃	—	2	4	no	—
153	C₂²×C₄×C₁₀₃	—	2	8	no	—
154	C₂²×C₄×C₁₀₃	—	2	16	no	—
155	C₂²×C₄×C₁₀₃	—	4	16	no	—
156	C₂²×C₄×C₁₀₃	C₂²×C₄	1	8	yes	—
157	C₂²×C₄×C₁₀₃	C₂²×C₄	1	8	yes	—
158	C₂²×C₄×C₁₀₃	C₂²×C₄	1	4	yes	—
159	C₂²×C₄×C₁₀₃	C₂²×C₄	1	16	yes	complemented
160	C₂²×C₄×C₁₀₃	C₂×D₄	1	4	yes	—
161	C₂²×C₄×C₁₀₃	C₂×D₄	1	16	yes	—
162	C₂²×C₄×C₁₀₃	C₂×D₄	1	4	yes	—
163	C₂²×C₄×C₁₀₃	#41	1	8	yes	—
164	C₂²×C₄×C₁₀₃	#41	1	8	yes	—
165	C₂²×C₄×C₁₀₃	C₂⁴	1	4	yes	—
166	C₂²×C₄×C₁₀₃	C₂⁴	1	2	yes	—
167	C₂²×C₄×C₁₀₃	C₂⁴	1	2	yes	—
168	C₂²×C₄×C₁₀₃	C₂⁴	1	4	yes	—
169	C₂²×C₄×C₁₀₃	C₂⁴	1	4	yes	—
170	C₂²×C₄×C₁₀₃	C₂⁴	1	2	yes	—
171	C₂²×C₄×C₁₀₃	C₂⁴	1	2	yes	—
172	C₂²×C₄×C₁₀₃	C₂⁴	1	4	yes	—
173	C₂²×C₄×C₁₀₃	C₂⁴	1	2	yes	—
174	C₄⋊C₄×C₁₀₃	—	2	8	no	—
175	C₄⋊C₄×C₁₀₃	—	2	16	no	—
176	C₄⋊C₄×C₁₀₃	C₂²×C₄	1	32	yes	complemented
177	C₂²⋊C₄×C₁₀₃	—	2	8	no	—
178	C₂²⋊C₄×C₁₀₃	—	2	8	no	—
179	C₂²⋊C₄×C₁₀₃	—	2	8	no	—
180	C₂²⋊C₄×C₁₀₃	—	2	16	no	—
181	C₂²⋊C₄×C₁₀₃	C₂²×C₄	1	16	yes	complemented
182	C₂²⋊C₄×C₁₀₃	C₂²×C₄	1	32	yes	complemented
183	C₄²×C₁₀₃	—	2	16	no	—
184	C₄²×C₁₀₃	—	2	16	no	—
185	C₄²×C₁₀₃	—	2	8	no	—
186	C₄²×C₁₀₃	—	2	16	no	—
187	C₂³×C₁₀₃	—	2	16	no	—
188	C₂³×C₁₀₃	—	2	8	no	—
189	C₂³×C₁₀₃	—	2	8	no	—
190	C₂³×C₁₀₃	—	2	16	no	—
191	C₂³×C₁₀₃	—	2	4	no	—
192	C₂³×C₁₀₃	—	2	4	no	—
193	C₂³×C₁₀₃	—	2	8	no	—
194	C₂³×C₁₀₃	—	2	16	no	—
195	C₂³×C₁₀₃	—	2	2	no	—
196	C₂³×C₁₀₃	—	2	4	no	—
197	C₂³×C₁₀₃	—	2	4	no	—
198	C₂³×C₁₀₃	—	2	2	no	—
199	C₂³×C₁₀₃	—	4	4	no	—
200	C₂³×C₁₀₃	—	4	4	no	—
201	C₂³×C₁₀₃	—	4	8	no	—
202	C₂³×C₁₀₃	C₄×D₄	1	16	yes	—
203	C₂³×C₁₀₃	C₂³×C₄	1	4	yes	—
204	C₂³×C₁₀₃	C₂³×C₄	1	4	yes	—
205	C₂³×C₁₀₃	C₂³×C₄	1	2	yes	—
206	C₂³×C₁₀₃	C₂²×D₄	1	4	yes	—
207	C₂³×C₁₀₃	C₂²×D₄	1	2	yes	—
208	C₂³×C₁₀₃	C₂×#41	1	4	yes	—
209	C₂³×C₁₀₃	C₂×#41	1	2	yes	—
210	C₂³×C₁₀₃	C₂×#41	1	4	yes	—
211	C₂³×C₁₀₃	C₂×#41	1	4	yes	—
212	C₂³×C₁₀₃	C₂⁵	1	1	yes	characteristic
213	D₄×C₁₀₃	—	2	32	no	—
214	C₂×C₄×C₁₀₃	—	2	32	no	—
215	C₂×C₄×C₁₀₃	—	2	16	no	—
216	C₂×C₄×C₁₀₃	—	2	32	no	—
217	C₂×C₄×C₁₀₃	—	2	8	no	—
218	C₂×C₄×C₁₀₃	—	2	16	no	—
219	C₂×C₄×C₁₀₃	—	2	8	no	—
220	C₂×C₄×C₁₀₃	—	2	16	no	—
221	C₂×C₄×C₁₀₃	—	2	4	no	—
222	C₂×C₄×C₁₀₃	—	2	4	no	—
223	C₂×C₄×C₁₀₃	—	2	2	no	—
224	C₂×C₄×C₁₀₃	—	2	4	no	—
225	C₂×C₄×C₁₀₃	—	2	4	no	—
226	C₂×C₄×C₁₀₃	—	2	4	no	—
227	C₂×C₄×C₁₀₃	—	2	4	no	—
228	C₂×C₄×C₁₀₃	—	2	4	no	—
229	C₂×C₄×C₁₀₃	—	2	2	no	—
230	C₂×C₄×C₁₀₃	—	2	32	no	—
231	C₂×C₄×C₁₀₃	—	2	2	no	—
232	C₂×C₄×C₁₀₃	—	2	2	no	—
233	C₂×C₄×C₁₀₃	—	2	4	no	—
234	C₂×C₄×C₁₀₃	—	2	4	no	—
235	C₂×C₄×C₁₀₃	—	2	4	no	—
236	C₂×C₄×C₁₀₃	—	2	4	no	—
237	C₂×C₄×C₁₀₃	—	2	4	no	—
238	C₂×C₄×C₁₀₃	—	4	4	no	—
239	C₂×C₄×C₁₀₃	—	4	4	no	—
240	C₂×C₄×C₁₀₃	—	4	8	no	—
241	C₂×C₄×C₁₀₃	—	4	16	no	—
242	C₂×C₄×C₁₀₃	#123	1	16	yes	direct product factor
243	C₂×C₄×C₁₀₃	C₂³×C₄	1	8	yes	—
244	C₂×C₄×C₁₀₃	C₂³×C₄	1	8	yes	—
245	C₂×C₄×C₁₀₃	C₂³×C₄	1	4	yes	—
246	C₂×C₄×C₁₀₃	C₂²×D₄	1	4	yes	—
247	C₂×C₄×C₁₀₃	C₂²×D₄	1	4	yes	—
248	C₂×C₄×C₁₀₃	C₂×#41	1	8	yes	—
249	C₂×C₄×C₁₀₃	C₂×#41	1	8	yes	—
250	C₂²×C₁₀₃	—	2	8	no	—
251	C₂²×C₁₀₃	—	2	4	no	—
252	C₂²×C₁₀₃	—	2	4	no	—
253	C₂²×C₁₀₃	—	2	8	no	—
254	C₂²×C₁₀₃	—	2	32	no	—
255	C₂²×C₁₀₃	—	2	4	no	—
256	C₂²×C₁₀₃	—	2	8	no	—
257	C₂²×C₁₀₃	—	4	2	no	—
258	C₂²×C₁₀₃	—	4	2	no	—
259	C₂²×C₁₀₃	—	4	4	no	—
260	C₂²×C₁₀₃	—	4	16	no	—
261	C₂²×C₁₀₃	C₂×C₄×D₄	1	8	yes	—
262	C₂²×C₁₀₃	C₂×C₄×D₄	1	4	yes	—
263	C₂²×C₁₀₃	C₄×#41	1	8	yes	—
264	C₂²×C₁₀₃	C₂×#123	1	4	yes	—
265	C₂²×C₁₀₃	#525	1	4	yes	—
266	C₂²×C₁₀₃	#529	1	8	yes	—
267	C₂²×C₁₀₃	C₂⁴×C₄	1	1	yes	characteristic
268	C₂²×C₁₀₃	C₂³×D₄	1	1	yes	characteristic
269	C₂²×C₁₀₃	C₂²×#41	1	1	yes	characteristic
270	C₂²×C₁₀₃	C₂²×#41	1	2	yes	—
271	C₂²×C₁₀₃	C₂²×#41	1	2	yes	—
272	C₄×C₁₀₃	—	2	8	no	—
273	C₄×C₁₀₃	—	2	4	no	—
274	C₄×C₁₀₃	—	2	8	no	—
275	C₄×C₁₀₃	—	2	4	no	—
276	C₄×C₁₀₃	—	2	8	no	—
277	C₄×C₁₀₃	—	4	2	no	—
278	C₄×C₁₀₃	—	4	2	no	—
279	C₄×C₁₀₃	—	4	4	no	—
280	C₄×C₁₀₃	C₂×#123	1	8	yes	direct product factor
281	C₂×C₄×#123	C₁₀₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
282	C₂×C₁₀₃	—	2	8	no	—
283	C₂×C₁₀₃	—	4	4	no	—
284	C₂×C₁₀₃	C₄×#123	1	8	yes	direct product factor
285	C₂×C₁₀₃	C₂²×C₄×D₄	1	1	yes	characteristic
286	C₂×C₁₀₃	C₂×C₄×#41	1	2	yes	—
287	C₂×C₁₀₃	C₂²×#123	1	1	yes	characteristic
288	C₂×C₁₀₃	C₂×#525	1	1	yes	characteristic
289	C₂×C₁₀₃	C₂×#529	1	2	yes	—
290	C₂²×#123	C₂×C₁₀₃	1	1	yes	characteristic
291	C₂²×C₄×D₄	C₂×C₁₀₃	1	1	yes	characteristic
292	C₂³×C₄²	C₂×C₁₀₃	1	1	yes	characteristic, complemented
293	C₄×#123	C₂×C₁₀₃	1	16	yes	direct product factor
294	C₂×#388	C₂×C₁₀₃	1	2	yes	complemented
295	C₂×#387	C₂×C₁₀₃	1	2	yes	complemented
296	C₂×#386	C₂×C₁₀₃	1	1	yes	characteristic
297	C₂×#385	C₂×C₁₀₃	1	1	yes	characteristic, complemented
298	C₂×#381	C₂×C₁₀₃	1	1	yes	characteristic, complemented
299	C₂×C₄×C₄⋊C₄	C₂×C₁₀₃	1	2	yes	complemented
300	C₂×C₄×C₂²⋊C₄	C₂×C₁₀₃	1	1	yes	characteristic, complemented
301	C₂×C₄×C₂²⋊C₄	C₂×C₁₀₃	1	2	yes	complemented
302	C₁₀₃	C₂×C₄×#123	1	1	yes	characteristic, direct product factor, Sylow
303	C₂³×D₄	C₂²×C₁₀₃	1	1	yes	characteristic
304	C₂⁴×C₄	C₂²×C₁₀₃	1	1	yes	characteristic
305	C₂⁴×C₄	C₂²×C₁₀₃	1	1	yes	characteristic
306	C₂⁴×C₄	C₂²×C₁₀₃	1	1	yes	characteristic
307	C₂⁴×C₄	C₂²×C₁₀₃	1	1	yes	characteristic
308	C₂×#123	C₄×C₁₀₃	1	16	yes	direct product factor
309	C₂×#123	C₂²×C₁₀₃	1	8	yes	—
310	C₂×C₄×D₄	—	2	8	no	—
311	C₂×C₄×D₄	C₂²×C₁₀₃	1	8	yes	—
312	C₂²×C₄⋊C₄	C₂²×C₁₀₃	1	1	yes	characteristic
313	C₂²×C₄⋊C₄	C₂²×C₁₀₃	1	2	yes	—
314	C₂²×C₄⋊C₄	C₂²×C₁₀₃	1	2	yes	—
315	C₂²×C₂²⋊C₄	C₂²×C₁₀₃	1	1	yes	characteristic
316	C₂²×C₂²⋊C₄	C₂²×C₁₀₃	1	1	yes	characteristic
317	C₂²×C₂²⋊C₄	C₂²×C₁₀₃	1	1	yes	characteristic
318	C₂²×C₂²⋊C₄	C₂²×C₁₀₃	1	2	yes	—
319	C₂²×C₂²⋊C₄	C₂²×C₁₀₃	1	1	yes	characteristic
320	C₂²×C₂²⋊C₄	C₂²×C₁₀₃	1	2	yes	—
321	C₂²×C₄²	—	2	8	no	—
322	C₂²×C₄²	C₂²×C₁₀₃	1	2	yes	—
323	C₂²×C₄²	C₂²×C₁₀₃	1	2	yes	—
324	C₂²×C₄²	C₂²×C₁₀₃	1	1	yes	characteristic
325	C₂²×C₄²	C₂²×C₁₀₃	1	2	yes	—
326	C₂²×C₄²	C₂²×C₁₀₃	1	8	yes	complemented
327	#388	C₂²×C₁₀₃	1	16	yes	complemented
328	#387	C₂²×C₁₀₃	1	16	yes	complemented
329	#386	C₂²×C₁₀₃	1	8	yes	—
330	#385	C₂²×C₁₀₃	1	8	yes	complemented
331	#381	C₂²×C₁₀₃	1	8	yes	complemented
332	C₄×C₄⋊C₄	C₂²×C₁₀₃	1	16	yes	complemented
333	C₄×C₂²⋊C₄	C₂²×C₁₀₃	1	16	yes	complemented
334	C₄×C₂²⋊C₄	C₂²×C₁₀₃	1	8	yes	complemented
335	C₂×#95	C₂²×C₁₀₃	1	2	yes	—
336	C₂×#95	C₂²×C₁₀₃	1	2	yes	—
337	C₂×#95	C₂²×C₁₀₃	1	2	yes	—
338	C₂×#95	C₂²×C₁₀₃	1	2	yes	—
339	C₂×#95	C₂²×C₁₀₃	1	2	yes	—
340	C₂⁵	C₂³×C₁₀₃	1	1	yes	characteristic
341	C₂⁵	C₂³×C₁₀₃	1	1	yes	characteristic
342	C₂²×D₄	—	2	4	no	—
343	C₂²×D₄	—	2	4	no	—
344	C₂²×D₄	C₂×C₄×C₁₀₃	1	8	yes	—
345	C₂²×D₄	C₂³×C₁₀₃	1	4	yes	—
346	C₂³×C₄	—	2	4	no	—
347	C₂³×C₄	—	2	4	no	—
348	C₂³×C₄	—	2	4	no	—
349	C₂³×C₄	—	2	8	no	—
350	C₂³×C₄	—	2	8	no	—
351	C₂³×C₄	—	2	4	no	—
352	C₂³×C₄	—	2	8	no	—
353	C₂³×C₄	C₂×C₄×C₁₀₃	1	8	yes	complemented
354	C₂³×C₄	D₄×C₁₀₃	1	8	yes	—
355	C₂³×C₄	C₂³×C₁₀₃	1	1	yes	characteristic
356	C₂³×C₄	C₂³×C₁₀₃	1	2	yes	—
357	C₂³×C₄	C₂³×C₁₀₃	1	1	yes	characteristic
358	C₂³×C₄	C₂³×C₁₀₃	1	4	yes	—
359	C₂³×C₄	C₂³×C₁₀₃	1	4	yes	—
360	C₂³×C₄	C₂³×C₁₀₃	1	2	yes	—
361	C₂³×C₄	C₂³×C₁₀₃	1	2	yes	—
362	C₂³×C₄	C₂³×C₁₀₃	1	1	yes	characteristic
363	C₂³×C₄	C₂³×C₁₀₃	1	4	yes	—
364	C₂³×C₄	C₂³×C₁₀₃	1	1	yes	characteristic
365	C₂³×C₄	C₂³×C₁₀₃	1	4	yes	—
366	C₂³×C₄	C₂³×C₁₀₃	1	2	yes	—
367	C₂³×C₄	C₂³×C₁₀₃	1	1	yes	characteristic
368	#123	C₂×C₄×C₁₀₃	1	64	yes	direct product factor
369	C₄×D₄	—	2	32	no	—
370	C₂×C₄⋊C₄	—	2	4	no	—
371	C₂×C₄⋊C₄	—	2	8	no	—
372	C₂×C₄⋊C₄	C₂×C₄×C₁₀₃	1	16	yes	complemented
373	C₂×C₄⋊C₄	C₂³×C₁₀₃	1	4	yes	—
374	C₂×C₄⋊C₄	C₂³×C₁₀₃	1	8	yes	—
375	C₂×C₄⋊C₄	C₂³×C₁₀₃	1	8	yes	—
376	C₂×C₂²⋊C₄	—	2	4	no	—
377	C₂×C₂²⋊C₄	—	2	4	no	—
378	C₂×C₂²⋊C₄	—	2	4	no	—
379	C₂×C₂²⋊C₄	—	2	8	no	—
380	C₂×C₂²⋊C₄	C₂×C₄×C₁₀₃	1	8	yes	complemented
381	C₂×C₂²⋊C₄	C₂×C₄×C₁₀₃	1	16	yes	complemented
382	C₂×C₂²⋊C₄	C₂³×C₁₀₃	1	4	yes	—
383	C₂×C₂²⋊C₄	C₂³×C₁₀₃	1	4	yes	—
384	C₂×C₂²⋊C₄	C₂³×C₁₀₃	1	4	yes	—
385	C₂×C₂²⋊C₄	C₂³×C₁₀₃	1	8	yes	—
386	C₂×C₂²⋊C₄	C₂³×C₁₀₃	1	4	yes	—
387	C₂×C₂²⋊C₄	C₂³×C₁₀₃	1	8	yes	—
388	C₂×C₄²	—	2	4	no	—
389	C₂×C₄²	—	2	8	no	—
390	C₂×C₄²	—	2	8	no	—
391	C₂×C₄²	—	2	32	no	—
392	C₂×C₄²	—	2	8	no	—
393	C₂×C₄²	C₂³×C₁₀₃	1	4	yes	—
394	C₂×C₄²	C₂³×C₁₀₃	1	8	yes	—
395	C₂×C₄²	C₂³×C₁₀₃	1	8	yes	—
396	C₂×C₄²	C₂³×C₁₀₃	1	8	yes	—
397	#95	C₂³×C₁₀₃	1	8	yes	—
398	#95	C₂³×C₁₀₃	1	8	yes	—
399	#95	C₂³×C₁₀₃	1	8	yes	—
400	#95	C₂³×C₁₀₃	1	8	yes	—
401	#95	C₂³×C₁₀₃	1	8	yes	—
402	C₂⁴	—	2	4	no	—
403	C₂⁴	—	2	4	no	—
404	C₂⁴	—	2	2	no	—
405	C₂⁴	—	2	4	no	—
406	C₂⁴	—	2	4	no	—
407	C₂⁴	—	2	2	no	—
408	C₂⁴	C₂²×C₄×C₁₀₃	1	4	yes	—
409	C₂⁴	C₂²×C₄×C₁₀₃	1	4	yes	—
410	C₂⁴	C₂×D₄×C₁₀₃	1	4	yes	—
411	C₂⁴	#41×C₁₀₃	1	4	yes	—
412	C₂⁴	C₂⁴×C₁₀₃	1	2	yes	—
413	C₂⁴	C₂⁴×C₁₀₃	1	2	yes	—
414	C₂⁴	C₂⁴×C₁₀₃	1	1	yes	characteristic
415	C₂×D₄	—	2	32	no	—
416	C₂×D₄	—	2	8	no	—
417	C₂×D₄	—	2	8	no	—
418	C₂×D₄	C₂²×C₄×C₁₀₃	1	16	yes	—
419	C₂²×C₄	—	2	32	no	—
420	C₂²×C₄	—	2	32	no	—
421	C₂²×C₄	—	2	8	no	—
422	C₂²×C₄	—	2	4	no	—
423	C₂²×C₄	—	2	8	no	—
424	C₂²×C₄	—	2	4	no	—
425	C₂²×C₄	—	2	2	no	—
426	C₂²×C₄	—	2	4	no	—
427	C₂²×C₄	—	2	4	no	—
428	C₂²×C₄	—	2	4	no	—
429	C₂²×C₄	—	2	8	no	—
430	C₂²×C₄	—	2	4	no	—
431	C₂²×C₄	—	2	4	no	—
432	C₂²×C₄	—	2	2	no	—
433	C₂²×C₄	—	2	32	no	—
434	C₂²×C₄	—	2	16	no	—
435	C₂²×C₄	—	2	16	no	—
436	C₂²×C₄	—	2	2	no	—
437	C₂²×C₄	—	2	2	no	—
438	C₂²×C₄	—	2	4	no	—
439	C₂²×C₄	—	2	4	no	—
440	C₂²×C₄	—	2	4	no	—
441	C₂²×C₄	—	2	4	no	—
442	C₂²×C₄	—	2	4	no	—
443	C₂²×C₄	—	2	8	no	—
444	C₂²×C₄	—	2	16	no	—
445	C₂²×C₄	—	4	16	no	—
446	C₂²×C₄	C₂²×C₄×C₁₀₃	1	8	yes	—
447	C₂²×C₄	C₂²×C₄×C₁₀₃	1	8	yes	—
448	C₂²×C₄	C₂²×C₄×C₁₀₃	1	4	yes	—
449	C₂²×C₄	C₂²×C₄×C₁₀₃	1	16	yes	complemented
450	C₂²×C₄	C₂×D₄×C₁₀₃	1	4	yes	—
451	C₂²×C₄	C₂×D₄×C₁₀₃	1	16	yes	—
452	C₂²×C₄	C₂×D₄×C₁₀₃	1	4	yes	—
453	C₂²×C₄	#41×C₁₀₃	1	8	yes	—
454	C₂²×C₄	#41×C₁₀₃	1	8	yes	—
455	C₂²×C₄	C₂⁴×C₁₀₃	1	4	yes	—
456	C₂²×C₄	C₂⁴×C₁₀₃	1	2	yes	—
457	C₂²×C₄	C₂⁴×C₁₀₃	1	2	yes	—
458	C₂²×C₄	C₂⁴×C₁₀₃	1	4	yes	—
459	C₂²×C₄	C₂⁴×C₁₀₃	1	4	yes	—
460	C₂²×C₄	C₂⁴×C₁₀₃	1	2	yes	—
461	C₂²×C₄	C₂⁴×C₁₀₃	1	2	yes	—
462	C₂²×C₄	C₂⁴×C₁₀₃	1	4	yes	—
463	C₂²×C₄	C₂⁴×C₁₀₃	1	2	yes	—
464	C₄⋊C₄	—	2	8	no	—
465	C₄⋊C₄	—	2	16	no	—
466	C₄⋊C₄	C₂²×C₄×C₁₀₃	1	32	yes	complemented
467	C₂²⋊C₄	—	2	8	no	—
468	C₂²⋊C₄	—	2	8	no	—
469	C₂²⋊C₄	—	2	8	no	—
470	C₂²⋊C₄	—	2	16	no	—
471	C₂²⋊C₄	C₂²×C₄×C₁₀₃	1	16	yes	complemented
472	C₂²⋊C₄	C₂²×C₄×C₁₀₃	1	32	yes	complemented
473	C₄²	—	2	16	no	—
474	C₄²	—	2	16	no	—
475	C₄²	—	2	8	no	—
476	C₄²	—	2	16	no	—
477	C₂³	—	2	16	no	—
478	C₂³	—	2	8	no	—
479	C₂³	—	2	8	no	—
480	C₂³	—	2	16	no	—
481	C₂³	—	2	4	no	—
482	C₂³	—	2	4	no	—
483	C₂³	—	2	8	no	—
484	C₂³	—	2	16	no	—
485	C₂³	—	2	2	no	—
486	C₂³	—	2	4	no	—
487	C₂³	—	2	4	no	—
488	C₂³	—	2	2	no	—
489	C₂³	—	4	4	no	—
490	C₂³	—	4	4	no	—
491	C₂³	—	4	8	no	—
492	C₂³	C₄×D₄×C₁₀₃	1	16	yes	—
493	C₂³	C₂³×C₄×C₁₀₃	1	4	yes	—
494	C₂³	C₂³×C₄×C₁₀₃	1	4	yes	—
495	C₂³	C₂³×C₄×C₁₀₃	1	2	yes	—
496	C₂³	C₂²×D₄×C₁₀₃	1	4	yes	—
497	C₂³	C₂²×D₄×C₁₀₃	1	2	yes	—
498	C₂³	C₂×#41×C₁₀₃	1	4	yes	—
499	C₂³	C₂×#41×C₁₀₃	1	2	yes	—
500	C₂³	C₂×#41×C₁₀₃	1	4	yes	—
501	C₂³	C₂×#41×C₁₀₃	1	4	yes	—
502	C₂³	C₂⁵×C₁₀₃	1	1	yes	characteristic
503	D₄	—	2	32	no	—
504	C₂×C₄	—	2	32	no	—
505	C₂×C₄	—	2	16	no	—
506	C₂×C₄	—	2	32	no	—
507	C₂×C₄	—	2	8	no	—
508	C₂×C₄	—	2	16	no	—
509	C₂×C₄	—	2	8	no	—
510	C₂×C₄	—	2	16	no	—
511	C₂×C₄	—	2	4	no	—
512	C₂×C₄	—	2	4	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	4	no	—
515	C₂×C₄	—	2	4	no	—
516	C₂×C₄	—	2	4	no	—
517	C₂×C₄	—	2	4	no	—
518	C₂×C₄	—	2	4	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	2	32	no	—
521	C₂×C₄	—	2	2	no	—
522	C₂×C₄	—	2	2	no	—
523	C₂×C₄	—	2	4	no	—
524	C₂×C₄	—	2	4	no	—
525	C₂×C₄	—	2	4	no	—
526	C₂×C₄	—	2	4	no	—
527	C₂×C₄	—	2	4	no	—
528	C₂×C₄	—	4	4	no	—
529	C₂×C₄	—	4	4	no	—
530	C₂×C₄	—	4	8	no	—
531	C₂×C₄	—	4	16	no	—
532	C₂×C₄	#123×C₁₀₃	1	16	yes	direct product factor
533	C₂×C₄	C₂³×C₄×C₁₀₃	1	8	yes	—
534	C₂×C₄	C₂³×C₄×C₁₀₃	1	8	yes	—
535	C₂×C₄	C₂³×C₄×C₁₀₃	1	4	yes	—
536	C₂×C₄	C₂²×D₄×C₁₀₃	1	4	yes	—
537	C₂×C₄	C₂²×D₄×C₁₀₃	1	4	yes	—
538	C₂×C₄	C₂×#41×C₁₀₃	1	8	yes	—
539	C₂×C₄	C₂×#41×C₁₀₃	1	8	yes	—
540	C₂²	—	2	32	no	—
541	C₂²	—	2	8	no	—
542	C₂²	—	2	4	no	—
543	C₂²	—	2	4	no	—
544	C₂²	—	2	8	no	—
545	C₂²	—	2	4	no	—
546	C₂²	—	2	8	no	—
547	C₂²	—	4	16	no	—
548	C₂²	—	4	2	no	—
549	C₂²	—	4	2	no	—
550	C₂²	—	4	4	no	—
551	C₂²	C₂×C₄×D₄×C₁₀₃	1	8	yes	—
552	C₂²	C₂×C₄×D₄×C₁₀₃	1	4	yes	—
553	C₂²	C₄×#41×C₁₀₃	1	8	yes	—
554	C₂²	C₂×#123×C₁₀₃	1	4	yes	—
555	C₂²	#525×C₁₀₃	1	4	yes	—
556	C₂²	#529×C₁₀₃	1	8	yes	—
557	C₂²	C₂⁴×C₄×C₁₀₃	1	1	yes	characteristic
558	C₂²	C₂³×D₄×C₁₀₃	1	1	yes	characteristic
559	C₂²	C₂²×#41×C₁₀₃	1	1	yes	characteristic
560	C₂²	C₂²×#41×C₁₀₃	1	2	yes	—
561	C₂²	C₂²×#41×C₁₀₃	1	2	yes	—
562	C₄	—	2	8	no	—
563	C₄	—	2	4	no	—
564	C₄	—	2	8	no	—
565	C₄	—	2	4	no	—
566	C₄	—	2	8	no	—
567	C₄	—	4	2	no	—
568	C₄	—	4	2	no	—
569	C₄	—	4	4	no	—
570	C₄	C₂×#123×C₁₀₃	1	8	yes	direct product factor
571	C₂	—	2	8	no	—
572	C₂	—	4	4	no	—
573	C₂	C₄×#123×C₁₀₃	1	8	yes	direct product factor
574	C₂	C₂²×C₄×D₄×C₁₀₃	1	1	yes	characteristic
575	C₂	C₂×C₄×#41×C₁₀₃	1	2	yes	—
576	C₂	C₂²×#123×C₁₀₃	1	1	yes	characteristic
577	C₂	C₂×#525×C₁₀₃	1	1	yes	characteristic
578	C₂	C₂×#529×C₁₀₃	1	2	yes	—

	subgroup	G/H
center	C₂³×C₄×C₁₀₃	C₂³
commutator	C₂²	C₂⁴×C₄×C₁₀₃
Frattini, cosocle	C₂³	C₂⁵×C₁₀₃
socle	C₂⁴×C₁₀₃	C₂⁴
prime radical	C₂³×D₄×C₁₀₃	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₄×C₁₀₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂³×C₄²×C₁₀₃	C₂	semidirect
4. C₄×#123×C₁₀₃	C₂	direct (N × H)
5. C₂×#388×C₁₀₃	C₂	semidirect
6. C₂×#387×C₁₀₃	C₂	semidirect
8. C₂×#385×C₁₀₃	C₂	semidirect
9. C₂×#381×C₁₀₃	C₂	semidirect
10. C₂×C₄×C₄⋊C₄×C₁₀₃	C₂	semidirect
11. C₂×C₄×C₂²⋊C₄×C₁₀₃	C₂	semidirect
12. C₂×C₄×C₂²⋊C₄×C₁₀₃	C₂	semidirect
18. C₂×#123×C₁₀₃	C₄	direct (N × H)
36. C₂²×C₄²×C₁₀₃	C₂²	semidirect
37. #388×C₁₀₃	C₂²	semidirect
38. #387×C₁₀₃	C₂²	semidirect
40. #385×C₁₀₃	C₂²	semidirect
41. #381×C₁₀₃	C₂²	semidirect
42. C₄×C₄⋊C₄×C₁₀₃	C₂²	semidirect
43. C₄×C₂²⋊C₄×C₁₀₃	C₂²	semidirect
44. C₄×C₂²⋊C₄×C₁₀₃	C₂²	semidirect
63. C₂³×C₄×C₁₀₃	C₂×C₄	semidirect
78. #123×C₁₀₃	C₂×C₄	direct (N × H)
82. C₂×C₄⋊C₄×C₁₀₃	C₂×C₄	semidirect
90. C₂×C₂²⋊C₄×C₁₀₃	C₂×C₄	semidirect
91. C₂×C₂²⋊C₄×C₁₀₃	C₂×C₄	semidirect
159. C₂²×C₄×C₁₀₃	C₂²×C₄	semidirect
176. C₄⋊C₄×C₁₀₃	C₂²×C₄	semidirect
181. C₂²⋊C₄×C₁₀₃	C₂²×C₄	semidirect
182. C₂²⋊C₄×C₁₀₃	C₂²×C₄	semidirect
242. C₂×C₄×C₁₀₃	#123	direct (N × H)
280. C₄×C₁₀₃	C₂×#123	direct (N × H)
281. C₂×C₄×#123	C₁₀₃	direct (N × H)
284. C₂×C₁₀₃	C₄×#123	direct (N × H)
292. C₂³×C₄²	C₂×C₁₀₃	semidirect
293. C₄×#123	C₂×C₁₀₃	direct (N × H)
294. C₂×#388	C₂×C₁₀₃	semidirect
295. C₂×#387	C₂×C₁₀₃	semidirect
297. C₂×#385	C₂×C₁₀₃	semidirect
298. C₂×#381	C₂×C₁₀₃	semidirect
299. C₂×C₄×C₄⋊C₄	C₂×C₁₀₃	semidirect
300. C₂×C₄×C₂²⋊C₄	C₂×C₁₀₃	semidirect
301. C₂×C₄×C₂²⋊C₄	C₂×C₁₀₃	semidirect
302. C₁₀₃	C₂×C₄×#123	direct (N × H)
308. C₂×#123	C₄×C₁₀₃	direct (N × H)
326. C₂²×C₄²	C₂²×C₁₀₃	semidirect
327. #388	C₂²×C₁₀₃	semidirect
328. #387	C₂²×C₁₀₃	semidirect
330. #385	C₂²×C₁₀₃	semidirect
331. #381	C₂²×C₁₀₃	semidirect
332. C₄×C₄⋊C₄	C₂²×C₁₀₃	semidirect
333. C₄×C₂²⋊C₄	C₂²×C₁₀₃	semidirect
334. C₄×C₂²⋊C₄	C₂²×C₁₀₃	semidirect
353. C₂³×C₄	C₂×C₄×C₁₀₃	semidirect
368. #123	C₂×C₄×C₁₀₃	direct (N × H)
372. C₂×C₄⋊C₄	C₂×C₄×C₁₀₃	semidirect
380. C₂×C₂²⋊C₄	C₂×C₄×C₁₀₃	semidirect
381. C₂×C₂²⋊C₄	C₂×C₄×C₁₀₃	semidirect
449. C₂²×C₄	C₂²×C₄×C₁₀₃	semidirect
466. C₄⋊C₄	C₂²×C₄×C₁₀₃	semidirect
471. C₂²⋊C₄	C₂²×C₄×C₁₀₃	semidirect
472. C₂²⋊C₄	C₂²×C₄×C₁₀₃	semidirect
532. C₂×C₄	#123×C₁₀₃	direct (N × H)
570. C₄	C₂×#123×C₁₀₃	direct (N × H)
573. C₂	C₄×#123×C₁₀₃	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×#123×C₁₀₃	2
C₂²×C₄×D₄×C₁₀₃	2
C₂³×C₄²×C₁₀₃	2
C₄×#123×C₁₀₃	2
C₂×#388×C₁₀₃	2
C₂×#387×C₁₀₃	2
C₂×#386×C₁₀₃	2
C₂×#385×C₁₀₃	2
C₂×#381×C₁₀₃	2
C₂×C₄×C₄⋊C₄×C₁₀₃	2
C₂×C₄×C₂²⋊C₄×C₁₀₃	2
C₂×C₄×#123	103

Subgroups — C2×C4×#123×C103 #39939304

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×#123×C₁₀₃ #39939304