Subgroups — C₂×H(5,𝔽₂)×#595 #17981040

Order 4352.

12378 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	H(5,𝔽₂)×#595	C₂	1	32	yes	maximal, direct product factor
2	C₂×#11763878	C₂	1	6	yes	maximal, complemented
3	C₂×#11763876	C₂	1	9	yes	maximal, complemented
4	C₂×#41×#595	C₂	1	6	yes	maximal, complemented
5	C₂²×D₄×#595	C₂	1	9	yes	maximal, complemented
6	C₂×H(5,𝔽₂)×D₁₇	C₂	1	1	yes	maximal, characteristic
7	C₂⁴×#595	C₂²	1	6	yes	complemented
8	#11763878	C₂²	1	96	yes	complemented
9	#11763876	C₂²	1	144	yes	complemented
10	#41×#595	C₂²	1	96	yes	complemented
11	C₂×Q₈×#595	C₂²	1	2	yes	complemented
12	C₂×Q₈×#595	C₂²	1	6	yes	complemented
13	C₂×D₄×#595	C₂²	1	18	yes	complemented
14	C₂×D₄×#595	C₂²	1	36	yes	complemented
15	C₂×D₄×#595	C₂²	1	18	yes	complemented
16	C₂×D₄×#595	C₂²	1	144	yes	complemented
17	C₂×#10587677	C₂²	1	18	yes	complemented
18	C₂²×C₄⋊#595	C₂²	1	9	yes	complemented
19	C₂²×C₂²⋊#595	C₂²	1	18	yes	complemented
20	C₂²×C₄×#595	C₂²	1	9	yes	complemented
21	C₂×#10587696	C₄	1	6	yes	complemented
22	C₂×#10587691	C₄	1	9	yes	complemented
23	H(5,𝔽₂)×D₁₇	C₄	1	16	yes	complemented
24	H(5,𝔽₂)×D₁₇	C₂²	1	16	yes	—
25	C₂×#41×D₁₇	C₂²	1	6	yes	—
26	C₂²×D₄×D₁₇	C₂²	1	9	yes	—
27	C₂×C₁₇×H(5,𝔽₂)	C₄	1	1	yes	characteristic, complemented
28	C₂⁴×D₁₇	C₂³	1	6	yes	—
29	C₂³×#595	—	4	24	no	—
30	C₂³×#595	C₂³	1	9	yes	—
31	C₂³×#595	C₂³	1	9	yes	—
32	C₂³×#595	C₂³	1	18	yes	—
33	C₂³×#595	C₂³	1	48	yes	complemented
34	C₁₇×H(5,𝔽₂)	C₂×C₄	1	16	yes	complemented
35	C₂×#41×C₁₇	C₂×C₄	1	6	yes	complemented
36	C₂²×D₄×C₁₇	C₂×C₄	1	9	yes	complemented
37	C₂²×C₂²⋊D₁₇	C₂×C₄	1	18	yes	complemented
38	#10587696	C₂×C₄	1	96	yes	complemented
39	#41×D₁₇	C₂×C₄	1	48	yes	complemented
40	#41×D₁₇	C₂³	1	48	yes	—
41	C₂×#63256	C₂×C₄	1	6	yes	complemented
42	C₂×Q₈×D₁₇	C₂³	1	2	yes	—
43	#10587691	C₂×C₄	1	144	yes	complemented
44	C₂×#63254	C₂×C₄	1	18	yes	complemented
45	C₂×D₄×D₁₇	C₂×C₄	1	72	yes	complemented
46	C₂×D₄×D₁₇	C₂×C₄	1	36	yes	complemented
47	C₂×D₄×D₁₇	C₂³	1	18	yes	—
48	C₂×D₄×D₁₇	C₂³	1	72	yes	—
49	C₂×#63252	C₂×C₄	1	18	yes	complemented
50	C₂²×D₆₈	C₂×C₄	1	9	yes	complemented
51	C₂²×C₄×D₁₇	C₂³	1	9	yes	—
52	C₂×C₂²⋊#595	C₂³	1	36	yes	—
53	C₂×C₂²⋊#595	C₂³	1	144	yes	complemented
54	Q₈×#595	C₂³	1	16	yes	complemented
55	Q₈×#595	C₂³	1	48	yes	complemented
56	D₄×#595	C₂³	1	144	yes	complemented
57	D₄×#595	C₂³	1	288	yes	complemented
58	D₄×#595	C₂³	1	144	yes	complemented
59	#10587677	C₂³	1	144	yes	complemented
60	C₂×C₄⋊#595	C₂³	1	18	yes	—
61	C₂×C₄⋊#595	C₂³	1	6	yes	—
62	C₂×C₄⋊#595	C₂³	1	72	yes	complemented
63	C₂×C₄×#595	C₂³	1	6	yes	—
64	C₂×C₄×#595	C₂³	1	18	yes	—
65	C₂×C₄×#595	C₂³	1	72	yes	complemented
66	C₂⁴×C₁₇	C₂²×C₄	1	6	yes	complemented
67	C₂³×D₁₇	—	4	12	no	—
68	C₂³×D₁₇	—	4	12	no	—
69	C₂³×D₁₇	C₂²×C₄	1	24	yes	complemented
70	C₂³×D₁₇	C₂²×C₄	1	18	yes	complemented
71	C₂³×D₁₇	C₂⁴	1	9	yes	—
72	C₂³×D₁₇	C₂⁴	1	24	yes	—
73	C₂²×#595	—	2	36	no	—
74	C₂²×#595	—	4	96	no	—
75	C₂²×#595	—	4	36	no	—
76	C₂²×#595	—	4	18	no	—
77	C₂²×#595	C₂⁴	1	6	yes	—
78	C₂²×#595	C₂⁴	1	9	yes	—
79	C₂²×#595	C₂⁴	1	36	yes	—
80	C₂²×#595	C₂⁴	1	36	yes	—
81	C₂²×#595	C₂⁴	1	72	yes	—
82	C₂²×#595	C₂⁴	1	1	yes	characteristic
83	#41×C₁₇	C₂²×C₄	1	48	yes	complemented
84	C₂×Q₈×C₁₇	C₂²×C₄	1	2	yes	complemented
85	C₂×D₄×C₁₇	C₂²×C₄	1	18	yes	complemented
86	C₂×D₄×C₁₇	C₂²×C₄	1	72	yes	complemented
87	C₂²×C₄×C₁₇	C₂²×C₄	1	9	yes	complemented
88	C₂×C₂²⋊D₁₇	C₂²×C₄	1	36	yes	complemented
89	C₂×C₂²⋊D₁₇	C₂²×C₄	1	144	yes	complemented
90	C₂²×Dic₁₇	C₂²×C₄	1	9	yes	complemented
91	#63256	C₂²×C₄	1	48	yes	complemented
92	Q₈×D₁₇	C₂²×C₄	1	8	yes	complemented
93	Q₈×D₁₇	C₂⁴	1	8	yes	—
94	#63254	C₂²×C₄	1	144	yes	complemented
95	D₄×D₁₇	C₂²×C₄	1	72	yes	complemented
96	D₄×D₁₇	C₂²×C₄	1	288	yes	complemented
97	D₄×D₁₇	C₂⁴	1	72	yes	—
98	#63252	C₂²×C₄	1	144	yes	complemented
99	C₂×D₆₈	C₂²×C₄	1	18	yes	complemented
100	C₂×D₆₈	C₂²×C₄	1	72	yes	complemented
101	C₂×C₄×D₁₇	C₂²×C₄	1	36	yes	complemented
102	C₂×C₄×D₁₇	C₂²×C₄	1	18	yes	complemented
103	C₂×C₄×D₁₇	C₂⁴	1	6	yes	—
104	C₂×C₄×D₁₇	C₂⁴	1	36	yes	—
105	C₂×Dic₃₄	C₂²×C₄	1	6	yes	complemented
106	C₂²⋊#595	C₂⁴	1	144	yes	—
107	C₄⋊#595	C₂⁴	1	72	yes	—
108	C₄⋊#595	C₂⁴	1	24	yes	—
109	C₄×#595	C₂⁴	1	24	yes	—
110	C₄×#595	C₂⁴	1	72	yes	—
111	C₂×C₄×H(5,𝔽₂)	—	17	1	no	maximal, Sylow
112	C₂³×C₁₇	—	4	12	no	—
113	C₂³×C₁₇	C₂³×C₄	1	9	yes	—
114	C₂³×C₁₇	C₂³×C₄	1	24	yes	complemented
115	C₂²×D₁₇	—	2	18	no	—
116	C₂²×D₁₇	—	2	18	no	—
117	C₂²×D₁₇	—	4	24	no	—
118	C₂²×D₁₇	—	4	48	no	—
119	C₂²×D₁₇	—	4	24	no	—
120	C₂²×D₁₇	—	4	36	no	—
121	C₂²×D₁₇	C₂³×C₄	1	9	yes	—
122	C₂²×D₁₇	C₂³×C₄	1	18	yes	—
123	C₂²×D₁₇	C₂³×C₄	1	72	yes	complemented
124	C₂²×D₁₇	C₂⁵	1	18	yes	—
125	C₂²×D₁₇	C₂⁵	1	1	yes	characteristic
126	C₂×#595	—	2	18	no	—
127	C₂×#595	—	2	12	no	—
128	C₂×#595	—	2	72	no	—
129	C₂×#595	—	4	72	no	—
130	C₂×#595	—	4	36	no	—
131	C₂×#595	H(5,𝔽₂)	1	4	yes	direct product factor
132	C₂×#595	C₂⁵	1	12	yes	—
133	C₂×#595	C₂⁵	1	18	yes	—
134	C₂×#595	C₂⁵	1	2	yes	—
135	Q₈×C₁₇	C₂³×C₄	1	8	yes	complemented
136	D₄×C₁₇	C₂³×C₄	1	72	yes	complemented
137	C₂×C₄×C₁₇	C₂³×C₄	1	6	yes	—
138	C₂×C₄×C₁₇	C₂³×C₄	1	36	yes	complemented
139	C₂²⋊D₁₇	C₂³×C₄	1	144	yes	complemented
140	C₂×Dic₁₇	C₂³×C₄	1	6	yes	—
141	C₂×Dic₁₇	C₂³×C₄	1	36	yes	complemented
142	D₆₈	C₂³×C₄	1	72	yes	complemented
143	C₄×D₁₇	C₂³×C₄	1	12	yes	—
144	C₄×D₁₇	C₂³×C₄	1	72	yes	complemented
145	C₄×D₁₇	C₂⁵	1	12	yes	—
146	Dic₃₄	C₂³×C₄	1	24	yes	complemented
147	C₂²×H(5,𝔽₂)	—	17	1	no	—
148	C₄×H(5,𝔽₂)	—	17	32	no	—
149	C₂×#520	—	17	6	no	—
150	C₂×#518	—	17	9	no	—
151	C₂×C₄×#41	—	17	6	no	—
152	C₂²×C₄×D₄	—	17	9	no	—
153	C₂²×C₁₇	—	2	18	no	—
154	C₂²×C₁₇	—	4	24	no	—
155	C₂²×C₁₇	C₂⁴×C₄	1	18	yes	—
156	C₂²×C₁₇	C₂⁴×C₄	1	1	yes	characteristic
157	C₂×D₁₇	—	2	18	no	—
158	C₂×D₁₇	—	2	18	no	—
159	C₂×D₁₇	—	2	18	no	—
160	C₂×D₁₇	—	2	36	no	—
161	C₂×D₁₇	—	4	72	no	—
162	C₂×D₁₇	C₂⁴×C₄	1	18	yes	—
163	C₂×D₁₇	C₂⁴×C₄	1	1	yes	characteristic
164	C₂×D₁₇	C₂×H(5,𝔽₂)	1	2	yes	—
165	C₂×D₁₇	#585	1	2	yes	—
166	C₂×D₁₇	C₂⁶	1	1	yes	characteristic
167	#595	—	2	18	no	—
168	#595	—	2	12	no	—
169	#595	C₂×H(5,𝔽₂)	1	4	yes	direct product factor
170	C₄×C₁₇	C₂⁴×C₄	1	12	yes	—
171	Dic₁₇	C₂⁴×C₄	1	12	yes	—
172	C₂×H(5,𝔽₂)	—	17	16	no	—
173	C₂×H(5,𝔽₂)	—	17	16	no	—
174	C₂×H(5,𝔽₂)	—	17	6	no	—
175	C₂×H(5,𝔽₂)	—	17	9	no	—
176	C₂×H(5,𝔽₂)	#595	1	1	yes	characteristic, direct product factor
177	C₂²×#41	—	17	6	no	—
178	C₂³×D₄	—	17	9	no	—
179	C₂⁴×C₄	—	17	6	no	—
180	#520	—	17	96	no	—
181	#518	—	17	144	no	—
182	C₄×#41	—	17	96	no	—
183	C₂×C₄×Q₈	—	17	2	no	—
184	C₂×C₄×Q₈	—	17	6	no	—
185	C₂×C₄×D₄	—	17	18	no	—
186	C₂×C₄×D₄	—	17	36	no	—
187	C₂×C₄×D₄	—	17	144	no	—
188	C₂×C₄×D₄	—	17	18	no	—
189	C₂×#117	—	17	18	no	—
190	C₂²×C₄⋊C₄	—	17	9	no	—
191	C₂²×C₂²⋊C₄	—	17	18	no	—
192	C₂²×C₄²	—	17	9	no	—
193	C₂×C₁₇	—	2	18	no	—
194	C₂×C₁₇	C₄×H(5,𝔽₂)	1	2	yes	complemented
195	C₂×C₁₇	C₂⁵×C₄	1	1	yes	characteristic
196	D₁₇	—	2	18	no	—
197	D₁₇	C₄×H(5,𝔽₂)	1	2	yes	complemented
198	D₁₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
199	D₁₇	C₂×#585	1	1	yes	characteristic
200	C₂⁵	—	17	6	no	—
201	H(5,𝔽₂)	—	17	96	no	—
202	H(5,𝔽₂)	—	17	144	no	—
203	H(5,𝔽₂)	C₂×#595	1	16	yes	direct product factor
204	C₂×#41	—	17	48	no	—
205	C₂×#41	—	17	48	no	—
206	C₂×#41	—	17	6	no	—
207	C₂×#41	—	17	18	no	—
208	C₂×#41	—	17	18	no	—
209	C₂×#41	C₂×#595	1	6	yes	complemented
210	C₂²×Q₈	—	17	2	no	—
211	C₂²×D₄	—	17	18	no	—
212	C₂²×D₄	—	17	18	no	—
213	C₂²×D₄	—	17	72	no	—
214	C₂²×D₄	—	17	36	no	—
215	C₂²×D₄	—	17	72	no	—
216	C₂²×D₄	—	17	9	no	—
217	C₂²×D₄	C₂×#595	1	9	yes	complemented
218	C₂³×C₄	—	17	9	no	—
219	C₂³×C₄	—	17	9	no	—
220	C₂³×C₄	—	17	9	no	—
221	C₂³×C₄	—	17	18	no	—
222	C₂³×C₄	—	17	48	no	—
223	C₂³×C₄	—	68	24	no	—
224	C₄×Q₈	—	17	16	no	—
225	C₄×Q₈	—	17	48	no	—
226	C₄×D₄	—	17	144	no	—
227	C₄×D₄	—	17	288	no	—
228	C₄×D₄	—	17	144	no	—
229	#117	—	17	144	no	—
230	C₂×C₄⋊C₄	—	17	18	no	—
231	C₂×C₄⋊C₄	—	17	72	no	—
232	C₂×C₄⋊C₄	—	17	6	no	—
233	C₂×C₂²⋊C₄	—	17	36	no	—
234	C₂×C₂²⋊C₄	—	17	144	no	—
235	C₂×C₄²	—	17	18	no	—
236	C₂×C₄²	—	17	6	no	—
237	C₂×C₄²	—	17	72	no	—
238	C₁₇	C₂×C₄×H(5,𝔽₂)	1	1	yes	characteristic, complemented, Sylow
239	C₂⁴	—	17	9	no	—
240	C₂⁴	—	17	18	no	—
241	C₂⁴	—	17	24	no	—
242	C₂⁴	—	17	24	no	—
243	C₂⁴	—	68	12	no	—
244	C₂⁴	—	68	12	no	—
245	C₂⁴	C₂²×#595	1	6	yes	complemented
246	#41	—	17	48	no	—
247	#41	—	17	144	no	—
248	#41	—	17	144	no	—
249	#41	C₂²×#595	1	48	yes	complemented
250	C₂×Q₈	—	17	8	no	—
251	C₂×Q₈	—	17	8	no	—
252	C₂×Q₈	—	17	6	no	—
253	C₂×Q₈	C₂²×#595	1	2	yes	complemented
254	C₂×D₄	—	17	36	no	—
255	C₂×D₄	—	17	144	no	—
256	C₂×D₄	—	17	72	no	—
257	C₂×D₄	—	17	288	no	—
258	C₂×D₄	—	17	72	no	—
259	C₂×D₄	—	17	18	no	—
260	C₂×D₄	—	17	72	no	—
261	C₂×D₄	C₂²×#595	1	18	yes	complemented
262	C₂×D₄	C₂²×#595	1	72	yes	complemented
263	C₂²×C₄	—	17	1	no	—
264	C₂²×C₄	—	17	9	no	—
265	C₂²×C₄	—	17	18	no	—
266	C₂²×C₄	—	17	6	no	—
267	C₂²×C₄	—	17	36	no	—
268	C₂²×C₄	—	17	36	no	—
269	C₂²×C₄	—	17	6	no	—
270	C₂²×C₄	—	17	9	no	—
271	C₂²×C₄	—	17	36	no	—
272	C₂²×C₄	—	17	36	no	—
273	C₂²×C₄	—	17	72	no	—
274	C₂²×C₄	—	34	36	no	—
275	C₂²×C₄	—	68	96	no	—
276	C₂²×C₄	—	68	18	no	—
277	C₂²×C₄	—	68	36	no	—
278	C₂²×C₄	C₂²×#595	1	9	yes	complemented
279	C₄⋊C₄	—	17	72	no	—
280	C₄⋊C₄	—	17	24	no	—
281	C₂²⋊C₄	—	17	144	no	—
282	C₄²	—	17	24	no	—
283	C₄²	—	17	72	no	—
284	C₂³	—	4	12	no	—
285	C₂³	—	17	1	no	—
286	C₂³	—	17	18	no	—
287	C₂³	—	17	18	no	—
288	C₂³	—	17	9	no	—
289	C₂³	—	17	72	no	—
290	C₂³	—	34	18	no	—
291	C₂³	—	34	18	no	—
292	C₂³	—	68	36	no	—
293	C₂³	—	68	24	no	—
294	C₂³	—	68	24	no	—
295	C₂³	—	68	48	no	—
296	C₂³	C₂³×#595	1	9	yes	—
297	C₂³	C₂³×#595	1	24	yes	complemented
298	Q₈	—	17	24	no	—
299	Q₈	C₂³×#595	1	8	yes	complemented
300	D₄	—	17	144	no	—
301	D₄	—	17	72	no	—
302	D₄	C₂³×#595	1	72	yes	complemented
303	C₂×C₄	—	17	2	no	—
304	C₂×C₄	—	17	4	no	—
305	C₂×C₄	—	17	36	no	—
306	C₂×C₄	—	17	6	no	—
307	C₂×C₄	—	17	12	no	—
308	C₂×C₄	—	17	12	no	—
309	C₂×C₄	—	17	72	no	—
310	C₂×C₄	—	17	12	no	—
311	C₂×C₄	—	17	18	no	—
312	C₂×C₄	—	34	72	no	—
313	C₂×C₄	—	34	18	no	—
314	C₂×C₄	—	34	12	no	—
315	C₂×C₄	—	68	72	no	—
316	C₂×C₄	—	68	36	no	—
317	C₂×C₄	C₂³×#595	1	6	yes	—
318	C₂×C₄	C₂³×#595	1	36	yes	complemented
319	C₂²	—	2	18	no	—
320	C₂²	—	4	24	no	—
321	C₂²	—	17	2	no	—
322	C₂²	—	17	2	no	—
323	C₂²	—	17	1	no	—
324	C₂²	—	17	1	no	—
325	C₂²	—	17	18	no	—
326	C₂²	—	34	18	no	—
327	C₂²	—	34	18	no	—
328	C₂²	—	34	36	no	—
329	C₂²	—	34	18	no	—
330	C₂²	—	68	72	no	—
331	C₂²	C₂⁴×#595	1	18	yes	—
332	C₂²	C₂⁴×#595	1	1	yes	characteristic
333	C₄	—	17	4	no	—
334	C₄	—	17	12	no	—
335	C₄	—	34	18	no	—
336	C₄	—	34	12	no	—
337	C₄	C₂⁴×#595	1	12	yes	—
338	C₂	—	2	18	no	—
339	C₂	—	17	1	no	—
340	C₂	—	17	1	no	—
341	C₂	—	17	2	no	—
342	C₂	—	34	18	no	—
343	C₂	H(5,𝔽₂)×#595	1	2	yes	direct product factor
344	C₂	C₂⁵×#595	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂⁴×#595
commutator	C₂×C₁₇	C₂⁵×C₄
Frattini	C₂	C₂⁵×#595
Fitting	C₂×C₁₇×H(5,𝔽₂)	C₄
socle	C₂²×C₁₇	C₂⁴×C₄
prime radical	C₂×H(5,𝔽₂)×D₁₇	C₂
cosocle	C₂×D₁₇	C₂⁶
hypercenter	C₂×H(5,𝔽₂)	#595
hypocenter	C₁₇	C₂×C₄×H(5,𝔽₂)
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₂×H(5,𝔽₂)

Complements

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

N	H ≅ G/N	type
1. H(5,𝔽₂)×#595	C₂	direct (N × H)
2. C₂×#11763878	C₂	semidirect
3. C₂×#11763876	C₂	semidirect
4. C₂×#41×#595	C₂	semidirect
5. C₂²×D₄×#595	C₂	semidirect
7. C₂⁴×#595	C₂²	semidirect
8. #11763878	C₂²	semidirect
9. #11763876	C₂²	semidirect
10. #41×#595	C₂²	semidirect
11. C₂×Q₈×#595	C₂²	semidirect
12. C₂×Q₈×#595	C₂²	semidirect
13. C₂×D₄×#595	C₂²	semidirect
14. C₂×D₄×#595	C₂²	semidirect
15. C₂×D₄×#595	C₂²	semidirect
16. C₂×D₄×#595	C₂²	semidirect
17. C₂×#10587677	C₂²	semidirect
18. C₂²×C₄⋊#595	C₂²	semidirect
19. C₂²×C₂²⋊#595	C₂²	semidirect
20. C₂²×C₄×#595	C₂²	semidirect
21. C₂×#10587696	C₄	semidirect
22. C₂×#10587691	C₄	semidirect
23. H(5,𝔽₂)×D₁₇	C₄	semidirect
27. C₂×C₁₇×H(5,𝔽₂)	C₄	semidirect
33. C₂³×#595	C₂³	semidirect
34. C₁₇×H(5,𝔽₂)	C₂×C₄	semidirect
35. C₂×#41×C₁₇	C₂×C₄	semidirect
36. C₂²×D₄×C₁₇	C₂×C₄	semidirect
37. C₂²×C₂²⋊D₁₇	C₂×C₄	semidirect
38. #10587696	C₂×C₄	semidirect
39. #41×D₁₇	C₂×C₄	semidirect
41. C₂×#63256	C₂×C₄	semidirect
43. #10587691	C₂×C₄	semidirect
44. C₂×#63254	C₂×C₄	semidirect
45. C₂×D₄×D₁₇	C₂×C₄	semidirect
46. C₂×D₄×D₁₇	C₂×C₄	semidirect
49. C₂×#63252	C₂×C₄	semidirect
50. C₂²×D₆₈	C₂×C₄	semidirect
53. C₂×C₂²⋊#595	C₂³	semidirect
54. Q₈×#595	C₂³	semidirect
55. Q₈×#595	C₂³	semidirect
56. D₄×#595	C₂³	semidirect
57. D₄×#595	C₂³	semidirect
58. D₄×#595	C₂³	semidirect
59. #10587677	C₂³	semidirect
62. C₂×C₄⋊#595	C₂³	semidirect
65. C₂×C₄×#595	C₂³	semidirect
66. C₂⁴×C₁₇	C₂²×C₄	semidirect
69. C₂³×D₁₇	C₂²×C₄	semidirect
70. C₂³×D₁₇	C₂²×C₄	semidirect
83. #41×C₁₇	C₂²×C₄	semidirect
84. C₂×Q₈×C₁₇	C₂²×C₄	semidirect
85. C₂×D₄×C₁₇	C₂²×C₄	semidirect
86. C₂×D₄×C₁₇	C₂²×C₄	semidirect
87. C₂²×C₄×C₁₇	C₂²×C₄	semidirect
88. C₂×C₂²⋊D₁₇	C₂²×C₄	semidirect
89. C₂×C₂²⋊D₁₇	C₂²×C₄	semidirect
90. C₂²×Dic₁₇	C₂²×C₄	semidirect
91. #63256	C₂²×C₄	semidirect
92. Q₈×D₁₇	C₂²×C₄	semidirect
94. #63254	C₂²×C₄	semidirect
95. D₄×D₁₇	C₂²×C₄	semidirect
96. D₄×D₁₇	C₂²×C₄	semidirect
98. #63252	C₂²×C₄	semidirect
99. C₂×D₆₈	C₂²×C₄	semidirect
100. C₂×D₆₈	C₂²×C₄	semidirect
101. C₂×C₄×D₁₇	C₂²×C₄	semidirect
102. C₂×C₄×D₁₇	C₂²×C₄	semidirect
105. C₂×Dic₃₄	C₂²×C₄	semidirect
114. C₂³×C₁₇	C₂³×C₄	semidirect
123. C₂²×D₁₇	C₂³×C₄	semidirect
131. C₂×#595	H(5,𝔽₂)	direct (N × H)
135. Q₈×C₁₇	C₂³×C₄	semidirect
136. D₄×C₁₇	C₂³×C₄	semidirect
138. C₂×C₄×C₁₇	C₂³×C₄	semidirect
139. C₂²⋊D₁₇	C₂³×C₄	semidirect
141. C₂×Dic₁₇	C₂³×C₄	semidirect
142. D₆₈	C₂³×C₄	semidirect
144. C₄×D₁₇	C₂³×C₄	semidirect
146. Dic₃₄	C₂³×C₄	semidirect
169. #595	C₂×H(5,𝔽₂)	direct (N × H)
176. C₂×H(5,𝔽₂)	#595	direct (N × H)
194. C₂×C₁₇	C₄×H(5,𝔽₂)	semidirect
197. D₁₇	C₄×H(5,𝔽₂)	semidirect
203. H(5,𝔽₂)	C₂×#595	direct (N × H)
209. C₂×#41	C₂×#595	semidirect
217. C₂²×D₄	C₂×#595	semidirect
238. C₁₇	C₂×C₄×H(5,𝔽₂)	semidirect
245. C₂⁴	C₂²×#595	semidirect
249. #41	C₂²×#595	semidirect
253. C₂×Q₈	C₂²×#595	semidirect
261. C₂×D₄	C₂²×#595	semidirect
262. C₂×D₄	C₂²×#595	semidirect
278. C₂²×C₄	C₂²×#595	semidirect
297. C₂³	C₂³×#595	semidirect
299. Q₈	C₂³×#595	semidirect
302. D₄	C₂³×#595	semidirect
318. C₂×C₄	C₂³×#595	semidirect
343. C₂	H(5,𝔽₂)×#595	direct (N × H)

Maximal subgroups

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

subgroup	index
H(5,𝔽₂)×#595	2
C₂×#11763878	2
C₂×#11763876	2
C₂×#41×#595	2
C₂²×D₄×#595	2
C₂×H(5,𝔽₂)×D₁₇	2
C₂×C₄×H(5,𝔽₂)	17

Subgroups — C2×H(5,𝔽2)×#595 #17981040

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×H(5,𝔽₂)×#595 #17981040