Subgroups — C₂×C₁₀₃×#1476 #39922708

Order 26368.

1430 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#41×C₁₀₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#431×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₄×C₈×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₀₃×#1476	C₂	1	8	yes	maximal, direct product factor
5	C₂×Q₈⋊C₈×C₁₀₃	C₂	1	2	yes	maximal, complemented
6	C₂×D₄⋊C₈×C₁₀₃	C₂	1	2	yes	maximal, complemented
7	C₂²×#41×C₁₀₃	C₄	1	1	yes	characteristic
8	C₂³×C₈×C₁₀₃	—	2	1	no	—
9	C₄×#41×C₁₀₃	—	2	2	no	—
10	C₄×#41×C₁₀₃	—	2	2	no	—
11	C₄×#41×C₁₀₃	C₄	1	4	yes	—
12	C₄×#41×C₁₀₃	C₂²	1	4	yes	—
13	C₂×C₄×Q₈×C₁₀₃	C₄	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₁₀₃	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₁₀₃	—	2	1	no	—
16	C₂×C₄×D₄×C₁₀₃	—	2	1	no	—
17	C₂×C₄×D₄×C₁₀₃	C₄	1	1	yes	characteristic
18	C₂×C₄×D₄×C₁₀₃	C₂²	1	1	yes	characteristic
19	C₂×#117×C₁₀₃	—	2	1	no	—
20	C₂×#117×C₁₀₃	C₄	1	1	yes	characteristic
21	C₂²×C₄²×C₁₀₃	—	2	1	no	—
22	C₂²×C₄²×C₁₀₃	C₂²	1	1	yes	characteristic
23	#431×C₁₀₃	—	2	2	no	—
24	#431×C₁₀₃	C₂²	1	4	yes	complemented
25	C₂×C₄⋊C₈×C₁₀₃	C₂²	1	2	yes	—
26	C₂×C₂²⋊C₈×C₁₀₃	—	2	1	no	—
27	C₂×C₄×C₈×C₁₀₃	—	2	2	no	—
28	C₂×C₄×C₈×C₁₀₃	—	2	1	no	—
29	C₂×C₄×C₈×C₁₀₃	—	2	1	no	—
30	C₂×C₄×C₈×C₁₀₃	C₂²	1	2	yes	—
31	C₂×C₄×C₈×C₁₀₃	C₂²	1	4	yes	complemented
32	Q₈⋊C₈×C₁₀₃	C₂²	1	8	yes	complemented
33	D₄⋊C₈×C₁₀₃	C₂²	1	8	yes	complemented
34	C₂×#41×C₁₀₃	—	2	2	no	—
35	C₂×#41×C₁₀₃	—	2	4	no	—
36	C₂×#41×C₁₀₃	C₈	1	8	yes	complemented
37	C₂×#41×C₁₀₃	C₂×C₄	1	4	yes	—
38	C₂²×Q₈×C₁₀₃	C₂×C₄	1	1	yes	characteristic
39	C₂²×D₄×C₁₀₃	—	2	1	no	—
40	C₂²×D₄×C₁₀₃	C₂×C₄	1	1	yes	characteristic
41	C₂³×C₄×C₁₀₃	—	2	1	no	—
42	C₂³×C₄×C₁₀₃	—	2	1	no	—
43	C₂³×C₄×C₁₀₃	—	2	1	no	—
44	C₂³×C₄×C₁₀₃	C₂×C₄	1	1	yes	characteristic
45	C₂³×C₄×C₁₀₃	D₄	1	1	yes	characteristic
46	C₂³×C₄×C₁₀₃	D₄	1	1	yes	characteristic
47	C₂²×C₈×C₁₀₃	—	2	8	no	—
48	C₂²×C₈×C₁₀₃	—	2	2	no	—
49	C₂²×C₈×C₁₀₃	—	2	4	no	—
50	C₂²×C₈×C₁₀₃	—	2	2	no	—
51	C₄×Q₈×C₁₀₃	—	2	2	no	—
52	C₄×Q₈×C₁₀₃	—	2	1	no	—
53	C₄×Q₈×C₁₀₃	—	2	1	no	—
54	C₄×Q₈×C₁₀₃	C₂×C₄	1	4	yes	—
55	C₄×Q₈×C₁₀₃	C₂×C₄	1	2	yes	—
56	C₄×Q₈×C₁₀₃	C₂³	1	2	yes	—
57	C₄×D₄×C₁₀₃	—	2	4	no	—
58	C₄×D₄×C₁₀₃	—	2	4	no	—
59	C₄×D₄×C₁₀₃	—	2	4	no	—
60	C₄×D₄×C₁₀₃	—	2	4	no	—
61	C₄×D₄×C₁₀₃	—	2	2	no	—
62	C₄×D₄×C₁₀₃	—	2	1	no	—
63	C₄×D₄×C₁₀₃	—	2	1	no	—
64	C₄×D₄×C₁₀₃	C₂×C₄	1	4	yes	—
65	C₄×D₄×C₁₀₃	C₂×C₄	1	2	yes	—
66	C₄×D₄×C₁₀₃	C₂³	1	2	yes	—
67	#117×C₁₀₃	—	2	2	no	—
68	#117×C₁₀₃	—	2	4	no	—
69	#117×C₁₀₃	—	2	4	no	—
70	#117×C₁₀₃	C₂×C₄	1	4	yes	—
71	C₂×C₄⋊C₄×C₁₀₃	—	2	1	no	—
72	C₂×C₄⋊C₄×C₁₀₃	—	2	1	no	—
73	C₂×C₄⋊C₄×C₁₀₃	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄⋊C₄×C₁₀₃	C₂×C₄	1	1	yes	characteristic
75	C₂×C₂²⋊C₄×C₁₀₃	—	2	1	no	—
76	C₂×C₂²⋊C₄×C₁₀₃	—	2	1	no	—
77	C₂×C₂²⋊C₄×C₁₀₃	—	2	1	no	—
78	C₂×C₄²×C₁₀₃	—	2	1	no	—
79	C₂×C₄²×C₁₀₃	—	2	1	no	—
80	C₂×C₄²×C₁₀₃	—	2	1	no	—
81	C₂×C₄²×C₁₀₃	—	2	4	no	—
82	C₂×C₄²×C₁₀₃	—	2	4	no	—
83	C₂×C₄²×C₁₀₃	C₂×C₄	1	1	yes	characteristic
84	C₂×C₄²×C₁₀₃	C₂×C₄	1	2	yes	—
85	C₂×C₄²×C₁₀₃	D₄	1	1	yes	characteristic
86	C₂×C₄²×C₁₀₃	D₄	1	2	yes	—
87	C₂×C₄²×C₁₀₃	D₄	1	2	yes	—
88	C₂×C₄²×C₁₀₃	D₄	1	1	yes	characteristic
89	C₂×C₄²×C₁₀₃	C₂³	1	1	yes	characteristic
90	C₂×C₄²×C₁₀₃	C₂³	1	2	yes	—
91	C₄⋊C₈×C₁₀₃	—	2	2	no	—
92	C₄⋊C₈×C₁₀₃	C₂³	1	4	yes	—
93	C₂²⋊C₈×C₁₀₃	—	2	4	no	—
94	C₄×C₈×C₁₀₃	—	2	2	no	—
95	C₄×C₈×C₁₀₃	—	2	4	no	—
96	C₄×C₈×C₁₀₃	—	2	4	no	—
97	C₄×C₈×C₁₀₃	C₂³	1	4	yes	—
98	C₂⁴×C₁₀₃	—	2	1	no	—
99	C₂⁴×C₁₀₃	C₂²⋊C₄	1	1	yes	characteristic
100	#41×C₁₀₃	—	2	16	no	—
101	#41×C₁₀₃	—	2	8	no	—
102	#41×C₁₀₃	C₂×C₈	1	16	yes	complemented
103	C₂×Q₈×C₁₀₃	—	2	1	no	—
104	C₂×Q₈×C₁₀₃	—	2	2	no	—
105	C₂×Q₈×C₁₀₃	C₂×C₈	1	4	yes	complemented
106	C₂×Q₈×C₁₀₃	C₂²×C₄	1	2	yes	—
107	C₂×D₄×C₁₀₃	—	2	8	no	—
108	C₂×D₄×C₁₀₃	—	2	4	no	—
109	C₂×D₄×C₁₀₃	—	2	1	no	—
110	C₂×D₄×C₁₀₃	—	2	2	no	—
111	C₂×D₄×C₁₀₃	C₂×C₈	1	4	yes	complemented
112	C₂×D₄×C₁₀₃	C₂²×C₄	1	2	yes	—
113	C₂²×C₄×C₁₀₃	—	2	1	no	—
114	C₂²×C₄×C₁₀₃	—	2	8	no	—
115	C₂²×C₄×C₁₀₃	—	2	4	no	—
116	C₂²×C₄×C₁₀₃	—	2	4	no	—
117	C₂²×C₄×C₁₀₃	—	2	4	no	—
118	C₂²×C₄×C₁₀₃	—	2	1	no	—
119	C₂²×C₄×C₁₀₃	—	2	1	no	—
120	C₂²×C₄×C₁₀₃	—	2	2	no	—
121	C₂²×C₄×C₁₀₃	—	2	4	no	—
122	C₂²×C₄×C₁₀₃	—	2	2	no	—
123	C₂²×C₄×C₁₀₃	—	4	4	no	—
124	C₂²×C₄×C₁₀₃	—	4	4	no	—
125	C₂²×C₄×C₁₀₃	C₂²⋊C₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₀₃	C₂²⋊C₄	1	2	yes	—
127	C₂²×C₄×C₁₀₃	C₂²⋊C₄	1	2	yes	—
128	C₂²×C₄×C₁₀₃	C₂²⋊C₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₀₃	C₂²⋊C₄	1	2	yes	—
130	C₂²×C₄×C₁₀₃	C₂²⋊C₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₀₃	C₂×C₈	1	4	yes	—
132	C₂²×C₄×C₁₀₃	M₁₆	1	4	yes	—
133	C₂²×C₄×C₁₀₃	C₂²×C₄	1	1	yes	characteristic
134	C₂²×C₄×C₁₀₃	C₂²×C₄	1	2	yes	—
135	C₂²×C₄×C₁₀₃	C₂×D₄	1	2	yes	—
136	C₂²×C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₀₃	C₂×D₄	1	2	yes	—
138	C₂²×C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
139	C₂×C₈×C₁₀₃	—	2	8	no	—
140	C₂×C₈×C₁₀₃	—	2	16	no	—
141	C₂×C₈×C₁₀₃	—	2	4	no	—
142	C₂×C₈×C₁₀₃	—	2	4	no	—
143	C₂×C₈×C₁₀₃	—	4	4	no	—
144	C₄⋊C₄×C₁₀₃	—	2	4	no	—
145	C₄⋊C₄×C₁₀₃	—	2	2	no	—
146	C₄⋊C₄×C₁₀₃	—	2	1	no	—
147	C₄⋊C₄×C₁₀₃	—	2	1	no	—
148	C₄⋊C₄×C₁₀₃	—	2	2	no	—
149	C₄⋊C₄×C₁₀₃	C₂²×C₄	1	2	yes	—
150	C₄⋊C₄×C₁₀₃	C₂²×C₄	1	2	yes	—
151	C₂²⋊C₄×C₁₀₃	—	2	4	no	—
152	C₂²⋊C₄×C₁₀₃	—	2	4	no	—
153	C₂²⋊C₄×C₁₀₃	—	2	2	no	—
154	C₂²⋊C₄×C₁₀₃	—	2	2	no	—
155	C₄²×C₁₀₃	—	2	4	no	—
156	C₄²×C₁₀₃	—	2	2	no	—
157	C₄²×C₁₀₃	—	2	4	no	—
158	C₄²×C₁₀₃	—	2	2	no	—
159	C₄²×C₁₀₃	C₂²⋊C₄	1	2	yes	—
160	C₄²×C₁₀₃	C₂²⋊C₄	1	2	yes	—
161	C₄²×C₁₀₃	C₂²⋊C₄	1	2	yes	—
162	C₄²×C₁₀₃	C₂²×C₄	1	1	yes	characteristic
163	C₄²×C₁₀₃	C₂²×C₄	1	2	yes	—
164	C₄²×C₁₀₃	C₂×D₄	1	2	yes	—
165	C₄²×C₁₀₃	C₂×D₄	1	2	yes	—
166	C₄²×C₁₀₃	C₂×D₄	1	1	yes	characteristic
167	C₄²×C₁₀₃	C₂×D₄	1	1	yes	characteristic
168	C₄²×C₁₀₃	C₂⁴	1	1	yes	characteristic
169	C₂³×C₁₀₃	—	2	2	no	—
170	C₂³×C₁₀₃	—	2	2	no	—
171	C₂³×C₁₀₃	—	2	2	no	—
172	C₂³×C₁₀₃	—	2	4	no	—
173	C₂³×C₁₀₃	—	4	2	no	—
174	C₂³×C₁₀₃	—	4	2	no	—
175	C₂³×C₁₀₃	C₂²⋊C₈	1	4	yes	—
176	C₂³×C₁₀₃	C₂×C₂²⋊C₄	1	2	yes	—
177	C₂³×C₁₀₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
178	Q₈×C₁₀₃	—	2	2	no	—
179	Q₈×C₁₀₃	—	2	4	no	—
180	Q₈×C₁₀₃	C₂²×C₈	1	4	yes	complemented
181	D₄×C₁₀₃	—	2	16	no	—
182	D₄×C₁₀₃	—	2	2	no	—
183	D₄×C₁₀₃	—	2	4	no	—
184	D₄×C₁₀₃	C₂²×C₈	1	4	yes	complemented
185	C₂×C₄×C₁₀₃	—	2	2	no	—
186	C₂×C₄×C₁₀₃	—	2	4	no	—
187	C₂×C₄×C₁₀₃	—	2	2	no	—
188	C₂×C₄×C₁₀₃	—	2	2	no	—
189	C₂×C₄×C₁₀₃	—	2	4	no	—
190	C₂×C₄×C₁₀₃	—	2	16	no	—
191	C₂×C₄×C₁₀₃	—	2	4	no	—
192	C₂×C₄×C₁₀₃	—	2	4	no	—
193	C₂×C₄×C₁₀₃	—	2	4	no	—
194	C₂×C₄×C₁₀₃	—	2	2	no	—
195	C₂×C₄×C₁₀₃	—	2	2	no	—
196	C₂×C₄×C₁₀₃	—	4	2	no	—
197	C₂×C₄×C₁₀₃	—	4	2	no	—
198	C₂×C₄×C₁₀₃	—	4	4	no	—
199	C₂×C₄×C₁₀₃	—	4	4	no	—
200	C₂×C₄×C₁₀₃	—	4	8	no	—
201	C₂×C₄×C₁₀₃	C₂²⋊C₈	1	4	yes	—
202	C₂×C₄×C₁₀₃	C₂²⋊C₈	1	8	yes	—
203	C₂×C₄×C₁₀₃	#104	1	4	yes	—
204	C₂×C₄×C₁₀₃	C₂×C₂²⋊C₄	1	2	yes	—
205	C₂×C₄×C₁₀₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
206	C₂×C₄×C₁₀₃	C₂×C₂²⋊C₄	1	2	yes	—
207	C₂×C₄×C₁₀₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
208	C₂×C₄×C₁₀₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
209	C₂×C₄×C₁₀₃	C₂×C₂²⋊C₄	1	2	yes	—
210	C₂×C₄×C₁₀₃	C₂²×C₈	1	2	yes	—
211	C₂×C₄×C₁₀₃	C₂²×C₈	1	4	yes	—
212	C₂×C₄×C₁₀₃	C₂×M₁₆	1	2	yes	—
213	C₂×C₄×C₁₀₃	C₂×M₁₆	1	4	yes	—
214	C₂×C₄×C₁₀₃	#135	1	4	yes	—
215	C₂×C₄×C₁₀₃	C₂³×C₄	1	1	yes	characteristic
216	C₂×C₄×C₁₀₃	C₂²×D₄	1	1	yes	characteristic
217	C₂×C₄×C₁₀₃	C₂²×D₄	1	1	yes	characteristic
218	C₈×C₁₀₃	—	2	8	no	—
219	C₈×C₁₀₃	—	4	4	no	—
220	C₂²×C₁₀₃	—	2	2	no	—
221	C₂²×C₁₀₃	—	2	2	no	—
222	C₂²×C₁₀₃	—	2	8	no	—
223	C₂²×C₁₀₃	—	2	4	no	—
224	C₂²×C₁₀₃	—	4	2	no	—
225	C₂²×C₁₀₃	—	4	2	no	—
226	C₂²×C₁₀₃	—	4	8	no	—
227	C₂²×C₁₀₃	C₂×C₂²⋊C₈	1	4	yes	—
228	C₂²×C₁₀₃	C₂×C₂²⋊C₈	1	2	yes	—
229	C₂²×C₁₀₃	#416	1	2	yes	—
230	C₂²×C₁₀₃	C₂×#104	1	2	yes	—
231	C₂²×C₁₀₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
232	C₄×C₁₀₃	—	2	4	no	—
233	C₄×C₁₀₃	—	2	2	no	—
234	C₄×C₁₀₃	—	2	1	no	—
235	C₄×C₁₀₃	—	2	1	no	—
236	C₄×C₁₀₃	—	4	2	no	—
237	C₄×C₁₀₃	—	4	2	no	—
238	C₄×C₁₀₃	C₂×C₂²⋊C₈	1	4	yes	—
239	C₄×C₁₀₃	C₂×C₂²⋊C₈	1	2	yes	—
240	C₄×C₁₀₃	#416	1	2	yes	—
241	C₄×C₁₀₃	C₂×#104	1	4	yes	—
242	C₄×C₁₀₃	C₂³×C₈	1	1	yes	characteristic
243	C₄×C₁₀₃	C₂²×M₁₆	1	1	yes	characteristic
244	C₄×C₁₀₃	C₂×#135	1	2	yes	—
245	C₂×#1476	C₁₀₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
246	C₂×C₁₀₃	—	2	4	no	—
247	C₂×C₁₀₃	—	4	4	no	—
248	C₂×C₁₀₃	#1476	1	4	yes	direct product factor
249	C₂×C₁₀₃	C₂²×C₂²⋊C₈	1	1	yes	characteristic
250	C₂×C₁₀₃	C₂×#416	1	1	yes	characteristic
251	C₂×C₁₀₃	C₂²×#104	1	1	yes	characteristic
252	C₂×C₄×#41	C₂×C₁₀₃	1	1	yes	characteristic
253	C₂×#431	C₂×C₁₀₃	1	1	yes	characteristic, complemented
254	C₂²×C₄×C₈	C₂×C₁₀₃	1	1	yes	characteristic, complemented
255	#1476	C₂×C₁₀₃	1	8	yes	direct product factor
256	C₂×Q₈⋊C₈	C₂×C₁₀₃	1	2	yes	complemented
257	C₂×D₄⋊C₈	C₂×C₁₀₃	1	2	yes	complemented
258	C₁₀₃	C₂×#1476	1	1	yes	characteristic, direct product factor, Sylow
259	C₂²×#41	C₄×C₁₀₃	1	1	yes	characteristic
260	C₂³×C₈	—	2	1	no	—
261	C₄×#41	—	2	2	no	—
262	C₄×#41	—	2	2	no	—
263	C₄×#41	C₄×C₁₀₃	1	4	yes	—
264	C₄×#41	C₂²×C₁₀₃	1	4	yes	—
265	C₂×C₄×Q₈	C₄×C₁₀₃	1	1	yes	characteristic
266	C₂×C₄×Q₈	C₂²×C₁₀₃	1	1	yes	characteristic
267	C₂×C₄×D₄	—	2	1	no	—
268	C₂×C₄×D₄	—	2	1	no	—
269	C₂×C₄×D₄	C₄×C₁₀₃	1	1	yes	characteristic
270	C₂×C₄×D₄	C₂²×C₁₀₃	1	1	yes	characteristic
271	C₂×#117	—	2	1	no	—
272	C₂×#117	C₄×C₁₀₃	1	1	yes	characteristic
273	C₂²×C₄²	—	2	1	no	—
274	C₂²×C₄²	C₂²×C₁₀₃	1	1	yes	characteristic
275	#431	—	2	2	no	—
276	#431	C₂²×C₁₀₃	1	4	yes	complemented
277	C₂×C₄⋊C₈	C₂²×C₁₀₃	1	2	yes	—
278	C₂×C₂²⋊C₈	—	2	1	no	—
279	C₂×C₄×C₈	—	2	2	no	—
280	C₂×C₄×C₈	—	2	1	no	—
281	C₂×C₄×C₈	—	2	1	no	—
282	C₂×C₄×C₈	C₂²×C₁₀₃	1	2	yes	—
283	C₂×C₄×C₈	C₂²×C₁₀₃	1	4	yes	complemented
284	Q₈⋊C₈	C₂²×C₁₀₃	1	8	yes	complemented
285	D₄⋊C₈	C₂²×C₁₀₃	1	8	yes	complemented
286	C₂×#41	—	2	2	no	—
287	C₂×#41	—	2	4	no	—
288	C₂×#41	C₈×C₁₀₃	1	8	yes	complemented
289	C₂×#41	C₂×C₄×C₁₀₃	1	4	yes	—
290	C₂²×Q₈	C₂×C₄×C₁₀₃	1	1	yes	characteristic
291	C₂²×D₄	—	2	1	no	—
292	C₂²×D₄	C₂×C₄×C₁₀₃	1	1	yes	characteristic
293	C₂³×C₄	—	2	1	no	—
294	C₂³×C₄	—	2	1	no	—
295	C₂³×C₄	—	2	1	no	—
296	C₂³×C₄	C₂×C₄×C₁₀₃	1	1	yes	characteristic
297	C₂³×C₄	D₄×C₁₀₃	1	1	yes	characteristic
298	C₂³×C₄	D₄×C₁₀₃	1	1	yes	characteristic
299	C₂²×C₈	—	2	8	no	—
300	C₂²×C₈	—	2	2	no	—
301	C₂²×C₈	—	2	4	no	—
302	C₂²×C₈	—	2	2	no	—
303	C₄×Q₈	—	2	2	no	—
304	C₄×Q₈	—	2	1	no	—
305	C₄×Q₈	—	2	1	no	—
306	C₄×Q₈	C₂×C₄×C₁₀₃	1	4	yes	—
307	C₄×Q₈	C₂×C₄×C₁₀₃	1	2	yes	—
308	C₄×Q₈	C₂³×C₁₀₃	1	2	yes	—
309	C₄×D₄	—	2	4	no	—
310	C₄×D₄	—	2	4	no	—
311	C₄×D₄	—	2	4	no	—
312	C₄×D₄	—	2	4	no	—
313	C₄×D₄	—	2	2	no	—
314	C₄×D₄	—	2	1	no	—
315	C₄×D₄	—	2	1	no	—
316	C₄×D₄	C₂×C₄×C₁₀₃	1	4	yes	—
317	C₄×D₄	C₂×C₄×C₁₀₃	1	2	yes	—
318	C₄×D₄	C₂³×C₁₀₃	1	2	yes	—
319	#117	—	2	2	no	—
320	#117	—	2	4	no	—
321	#117	—	2	4	no	—
322	#117	C₂×C₄×C₁₀₃	1	4	yes	—
323	C₂×C₄⋊C₄	—	2	1	no	—
324	C₂×C₄⋊C₄	—	2	1	no	—
325	C₂×C₄⋊C₄	C₂×C₄×C₁₀₃	1	1	yes	characteristic
326	C₂×C₄⋊C₄	C₂×C₄×C₁₀₃	1	1	yes	characteristic
327	C₂×C₂²⋊C₄	—	2	1	no	—
328	C₂×C₂²⋊C₄	—	2	1	no	—
329	C₂×C₂²⋊C₄	—	2	1	no	—
330	C₂×C₄²	—	2	1	no	—
331	C₂×C₄²	—	2	1	no	—
332	C₂×C₄²	—	2	1	no	—
333	C₂×C₄²	—	2	4	no	—
334	C₂×C₄²	—	2	4	no	—
335	C₂×C₄²	C₂×C₄×C₁₀₃	1	1	yes	characteristic
336	C₂×C₄²	C₂×C₄×C₁₀₃	1	2	yes	—
337	C₂×C₄²	D₄×C₁₀₃	1	1	yes	characteristic
338	C₂×C₄²	D₄×C₁₀₃	1	2	yes	—
339	C₂×C₄²	D₄×C₁₀₃	1	2	yes	—
340	C₂×C₄²	D₄×C₁₀₃	1	1	yes	characteristic
341	C₂×C₄²	C₂³×C₁₀₃	1	1	yes	characteristic
342	C₂×C₄²	C₂³×C₁₀₃	1	2	yes	—
343	C₄⋊C₈	—	2	2	no	—
344	C₄⋊C₈	C₂³×C₁₀₃	1	4	yes	—
345	C₂²⋊C₈	—	2	4	no	—
346	C₄×C₈	—	2	2	no	—
347	C₄×C₈	—	2	4	no	—
348	C₄×C₈	—	2	4	no	—
349	C₄×C₈	C₂³×C₁₀₃	1	4	yes	—
350	C₂⁴	—	2	1	no	—
351	C₂⁴	C₂²⋊C₄×C₁₀₃	1	1	yes	characteristic
352	#41	—	2	16	no	—
353	#41	—	2	8	no	—
354	#41	C₂×C₈×C₁₀₃	1	16	yes	complemented
355	C₂×Q₈	—	2	1	no	—
356	C₂×Q₈	—	2	2	no	—
357	C₂×Q₈	C₂×C₈×C₁₀₃	1	4	yes	complemented
358	C₂×Q₈	C₂²×C₄×C₁₀₃	1	2	yes	—
359	C₂×D₄	—	2	8	no	—
360	C₂×D₄	—	2	4	no	—
361	C₂×D₄	—	2	1	no	—
362	C₂×D₄	—	2	2	no	—
363	C₂×D₄	C₂×C₈×C₁₀₃	1	4	yes	complemented
364	C₂×D₄	C₂²×C₄×C₁₀₃	1	2	yes	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	2	8	no	—
367	C₂²×C₄	—	2	4	no	—
368	C₂²×C₄	—	2	4	no	—
369	C₂²×C₄	—	2	4	no	—
370	C₂²×C₄	—	2	1	no	—
371	C₂²×C₄	—	2	1	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	4	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	4	4	no	—
376	C₂²×C₄	—	4	4	no	—
377	C₂²×C₄	C₂²⋊C₄×C₁₀₃	1	1	yes	characteristic
378	C₂²×C₄	C₂²⋊C₄×C₁₀₃	1	2	yes	—
379	C₂²×C₄	C₂²⋊C₄×C₁₀₃	1	2	yes	—
380	C₂²×C₄	C₂²⋊C₄×C₁₀₃	1	1	yes	characteristic
381	C₂²×C₄	C₂²⋊C₄×C₁₀₃	1	2	yes	—
382	C₂²×C₄	C₂²⋊C₄×C₁₀₃	1	1	yes	characteristic
383	C₂²×C₄	C₂×C₈×C₁₀₃	1	4	yes	—
384	C₂²×C₄	M₁₆×C₁₀₃	1	4	yes	—
385	C₂²×C₄	C₂²×C₄×C₁₀₃	1	1	yes	characteristic
386	C₂²×C₄	C₂²×C₄×C₁₀₃	1	2	yes	—
387	C₂²×C₄	C₂×D₄×C₁₀₃	1	2	yes	—
388	C₂²×C₄	C₂×D₄×C₁₀₃	1	1	yes	characteristic
389	C₂²×C₄	C₂×D₄×C₁₀₃	1	2	yes	—
390	C₂²×C₄	C₂×D₄×C₁₀₃	1	1	yes	characteristic
391	C₂×C₈	—	2	8	no	—
392	C₂×C₈	—	2	16	no	—
393	C₂×C₈	—	2	4	no	—
394	C₂×C₈	—	2	4	no	—
395	C₂×C₈	—	4	4	no	—
396	C₄⋊C₄	—	2	4	no	—
397	C₄⋊C₄	—	2	2	no	—
398	C₄⋊C₄	—	2	1	no	—
399	C₄⋊C₄	—	2	1	no	—
400	C₄⋊C₄	—	2	2	no	—
401	C₄⋊C₄	C₂²×C₄×C₁₀₃	1	2	yes	—
402	C₄⋊C₄	C₂²×C₄×C₁₀₃	1	2	yes	—
403	C₂²⋊C₄	—	2	4	no	—
404	C₂²⋊C₄	—	2	4	no	—
405	C₂²⋊C₄	—	2	2	no	—
406	C₂²⋊C₄	—	2	2	no	—
407	C₄²	—	2	4	no	—
408	C₄²	—	2	2	no	—
409	C₄²	—	2	4	no	—
410	C₄²	—	2	2	no	—
411	C₄²	C₂²⋊C₄×C₁₀₃	1	2	yes	—
412	C₄²	C₂²⋊C₄×C₁₀₃	1	2	yes	—
413	C₄²	C₂²⋊C₄×C₁₀₃	1	2	yes	—
414	C₄²	C₂²×C₄×C₁₀₃	1	1	yes	characteristic
415	C₄²	C₂²×C₄×C₁₀₃	1	2	yes	—
416	C₄²	C₂×D₄×C₁₀₃	1	2	yes	—
417	C₄²	C₂×D₄×C₁₀₃	1	2	yes	—
418	C₄²	C₂×D₄×C₁₀₃	1	1	yes	characteristic
419	C₄²	C₂×D₄×C₁₀₃	1	1	yes	characteristic
420	C₄²	C₂⁴×C₁₀₃	1	1	yes	characteristic
421	C₂³	—	2	2	no	—
422	C₂³	—	2	2	no	—
423	C₂³	—	2	4	no	—
424	C₂³	—	2	2	no	—
425	C₂³	—	4	2	no	—
426	C₂³	—	4	2	no	—
427	C₂³	C₂²⋊C₈×C₁₀₃	1	4	yes	—
428	C₂³	C₂×C₂²⋊C₄×C₁₀₃	1	2	yes	—
429	C₂³	C₂×C₂²⋊C₄×C₁₀₃	1	1	yes	characteristic
430	Q₈	—	2	4	no	—
431	Q₈	—	2	2	no	—
432	Q₈	C₂²×C₈×C₁₀₃	1	4	yes	complemented
433	D₄	—	2	16	no	—
434	D₄	—	2	4	no	—
435	D₄	—	2	2	no	—
436	D₄	C₂²×C₈×C₁₀₃	1	4	yes	complemented
437	C₂×C₄	—	2	4	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	16	no	—
442	C₂×C₄	—	2	4	no	—
443	C₂×C₄	—	2	4	no	—
444	C₂×C₄	—	2	4	no	—
445	C₂×C₄	—	2	4	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	2	no	—
450	C₂×C₄	—	4	4	no	—
451	C₂×C₄	—	4	8	no	—
452	C₂×C₄	—	4	4	no	—
453	C₂×C₄	C₂²⋊C₈×C₁₀₃	1	4	yes	—
454	C₂×C₄	C₂²⋊C₈×C₁₀₃	1	8	yes	—
455	C₂×C₄	#104×C₁₀₃	1	4	yes	—
456	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₃	1	2	yes	—
457	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₃	1	1	yes	characteristic
458	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₃	1	2	yes	—
459	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₃	1	1	yes	characteristic
460	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₃	1	1	yes	characteristic
461	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₃	1	2	yes	—
462	C₂×C₄	C₂²×C₈×C₁₀₃	1	2	yes	—
463	C₂×C₄	C₂²×C₈×C₁₀₃	1	4	yes	—
464	C₂×C₄	C₂×M₁₆×C₁₀₃	1	2	yes	—
465	C₂×C₄	C₂×M₁₆×C₁₀₃	1	4	yes	—
466	C₂×C₄	#135×C₁₀₃	1	4	yes	—
467	C₂×C₄	C₂³×C₄×C₁₀₃	1	1	yes	characteristic
468	C₂×C₄	C₂²×D₄×C₁₀₃	1	1	yes	characteristic
469	C₂×C₄	C₂²×D₄×C₁₀₃	1	1	yes	characteristic
470	C₈	—	2	8	no	—
471	C₈	—	4	4	no	—
472	C₂²	—	2	8	no	—
473	C₂²	—	2	2	no	—
474	C₂²	—	2	2	no	—
475	C₂²	—	2	4	no	—
476	C₂²	—	4	8	no	—
477	C₂²	—	4	2	no	—
478	C₂²	—	4	2	no	—
479	C₂²	C₂×C₂²⋊C₈×C₁₀₃	1	4	yes	—
480	C₂²	C₂×C₂²⋊C₈×C₁₀₃	1	2	yes	—
481	C₂²	#416×C₁₀₃	1	2	yes	—
482	C₂²	C₂×#104×C₁₀₃	1	2	yes	—
483	C₂²	C₂²×C₂²⋊C₄×C₁₀₃	1	1	yes	characteristic
484	C₄	—	2	4	no	—
485	C₄	—	2	2	no	—
486	C₄	—	2	1	no	—
487	C₄	—	2	1	no	—
488	C₄	—	4	2	no	—
489	C₄	—	4	2	no	—
490	C₄	C₂×C₂²⋊C₈×C₁₀₃	1	4	yes	—
491	C₄	C₂×C₂²⋊C₈×C₁₀₃	1	2	yes	—
492	C₄	#416×C₁₀₃	1	2	yes	—
493	C₄	C₂×#104×C₁₀₃	1	4	yes	—
494	C₄	C₂³×C₈×C₁₀₃	1	1	yes	characteristic
495	C₄	C₂²×M₁₆×C₁₀₃	1	1	yes	characteristic
496	C₄	C₂×#135×C₁₀₃	1	2	yes	—
497	C₂	—	2	4	no	—
498	C₂	—	4	4	no	—
499	C₂	C₁₀₃×#1476	1	4	yes	direct product factor
500	C₂	C₂²×C₂²⋊C₈×C₁₀₃	1	1	yes	characteristic
501	C₂	C₂×#416×C₁₀₃	1	1	yes	characteristic
502	C₂	C₂²×#104×C₁₀₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄²×C₁₀₃	D₄
commutator	C₄	C₂³×C₈×C₁₀₃
Frattini, cosocle	C₄²	C₂⁴×C₁₀₃
socle	C₂³×C₁₀₃	C₂×C₂²⋊C₄
prime radical	C₂²×#41×C₁₀₃	C₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄²×C₁₀₃ ◁ C₂²×C₄²×C₁₀₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#431×C₁₀₃	C₂	semidirect
3. C₂²×C₄×C₈×C₁₀₃	C₂	semidirect
4. C₁₀₃×#1476	C₂	direct (N × H)
5. C₂×Q₈⋊C₈×C₁₀₃	C₂	semidirect
6. C₂×D₄⋊C₈×C₁₀₃	C₂	semidirect
24. #431×C₁₀₃	C₂²	semidirect
31. C₂×C₄×C₈×C₁₀₃	C₂²	semidirect
32. Q₈⋊C₈×C₁₀₃	C₂²	semidirect
33. D₄⋊C₈×C₁₀₃	C₂²	semidirect
36. C₂×#41×C₁₀₃	C₈	semidirect
102. #41×C₁₀₃	C₂×C₈	semidirect
105. C₂×Q₈×C₁₀₃	C₂×C₈	semidirect
111. C₂×D₄×C₁₀₃	C₂×C₈	semidirect
180. Q₈×C₁₀₃	C₂²×C₈	semidirect
184. D₄×C₁₀₃	C₂²×C₈	semidirect
245. C₂×#1476	C₁₀₃	direct (N × H)
248. C₂×C₁₀₃	#1476	direct (N × H)
253. C₂×#431	C₂×C₁₀₃	semidirect
254. C₂²×C₄×C₈	C₂×C₁₀₃	semidirect
255. #1476	C₂×C₁₀₃	direct (N × H)
256. C₂×Q₈⋊C₈	C₂×C₁₀₃	semidirect
257. C₂×D₄⋊C₈	C₂×C₁₀₃	semidirect
258. C₁₀₃	C₂×#1476	direct (N × H)
276. #431	C₂²×C₁₀₃	semidirect
283. C₂×C₄×C₈	C₂²×C₁₀₃	semidirect
284. Q₈⋊C₈	C₂²×C₁₀₃	semidirect
285. D₄⋊C₈	C₂²×C₁₀₃	semidirect
288. C₂×#41	C₈×C₁₀₃	semidirect
354. #41	C₂×C₈×C₁₀₃	semidirect
357. C₂×Q₈	C₂×C₈×C₁₀₃	semidirect
363. C₂×D₄	C₂×C₈×C₁₀₃	semidirect
432. Q₈	C₂²×C₈×C₁₀₃	semidirect
436. D₄	C₂²×C₈×C₁₀₃	semidirect
499. C₂	C₁₀₃×#1476	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄×#41×C₁₀₃	2
C₂×#431×C₁₀₃	2
C₂²×C₄×C₈×C₁₀₃	2
C₁₀₃×#1476	2
C₂×Q₈⋊C₈×C₁₀₃	2
C₂×D₄⋊C₈×C₁₀₃	2
C₂×#1476	103

Subgroups — C2×C103×#1476 #39922708

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₀₃×#1476 #39922708