Subgroups — C₂×C₆₇×#3554 #30741997

Order 17152.

7182 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3554	C₂	1	32	yes	maximal, direct product factor
2	C₂×#562×C₆₇	C₂	1	4	yes	maximal, complemented
3	C₂×#559×C₆₇	C₂	1	2	yes	maximal, complemented
4	C₂×#559×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#557×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#554×C₆₇	C₂	1	2	yes	maximal, complemented
7	C₂×#550×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×D₄×Q₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#548×C₆₇	C₂	1	2	yes	maximal, complemented
10	C₂×#547×C₆₇	C₂	1	2	yes	maximal, complemented
11	C₂×#542×C₆₇	C₂	1	2	yes	maximal, complemented
12	C₂×#542×C₆₇	C₂	1	2	yes	maximal, complemented
13	C₂×#540×C₆₇	C₂	1	2	yes	maximal, complemented
14	C₂×#539×C₆₇	C₂	1	4	yes	maximal, complemented
15	C₂×#536×C₆₇	C₂	1	2	yes	maximal, complemented
16	C₂×#533×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#532×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#529×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂²×#41×C₆₇	C₂²	1	2	yes	—
20	C₂²×#41×C₆₇	C₂²	1	2	yes	—
21	C₂³×Q₈×C₆₇	C₂²	1	2	yes	—
22	#562×C₆₇	C₂²	1	64	yes	complemented
23	#559×C₆₇	C₂²	1	32	yes	complemented
24	#559×C₆₇	C₂²	1	16	yes	complemented
25	#557×C₆₇	C₂²	1	16	yes	complemented
26	#554×C₆₇	C₂²	1	32	yes	complemented
27	#550×C₆₇	C₂²	1	16	yes	complemented
28	D₄×Q₈×C₆₇	C₂²	1	16	yes	complemented
29	#548×C₆₇	C₂²	1	32	yes	complemented
30	#547×C₆₇	C₂²	1	32	yes	complemented
31	#542×C₆₇	C₂²	1	32	yes	complemented
32	#542×C₆₇	C₂²	1	32	yes	complemented
33	#540×C₆₇	C₂²	1	32	yes	complemented
34	#539×C₆₇	C₂²	1	64	yes	complemented
35	#536×C₆₇	C₂²	1	32	yes	complemented
36	#533×C₆₇	C₂²	1	16	yes	complemented
37	#532×C₆₇	C₂²	1	16	yes	complemented
38	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
39	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
40	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
41	C₂×C₄⋊Q₈×C₆₇	C₂²	1	2	yes	—
42	C₂×C₄⋊Q₈×C₆₇	C₂²	1	2	yes	—
43	C₂×#127×C₆₇	C₂²	1	1	yes	characteristic
44	C₂×#127×C₆₇	C₂²	1	2	yes	—
45	#529×C₆₇	C₂²	1	16	yes	complemented
46	C₂×#126×C₆₇	C₂²	1	2	yes	—
47	C₂×#126×C₆₇	C₂²	1	4	yes	—
48	C₂×#125×C₆₇	C₂²	1	4	yes	—
49	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic
50	C₂×#125×C₆₇	C₂²	1	2	yes	—
51	C₂×#125×C₆₇	C₂²	1	2	yes	—
52	C₂×#124×C₆₇	C₂²	1	4	yes	—
53	C₂×#124×C₆₇	C₂²	1	4	yes	—
54	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
55	C₂×#124×C₆₇	C₂²	1	2	yes	—
56	C₂×#124×C₆₇	C₂²	1	2	yes	—
57	C₂×#124×C₆₇	C₂²	1	2	yes	—
58	C₂×#123×C₆₇	C₂²	1	2	yes	—
59	C₂×#123×C₆₇	C₂²	1	4	yes	—
60	C₂×#123×C₆₇	C₂²	1	4	yes	—
61	C₂×#123×C₆₇	C₂²	1	4	yes	—
62	C₂×#123×C₆₇	C₂²	1	4	yes	—
63	C₂×#123×C₆₇	C₂²	1	4	yes	—
64	C₂×#123×C₆₇	C₂²	1	4	yes	—
65	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
66	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	4	yes	—
67	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	4	yes	—
68	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	4	yes	—
69	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
70	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
71	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
72	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	4	yes	—
73	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	4	yes	—
74	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
75	C₂×#121×C₆₇	C₂²	1	2	yes	—
76	C₂×#121×C₆₇	C₂²	1	4	yes	—
77	C₂×#121×C₆₇	C₂²	1	4	yes	—
78	C₂×#121×C₆₇	C₂²	1	4	yes	—
79	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
80	C₂×#121×C₆₇	C₂²	1	2	yes	—
81	C₂×#121×C₆₇	C₂²	1	2	yes	—
82	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
83	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
84	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
85	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	—
86	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	—
87	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	—
88	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
89	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
90	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
91	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
92	C₂×C₄×D₄×C₆₇	C₂²	1	4	yes	—
93	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
94	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
95	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
96	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
97	C₂×#117×C₆₇	C₂²	1	2	yes	—
98	C₂×#117×C₆₇	C₂²	1	2	yes	—
99	C₂²×C₄⋊C₄×C₆₇	C₂²	1	4	yes	—
100	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
101	C₂×#41×C₆₇	—	4	8	no	—
102	C₂×#41×C₆₇	—	4	8	no	—
103	C₂×#41×C₆₇	C₂³	1	16	yes	—
104	C₂×#41×C₆₇	C₂³	1	16	yes	—
105	C₂²×Q₈×C₆₇	—	4	8	no	—
106	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
107	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
109	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
110	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
111	C₂²×Q₈×C₆₇	C₂³	1	4	yes	—
112	C₂²×Q₈×C₆₇	C₂³	1	16	yes	—
113	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
114	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
115	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
116	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
117	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
118	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
119	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
120	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
121	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
122	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
123	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
124	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
125	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
126	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
127	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
128	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
129	C₄⋊Q₈×C₆₇	C₂³	1	8	yes	—
130	C₄⋊Q₈×C₆₇	C₂³	1	8	yes	—
131	C₄⋊Q₈×C₆₇	C₂³	1	8	yes	—
132	C₄⋊Q₈×C₆₇	C₂³	1	16	yes	—
133	C₄⋊Q₈×C₆₇	C₂³	1	16	yes	—
134	#127×C₆₇	C₂³	1	8	yes	—
135	#127×C₆₇	C₂³	1	16	yes	—
136	#126×C₆₇	C₂³	1	16	yes	—
137	#126×C₆₇	C₂³	1	32	yes	—
138	#125×C₆₇	C₂³	1	8	yes	—
139	#125×C₆₇	C₂³	1	16	yes	—
140	#125×C₆₇	C₂³	1	32	yes	—
141	#125×C₆₇	C₂³	1	16	yes	—
142	#124×C₆₇	C₂³	1	8	yes	—
143	#124×C₆₇	C₂³	1	16	yes	—
144	#124×C₆₇	C₂³	1	16	yes	—
145	#124×C₆₇	C₂³	1	32	yes	—
146	#124×C₆₇	C₂³	1	16	yes	—
147	#124×C₆₇	C₂³	1	32	yes	—
148	#123×C₆₇	C₂³	1	16	yes	—
149	#123×C₆₇	C₂³	1	32	yes	—
150	#123×C₆₇	C₂³	1	32	yes	—
151	#123×C₆₇	C₂³	1	32	yes	—
152	#123×C₆₇	C₂³	1	32	yes	—
153	#123×C₆₇	C₂³	1	32	yes	—
154	#123×C₆₇	C₂³	1	32	yes	—
155	C₂²⋊Q₈×C₆₇	C₂³	1	8	yes	—
156	C₂²⋊Q₈×C₆₇	C₂³	1	8	yes	—
157	C₂²⋊Q₈×C₆₇	C₂³	1	8	yes	—
158	C₂²⋊Q₈×C₆₇	C₂³	1	16	yes	—
159	C₂²⋊Q₈×C₆₇	C₂³	1	32	yes	—
160	C₂²⋊Q₈×C₆₇	C₂³	1	32	yes	—
161	C₂²⋊Q₈×C₆₇	C₂³	1	32	yes	—
162	C₂²⋊Q₈×C₆₇	C₂³	1	32	yes	—
163	C₂²⋊Q₈×C₆₇	C₂³	1	16	yes	—
164	C₂²⋊Q₈×C₆₇	C₂³	1	32	yes	—
165	#121×C₆₇	C₂³	1	8	yes	—
166	#121×C₆₇	C₂³	1	16	yes	—
167	#121×C₆₇	C₂³	1	16	yes	—
168	#121×C₆₇	C₂³	1	32	yes	—
169	#121×C₆₇	C₂³	1	32	yes	—
170	#121×C₆₇	C₂³	1	32	yes	—
171	#121×C₆₇	C₂³	1	16	yes	—
172	C₄×Q₈×C₆₇	C₂³	1	8	yes	—
173	C₄×Q₈×C₆₇	C₂³	1	8	yes	—
174	C₄×Q₈×C₆₇	C₂³	1	8	yes	—
175	C₄×Q₈×C₆₇	C₂³	1	16	yes	—
176	C₄×Q₈×C₆₇	C₂³	1	16	yes	—
177	C₄×Q₈×C₆₇	C₂³	1	16	yes	—
178	C₄×D₄×C₆₇	C₂³	1	16	yes	—
179	C₄×D₄×C₆₇	C₂³	1	8	yes	—
180	C₄×D₄×C₆₇	C₂³	1	16	yes	—
181	C₄×D₄×C₆₇	C₂³	1	16	yes	—
182	C₄×D₄×C₆₇	C₂³	1	32	yes	—
183	C₄×D₄×C₆₇	C₂³	1	16	yes	—
184	C₄×D₄×C₆₇	C₂³	1	16	yes	—
185	C₄×D₄×C₆₇	C₂³	1	16	yes	—
186	C₄×D₄×C₆₇	C₂³	1	16	yes	—
187	#117×C₆₇	C₂³	1	16	yes	—
188	#117×C₆₇	C₂³	1	16	yes	—
189	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
190	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
191	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
192	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
193	C₂×C₄⋊C₄×C₆₇	C₂³	1	32	yes	—
194	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
195	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
196	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
197	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
198	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
199	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
200	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
201	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
202	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
203	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
204	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
205	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
206	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
207	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
208	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
209	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
210	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
211	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
212	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
213	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
214	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
215	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
216	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
217	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
218	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
219	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
220	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
221	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
222	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
223	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
224	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
225	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
226	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
227	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
228	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
229	C₂×C₄²×C₆₇	C₂³	1	8	yes	—
230	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
231	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
232	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
233	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
234	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
235	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
236	C₂⁴×C₆₇	C₂⁴	1	4	yes	—
237	#41×C₆₇	—	4	32	no	—
238	#41×C₆₇	—	4	32	no	—
239	C₂×Q₈×C₆₇	—	2	4	no	—
240	C₂×Q₈×C₆₇	—	2	8	no	—
241	C₂×Q₈×C₆₇	—	2	4	no	—
242	C₂×Q₈×C₆₇	—	2	4	no	—
243	C₂×Q₈×C₆₇	—	4	8	no	—
244	C₂×Q₈×C₆₇	—	4	4	no	—
245	C₂×Q₈×C₆₇	—	4	32	no	—
246	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
247	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
248	C₂×Q₈×C₆₇	C₂⁴	1	8	yes	—
249	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
250	C₂×Q₈×C₆₇	C₂⁴	1	8	yes	—
251	C₂×Q₈×C₆₇	C₂⁴	1	16	yes	—
252	C₂×D₄×C₆₇	—	2	8	no	—
253	C₂×D₄×C₆₇	—	2	4	no	—
254	C₂×D₄×C₆₇	—	2	8	no	—
255	C₂×D₄×C₆₇	—	4	4	no	—
256	C₂×D₄×C₆₇	—	4	4	no	—
257	C₂×D₄×C₆₇	—	4	8	no	—
258	C₂×D₄×C₆₇	—	4	8	no	—
259	C₂×D₄×C₆₇	—	4	8	no	—
260	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
261	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
262	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
263	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
264	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
265	C₂×D₄×C₆₇	C₂⁴	1	16	yes	—
266	C₂×D₄×C₆₇	C₂⁴	1	16	yes	—
267	C₂×D₄×C₆₇	C₂⁴	1	16	yes	—
268	C₂²×C₄×C₆₇	—	2	8	no	—
269	C₂²×C₄×C₆₇	—	2	4	no	—
270	C₂²×C₄×C₆₇	—	2	4	no	—
271	C₂²×C₄×C₆₇	—	4	8	no	—
272	C₂²×C₄×C₆₇	—	4	2	no	—
273	C₂²×C₄×C₆₇	—	4	8	no	—
274	C₂²×C₄×C₆₇	—	4	8	no	—
275	C₂²×C₄×C₆₇	—	4	8	no	—
276	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
277	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
278	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
279	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
280	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
281	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
282	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
283	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
284	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
285	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
286	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
287	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
288	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
289	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
290	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
291	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
292	C₂²×C₄×C₆₇	C₂⁴	1	16	yes	—
293	C₂²×C₄×C₆₇	C₂⁴	1	16	yes	—
294	C₂²×C₄×C₆₇	C₂⁴	1	16	yes	—
295	C₂²×C₄×C₆₇	C₂⁴	1	16	yes	—
296	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
297	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
298	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
299	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
300	C₄⋊C₄×C₆₇	C₂⁴	1	16	yes	—
301	C₄⋊C₄×C₆₇	C₂⁴	1	16	yes	—
302	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
303	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
304	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
305	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
306	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
307	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
308	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
309	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
310	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
311	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
312	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
313	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
314	C₄⋊C₄×C₆₇	C₂⁴	1	16	yes	—
315	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
316	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
317	C₄⋊C₄×C₆₇	C₂⁴	1	16	yes	—
318	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
319	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
320	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
321	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
322	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
323	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
324	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
325	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
326	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
327	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
328	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
329	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
330	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
331	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
332	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
333	C₄²×C₆₇	C₂⁴	1	4	yes	—
334	C₄²×C₆₇	C₂⁴	1	4	yes	—
335	C₄²×C₆₇	C₂⁴	1	4	yes	—
336	C₄²×C₆₇	C₂⁴	1	4	yes	—
337	C₄²×C₆₇	C₂⁴	1	8	yes	—
338	C₄²×C₆₇	C₂⁴	1	8	yes	—
339	C₄²×C₆₇	C₂⁴	1	8	yes	—
340	C₄²×C₆₇	C₂⁴	1	16	yes	—
341	C₂³×C₆₇	—	2	4	no	—
342	C₂³×C₆₇	—	2	2	no	—
343	C₂³×C₆₇	—	2	8	no	—
344	C₂³×C₆₇	—	2	2	no	—
345	C₂³×C₆₇	—	2	4	no	—
346	C₂³×C₆₇	—	2	8	no	—
347	C₂³×C₆₇	—	2	2	no	—
348	C₂³×C₆₇	—	2	8	no	—
349	C₂³×C₆₇	—	2	4	no	—
350	C₂³×C₆₇	C₂⁵	1	4	yes	—
351	C₂³×C₆₇	C₂⁵	1	2	yes	—
352	C₂³×C₆₇	C₂⁵	1	8	yes	—
353	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
354	Q₈×C₆₇	—	2	8	no	—
355	Q₈×C₆₇	—	2	16	no	—
356	Q₈×C₆₇	—	2	8	no	—
357	Q₈×C₆₇	—	2	8	no	—
358	Q₈×C₆₇	—	4	16	no	—
359	Q₈×C₆₇	—	4	8	no	—
360	D₄×C₆₇	—	2	16	no	—
361	D₄×C₆₇	—	2	8	no	—
362	D₄×C₆₇	—	2	16	no	—
363	D₄×C₆₇	—	4	8	no	—
364	D₄×C₆₇	—	4	8	no	—
365	D₄×C₆₇	—	4	16	no	—
366	D₄×C₆₇	—	4	16	no	—
367	D₄×C₆₇	—	4	16	no	—
368	C₂×C₄×C₆₇	—	2	2	no	—
369	C₂×C₄×C₆₇	—	2	4	no	—
370	C₂×C₄×C₆₇	—	2	4	no	—
371	C₂×C₄×C₆₇	—	2	8	no	—
372	C₂×C₄×C₆₇	—	2	4	no	—
373	C₂×C₄×C₆₇	—	2	2	no	—
374	C₂×C₄×C₆₇	—	2	4	no	—
375	C₂×C₄×C₆₇	—	2	4	no	—
376	C₂×C₄×C₆₇	—	2	4	no	—
377	C₂×C₄×C₆₇	—	2	2	no	—
378	C₂×C₄×C₆₇	—	2	2	no	—
379	C₂×C₄×C₆₇	—	2	4	no	—
380	C₂×C₄×C₆₇	—	2	16	no	—
381	C₂×C₄×C₆₇	—	2	8	no	—
382	C₂×C₄×C₆₇	—	2	8	no	—
383	C₂×C₄×C₆₇	—	4	16	no	—
384	C₂×C₄×C₆₇	—	4	4	no	—
385	C₂×C₄×C₆₇	—	4	16	no	—
386	C₂×C₄×C₆₇	—	4	16	no	—
387	C₂×C₄×C₆₇	—	4	16	no	—
388	C₂×C₄×C₆₇	H(5,𝔽₂)	1	4	yes	—
389	C₂×C₄×C₆₇	2₋¹⁺⁴	1	4	yes	—
390	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
391	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
392	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
393	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
394	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
395	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
396	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
397	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
398	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
399	C₂×C₄×C₆₇	C₂⁵	1	8	yes	—
400	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
401	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
402	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
403	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
404	C₂²×C₆₇	—	2	4	no	—
405	C₂²×C₆₇	—	2	2	no	—
406	C₂²×C₆₇	—	2	8	no	—
407	C₂²×C₆₇	—	2	2	no	—
408	C₂²×C₆₇	—	2	4	no	—
409	C₂²×C₆₇	—	2	8	no	—
410	C₂²×C₆₇	—	2	2	no	—
411	C₂²×C₆₇	—	2	8	no	—
412	C₂²×C₆₇	—	2	4	no	—
413	C₂²×C₆₇	—	4	8	no	—
414	C₂²×C₆₇	—	4	4	no	—
415	C₂²×C₆₇	—	4	16	no	—
416	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
417	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	2	yes	—
418	C₂²×C₆₇	#585	1	2	yes	—
419	C₂²×C₆₇	C₂⁶	1	1	yes	characteristic
420	C₄×C₆₇	—	2	2	no	—
421	C₄×C₆₇	—	2	4	no	—
422	C₄×C₆₇	—	2	4	no	—
423	C₄×C₆₇	—	2	8	no	—
424	C₄×C₆₇	—	2	4	no	—
425	C₄×C₆₇	—	2	2	no	—
426	C₄×C₆₇	—	2	4	no	—
427	C₄×C₆₇	—	2	4	no	—
428	C₄×C₆₇	—	2	4	no	—
429	C₄×C₆₇	—	2	2	no	—
430	C₄×C₆₇	—	2	2	no	—
431	C₄×C₆₇	—	2	4	no	—
432	C₄×C₆₇	C₂×H(5,𝔽₂)	1	4	yes	—
433	C₄×C₆₇	C₂×2₋¹⁺⁴	1	4	yes	—
434	C₂×#3554	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
435	C₂×C₆₇	—	4	4	no	—
436	C₂×C₆₇	—	4	2	no	—
437	C₂×C₆₇	—	4	8	no	—
438	C₂×C₆₇	#3554	1	4	yes	direct product factor
439	C₂×C₆₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
440	C₂×C₆₇	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
441	C₂×C₆₇	C₂×#585	1	1	yes	characteristic
442	#3554	C₂×C₆₇	1	32	yes	direct product factor
443	C₂×#562	C₂×C₆₇	1	4	yes	complemented
444	C₂×#559	C₂×C₆₇	1	2	yes	complemented
445	C₂×#559	C₂×C₆₇	1	1	yes	characteristic, complemented
446	C₂×#557	C₂×C₆₇	1	1	yes	characteristic, complemented
447	C₂×#554	C₂×C₆₇	1	2	yes	complemented
448	C₂×#550	C₂×C₆₇	1	1	yes	characteristic, complemented
449	C₂×D₄×Q₈	C₂×C₆₇	1	1	yes	characteristic, complemented
450	C₂×#548	C₂×C₆₇	1	2	yes	complemented
451	C₂×#547	C₂×C₆₇	1	2	yes	complemented
452	C₂×#542	C₂×C₆₇	1	2	yes	complemented
453	C₂×#542	C₂×C₆₇	1	2	yes	complemented
454	C₂×#540	C₂×C₆₇	1	2	yes	complemented
455	C₂×#539	C₂×C₆₇	1	4	yes	complemented
456	C₂×#536	C₂×C₆₇	1	2	yes	complemented
457	C₂×#533	C₂×C₆₇	1	1	yes	characteristic, complemented
458	C₂×#532	C₂×C₆₇	1	1	yes	characteristic, complemented
459	C₂×#529	C₂×C₆₇	1	1	yes	characteristic, complemented
460	C₆₇	C₂×#3554	1	1	yes	characteristic, direct product factor, Sylow
461	C₂²×#41	C₂²×C₆₇	1	2	yes	—
462	C₂²×#41	C₂²×C₆₇	1	2	yes	—
463	C₂³×Q₈	C₂²×C₆₇	1	2	yes	—
464	#562	C₂²×C₆₇	1	64	yes	complemented
465	#559	C₂²×C₆₇	1	32	yes	complemented
466	#559	C₂²×C₆₇	1	16	yes	complemented
467	#557	C₂²×C₆₇	1	16	yes	complemented
468	#554	C₂²×C₆₇	1	32	yes	complemented
469	#550	C₂²×C₆₇	1	16	yes	complemented
470	D₄×Q₈	C₂²×C₆₇	1	16	yes	complemented
471	#548	C₂²×C₆₇	1	32	yes	complemented
472	#547	C₂²×C₆₇	1	32	yes	complemented
473	#542	C₂²×C₆₇	1	32	yes	complemented
474	#542	C₂²×C₆₇	1	32	yes	complemented
475	#540	C₂²×C₆₇	1	32	yes	complemented
476	#539	C₂²×C₆₇	1	64	yes	complemented
477	#536	C₂²×C₆₇	1	32	yes	complemented
478	#533	C₂²×C₆₇	1	16	yes	complemented
479	#532	C₂²×C₆₇	1	16	yes	complemented
480	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
481	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
482	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
483	C₂×C₄⋊Q₈	C₂²×C₆₇	1	2	yes	—
484	C₂×C₄⋊Q₈	C₂²×C₆₇	1	2	yes	—
485	C₂×#127	C₂²×C₆₇	1	1	yes	characteristic
486	C₂×#127	C₂²×C₆₇	1	2	yes	—
487	#529	C₂²×C₆₇	1	16	yes	complemented
488	C₂×#126	C₂²×C₆₇	1	2	yes	—
489	C₂×#126	C₂²×C₆₇	1	4	yes	—
490	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic
491	C₂×#125	C₂²×C₆₇	1	2	yes	—
492	C₂×#125	C₂²×C₆₇	1	4	yes	—
493	C₂×#125	C₂²×C₆₇	1	2	yes	—
494	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic
495	C₂×#124	C₂²×C₆₇	1	2	yes	—
496	C₂×#124	C₂²×C₆₇	1	2	yes	—
497	C₂×#124	C₂²×C₆₇	1	4	yes	—
498	C₂×#124	C₂²×C₆₇	1	2	yes	—
499	C₂×#124	C₂²×C₆₇	1	4	yes	—
500	C₂×#123	C₂²×C₆₇	1	2	yes	—
501	C₂×#123	C₂²×C₆₇	1	4	yes	—
502	C₂×#123	C₂²×C₆₇	1	4	yes	—
503	C₂×#123	C₂²×C₆₇	1	4	yes	—
504	C₂×#123	C₂²×C₆₇	1	4	yes	—
505	C₂×#123	C₂²×C₆₇	1	4	yes	—
506	C₂×#123	C₂²×C₆₇	1	4	yes	—
507	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
508	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
509	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
510	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
511	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	4	yes	—
512	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	4	yes	—
513	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	4	yes	—
514	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	4	yes	—
515	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
516	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	4	yes	—
517	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
518	C₂×#121	C₂²×C₆₇	1	2	yes	—
519	C₂×#121	C₂²×C₆₇	1	2	yes	—
520	C₂×#121	C₂²×C₆₇	1	4	yes	—
521	C₂×#121	C₂²×C₆₇	1	4	yes	—
522	C₂×#121	C₂²×C₆₇	1	4	yes	—
523	C₂×#121	C₂²×C₆₇	1	2	yes	—
524	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
525	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
526	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
527	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	—
528	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	—
529	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	—
530	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
531	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
532	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
533	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
534	C₂×C₄×D₄	C₂²×C₆₇	1	4	yes	—
535	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
536	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
537	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
538	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
539	C₂×#117	C₂²×C₆₇	1	2	yes	—
540	C₂×#117	C₂²×C₆₇	1	2	yes	—
541	C₂²×C₄⋊C₄	C₂²×C₆₇	1	4	yes	—
542	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
543	C₂×#41	—	4	8	no	—
544	C₂×#41	—	4	8	no	—
545	C₂×#41	C₂³×C₆₇	1	16	yes	—
546	C₂×#41	C₂³×C₆₇	1	16	yes	—
547	C₂²×Q₈	—	4	8	no	—
548	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
549	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
550	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
551	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
552	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
553	C₂²×Q₈	C₂³×C₆₇	1	4	yes	—
554	C₂²×Q₈	C₂³×C₆₇	1	16	yes	—
555	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
556	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
557	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
558	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
559	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
560	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
561	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
562	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
563	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
564	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
565	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
566	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
567	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
568	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
569	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
570	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
571	C₄⋊Q₈	C₂³×C₆₇	1	8	yes	—
572	C₄⋊Q₈	C₂³×C₆₇	1	8	yes	—
573	C₄⋊Q₈	C₂³×C₆₇	1	8	yes	—
574	C₄⋊Q₈	C₂³×C₆₇	1	16	yes	—
575	C₄⋊Q₈	C₂³×C₆₇	1	16	yes	—
576	#127	C₂³×C₆₇	1	8	yes	—
577	#127	C₂³×C₆₇	1	16	yes	—
578	#126	C₂³×C₆₇	1	16	yes	—
579	#126	C₂³×C₆₇	1	32	yes	—
580	#125	C₂³×C₆₇	1	8	yes	—
581	#125	C₂³×C₆₇	1	16	yes	—
582	#125	C₂³×C₆₇	1	32	yes	—
583	#125	C₂³×C₆₇	1	16	yes	—
584	#124	C₂³×C₆₇	1	8	yes	—
585	#124	C₂³×C₆₇	1	16	yes	—
586	#124	C₂³×C₆₇	1	16	yes	—
587	#124	C₂³×C₆₇	1	32	yes	—
588	#124	C₂³×C₆₇	1	16	yes	—
589	#124	C₂³×C₆₇	1	32	yes	—
590	#123	C₂³×C₆₇	1	16	yes	—
591	#123	C₂³×C₆₇	1	32	yes	—
592	#123	C₂³×C₆₇	1	32	yes	—
593	#123	C₂³×C₆₇	1	32	yes	—
594	#123	C₂³×C₆₇	1	32	yes	—
595	#123	C₂³×C₆₇	1	32	yes	—
596	#123	C₂³×C₆₇	1	32	yes	—
597	C₂²⋊Q₈	C₂³×C₆₇	1	8	yes	—
598	C₂²⋊Q₈	C₂³×C₆₇	1	8	yes	—
599	C₂²⋊Q₈	C₂³×C₆₇	1	8	yes	—
600	C₂²⋊Q₈	C₂³×C₆₇	1	16	yes	—
601	C₂²⋊Q₈	C₂³×C₆₇	1	32	yes	—
602	C₂²⋊Q₈	C₂³×C₆₇	1	32	yes	—
603	C₂²⋊Q₈	C₂³×C₆₇	1	32	yes	—
604	C₂²⋊Q₈	C₂³×C₆₇	1	32	yes	—
605	C₂²⋊Q₈	C₂³×C₆₇	1	16	yes	—
606	C₂²⋊Q₈	C₂³×C₆₇	1	32	yes	—
607	#121	C₂³×C₆₇	1	8	yes	—
608	#121	C₂³×C₆₇	1	16	yes	—
609	#121	C₂³×C₆₇	1	16	yes	—
610	#121	C₂³×C₆₇	1	32	yes	—
611	#121	C₂³×C₆₇	1	32	yes	—
612	#121	C₂³×C₆₇	1	32	yes	—
613	#121	C₂³×C₆₇	1	16	yes	—
614	C₄×Q₈	C₂³×C₆₇	1	8	yes	—
615	C₄×Q₈	C₂³×C₆₇	1	8	yes	—
616	C₄×Q₈	C₂³×C₆₇	1	8	yes	—
617	C₄×Q₈	C₂³×C₆₇	1	16	yes	—
618	C₄×Q₈	C₂³×C₆₇	1	16	yes	—
619	C₄×Q₈	C₂³×C₆₇	1	16	yes	—
620	C₄×D₄	C₂³×C₆₇	1	16	yes	—
621	C₄×D₄	C₂³×C₆₇	1	8	yes	—
622	C₄×D₄	C₂³×C₆₇	1	16	yes	—
623	C₄×D₄	C₂³×C₆₇	1	16	yes	—
624	C₄×D₄	C₂³×C₆₇	1	32	yes	—
625	C₄×D₄	C₂³×C₆₇	1	16	yes	—
626	C₄×D₄	C₂³×C₆₇	1	16	yes	—
627	C₄×D₄	C₂³×C₆₇	1	16	yes	—
628	C₄×D₄	C₂³×C₆₇	1	16	yes	—
629	#117	C₂³×C₆₇	1	16	yes	—
630	#117	C₂³×C₆₇	1	16	yes	—
631	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
632	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
633	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
634	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
635	C₂×C₄⋊C₄	C₂³×C₆₇	1	32	yes	—
636	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
637	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
638	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
639	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
640	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
641	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
642	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
643	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
644	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
645	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
646	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
647	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
648	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
649	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
650	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
651	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
652	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
653	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
654	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
655	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
656	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
657	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
658	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
659	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
660	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
661	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
662	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
663	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
664	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
665	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
666	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
667	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
668	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
669	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
670	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
671	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
672	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
673	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
674	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
675	C₂×C₄²	C₂³×C₆₇	1	8	yes	—
676	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
677	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
678	C₂⁴	C₂⁴×C₆₇	1	4	yes	—
679	#41	—	4	32	no	—
680	#41	—	4	32	no	—
681	C₂×Q₈	—	2	4	no	—
682	C₂×Q₈	—	2	8	no	—
683	C₂×Q₈	—	2	4	no	—
684	C₂×Q₈	—	2	4	no	—
685	C₂×Q₈	—	4	8	no	—
686	C₂×Q₈	—	4	4	no	—
687	C₂×Q₈	—	4	32	no	—
688	C₂×Q₈	C₂⁴×C₆₇	1	4	yes	—
689	C₂×Q₈	C₂⁴×C₆₇	1	4	yes	—
690	C₂×Q₈	C₂⁴×C₆₇	1	8	yes	—
691	C₂×Q₈	C₂⁴×C₆₇	1	4	yes	—
692	C₂×Q₈	C₂⁴×C₆₇	1	8	yes	—
693	C₂×Q₈	C₂⁴×C₆₇	1	16	yes	—
694	C₂×D₄	—	2	8	no	—
695	C₂×D₄	—	2	4	no	—
696	C₂×D₄	—	2	8	no	—
697	C₂×D₄	—	4	8	no	—
698	C₂×D₄	—	4	8	no	—
699	C₂×D₄	—	4	4	no	—
700	C₂×D₄	—	4	4	no	—
701	C₂×D₄	—	4	8	no	—
702	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
703	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
704	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
705	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
706	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
707	C₂×D₄	C₂⁴×C₆₇	1	16	yes	—
708	C₂×D₄	C₂⁴×C₆₇	1	16	yes	—
709	C₂×D₄	C₂⁴×C₆₇	1	16	yes	—
710	C₂²×C₄	—	2	8	no	—
711	C₂²×C₄	—	2	4	no	—
712	C₂²×C₄	—	2	4	no	—
713	C₂²×C₄	—	4	8	no	—
714	C₂²×C₄	—	4	8	no	—
715	C₂²×C₄	—	4	8	no	—
716	C₂²×C₄	—	4	8	no	—
717	C₂²×C₄	—	4	2	no	—
718	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
719	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
720	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
721	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
722	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
723	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
724	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
725	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
726	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
727	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
728	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
729	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
730	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
731	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
732	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
733	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
734	C₂²×C₄	C₂⁴×C₆₇	1	16	yes	—
735	C₂²×C₄	C₂⁴×C₆₇	1	16	yes	—
736	C₂²×C₄	C₂⁴×C₆₇	1	16	yes	—
737	C₂²×C₄	C₂⁴×C₆₇	1	16	yes	—
738	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
739	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
740	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
741	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
742	C₄⋊C₄	C₂⁴×C₆₇	1	16	yes	—
743	C₄⋊C₄	C₂⁴×C₆₇	1	16	yes	—
744	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
745	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
746	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
747	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
748	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
749	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
750	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
751	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
752	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
753	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
754	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
755	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
756	C₄⋊C₄	C₂⁴×C₆₇	1	16	yes	—
757	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
758	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
759	C₄⋊C₄	C₂⁴×C₆₇	1	16	yes	—
760	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
761	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
762	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
763	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
764	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
765	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
766	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
767	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
768	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
769	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
770	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
771	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
772	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
773	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
774	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
775	C₄²	C₂⁴×C₆₇	1	4	yes	—
776	C₄²	C₂⁴×C₆₇	1	4	yes	—
777	C₄²	C₂⁴×C₆₇	1	4	yes	—
778	C₄²	C₂⁴×C₆₇	1	4	yes	—
779	C₄²	C₂⁴×C₆₇	1	8	yes	—
780	C₄²	C₂⁴×C₆₇	1	8	yes	—
781	C₄²	C₂⁴×C₆₇	1	8	yes	—
782	C₄²	C₂⁴×C₆₇	1	16	yes	—
783	C₂³	—	2	4	no	—
784	C₂³	—	2	2	no	—
785	C₂³	—	2	8	no	—
786	C₂³	—	2	2	no	—
787	C₂³	—	2	4	no	—
788	C₂³	—	2	8	no	—
789	C₂³	—	2	2	no	—
790	C₂³	—	2	8	no	—
791	C₂³	—	2	4	no	—
792	C₂³	C₂⁵×C₆₇	1	4	yes	—
793	C₂³	C₂⁵×C₆₇	1	2	yes	—
794	C₂³	C₂⁵×C₆₇	1	8	yes	—
795	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
796	Q₈	—	2	8	no	—
797	Q₈	—	2	16	no	—
798	Q₈	—	2	8	no	—
799	Q₈	—	2	8	no	—
800	Q₈	—	4	16	no	—
801	Q₈	—	4	8	no	—
802	D₄	—	2	16	no	—
803	D₄	—	2	8	no	—
804	D₄	—	2	16	no	—
805	D₄	—	4	16	no	—
806	D₄	—	4	16	no	—
807	D₄	—	4	8	no	—
808	D₄	—	4	8	no	—
809	D₄	—	4	16	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	4	no	—
812	C₂×C₄	—	2	4	no	—
813	C₂×C₄	—	2	8	no	—
814	C₂×C₄	—	2	4	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	4	no	—
817	C₂×C₄	—	2	4	no	—
818	C₂×C₄	—	2	4	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	4	no	—
822	C₂×C₄	—	2	16	no	—
823	C₂×C₄	—	2	8	no	—
824	C₂×C₄	—	2	8	no	—
825	C₂×C₄	—	4	16	no	—
826	C₂×C₄	—	4	16	no	—
827	C₂×C₄	—	4	16	no	—
828	C₂×C₄	—	4	16	no	—
829	C₂×C₄	—	4	4	no	—
830	C₂×C₄	H(5,𝔽₂)×C₆₇	1	4	yes	—
831	C₂×C₄	2₋¹⁺⁴×C₆₇	1	4	yes	—
832	C₂×C₄	C₂⁵×C₆₇	1	4	yes	—
833	C₂×C₄	C₂⁵×C₆₇	1	4	yes	—
834	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
835	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
836	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
837	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
838	C₂×C₄	C₂⁵×C₆₇	1	4	yes	—
839	C₂×C₄	C₂⁵×C₆₇	1	4	yes	—
840	C₂×C₄	C₂⁵×C₆₇	1	4	yes	—
841	C₂×C₄	C₂⁵×C₆₇	1	8	yes	—
842	C₂×C₄	C₂⁵×C₆₇	1	4	yes	—
843	C₂×C₄	C₂⁵×C₆₇	1	4	yes	—
844	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
845	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
846	C₂²	—	2	4	no	—
847	C₂²	—	2	2	no	—
848	C₂²	—	2	8	no	—
849	C₂²	—	2	2	no	—
850	C₂²	—	2	4	no	—
851	C₂²	—	2	8	no	—
852	C₂²	—	2	2	no	—
853	C₂²	—	2	8	no	—
854	C₂²	—	2	4	no	—
855	C₂²	—	4	8	no	—
856	C₂²	—	4	4	no	—
857	C₂²	—	4	16	no	—
858	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	2	yes	—
859	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	2	yes	—
860	C₂²	#585×C₆₇	1	2	yes	—
861	C₂²	C₂⁶×C₆₇	1	1	yes	characteristic
862	C₄	—	2	2	no	—
863	C₄	—	2	4	no	—
864	C₄	—	2	4	no	—
865	C₄	—	2	8	no	—
866	C₄	—	2	4	no	—
867	C₄	—	2	2	no	—
868	C₄	—	2	4	no	—
869	C₄	—	2	4	no	—
870	C₄	—	2	4	no	—
871	C₄	—	2	2	no	—
872	C₄	—	2	2	no	—
873	C₄	—	2	4	no	—
874	C₄	C₂×H(5,𝔽₂)×C₆₇	1	4	yes	—
875	C₄	C₂×2₋¹⁺⁴×C₆₇	1	4	yes	—
876	C₂	—	4	4	no	—
877	C₂	—	4	2	no	—
878	C₂	—	4	8	no	—
879	C₂	C₆₇×#3554	1	4	yes	direct product factor
880	C₂	C₂²×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
881	C₂	C₂²×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
882	C₂	C₂×#585×C₆₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₆₇
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3554	C₂	direct (N × H)
2. C₂×#562×C₆₇	C₂	semidirect
3. C₂×#559×C₆₇	C₂	semidirect
4. C₂×#559×C₆₇	C₂	semidirect
5. C₂×#557×C₆₇	C₂	semidirect
6. C₂×#554×C₆₇	C₂	semidirect
7. C₂×#550×C₆₇	C₂	semidirect
8. C₂×D₄×Q₈×C₆₇	C₂	semidirect
9. C₂×#548×C₆₇	C₂	semidirect
10. C₂×#547×C₆₇	C₂	semidirect
11. C₂×#542×C₆₇	C₂	semidirect
12. C₂×#542×C₆₇	C₂	semidirect
13. C₂×#540×C₆₇	C₂	semidirect
14. C₂×#539×C₆₇	C₂	semidirect
15. C₂×#536×C₆₇	C₂	semidirect
16. C₂×#533×C₆₇	C₂	semidirect
17. C₂×#532×C₆₇	C₂	semidirect
18. C₂×#529×C₆₇	C₂	semidirect
22. #562×C₆₇	C₂²	semidirect
23. #559×C₆₇	C₂²	semidirect
24. #559×C₆₇	C₂²	semidirect
25. #557×C₆₇	C₂²	semidirect
26. #554×C₆₇	C₂²	semidirect
27. #550×C₆₇	C₂²	semidirect
28. D₄×Q₈×C₆₇	C₂²	semidirect
29. #548×C₆₇	C₂²	semidirect
30. #547×C₆₇	C₂²	semidirect
31. #542×C₆₇	C₂²	semidirect
32. #542×C₆₇	C₂²	semidirect
33. #540×C₆₇	C₂²	semidirect
34. #539×C₆₇	C₂²	semidirect
35. #536×C₆₇	C₂²	semidirect
36. #533×C₆₇	C₂²	semidirect
37. #532×C₆₇	C₂²	semidirect
45. #529×C₆₇	C₂²	semidirect
434. C₂×#3554	C₆₇	direct (N × H)
438. C₂×C₆₇	#3554	direct (N × H)
442. #3554	C₂×C₆₇	direct (N × H)
443. C₂×#562	C₂×C₆₇	semidirect
444. C₂×#559	C₂×C₆₇	semidirect
445. C₂×#559	C₂×C₆₇	semidirect
446. C₂×#557	C₂×C₆₇	semidirect
447. C₂×#554	C₂×C₆₇	semidirect
448. C₂×#550	C₂×C₆₇	semidirect
449. C₂×D₄×Q₈	C₂×C₆₇	semidirect
450. C₂×#548	C₂×C₆₇	semidirect
451. C₂×#547	C₂×C₆₇	semidirect
452. C₂×#542	C₂×C₆₇	semidirect
453. C₂×#542	C₂×C₆₇	semidirect
454. C₂×#540	C₂×C₆₇	semidirect
455. C₂×#539	C₂×C₆₇	semidirect
456. C₂×#536	C₂×C₆₇	semidirect
457. C₂×#533	C₂×C₆₇	semidirect
458. C₂×#532	C₂×C₆₇	semidirect
459. C₂×#529	C₂×C₆₇	semidirect
460. C₆₇	C₂×#3554	direct (N × H)
464. #562	C₂²×C₆₇	semidirect
465. #559	C₂²×C₆₇	semidirect
466. #559	C₂²×C₆₇	semidirect
467. #557	C₂²×C₆₇	semidirect
468. #554	C₂²×C₆₇	semidirect
469. #550	C₂²×C₆₇	semidirect
470. D₄×Q₈	C₂²×C₆₇	semidirect
471. #548	C₂²×C₆₇	semidirect
472. #547	C₂²×C₆₇	semidirect
473. #542	C₂²×C₆₇	semidirect
474. #542	C₂²×C₆₇	semidirect
475. #540	C₂²×C₆₇	semidirect
476. #539	C₂²×C₆₇	semidirect
477. #536	C₂²×C₆₇	semidirect
478. #533	C₂²×C₆₇	semidirect
479. #532	C₂²×C₆₇	semidirect
487. #529	C₂²×C₆₇	semidirect
879. C₂	C₆₇×#3554	direct (N × H)

Maximal subgroups

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

subgroup	index
C₆₇×#3554	2
C₂×#562×C₆₇	2
C₂×#559×C₆₇	2
C₂×#557×C₆₇	2
C₂×#554×C₆₇	2
C₂×#550×C₆₇	2
C₂×D₄×Q₈×C₆₇	2
C₂×#548×C₆₇	2
C₂×#547×C₆₇	2
C₂×#542×C₆₇	2
C₂×#540×C₆₇	2
C₂×#539×C₆₇	2
C₂×#536×C₆₇	2
C₂×#533×C₆₇	2
C₂×#532×C₆₇	2
C₂×#529×C₆₇	2
C₂×#3554	67

Subgroups — C2×C67×#3554 #30741997

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₇×#3554 #30741997