Subgroups — C₁₇×#61564 #16919308

Order 4352.

2142 conjugacy classes of subgroups.

The subgroup lattice has 926 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×#3505	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₇×#548	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₇×#3301	C₂	1	4	yes	maximal, complemented
4	C₁₇×#3300	C₂	1	4	yes	maximal, complemented
5	C₁₇×#3285	C₂	1	4	yes	maximal, complemented
6	C₁₇×#3282	C₂	1	4	yes	maximal, complemented
7	C₁₇×#3211	C₂	1	2	yes	maximal, complemented
8	C₁₇×#3190	C₂	1	2	yes	maximal, complemented
9	C₁₇×#3187	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₇×#3186	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₇×#3108	C₂	1	2	yes	maximal, complemented
12	C₁₇×#3002	C₂	1	2	yes	maximal, complemented
13	C₂×C₁₇×#451	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₁₇×#448	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₇×#2972	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₁₇	C₂²	1	1	yes	characteristic, complemented
17	C₂³×Q₈×C₁₇	C₂²	1	1	yes	characteristic
18	C₂×C₁₇×#135	C₂²	1	4	yes	complemented
19	C₂²×Q₁₆×C₁₇	C₂²	1	2	yes	complemented
20	C₂²×SD₁₆×C₁₇	C₂²	1	2	yes	complemented
21	C₁₇×#553	—	2	2	no	—
22	C₁₇×#553	C₂²	1	2	yes	complemented
23	C₁₇×#552	C₂²	1	2	yes	complemented
24	C₁₇×#551	—	2	2	no	—
25	C₁₇×#548	—	2	2	no	—
26	C₁₇×#548	—	2	2	no	—
27	C₁₇×#548	C₂²	1	4	yes	—
28	C₁₇×#548	C₂²	1	4	yes	complemented
29	C₁₇×#548	C₂²	1	2	yes	complemented
30	C₁₇×#546	C₂²	1	2	yes	complemented
31	C₁₇×#539	—	2	1	no	—
32	C₁₇×#538	—	2	1	no	—
33	C₁₇×#534	—	2	1	no	—
34	C₁₇×#529	C₂²	1	2	yes	—
35	C₂×C₁₇×#124	—	2	1	no	—
36	C₂×C₁₇×#124	C₂²	1	1	yes	characteristic, complemented
37	C₁₇×#525	C₂²	1	2	yes	—
38	C₂×C₁₇×C₂²⋊Q₈	—	2	1	no	—
39	C₂×C₁₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
40	C₂×C₁₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₁₇×#121	—	2	1	no	—
42	C₂×C₁₇×#121	C₂²	1	1	yes	characteristic
43	C₂×C₁₇×#121	C₂²	1	1	yes	characteristic
44	C₁₇×#518	—	2	1	no	—
45	C₂×C₄×Q₈×C₁₇	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₄×D₄×C₁₇	—	2	1	no	—
47	C₂×C₄×D₄×C₁₇	C₂²	1	1	yes	characteristic
48	C₁₇×#495	C₂²	1	4	yes	complemented
49	C₁₇×#488	C₂²	1	4	yes	complemented
50	C₁₇×#485	C₂²	1	4	yes	complemented
51	C₁₇×#483	C₂²	1	2	yes	complemented
52	C₁₇×#481	C₂²	1	2	yes	complemented
53	C₁₇×#480	C₂²	1	2	yes	—
54	C₁₇×#480	C₂²	1	2	yes	complemented
55	C₁₇×#479	C₂²	1	4	yes	complemented
56	C₁₇×#467	C₂²	1	4	yes	complemented
57	C₁₇×#466	C₂²	1	4	yes	complemented
58	C₁₇×#465	C₂²	1	4	yes	complemented
59	C₁₇×#465	C₂²	1	4	yes	complemented
60	C₁₇×#464	C₂²	1	4	yes	complemented
61	C₁₇×#464	C₂²	1	4	yes	complemented
62	C₁₇×#463	C₂²	1	4	yes	complemented
63	C₁₇×#452	C₂²	1	4	yes	complemented
64	C₁₇×#452	C₂²	1	4	yes	complemented
65	C₁₇×#451	C₂²	1	2	yes	complemented
66	C₁₇×#451	C₂²	1	2	yes	complemented
67	C₁₇×#451	C₂²	1	4	yes	complemented
68	C₁₇×#450	C₂²	1	2	yes	complemented
69	C₁₇×#449	C₂²	1	4	yes	complemented
70	C₁₇×#448	C₂²	1	2	yes	—
71	C₁₇×#448	C₂²	1	2	yes	—
72	C₁₇×#448	C₂²	1	4	yes	complemented
73	C₁₇×#448	C₂²	1	2	yes	complemented
74	C₁₇×#447	C₂²	1	2	yes	—
75	C₁₇×#447	C₂²	1	2	yes	complemented
76	C₄×Q₁₆×C₁₇	C₂²	1	4	yes	complemented
77	C₄×SD₁₆×C₁₇	C₂²	1	4	yes	complemented
78	C₈×D₄×C₁₇	C₂²	1	4	yes	complemented
79	C₈×D₄×C₁₇	C₂²	1	4	yes	complemented
80	C₁₇×#431	C₂²	1	2	yes	complemented
81	C₁₇×#416	C₂²	1	4	yes	complemented
82	C₂×C₁₇×#103	C₂²	1	2	yes	complemented
83	C₂×C₁₇×#103	C₂²	1	2	yes	complemented
84	C₂×C₁₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
85	C₂×C₁₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
86	C₂×C₁₇×C₂²⋊C₈	C₂²	1	2	yes	complemented
87	C₂×#41×C₁₇	—	2	2	no	—
88	C₂×#41×C₁₇	—	4	4	no	—
89	C₂×#41×C₁₇	C₂³	1	4	yes	—
90	C₂×#41×C₁₇	C₂³	1	2	yes	—
91	C₂²×Q₈×C₁₇	—	2	1	no	—
92	C₂²×Q₈×C₁₇	—	2	1	no	—
93	C₂²×Q₈×C₁₇	—	2	1	no	—
94	C₂²×Q₈×C₁₇	—	4	4	no	—
95	C₂²×Q₈×C₁₇	C₂³	1	1	yes	characteristic
96	C₂²×Q₈×C₁₇	C₂³	1	2	yes	—
97	C₂²×Q₈×C₁₇	C₂³	1	2	yes	—
98	C₂²×Q₈×C₁₇	C₂³	1	1	yes	characteristic
99	C₂²×Q₈×C₁₇	C₂³	1	1	yes	characteristic
100	C₂²×D₄×C₁₇	—	2	1	no	—
101	C₂²×D₄×C₁₇	—	2	1	no	—
102	C₂²×D₄×C₁₇	—	2	1	no	—
103	C₂²×D₄×C₁₇	D₄	1	1	yes	characteristic
104	C₂²×D₄×C₁₇	C₂³	1	1	yes	characteristic
105	C₂²×D₄×C₁₇	C₂³	1	1	yes	characteristic
106	C₂³×C₄×C₁₇	—	2	1	no	—
107	C₂³×C₄×C₁₇	—	2	1	no	—
108	C₂³×C₄×C₁₇	C₂³	1	1	yes	characteristic
109	C₂³×C₄×C₁₇	C₂³	1	1	yes	characteristic
110	C₁₇×#135	—	4	8	no	—
111	C₂×Q₁₆×C₁₇	—	4	4	no	—
112	C₂×Q₁₆×C₁₇	C₂³	1	4	yes	—
113	C₂×Q₁₆×C₁₇	C₂³	1	4	yes	—
114	C₂×SD₁₆×C₁₇	—	4	4	no	—
115	C₂×SD₁₆×C₁₇	C₂³	1	4	yes	—
116	C₂×SD₁₆×C₁₇	C₂³	1	4	yes	—
117	C₂×SD₁₆×C₁₇	C₂³	1	4	yes	—
118	C₂×D₈×C₁₇	C₂³	1	4	yes	—
119	C₂²×C₈×C₁₇	C₂³	1	2	yes	—
120	C₂²×C₈×C₁₇	C₂³	1	2	yes	—
121	C₂²×C₈×C₁₇	C₂³	1	4	yes	—
122	C₁₇×#126	—	2	2	no	—
123	C₁₇×#126	—	2	2	no	—
124	C₁₇×#126	—	2	2	no	—
125	C₁₇×#125	—	2	2	no	—
126	C₁₇×#125	C₂³	1	2	yes	—
127	C₁₇×#124	—	2	4	no	—
128	C₁₇×#124	—	2	4	no	—
129	C₁₇×#124	—	2	2	no	—
130	C₁₇×#124	—	2	2	no	—
131	C₁₇×#124	C₂³	1	2	yes	—
132	C₁₇×#124	C₂³	1	4	yes	—
133	C₁₇×#123	—	2	2	no	—
134	C₁₇×#123	—	2	2	no	—
135	C₁₇×#123	—	2	2	no	—
136	C₁₇×#123	—	2	2	no	—
137	C₁₇×#123	—	2	2	no	—
138	C₁₇×C₂²⋊Q₈	—	2	1	no	—
139	C₁₇×C₂²⋊Q₈	—	2	1	no	—
140	C₁₇×C₂²⋊Q₈	—	2	2	no	—
141	C₁₇×C₂²⋊Q₈	—	2	4	no	—
142	C₁₇×C₂²⋊Q₈	—	2	4	no	—
143	C₁₇×C₂²⋊Q₈	—	2	2	no	—
144	C₁₇×C₂²⋊Q₈	C₂³	1	2	yes	—
145	C₁₇×C₂²⋊Q₈	C₂³	1	2	yes	—
146	C₁₇×C₂²⋊Q₈	C₂³	1	4	yes	—
147	C₁₇×C₂²⋊Q₈	C₂³	1	2	yes	—
148	C₁₇×#121	—	2	4	no	—
149	C₁₇×#121	—	2	4	no	—
150	C₁₇×#121	—	2	2	no	—
151	C₁₇×#121	—	2	2	no	—
152	C₁₇×#121	—	2	1	no	—
153	C₁₇×#121	—	2	1	no	—
154	C₁₇×#121	—	2	1	no	—
155	C₁₇×#121	—	2	1	no	—
156	C₁₇×#121	—	2	2	no	—
157	C₁₇×#121	C₂³	1	2	yes	—
158	C₁₇×#121	C₂³	1	2	yes	—
159	C₁₇×#121	C₂³	1	2	yes	—
160	C₁₇×#121	C₂³	1	2	yes	—
161	C₁₇×#121	C₂³	1	2	yes	—
162	C₁₇×#120	—	2	2	no	—
163	C₁₇×#120	—	2	2	no	—
164	C₄×Q₈×C₁₇	—	2	2	no	—
165	C₄×Q₈×C₁₇	C₂³	1	4	yes	—
166	C₄×Q₈×C₁₇	C₂³	1	2	yes	—
167	C₄×D₄×C₁₇	—	2	2	no	—
168	C₄×D₄×C₁₇	—	2	2	no	—
169	C₄×D₄×C₁₇	—	2	2	no	—
170	C₄×D₄×C₁₇	—	2	4	no	—
171	C₄×D₄×C₁₇	—	2	4	no	—
172	C₄×D₄×C₁₇	—	2	2	no	—
173	C₄×D₄×C₁₇	—	2	2	no	—
174	C₄×D₄×C₁₇	D₄	1	2	yes	—
175	C₄×D₄×C₁₇	D₄	1	2	yes	—
176	C₄×D₄×C₁₇	C₂³	1	2	yes	—
177	C₄×D₄×C₁₇	C₂³	1	2	yes	—
178	C₄×D₄×C₁₇	C₂³	1	2	yes	—
179	C₁₇×#117	—	2	2	no	—
180	C₁₇×#117	—	2	2	no	—
181	C₁₇×#117	C₂³	1	2	yes	—
182	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
183	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
184	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
185	C₂×C₄⋊C₄×C₁₇	D₄	1	1	yes	characteristic
186	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
187	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
188	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
189	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
190	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
191	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
192	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
193	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
194	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
195	C₂×C₂²⋊C₄×C₁₇	—	2	2	no	—
196	C₂×C₂²⋊C₄×C₁₇	D₄	1	1	yes	characteristic
197	C₂×C₂²⋊C₄×C₁₇	D₄	1	1	yes	characteristic
198	C₂×C₄²×C₁₇	—	2	1	no	—
199	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
200	C₁₇×#107	C₂³	1	4	yes	—
201	C₁₇×#106	C₂³	1	4	yes	—
202	C₁₇×C₄⋊C₈	C₂³	1	4	yes	—
203	C₁₇×#103	C₂³	1	4	yes	—
204	C₁₇×#103	C₂³	1	4	yes	—
205	C₁₇×#103	C₂³	1	4	yes	—
206	C₁₇×#103	C₂³	1	4	yes	—
207	C₁₇×#103	C₂³	1	4	yes	—
208	C₁₇×#102	C₂³	1	4	yes	—
209	C₁₇×#102	C₂³	1	4	yes	—
210	C₁₇×#102	C₂³	1	4	yes	—
211	C₁₇×C₂²⋊C₈	C₂³	1	2	yes	—
212	C₁₇×C₂²⋊C₈	C₂³	1	2	yes	—
213	C₁₇×C₂²⋊C₈	C₂³	1	2	yes	—
214	C₁₇×C₂²⋊C₈	C₂³	1	2	yes	—
215	C₁₇×C₂²⋊C₈	C₂³	1	4	yes	—
216	C₄×C₈×C₁₇	C₂³	1	4	yes	—
217	C₂⁴×C₁₇	—	2	1	no	—
218	C₂⁴×C₁₇	—	2	1	no	—
219	C₂⁴×C₁₇	C₂×D₄	1	1	yes	characteristic
220	C₂⁴×C₁₇	C₂×D₄	1	1	yes	characteristic
221	#41×C₁₇	—	2	8	no	—
222	#41×C₁₇	—	4	4	no	—
223	#41×C₁₇	—	4	4	no	—
224	#41×C₁₇	—	4	8	no	—
225	C₂×Q₈×C₁₇	—	2	4	no	—
226	C₂×Q₈×C₁₇	—	2	1	no	—
227	C₂×Q₈×C₁₇	—	2	2	no	—
228	C₂×Q₈×C₁₇	—	2	2	no	—
229	C₂×Q₈×C₁₇	—	2	1	no	—
230	C₂×Q₈×C₁₇	—	2	1	no	—
231	C₂×Q₈×C₁₇	—	2	4	no	—
232	C₂×Q₈×C₁₇	—	2	4	no	—
233	C₂×Q₈×C₁₇	—	4	2	no	—
234	C₂×Q₈×C₁₇	—	4	2	no	—
235	C₂×Q₈×C₁₇	—	4	2	no	—
236	C₂×Q₈×C₁₇	—	4	4	no	—
237	C₂×Q₈×C₁₇	—	4	2	no	—
238	C₂×Q₈×C₁₇	—	4	4	no	—
239	C₂×Q₈×C₁₇	—	4	4	no	—
240	C₂×Q₈×C₁₇	C₂⁴	1	2	yes	—
241	C₂×Q₈×C₁₇	C₂⁴	1	2	yes	—
242	C₂×Q₈×C₁₇	C₂⁴	1	2	yes	—
243	C₂×D₄×C₁₇	—	2	4	no	—
244	C₂×D₄×C₁₇	—	2	2	no	—
245	C₂×D₄×C₁₇	—	2	4	no	—
246	C₂×D₄×C₁₇	—	2	2	no	—
247	C₂×D₄×C₁₇	—	2	2	no	—
248	C₂×D₄×C₁₇	—	2	2	no	—
249	C₂×D₄×C₁₇	—	2	2	no	—
250	C₂×D₄×C₁₇	—	2	2	no	—
251	C₂×D₄×C₁₇	—	2	1	no	—
252	C₂×D₄×C₁₇	—	2	1	no	—
253	C₂×D₄×C₁₇	—	4	2	no	—
254	C₂×D₄×C₁₇	—	4	2	no	—
255	C₂×D₄×C₁₇	—	4	4	no	—
256	C₂×D₄×C₁₇	—	4	4	no	—
257	C₂×D₄×C₁₇	—	4	4	no	—
258	C₂×D₄×C₁₇	C₂×D₄	1	2	yes	—
259	C₂×D₄×C₁₇	C₂×D₄	1	2	yes	—
260	C₂×D₄×C₁₇	C₂⁴	1	2	yes	—
261	C₂×D₄×C₁₇	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₁₇	—	2	1	no	—
263	C₂²×C₄×C₁₇	—	2	1	no	—
264	C₂²×C₄×C₁₇	—	2	1	no	—
265	C₂²×C₄×C₁₇	—	2	2	no	—
266	C₂²×C₄×C₁₇	—	2	2	no	—
267	C₂²×C₄×C₁₇	—	2	1	no	—
268	C₂²×C₄×C₁₇	—	2	1	no	—
269	C₂²×C₄×C₁₇	—	2	1	no	—
270	C₂²×C₄×C₁₇	—	2	4	no	—
271	C₂²×C₄×C₁₇	—	2	2	no	—
272	C₂²×C₄×C₁₇	—	2	2	no	—
273	C₂²×C₄×C₁₇	—	4	2	no	—
274	C₂²×C₄×C₁₇	—	4	2	no	—
275	C₂²×C₄×C₁₇	—	4	4	no	—
276	C₂²×C₄×C₁₇	—	4	4	no	—
277	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
278	C₂²×C₄×C₁₇	C₂×D₄	1	2	yes	—
279	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
280	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
281	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
282	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
283	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
284	C₂²×C₄×C₁₇	C₂⁴	1	2	yes	—
285	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
286	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
287	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
288	Q₁₆×C₁₇	—	2	8	no	—
289	Q₁₆×C₁₇	—	4	4	no	—
290	SD₁₆×C₁₇	—	2	8	no	—
291	SD₁₆×C₁₇	—	4	4	no	—
292	SD₁₆×C₁₇	—	4	4	no	—
293	D₈×C₁₇	—	4	4	no	—
294	C₂×C₈×C₁₇	—	4	2	no	—
295	C₂×C₈×C₁₇	—	4	2	no	—
296	C₂×C₈×C₁₇	—	4	4	no	—
297	C₂×C₈×C₁₇	C₂⁴	1	4	yes	—
298	C₂×C₈×C₁₇	C₂⁴	1	4	yes	—
299	C₄⋊C₄×C₁₇	—	2	4	no	—
300	C₄⋊C₄×C₁₇	—	2	1	no	—
301	C₄⋊C₄×C₁₇	—	2	4	no	—
302	C₄⋊C₄×C₁₇	—	2	1	no	—
303	C₄⋊C₄×C₁₇	—	2	2	no	—
304	C₄⋊C₄×C₁₇	—	2	2	no	—
305	C₄⋊C₄×C₁₇	—	2	2	no	—
306	C₄⋊C₄×C₁₇	—	2	2	no	—
307	C₄⋊C₄×C₁₇	—	2	2	no	—
308	C₄⋊C₄×C₁₇	—	2	2	no	—
309	C₄⋊C₄×C₁₇	—	2	1	no	—
310	C₄⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
311	C₄⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
312	C₄⋊C₄×C₁₇	C₂⁴	1	2	yes	—
313	C₄⋊C₄×C₁₇	C₂⁴	1	2	yes	—
314	C₄⋊C₄×C₁₇	C₂⁴	1	2	yes	—
315	C₂²⋊C₄×C₁₇	—	2	2	no	—
316	C₂²⋊C₄×C₁₇	—	2	2	no	—
317	C₂²⋊C₄×C₁₇	—	2	4	no	—
318	C₂²⋊C₄×C₁₇	—	2	2	no	—
319	C₂²⋊C₄×C₁₇	—	2	2	no	—
320	C₂²⋊C₄×C₁₇	—	2	2	no	—
321	C₂²⋊C₄×C₁₇	—	2	2	no	—
322	C₂²⋊C₄×C₁₇	—	2	4	no	—
323	C₂²⋊C₄×C₁₇	—	2	2	no	—
324	C₂²⋊C₄×C₁₇	—	2	2	no	—
325	C₂²⋊C₄×C₁₇	—	2	2	no	—
326	C₂²⋊C₄×C₁₇	—	2	2	no	—
327	C₂²⋊C₄×C₁₇	—	2	2	no	—
328	C₂²⋊C₄×C₁₇	—	2	4	no	—
329	C₂²⋊C₄×C₁₇	—	2	2	no	—
330	C₂²⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
331	C₂²⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
332	C₂²⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
333	C₂²⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
334	C₄²×C₁₇	—	2	4	no	—
335	C₄²×C₁₇	—	2	2	no	—
336	C₄²×C₁₇	—	2	2	no	—
337	C₄²×C₁₇	C₂×D₄	1	2	yes	—
338	C₄²×C₁₇	C₂⁴	1	2	yes	—
339	#61564	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
340	C₂³×C₁₇	—	2	2	no	—
341	C₂³×C₁₇	—	2	2	no	—
342	C₂³×C₁₇	—	2	2	no	—
343	C₂³×C₁₇	—	4	1	no	—
344	C₂³×C₁₇	—	4	1	no	—
345	C₂³×C₁₇	—	4	1	no	—
346	C₂³×C₁₇	—	4	1	no	—
347	C₂³×C₁₇	—	4	2	no	—
348	C₂³×C₁₇	—	4	2	no	—
349	C₂³×C₁₇	—	4	2	no	—
350	C₂³×C₁₇	—	4	2	no	—
351	C₂³×C₁₇	—	8	1	no	—
352	C₂³×C₁₇	—	8	1	no	—
353	C₂³×C₁₇	#135	1	4	yes	complemented
354	C₂³×C₁₇	C₂²×D₄	1	2	yes	—
355	C₂³×C₁₇	C₂²×D₄	1	1	yes	characteristic
356	C₂³×C₁₇	C₂²×D₄	1	1	yes	characteristic
357	C₂³×C₁₇	C₂²×D₄	1	1	yes	characteristic
358	Q₈×C₁₇	—	2	4	no	—
359	Q₈×C₁₇	—	2	2	no	—
360	Q₈×C₁₇	—	2	2	no	—
361	Q₈×C₁₇	—	2	4	no	—
362	Q₈×C₁₇	—	2	2	no	—
363	Q₈×C₁₇	—	4	4	no	—
364	Q₈×C₁₇	—	4	4	no	—
365	Q₈×C₁₇	—	4	2	no	—
366	Q₈×C₁₇	—	8	1	no	—
367	Q₈×C₁₇	H(5,𝔽₂)	1	4	yes	—
368	D₄×C₁₇	—	2	4	no	—
369	D₄×C₁₇	—	2	4	no	—
370	D₄×C₁₇	—	2	4	no	—
371	D₄×C₁₇	—	2	4	no	—
372	D₄×C₁₇	—	4	8	no	—
373	D₄×C₁₇	—	4	2	no	—
374	D₄×C₁₇	—	4	4	no	—
375	D₄×C₁₇	—	4	4	no	—
376	D₄×C₁₇	—	4	4	no	—
377	D₄×C₁₇	—	4	4	no	—
378	D₄×C₁₇	—	8	1	no	—
379	D₄×C₁₇	—	8	2	no	—
380	D₄×C₁₇	—	8	2	no	—
381	C₂×C₄×C₁₇	—	2	4	no	—
382	C₂×C₄×C₁₇	—	2	2	no	—
383	C₂×C₄×C₁₇	—	2	2	no	—
384	C₂×C₄×C₁₇	—	2	2	no	—
385	C₂×C₄×C₁₇	—	2	2	no	—
386	C₂×C₄×C₁₇	—	2	4	no	—
387	C₂×C₄×C₁₇	—	2	2	no	—
388	C₂×C₄×C₁₇	—	2	2	no	—
389	C₂×C₄×C₁₇	—	2	2	no	—
390	C₂×C₄×C₁₇	—	2	2	no	—
391	C₂×C₄×C₁₇	—	2	2	no	—
392	C₂×C₄×C₁₇	—	2	2	no	—
393	C₂×C₄×C₁₇	—	4	1	no	—
394	C₂×C₄×C₁₇	—	4	1	no	—
395	C₂×C₄×C₁₇	—	4	1	no	—
396	C₂×C₄×C₁₇	—	4	1	no	—
397	C₂×C₄×C₁₇	—	4	2	no	—
398	C₂×C₄×C₁₇	—	4	1	no	—
399	C₂×C₄×C₁₇	—	4	8	no	—
400	C₂×C₄×C₁₇	—	4	4	no	—
401	C₂×C₄×C₁₇	—	4	4	no	—
402	C₂×C₄×C₁₇	—	4	2	no	—
403	C₂×C₄×C₁₇	—	4	2	no	—
404	C₂×C₄×C₁₇	—	4	2	no	—
405	C₂×C₄×C₁₇	—	8	2	no	—
406	C₂×C₄×C₁₇	—	8	2	no	—
407	C₂×C₄×C₁₇	—	8	1	no	—
408	C₂×C₄×C₁₇	—	8	1	no	—
409	C₂×C₄×C₁₇	C₂²×D₄	1	2	yes	—
410	C₂×C₄×C₁₇	C₂²×D₄	1	2	yes	—
411	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
412	C₂×C₄×C₁₇	C₂²×D₄	1	2	yes	—
413	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
414	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
415	C₂×C₄×C₁₇	C₂⁵	1	1	yes	characteristic
416	C₈×C₁₇	—	2	4	no	—
417	C₈×C₁₇	—	2	4	no	—
418	#3505	C₂×C₁₇	1	1	yes	characteristic, complemented
419	C₂×#548	C₂×C₁₇	1	1	yes	characteristic, complemented
420	#3301	C₂×C₁₇	1	4	yes	complemented
421	#3300	C₂×C₁₇	1	4	yes	complemented
422	#3285	C₂×C₁₇	1	4	yes	complemented
423	#3282	C₂×C₁₇	1	4	yes	complemented
424	#3211	C₂×C₁₇	1	2	yes	complemented
425	#3190	C₂×C₁₇	1	2	yes	complemented
426	#3187	C₂×C₁₇	1	1	yes	characteristic, complemented
427	#3186	C₂×C₁₇	1	1	yes	characteristic, complemented
428	#3108	C₂×C₁₇	1	2	yes	complemented
429	#3002	C₂×C₁₇	1	2	yes	complemented
430	C₂×#451	C₂×C₁₇	1	1	yes	characteristic, complemented
431	C₂×#448	C₂×C₁₇	1	1	yes	characteristic, complemented
432	#2972	C₂×C₁₇	1	1	yes	characteristic, complemented
433	C₂²×C₁₇	—	2	1	no	—
434	C₂²×C₁₇	—	2	1	no	—
435	C₂²×C₁₇	—	2	1	no	—
436	C₂²×C₁₇	—	2	1	no	—
437	C₂²×C₁₇	—	2	1	no	—
438	C₂²×C₁₇	—	2	1	no	—
439	C₂²×C₁₇	—	2	2	no	—
440	C₂²×C₁₇	—	2	2	no	—
441	C₂²×C₁₇	—	2	2	no	—
442	C₂²×C₁₇	—	4	4	no	—
443	C₂²×C₁₇	—	4	2	no	—
444	C₂²×C₁₇	—	4	2	no	—
445	C₂²×C₁₇	—	4	2	no	—
446	C₂²×C₁₇	—	4	2	no	—
447	C₂²×C₁₇	—	4	2	no	—
448	C₂²×C₁₇	—	4	2	no	—
449	C₂²×C₁₇	—	8	2	no	—
450	C₂²×C₁₇	—	8	4	no	—
451	C₂²×C₁₇	—	16	2	no	—
452	C₂²×C₁₇	C₂×#135	1	2	yes	—
453	C₂²×C₁₇	C₂×#135	1	2	yes	—
454	C₂²×C₁₇	C₂×#135	1	2	yes	—
455	C₂²×C₁₇	C₂³×D₄	1	1	yes	characteristic
456	C₄×C₁₇	—	2	2	no	—
457	C₄×C₁₇	—	2	4	no	—
458	C₄×C₁₇	—	2	2	no	—
459	C₄×C₁₇	—	2	1	no	—
460	C₄×C₁₇	—	2	1	no	—
461	C₄×C₁₇	—	2	1	no	—
462	C₄×C₁₇	—	2	2	no	—
463	C₄×C₁₇	—	4	2	no	—
464	C₄×C₁₇	—	4	2	no	—
465	C₄×C₁₇	—	4	2	no	—
466	C₄×C₁₇	—	4	2	no	—
467	C₄×C₁₇	—	4	2	no	—
468	C₄×C₁₇	C₂×H(5,𝔽₂)	1	2	yes	—
469	C₂²×#41	C₂²×C₁₇	1	1	yes	characteristic, complemented
470	C₂³×Q₈	C₂²×C₁₇	1	1	yes	characteristic
471	C₂×#135	C₂²×C₁₇	1	4	yes	complemented
472	C₂²×Q₁₆	C₂²×C₁₇	1	2	yes	complemented
473	C₂²×SD₁₆	C₂²×C₁₇	1	2	yes	complemented
474	#553	—	2	2	no	—
475	#553	C₂²×C₁₇	1	2	yes	complemented
476	#552	C₂²×C₁₇	1	2	yes	complemented
477	#551	—	2	2	no	—
478	#548	—	2	2	no	—
479	#548	—	2	2	no	—
480	#548	C₂²×C₁₇	1	4	yes	—
481	#548	C₂²×C₁₇	1	4	yes	complemented
482	#548	C₂²×C₁₇	1	2	yes	complemented
483	#546	C₂²×C₁₇	1	2	yes	complemented
484	#539	—	2	1	no	—
485	#538	—	2	1	no	—
486	#534	—	2	1	no	—
487	#529	C₂²×C₁₇	1	2	yes	—
488	C₂×#124	—	2	1	no	—
489	C₂×#124	C₂²×C₁₇	1	1	yes	characteristic, complemented
490	#525	C₂²×C₁₇	1	2	yes	—
491	C₂×C₂²⋊Q₈	—	2	1	no	—
492	C₂×C₂²⋊Q₈	C₂²×C₁₇	1	1	yes	characteristic
493	C₂×C₂²⋊Q₈	C₂²×C₁₇	1	1	yes	characteristic, complemented
494	C₂×#121	—	2	1	no	—
495	C₂×#121	C₂²×C₁₇	1	1	yes	characteristic
496	C₂×#121	C₂²×C₁₇	1	1	yes	characteristic
497	#518	—	2	1	no	—
498	C₂×C₄×Q₈	C₂²×C₁₇	1	1	yes	characteristic, complemented
499	C₂×C₄×D₄	—	2	1	no	—
500	C₂×C₄×D₄	C₂²×C₁₇	1	1	yes	characteristic
501	#495	C₂²×C₁₇	1	4	yes	complemented
502	#488	C₂²×C₁₇	1	4	yes	complemented
503	#485	C₂²×C₁₇	1	4	yes	complemented
504	#483	C₂²×C₁₇	1	2	yes	complemented
505	#481	C₂²×C₁₇	1	2	yes	complemented
506	#480	C₂²×C₁₇	1	2	yes	—
507	#480	C₂²×C₁₇	1	2	yes	complemented
508	#479	C₂²×C₁₇	1	4	yes	complemented
509	#467	C₂²×C₁₇	1	4	yes	complemented
510	#466	C₂²×C₁₇	1	4	yes	complemented
511	#465	C₂²×C₁₇	1	4	yes	complemented
512	#465	C₂²×C₁₇	1	4	yes	complemented
513	#464	C₂²×C₁₇	1	4	yes	complemented
514	#464	C₂²×C₁₇	1	4	yes	complemented
515	#463	C₂²×C₁₇	1	4	yes	complemented
516	#452	C₂²×C₁₇	1	4	yes	complemented
517	#452	C₂²×C₁₇	1	4	yes	complemented
518	#451	C₂²×C₁₇	1	2	yes	complemented
519	#451	C₂²×C₁₇	1	2	yes	complemented
520	#451	C₂²×C₁₇	1	4	yes	complemented
521	#450	C₂²×C₁₇	1	2	yes	complemented
522	#449	C₂²×C₁₇	1	4	yes	complemented
523	#448	C₂²×C₁₇	1	2	yes	—
524	#448	C₂²×C₁₇	1	2	yes	—
525	#448	C₂²×C₁₇	1	2	yes	complemented
526	#448	C₂²×C₁₇	1	4	yes	complemented
527	#447	C₂²×C₁₇	1	2	yes	—
528	#447	C₂²×C₁₇	1	2	yes	complemented
529	C₄×Q₁₆	C₂²×C₁₇	1	4	yes	complemented
530	C₄×SD₁₆	C₂²×C₁₇	1	4	yes	complemented
531	C₈×D₄	C₂²×C₁₇	1	4	yes	complemented
532	C₈×D₄	C₂²×C₁₇	1	4	yes	complemented
533	#431	C₂²×C₁₇	1	2	yes	complemented
534	#416	C₂²×C₁₇	1	4	yes	complemented
535	C₂×#103	C₂²×C₁₇	1	2	yes	complemented
536	C₂×#103	C₂²×C₁₇	1	2	yes	complemented
537	C₂×C₂²⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
538	C₂×C₂²⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
539	C₂×C₂²⋊C₈	C₂²×C₁₇	1	2	yes	complemented
540	C₂×C₁₇	—	2	2	no	—
541	C₂×C₁₇	—	2	2	no	—
542	C₂×C₁₇	—	2	2	no	—
543	C₂×C₁₇	—	4	2	no	—
544	C₂×C₁₇	—	8	2	no	—
545	C₂×C₁₇	—	8	2	no	—
546	C₂×C₁₇	#3484	1	1	yes	characteristic
547	C₂×C₁₇	C₂²×#135	1	1	yes	characteristic
548	C₂×C₁₇	#3586	1	1	yes	characteristic
549	C₂×#41	—	2	2	no	—
550	C₂×#41	—	4	4	no	—
551	C₂×#41	C₂³×C₁₇	1	4	yes	—
552	C₂×#41	C₂³×C₁₇	1	2	yes	—
553	C₂²×Q₈	—	2	1	no	—
554	C₂²×Q₈	—	2	1	no	—
555	C₂²×Q₈	—	2	1	no	—
556	C₂²×Q₈	—	4	4	no	—
557	C₂²×Q₈	C₂³×C₁₇	1	1	yes	characteristic
558	C₂²×Q₈	C₂³×C₁₇	1	2	yes	—
559	C₂²×Q₈	C₂³×C₁₇	1	2	yes	—
560	C₂²×Q₈	C₂³×C₁₇	1	1	yes	characteristic
561	C₂²×Q₈	C₂³×C₁₇	1	1	yes	characteristic
562	C₂²×D₄	—	2	1	no	—
563	C₂²×D₄	—	2	1	no	—
564	C₂²×D₄	—	2	1	no	—
565	C₂²×D₄	D₄×C₁₇	1	1	yes	characteristic
566	C₂²×D₄	C₂³×C₁₇	1	1	yes	characteristic
567	C₂²×D₄	C₂³×C₁₇	1	1	yes	characteristic
568	C₂³×C₄	—	2	1	no	—
569	C₂³×C₄	—	2	1	no	—
570	C₂³×C₄	C₂³×C₁₇	1	1	yes	characteristic
571	C₂³×C₄	C₂³×C₁₇	1	1	yes	characteristic
572	#135	—	4	8	no	—
573	C₂×Q₁₆	—	4	4	no	—
574	C₂×Q₁₆	C₂³×C₁₇	1	4	yes	—
575	C₂×Q₁₆	C₂³×C₁₇	1	4	yes	—
576	C₂×SD₁₆	—	4	4	no	—
577	C₂×SD₁₆	C₂³×C₁₇	1	4	yes	—
578	C₂×SD₁₆	C₂³×C₁₇	1	4	yes	—
579	C₂×SD₁₆	C₂³×C₁₇	1	4	yes	—
580	C₂×D₈	C₂³×C₁₇	1	4	yes	—
581	C₂²×C₈	C₂³×C₁₇	1	2	yes	—
582	C₂²×C₈	C₂³×C₁₇	1	2	yes	—
583	C₂²×C₈	C₂³×C₁₇	1	4	yes	—
584	#126	—	2	2	no	—
585	#126	—	2	2	no	—
586	#126	—	2	2	no	—
587	#125	—	2	2	no	—
588	#125	C₂³×C₁₇	1	2	yes	—
589	#124	—	2	4	no	—
590	#124	—	2	4	no	—
591	#124	—	2	2	no	—
592	#124	—	2	2	no	—
593	#124	C₂³×C₁₇	1	4	yes	—
594	#124	C₂³×C₁₇	1	2	yes	—
595	#123	—	2	2	no	—
596	#123	—	2	2	no	—
597	#123	—	2	2	no	—
598	#123	—	2	2	no	—
599	#123	—	2	2	no	—
600	C₂²⋊Q₈	—	2	1	no	—
601	C₂²⋊Q₈	—	2	1	no	—
602	C₂²⋊Q₈	—	2	2	no	—
603	C₂²⋊Q₈	—	2	4	no	—
604	C₂²⋊Q₈	—	2	4	no	—
605	C₂²⋊Q₈	—	2	2	no	—
606	C₂²⋊Q₈	C₂³×C₁₇	1	2	yes	—
607	C₂²⋊Q₈	C₂³×C₁₇	1	2	yes	—
608	C₂²⋊Q₈	C₂³×C₁₇	1	4	yes	—
609	C₂²⋊Q₈	C₂³×C₁₇	1	2	yes	—
610	#121	—	2	4	no	—
611	#121	—	2	4	no	—
612	#121	—	2	2	no	—
613	#121	—	2	2	no	—
614	#121	—	2	1	no	—
615	#121	—	2	1	no	—
616	#121	—	2	1	no	—
617	#121	—	2	1	no	—
618	#121	—	2	2	no	—
619	#121	C₂³×C₁₇	1	2	yes	—
620	#121	C₂³×C₁₇	1	2	yes	—
621	#121	C₂³×C₁₇	1	2	yes	—
622	#121	C₂³×C₁₇	1	2	yes	—
623	#121	C₂³×C₁₇	1	2	yes	—
624	#120	—	2	2	no	—
625	#120	—	2	2	no	—
626	C₄×Q₈	—	2	2	no	—
627	C₄×Q₈	C₂³×C₁₇	1	4	yes	—
628	C₄×Q₈	C₂³×C₁₇	1	2	yes	—
629	C₄×D₄	—	2	2	no	—
630	C₄×D₄	—	2	2	no	—
631	C₄×D₄	—	2	2	no	—
632	C₄×D₄	—	2	4	no	—
633	C₄×D₄	—	2	4	no	—
634	C₄×D₄	—	2	2	no	—
635	C₄×D₄	—	2	2	no	—
636	C₄×D₄	D₄×C₁₇	1	2	yes	—
637	C₄×D₄	D₄×C₁₇	1	2	yes	—
638	C₄×D₄	C₂³×C₁₇	1	2	yes	—
639	C₄×D₄	C₂³×C₁₇	1	2	yes	—
640	C₄×D₄	C₂³×C₁₇	1	2	yes	—
641	#117	—	2	2	no	—
642	#117	—	2	2	no	—
643	#117	C₂³×C₁₇	1	2	yes	—
644	C₂×C₄⋊C₄	—	2	1	no	—
645	C₂×C₄⋊C₄	—	2	1	no	—
646	C₂×C₄⋊C₄	—	2	1	no	—
647	C₂×C₄⋊C₄	D₄×C₁₇	1	1	yes	characteristic
648	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
649	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
650	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
651	C₂×C₂²⋊C₄	—	2	1	no	—
652	C₂×C₂²⋊C₄	—	2	1	no	—
653	C₂×C₂²⋊C₄	—	2	1	no	—
654	C₂×C₂²⋊C₄	—	2	1	no	—
655	C₂×C₂²⋊C₄	—	2	1	no	—
656	C₂×C₂²⋊C₄	—	2	1	no	—
657	C₂×C₂²⋊C₄	—	2	2	no	—
658	C₂×C₂²⋊C₄	D₄×C₁₇	1	1	yes	characteristic
659	C₂×C₂²⋊C₄	D₄×C₁₇	1	1	yes	characteristic
660	C₂×C₄²	—	2	1	no	—
661	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
662	#107	C₂³×C₁₇	1	4	yes	—
663	#106	C₂³×C₁₇	1	4	yes	—
664	C₄⋊C₈	C₂³×C₁₇	1	4	yes	—
665	#103	C₂³×C₁₇	1	4	yes	—
666	#103	C₂³×C₁₇	1	4	yes	—
667	#103	C₂³×C₁₇	1	4	yes	—
668	#103	C₂³×C₁₇	1	4	yes	—
669	#103	C₂³×C₁₇	1	4	yes	—
670	#102	C₂³×C₁₇	1	4	yes	—
671	#102	C₂³×C₁₇	1	4	yes	—
672	#102	C₂³×C₁₇	1	4	yes	—
673	C₂²⋊C₈	C₂³×C₁₇	1	2	yes	—
674	C₂²⋊C₈	C₂³×C₁₇	1	2	yes	—
675	C₂²⋊C₈	C₂³×C₁₇	1	2	yes	—
676	C₂²⋊C₈	C₂³×C₁₇	1	2	yes	—
677	C₂²⋊C₈	C₂³×C₁₇	1	4	yes	—
678	C₄×C₈	C₂³×C₁₇	1	4	yes	—
679	C₁₇	#61564	1	1	yes	characteristic, direct product factor, Sylow
680	C₂⁴	—	2	1	no	—
681	C₂⁴	—	2	1	no	—
682	C₂⁴	C₂×D₄×C₁₇	1	1	yes	characteristic
683	C₂⁴	C₂×D₄×C₁₇	1	1	yes	characteristic
684	#41	—	2	8	no	—
685	#41	—	4	4	no	—
686	#41	—	4	4	no	—
687	#41	—	4	8	no	—
688	C₂×Q₈	—	2	4	no	—
689	C₂×Q₈	—	2	1	no	—
690	C₂×Q₈	—	2	2	no	—
691	C₂×Q₈	—	2	2	no	—
692	C₂×Q₈	—	2	1	no	—
693	C₂×Q₈	—	2	1	no	—
694	C₂×Q₈	—	2	4	no	—
695	C₂×Q₈	—	2	4	no	—
696	C₂×Q₈	—	4	2	no	—
697	C₂×Q₈	—	4	2	no	—
698	C₂×Q₈	—	4	2	no	—
699	C₂×Q₈	—	4	4	no	—
700	C₂×Q₈	—	4	2	no	—
701	C₂×Q₈	—	4	4	no	—
702	C₂×Q₈	—	4	4	no	—
703	C₂×Q₈	C₂⁴×C₁₇	1	2	yes	—
704	C₂×Q₈	C₂⁴×C₁₇	1	2	yes	—
705	C₂×Q₈	C₂⁴×C₁₇	1	2	yes	—
706	C₂×D₄	—	2	4	no	—
707	C₂×D₄	—	2	2	no	—
708	C₂×D₄	—	2	2	no	—
709	C₂×D₄	—	2	2	no	—
710	C₂×D₄	—	2	2	no	—
711	C₂×D₄	—	2	4	no	—
712	C₂×D₄	—	2	2	no	—
713	C₂×D₄	—	2	2	no	—
714	C₂×D₄	—	2	1	no	—
715	C₂×D₄	—	2	1	no	—
716	C₂×D₄	—	4	2	no	—
717	C₂×D₄	—	4	2	no	—
718	C₂×D₄	—	4	4	no	—
719	C₂×D₄	—	4	4	no	—
720	C₂×D₄	—	4	4	no	—
721	C₂×D₄	C₂×D₄×C₁₇	1	2	yes	—
722	C₂×D₄	C₂×D₄×C₁₇	1	2	yes	—
723	C₂×D₄	C₂⁴×C₁₇	1	2	yes	—
724	C₂×D₄	C₂⁴×C₁₇	1	2	yes	—
725	C₂²×C₄	—	2	1	no	—
726	C₂²×C₄	—	2	1	no	—
727	C₂²×C₄	—	2	1	no	—
728	C₂²×C₄	—	2	1	no	—
729	C₂²×C₄	—	2	2	no	—
730	C₂²×C₄	—	2	2	no	—
731	C₂²×C₄	—	2	1	no	—
732	C₂²×C₄	—	2	1	no	—
733	C₂²×C₄	—	2	4	no	—
734	C₂²×C₄	—	2	2	no	—
735	C₂²×C₄	—	2	2	no	—
736	C₂²×C₄	—	4	2	no	—
737	C₂²×C₄	—	4	2	no	—
738	C₂²×C₄	—	4	4	no	—
739	C₂²×C₄	—	4	4	no	—
740	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
741	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
742	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
743	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
744	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
745	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
746	C₂²×C₄	C₂×D₄×C₁₇	1	2	yes	—
747	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
748	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
749	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
750	C₂²×C₄	C₂⁴×C₁₇	1	2	yes	—
751	Q₁₆	—	2	8	no	—
752	Q₁₆	—	4	4	no	—
753	SD₁₆	—	2	8	no	—
754	SD₁₆	—	4	4	no	—
755	SD₁₆	—	4	4	no	—
756	D₈	—	4	4	no	—
757	C₂×C₈	—	4	2	no	—
758	C₂×C₈	—	4	2	no	—
759	C₂×C₈	—	4	4	no	—
760	C₂×C₈	C₂⁴×C₁₇	1	4	yes	—
761	C₂×C₈	C₂⁴×C₁₇	1	4	yes	—
762	C₄⋊C₄	—	2	2	no	—
763	C₄⋊C₄	—	2	4	no	—
764	C₄⋊C₄	—	2	4	no	—
765	C₄⋊C₄	—	2	2	no	—
766	C₄⋊C₄	—	2	1	no	—
767	C₄⋊C₄	—	2	1	no	—
768	C₄⋊C₄	—	2	1	no	—
769	C₄⋊C₄	—	2	2	no	—
770	C₄⋊C₄	—	2	2	no	—
771	C₄⋊C₄	—	2	2	no	—
772	C₄⋊C₄	—	2	2	no	—
773	C₄⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
774	C₄⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
775	C₄⋊C₄	C₂⁴×C₁₇	1	2	yes	—
776	C₄⋊C₄	C₂⁴×C₁₇	1	2	yes	—
777	C₄⋊C₄	C₂⁴×C₁₇	1	2	yes	—
778	C₂²⋊C₄	—	2	2	no	—
779	C₂²⋊C₄	—	2	2	no	—
780	C₂²⋊C₄	—	2	4	no	—
781	C₂²⋊C₄	—	2	2	no	—
782	C₂²⋊C₄	—	2	2	no	—
783	C₂²⋊C₄	—	2	2	no	—
784	C₂²⋊C₄	—	2	2	no	—
785	C₂²⋊C₄	—	2	2	no	—
786	C₂²⋊C₄	—	2	4	no	—
787	C₂²⋊C₄	—	2	4	no	—
788	C₂²⋊C₄	—	2	2	no	—
789	C₂²⋊C₄	—	2	2	no	—
790	C₂²⋊C₄	—	2	2	no	—
791	C₂²⋊C₄	—	2	2	no	—
792	C₂²⋊C₄	—	2	2	no	—
793	C₂²⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
794	C₂²⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
795	C₂²⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
796	C₂²⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
797	C₄²	—	2	4	no	—
798	C₄²	—	2	2	no	—
799	C₄²	—	2	2	no	—
800	C₄²	C₂×D₄×C₁₇	1	2	yes	—
801	C₄²	C₂⁴×C₁₇	1	2	yes	—
802	C₂³	—	2	2	no	—
803	C₂³	—	2	2	no	—
804	C₂³	—	2	2	no	—
805	C₂³	—	4	1	no	—
806	C₂³	—	4	1	no	—
807	C₂³	—	4	1	no	—
808	C₂³	—	4	1	no	—
809	C₂³	—	4	2	no	—
810	C₂³	—	4	2	no	—
811	C₂³	—	4	2	no	—
812	C₂³	—	4	2	no	—
813	C₂³	—	8	1	no	—
814	C₂³	—	8	1	no	—
815	C₂³	C₁₇×#135	1	4	yes	complemented
816	C₂³	C₂²×D₄×C₁₇	1	2	yes	—
817	C₂³	C₂²×D₄×C₁₇	1	1	yes	characteristic
818	C₂³	C₂²×D₄×C₁₇	1	1	yes	characteristic
819	C₂³	C₂²×D₄×C₁₇	1	1	yes	characteristic
820	Q₈	—	2	4	no	—
821	Q₈	—	2	2	no	—
822	Q₈	—	2	2	no	—
823	Q₈	—	2	4	no	—
824	Q₈	—	2	2	no	—
825	Q₈	—	4	4	no	—
826	Q₈	—	4	4	no	—
827	Q₈	—	4	2	no	—
828	Q₈	—	8	1	no	—
829	Q₈	C₁₇×H(5,𝔽₂)	1	4	yes	—
830	D₄	—	2	4	no	—
831	D₄	—	2	4	no	—
832	D₄	—	2	4	no	—
833	D₄	—	2	4	no	—
834	D₄	—	4	8	no	—
835	D₄	—	4	2	no	—
836	D₄	—	4	4	no	—
837	D₄	—	4	4	no	—
838	D₄	—	4	4	no	—
839	D₄	—	4	4	no	—
840	D₄	—	8	1	no	—
841	D₄	—	8	2	no	—
842	D₄	—	8	2	no	—
843	C₂×C₄	—	2	4	no	—
844	C₂×C₄	—	2	2	no	—
845	C₂×C₄	—	2	2	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	4	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	2	2	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	4	1	no	—
856	C₂×C₄	—	4	1	no	—
857	C₂×C₄	—	4	1	no	—
858	C₂×C₄	—	4	1	no	—
859	C₂×C₄	—	4	2	no	—
860	C₂×C₄	—	4	1	no	—
861	C₂×C₄	—	4	8	no	—
862	C₂×C₄	—	4	4	no	—
863	C₂×C₄	—	4	4	no	—
864	C₂×C₄	—	4	2	no	—
865	C₂×C₄	—	4	2	no	—
866	C₂×C₄	—	4	2	no	—
867	C₂×C₄	—	8	2	no	—
868	C₂×C₄	—	8	2	no	—
869	C₂×C₄	—	8	1	no	—
870	C₂×C₄	—	8	1	no	—
871	C₂×C₄	C₂²×D₄×C₁₇	1	2	yes	—
872	C₂×C₄	C₂²×D₄×C₁₇	1	2	yes	—
873	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
874	C₂×C₄	C₂²×D₄×C₁₇	1	2	yes	—
875	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
876	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
877	C₂×C₄	C₂⁵×C₁₇	1	1	yes	characteristic
878	C₈	—	2	4	no	—
879	C₈	—	2	4	no	—
880	C₂²	—	2	1	no	—
881	C₂²	—	2	1	no	—
882	C₂²	—	2	1	no	—
883	C₂²	—	2	1	no	—
884	C₂²	—	2	1	no	—
885	C₂²	—	2	1	no	—
886	C₂²	—	2	2	no	—
887	C₂²	—	2	2	no	—
888	C₂²	—	2	2	no	—
889	C₂²	—	4	4	no	—
890	C₂²	—	4	2	no	—
891	C₂²	—	4	2	no	—
892	C₂²	—	4	2	no	—
893	C₂²	—	4	2	no	—
894	C₂²	—	4	2	no	—
895	C₂²	—	4	2	no	—
896	C₂²	—	8	2	no	—
897	C₂²	—	8	4	no	—
898	C₂²	—	16	2	no	—
899	C₂²	C₂×C₁₇×#135	1	2	yes	—
900	C₂²	C₂×C₁₇×#135	1	2	yes	—
901	C₂²	C₂×C₁₇×#135	1	2	yes	—
902	C₂²	C₂³×D₄×C₁₇	1	1	yes	characteristic
903	C₄	—	2	4	no	—
904	C₄	—	2	2	no	—
905	C₄	—	2	1	no	—
906	C₄	—	2	1	no	—
907	C₄	—	2	1	no	—
908	C₄	—	2	2	no	—
909	C₄	—	2	2	no	—
910	C₄	—	4	2	no	—
911	C₄	—	4	2	no	—
912	C₄	—	4	2	no	—
913	C₄	—	4	2	no	—
914	C₄	—	4	2	no	—
915	C₄	C₂×C₁₇×H(5,𝔽₂)	1	2	yes	—
916	C₂	—	2	2	no	—
917	C₂	—	2	2	no	—
918	C₂	—	2	2	no	—
919	C₂	—	4	2	no	—
920	C₂	—	8	2	no	—
921	C₂	—	8	2	no	—
922	C₂	C₁₇×#3484	1	1	yes	characteristic
923	C₂	C₂²×C₁₇×#135	1	1	yes	characteristic
924	C₂	C₁₇×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂×C₄×D₄×C₁₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₇×#3505	C₂	semidirect
2. C₂×C₁₇×#548	C₂	semidirect
3. C₁₇×#3301	C₂	semidirect
4. C₁₇×#3300	C₂	semidirect
5. C₁₇×#3285	C₂	semidirect
6. C₁₇×#3282	C₂	semidirect
7. C₁₇×#3211	C₂	semidirect
8. C₁₇×#3190	C₂	semidirect
9. C₁₇×#3187	C₂	semidirect
10. C₁₇×#3186	C₂	semidirect
11. C₁₇×#3108	C₂	semidirect
12. C₁₇×#3002	C₂	semidirect
13. C₂×C₁₇×#451	C₂	semidirect
14. C₂×C₁₇×#448	C₂	semidirect
15. C₁₇×#2972	C₂	semidirect
16. C₂²×#41×C₁₇	C₂²	semidirect
18. C₂×C₁₇×#135	C₂²	semidirect
19. C₂²×Q₁₆×C₁₇	C₂²	semidirect
20. C₂²×SD₁₆×C₁₇	C₂²	semidirect
22. C₁₇×#553	C₂²	semidirect
23. C₁₇×#552	C₂²	semidirect
28. C₁₇×#548	C₂²	semidirect
29. C₁₇×#548	C₂²	semidirect
30. C₁₇×#546	C₂²	semidirect
36. C₂×C₁₇×#124	C₂²	semidirect
40. C₂×C₁₇×C₂²⋊Q₈	C₂²	semidirect
45. C₂×C₄×Q₈×C₁₇	C₂²	semidirect
48. C₁₇×#495	C₂²	semidirect
49. C₁₇×#488	C₂²	semidirect
50. C₁₇×#485	C₂²	semidirect
51. C₁₇×#483	C₂²	semidirect
52. C₁₇×#481	C₂²	semidirect
54. C₁₇×#480	C₂²	semidirect
55. C₁₇×#479	C₂²	semidirect
56. C₁₇×#467	C₂²	semidirect
57. C₁₇×#466	C₂²	semidirect
58. C₁₇×#465	C₂²	semidirect
59. C₁₇×#465	C₂²	semidirect
60. C₁₇×#464	C₂²	semidirect
61. C₁₇×#464	C₂²	semidirect
62. C₁₇×#463	C₂²	semidirect
63. C₁₇×#452	C₂²	semidirect
64. C₁₇×#452	C₂²	semidirect
65. C₁₇×#451	C₂²	semidirect
66. C₁₇×#451	C₂²	semidirect
67. C₁₇×#451	C₂²	semidirect
68. C₁₇×#450	C₂²	semidirect
69. C₁₇×#449	C₂²	semidirect
72. C₁₇×#448	C₂²	semidirect
73. C₁₇×#448	C₂²	semidirect
75. C₁₇×#447	C₂²	semidirect
76. C₄×Q₁₆×C₁₇	C₂²	semidirect
77. C₄×SD₁₆×C₁₇	C₂²	semidirect
78. C₈×D₄×C₁₇	C₂²	semidirect
79. C₈×D₄×C₁₇	C₂²	semidirect
80. C₁₇×#431	C₂²	semidirect
81. C₁₇×#416	C₂²	semidirect
82. C₂×C₁₇×#103	C₂²	semidirect
83. C₂×C₁₇×#103	C₂²	semidirect
86. C₂×C₁₇×C₂²⋊C₈	C₂²	semidirect
339. #61564	C₁₇	direct (N × H)
353. C₂³×C₁₇	#135	semidirect
418. #3505	C₂×C₁₇	semidirect
419. C₂×#548	C₂×C₁₇	semidirect
420. #3301	C₂×C₁₇	semidirect
421. #3300	C₂×C₁₇	semidirect
422. #3285	C₂×C₁₇	semidirect
423. #3282	C₂×C₁₇	semidirect
424. #3211	C₂×C₁₇	semidirect
425. #3190	C₂×C₁₇	semidirect
426. #3187	C₂×C₁₇	semidirect
427. #3186	C₂×C₁₇	semidirect
428. #3108	C₂×C₁₇	semidirect
429. #3002	C₂×C₁₇	semidirect
430. C₂×#451	C₂×C₁₇	semidirect
431. C₂×#448	C₂×C₁₇	semidirect
432. #2972	C₂×C₁₇	semidirect
469. C₂²×#41	C₂²×C₁₇	semidirect
471. C₂×#135	C₂²×C₁₇	semidirect
472. C₂²×Q₁₆	C₂²×C₁₇	semidirect
473. C₂²×SD₁₆	C₂²×C₁₇	semidirect
475. #553	C₂²×C₁₇	semidirect
476. #552	C₂²×C₁₇	semidirect
481. #548	C₂²×C₁₇	semidirect
482. #548	C₂²×C₁₇	semidirect
483. #546	C₂²×C₁₇	semidirect
489. C₂×#124	C₂²×C₁₇	semidirect
493. C₂×C₂²⋊Q₈	C₂²×C₁₇	semidirect
498. C₂×C₄×Q₈	C₂²×C₁₇	semidirect
501. #495	C₂²×C₁₇	semidirect
502. #488	C₂²×C₁₇	semidirect
503. #485	C₂²×C₁₇	semidirect
504. #483	C₂²×C₁₇	semidirect
505. #481	C₂²×C₁₇	semidirect
507. #480	C₂²×C₁₇	semidirect
508. #479	C₂²×C₁₇	semidirect
509. #467	C₂²×C₁₇	semidirect
510. #466	C₂²×C₁₇	semidirect
511. #465	C₂²×C₁₇	semidirect
512. #465	C₂²×C₁₇	semidirect
513. #464	C₂²×C₁₇	semidirect
514. #464	C₂²×C₁₇	semidirect
515. #463	C₂²×C₁₇	semidirect
516. #452	C₂²×C₁₇	semidirect
517. #452	C₂²×C₁₇	semidirect
518. #451	C₂²×C₁₇	semidirect
519. #451	C₂²×C₁₇	semidirect
520. #451	C₂²×C₁₇	semidirect
521. #450	C₂²×C₁₇	semidirect
522. #449	C₂²×C₁₇	semidirect
525. #448	C₂²×C₁₇	semidirect
526. #448	C₂²×C₁₇	semidirect
528. #447	C₂²×C₁₇	semidirect
529. C₄×Q₁₆	C₂²×C₁₇	semidirect
530. C₄×SD₁₆	C₂²×C₁₇	semidirect
531. C₈×D₄	C₂²×C₁₇	semidirect
532. C₈×D₄	C₂²×C₁₇	semidirect
533. #431	C₂²×C₁₇	semidirect
534. #416	C₂²×C₁₇	semidirect
535. C₂×#103	C₂²×C₁₇	semidirect
536. C₂×#103	C₂²×C₁₇	semidirect
539. C₂×C₂²⋊C₈	C₂²×C₁₇	semidirect
679. C₁₇	#61564	direct (N × H)
815. C₂³	C₁₇×#135	semidirect

Maximal subgroups

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

subgroup	index
C₁₇×#3505	2
C₂×C₁₇×#548	2
C₁₇×#3301	2
C₁₇×#3300	2
C₁₇×#3285	2
C₁₇×#3282	2
C₁₇×#3211	2
C₁₇×#3190	2
C₁₇×#3187	2
C₁₇×#3186	2
C₁₇×#3108	2
C₁₇×#3002	2
C₂×C₁₇×#451	2
C₂×C₁₇×#448	2
C₁₇×#2972	2
#61564	17

Subgroups — C17×#61564 #16919308

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#61564 #16919308