Subgroups — C₄×H(5,𝔽₂)×D₁₇ #17940923

Order 4352.

12378 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×H(5,𝔽₂)×D₁₇	C₂	1	1	yes	maximal, characteristic
2	H(5,𝔽₂)×Dic₁₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#10587696	C₂	1	6	yes	maximal, complemented
4	#14541990	C₂	1	6	yes	maximal, complemented
5	C₄×#10587691	C₂	1	9	yes	maximal, complemented
6	#14541988	C₂	1	9	yes	maximal, complemented
7	D₁₇×#520	C₂	1	6	yes	maximal, complemented
8	D₁₇×#518	C₂	1	9	yes	maximal, complemented
9	C₄×#41×D₁₇	C₂	1	6	yes	maximal, complemented
10	C₂×C₄×D₄×D₁₇	C₂	1	9	yes	maximal, complemented
11	C₄×C₁₇×H(5,𝔽₂)	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#10587696	C₂²	1	6	yes	—
13	C₂×#10587691	C₂²	1	9	yes	—
14	H(5,𝔽₂)×D₁₇	C₄	1	32	yes	direct product factor
15	C₂×#41×D₁₇	C₂²	1	6	yes	—
16	C₂²×D₄×D₁₇	C₂²	1	9	yes	—
17	C₂³×C₄×D₁₇	C₂²	1	6	yes	complemented
18	#11763292	C₂²	1	6	yes	complemented
19	#11763291	C₂²	1	12	yes	complemented
20	#11763290	C₂²	1	18	yes	complemented
21	#11763289	C₂²	1	18	yes	complemented
22	#11763288	C₂²	1	36	yes	complemented
23	#11763284	C₂²	1	9	yes	complemented
24	#11763283	C₂²	1	18	yes	complemented
25	#11763282	C₂²	1	36	yes	complemented
26	#11763281	C₂²	1	36	yes	complemented
27	#11763281	C₂²	1	36	yes	complemented
28	#41×Dic₁₇	C₂²	1	6	yes	complemented
29	C₄×#63256	C₂²	1	6	yes	complemented
30	C₄×#63256	C₂²	1	6	yes	complemented
31	C₄×#63252	C₂²	1	18	yes	complemented
32	#11763277	C₂²	1	18	yes	complemented
33	C₄×#63254	C₂²	1	18	yes	complemented
34	C₄×#63254	C₂²	1	18	yes	complemented
35	C₄×Q₈×D₁₇	C₂²	1	2	yes	complemented
36	C₄×Q₈×D₁₇	C₂²	1	6	yes	complemented
37	C₂×C₄×D₆₈	C₂²	1	9	yes	complemented
38	C₂×D₄×Dic₁₇	C₂²	1	9	yes	complemented
39	C₂×#10587579	C₂²	1	9	yes	complemented
40	C₂×C₄×C₂²⋊D₁₇	C₂²	1	18	yes	complemented
41	C₂×#10587567	C₂²	1	18	yes	complemented
42	C₄×D₄×D₁₇	C₂²	1	18	yes	complemented
43	C₄×D₄×D₁₇	C₂²	1	36	yes	complemented
44	C₄×D₄×D₁₇	C₂²	1	18	yes	complemented
45	C₄×D₄×D₁₇	C₂²	1	36	yes	complemented
46	C₄×D₄×D₁₇	C₂²	1	36	yes	complemented
47	#117×D₁₇	C₂²	1	18	yes	complemented
48	C₂×C₄⋊C₄×D₁₇	C₂²	1	9	yes	complemented
49	C₂×C₂²⋊C₄×D₁₇	C₂²	1	18	yes	complemented
50	C₂×C₄²×D₁₇	C₂²	1	9	yes	complemented
51	C₂×C₁₇×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
52	C₁₇×#520	C₂²	1	6	yes	complemented
53	C₁₇×#518	C₂²	1	9	yes	complemented
54	C₄×#41×C₁₇	C₂²	1	6	yes	complemented
55	C₂×C₄×D₄×C₁₇	C₂²	1	9	yes	complemented
56	C₂⁴×D₁₇	C₂³	1	6	yes	—
57	C₁₇×H(5,𝔽₂)	C₂×C₄	1	16	yes	complemented
58	C₂×#41×C₁₇	C₂³	1	6	yes	—
59	C₂²×D₄×C₁₇	C₂³	1	9	yes	—
60	C₂³×C₄×C₁₇	C₂³	1	6	yes	complemented
61	C₂²×C₂²⋊D₁₇	C₂³	1	18	yes	—
62	C₂³×Dic₁₇	C₂³	1	6	yes	complemented
63	#10587696	C₂×C₄	1	96	yes	complemented
64	#41×D₁₇	C₂×C₄	1	96	yes	complemented
65	C₂×#63256	C₂³	1	6	yes	—
66	C₂×Q₈×D₁₇	C₂³	1	2	yes	—
67	#10587691	C₂×C₄	1	144	yes	complemented
68	C₂×#63254	C₂³	1	18	yes	—
69	C₂×D₄×D₁₇	C₂×C₄	1	144	yes	complemented
70	C₂×D₄×D₁₇	C₂³	1	18	yes	—
71	C₂×D₄×D₁₇	C₂³	1	36	yes	—
72	C₂×#63252	C₂³	1	18	yes	—
73	C₂²×D₆₈	C₂³	1	9	yes	—
74	C₂²×C₄×D₁₇	—	4	24	no	—
75	C₂²×C₄×D₁₇	C₂³	1	9	yes	—
76	C₂²×C₄×D₁₇	C₂³	1	9	yes	—
77	C₂²×C₄×D₁₇	C₂³	1	18	yes	—
78	C₂²×C₄×D₁₇	C₂³	1	9	yes	—
79	C₂²×C₄×D₁₇	C₂³	1	18	yes	complemented
80	C₂²×C₄×D₁₇	C₂³	1	18	yes	complemented
81	C₄×Q₈×C₁₇	C₂³	1	2	yes	complemented
82	C₄×Q₈×C₁₇	C₂³	1	6	yes	complemented
83	C₄×D₄×C₁₇	C₂³	1	18	yes	complemented
84	C₄×D₄×C₁₇	C₂³	1	36	yes	complemented
85	C₄×D₄×C₁₇	C₂³	1	18	yes	complemented
86	C₁₇×#117	C₂³	1	18	yes	complemented
87	C₂×C₄⋊C₄×C₁₇	C₂³	1	9	yes	complemented
88	C₂×C₂²⋊C₄×C₁₇	C₂³	1	18	yes	complemented
89	C₂×C₄²×C₁₇	C₂³	1	9	yes	complemented
90	C₂×C₂²⋊Dic₁₇	C₂³	1	18	yes	complemented
91	Q₈×Dic₁₇	C₂³	1	2	yes	complemented
92	Q₈×Dic₁₇	C₂³	1	6	yes	complemented
93	D₄×Dic₁₇	C₂³	1	18	yes	complemented
94	D₄×Dic₁₇	C₂³	1	36	yes	complemented
95	D₄×Dic₁₇	C₂³	1	18	yes	complemented
96	C₄×C₂²⋊D₁₇	C₂³	1	36	yes	complemented
97	C₄×C₂²⋊D₁₇	C₂³	1	72	yes	complemented
98	C₄×C₂²⋊D₁₇	C₂³	1	36	yes	complemented
99	C₂×#63227	C₂³	1	18	yes	complemented
100	C₂×#63227	C₂³	1	18	yes	complemented
101	#10587612	C₂³	1	18	yes	complemented
102	C₂×C₄⋊Dic₁₇	C₂³	1	9	yes	complemented
103	C₂×#63225	C₂³	1	18	yes	complemented
104	C₂×C₄×Dic₁₇	C₂³	1	9	yes	complemented
105	C₂×C₄×Dic₁₇	C₂³	1	9	yes	complemented
106	C₂×C₄×Dic₁₇	C₂³	1	9	yes	complemented
107	#10587579	C₂³	1	18	yes	complemented
108	#10587579	C₂³	1	36	yes	complemented
109	#10587579	C₂³	1	18	yes	complemented
110	#10587578	C₂³	1	18	yes	complemented
111	#10587578	C₂³	1	18	yes	complemented
112	C₄⋊C₄×D₁₇	C₂³	1	18	yes	—
113	C₄⋊C₄×D₁₇	C₂³	1	6	yes	—
114	C₄⋊C₄×D₁₇	C₂³	1	36	yes	complemented
115	#10587573	C₂³	1	6	yes	complemented
116	#10587573	C₂³	1	18	yes	complemented
117	#10587567	C₂³	1	36	yes	complemented
118	#10587567	C₂³	1	72	yes	complemented
119	#10587567	C₂³	1	36	yes	complemented
120	C₂²⋊C₄×D₁₇	C₂³	1	36	yes	—
121	C₂²⋊C₄×D₁₇	C₂³	1	72	yes	complemented
122	#10587563	C₂³	1	36	yes	complemented
123	C₄×D₆₈	C₂³	1	18	yes	complemented
124	C₄×D₆₈	C₂³	1	36	yes	complemented
125	C₄×D₆₈	C₂³	1	18	yes	complemented
126	#10587558	C₂³	1	36	yes	complemented
127	C₄²×D₁₇	C₂³	1	6	yes	—
128	C₄²×D₁₇	C₂³	1	18	yes	—
129	C₄²×D₁₇	C₂³	1	18	yes	complemented
130	C₄²×D₁₇	C₂³	1	18	yes	complemented
131	C₄×Dic₃₄	C₂³	1	6	yes	complemented
132	C₄×Dic₃₄	C₂³	1	18	yes	complemented
133	C₂⁴×C₁₇	C₂⁴	1	6	yes	—
134	C₂³×D₁₇	—	4	12	no	—
135	C₂³×D₁₇	—	4	12	no	—
136	C₂³×D₁₇	C₂²×C₄	1	48	yes	complemented
137	C₂³×D₁₇	C₂⁴	1	9	yes	—
138	C₂³×D₁₇	C₂⁴	1	18	yes	—
139	#41×C₁₇	C₂²×C₄	1	48	yes	complemented
140	C₂×Q₈×C₁₇	C₂⁴	1	2	yes	—
141	C₂×D₄×C₁₇	C₂²×C₄	1	72	yes	complemented
142	C₂×D₄×C₁₇	C₂⁴	1	18	yes	—
143	C₂²×C₄×C₁₇	—	4	12	no	—
144	C₂²×C₄×C₁₇	C₂⁴	1	9	yes	—
145	C₂²×C₄×C₁₇	C₂⁴	1	18	yes	—
146	C₂²×C₄×C₁₇	C₂⁴	1	9	yes	—
147	C₂²×C₄×C₁₇	C₂⁴	1	9	yes	—
148	C₂×C₂²⋊D₁₇	C₂²×C₄	1	144	yes	complemented
149	C₂×C₂²⋊D₁₇	C₂⁴	1	36	yes	—
150	C₂²×Dic₁₇	—	4	12	no	—
151	C₂²×Dic₁₇	C₂⁴	1	9	yes	—
152	C₂²×Dic₁₇	C₂⁴	1	18	yes	—
153	C₂²×Dic₁₇	C₂⁴	1	9	yes	—
154	C₂²×Dic₁₇	C₂⁴	1	9	yes	—
155	#63256	C₂²×C₄	1	48	yes	complemented
156	Q₈×D₁₇	C₂²×C₄	1	16	yes	complemented
157	#63254	C₂²×C₄	1	144	yes	complemented
158	D₄×D₁₇	C₂²×C₄	1	144	yes	complemented
159	D₄×D₁₇	C₂²×C₄	1	288	yes	complemented
160	#63252	C₂²×C₄	1	144	yes	complemented
161	C₂×D₆₈	C₂²×C₄	1	72	yes	complemented
162	C₂×D₆₈	C₂⁴	1	18	yes	—
163	C₂×C₄×D₁₇	—	2	36	no	—
164	C₂×C₄×D₁₇	—	4	36	no	—
165	C₂×C₄×D₁₇	—	4	36	no	—
166	C₂×C₄×D₁₇	—	4	36	no	—
167	C₂×C₄×D₁₇	—	4	18	no	—
168	C₂×C₄×D₁₇	C₂²×C₄	1	72	yes	complemented
169	C₂×C₄×D₁₇	C₂⁴	1	9	yes	—
170	C₂×C₄×D₁₇	C₂⁴	1	6	yes	—
171	C₂×C₄×D₁₇	C₂⁴	1	9	yes	—
172	C₂×C₄×D₁₇	C₂⁴	1	9	yes	—
173	C₂×C₄×D₁₇	C₂⁴	1	36	yes	—
174	C₂×C₄×D₁₇	C₂⁴	1	18	yes	—
175	C₂×C₄×D₁₇	C₂⁴	1	6	yes	—
176	C₂×C₄×D₁₇	C₂⁴	1	18	yes	—
177	C₂×C₄×D₁₇	C₂⁴	1	1	yes	characteristic
178	C₂×Dic₃₄	C₂⁴	1	6	yes	—
179	C₄⋊C₄×C₁₇	C₂⁴	1	18	yes	—
180	C₄⋊C₄×C₁₇	C₂⁴	1	6	yes	—
181	C₂²⋊C₄×C₁₇	C₂⁴	1	36	yes	—
182	C₄²×C₁₇	C₂⁴	1	6	yes	—
183	C₄²×C₁₇	C₂⁴	1	18	yes	—
184	C₂²⋊Dic₁₇	C₂⁴	1	36	yes	—
185	#63227	C₂⁴	1	36	yes	—
186	#63227	C₂⁴	1	36	yes	—
187	C₄⋊Dic₁₇	C₂⁴	1	18	yes	—
188	C₄⋊Dic₁₇	C₂⁴	1	6	yes	—
189	#63225	C₂⁴	1	12	yes	—
190	#63225	C₂⁴	1	36	yes	—
191	C₄×Dic₁₇	C₂⁴	1	6	yes	—
192	C₄×Dic₁₇	C₂⁴	1	18	yes	—
193	C₄×Dic₁₇	C₂⁴	1	6	yes	—
194	C₄×Dic₁₇	C₂⁴	1	6	yes	—
195	C₄×Dic₁₇	C₂⁴	1	18	yes	—
196	C₄×Dic₁₇	C₂⁴	1	18	yes	—
197	C₂×C₄×H(5,𝔽₂)	—	17	1	no	maximal, Sylow
198	C₂³×C₁₇	—	4	6	no	—
199	C₂³×C₁₇	—	4	6	no	—
200	C₂³×C₁₇	C₂³×C₄	1	24	yes	complemented
201	C₂³×C₁₇	C₂⁵	1	9	yes	—
202	C₂²×D₁₇	—	2	18	no	—
203	C₂²×D₁₇	—	2	18	no	—
204	C₂²×D₁₇	—	4	96	no	—
205	C₂²×D₁₇	—	4	18	no	—
206	C₂²×D₁₇	—	4	18	no	—
207	C₂²×D₁₇	C₂³×C₄	1	36	yes	—
208	C₂²×D₁₇	C₂³×C₄	1	72	yes	complemented
209	C₂²×D₁₇	C₂⁵	1	9	yes	—
210	C₂²×D₁₇	C₂⁵	1	1	yes	characteristic
211	Q₈×C₁₇	C₂³×C₄	1	8	yes	complemented
212	D₄×C₁₇	C₂³×C₄	1	72	yes	complemented
213	C₂×C₄×C₁₇	—	2	18	no	—
214	C₂×C₄×C₁₇	—	4	18	no	—
215	C₂×C₄×C₁₇	—	4	9	no	—
216	C₂×C₄×C₁₇	C₂³×C₄	1	36	yes	complemented
217	C₂×C₄×C₁₇	C₂⁵	1	6	yes	—
218	C₂×C₄×C₁₇	C₂⁵	1	9	yes	—
219	C₂×C₄×C₁₇	C₂⁵	1	6	yes	—
220	C₂×C₄×C₁₇	C₂⁵	1	1	yes	characteristic
221	C₂²⋊D₁₇	C₂³×C₄	1	144	yes	complemented
222	C₂×Dic₁₇	—	2	18	no	—
223	C₂×Dic₁₇	—	4	18	no	—
224	C₂×Dic₁₇	—	4	9	no	—
225	C₂×Dic₁₇	C₂³×C₄	1	36	yes	complemented
226	C₂×Dic₁₇	C₂⁵	1	6	yes	—
227	C₂×Dic₁₇	C₂⁵	1	9	yes	—
228	C₂×Dic₁₇	C₂⁵	1	6	yes	—
229	C₂×Dic₁₇	C₂⁵	1	1	yes	characteristic
230	D₆₈	C₂³×C₄	1	72	yes	complemented
231	C₄×D₁₇	—	2	18	no	—
232	C₄×D₁₇	—	2	12	no	—
233	C₄×D₁₇	—	2	18	no	—
234	C₄×D₁₇	—	2	18	no	—
235	C₄×D₁₇	—	4	36	no	—
236	C₄×D₁₇	—	4	18	no	—
237	C₄×D₁₇	C₂³×C₄	1	24	yes	—
238	C₄×D₁₇	C₂³×C₄	1	72	yes	complemented
239	C₄×D₁₇	H(5,𝔽₂)	1	4	yes	direct product factor
240	Dic₃₄	C₂³×C₄	1	24	yes	complemented
241	C₂²×H(5,𝔽₂)	—	17	1	no	—
242	C₄×H(5,𝔽₂)	—	17	1	no	—
243	C₄×H(5,𝔽₂)	—	17	6	no	—
244	C₄×H(5,𝔽₂)	—	17	9	no	—
245	C₄×H(5,𝔽₂)	—	17	6	no	—
246	C₄×H(5,𝔽₂)	—	17	9	no	—
247	C₄×H(5,𝔽₂)	D₁₇	1	1	yes	characteristic, direct product factor
248	C₂×#520	—	17	6	no	—
249	C₂×#518	—	17	9	no	—
250	C₂×C₄×#41	—	17	6	no	—
251	C₂²×C₄×D₄	—	17	9	no	—
252	C₂²×C₁₇	—	2	9	no	—
253	C₂²×C₁₇	—	2	9	no	—
254	C₂²×C₁₇	—	4	24	no	—
255	C₂²×C₁₇	C₂⁴×C₄	1	18	yes	—
256	C₂²×C₁₇	C₂⁶	1	1	yes	characteristic
257	C₂×D₁₇	—	2	9	no	—
258	C₂×D₁₇	—	2	9	no	—
259	C₂×D₁₇	—	2	72	no	—
260	C₂×D₁₇	—	4	72	no	—
261	C₂×D₁₇	C₂⁴×C₄	1	18	yes	—
262	C₂×D₁₇	C₂⁴×C₄	1	2	yes	—
263	C₂×D₁₇	C₂×H(5,𝔽₂)	1	2	yes	—
264	C₂×D₁₇	#585	1	2	yes	—
265	C₄×C₁₇	—	2	9	no	—
266	C₄×C₁₇	—	2	6	no	—
267	C₄×C₁₇	C₂⁴×C₄	1	12	yes	—
268	C₄×C₁₇	C₂×H(5,𝔽₂)	1	2	yes	complemented
269	Dic₁₇	—	2	9	no	—
270	Dic₁₇	—	2	6	no	—
271	Dic₁₇	C₂⁴×C₄	1	12	yes	—
272	Dic₁₇	C₂×H(5,𝔽₂)	1	2	yes	complemented
273	C₂×H(5,𝔽₂)	—	17	32	no	—
274	C₂×H(5,𝔽₂)	—	17	6	no	—
275	C₂×H(5,𝔽₂)	—	17	9	no	—
276	C₂×H(5,𝔽₂)	C₂×D₁₇	1	1	yes	characteristic
277	C₂²×#41	—	17	6	no	—
278	C₂³×D₄	—	17	9	no	—
279	C₂⁴×C₄	—	17	6	no	—
280	#520	—	17	6	no	—
281	#520	—	17	12	no	—
282	#520	—	17	36	no	—
283	#520	—	17	18	no	—
284	#520	—	17	18	no	—
285	#520	C₂×D₁₇	1	6	yes	complemented
286	#518	—	17	9	no	—
287	#518	—	17	36	no	—
288	#518	—	17	36	no	—
289	#518	—	17	18	no	—
290	#518	—	17	36	no	—
291	#518	C₂×D₁₇	1	9	yes	complemented
292	C₄×#41	—	17	6	no	—
293	C₄×#41	—	17	6	no	—
294	C₄×#41	—	17	6	no	—
295	C₄×#41	—	17	18	no	—
296	C₄×#41	—	17	18	no	—
297	C₄×#41	—	17	18	no	—
298	C₄×#41	—	17	18	no	—
299	C₄×#41	C₂×D₁₇	1	6	yes	complemented
300	C₂×C₄×Q₈	—	17	2	no	—
301	C₂×C₄×Q₈	—	17	6	no	—
302	C₂×C₄×D₄	—	17	9	no	—
303	C₂×C₄×D₄	—	17	18	no	—
304	C₂×C₄×D₄	—	17	18	no	—
305	C₂×C₄×D₄	—	17	36	no	—
306	C₂×C₄×D₄	—	17	36	no	—
307	C₂×C₄×D₄	—	17	36	no	—
308	C₂×C₄×D₄	—	17	18	no	—
309	C₂×C₄×D₄	—	17	9	no	—
310	C₂×C₄×D₄	—	17	18	no	—
311	C₂×C₄×D₄	—	17	9	no	—
312	C₂×C₄×D₄	C₂×D₁₇	1	9	yes	complemented
313	C₂×#117	—	17	18	no	—
314	C₂²×C₄⋊C₄	—	17	9	no	—
315	C₂²×C₂²⋊C₄	—	17	18	no	—
316	C₂²×C₄²	—	17	9	no	—
317	C₂×C₁₇	—	2	18	no	—
318	C₂×C₁₇	C₂⁵×C₄	1	1	yes	characteristic
319	C₂×C₁₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
320	C₂×C₁₇	C₂×#585	1	1	yes	characteristic
321	D₁₇	—	2	18	no	—
322	D₁₇	C₄×H(5,𝔽₂)	1	4	yes	direct product factor
323	C₂⁵	—	17	6	no	—
324	H(5,𝔽₂)	—	17	96	no	—
325	H(5,𝔽₂)	—	17	144	no	—
326	H(5,𝔽₂)	C₄×D₁₇	1	16	yes	direct product factor
327	C₂×#41	—	17	96	no	—
328	C₂×#41	—	17	6	no	—
329	C₂×#41	—	17	18	no	—
330	C₂×#41	—	17	18	no	—
331	C₂×#41	C₂²×D₁₇	1	6	yes	—
332	C₂²×Q₈	—	17	2	no	—
333	C₂²×D₄	—	17	18	no	—
334	C₂²×D₄	—	17	144	no	—
335	C₂²×D₄	—	17	18	no	—
336	C₂²×D₄	—	17	36	no	—
337	C₂²×D₄	—	17	9	no	—
338	C₂²×D₄	C₂²×D₁₇	1	9	yes	—
339	C₂³×C₄	—	17	9	no	—
340	C₂³×C₄	—	17	6	no	—
341	C₂³×C₄	—	17	9	no	—
342	C₂³×C₄	—	17	9	no	—
343	C₂³×C₄	—	17	18	no	—
344	C₂³×C₄	—	17	18	no	—
345	C₂³×C₄	—	17	18	no	—
346	C₂³×C₄	—	68	24	no	—
347	C₂³×C₄	C₂²×D₁₇	1	6	yes	complemented
348	C₄×Q₈	—	17	2	no	—
349	C₄×Q₈	—	17	6	no	—
350	C₄×Q₈	—	17	6	no	—
351	C₄×Q₈	—	17	18	no	—
352	C₄×Q₈	—	17	6	no	—
353	C₄×Q₈	—	17	18	no	—
354	C₄×Q₈	C₂²×D₁₇	1	2	yes	complemented
355	C₄×Q₈	C₂²×D₁₇	1	6	yes	complemented
356	C₄×D₄	—	17	18	no	—
357	C₄×D₄	—	17	36	no	—
358	C₄×D₄	—	17	18	no	—
359	C₄×D₄	—	17	36	no	—
360	C₄×D₄	—	17	72	no	—
361	C₄×D₄	—	17	36	no	—
362	C₄×D₄	—	17	18	no	—
363	C₄×D₄	—	17	36	no	—
364	C₄×D₄	—	17	18	no	—
365	C₄×D₄	—	17	36	no	—
366	C₄×D₄	—	17	72	no	—
367	C₄×D₄	—	17	36	no	—
368	C₄×D₄	—	17	18	no	—
369	C₄×D₄	—	17	36	no	—
370	C₄×D₄	—	17	18	no	—
371	C₄×D₄	C₂²×D₁₇	1	18	yes	complemented
372	C₄×D₄	C₂²×D₁₇	1	36	yes	complemented
373	C₄×D₄	C₂²×D₁₇	1	18	yes	complemented
374	#117	—	17	18	no	—
375	#117	—	17	18	no	—
376	#117	—	17	18	no	—
377	#117	—	17	36	no	—
378	#117	—	17	36	no	—
379	#117	C₂²×D₁₇	1	18	yes	complemented
380	C₂×C₄⋊C₄	—	17	18	no	—
381	C₂×C₄⋊C₄	—	17	9	no	—
382	C₂×C₄⋊C₄	—	17	18	no	—
383	C₂×C₄⋊C₄	—	17	36	no	—
384	C₂×C₄⋊C₄	—	17	6	no	—
385	C₂×C₄⋊C₄	C₂²×D₁₇	1	9	yes	complemented
386	C₂×C₂²⋊C₄	—	17	18	no	—
387	C₂×C₂²⋊C₄	—	17	18	no	—
388	C₂×C₂²⋊C₄	—	17	18	no	—
389	C₂×C₂²⋊C₄	—	17	36	no	—
390	C₂×C₂²⋊C₄	—	17	72	no	—
391	C₂×C₂²⋊C₄	C₂²×D₁₇	1	18	yes	complemented
392	C₂×C₄²	—	17	9	no	—
393	C₂×C₄²	—	17	9	no	—
394	C₂×C₄²	—	17	9	no	—
395	C₂×C₄²	—	17	18	no	—
396	C₂×C₄²	—	17	6	no	—
397	C₂×C₄²	—	17	18	no	—
398	C₂×C₄²	—	17	18	no	—
399	C₂×C₄²	C₂²×D₁₇	1	9	yes	complemented
400	C₁₇	C₂×C₄×H(5,𝔽₂)	1	1	yes	characteristic, complemented, Sylow
401	C₂⁴	—	17	9	no	—
402	C₂⁴	—	17	48	no	—
403	C₂⁴	—	17	18	no	—
404	C₂⁴	—	68	12	no	—
405	C₂⁴	—	68	12	no	—
406	C₂⁴	C₂³×D₁₇	1	6	yes	—
407	#41	—	17	48	no	—
408	#41	—	17	144	no	—
409	#41	—	17	144	no	—
410	#41	C₂×C₄×D₁₇	1	48	yes	complemented
411	C₂×Q₈	—	17	16	no	—
412	C₂×Q₈	—	17	6	no	—
413	C₂×Q₈	C₂³×D₁₇	1	2	yes	—
414	C₂×D₄	—	17	144	no	—
415	C₂×D₄	—	17	36	no	—
416	C₂×D₄	—	17	144	no	—
417	C₂×D₄	—	17	288	no	—
418	C₂×D₄	—	17	72	no	—
419	C₂×D₄	—	17	18	no	—
420	C₂×D₄	C₂×C₄×D₁₇	1	72	yes	complemented
421	C₂×D₄	C₂³×D₁₇	1	18	yes	—
422	C₂²×C₄	—	4	12	no	—
423	C₂²×C₄	—	17	9	no	—
424	C₂²×C₄	—	17	72	no	—
425	C₂²×C₄	—	17	6	no	—
426	C₂²×C₄	—	17	18	no	—
427	C₂²×C₄	—	17	1	no	—
428	C₂²×C₄	—	17	9	no	—
429	C₂²×C₄	—	17	9	no	—
430	C₂²×C₄	—	17	18	no	—
431	C₂²×C₄	—	17	6	no	—
432	C₂²×C₄	—	17	9	no	—
433	C₂²×C₄	—	17	9	no	—
434	C₂²×C₄	—	17	9	no	—
435	C₂²×C₄	—	17	18	no	—
436	C₂²×C₄	—	17	36	no	—
437	C₂²×C₄	—	34	36	no	—
438	C₂²×C₄	—	68	36	no	—
439	C₂²×C₄	—	68	36	no	—
440	C₂²×C₄	—	68	18	no	—
441	C₂²×C₄	—	68	36	no	—
442	C₂²×C₄	—	68	12	no	—
443	C₂²×C₄	C₂³×D₁₇	1	9	yes	—
444	C₂²×C₄	C₂³×D₁₇	1	9	yes	—
445	C₂²×C₄	C₂³×D₁₇	1	18	yes	—
446	C₂²×C₄	C₂³×D₁₇	1	9	yes	—
447	C₄⋊C₄	—	17	36	no	—
448	C₄⋊C₄	—	17	18	no	—
449	C₄⋊C₄	—	17	12	no	—
450	C₄⋊C₄	—	17	6	no	—
451	C₄⋊C₄	C₂³×D₁₇	1	18	yes	—
452	C₄⋊C₄	C₂³×D₁₇	1	6	yes	—
453	C₂²⋊C₄	—	17	36	no	—
454	C₂²⋊C₄	—	17	36	no	—
455	C₂²⋊C₄	—	17	36	no	—
456	C₂²⋊C₄	C₂³×D₁₇	1	36	yes	—
457	C₄²	—	17	6	no	—
458	C₄²	—	17	6	no	—
459	C₄²	—	17	18	no	—
460	C₄²	—	17	18	no	—
461	C₄²	—	17	18	no	—
462	C₄²	—	17	6	no	—
463	C₄²	C₂³×D₁₇	1	18	yes	—
464	C₄²	C₂³×D₁₇	1	6	yes	—
465	C₂³	—	4	6	no	—
466	C₂³	—	4	6	no	—
467	C₂³	—	17	1	no	—
468	C₂³	—	17	36	no	—
469	C₂³	—	17	9	no	—
470	C₂³	—	17	72	no	—
471	C₂³	—	34	18	no	—
472	C₂³	—	34	18	no	—
473	C₂³	—	68	18	no	—
474	C₂³	—	68	18	no	—
475	C₂³	—	68	96	no	—
476	C₂³	C₂²×C₄×D₁₇	1	24	yes	complemented
477	C₂³	C₂⁴×D₁₇	1	9	yes	—
478	Q₈	—	17	24	no	—
479	Q₈	C₂²×C₄×D₁₇	1	8	yes	complemented
480	D₄	—	17	144	no	—
481	D₄	—	17	72	no	—
482	D₄	C₂²×C₄×D₁₇	1	72	yes	complemented
483	C₂×C₄	—	2	18	no	—
484	C₂×C₄	—	4	18	no	—
485	C₂×C₄	—	4	9	no	—
486	C₂×C₄	—	17	36	no	—
487	C₂×C₄	—	17	1	no	—
488	C₂×C₄	—	17	6	no	—
489	C₂×C₄	—	17	24	no	—
490	C₂×C₄	—	17	72	no	—
491	C₂×C₄	—	17	4	no	—
492	C₂×C₄	—	17	6	no	—
493	C₂×C₄	—	17	9	no	—
494	C₂×C₄	—	34	18	no	—
495	C₂×C₄	—	34	18	no	—
496	C₂×C₄	—	34	12	no	—
497	C₂×C₄	—	34	18	no	—
498	C₂×C₄	—	34	18	no	—
499	C₂×C₄	—	68	36	no	—
500	C₂×C₄	—	68	18	no	—
501	C₂×C₄	—	68	18	no	—
502	C₂×C₄	—	68	9	no	—
503	C₂×C₄	C₂²×C₄×D₁₇	1	36	yes	complemented
504	C₂×C₄	C₂⁴×D₁₇	1	6	yes	—
505	C₂×C₄	C₂⁴×D₁₇	1	9	yes	—
506	C₂×C₄	C₂⁴×D₁₇	1	6	yes	—
507	C₂×C₄	C₂⁴×D₁₇	1	1	yes	characteristic
508	C₂²	—	2	9	no	—
509	C₂²	—	2	9	no	—
510	C₂²	—	4	24	no	—
511	C₂²	—	17	2	no	—
512	C₂²	—	17	2	no	—
513	C₂²	—	17	2	no	—
514	C₂²	—	17	18	no	—
515	C₂²	—	34	72	no	—
516	C₂²	—	34	9	no	—
517	C₂²	—	34	9	no	—
518	C₂²	—	68	72	no	—
519	C₂²	C₂³×C₄×D₁₇	1	18	yes	—
520	C₂²	C₂⁵×D₁₇	1	1	yes	characteristic
521	C₄	—	2	9	no	—
522	C₄	—	2	6	no	—
523	C₄	—	17	12	no	—
524	C₄	—	17	2	no	—
525	C₄	—	34	9	no	—
526	C₄	—	34	6	no	—
527	C₄	C₂³×C₄×D₁₇	1	12	yes	—
528	C₄	H(5,𝔽₂)×D₁₇	1	2	yes	direct product factor
529	C₂	—	2	18	no	—
530	C₂	—	17	4	no	—
531	C₂	—	34	18	no	—
532	C₂	C₂⁴×C₄×D₁₇	1	1	yes	characteristic
533	C₂	C₂×H(5,𝔽₂)×D₁₇	1	1	yes	characteristic
534	C₂	D₁₇×#585	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂⁴×D₁₇
commutator	C₂×C₁₇	C₂⁵×C₄
Frattini	C₂²	C₂⁵×D₁₇
Fitting	C₄×C₁₇×H(5,𝔽₂)	C₂
socle, cosocle	C₂²×C₁₇	C₂⁶
prime radical	C₂×H(5,𝔽₂)×D₁₇	C₂
hypercenter	C₄×H(5,𝔽₂)	D₁₇
hypocenter	C₁₇	C₂×C₄×H(5,𝔽₂)
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×H(5,𝔽₂)

Complements

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

N	H ≅ G/N	type
2. H(5,𝔽₂)×Dic₁₇	C₂	semidirect
3. C₄×#10587696	C₂	semidirect
4. #14541990	C₂	semidirect
5. C₄×#10587691	C₂	semidirect
6. #14541988	C₂	semidirect
7. D₁₇×#520	C₂	semidirect
8. D₁₇×#518	C₂	semidirect
9. C₄×#41×D₁₇	C₂	semidirect
10. C₂×C₄×D₄×D₁₇	C₂	semidirect
11. C₄×C₁₇×H(5,𝔽₂)	C₂	semidirect
14. H(5,𝔽₂)×D₁₇	C₄	direct (N × H)
17. C₂³×C₄×D₁₇	C₂²	semidirect
18. #11763292	C₂²	semidirect
19. #11763291	C₂²	semidirect
20. #11763290	C₂²	semidirect
21. #11763289	C₂²	semidirect
22. #11763288	C₂²	semidirect
23. #11763284	C₂²	semidirect
24. #11763283	C₂²	semidirect
25. #11763282	C₂²	semidirect
26. #11763281	C₂²	semidirect
27. #11763281	C₂²	semidirect
28. #41×Dic₁₇	C₂²	semidirect
29. C₄×#63256	C₂²	semidirect
30. C₄×#63256	C₂²	semidirect
31. C₄×#63252	C₂²	semidirect
32. #11763277	C₂²	semidirect
33. C₄×#63254	C₂²	semidirect
34. C₄×#63254	C₂²	semidirect
35. C₄×Q₈×D₁₇	C₂²	semidirect
36. C₄×Q₈×D₁₇	C₂²	semidirect
37. C₂×C₄×D₆₈	C₂²	semidirect
38. C₂×D₄×Dic₁₇	C₂²	semidirect
39. C₂×#10587579	C₂²	semidirect
40. C₂×C₄×C₂²⋊D₁₇	C₂²	semidirect
41. C₂×#10587567	C₂²	semidirect
42. C₄×D₄×D₁₇	C₂²	semidirect
43. C₄×D₄×D₁₇	C₂²	semidirect
44. C₄×D₄×D₁₇	C₂²	semidirect
45. C₄×D₄×D₁₇	C₂²	semidirect
46. C₄×D₄×D₁₇	C₂²	semidirect
47. #117×D₁₇	C₂²	semidirect
48. C₂×C₄⋊C₄×D₁₇	C₂²	semidirect
49. C₂×C₂²⋊C₄×D₁₇	C₂²	semidirect
50. C₂×C₄²×D₁₇	C₂²	semidirect
52. C₁₇×#520	C₂²	semidirect
53. C₁₇×#518	C₂²	semidirect
54. C₄×#41×C₁₇	C₂²	semidirect
55. C₂×C₄×D₄×C₁₇	C₂²	semidirect
57. C₁₇×H(5,𝔽₂)	C₂×C₄	semidirect
60. C₂³×C₄×C₁₇	C₂³	semidirect
62. C₂³×Dic₁₇	C₂³	semidirect
63. #10587696	C₂×C₄	semidirect
64. #41×D₁₇	C₂×C₄	semidirect
67. #10587691	C₂×C₄	semidirect
69. C₂×D₄×D₁₇	C₂×C₄	semidirect
79. C₂²×C₄×D₁₇	C₂³	semidirect
80. C₂²×C₄×D₁₇	C₂³	semidirect
81. C₄×Q₈×C₁₇	C₂³	semidirect
82. C₄×Q₈×C₁₇	C₂³	semidirect
83. C₄×D₄×C₁₇	C₂³	semidirect
84. C₄×D₄×C₁₇	C₂³	semidirect
85. C₄×D₄×C₁₇	C₂³	semidirect
86. C₁₇×#117	C₂³	semidirect
87. C₂×C₄⋊C₄×C₁₇	C₂³	semidirect
88. C₂×C₂²⋊C₄×C₁₇	C₂³	semidirect
89. C₂×C₄²×C₁₇	C₂³	semidirect
90. C₂×C₂²⋊Dic₁₇	C₂³	semidirect
91. Q₈×Dic₁₇	C₂³	semidirect
92. Q₈×Dic₁₇	C₂³	semidirect
93. D₄×Dic₁₇	C₂³	semidirect
94. D₄×Dic₁₇	C₂³	semidirect
95. D₄×Dic₁₇	C₂³	semidirect
96. C₄×C₂²⋊D₁₇	C₂³	semidirect
97. C₄×C₂²⋊D₁₇	C₂³	semidirect
98. C₄×C₂²⋊D₁₇	C₂³	semidirect
99. C₂×#63227	C₂³	semidirect
100. C₂×#63227	C₂³	semidirect
101. #10587612	C₂³	semidirect
102. C₂×C₄⋊Dic₁₇	C₂³	semidirect
103. C₂×#63225	C₂³	semidirect
104. C₂×C₄×Dic₁₇	C₂³	semidirect
105. C₂×C₄×Dic₁₇	C₂³	semidirect
106. C₂×C₄×Dic₁₇	C₂³	semidirect
107. #10587579	C₂³	semidirect
108. #10587579	C₂³	semidirect
109. #10587579	C₂³	semidirect
110. #10587578	C₂³	semidirect
111. #10587578	C₂³	semidirect
114. C₄⋊C₄×D₁₇	C₂³	semidirect
115. #10587573	C₂³	semidirect
116. #10587573	C₂³	semidirect
117. #10587567	C₂³	semidirect
118. #10587567	C₂³	semidirect
119. #10587567	C₂³	semidirect
121. C₂²⋊C₄×D₁₇	C₂³	semidirect
122. #10587563	C₂³	semidirect
123. C₄×D₆₈	C₂³	semidirect
124. C₄×D₆₈	C₂³	semidirect
125. C₄×D₆₈	C₂³	semidirect
126. #10587558	C₂³	semidirect
129. C₄²×D₁₇	C₂³	semidirect
130. C₄²×D₁₇	C₂³	semidirect
131. C₄×Dic₃₄	C₂³	semidirect
132. C₄×Dic₃₄	C₂³	semidirect
136. C₂³×D₁₇	C₂²×C₄	semidirect
139. #41×C₁₇	C₂²×C₄	semidirect
141. C₂×D₄×C₁₇	C₂²×C₄	semidirect
148. C₂×C₂²⋊D₁₇	C₂²×C₄	semidirect
155. #63256	C₂²×C₄	semidirect
156. Q₈×D₁₇	C₂²×C₄	semidirect
157. #63254	C₂²×C₄	semidirect
158. D₄×D₁₇	C₂²×C₄	semidirect
159. D₄×D₁₇	C₂²×C₄	semidirect
160. #63252	C₂²×C₄	semidirect
161. C₂×D₆₈	C₂²×C₄	semidirect
168. C₂×C₄×D₁₇	C₂²×C₄	semidirect
200. C₂³×C₁₇	C₂³×C₄	semidirect
208. C₂²×D₁₇	C₂³×C₄	semidirect
211. Q₈×C₁₇	C₂³×C₄	semidirect
212. D₄×C₁₇	C₂³×C₄	semidirect
216. C₂×C₄×C₁₇	C₂³×C₄	semidirect
221. C₂²⋊D₁₇	C₂³×C₄	semidirect
225. C₂×Dic₁₇	C₂³×C₄	semidirect
230. D₆₈	C₂³×C₄	semidirect
238. C₄×D₁₇	C₂³×C₄	semidirect
239. C₄×D₁₇	H(5,𝔽₂)	direct (N × H)
240. Dic₃₄	C₂³×C₄	semidirect
247. C₄×H(5,𝔽₂)	D₁₇	direct (N × H)
268. C₄×C₁₇	C₂×H(5,𝔽₂)	semidirect
272. Dic₁₇	C₂×H(5,𝔽₂)	semidirect
285. #520	C₂×D₁₇	semidirect
291. #518	C₂×D₁₇	semidirect
299. C₄×#41	C₂×D₁₇	semidirect
312. C₂×C₄×D₄	C₂×D₁₇	semidirect
322. D₁₇	C₄×H(5,𝔽₂)	direct (N × H)
326. H(5,𝔽₂)	C₄×D₁₇	direct (N × H)
347. C₂³×C₄	C₂²×D₁₇	semidirect
354. C₄×Q₈	C₂²×D₁₇	semidirect
355. C₄×Q₈	C₂²×D₁₇	semidirect
371. C₄×D₄	C₂²×D₁₇	semidirect
372. C₄×D₄	C₂²×D₁₇	semidirect
373. C₄×D₄	C₂²×D₁₇	semidirect
379. #117	C₂²×D₁₇	semidirect
385. C₂×C₄⋊C₄	C₂²×D₁₇	semidirect
391. C₂×C₂²⋊C₄	C₂²×D₁₇	semidirect
399. C₂×C₄²	C₂²×D₁₇	semidirect
400. C₁₇	C₂×C₄×H(5,𝔽₂)	semidirect
410. #41	C₂×C₄×D₁₇	semidirect
420. C₂×D₄	C₂×C₄×D₁₇	semidirect
476. C₂³	C₂²×C₄×D₁₇	semidirect
479. Q₈	C₂²×C₄×D₁₇	semidirect
482. D₄	C₂²×C₄×D₁₇	semidirect
503. C₂×C₄	C₂²×C₄×D₁₇	semidirect
528. C₄	H(5,𝔽₂)×D₁₇	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×H(5,𝔽₂)×D₁₇	2
H(5,𝔽₂)×Dic₁₇	2
C₄×#10587696	2
#14541990	2
C₄×#10587691	2
#14541988	2
D₁₇×#520	2
D₁₇×#518	2
C₄×#41×D₁₇	2
C₂×C₄×D₄×D₁₇	2
C₄×C₁₇×H(5,𝔽₂)	2
C₂×C₄×H(5,𝔽₂)	17

Subgroups — C4×H(5,𝔽2)×D17 #17940923

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×H(5,𝔽₂)×D₁₇ #17940923